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83850121 | 10.1007/s00009-017-1044-1 | By means of classical fixed point index, we prove new results on the
existence, non-existence, localization and multiplicity of nontrivial solutions
for systems of Hammerstein integral equations where the nonlinearities are
allowed to depend on the first derivative. As a byproduct of our theory we
discuss the existence of positive solutions of a system of third order ODEs
subject to nonlocal boundary conditions. Some examples are provided in order to
illustrate the applicability of the theoretical results.Comment: 18 page | Nontrivial solutions of systems of Hammerstein integral equations with
first derivative dependence | nontrivial solutions of systems of hammerstein integral equations with first derivative dependence | localization multiplicity nontrivial hammerstein nonlinearities derivative. byproduct odes nonlocal conditions. illustrate applicability | non_dup | [] |
86414165 | 10.1007/s00009-018-1109-9 | The consideration of the so-called rotation minimizing frames allows for a
simple and elegant characterization of plane and spherical curves in Euclidean
space via a linear equation relating the coefficients that dictate the frame
motion. In this work, we extend these investigations to characterize curves
that lie on a geodesic sphere or totally geodesic hypersurface in a Riemannian
manifold of constant curvature. Using that geodesic spherical curves are normal
curves, i.e., they are the image of an Euclidean spherical curve under the
exponential map, we are able to characterize geodesic spherical curves in
hyperbolic spaces and spheres through a non-homogeneous linear equation.
Finally, we also show that curves on totally geodesic hypersurfaces, which play
the role of hyperplanes in Riemannian geometry, should be characterized by a
homogeneous linear equation. In short, our results give interesting and
significant similarities between hyperbolic, spherical, and Euclidean
geometries.Comment: 15 pages, 3 figures; comments are welcom | Characterization of curves that lie on a geodesic sphere or on a totally
geodesic hypersurface in a hyperbolic space or in a sphere | characterization of curves that lie on a geodesic sphere or on a totally geodesic hypersurface in a hyperbolic space or in a sphere | consideration minimizing frames elegant spherical euclidean relating dictate motion. extend investigations characterize geodesic sphere totally geodesic hypersurface riemannian manifold curvature. geodesic spherical i.e. euclidean spherical exponential characterize geodesic spherical hyperbolic spheres homogeneous equation. totally geodesic hypersurfaces hyperplanes riemannian homogeneous equation. similarities hyperbolic spherical euclidean pages comments welcom | non_dup | [] |
93960287 | 10.1007/s00009-018-1193-x | In this note, two numerical methods of solving fractional differential
equations (FDEs) are briefly described, namely predictor-corrector approach of
Adams-Bashforth-Moulton type and multi-step generalized differential transform
method (MSGDTM), and then a demonstrating example is given to compare the
results of the methods. It is shown that the MSGDTM, which is an enhancement of
the generalized differential transform method, neglects the effect of non-local
structure of fractional differentiation operators and fails to accurately solve
the FDEs over large domains.Comment: 12 pages, 2 figure | A comparison between numerical solutions to fractional differential
equations: Adams-type predictor-corrector and multi-step generalized
differential transform method | a comparison between numerical solutions to fractional differential equations: adams-type predictor-corrector and multi-step generalized differential transform method | solving fractional fdes briefly predictor corrector adams bashforth moulton transform msgdtm demonstrating methods. msgdtm enhancement transform neglects fractional fails accurately solve fdes pages | non_dup | [] |
2563880 | 10.1007/s00010-003-2676-8 | On every set A there is a rigid binary relation i.e. such a relation R
\subseteq A \times A that there is no homomorphism (A,R) \rightarrow (A,R)
except the identity (Vop{\v{e}}nka et al. [1965]). We prove that for each
infinite cardinal number \kappa if card A \leq 2^\kappa, then there exists a
relation R \subseteq A \times A with the following property:
\forall (x \in A) \exists ({x} \subseteq A(x) \subseteq A, card A(x) \leq
\kappa) \forall (f: A(x) \rightarrow A, f \neq id_A(x))
f is not a homomorphism of R.
The above property implies that R is rigid. If a relation R \subseteq A
\times A has the above property, then card A \leq 2^\kappa.Comment: an enlarged version, 8 page | A stronger form of the theorem constructing a rigid binary relation on
any set | a stronger form of the theorem constructing a rigid binary relation on any set | rigid i.e. subseteq homomorphism rightarrow infinite cardinal kappa card kappa subseteq forall subseteq subseteq card kappa forall rightarrow homomorphism rigid. subseteq card enlarged | non_dup | [] |
2577835 | 10.1007/s00010-005-2819-1 | Let varphi_n:C^n times C^n->C,
varphi_n((x_1,...,x_n),(y_1,...,y_n))=sum_{i=1}^n (x_i-y_i)^2. We say that
f:C^n->C^n preserves distance d>=0, if for each X,Y in C^n varphi_n(X,Y)=d^2
implies varphi_n(f(X),f(Y))=d^2. We prove: if n>=2 and a continuous f:C^n->C^n
preserves unit distance, then f has a form I circ (rho,...,rho), where
I:C^n->C^n is an affine mapping with orthogonal linear part and rho:C->C is the
identity or the complex conjugation. For n >=3 and bijective f the theorem
follows from Theorem 2 in [8].Comment: 10 pages, LaTeX2e, the version which appeared in Aequationes
Mathematica | The Beckman-Quarles theorem for continuous mappings from C^n to C^n | the beckman-quarles theorem for continuous mappings from c^n to c^n | varphi varphi preserves varphi varphi preserves circ affine orthogonal conjugation. bijective .comment pages latex appeared aequationes mathematica | non_dup | [] |
2579544 | 10.1007/s00010-006-2825-y | In this paper we consider two notions that have been discovered and
rediscovered by geometers and analysts since 1917 up to the present day: Radon
curves and antinorms.
A Radon curve is a special kind of centrally symmetric closed convex curve in
the plane. A Radon plane is a normed plane obtained by using a Radon curve as
(the boundary of) the unit ball. Many known results in Euclidean geometry also
hold for Radon planes, for example the triangle and parallelogram area
formulas, certain theorems on angular bisectors, the area formula of a polygon
circumscribed about a circle, certain isoperimetric inequalities, and the
non-expansive property of certain non-linear projections.
These results may be further generalized to arbitrary normed planes if we
formally change the statement of the result by referring in some places to the
antinorm instead of the norm. The antinorm is a norm dual to the norm of an
arbitrarily given normed plane, although it lives in the same plane as the
original norm.
It is the purpose of this mainly expository paper to give a list of results
on antinorms that generalize results true for Radon norms, and in many cases
characterize Radon norms among all norms in the plane. Many of the results are
old, well-known, and have often been rediscovered. However, for most of the
results we give streamlined proofs. Also, some of the characterizations of
Radon curves given here seem not to have appeared previously in print.Comment: 24 pages, 7 figure | Antinorms and Radon curves | antinorms and radon curves | notions discovered rediscovered geometers analysts radon antinorms. radon kind centrally convex plane. radon normed radon ball. euclidean hold radon planes triangle parallelogram formulas theorems bisectors polygon circumscribed circle isoperimetric inequalities expansive projections. normed planes formally statement referring places antinorm norm. antinorm norm norm arbitrarily normed lives norm. expository antinorms generalize radon norms characterize radon norms norms plane. rediscovered. streamlined proofs. characterizations radon seem appeared pages | non_dup | [] |
24944455 | 10.1007/s00010-010-0026-1 | In this paper the following implication is verified for certain basic
algebraic curves: if the additive real function $f$ approximately (i.e., with a
bounded error) satisfies the derivation rule along the graph of the algebraic
curve in consideration, then $f$ can be represented as the sum of a derivation
and a linear function. When, instead of the additivity of $f$, it is assumed
that, in addition, the Cauchy difference of $f$ is bounded, a stability theorem
is obtained for such characterizations of derivations.Comment: 9 pages; published in Aequationes Mathematicae in 201 | Hyers--Ulam stability of derivations and linear functions | hyers--ulam stability of derivations and linear functions | implication verified algebraic additive i.e. satisfies derivation algebraic consideration derivation function. additivity cauchy characterizations pages aequationes mathematicae | non_dup | [] |
2088847 | 10.1007/s00010-010-0032-3 | In many regular cases, there exists a (properly defined) limit of iterations
of a function in several real variables, and this limit satisfies the
functional equation (1-z)f(x)=f(f(xz)(1-z)/z); here z is a scalar and x is a
vector. This is a special case of a well-known translation equation. In this
paper we present a complete solution to this functional equation in case f is a
continuous function on a single point compactification of a 2-dimensional real
vector space. It appears that, up to conjugation by a homogeneous continuous
function, there are exactly four solutions. Further, in a 1-dimensional case we
present a solution with no regularity assumptions on f.Comment: 15 page | Multi-variable translation equation which arises from homothety | multi-variable translation equation which arises from homothety | properly iterations satisfies vector. translation equation. compactification space. conjugation homogeneous solutions. regularity assumptions | non_dup | [] |
398202 | 10.1007/s00010-010-0051-0 | We consider a self-convolutive recurrence whose solution is the sequence of coefficients in the asymptotic expansion of the logarithmic derivative of the confluent hypergeometic function U(a, b, z). By application of the Hilbert transform we convert this expression into an explicit, non-recursive solution in which the nth coefficient is expressed as the (n − 1)th moment of a measure, and also as the trace of the (n − 1)th iterate of a linear operator. Applications of these sequences, and hence of the explicit solution provided, are found in quantum field theory as the number of Feynman diagrams of a certain type and order, in Brownian motion theory, and in combinatorics | An exactly solvable self-convolutive recurrence | an exactly solvable self-convolutive recurrence | convolutive recurrence asymptotic logarithmic confluent hypergeometic hilbert transform convert recursive moment trace iterate operator. feynman diagrams brownian combinatorics | non_dup | [] |
2162313 | 10.1007/s00010-011-0091-0 | We introduce the concept of quasi-Lov\'asz extension as being a mapping
$f\colon I^n\to\R$ defined on a nonempty real interval $I$ containing the
origin and which can be factorized as
$f(x_1,...,x_n)=L(\phi(x_1),...,\phi(x_n))$, where $L$ is the Lov\'asz
extension of a pseudo-Boolean function $\psi\colon\{0,1\}^n\to\R$ (i.e., the
function $L\colon\R^n\to\R$ whose restriction to each simplex of the standard
triangulation of $[0,1]^n$ is the unique affine function which agrees with
$\psi$ at the vertices of this simplex) and $\phi\colon I\to\R$ is a
nondecreasing function vanishing at the origin. These functions appear
naturally within the scope of decision making under uncertainty since they
subsume overall preference functionals associated with discrete Choquet
integrals whose variables are transformed by a given utility function. To
axiomatize the class of quasi-Lov\'asz extensions, we propose generalizations
of properties used to characterize the Lov\'asz extensions, including a
comonotonic version of modularity and a natural relaxation of homogeneity. A
variant of the latter property enables us to axiomatize also the class of
symmetric quasi-Lov\'asz extensions, which are compositions of symmetric
Lov\'asz extensions with 1-place nondecreasing odd functions | Axiomatizations of quasi-Lov\'asz extensions of pseudo-Boolean functions | axiomatizations of quasi-lov\'asz extensions of pseudo-boolean functions | quasi colon nonempty factorized pseudo boolean colon i.e. colon restriction simplex triangulation affine agrees simplex colon nondecreasing vanishing origin. naturally scope subsume preference functionals choquet integrals transformed utility function. axiomatize quasi extensions propose generalizations characterize extensions comonotonic modularity relaxation homogeneity. variant enables axiomatize quasi extensions compositions extensions nondecreasing | non_dup | [] |
2141494 | 10.1007/s00010-011-0108-8 | Every finite metric tree has generalized roundness strictly greater than one.
On the other hand, some countable metric trees have generalized roundness
precisely one. The purpose of this paper is to identify some large classes of
countable metric trees that have generalized roundness precisely one.
At the outset we consider spherically symmetric trees endowed with the usual
combinatorial metric (SSTs). Using a simple geometric argument we show how to
determine decent upper bounds on the generalized roundness of finite SSTs that
depend only on the downward degree sequence of the tree in question. By
considering limits it follows that if the downward degree sequence $(d_{0},
d_{1}, d_{2}...)$ of a SST $(T,\rho)$ satisfies $|\{j \, | \, d_{j} > 1 \}| =
\aleph_{0}$, then $(T,\rho)$ has generalized roundness one. Included among the
trees that satisfy this condition are all complete $n$-ary trees of depth
$\infty$ ($n \geq 2$), all $k$-regular trees ($k \geq 3$) and inductive limits
of Cantor trees.
The remainder of the paper deals with two classes of countable metric trees
of generalized roundness one whose members are not, in general, spherically
symmetric. The first such class of trees are merely required to spread out at a
sufficient rate (with a restriction on the number of leaves) and the second
such class of trees resemble infinite combs.Comment: 14 pages, 2 figures, 2 table | Metric trees of generalized roundness one | metric trees of generalized roundness one | roundness strictly one. countable trees roundness precisely one. countable trees roundness precisely one. outset spherically trees endowed usual combinatorial ssts geometric argument decent bounds roundness ssts downward question. downward satisfies aleph roundness one. trees satisfy trees infty trees inductive cantor trees. remainder deals countable trees roundness spherically symmetric. trees merely spread restriction leaves trees resemble infinite pages | non_dup | [] |
24963680 | 10.1007/s00010-012-0141-2 | We explore a number of functional properties of the $q$-gamma function and a
class of its quotients; including the $q$-beta function. We obtain formulas for
all higher logarithmic derivatives of these quotients and give precise
conditions on their sign. We prove how these and other functional properties,
such as the multiplication formula or the asymptotic expansion, together with
the fundamental functional equation of the $q$-gamma function uniquely define
those functions. We also study reciprocal "relatives" of the fundamental
$q$-gamma functional equation, and prove uniqueness of solution results for
them. In addition, we also use a reflection formula of Askey to derive
expressions relating the classical sine function and the number $\pi$ to the
$q$-gamma function. Throughout we highlight the similarities and differences
between the cases $0<q<1$ and $q>1$.Comment: 29 page | Functional definitions for $q$-analogues of eulerian functions and
applications | functional definitions for $q$-analogues of eulerian functions and applications | explore gamma quotients beta function. formulas logarithmic derivatives quotients precise sign. multiplication asymptotic gamma uniquely functions. reciprocal relatives gamma uniqueness them. reflection askey derive expressions relating sine gamma function. highlight similarities .comment | non_dup | [] |
42936966 | 10.1007/s00010-012-0160-z | Let C⊂R^n be a convex body. We introduce two notions of convexity associated to C. A set K is C-ball convex if it is the intersection of translates of C, or it is either ∅ , or R^n . The C-ball convex hull of two points is called a C-spindle. K is C-spindle convex if it contains the C-spindle of any pair of its points. We investigate how some fundamental properties of conventional convex sets can be adapted to C-spindle convex and C-ball convex sets. We study separation properties and Carathéodory numbers of these two convexity structures. We investigate the basic properties of arc-distance, a quantity defined by a centrally symmetric planar disc C, which is the length of an arc of a translate of C, measured in the C-norm that connects two points. Then we characterize those n-dimensional convex bodies C for which every C-ball convex set is the C-ball convex hull of finitely many points. Finally, we obtain a stability result concerning covering numbers of some C-ball convex sets, and diametrically maximal sets in n-dimensional Minkowski spaces | Ball and spindle convexity with respect to a convex body | ball and spindle convexity with respect to a convex body | convex body. notions convexity ball convex intersection translates ball convex hull spindle. spindle convex spindle points. convex adapted spindle convex ball convex sets. carathéodory convexity structures. quantity centrally planar disc translate norm connects points. characterize convex bodies ball convex ball convex hull finitely points. concerning covering ball convex diametrically maximal minkowski | non_dup | [] |
24795148 | 10.1007/s00010-012-0179-1 | This paper studies algebraic properties of Hermitian solutions and Hermitian
definite solutions of the two types of matrix equation $AX = B$ and $AXA^* =
B$. We first establish a variety of rank and inertia formulas for calculating
the maximal and minimal ranks and inertias of Hermitian solutions and Hermitian
definite solutions of the matrix equations $AX = B$ and $AXA^* = B$, and then
use them to characterize many qualities and inequalities for Hermitian
solutions and Hermitian definite solutions of the two matrix equations and
their variations.Comment: 22 page | Equalities and inequalities for Hermitian solutions and Hermitian
definite solutions of the two matrix equations $AX = B$ and $AXA^* = B$ | equalities and inequalities for hermitian solutions and hermitian definite solutions of the two matrix equations $ax = b$ and $axa^* = b$ | algebraic hermitian hermitian definite establish inertia formulas calculating maximal ranks inertias hermitian hermitian definite characterize qualities inequalities hermitian hermitian definite | non_dup | [] |
2246204 | 10.1007/s00010-013-0190-1 | Let X=(x,y). A plane flow is a function F(X,t): R^2*R->R^2 such that
F(F(X,s),t)=F(X,s+t) for (almost) all real numbers x,y,s,t (the function F
might not be well-defined for certain x,y,t). In this paper we investigate
rational plane flows which are of the form F(X,t)=f(Xt)/t; here f is a pair of
rational functions in 2 real variables. These may be called projective flows,
and for a description of such flows only the knowledge of Cremona group in
dimension 1 is needed. Thus, the aim of this work is to completely describe
over R all rational solutions of the two dimensional translation equation
(1-z)f(X)=f(f(Xz)(1-z)/z). We show that, up to conjugation with a 1-homogenic
birational plane transformation (1-BIR), all solutions are as follows: a zero
flow, two singular flows, an identity flow, and one non-singular flow for each
non-negative integer N, called the level of the flow. The case N=0 stands
apart, while the case N=1 has special features as well. Conjugation of these
canonical solutions with 1-BIR produce a variety of flows with different
properties and invariants, depending on the level and on the conjugation
itself. We explore many more features of these flows; for example, there are 1,
4, and 2 essentially different symmetric flows in cases N=0, N=1, and N>=2,
respectively. Many more questions will be treated in the second part of this
work.Comment: 54 pages, 6 figures. Final version before proof | The projective translation equation and rational plane flows. I | the projective translation equation and rational plane flows. i | rational flows rational variables. projective flows flows cremona needed. rational translation conjugation homogenic birational singular flows singular integer flow. stands apart well. conjugation canonical flows invariants conjugation itself. explore flows essentially flows respectively. pages figures. | non_dup | [] |
20543142 | 10.1007/s00010-014-0260-z | The class of 'self-neglecting' functions at the heart of Beurling slow variation is expanded by permitting a positive asymptotic limit function λ(t), in place of the usual limit 1, necessarily satisfying the following 'self-neglect' condition:(Formula presented.)known as the Goła{ogonek}b-Schinzel functional equation, a relative of the Cauchy equation (which is itself also central to Karamata regular variation). This equation, due independently to Aczél and Goła{ogonek}b, occurring in the study of one-parameter subgroups, is here accessory to the λ -Uniform Convergence Theorem (λ-UCT) for the recent, flow-motivated, 'Beurling regular variation'. Positive solutions, when continuous, are known to be λ(t) = 1 + at (below a new, 'flow', proof is given); a = 0 recovers the usual limit 1 for self-neglecting functions. The λ-UCT allows the inclusion of Karamata multiplicative regular variation in the Beurling theory of regular variation, with λ (t) = 1 + t being the relevant case here, and generalizes Bloom's theorem concerning self-neglecting functions | Beurling regular variation, Bloom dichotomy, and the Gołąb–Schinzel functional equation | beurling regular variation, bloom dichotomy, and the gołąb–schinzel functional equation | neglecting beurling slow expanded permitting asymptotic usual necessarily satisfying neglect presented. goła ogonek schinzel cauchy karamata independently aczél goła ogonek occurring subgroups accessory motivated beurling recovers usual neglecting functions. inclusion karamata multiplicative beurling generalizes bloom concerning neglecting | non_dup | [] |
42667119 | 10.1007/s00010-014-0281-7 | In this paper we investigate continuity properties of functions
$f:\mathbb{R}_+\to\mathbb{R}_+$ that satisfy the $(p,q)$-Jensen convexity
inequality $$ f\big(H_p(x,y)\big)\leq H_q(f(x),f(y)) \qquad(x,y>0), $$ where
$H_p$ stands for the $p$th power (or H\"older) mean. One of the main results
shows that there exist discontinuous multiplicative functions that are
$(p,p)$-Jensen convex for all positive rational number $p$. A counterpart of
this result states that if $f$ is $(p,p)$-Jensen convex for all $p\in
P\subseteq\mathbb{R}_+$, where $P$ is a set of positive Lebesgue measure, then
$f$ must be continuous | Convexity with respect to families of means | convexity with respect to families of means | continuity mathbb mathbb satisfy jensen convexity inequality qquad stands older mean. discontinuous multiplicative jensen convex rational counterpart jensen convex subseteq mathbb lebesgue | non_dup | [] |
42670575 | 10.1007/s00010-015-0338-2 | We discuss closed-form formulas for the (n; k)-th partial Bell polynomials
derived in Cvijovic. We show that partial Bell polynomials are special cases of
weighted integer compositions, and demonstrate how the identities for partial
Bell polynomials easily follow from more general identities for weighted
integer compositions. We also provide short and elegant probabilistic proofs of
the latter, in terms of sums of discrete integer-valued random variables.
Finally, we outline further identities for the partial Bell polynomials.Comment: Aequationes mathematicae, 2015, pp. 1- | Identities for partial Bell polynomials derived from identities for
weighted integer compositions | identities for partial bell polynomials derived from identities for weighted integer compositions | formulas bell polynomials cvijovic. bell polynomials weighted integer compositions identities bell polynomials identities weighted integer compositions. elegant probabilistic proofs sums integer valued variables. outline identities bell aequationes mathematicae | non_dup | [] |
158833437 | 10.1007/s00010-015-0341-7 | Given two means M and N, the operator MM,NMM,N assigning to a given mean μ the mean MM,N(μ)(x,y)=M(μ(x,N(x,y)),μ(N(x,y),y)) was defined in Berrone and Moro (Aequationes Math 60:1–14, 2000) in connection with Cauchy means: the Cauchy mean generated by the pair f, g of continuous and strictly monotonic functions is the unique solution μ to the fixed point equation MA(f),A(g)(μ)=μ, where A(f) and A(g) are the quasiarithmetic means respectively generated by f and g. In this article, the operator MM,NMM,N is studied under less restrictive conditions and a general fixed point theorem is derived from an explicit formula for the iterates MnM,NMM,Nn . The concept of class of generalized Cauchy means associated to a given family of mixing pairs of means is introduced and some distinguished families of pairs are presented. The question of equality in these classes of means remains a challenging open problem.Fil: Berrone, Lucio Renato. Universidad Nacional de Rosario. Facultad de Ciencias Exactas, Ingeniería y Agrimensura; Argentina. Consejo Nacional de Investigaciones Científicas y Técnicas; Argentin | Generalized Cauchy means | generalized cauchy means | assigning berrone moro aequationes math connection cauchy cauchy strictly monotonic quasiarithmetic restrictive iterates cauchy distinguished families presented. equality challenging problem.fil berrone lucio renato. universidad nacional rosario. facultad ciencias exactas ingeniería agrimensura argentina. consejo nacional investigaciones científicas técnicas argentin | non_dup | [] |
35435598 | 10.1007/s00010-015-0357-z | The theory of regular variation, in its Karamata and Bojani´c-Karamata/de Haan forms, is long established and makes essential use of the Cauchy functional equation. Both forms are subsumed within the recent theory of Beurling regular variation, developed elsewhere. Various generalizations of the Cauchy equation, including the Gołab–Schinzel functional equation (GS) and Goldie's equation (GBE) below, are prominent there. Here we unify their treatment by algebraicization: extensive use of group structures introduced by Popa and Javor in the 1960s turn all the various (known) solutions into homomorphisms, in fact identifying them 'en passant', and show that (GS) is present everywhere, even if in a thick disguise | Homomorphisms from functional equations: the Goldie equation | homomorphisms from functional equations: the goldie equation | karamata bojani´c karamata haan cauchy equation. subsumed beurling elsewhere. generalizations cauchy gołab–schinzel goldie prominent there. unify algebraicization extensive popa javor homomorphisms identifying passant everywhere thick disguise | non_dup | [] |
42643196 | 10.1007/s00010-015-0396-5 | The concept of weighted entropy takes into account values of different
outcomes, i.e., makes entropy context-dependent, through the weight function.
In this paper, we establish a number of simple inequalities for the weighted
entropies (general as well as specific), mirroring similar bounds on standard
(Shannon) entropies and related quantities. The required assumptions are
written in terms of various expectations of the weight functions. Examples are
weighted Ky Fan and weighted Hadamard inequalities involving determinants of
positive-definite matrices, and weighted Cram\'{e}r-Rao inequalities involving
the weighted Fisher information matrix.Comment: arXiv admin note: substantial text overlap with arXiv:1409.410 | Basic inequalities for weighted entropies | basic inequalities for weighted entropies | weighted i.e. function. establish inequalities weighted entropies mirroring bounds shannon entropies quantities. assumptions expectations functions. weighted weighted hadamard inequalities involving determinants definite weighted cram inequalities involving weighted fisher admin substantial overlap | non_dup | [] |
29548708 | 10.1007/s00010-016-0410-6 | Let $\mathbf{x}=(x,y)$. A projective 2-dimensional flow is a solution to a
2-dimensional projective translation equation (PrTE)
$(1-z)\phi(\mathbf{x})=\phi(\phi(\mathbf{x}z)(1-z)/z)$,
$\phi:\mathbb{C}^{2}\mapsto\mathbb{C}^{2}$. Previously we have found all
solutions of the PrTE which are rational functions. The rational flow gives
rise to a vector field $\varpi(x,y)\bullet\varrho(x,y)$ which is a pair of
2-homogenic rational functions. On the other hand, only very special pairs of
2-homogenic rational functions, as vector fields, give rise to rational flows.
The main ingredient in the proof of the classifying theorem is a reduction
algorithm for a pair of 2-homogenic rational functions. This reduction method
in fact allows to derive more results.
Namely, in this work we find all projective flows with rational vector fields
whose orbits are algebraic curves. We call these flows abelian projective
flows, since either these flows are parametrized by abelian functions and with
the help of 1-homogenic birational plane transformations (1-BIR) the orbits of
these flows can be transformed into algebraic curves
$x^{A}(x-y)^{B}y^{C}\equiv\mathrm{const.}$ (abelian flows of type I), or there
exists a 1-BIR which transforms the orbits into the lines
$y\equiv\mathrm{const.}$ (abelian flows of type II), and generally the latter
flows are described in terms of non-arithmetic functions.
Our second result classifies all abelian flows which are given by two
variable algebraic functions. We call these flows algebraic projective flows,
and these are abelian flows of type I. We also provide many examples of
algebraic, abelian and non-abelian flows.Comment: 31 pages, 5 figure | Algebraic and abelian solutions to the projective translation equation | algebraic and abelian solutions to the projective translation equation | mathbf projective projective translation prte mathbf mathbf mathbb mapsto mathbb prte rational functions. rational varpi bullet varrho homogenic rational functions. homogenic rational rational flows. ingredient classifying homogenic rational functions. derive results. projective flows rational orbits algebraic curves. call flows abelian projective flows flows parametrized abelian homogenic birational transformations orbits flows transformed algebraic equiv mathrm const. abelian flows transforms orbits equiv mathrm const. abelian flows flows arithmetic functions. classifies abelian flows algebraic functions. call flows algebraic projective flows abelian flows algebraic abelian abelian pages | non_dup | [] |
42695300 | 10.1007/s00010-016-0426-y | We study the class $\mathcal{M}$ of functions meromorphic outside a countable
closed set of essential singularities. We show that if a function in
$\mathcal{M}$, with at least one essential singularity, permutes with a
non-constant rational map $g$, then $g$ is a M\"{o}bius map that is not
conjugate to an irrational rotation. For a given function $ f \in\mathcal{M}$
which is not a M\"{o}bius map, we show that the set of functions in
$\mathcal{M}$ that permute with $ f $ is countably infinite. Finally, we show
that there exist transcendental meromorphic functions $f: \mathbb{C} \to
\mathbb{C}$ such that, among functions meromorphic in the plane, $f$ permutes
only with itself and with the identity map | On permutable meromorphic functions | on permutable meromorphic functions | mathcal meromorphic countable singularities. mathcal singularity permutes rational bius conjugate irrational rotation. mathcal bius mathcal permute countably infinite. transcendental meromorphic mathbb mathbb meromorphic permutes | non_dup | [] |
42712476 | 10.1007/s00010-016-0434-y | Peter McMullen has developed a theory of realizations of abstract regular
polytopes, and has shown that the realizations up to congruence form a pointed
convex cone which is the direct product of certain irreducible subcones. We
show that each of these subcones is isomorphic to a set of positive
semi-definite hermitian matrices of dimension $m$ over either the real numbers,
the complex numbers or the quaternions. In particular, we correct an erroneous
computation of the dimension of these subcones by McMullen and Monson. We show
that the automorphism group of an abstract regular polytope can have an
irreducible character $\chi$ with $\chi\neq \overline{\chi}$ and with
arbitrarily large essential Wythoff dimension. This gives counterexamples to a
result of Herman and Monson, which was derived from the erroneous computation
mentioned before.
We also discuss a relation between cosine vectors of certain pure
realizations and the spherical functions appearing in the theory of Gelfand
pairs.Comment: 22 pages, PDFLaTex + biblatex. v2: corrected a few typos. Content
identical to final publication. in Aequationes Math. (2016 | Realizations of abstract regular polytopes from a representation
theoretic view | realizations of abstract regular polytopes from a representation theoretic view | peter mcmullen realizations polytopes realizations congruence pointed convex cone irreducible subcones. subcones isomorphic definite hermitian quaternions. erroneous subcones mcmullen monson. automorphism polytope irreducible character overline arbitrarily wythoff dimension. counterexamples herman monson erroneous before. cosine realizations spherical appearing gelfand pages pdflatex biblatex. corrected typos. publication. aequationes math. | non_dup | [] |
29555726 | 10.1007/s00010-016-0439-6 | We consider regularity for solutions of a class of de Rham's functional
equations. Under some smoothness conditions of functions consisting the
equation, we improve some results in Hata (Japan J. Appl. Math. 1985). Our
results are applicable to some cases that the functions consisting the equation
are non-linear functions on an interval, specifically, polynomials and linear
fractional transformations. Our results imply singularity of some well-known
singular functions, in particular, Minkowski's question-mark function, and,
some small perturbed functions of the singular functions.Comment: 14 pages, 3 figure | On regularity for de Rham's functional equations | on regularity for de rham's functional equations | regularity rham equations. smoothness consisting hata appl. math. applicable consisting polynomials fractional transformations. imply singularity singular minkowski mark perturbed singular pages | non_dup | [] |
42753575 | 10.1007/s00010-016-0450-y | The so-called generalized associativity functional equation G(J(x,y),z) =
H(x,K(y,z)) has been investigated under various assumptions, for instance when
the unknown functions G, H, J, and K are real, continuous, and strictly
monotonic in each variable. In this note we investigate the following related
problem: given the functions J and K, find every function F that can be written
in the form F(x,y,z) = G(J(x,y),z) = H(x,K(y,z)) for some functions G and H. We
show how this problem can be solved when any of the inner functions J and K has
the same range as one of its sections | On the generalized associativity equation | on the generalized associativity equation | associativity assumptions unknown strictly monotonic variable. solved | non_dup | [] |
42749214 | 10.1007/s00010-016-0459-2 | It is well-known that if a real valued function acting on a convex set
satisfies the $n$-variable Jensen inequality, for some natural number $n\geq
2$, then, for all $k\in\{1,\dots, n\}$, it fulfills the $k$-variable Jensen
inequality as well. In other words, the arithmetic mean and the Jensen
inequality (as a convexity property) are both reducible. Motivated by this
phenomenon, we investigate this property concerning more general means and
convexity notions. We introduce a wide class of means which generalize the
well-known means for arbitrary linear spaces and enjoy a so-called reducibility
property. Finally, we give a sufficient condition for the reducibility of the
$(M,N)$-convexity property of functions and also for H\"older--Minkowski type
inequalities | Reducible means and reducible inequalities | reducible means and reducible inequalities | valued acting convex satisfies jensen inequality dots fulfills jensen inequality well. arithmetic jensen inequality convexity reducible. motivated phenomenon concerning convexity notions. generalize enjoy reducibility property. reducibility convexity older minkowski inequalities | non_dup | [] |
29554943 | 10.1007/s00010-017-0478-7 | The goal of this paper is to point out that the results obtained in the
recent papers [7,8,10,11] can be seriously strengthened in the sense that we
can significantly relax the assumptions of the main results so that we still
get the same conclusions. In order to do this first, we prove that for $n \geq
3$ any transformation which preserves the $n$-norm of any $n$ vectors is
automatically plus-minus linear. This will give a re-proof of the well-known
Mazur--Ulam-type result that every $n$-isometry is automatically affine ($n
\geq 2$) which was proven in several papers, e.g. in [9]. Second, following the
work of Rassias and \v{S}emrl [23], we provide the solution of a natural
Aleksandrov-type problem in $n$-normed spaces, namely, we show that every
surjective transformation which preserves the unit $n$-distance in both
directions ($n\geq 2$) is automatically an $n$-isometry | On $n$-norm preservers and the Aleksandrov conservative $n$-distance
problem | on $n$-norm preservers and the aleksandrov conservative $n$-distance problem | goal papers seriously strengthened relax assumptions conclusions. preserves norm automatically minus linear. mazur ulam isometry automatically affine proven papers e.g. rassias emrl aleksandrov normed surjective preserves directions automatically isometry | non_dup | [] |
77615531 | 10.1007/s00010-017-0486-7 | Category-measure duality concerns applications of Baire-category methods that have measure-theoretic analogues. The set-theoretic axiom needed in connection with the Baire category theorem is the Axiom of Dependent Choice, DC rather than the Axiom of Choice, AC. Berz used the Hahn–Banach theorem over Q to prove that the graph of a measurable sublinear function that is Q+ -homogeneous consists of two half-lines through the origin. We give a category form of the Berz theorem. Our proof is simpler than that of the classical measure-theoretic Berz theorem, our result contains Berz’s theorem rather than simply being an analogue of it, and we use only DC rather than AC. Furthermore, the category form easily generalizes: the graph of a Baire sublinear function defined on a Banach space is a cone. The results are seen to be of automatic-continuity type. We use Christensen Haar null sets to extend the category approach beyond the locally compact setting where Haar measure exists. We extend Berz’s result from Euclidean to Banach spaces, and beyond. Passing from sublinearity to convexity, we extend the Bernstein–Doetsch theorem and related continuity results, allowing our conditions to be ‘local’—holding off some exceptional set | Category-measure duality: convexity, mid-point convexity and Berz sublinearity | category-measure duality: convexity, mid-point convexity and berz sublinearity | duality concerns baire theoretic analogues. theoretic axiom connection baire axiom axiom berz hahn–banach measurable sublinear homogeneous origin. berz theorem. simpler theoretic berz berz’s analogue generalizes baire sublinear banach cone. automatic continuity type. christensen haar extend locally haar exists. extend berz’s euclidean banach beyond. passing sublinearity convexity extend bernstein–doetsch continuity allowing ‘local’—holding exceptional | non_dup | [] |
73420786 | 10.1007/s00010-017-0496-5 | In this paper we use basic properties of strongly convex functions to obtain
new inequalities including Jensen's type and Jensen-Mercer type inequalities.
Applications for special means are pointed out as well. We also give a Jensen's
operator inequality for strongly convex functions. As a corollary, we improve
H\"older-McCarthy inequality under suitable conditions. More precisely we show
that if $Sp\left( A \right)\subset I\subseteq \left( 1,\infty \right)$, then
\[{{\left\langle Ax,x \right\rangle }^{r}}\le \left\langle {{A}^{r}}x,x
\right\rangle -\frac{{{r}^{2}}-r}{2}\left( \left\langle {{A}^{2}}x,x
\right\rangle -{{\left\langle Ax,x \right\rangle }^{2}} \right),\quad r\ge 2\]
and if $Sp\left( A \right)\subset I\subseteq \left( 0,1 \right)$, then
\[\left\langle {{A}^{r}}x,x \right\rangle \le {{\left\langle Ax,x \right\rangle
}^{r}}+\frac{r-{{r}^{2}}}{2}\left( {{\left\langle Ax,x \right\rangle
}^{2}}-\left\langle {{A}^{2}}x,x \right\rangle \right),\quad 0<r<1\] for each
positive operator $A$ and $x\in \mathcal{H}$ with $\left\| x \right\|=1$.Comment: arXiv admin note: text overlap with arXiv:1611.01084, to appear in
Aequationes Mat | Around Jensen's inequality for strongly convex functions | around jensen's inequality for strongly convex functions | convex inequalities jensen jensen mercer inequalities. pointed well. jensen inequality convex functions. corollary older mccarthy inequality conditions. precisely subseteq infty langle rangle langle rangle frac langle rangle langle rangle quad subseteq langle rangle langle rangle frac langle rangle langle rangle quad mathcal .comment admin overlap aequationes | non_dup | [] |
73395111 | 10.1007/s00010-017-0500-0 | In this second part of the work, we correct the flaw which was left in the
proof of the main Theorem in the first part. This affects only a small part of
the text in this first part and two consecutive papers. Yet, some additional
arguments and additions are needed to claim the validity of the classification
results.
With these new results in a disposition, algebraic and rational flows can be
much more easily and transparently classified. It also turns out that the
notion of an algebraic projective flow is a very natural one. For example, we
give an inductive (on dimension) method to build algebraic projective flows
with rational vector fields, and ask whether these account for all such flows.
Further, we expand on results concerning rational flows in dimension $2$.
Previously we found such flows symmetric with respect to a linear involution
$i(x,y)=(y,x)$. Here we find all rational flows symmetric with respect to a
non-linear $1$-homogeneous involution $i(x,y)=(\frac{y^2}{x},y)$. We also find
all solenoidal rational flows. Up to linear conjugation, there appears to be
exactly two non-trivial examples.Comment: 32 pages, 1 figur | The projective translation equation and rational plane flows. II.
Corrections and additions | the projective translation equation and rational plane flows. ii. corrections and additions | flaw part. affects consecutive papers. arguments additions claim validity results. disposition algebraic rational flows transparently classified. turns notion algebraic projective one. inductive build algebraic projective flows rational flows. expand concerning rational flows flows involution rational flows homogeneous involution frac solenoidal rational flows. conjugation trivial pages figur | non_dup | [] |
42712392 | 10.1007/s00010-017-0513-8 | Quasi-arithmetic means are defined for every continuous, strictly monotone
function $f \colon U \rightarrow \mathbb{R}$, ($U$ -- an interval). For an
$n$-tuple $a \in U^n$ with corresponding vector of weights $w=(w_1,\dots,w_n)$
($w_i>0$, $\sum w_i=1$) it equals $f^{-1}\left( \sum_{i=1}^{n} w_i
f(a_i)\right)$. In 1960s Cargo and Shisha defined a metric in a family of
quasi-arithmetic means defined on a common interval as the maximal possible
difference between these means taken over all admissible vectors with
corresponding weights. During the years 2013--16 we proved that, having two
quasi-arithmetic means, we can majorized distance between them in terms of
Arrow-Pratt index $f''/f'$. In this paper we are going to proof that this
operator can be also used to establish certain lower boundaries of this
distance.Comment: 14 page | Lower estimation of the difference among quasi-arithmetic means | lower estimation of the difference among quasi-arithmetic means | quasi arithmetic strictly monotone colon rightarrow mathbb tuple weights dots equals cargo shisha quasi arithmetic maximal admissible weights. proved quasi arithmetic majorized arrow pratt going establish boundaries | non_dup | [] |
83868228 | 10.1007/s00010-018-0541-z | In 1970, Coxeter gave a short and elegant geometric proof showing that if
$p_1, p_2, \ldots, p_n$ are vertices of an $n$-gon $P$ in cyclic order, then
$P$ is affinely regular if, and only if there is some $\lambda \geq 0$ such
that $p_{j+2}-p_{j-1} = \lambda (p_{j+1}-p_j)$ for $j=1,2,\ldots, n$. The aim
of this paper is to examine the properties of polygons whose vertices
$p_1,p_2,\ldots,p_n \in \mathbb{C}$ satisfy the property that
$p_{j+m_1}-p_{j+m_2} = w (p_{j+k}-p_j)$ for some $w \in \mathbb{C}$ and
$m_1,m_2,k \in \mathbb{Z}$. In particular, we show that in `most' cases this
implies that the polygon is affinely regular, but in some special cases there
are polygons which satisfy this property but are not affinely regular. The
proofs are based on the use of linear algebraic and number theoretic tools. In
addition, we apply our method to characterize polytopes with certain symmetry
groups.Comment: 11 pages, 1 figur | A characterization of affinely regular polygons | a characterization of affinely regular polygons | coxeter gave elegant geometric ldots cyclic affinely lambda lambda ldots examine polygons ldots mathbb satisfy mathbb mathbb polygon affinely polygons satisfy affinely regular. proofs algebraic theoretic tools. characterize polytopes pages figur | non_dup | [] |
75997273 | 10.1007/s00011-006-0078-9 | Objective
To assess the role of nitric oxide in the most relevant local and systemic manifestations in mice injected with the venom of the snake Bothrops asper. Mice were pretreated with nitric oxide synthase inhibitors, and the modifications of the pathological effects induced by the venom were tested.
Results
Inhibition of NO synthesis did not affect acute local myonecrosis and hemorrhage in muscle tissue upon intramuscular injection of venom. Local footpad edema was reduced in mice pretreated with the NO synthase inhibitor L-NAME, and a reduction in the extent of inflammatory infiltrate in muscle tissue was observed after envenomation in mice pretreated with L-NAME and aminoguanidine. The most pronounced effect of NOS inhibition by L-NAME was an increment in the lethal activity of the venom, when injected by the intraperitoneal route.
Conclusion
Nitric oxide does not seem to play a significant role in the local acute pathological alterations (hemorrhage and myonecrosis) induced by B. asper venom in mice, although it contributes to edema and inflammatory infiltrate. Nitric oxide exerts a protective role in the systemic pathophysiological manifestations leading to lethality.Universidad de Costa Rica/[2075-06-01]/UCR/Costa RicaUCR::Investigación::Unidades de Investigación::Ciencias de la Salud::Instituto Clodomiro Picado (ICP | Role of nitric oxide in the local and systemic pathophysiological effects induced by Bothrops asper snake venom in mice | role of nitric oxide in the local and systemic pathophysiological effects induced by bothrops asper snake venom in mice | nitric oxide systemic manifestations injected venom snake bothrops asper. pretreated nitric oxide synthase inhibitors modifications pathological venom tested. myonecrosis hemorrhage intramuscular injection venom. footpad edema pretreated synthase inhibitor name inflammatory infiltrate envenomation pretreated name aminoguanidine. pronounced name increment lethal venom injected intraperitoneal route. nitric oxide seem pathological alterations hemorrhage myonecrosis asper venom contributes edema inflammatory infiltrate. nitric oxide exerts protective systemic pathophysiological manifestations lethality.universidad costa rica costa ricaucr investigación unidades investigación ciencias salud instituto clodomiro picado | non_dup | [] |
190331589 | 10.1007/s00011-007-7046-x | Inflammation Research, 56(12): pp. 502-510.Objective and Design: Myeloperoxidase (MPO) and proinflammatory cytokines play an important role in the development of inflammation. These markers are generally measured using tedious ELISA procedures. In this study, a novel technique utilizing antibody conjugated quantum dot nanoparticles was developed to detect myeloperoxidase, IL-1 α and TNF-α in vivo in the dextran sodium sulfate (DSS) model of experimental colitis. Materials and Methods: Colitis was induced in animals (n=8 animals/ group) by feeding 4% DSS solution ad libitum for seven to eight days. Quantum Dots exhibiting fluorescence at various wavelengths were conjugated to MPO, IL-1 α and TNF-α polyclonal antibodies and tested in vivo at various stages of colitis. Tissue sections obtained were imaged with confocal microscope. The image intensity obtained from the tissue specimen was correlated with clinical activity measured as Disease Activity Index (DAI).
Results: Myeloperoxidase, IL-1α and TNF-α were visualized with quantum dots on various days of disease. The intensity of quantum dots increased with increase in inflammation. The increase in intensity showed an excellent correlation with the DAI based on the clinical parameters.
Conclusion: The study demonstrated that multiple biomarkers can be detected simultaneously and their quantitative expression correlated well with clinical disease severity. This novel technology should facilitate design of a novel optical platform for imaging various biomarkers of inflammation, early detection of acute and chronic disease markers and inflammation-mediated cancer markers. This detection may also facilitate determination of therapeutic success | Imaging biomarkers of inflammation in situ with functionalized quantum dots in the dextran sodium sulfate (DSS) model of mouse colitis | imaging biomarkers of inflammation in situ with functionalized quantum dots in the dextran sodium sulfate (dss) model of mouse colitis | inflammation .objective myeloperoxidase proinflammatory cytokines inflammation. markers tedious elisa procedures. utilizing conjugated nanoparticles detect myeloperoxidase dextran sodium sulfate colitis. colitis feeding libitum seven eight days. dots exhibiting fluorescence wavelengths conjugated polyclonal antibodies colitis. imaged confocal microscope. specimen myeloperoxidase visualized dots disease. dots inflammation. excellent parameters. biomarkers simultaneously severity. facilitate platform biomarkers inflammation markers inflammation markers. facilitate therapeutic success | non_dup | [] |
1639918 | 10.1007/s00011-008-8171-x | ???The original publication is available at www.springerlink.com???. Copyright Springer. DOI: 10.1007/s00011-008-8171-xAim and objective: The aim of the work was to characterise the nAChRs on human PBMC. Method: PBMC were isolated from human blood buffy coats provided by the blood transfusion service and were used for radioligand binding studies with [3H]-nicotine. RT-PCR experiments were used to determine nAChR subunit expression while immunoblotting experiments were used to confirm that nAChR subunits identified by RT-PCR were translated into protein. Results: Binding studies suggested the presence of one binding site for (-)- nicotine on human peripheral blood lymphocytes. Competition studies showed that only (-)- nicotine, epibatidine and ??-bungarotoxin, displaced radiolabelled nicotine from cells. RT-PCR studies demonstrated mRNA for ??4, ??5, ??7, ??1 and ??2 nAChRs subunits in PBMC. Expression of mRNA for the a5 subunit of nAChR was observed in all lymphocyte samples tested. In contrast, the expression pattern of mRNAs for ??4, ??7, ??1, and ??2 mRNAs subunits of nAChRs, varied between samples. Western blot analysis showed that protein for ??4, ??5, and ??7 and ??2 nAChR subunits was expressed in most, but not all of the PBMC samples tested but some of the bands obtained were faint. Conclusion: The results obtained suggest that human PBMC contain nAChRs containing ??4??2, ??4??2??5, and/or ??7 subunits | Characterisation of nicotine receptors on human peripheral blood mononuclear cells (PBMC) | characterisation of nicotine receptors on human peripheral blood mononuclear cells (pbmc) | publication copyright springer. xaim characterise nachrs pbmc. pbmc buffy coats transfusion radioligand nicotine. nachr subunit immunoblotting confirm nachr subunits translated protein. nicotine peripheral lymphocytes. competition nicotine epibatidine bungarotoxin displaced radiolabelled nicotine cells. nachrs subunits pbmc. subunit nachr lymphocyte tested. mrnas mrnas subunits nachrs varied samples. blot nachr subunits pbmc faint. pbmc nachrs subunits | non_dup | [] |
1640021 | 10.1007/s00011-009-8112-3 | ???The original publication is available at www.springerlink.com???. Copyright Springer. DOI: 10.1007/s00011-009-8112-3Objective and design: Prostaglandin D2 (PGD2) has been shown to cause eosinophil, basophil and Th2 cell chemotaxis in vitro and in vivo through an action on the prostaglandin CRTH2 receptor. In the present study, the dependence of PGD2-induced eosinophil accumulation in vivo on interleukin-5 (IL-5) blood eosinophilia was investigated. Materials: Guinea-pigs were exposed to aerosols of 13,14dihydro 15-keto PGD2 (DK-PGD2) or platelet activating factor (PAF) and the eosinophil content of the bronchoalveolar lavage fluid or blood determined. In some experiments, DK-PGD2 was administered systemically and eosinophilia measured. Results: Aerosols of DK-PGD2 caused eosinophil accumulation in the lungs 24h after exposure. DK-PGD2 (10 ??g.ml-1) -induced airway eosinophilia was inhibited when animals were treated with the CRTH2 receptor antagonist ramatroban. 1???4h after exposure to DK-PGD2 a significant decrease in blood eosinophil count was measured. The anti-IL-5 antibody TRFK-5 had no inhibitory effect of DK-PGD2-induced airway eosinophilia, but abolished airway eosinophilia induced by exposure of guinea-pigs to aerosols of PAF. Intracardiac injection of DK-PGD2 induced a dose-related increase in blood eosinophil numbers. Conclusions: It is concluded that, in the guinea-pig, DKPGD2-induced airway eosinophilia is mediated by an action on prostaglandin CRTH2 receptors and that this response appears to be independent of IL-5 | Evidence that 13???14 di-hydro, 15-keto prostaglandin D2-induced airway eosinophilia in guinea-pigs is independent of interleukin-5 | evidence that 13???14 di-hydro, 15-keto prostaglandin d2-induced airway eosinophilia in guinea-pigs is independent of interleukin-5 | publication copyright springer. prostaglandin eosinophil basophil chemotaxis prostaglandin crth receptor. eosinophil accumulation interleukin eosinophilia investigated. guinea pigs exposed aerosols dihydro keto platelet activating eosinophil bronchoalveolar lavage determined. administered systemically eosinophilia measured. aerosols eosinophil accumulation lungs exposure. g.ml airway eosinophilia inhibited crth antagonist ramatroban. eosinophil count measured. trfk inhibitory airway eosinophilia abolished airway eosinophilia guinea pigs aerosols paf. intracardiac injection eosinophil numbers. concluded guinea dkpgd airway eosinophilia prostaglandin crth receptors | non_dup | [] |
55629508 | 10.1007/s00011-010-0185-5 | The selective COX-2 inhibitor Etoricoxib reduces acute inflammatory markers in a model of neurogenic laryngitis but loses its efficacy with prolonged treatment.OBJECTIVE:
A randomised experimental study was used to evaluate the therapeutic effect of a selective cyclooxygenase-2 (COX-2) inhibitor in neurogenic laryngitis.
MATERIALS AND METHODS:
Male Wistar Han rats were subjected to the nasogastric intubation model (NGI) of laryngitis for 1 and 2 weeks. The NGI animals were divided into three groups: (1) treated with COX-2 inhibitor Etoricoxib, (2) vehicle and (3) non-intubated animals. A fourth group of animals was submitted to NGI only. Laryngeal sections were immunostained for substance P (SP) and calcitonin gene-related peptide (CGRP) fibre-immunoreactivity (IR) and quantification of COX-2 positive cells through stereological analysis. The expression of COX-2, interleukins IL-1beta, IL-6, IL-10 and tumour necrosis factor-alpha (TNF-alpha) was determined by quantitative real time QRT-PCR.
TREATMENT:
Etoricoxib (6 mg/kg/day) was prepared in 0.9% sterile saline with 5% glucose (vehicle) and administered daily during 1 or 2 weeks.
RESULTS:
Treatment for 1 week with Etoricoxib attenuated the CGRP-IR fibre depletion, the COX-2-IR increased cell number and the TNF-alpha and COX-2 mRNA increased levels induced by NGI. Two weeks of treatment had no beneficial effect.
CONCLUSIONS:
Etoricoxib is effective in neurogenic laryngitis for limited periods of administration, indicating that selective COX-2 inhibitors should be evaluated in the future.This study was supported by Fundacao Calouste Gulbenkian Project No 74551 and Fundacao Grunenthal (Portugal) | The selective COX-2 inhibitor etoricoxib reduces acute inflammatory markers in a model of neurogenic laryngitis but loses its efficacy with prolonged treatment | the selective cox-2 inhibitor etoricoxib reduces acute inflammatory markers in a model of neurogenic laryngitis but loses its efficacy with prolonged treatment | selective inhibitor etoricoxib reduces inflammatory markers neurogenic laryngitis loses efficacy prolonged treatment.objective randomised therapeutic selective cyclooxygenase inhibitor neurogenic laryngitis. wistar rats subjected nasogastric intubation laryngitis weeks. divided inhibitor etoricoxib vehicle intubated animals. fourth submitted only. laryngeal immunostained substance calcitonin cgrp fibre immunoreactivity quantification stereological analysis. interleukins beta tumour necrosis alpha alpha pcr. etoricoxib sterile saline glucose vehicle administered weeks. week etoricoxib attenuated cgrp fibre depletion alpha ngi. beneficial effect. etoricoxib neurogenic laryngitis administration selective inhibitors future.this fundacao calouste gulbenkian fundacao grunenthal portugal | non_dup | [] |
148769057 | 10.1007/s00011-010-0204-6 | The present study was performed to compare the effects of high frequency oscillatory ventilation (HFOV) with conventional mechanical ventilation (CMV) on pulmonary inflammatory responses in a rat acid-induced lung injury model. Anesthetized rats were instilled intratracheally with HCl (0.1 N, 2 mL/kg) and then randomly divided into three mechanical ventilation settings: HFOV (an oscillatory frequency of 15 Hz, mean airway pressure (MAP) of 9 cmH(2)O), CMV at tidal volume of 12 and 6 mL/kg for 5 h. After HCl instillation, HFOV significantly attenuated the increases in neutrophil infiltration and TNF-alpha concentration in bronchoalveolar lavage fluid compared with the CMV groups. During HFOV, there was an inhibition of an increase in TNF-alpha mRNA expression and a decrease in SP-A mRNA expression induced by acid instillation. This animal study demonstrates that HFOV is a suitable form of mechanical ventilation to prevent inflammatory responses in acid-induced lung injury | Comparison of acid-induced inflammatory responses in the rat lung during high frequency oscillatory and conventional mechanical ventilation | comparison of acid-induced inflammatory responses in the rat lung during high frequency oscillatory and conventional mechanical ventilation | oscillatory ventilation hfov ventilation pulmonary inflammatory injury model. anesthetized rats instilled intratracheally randomly divided ventilation settings hfov oscillatory airway tidal instillation hfov attenuated neutrophil infiltration alpha bronchoalveolar lavage groups. hfov alpha instillation. demonstrates hfov ventilation prevent inflammatory injury | non_dup | [] |
28938792 | 10.1007/s00011-011-0395-5 | Objectives: Numerous receptors have been implicated in recognition of pathogenic fungi by macrophages, including the \(\beta\)-glucan receptor dectin-1. The role of scavenger receptors (SRs) in anti-fungal immunity is not well characterized. Methods: We studied uptake of unopsonized Saccharomycetes cerevisiae (zymosan) and live Candida albicans yeasts as well as zymosan-stimulated \(H_2O_2\) production in J774 macrophage-like cells and peritoneal exudate macrophages (PEMs). The role of different receptors was assessed with the use of competitive ligands, transfected cells and receptor-deficient macrophages. Results: The uptake of zymosan by untreated J774 cells was mediated approximately half by SRs and half by a \(\beta\)-glucan receptor which was distinct from dectin-1 and not linked to stimulation of \(H_2O_2\) production. Ligands of \(\beta\)-glucan receptors and of SRs also inhibited uptake of C. albicans by macrophages (J774 cells and PEMs). In macrophages pretreated with a CpG motif-containing oligodeoxynucleotide (CpG-ODN) the relative contribution of SRs to yeast uptake increased and that of \(\beta\)-glucan receptors decreased. Whereas the class A SR MARCO participated in the uptake of both zymosan and C. albicans by CpG-ODN-pretreated, but not untreated macrophages, the related receptor SR-A/CD204 was involved in the uptake of zymosan, but not of C. albicans. The reduction of zymosan-stimulated \(H_2O_2\) production observed in DS-pretreated J774 cells and in class A SRs-deficient PEMs suggest that class A SRs mediate part of this process. Conclusions: Our results revealed that SRs belong to a redundant system of receptors for yeasts. Binding of yeasts to different receptors in resting versus CpG-ODN-pre-exposed macrophages may differentially affect polarization of adaptive immune responses | Scavenger Receptors and \(\beta\)-Glucan Receptors Participate in the Recognition of Yeasts by Murine Macrophages | scavenger receptors and \(\beta\)-glucan receptors participate in the recognition of yeasts by murine macrophages | objectives numerous receptors implicated recognition pathogenic fungi macrophages beta glucan dectin scavenger receptors fungal immunity characterized. uptake unopsonized saccharomycetes cerevisiae zymosan live candida albicans yeasts zymosan stimulated macrophage peritoneal exudate macrophages pems receptors competitive ligands transfected deficient macrophages. uptake zymosan untreated beta glucan dectin stimulation production. ligands beta glucan receptors inhibited uptake albicans macrophages pems macrophages pretreated motif oligodeoxynucleotide yeast uptake beta glucan receptors decreased. marco participated uptake zymosan albicans pretreated untreated macrophages uptake zymosan albicans. zymosan stimulated pretreated deficient pems mediate process. belong redundant receptors yeasts. yeasts receptors resting exposed macrophages differentially adaptive immune | non_dup | [] |
37509338 | 10.1007/s00011-011-0400-z | Cyclosporine (CsA) remains an important immunosuppressant for transplantation and for treatment of autoimmune diseases. The most troublesome side effect of CsA is renal injury. Acute CsA-induced nephrotoxicity is characterized by reduced renal blood flow (RBF) and glomerular filtration rate (GFR) due to afferent arteriole vasoconstriction. Annexin A1 (ANXA1) is a potent anti-inflammatory protein with protective effect in renal ischemia/reperfusion injury. Here we study the effects of ANXA1 treatment in an experimental model of acute CsA nephrotoxicity. Salt-depleted rats were randomized to treatment with VH (vehicles 1 mL/kg body weight/day), ANXA1 (Ac2-26 peptide 1 mg/kg body weight/day intraperitoneally), CsA (20 mg/kg body weight/day subcutaneously) and CsA + ANXA1 (combination) for seven days. We compared renal function and hemodynamics, renal histopathology, renal tissue macrophage infiltration and renal ANXA1 expression between the four groups. CsA significantly impaired GFR and RBF, caused tubular dilation and macrophage infiltration and increased ANXA1 renal tissue expression. Treatment with ANXA1 attenuated CSA-induced hemodynamic changes, tubular injury and macrophage infiltration. ANXA1 treatment attenuated renal hemodynamic injury and inflammation in an acute CsA nephrotoxicity model.Fundacao de Amparo a Pesquisa do Estado de Sao Paulo - FAPESP [2008/01,048-9]Conselho Nacional de Desenvolvimento Cientifico e Tecnologico-CNPq [306,074/2007-9, 307,371/2006-9 | Annexin A1 protein attenuates cyclosporine-induced renal hemodynamics changes and macrophage infiltration in rats | annexin a1 protein attenuates cyclosporine-induced renal hemodynamics changes and macrophage infiltration in rats | cyclosporine immunosuppressant transplantation autoimmune diseases. troublesome injury. nephrotoxicity glomerular filtration afferent arteriole vasoconstriction. annexin anxa potent inflammatory protective ischemia reperfusion injury. anxa nephrotoxicity. salt depleted rats randomized vehicles anxa intraperitoneally subcutaneously anxa seven days. hemodynamics histopathology macrophage infiltration anxa groups. impaired tubular dilation macrophage infiltration anxa expression. anxa attenuated hemodynamic tubular injury macrophage infiltration. anxa attenuated hemodynamic injury inflammation nephrotoxicity model.fundacao amparo pesquisa estado paulo fapesp conselho nacional desenvolvimento cientifico tecnologico cnpq | non_dup | [] |
37508361 | 10.1007/s00011-011-0415-5 | Endothelins (ETs) are involved in several inflammatory events. The present study investigated the efficacy of bosentan, a dual ETA/ETB receptor antagonist, in collagen-induced arthritis (CIA) in mice. CIA was induced in DBA/1J mice. Arthritic mice were treated with bosentan (100 mg/kg) once a day, starting from the day when arthritis was clinically detectable. CIA progression was assessed by measurements of visual clinical score, paw swelling and hypernociception. Histological changes, neutrophil infiltration and pro-inflammatory cytokines were evaluated in the joints. Gene expression in the lymph nodes of arthritic mice was evaluated by microarray technology. PreproET-1 mRNA expression in the lymph nodes of mice and in peripheral blood mononuclear cells (PBMCs) was evaluated by real-time PCR. The differences were evaluated by one-way ANOVA or Student's t test. Oral treatment with bosentan markedly ameliorated the clinical aspects of CIA (visual clinical score, paw swelling and hyperalgesia). Bosentan treatment also reduced joint damage, leukocyte infiltration and pro-inflammatory cytokine levels (IL-1 beta, TNF alpha and IL-17) in the joint tissues. Changes in gene expression in the lymph nodes of arthritic mice returned to the levels of the control mice after bosentan treatment. PreproET mRNA expression increased in PBMCs from rheumatoid arthritis (RA) patients but returned to basal level in PBMCs from patients under anti-TNF therapy. In-vitro treatment of PBMCs with TNF alpha upregulated ET system genes. These findings indicate that ET receptor antagonists, such as bosentan, might be useful in controlling RA. Moreover, it seems that ET mediation of arthritis is triggered by TNF alpha.Fundacao de Amparo a Pesquisa do Estado de Sao Paulo (FAPESP)Fundacao de Amparo a Pesquisa do Estado de Sao Paulo (FAPESP)Conselho Nacional de Desenvolvimento Cientifico e Tecnologico (CNPq) (Sao Paulo, Brazil)Conselho Nacional de Desenvolvimento Cientifico e Tecnologico (CNPq) (Sao Paulo, Brazil | Bosentan, an endothelin receptor antagonist, ameliorates collagen-induced arthritis: the role of TNF-alpha in the induction of endothelin system genes | bosentan, an endothelin receptor antagonist, ameliorates collagen-induced arthritis: the role of tnf-alpha in the induction of endothelin system genes | endothelins inflammatory events. efficacy bosentan antagonist collagen arthritis mice. mice. arthritic bosentan arthritis clinically detectable. progression swelling hypernociception. histological neutrophil infiltration inflammatory cytokines joints. lymph arthritic microarray technology. preproet lymph peripheral mononuclear pbmcs pcr. anova student test. oral bosentan markedly ameliorated swelling hyperalgesia bosentan leukocyte infiltration inflammatory cytokine beta alpha tissues. lymph arthritic returned bosentan treatment. preproet pbmcs rheumatoid arthritis returned basal pbmcs therapy. pbmcs alpha upregulated genes. antagonists bosentan controlling mediation arthritis triggered alpha.fundacao amparo pesquisa estado paulo fapesp fundacao amparo pesquisa estado paulo fapesp conselho nacional desenvolvimento cientifico tecnologico cnpq paulo brazil conselho nacional desenvolvimento cientifico tecnologico cnpq paulo brazil | non_dup | [] |
33635270 | 10.1007/s00011-015-0833-x | OBJECTIVE: N-methyl pyrrolidone (NMP), a small bioactive molecule, stimulates bone formation and inhibits osteoclast differentiation and bone resorption. The present study was aimed to evaluate the anti-inflammatory potentials of NMP on the inflammatory process and the underlying molecular mechanisms in RAW264.7 macrophages.\ud
MATERIALS AND METHODS: RAW264.7 macrophages and mouse primary bone marrow macrophages (mBMMs) were used as an in vitro model to investigate inflammatory processes. Cells were pre-treated with or without NMP and then stimulated with lipopolysaccharides (LPS). The productions of cytokines and NO were determined by proteome profiler method and nitrite analysis, respectively. The expressions of nitric oxide synthase (iNOS) and cyclooxygenase-2 (COX-2) were measured by Western blotting and/or qPCR. Western blot, ELISA-base reporter assay, and immunofluorescence were used to evaluate the activation of MAP kinases and NF-κB.\ud
RESULTS: LPS-induced mRNA expressions of TNF-α, IL-1β, IL-6, iNOS, and COX-2 were inhibited by NMP in a dose-dependent manner. NMP also suppressed the LPS-increased productions of iNOS and NO. The proteome profiler array showed that several cytokines and chemokines involved in inflammation and up-regulated by LPS stimulation were significantly down-regulated by NMP. Additionally, this study shows that the effect of NMP is mediated through down-regulation of NFκB pathway.\ud
CONCLUSIONS: Our results show that NMP inhibits the inflammatory mediators in macrophages by an NFκB-dependent mechanism, based on the epigenetical activity of NMP as bromodomain inhibitor. In the light of its action on osteoblast and osteoclast differentiation process and its anti-inflammatory potential, NMP might be used in inflammation-related bone loss | N-methyl pyrrolidone (NMP) inhibits lipopolysaccharide-induced inflammation by suppressing NF-κB signaling | n-methyl pyrrolidone (nmp) inhibits lipopolysaccharide-induced inflammation by suppressing nf-κb signaling | methyl pyrrolidone bioactive molecule stimulates inhibits osteoclast resorption. aimed inflammatory potentials inflammatory macrophages. macrophages marrow macrophages mbmms inflammatory processes. stimulated lipopolysaccharides productions cytokines proteome profiler nitrite respectively. expressions nitric oxide synthase inos cyclooxygenase blotting qpcr. blot elisa reporter immunofluorescence kinases expressions inos inhibited manner. suppressed productions inos proteome profiler array cytokines chemokines inflammation regulated stimulation regulated nmp. additionally nfκb pathway. inhibits inflammatory mediators macrophages nfκb epigenetical bromodomain inhibitor. osteoblast osteoclast inflammatory inflammation | non_dup | [] |
80918070 | 10.1007/s00011-017-1030-x | INTRODUCTION : Type 2 diabetes mellitus is a pandemic associated with disturbance inhaemostasis that could contribute to the development of diabetic vascular disease and accelerated atherosclerosis. In this population, hypercoagulation is prevalent, as well as pathological changes to erythrocytes. This is mainly due to upregulated circulating inflammatory markers.
MATERIALS AND METHODS : Here we looked at tissue factor (TF) levels using ELISA, in a sample of diabetics, with and without cardiovascular complications. Diabetic subjects were recruited from the diabetic clinic at Steve Biko Academic Hospital, Pretoria, South Africa. 20 diabetics with cardiovascular disease and 22 without were enrolled to participate. RESULTS AND CONCLUSION : TF levels were significantly elevated in both diabetic groups when compared to the controls. We suggest that pathologic plasma TF activity, as marker of increased propensity of clot pathology, should be investigated. Agents that might lower TF levels might also possibly lower thrombotic complications.This work is based on the research supported in part by the National Research
Foundation of South Africa (UNIQUE GRANT NO: 92709) and the MRC : E Pretorius
(fund number A0X331).http://link.springer.com/journal/112018-02-28hb2017Physiolog | Tissue factor levels in type 2 diabetes mellitus | tissue factor levels in type 2 diabetes mellitus | mellitus pandemic disturbance inhaemostasis diabetic vascular accelerated atherosclerosis. hypercoagulation prevalent pathological erythrocytes. upregulated circulating inflammatory markers. looked elisa diabetics cardiovascular complications. diabetic recruited diabetic clinic steve biko academic pretoria africa. diabetics cardiovascular enrolled participate. elevated diabetic controls. pathologic marker propensity clot pathology investigated. possibly thrombotic complications.this foundation africa pretorius fund physiolog | non_dup | [] |
2579632 | 10.1007/s00012-005-1934-0 | Properties of several sorts of lattices of convex subsets of R^n are
examined. The lattice of convex sets containing the origin turns out, for n>1,
to satisfy a set of identities strictly between those of the lattice of all
convex subsets of R^n and the lattice of all convex subsets of R^{n-1}. The
lattices of arbitrary, of open bounded, and of compact convex sets in R^n all
satisfy the same identities, but the last of these is join-semidistributive,
while for n>1 the first two are not. The lattice of relatively convex subsets
of a fixed set S \subseteq R^n satisfies some, but in general not all of the
identities of the lattice of ``genuine'' convex subsets of R^n.Comment: 35 pages, to appear in Algebra Universalis, Ivan Rival memorial
issue. See also http://math.berkeley.edu/~gbergman/paper | On lattices of convex sets in R^n | on lattices of convex sets in r^n | sorts lattices convex subsets examined. convex turns satisfy identities strictly convex subsets convex subsets lattices convex satisfy identities join semidistributive not. convex subsets subseteq satisfies identities genuine convex subsets pages universalis ivan rival memorial issue. gbergman | non_dup | [] |
2575420 | 10.1007/s00012-006-1959-z | Let S=Sym(\Omega) be the group of all permutations of a countably infinite
set \Omega, and for subgroups G_1, G_2\leq S let us write G_1\approx G_2 if
there exists a finite set U\subseteq S such that < G_1\cup U > = < G_2\cup U >.
It is shown that the subgroups closed in the function topology on S lie in
precisely four equivalence classes under this relation. Which of these classes
a closed subgroup G belongs to depends on which of the following statements
about pointwise stabilizer subgroups G_{(\Gamma)} of finite subsets
\Gamma\subseteq\Omega holds:
(i) For every finite set \Gamma, the subgroup G_{(\Gamma)} has at least one
infinite orbit in \Omega.
(ii) There exist finite sets \Gamma such that all orbits of G_{(\Gamma)} are
finite, but none such that the cardinalities of these orbits have a common
finite bound.
(iii) There exist finite sets \Gamma such that the cardinalities of the
orbits of G_{(\Gamma)} have a common finite bound, but none such that
G_{(\Gamma)}=\{1\}.
(iv) There exist finite sets \Gamma such that G_{(\Gamma)}=\{1\}.
Some questions for further investigation are discussed.Comment: 33 pages. See also http://math.berkeley.edu/~gbergman/papers and
http://shelah.logic.at (pub. 823). To appear, Alg.Univ., issue honoring
W.Taylor. Main results as before (greater length due to AU formatting), but
some new results in \S\S11-12. Errors in subscripts between displays (12) and
(13) fixed. Error in title of orig. posting fixed. 1 ref. adde | Closed subgroups of the infinite symmetric group | closed subgroups of the infinite symmetric group | omega permutations countably infinite omega subgroups approx subseteq subgroups topology precisely equivalence relation. subgroup belongs statements pointwise stabilizer subgroups gamma subsets gamma subseteq omega gamma subgroup gamma infinite orbit omega. gamma orbits gamma none cardinalities orbits bound. gamma cardinalities orbits gamma none gamma gamma gamma pages. gbergman papers shelah.logic.at pub. alg.univ. honoring w.taylor. formatting subscripts displays fixed. title orig. posting fixed. ref. adde | non_dup | [] |
55612226 | 10.1007/s00012-006-1975-z | For $n ∈ \mathbb{N}$ and $m ∈ \mathbb{N}_0$, an algebra $L = (L, ∧, ∨, f, g, 0, 1)$ of type $(2, 2, 1, 1, 0, 0)$
is said to be a double $K_{n,m}$-algebra, if L is a double Ockham algebra that satisfies the
identities $f^{2n+m} = f^m, g^{2n+m} = g^m, fg = g^{2zn} and gf = f^{2zn}, where z is the smallest
natural number greater than or equal to m/2n. In this papaer we describe the complement (when it
exists) of a principal congruence and, using this description, we also determine when the
complement exists.Fundação para a Ciência e a Tecnologia (FCT) - programa POCT | Complemented congruences on double Ockham algebras | complemented congruences on double ockham algebras | mathbb mathbb said ockham satisfies identities smallest papaer complement principal congruence complement exists.fundação para ciência tecnologia programa poct | non_dup | [] |
2600967 | 10.1007/s00012-008-2063-3 | A new class of partial order-types, class $\gbqo^+$ is defined and
investigated here. A poset $P$ is in the class $W^+ $ iff the free poset
algebra $F(P)$ is generated by a better quasi-order $G$ that is included in the
free lattice $L(P)$.
We prove that if $P$ is any well quasi-ordering, then $L(P)$ is well founded,
and is a countable union of well quasi-orderings. We prove that the class $W^+$
is contained in the class of well quasi-ordered sets. We prove that $W^+$ is
preserved under homomorphic image, finite products, and lexicographic sum over
better quasi-ordered index sets. We prove also that every countable well
quasi-ordered set is in $W^+$. We do not know, however if the class of well
quasi-ordered sets is contained in $W^+$. Additional results concern
homomorphic images of posets algebras.Comment: 28 page | Poset algebras over well quasi-ordered posets | poset algebras over well quasi-ordered posets | gbqo here. poset poset quasi quasi ordering founded countable union quasi orderings. quasi ordered sets. preserved homomorphic lexicographic quasi ordered sets. countable quasi ordered quasi ordered concern homomorphic posets | non_dup | [] |
47182057 | 10.1007/s00012-009-0013-3 | The maximality property was introduced in [9] in orthomodular posets as
a common generalization of orthomodular lattices and orthocomplete orthomodular
posets. We show that various conditions used in the theory of e ect
algebras are stronger than the maximality property, clear up the connections
between them and show some consequences of these conditions. In particular,
we prove that a Jauch{Piron e ect algebra with a countable unital set of states
is an orthomodular lattice and that a unital set of Jauch{Piron states on an
e ect algebra with the maximality property is strongly order determining | Effect algebras with the maximality property | effect algebras with the maximality property | maximality orthomodular posets generalization orthomodular lattices orthocomplete orthomodular posets. algebras stronger maximality connections consequences conditions. jauch piron countable unital orthomodular unital jauch piron maximality determining | non_dup | [] |
2255268 | 10.1007/s00012-009-0028-9 | Following Bezhanishvili & Vosmaer, we confirm a conjecture of Yde Venema by
piecing together results from various authors. Specifically, we show that if
$\mathbb{A}$ is a residually finite, finitely generated modal algebra such that
$\operatorname{HSP}(\mathbb{A})$ has equationally definable principal
congruences, then the profinite completion of $\mathbb{A}$ is isomorphic to its
MacNeille completion, and $\Diamond$ is smooth. Specific examples of such modal
algebras are the free $\mathbf{K4}$-algebra and the free
$\mathbf{PDL}$-algebra.Comment: 5 page | MacNeille completion and profinite completion can coincide on finitely
generated modal algebras | macneille completion and profinite completion can coincide on finitely generated modal algebras | bezhanishvili vosmaer confirm conjecture venema piecing authors. mathbb residually finitely modal operatorname mathbb equationally definable principal congruences profinite completion mathbb isomorphic macneille completion diamond smooth. modal algebras mathbf mathbf | non_dup | [] |
52463312 | 10.1007/s00012-010-0073-4 | To appear in the journal Algebra UniversalisInternational audienceFor L a finite lattice, let C(L) denote the set of pairs g = (g_0,g_1) such that g_0 is a lower cover of g_1 and order it as follows: g <= d iff g_0 <= d_0, g_1 <= d_1, but not g_1 <= d_0. Let C(L,g) denote the connected component of g in this poset. Our main result states that C(L,g) is a semidistributive lattice if L is semidistributive, and that C(L,g) is a bounded lattice if L is bounded. Let S_n be the permutohedron on n letters and T_n be the associahedron on n+1 letters. Explicit computations show that C(S_n,a) = S_{n-1} and C(T_n,a) = T_{n-1}, up to isomorphism, whenever a is an atom. These results are consequences of new characterizations of finite join semidistributive and finite lower bounded lattices: (i) a finite lattice is join semidistributive if and only if the projection sending g in C(L) to g_0 in L creates pullbacks, (ii) a finite join semidistributive lattice is lower bounded if and only if it has a strict facet labelling. Strict facet labellings, as defined here, are generalization of the tools used by Barbut et al. to prove that lattices of Coxeter groups are bounded | Derived Semidistributive Lattices | derived semidistributive lattices | universalisinternational audiencefor cover poset. semidistributive semidistributive bounded. permutohedron associahedron letters. computations isomorphism whenever atom. consequences characterizations join semidistributive lattices join semidistributive projection sending creates pullbacks join semidistributive strict facet labelling. strict facet labellings generalization barbut lattices coxeter | non_dup | [] |
2187391 | 10.1007/s00012-011-0121-8 | We prove that the relative commutator with respect to a subvariety of a
variety of Omega-groups introduced by the first author can be described in
terms of categorical Galois theory. This extends the known correspondence
between the Froehlich-Lue and the Janelidze-Kelly notions of central extension.
As an example outside the context of Omega-groups we study the reflection of
the category of loops to the category of groups where we obtain an
interpretation of the associator as a relative commutator.Comment: 14 page | Galois theory and commutators | galois theory and commutators | commutator subvariety omega categorical galois theory. extends correspondence froehlich janelidze kelly notions extension. omega reflection loops associator | non_dup | [] |
2086786 | 10.1007/s00012-012-0184-1 | We consider sets of operations on a set A that are closed under permutation
of variables, addition of dummy variables and composition. We describe these
closed sets in terms of a Galois connection between operations and systems of
pointed multisets, and we also describe the closed sets of the dual objects by
means of necessary and sufficient closure conditions. Moreover, we show that
the corresponding closure systems are uncountable for every A with at least two
elements.Comment: 22 pages; Section 4 adde | Galois connection for sets of operations closed under permutation,
cylindrification and composition | galois connection for sets of operations closed under permutation, cylindrification and composition | operations permutation dummy composition. galois connection operations pointed multisets closure conditions. closure uncountable pages adde | non_dup | [] |
24940208 | 10.1007/s00012-013-0250-3 | If V and W are varieties of algebras such that any V-algebra A has a reduct
U(A) in W, there is a forgetful functor U: V->W that acts by A |-> U(A) on
objects, and identically on homomorphisms. This functor U always has a left
adjoint F: W->V by general considerations. One calls F(B) the V-algebra freely
generated by the W-algebra B. Two problems arise naturally in this broad
setting. The description problem is to describe the structure of the V-algebra
F(B) as explicitly as possible in terms of the structure of the W-algebra B.
The recognition problem is to find conditions on the structure of a given
V-algebra A that are necessary and sufficient for the existence of a W-algebra
B such that F(B) is isomorphic to A. Building on and extending previous work on
MV-algebras freely generated by finite distributive lattices, in this paper we
provide solutions to the description and recognition problems in case V is the
variety of MV-algebras, W is the variety of Kleene algebras, and B is finitely
generated--equivalently, finite. The proofs rely heavily on the Davey-Werner
natural duality for Kleene algebras, on the representation of finitely
presented MV-algebras by compact rational polyhedra, and on the theory of bases
of MV-algebras.Comment: 27 pages, 8 figures. Submitted to Algebra Universali | MV-algebras freely generated by finite Kleene algebras | mv-algebras freely generated by finite kleene algebras | varieties algebras reduct forgetful functor acts identically homomorphisms. functor adjoint considerations. calls freely arise naturally broad setting. explicitly recognition isomorphic extending algebras freely distributive lattices recognition algebras kleene algebras finitely equivalently finite. proofs rely heavily davey werner duality kleene algebras finitely algebras rational polyhedra bases pages figures. submitted universali | non_dup | [] |
24767928 | 10.1007/s00012-013-0261-0 | We prove that for each universal algebra $(A,\mathcal A)$ of cardinality
$|A|\ge 2$ and an infinite set $X$ of cardinality $|X|\ge|\mathcal A|$, the
$X$-th power $(A^X,\mathcal A^X)$ of the algebra $(A,\mathcal A)$ contains a
free subset $\mathcal F\subset A^X$ of cardinality $|\mathcal F|=2^{|X|}$. This
generalizes the classical Fichtenholtz-Kantorovitch-Hausdorff result on the
existence of an independent family $\mathcal I\subset\mathcal P(X)$ of
cardinality $|\mathcal I|=|\mathcal P(X)|$ in the Boolean algebra $\mathcal
P(X)$ of subsets of an infinite set $X$.Comment: 4 page | Large free sets in universal algebras | large free sets in universal algebras | universal mathcal cardinality infinite cardinality mathcal mathcal mathcal mathcal cardinality mathcal generalizes fichtenholtz kantorovitch hausdorff mathcal mathcal cardinality mathcal mathcal boolean mathcal subsets infinite .comment | non_dup | [] |
30319273 | 10.1007/s00012-014-0293-0 | Automatic presentations, also called FA-presentations, were introduced to extend finite model theory to infinite structures whilst retaining the solubility of fundamental decision problems. This paper studies FA-presentable algebras. First, an example is given to show that the class of finitely generated FA-presentable algebras is not closed under forming finitely generated subalgebras, even within the class of algebras with only unary operations. In contrast, a finitely generated subalgebra of an FA-presentable algebra with a single unary operation is itself FA-presentable. Furthermore, it is proven that the class of unary FA-presentable algebras is closed under forming finitely generated subalgebras and that the membership problem for such subalgebras is decidable.PostprintPeer reviewe | Subalgebras of FA-presentable algebras | subalgebras of fa-presentable algebras | automatic presentations presentations extend infinite whilst retaining solubility problems. presentable algebras. finitely presentable algebras forming finitely subalgebras algebras unary operations. finitely subalgebra presentable unary presentable. proven unary presentable algebras forming finitely subalgebras membership subalgebras decidable.postprintpeer reviewe | non_dup | [] |
24930516 | 10.1007/s00012-014-0310-3 | A relational structure is homomorphism-homogeneous if every homomorphism
between finite substructures extends to an endomorphism of the structure. This
notion was introduced recently by Cameron and Ne\v{s}et\v{r}il. In this paper
we consider a strengthening of homomorphism-homogeneity --- we call a
relational structure polymorphism-homogeneous if every partial polymorphism
with a finite domain extends to a global polymorphism of the structure. It
turns out that this notion (under various names and in completely different
contexts) has been existing in algebraic literature for at least 30 years.
Motivated by this observation, we dedicate this paper to the topic of
polymorphism-homogeneous structures. We study polymorphism-homogeneity from a
model-theoretic, an algebraic, and a combinatorial point of view. E.g., we
study structures that have quantifier elimination for positive primitive
formulae, and show that this notion is equivalent to polymorphism-homogeneity
for weakly oligomorphic structures. We demonstrate how the Baker-Pixley theorem
can be used to show that polymorphism-homogeneity is a decidable property for
finite relational structures. Eventually, we completely characterize the
countable polymorphism-homogeneous graphs, the polymorphism-homogeneous posets
of arbitrary size, and the countable polymorphism-homogeneous strict posets.Comment: 31 page | On polymorphism-homogeneous relational structures and their clones | on polymorphism-homogeneous relational structures and their clones | relational homomorphism homogeneous homomorphism substructures extends endomorphism structure. notion cameron strengthening homomorphism homogeneity call relational polymorphism homogeneous polymorphism extends polymorphism structure. turns notion names contexts algebraic years. motivated dedicate topic polymorphism homogeneous structures. polymorphism homogeneity theoretic algebraic combinatorial view. e.g. quantifier elimination primitive formulae notion polymorphism homogeneity weakly oligomorphic structures. baker pixley polymorphism homogeneity decidable relational structures. eventually characterize countable polymorphism homogeneous polymorphism homogeneous posets countable polymorphism homogeneous strict | non_dup | [] |
25051276 | 10.1007/s00012-015-0319-2 | The classical Cauchy completion of a metric space (by means of Cauchy
sequences) as well as the completion of a uniform space (by means of Cauchy
filters) are well-known to rely on the symmetry of the metric space or uniform
space in question. For qausi-metric spaces and quasi-uniform spaces various
non-equivalent completions exist, often defined on a certain subcategory of
spaces that satisfy a key property required for the particular completion to
exist. The classical filter completion of a uniform space can be adapted to
yield a filter completion of a metric space. We show that this completion by
filters generalizes to continuity spaces that satisfy a form of symmetry which
we call uniformly vanishing asymmetry | Completion of continuity spaces with uniformly vanishing asymmetry | completion of continuity spaces with uniformly vanishing asymmetry | cauchy completion cauchy completion cauchy filters rely question. qausi quasi completions subcategory satisfy completion exist. filter completion adapted filter completion space. completion filters generalizes continuity satisfy call uniformly vanishing asymmetry | non_dup | [] |
79609050 | 10.1007/s00012-015-0327-2 | ame congruence theory identifies six Maltsev conditions associated with locally finite varieties omitting certain types of local behaviour. Extending a result of Siggers, we show that of these six Maltsev conditions only two of them are equivalent to strong Maltsev conditions for locally finite varieties. Besides omitting the unary type, the only other of these conditions that is strong is that of omitting the unary and affine types.\ud
\ud
We also provide novel presentations of some of the above Maltsev conditions | Characterizations of several Maltsev conditions. | characterizations of several maltsev conditions. | congruence identifies maltsev locally varieties omitting behaviour. extending siggers maltsev maltsev locally varieties. besides omitting unary omitting unary affine types. presentations maltsev | non_dup | [] |
44289537 | 10.1007/s00012-015-0344-1 | In any 0-normal variety (0-regular variety in which {0} is a subalgebra), every congruence class containing 0 is a subalgebra. These “normal subalgebras” of a fixed algebra constitute a lattice, isomorphic to its congruence lattice. We are interested in those 0-normal varieties for which the join of two normal subalgebras in the lattice of normal subalgebras of an algebra equals their join in the lattice of subalgebras, as happens with groups and rings. We characterise this property in terms of a Mal’cev condition, and use examples to show it is strictly stronger than being ideal determined but strictly weaker than being 0-coherent (classically ideal determined) and does not imply congruence permutability | Joins of subalgebras and normals in 0-regular varieties | joins of subalgebras and normals in 0-regular varieties | subalgebra congruence subalgebra. “normal subalgebras” constitute isomorphic congruence lattice. interested varieties join subalgebras subalgebras equals join subalgebras happens rings. characterise mal’cev strictly stronger ideal strictly weaker coherent classically ideal imply congruence permutability | non_dup | [] |
24964131 | 10.1007/s00012-015-0348-x | Modular lattices, introduced by R. Dedekind, are an important subvariety of
lattices that includes all distributive lattices. Heitzig and Reinhold
developed an algorithm to enumerate, up to isomorphism, all finite lattices up
to size 18. Here we adapt and improve this algorithm to construct and count
modular lattices up to size 24, semimodular lattices up to size 22, and
lattices of size 19. We also show that $2^{n-3}$ is a lower bound for the
number of nonisomorphic modular lattices of size $n$.Comment: Preprint, 12 pages, 2 figures, 1 tabl | Generating all finite modular lattices of a given size | generating all finite modular lattices of a given size | modular lattices dedekind subvariety lattices distributive lattices. heitzig reinhold enumerate isomorphism lattices adapt count modular lattices semimodular lattices lattices nonisomorphic modular lattices .comment preprint pages tabl | non_dup | [] |
44289538 | 10.1007/s00012-015-0349-9 | If X is a set, the fix-set quasiorder on a group of permutations of X is the quasiorder induced by containment of the fix-sets of elements of SX. Axioms for such quasiorders on groups have previously been given. We generalise these to allow non-faithful group actions, the resulting abstract quasiorders being called fix-orders. We characterise the possible fix-orders on a given group G in terms of certain families of subgroups of G. The special case in which the members of the defining family of subgroups are all normal is considered. Software is used to construct and analyse the lattices of fix-orders of many small finite groups | Groups with fix-set quasi-order | groups with fix-set quasi-order | quasiorder permutations quasiorder containment axioms quasiorders given. generalise faithful quasiorders orders. characterise orders families subgroups defining subgroups considered. analyse lattices orders | non_dup | [] |
42638040 | 10.1007/s00012-016-0407-y | We present a Galois theory connecting finitary operations with pairs of
finitary relations one of which is contained in the other. The Galois closed
sets on both sides are characterised as locally closed subuniverses of the full
iterative function algebra (semiclones) and relation pair clones, respectively.
Moreover, we describe the modified closure operators if only functions and
relation pairs of a certain bounded arity, respectively, are considered.Comment: 38 pages; supported by the Austrian Science Fund (FWF) under grant
I836-N2 | Galois theory for semiclones | galois theory for semiclones | galois connecting finitary operations finitary other. galois sides characterised locally subuniverses iterative semiclones clones respectively. closure arity pages austrian fund | non_dup | [] |
29566295 | 10.1007/s00012-017-0427-2 | A topological monoid is isomorphic to an endomorphism monoid of a countable
structure if and only if it is separable and has a compatible complete
ultrametric such that composition from the left is non-expansive. We also give
a topological characterisation of those topological monoids that are isomorphic
to endomorphism monoids of countable omega-categorical structures. Finally we
present analogous characterisations for polymorphism clones of countable
structures and for polymorphism clones of countable omega-categorical
structures.Comment: 16 pages; minor corrections have been made in version | A topological characterisation of endomorphism monoids of countable
structures | a topological characterisation of endomorphism monoids of countable structures | topological monoid isomorphic endomorphism monoid countable separable compatible ultrametric expansive. topological characterisation topological monoids isomorphic endomorphism monoids countable omega categorical structures. analogous characterisations polymorphism clones countable polymorphism clones countable omega categorical pages minor | non_dup | [] |
83861083 | 10.1007/s00012-017-0439-y | Madden has shown that in contrast to the situation with frames, the smallest
dense quotient of a $\kappa$-frame need not be Boolean. We characterise these
so-called d-reduced $\kappa$-frames as those which may be embedded as a
generating sub-$\kappa$-frame of a Boolean frame. We introduce the notion of
the closure of a $\kappa$-frame congruence and call a congruence clear if it is
the largest congruence with a given closure. These ideas are used to prove
$\kappa$-frame analogues of known results concerning Boolean frame quotients.
In particular, we show that d-reduced $\kappa$-frames are precisely the
quotients of $\kappa$-frames by clear congruences and that every $\kappa$-frame
congruence is the meet of clear congruences.Comment: 6 pages, 0 figures. To be published in Algebra Universali | A special class of congruences on $\kappa$-frames | a special class of congruences on $\kappa$-frames | madden frames smallest dense quotient kappa boolean. characterise kappa frames embedded generating kappa boolean frame. notion closure kappa congruence call congruence congruence closure. ideas kappa analogues concerning boolean quotients. kappa frames precisely quotients kappa frames congruences kappa congruence meet pages figures. universali | non_dup | [] |
29556064 | 10.1007/s00012-017-0452-1 | We define antidomain operations for algebras of multiplace partial functions.
For all signatures containing composition, the antidomain operations and any
subset of intersection, preferential union and fixset, we give finite
equational or quasiequational axiomatisations for the representation class. We
do the same for the question of representability by injective multiplace
partial functions. For all our representation theorems, it is an immediate
corollary of our proof that the finite representation property holds for the
representation class. We show that for a large set of signatures, the
representation classes have equational theories that are coNP-complete.Comment: 33 pages. Added brief discussion of square algebra | Algebras of multiplace functions for signatures containing antidomain | algebras of multiplace functions for signatures containing antidomain | antidomain operations algebras multiplace functions. signatures antidomain operations intersection preferential union fixset equational quasiequational axiomatisations class. representability injective multiplace functions. theorems immediate corollary class. signatures equational conp pages. brief | non_dup | [] |
42644178 | 10.1007/s00012-017-0460-1 | Garret Birkhoff's HSP theorem characterizes the classes of models of
algebraic theories as those being closed with respect to homomorphic images,
subalgebras, and products. In particular, it implies that an algebra
$\mathbf{B}$ satisfies all equations that hold in an algebra $\mathbf{A}$ of
the same type if and only if $\mathbf{B}$ is a homomorphic image of a
subalgebra of a (possibly infinite) direct power of $\mathbf{A}$. The former
statement is equivalent to the existence of a natural map sending term
functions of the algebra $\mathbf{A}$ to those of $\mathbf{B}$, and it is
natural to wonder about continuity properties of this mapping. We show that
this map is uniformly continuous if and only if every finitely generated
subalgebra of $\mathbf{B}$ is a homomorphic image of a subalgebra of a finite
power of $\mathbf{A}$ -- without any additional assumptions concerning the
algebras $\mathbf{A}$ and $\mathbf{B}$. Moreover, provided that $\mathbf{A}$ is
almost locally finite (for instance if $\mathbf{A}$ is locally oligomorphic or
locally finite), the considered map is uniformly continuous if and only if it
is Cauchy-continuous. In particular, our results extend a recent theorem by
Bodirsky and Pinsker beyond the countable $\omega$-categorical setting.Comment: 15 page | A uniform Birkhoff theorem | a uniform birkhoff theorem | garret birkhoff characterizes algebraic homomorphic subalgebras products. mathbf satisfies hold mathbf mathbf homomorphic subalgebra possibly infinite mathbf former statement sending mathbf mathbf wonder continuity mapping. uniformly finitely subalgebra mathbf homomorphic subalgebra mathbf assumptions concerning algebras mathbf mathbf mathbf locally mathbf locally oligomorphic locally uniformly cauchy continuous. extend bodirsky pinsker countable omega categorical | non_dup | [] |
78510749 | 10.1007/s00012-018-0491-2 | Suppose throughout that $\mathcal V$ is a congruence distributive variety. If
$m \geq 1$, let $ J _{ \mathcal V} (m) $ be the smallest natural number $k$
such that the congruence identity $\alpha ( \beta \circ \gamma \circ \beta
\dots ) \subseteq \alpha \beta \circ \alpha \gamma \circ \alpha \beta \circ
\dots $ holds in $\mathcal V$, with $m$ occurrences of $ \circ$ on the left and
$k$ occurrences of $\circ$ on the right. We show that if $ J _{ \mathcal V} (m)
=k$, then $ J _{ \mathcal V} (m \ell ) \leq k \ell $, for every natural number
$\ell$. The key to the proof is an identity which, through a variety, is
equivalent to the above congruence identity, but involves also reflexive and
admissible relations. If $ J _{ \mathcal V} (1)=2 $, that is, $\mathcal V$ is
$3$-distributive, then $ J _{ \mathcal V} (m) \leq m $, for every $m \geq 3$
(actually, a more general result is presented which holds even in
nondistributive varieties). If $\mathcal V$ is $m$-modular, that is, congruence
modularity of $\mathcal V$ is witnessed by $m+1$ Day terms, then $ J _{
\mathcal V} (2) \leq J _{ \mathcal V} (1) + 2m^2-2m -1 $. Various problems are
stated at various places.Comment: v. 4, added somethin | On the J\'onsson distributivity spectrum | on the j\'onsson distributivity spectrum | mathcal congruence distributive variety. mathcal smallest congruence alpha beta circ gamma circ beta dots subseteq alpha beta circ alpha gamma circ alpha beta circ dots mathcal occurrences circ occurrences circ right. mathcal mathcal congruence involves reflexive admissible relations. mathcal mathcal distributive mathcal nondistributive varieties mathcal modular congruence modularity mathcal witnessed mathcal mathcal stated somethin | non_dup | [] |
25037310 | 10.1007/s00012-018-0497-9 | $\mathit{C}$-clones are polymorphism sets of so-called clausal relations, a
special type of relations on a finite domain, which first appeared in
connection with constraint satisfaction problems in [Creignou et al. 2008]. We
completely describe the relationship w.r.t. set inclusion between maximal
$\mathit{C}$-clones and maximal clones. As a main result we obtain that for
every maximal $\mathit{C}$-clone there exists exactly one maximal clone in
which it is contained. A precise description of this unique maximal clone, as
well as a corresponding completeness criterion for $\mathit{C}$-clones is
given.Comment: 20 page | Unique inclusions of maximal C-clones in maximal clones | unique inclusions of maximal c-clones in maximal clones | mathit clones polymorphism clausal appeared connection satisfaction creignou w.r.t. inclusion maximal mathit clones maximal clones. maximal mathit clone maximal clone contained. precise maximal clone completeness criterion mathit clones | non_dup | [] |
73955393 | 10.1007/s00012-018-0499-7 | It is a classical result from universal algebra that the notions of
polymorphisms and invariants provide a Galois connection between suitably
closed classes (clones) of finitary operations $f\colon B^n\to B$, and classes
(coclones) of relations $r\subseteq B^k$. We will present a generalization of
this duality to classes of (multi-valued, partial) functions $f\colon B^n\to
B^m$, employing invariants valued in partially ordered monoids instead of
relations. In particular, our set-up encompasses the case of permutations
$f\colon B^n\to B^n$, motivated by problems in reversible computing.Comment: 36 pages; to appear in Algebra Universali | Galois connection for multiple-output operations | galois connection for multiple-output operations | universal notions polymorphisms invariants galois connection suitably clones finitary operations colon coclones subseteq generalization duality valued colon employing invariants valued partially ordered monoids relations. encompasses permutations colon motivated reversible pages universali | non_dup | [] |
93952826 | 10.1007/s00012-018-0562-4 | J{\'o}nsson and Tarski's notion of the perfect extension of a Boolean algebra
with operators has evolved into an extensive theory of canonical extensions of
lattice-based algebras. After reviewing this evolution we make two
contributions. First it is shown that the failure of a variety of algebras to
be closed under canonical extensions is witnessed by a particular one of its
free algebras. The size of the set of generators of this algebra can be made a
function of a collection of varieties and is a kind of Hanf number for
canonical closure. Secondly we study the complete lattice of stable subsets of
a polarity structure, and show that if a class of polarities is closed under
ultraproducts, then its stable set lattices generate a variety that is closed
under canonical extensions. This generalises an earlier result of the author
about generation of canonically closed varieties of Boolean algebras with
operators, which was in turn an abstraction of the result that a first-order
definable class of Kripke frames determines a modal logic that is valid in its
so-called canonical frames | Canonical extensions and ultraproducts of polarities | canonical extensions and ultraproducts of polarities | nsson tarski notion perfect boolean evolved extensive canonical extensions algebras. reviewing contributions. algebras canonical extensions witnessed algebras. generators varieties kind hanf canonical closure. secondly subsets polarity polarities ultraproducts lattices canonical extensions. generalises canonically varieties boolean algebras abstraction definable kripke frames determines modal logic valid canonical frames | non_dup | [] |
2573386 | 10.1007/s00013-003-4840-8 | R. B. Kusner [R. Guy, Amer. Math. Monthly 90 (1983), 196--199] asked whether
a set of vectors in a d-dimensional real vector space such that the l-p
distance between any pair is 1, has cardinality at most d+1. We show that this
is true for p=4 and any d >= 1, and false for all 1<p<2 with d sufficiently
large, depending on p.
More generally we show that the maximum cardinality is at most $(2\lceil
p/4\rceil-1)d+1$ if p is an even integer, and at least $(1+\epsilon_p)d$ if
1<p<2, where $\epsilon_p>0$ depends on p.Comment: 6 pages. Small correction to Proposition | A problem of Kusner on equilateral sets | a problem of kusner on equilateral sets | kusner amer. math. monthly asked cardinality false sufficiently cardinality lceil rceil integer epsilon epsilon pages. | non_dup | [] |
18406124 | 10.1007/s00013-004-1102-3 | A basic result in semigroup theory states that every C-0-semigroup is quasi-contractive with respect to some appropriately chosen equivalent norm. This paper contains a counterpart of this well-known fact. Namely, by examining the convergence of the Trotter-type formula (e(t/n) (A) p)(n) (where P denotes a bounded projection), we prove that whenever the generator A is unbounded it is possible to introduce an equivalent norm on the space with respect to which the semigroup is not quasi-contractive | On quasi-contractivity of C 0-semigroups on Banach spaces | on quasi-contractivity of c 0-semigroups on banach spaces | semigroup semigroup quasi contractive appropriately norm. counterpart fact. examining trotter projection whenever generator unbounded norm semigroup quasi contractive | non_dup | [] |
2578884 | 10.1007/s00013-005-1243-z | In 1934, Garrett Birkhoff has shown that the number of isomorphism classes of
finite metabelian groups of order $p^{22}$ tends to infinity with $p$. More
precisely, for each prime number $p$ there is a family
$(M_\lambda)_{\lambda=0,...,p-1}$ of indecomposable and pairwise nonisomorphic
metabelian $p$-groups of the given order. In this manuscript we use recent
results on the classification of possible embeddings of a subgroup in a finite
abelian $p$-group to construct families of indecomposable metabelian groups,
indexed by several parameters, which have upper bounds on the exponents of the
center and the commutator subgroup.Comment: 5 pages; to appear in Archiv der Mathemati | A Construction of Metabelian Groups | a construction of metabelian groups | garrett birkhoff isomorphism metabelian tends infinity precisely prime lambda lambda indecomposable pairwise nonisomorphic metabelian order. embeddings subgroup abelian families indecomposable metabelian indexed bounds exponents commutator pages archiv mathemati | non_dup | [] |
2579506 | 10.1007/s00013-005-1299-9 | In this paper we show that if $\Lambda=\amalg_{i\geq 0}\Lambda_i$ is a Koszul
algebra with $\Lambda_0$ isomorphic to a product of copies of a field, then the
minimal projective resolution of $\Lambda_0$ as a right $\Lambda$-module
provides all the information necessary to construct both a minimal projective
resolution of $\Lambda_0$ as a left $\Lambda$-module and a minimal projective
resolution of $\Lambda$ as a right module over the enveloping algebra of
$\Lambda$. The main tool for this is showing that there is a comultiplicative
structure on a minimal projective resolution of $\Lambda_0$ as a right
$\Lambda$-module | Resolutions over Koszul algebras | resolutions over koszul algebras | lambda amalg lambda koszul lambda isomorphic copies projective lambda lambda module projective lambda lambda module projective lambda module enveloping lambda comultiplicative projective lambda lambda module | non_dup | [] |
2586229 | 10.1007/s00013-006-1704-z | Let m>=1 be an arbitrary fixed integer and let N_m(x) count the number of odd
integers u<=x such that the order of 2 modulo u is not divisible by m. In case
m is prime estimates for N_m(x) were given by H. Mueller that were subsequently
sharpened into an asymptotic estimate by the present author. Mueller on his
turn extended the author's result to the case where m is a prime power and gave
bounds in the case m is not a prime power. Here an asymptotic for N_m(x) is
derived that is valid for all integers m. This asymptotic would easily have
followed from Mueller's approach were it not for the fact that a certain
Diophantine equation has non-trivial solutions. All solutions of this equation
are determined. We also generalize to other base numbers than 2. For a very
sparse set of these numbers Mueller's approach does work.Comment: 11 pages, 2 Tables; Proposition 3 has now been corrected along with a
few typo | Improvement of an estimate of H. Mueller involving the order of 2(mod u)
II | improvement of an estimate of h. mueller involving the order of 2(mod u) ii | integer count integers modulo divisible prime mueller subsequently sharpened asymptotic author. mueller prime gave bounds prime power. asymptotic valid integers asymptotic mueller diophantine trivial solutions. determined. generalize sparse mueller pages tables corrected typo | non_dup | [] |
71046594 | 10.1007/s00013-009-2976-x | The aim of this paper is to prove certain characterization theorems for groups in which permutability is a transitive relation, the so called PT -groups. In particular, it is shown that the finite solvable PT -groups, the finite solvable groups in which every subnormal subgroup of defect two is permutable, the finite solvable groups in which every normal subgroup is permutable sensitive, and the finite solvable groups in which conjugate-permutability and permutability coincide are all one and the same class. This follows from our main result which says that the finite modular p-groups, p a prime, are those p-groups in which every subnormal subgroup of defect two is permutable or, equivalently, in which every normal subgroup is permutable sensitive. However, there exist finite insolvable groups which are not PT -groups but all subnormal subgroups of defect two are permutable | Permutable subnormal subgroups of finite groups | permutable subnormal subgroups of finite groups | theorems permutability transitive groups. solvable solvable subnormal subgroup defect permutable solvable subgroup permutable solvable conjugate permutability permutability coincide class. says modular prime subnormal subgroup defect permutable equivalently subgroup permutable sensitive. insolvable subnormal subgroups defect permutable | non_dup | [] |
2075908 | 10.1007/s00013-010-0166-5 | We study the problem of the existence of arithmetic progressions of three
cubes over quadratic number fields Q(sqrt(D)), where D is a squarefree integer.
For this purpose, we give a characterization in terms of Q(sqrt(D))-rational
points on the elliptic curve E:y^2=x^3-27. We compute the torsion subgroup of
the Mordell-Weil group of this elliptic curve over Q(sqrt(D)) and we give
partial answers to the finiteness of the free part of E(Q(sqrt(D))). This last
task will be translated to compute if the rank of the quadratic D-twist of the
modular curve X_0(36) is zero or not | Three cubes in arithmetic progression over quadratic fields | three cubes in arithmetic progression over quadratic fields | arithmetic progressions cubes quadratic sqrt squarefree integer. sqrt rational elliptic torsion subgroup mordell weil elliptic sqrt answers finiteness sqrt translated quadratic twist modular | non_dup | [] |
2114795 | 10.1007/s00013-010-0173-6 | When K is an arbitrary field, we study the affine automorphisms of M_n(K)
that stabilize GL_n(K). Using a theorem of Dieudonn\'e on maximal affine
subspaces of singular matrices, this is easily reduced to the known case of
linear preservers when n>2 or #K>2. We include a short new proof of the more
general Flanders' theorem for affine subspaces of M_{p,q}(K) with bounded rank.
We also find that the group of affine transformations of M_2(F_2) that
stabilize GL_2(F_2) does not consist solely of linear maps. Using the theory of
quadratic forms over F_2, we construct explicit isomorphisms between it, the
symplectic group Sp_4(F_2) and the symmetric group S_6.Comment: 13 pages, very minor corrections from the first versio | The affine preservers of non-singular matrices | the affine preservers of non-singular matrices | affine automorphisms stabilize dieudonn maximal affine subspaces singular preservers flanders affine subspaces rank. affine transformations stabilize consist solely maps. quadratic isomorphisms symplectic pages minor versio | non_dup | [] |
2108208 | 10.1007/s00013-011-0247-0 | In this paper we give an effective criterion as to when a prime number p is
the order of an automorphism of a smooth cubic hypersurface of P^{n+1}, for a
fixed n > 1. We also provide a computational method to classify all such
hypersurfaces that admit an automorphism of prime order p. In particular, we
show that p<2^{n+1} and that any such hypersurface admitting an automorphism of
order p>2^n is isomorphic to the Klein n-fold. We apply our method to compute
exhaustive lists of automorphism of prime order of smooth cubic threefolds and
fourfolds. Finally, we provide an application to the moduli space of
principally polarized abelian varieties.Comment: 10 page | Automorphisms of prime order of smooth cubic n-folds | automorphisms of prime order of smooth cubic n-folds | criterion prime automorphism cubic hypersurface classify hypersurfaces admit automorphism prime hypersurface admitting automorphism isomorphic klein fold. exhaustive lists automorphism prime cubic threefolds fourfolds. moduli principally polarized abelian | non_dup | [] |
25037870 | 10.1007/s00013-011-0339-x | Countable projective limits of countable inductive limits, called PLB-spaces,
of weighted Banach spaces of continuous functions have recently been
investigated by Agethen, Bierstedt and Bonet. In a previous article, the author
extended their investigation to the case of holomorphic functions and
characterized when spaces over the unit disc w.r.t. weights whose decay,
roughly speaking, is neither faster nor slower than that of a polynomial are
ultrabornological or barrelled. In this note, we prove a similar
characterization for the case of weights which tend to zero logarithmically.Comment: Version of November 23, 2011. 9 page | PLB-spaces of holomorphic functions with logarithmic growth conditions | plb-spaces of holomorphic functions with logarithmic growth conditions | countable projective countable inductive weighted banach agethen bierstedt bonet. holomorphic disc w.r.t. weights roughly speaking neither faster slower ultrabornological barrelled. weights tend november | non_dup | [] |
2152503 | 10.1007/s00013-012-0460-5 | Let $\tau$ be a locally convex topology on the countable dimensional
polynomial $\reals$-algebra $\rx:=\reals[X_1,...,X_n]$. Let $K$ be a closed
subset of $\reals^n$, and let $M:=M_{\{g_1, ... g_s\}}$ be a finitely generated
quadratic module in $\rx$. We investigate the following question: When is the
cone $\Pos(K)$ (of polynomials nonnegative on $K$) included in the closure of
$M$? We give an interpretation of this inclusion with respect to representing
continuous linear functionals by measures. We discuss several examples; we
compute the closure of $M=\sos$ with respect to weighted norm-$p$ topologies.
We show that this closure coincides with the cone $\Pos(K)$ where $K$ is a
certain convex compact polyhedron.Comment: 14 page | The Moment Problem for Continuous Positive Semidefinite Linear
functionals | the moment problem for continuous positive semidefinite linear functionals | locally convex topology countable reals reals reals finitely quadratic module cone polynomials nonnegative closure inclusion representing functionals measures. closure weighted norm topologies. closure coincides cone convex | non_dup | [] |
24765104 | 10.1007/s00013-012-0473-0 | Robinson showed that the character degrees are determined by knowing, for all
$n$, the number of ways that the identity can be expressed as a product of $n$
commutators. Earlier, Strunkov showed that the existence of characters of
$p$-defect 0 can be determined by counting solutions to certain equations
involving commutators and conjugates. In this paper, we prove analogs to
Robinson's and Strunkov's theorems by switching conjugacy classes and
characters. We show that counting the multiplicity of the trivial character in
certain products of characters determines the conjugacy class sizes and
existence of conjugacy classes with $p$-defect 0.Comment: 7 page | Determination of Conjugacy Class Sizes from Products of Characters | determination of conjugacy class sizes from products of characters | robinson character knowing ways commutators. strunkov characters defect counting involving commutators conjugates. analogs robinson strunkov theorems switching conjugacy characters. counting multiplicity trivial character characters determines conjugacy sizes conjugacy defect | non_dup | [] |
5252343 | 10.1007/s00013-013-0514-3 | Let S be a smooth cubic surface defined over a field K. As observed by Segre
and Manin, there is a secant and tangent process on S that generates new
K-rational points from old. It is natural to ask for the size of a minimal
generating set for S(K). In a recent paper, for fields K with at least 13
elements, Siksek showed that if S contains a skew pair of K-lines then S(K) can
be generated from one point. In this paper we prove the corresponding version
of this result for fields K having at least 4 elements, and slightly milder
results for #K=2 or 3.Comment: 10 pages. arXiv admin note: text overlap with arXiv:1012.1838 by
other author | Generators for Cubic Surfaces with two Skew Lines over Finite Fields | generators for cubic surfaces with two skew lines over finite fields | cubic segre manin secant tangent generates rational old. generating siksek skew point. milder pages. admin overlap | non_dup | [] |
5239710 | 10.1007/s00013-013-0520-5 | In [1], J. Ax proved a transcendency theorem for certain differential fields
of characteristic zero: the differential counterpart of the still open
Schanuel's conjecture about the exponential function over the field of complex
numbers [11, page 30]. In this article, we derive from Ax's theorem
transcendency results in the context of differential valued exponential fields.
In particular, we obtain results for exponential Hardy fields,
Logarithmic-Exponential power series fields and Exponential-Logarithmic power
series fields.Comment: 6 pages, to appear in Archiv der Mathemati | A Note on Schanuel's Conjectures for Exponential Logarithmic Power
Series Fields | a note on schanuel's conjectures for exponential logarithmic power series fields | proved transcendency counterpart schanuel conjecture exponential derive transcendency valued exponential fields. exponential hardy logarithmic exponential exponential logarithmic pages archiv mathemati | non_dup | [] |
5255879 | 10.1007/s00013-013-0523-2 | We show that the Generalized Vanishing Conjecture $$\forall_{m \ge 1} [\Lam^m
f^m = 0] \Longrightarrow \forall_{m \gg 0} [\Lam^m (g f^m) = 0]$$ for a fixed
differential operator $\Lam \in k[\partial]$ follows from a special case of it,
namely that the additional factor $g$ is a power of the radical polynomial $f$.
Next we show that in order to prove the Generalized Vanishing Conjecture (up to
some bound on the degree of $\Lam$), we may assume that $\Lam$ is a linear
combination of powers of distinct partial derivatives. At last, we show that
the Generalized Vanishing Conjecture holds for products of linear forms in
$\partial$, in particular homogeneous differential operators $\Lambda \in
k[\partial_1,\partial_2]$.Comment: 7 page | A few remarks on the Generalized Vanishing Conjecture | a few remarks on the generalized vanishing conjecture | vanishing conjecture forall longrightarrow forall radical vanishing conjecture powers derivatives. vanishing conjecture homogeneous lambda .comment | non_dup | [] |
25040130 | 10.1007/s00013-013-0544-x | The Green-Tao Theorem, one of the most celebrated theorems in modern number
theory, states that there exist arbitrarily long arithmetic progressions of
prime numbers. In a related but different direction, a recent theorem of Shiu
proves that there exist arbitrarily long strings of consecutive primes that lie
in any arithmetic progression that contains infinitely many primes. Using the
techniques of Shiu and Maier, this paper generalizes Shiu's Theorem to certain
subsets of the primes such as primes of the form $\lfloor \pi n\rfloor$ and
some of arithmetic density zero such as primes of the form $\lfloor n\log\log
n\rfloor$.Comment: 14 pages; preprint of article published in Archiv der Mathemati | Strings of special primes in arithmetic progressions | strings of special primes in arithmetic progressions | celebrated theorems modern arbitrarily arithmetic progressions prime numbers. shiu proves arbitrarily strings consecutive primes arithmetic progression infinitely primes. shiu maier generalizes shiu subsets primes primes lfloor rfloor arithmetic primes lfloor rfloor .comment pages preprint archiv mathemati | non_dup | [] |
24770433 | 10.1007/s00013-013-0566-4 | Let f be a cusp form of weight k+1/2 and at most quadratic nebentype
character whose Fourier coefficients a(n) are all real. We study an
equidistribution conjecture of Bruinier and Kohnen for the signs of a(n). We
prove this conjecture for certain subfamilies of coefficients that are
accessible via the Shimura lift by using the Sato-Tate equidistribution theorem
for integral weight modular forms. Firstly, an unconditional proof is given for
the family {a(tp^2)}_p where t is a squarefree number and p runs through the
primes. In this case, the result is in terms of natural density. To prove it
for the family {a(tn^2)}_n where t is a squarefree number and n runs through
all natural numbers, we assume the existence of a suitable error term for the
convergence of the Sato-Tate distribution, which is weaker than one conjectured
by Akiyama and Tanigawa. In this case, the results are in terms of
Dedekind-Dirichlet density.Comment: 8 pages; typos corrected, final version, accepted for publication in
Archiv der Mathemati | Equidistribution of Signs for Modular Eigenforms of Half Integral Weight | equidistribution of signs for modular eigenforms of half integral weight | cusp quadratic nebentype character fourier real. equidistribution conjecture bruinier kohnen signs conjecture subfamilies accessible shimura lift sato tate equidistribution modular forms. firstly unconditional squarefree runs primes. density. squarefree runs sato tate weaker conjectured akiyama tanigawa. dedekind dirichlet pages typos corrected publication archiv mathemati | non_dup | [] |
51442698 | 10.1007/s00013-013-0590-4 | minimal correctionInternational audienceThe Harborth constant of a finite abelian group is the smallest integer $\ell$ such that each subset of $G$ of cardinality $\ell$ has a subset of cardinality equal to the exponent of the group whose elements sum to the neutral element of the group. The plus-minus weighted analogue of this constant is defined in the same way except that instead of considering the sum of all elements of the subset one can choose to add either the element or its inverse. We determine these constants for certain groups, mainly groups that are the direct sum of a cyclic group and a group of order $2$. Moreover, we contrast these results with existing results and conjectures on these problems | Some exact values of the Harborth constant and its plus-minus weighted analogue | some exact values of the harborth constant and its plus-minus weighted analogue | correctioninternational audiencethe harborth abelian smallest integer cardinality cardinality exponent neutral group. minus weighted analogue inverse. cyclic conjectures | non_dup | [] |
24987348 | 10.1007/s00013-013-0598-9 | Let $I$ denote an ideal in a commutative Noetherian ring $R$. Let $M$ be an
$R$-module. The $I$-adic completion is defined by $\hat{M}^I =
\varprojlim{}_{\alpha} M/I^{\alpha}M$. Then $M$ is called $I$-adic complete
whenever the natural homomorphism $M \to \hat{M}^I$ is an isomorphism. Let $M$
be $I$-separated, i.e. $\cap_{\alpha} I^{\alpha}M = 0$. In the main result of
the paper it is shown that $M$ is $I$-adic complete if and only if
$\Ext_R^1(F,M) = 0$ for the flat test module $F = \oplus_{i = 1}^r R_{x_i}$
where $\{x_1,\ldots,x_r\}$ is a system of elements such that $\Rad I = \Rad \xx
R$. This result extends several known statements starting with C. U. Jensen's
result (see \cite[Proposition 3]{J}) that a finitely generated $R$-module $M$
over a local ring $R$ is complete if and only if $\Ext^1_R(F,M) = 0$ for any
flat $R$-module $F$.Comment: to appear in Archiv der Mat | A criterion for I-adic completeness | a criterion for i-adic completeness | ideal commutative noetherian module. adic completion varprojlim alpha alpha adic whenever homomorphism isomorphism. separated i.e. alpha alpha adic module oplus ldots extends statements jensen cite finitely module module .comment archiv | non_dup | [] |
24967294 | 10.1007/s00013-014-0607-7 | Skeletal signatures were introduced in [J W Anderson and A Wootton, A Lower
Bound for the Number of Group Actions on a Compact Riemann Surface, Algebr.
Geom. Topol. 12 (2012) 19--35.] as a tool to describe the space of all
signatures with which a group can act on a surface of genus $\sigma \geq 2$. In
the present paper we provide a complete description of the gaps that appear in
the space of skeletal signatures, together with proofs of the conjectures posed
in our earlier work.Comment: 10 pages, 1 figur | Gaps in the space of skeletal signatures | gaps in the space of skeletal signatures | skeletal signatures anderson wootton riemann algebr. geom. topol. signatures genus sigma gaps skeletal signatures proofs conjectures posed pages figur | non_dup | [] |
25018224 | 10.1007/s00013-014-0667-8 | We provide a new proof of Volberg's Theorem characterizing thin interpolating
sequences as those for which the Gram matrix associated to the normalized
reproducing kernels is a compact perturbation of the identity. In the same
paper, Volberg characterized sequences for which the Gram matrix is a compact
perturbation of a unitary as well as those for which the Gram matrix is a
Schatten-$2$ class perturbation of a unitary operator. We extend this
characterization from $2$ to $p$, where $2 \le p \le \infty$.Comment: v1: 6 pages. v2: 6 pages, referee comments incorporate | Thin sequences and the Gram matrix | thin sequences and the gram matrix | volberg characterizing interpolating gram reproducing kernels perturbation identity. volberg gram perturbation unitary gram schatten perturbation unitary operator. extend infty .comment pages. pages referee comments incorporate | non_dup | [] |
25020158 | 10.1007/s00013-014-0676-7 | Let $R$ be a valuation ring with fraction field $K$ and $2\in R^\times$. We
give an elementary proof of the following known result: Two unimodular
quadratic forms over $R$ are isometric over $K$ if and only if they are
isometric over $R$. Our proof does not use Witt's Cancelation Theorem and
yields an explicit algorithm to construct an isometry over $R$ from a given
isometry over $K$. The statement actually holds for hermitian forms over
valuated involutary division rings, provided mild assumptions.
A python implementation of the algorithm derived from the proof can be found
on the author's home page.Comment: 5 page | An Elementary Proof That Rationally Isometric Quadratic Forms Are
Isometric | an elementary proof that rationally isometric quadratic forms are isometric | valuation elementary unimodular quadratic isometric isometric witt cancelation isometry isometry statement hermitian valuated involutary division rings mild assumptions. python home | non_dup | [] |
29505199 | 10.1007/s00013-014-0719-0 | The support measures of a convex body are a common generalization of the
curvature measures and the area measures. With respect to the Hausdorff metric
on the space of convex bodies, they are weakly continuous. We provide a
quantitative improvement of this result, by establishing a H\"older estimate
for the support measures in terms of the bounded Lipschitz metric, which
metrizes the weak convergence. Specializing the result to area measures yields
a reverse counterpart to earlier stability estimates, concerning Minkowski's
existence theorem for convex bodies with given area measure.Comment: The manuscript is an extended and improved version of the second part
of the manuscript number arxiv:1310.151 | H\"older continuity for support measures of convex bodies | h\"older continuity for support measures of convex bodies | convex generalization curvature measures. hausdorff convex bodies weakly continuous. establishing older lipschitz metrizes convergence. specializing reverse counterpart concerning minkowski convex bodies | non_dup | [] |
29539743 | 10.1007/s00013-015-0794-x | Let $C\subset \mathbb{P}^{g-1}$ be a general curve of genus $g$ and let $k$
be a positive integer such that the Brill-Noether number $\rho(g,k,1)\geq 0$
and $g > k+1$. The aim of this short note is to study the relative canonical
resolution of $C$ on a rational normal scroll swept out by a $g^1_k=|L|$ with
$L\in W^1_k(C)$ general. We show that the bundle of quadrics appearing in the
relative canonical resolution is unbalanced if and only if $\rho>0$ and
$(k-\rho-\frac{7}{2})^2-2k+\frac{23}{4}>0$.Comment: 11 pages, 1 figur | Resolutions of General Canonical Curves on Rational Normal Scrolls | resolutions of general canonical curves on rational normal scrolls | mathbb genus integer brill noether canonical rational scroll swept general. bundle quadrics appearing canonical unbalanced frac frac .comment pages figur | non_dup | [] |
29555564 | 10.1007/s00013-015-0817-7 | Let $\mathcal A\subset\mathbb P^{k-1}$ be a rank $k$ arrangement of $n$
hyperplanes, with the property that any $k$ of the defining linear forms are
linearly independent (i.e., $\mathcal A$ is called $k-$generic). We show that
for any $j=0,\ldots,k-2$, the subspace arrangement with defining ideal
generated by the $(n-j)-$fold products of the defining linear forms of
$\mathcal A$ is a set-theoretic complete intersection, which is equivalent to
saying that star configurations have this property.Comment: 5 pages. In this version we present an update with an example
answering negatively the question asked previously whether or not, for ANY
hyperplane arrangement, all the ideals generated by a-fold products of the
defining linear forms are set-theoretic complete intersection | Star Configurations are Set-Theoretic Complete Intersections | star configurations are set-theoretic complete intersections | mathcal mathbb arrangement hyperplanes defining linearly i.e. mathcal generic ldots subspace arrangement defining ideal defining mathcal theoretic intersection saying configurations pages. update answering negatively asked hyperplane arrangement ideals defining theoretic intersection | non_dup | [] |
29527219 | 10.1007/s00013-015-0842-6 | We show in this short note that if a rational linear combination of
Pontrjagin numbers vanishes on all simply-connected $4k$-dimensional closed
connected and oriented spin manifolds admitting a Riemannian metric whose Ricci
curvature is nonnegative and nonzero at any point, then this linear combination
must be a multiple of the $\hat{A}$-genus, which improves on a result of Gromov
and Lawson. Our proof combines an idea of Atiyah and Hirzebruch and the
celebrated Calabi-Yau theorem.Comment: 5 page | A characterization of the $\hat{A}$-genus as a linear combination of
Pontrjagin numbers | a characterization of the $\hat{a}$-genus as a linear combination of pontrjagin numbers | rational pontrjagin vanishes oriented manifolds admitting riemannian ricci curvature nonnegative nonzero genus improves gromov lawson. combines atiyah hirzebruch celebrated calabi | non_dup | [] |
42682392 | 10.1007/s00013-016-0890-6 | For a subgroup $L$ of the symmetric group $S_\ell$, we determine the minimal
base size of $GL_d(q)\wr L$ acting on $V_d(q)^\ell$ as an imprimitive linear
group. This is achieved by computing the number of orbits of $GL_d(q)$ on
spanning $m$-tuples, which turns out to be the number of $d$-dimensional
subspaces of $V_m(q)$. We then use these results to prove that for certain
families of subgroups $L$, the affine groups whose stabilisers are large
subgroups of $GL_d(q)\wr L$ satisfy a conjecture of Pyber concerning bases.Comment: 8 page | Base sizes of imprimitive linear groups and orbits of general linear
groups on spanning tuples | base sizes of imprimitive linear groups and orbits of general linear groups on spanning tuples | subgroup acting imprimitive group. orbits spanning tuples turns subspaces families subgroups affine stabilisers subgroups satisfy conjecture pyber concerning | non_dup | [] |
42663627 | 10.1007/s00013-016-0911-5 | We introduce the quantum $j$-invariant in positive characteristic as a
multi-valued, modular-invariant function of a local function field. In this
paper, we concentrate on basic definitions and questions of convergence.
Note: This version contains a correction to the published version of Theorem
3. The error that was found is not in any way serious, but its correction does
change slightly the statement of Theorem 3 appearing in the published version.
Otherwise, it has no impact on this article nor any of its sequels.Comment: 10 page | Quantum j-invariant in positive characteristic I: Definition and
Convergence | quantum j-invariant in positive characteristic i: definition and convergence | valued modular field. concentrate definitions convergence. serious statement appearing version. | non_dup | [] |
42669005 | 10.1007/s00013-016-0925-z | We give upper bounds on the essential dimension of (quasi-)simple algebraic
groups over an algebraically closed field that hold in all characteristics. The
results depend on showing that certain representations are generically free. In
particular, aside from the cases of spin and half-spin groups, we prove that
the essential dimension of a simple algebraic group $G$ of rank at least two is
at most $\mathrm{dim}(G) - 2(\mathrm{rank}(G)) - 1$. It is known that the
essential dimension of spin and half-spin groups grows exponentially in the
rank. In most cases, our bounds are as good or better than those known in
characteristic zero and the proofs are shorter. We also compute the generic
stabilizer of an adjoint group on its Lie algebra.Comment: v2 is a substantial revisio | Essential dimension of algebraic groups, including bad characteristic | essential dimension of algebraic groups, including bad characteristic | bounds quasi algebraic algebraically hold characteristics. representations generically free. aside algebraic mathrm mathrm grows exponentially rank. bounds proofs shorter. generic stabilizer adjoint substantial revisio | non_dup | [] |