bluuebunny/crossref_metadata_2025_split huggingface dataset:
A unified treatment of transfinite constructions for free algebras, free monoids, colimits, associated sheaves, and so on
Authors: Kelly G.M. 
Published: April 2009

Many problems lead to the consideration of “algebras”, given by an object A of a category A together with “actions” TkA → A on A of one or more endofunctors of A, subjected to equational axioms. Such problems include those of free monads and free monoids, of cocompleteness in categories of monads and of monoids, of orthogonal subcategories (= generalized sheaf-categories), of categories of continuous functors, and so on; apart from problems involving the algebras for their own sake.Desirable properties of the category of algebras - existence of free ones, cocompleteness, existence of adjoints to algebraic functors - all follow if this category can be proved reflective in some well-behaved category: for which we choose a certain comma-category T/AWe show that the reflexion exists and is given as the colimit of a simple transfinite sequence, if A is cocomplete and the Tk preserve either colimits or unions of suitably-long chains of subobjects.The article draws heavily on the work of earlier authors, unifies and simplifies this, and extends it to new problems. Moreover the reflectivity in T/A is stronger than any earlier result, and will be applied in forthcoming articles, in an enriched version, to the study of categories with structure.
Generalized absolute continuity of a function of Wiener's class
Authors: Siddiqi Rafat Nabi 
Published: April 2009

In the present paper we give a criterion for a function of Wiener's class to belong to the class of generalized absolute continuity, in terms of Fourier-Young coefficients {Ck}. More precisely, we prove the following theorem.THEOREM. Let Λ = (λn,k) be a normal almost periodic matrix of real numbers such that λn,k ≥ λn,k+1 for all n and k. Then for any function f of Wiener's class Vν (1 < ν < 2) to be of class of generalized absolute continuity Ap (1 < p < ∞) it is necessary and sufficient that {|Ck|2} is summable Λ to zero.
Operator semistable probability measures on a Hilbert space: Corrigenda
Authors: Laha R.G. , Rohatgi V.K. 
Published: April 2009

A faulty typescript of [2] was, regrettably, submitted. The following changes should be made:Page 398, line 7: replace A є G with A є L.Page 398, line 12: replace A є G with A є L.
Factorisation of Lipschitz functions on zero dimensional groups
Authors: Bloom Walter R. 
Published: April 2009

Let G denote a locally compact metrisable zero dimensional group with left translation invariant metric d. The Lipschitz spaces are defined bywhere af: x → f(ax) and α > 0; when r = ∞ the members of Lip(α; r) are taken to be continuous. For a suitable choice of metric it is shown that , where 1 ≤ p ≤ 2, α > q−1, p, q are conjugate indices and . It is also shown that for G infinite the range of values of α cannot be extended.
Oscillation theorems for semilinear hyperbolic and ultrahyperbolic operators
Authors: Narita Mamoru 
Published: April 2009

The oscillation property of the semilinear hyperbolic or ultra-hyperbolic operator L defined byis studied. Sufficient conditions are provided for all solutions of uL[u] ≤ 0 satisfying certain boundary conditions to be oscillatory. The basis of our results is the non-existence of positive solutions of the associated differential inequalities.
On the rate of convergence of interpolation polynomials of Hermite-Fejér type
Authors: Prasad J. 
Published: April 2009

For the interpolation polynomial of Hermite-Fejér type An[f] of degree less than or equal to 4n − 1 constructed on the nodes , k = 1, 2, …, n, it is shown that for f ∈ CM(Ω) the inequalityholds where CM(Ω) is the class of continuous functions on [−1, 1] satisfying certain conditions, Ω is a certain modulus of continuity, and c3 and M are positive constants.
A sequence algebra associated with distributions
Authors: Petersen G.M. 
Published: April 2009

If A = {am,n} is a regular summability matrix, the sequence s = {sn} is said to be A uniformly distributed (see L. Kuipers, H. Niederreiter, Uniform distribution of sequences, p. 221, John Wiley & Sons, New York, London, Sydney, Toronto, 1974), if(h = 1, 2, …). In this paper we examine sequences belonging to A*, where t ∈ A* if and only if t is bounded and s + t is A uniformly distributed whenever s is A uniformly distributed. By A′ are denoted those members t of A* such that at ∈ A* for every real a. The members of A′ form a Banach algebra, A* is not connected under the sup norm, but A′ is a component.
Action of a force near the planar surface between semi-infinite immiscible liquids at very low Reynolds numbers: Addendum
Authors: Aderogba K. , Blake J.R. 
Published: April 2009

In the paper by Aderogba and Blake [1], the first order approximation to the shape of the interface between two immiscible liquids, at which surface tension acted, was obtained in the case of a point force directed parallel to the interface. In the case of the normal force no solution was obtained due to the logarithmic singularity associated with problems of this type. However, the problem is not physically well-posed in the case of the normal force. Surface tension is not suitable because it cannot alone balance the induced stress on the interface due to a point force. We need an additional force to balance the action of the point force on the interface. The obvious solution is to include a density difference Δρ* between the two fluidswhere and are the densities of the lower and upper fluid respectively.
Locally irreducible rings
Authors: Vinsonhaler C. , Wickless W. 
Published: April 2009

In the study of torsion-free abelian groups of finite rank the notions of irreducibility, field of definition and E-ring have played significant rôles. These notions are tied together in the following theorem of R. S. Pierce:THEOREM. Let R be a ring whose additive group is torsion free finite rank irreducible and let Γ be the centralizer of QR as a QE(R) module. Then Γ is the unique smallest field of definition of R. Moreover, Γ ∩ R is an E-ring, in fact, it is a maximal E-subring of R.In this paper we consider extensions of Pierce's result to the infinite rank case. This leads to the concept of local irreducibility for torsion free groups.
Nilpotent injectors in finite groups
Authors: Förster Peter 
Published: April 2009

Nilpotent injectors exist in all finite groups.For every Fitting class F of finite groups (see [2]), InjF(G) denotes the set of all H ≤ G such that for each N ⊴ ⊴ G , H ∩ N is an F -maximal subgroup of N (that is, belongs to F and i s maximal among the subgroups of N with this property). Let W and N* denote the Fitting class of all nilpotent and quasi-nilpotent groups, respectively. (For the basic properties of quasi-nilpotent groups, and of the N*-radical F*(G) of a finite group G3 the reader is referred to [5].,X. %13; we shall use these properties without further reference.) Blessenohl and H. Laue have shown in CJ] that for every finite group G, InjN*(G) = {H ≤ G | H ≥ F*(G) N*-maximal in G} is a non-empty conjugacy class of subgroups of G. More recently, Iranzo and Perez-Monasor have verified InjN(G) ≠ Φ for all finite groups G satisfying G = CG(E(G))E(G) (see [6]), and have extended this result to a somewhat larger class M of finite groups C(see [7]). One checks, however, that M does not contain all finite groups; for example, S5 ε M.
Representing a distribution by stopping a Brownian Motion: Root's construction
Authors: Sheu Shey Shiung 
Published: April 2009

A closed subset c of [0,∞]×[−∞,∞] is called a barrier if(i) (∞,x) ∈ C, ∀̱x,(ii) (t, ±∞) ∈ C, ∀̱t,(iii) (t, x) ∈ C implies (s, x) ∈ C, ∀̱S ≥ t.Given a Brownian motion (B (t)) Starting at the origin and a barrier C, let τ(C) be inf{t: (t, B (t)) ∈ C}. A random variable x (or a distribution F) is called achievable if there exists a barrier C so that B (τ(C)) is distributed as x (F). In this paper we shall show that if x is bounded above or below with finite mean or if x has zero mean and E (|x| log+ |x|) < ∞ then x is achievable. This result gives a partial answer to a problem raised by Loynes [7].
Weak and semi-strong solutions of the Schneider-Tricomi problem in the euclidean plane
Authors: Rassias John M.S. 
Published: April 2009

Schneider (Math. Nachr. 60 (1974), 167–180) has established the following result. Consider the mixed type equationin G ⊂ R2 which is a simply connected region, bounded for y > 0 by a piece-wise smooth curve Γ0 connecting the points A(0, 0) and B(1, 0), and for y < 0 by the solutions of k(y).(dy)2 + (dx)2 = 0 which meet at the point G(½, yc), such that for ,S(x, y) = F(yy) + 8λ·(k/k′)2 > 0 in Ḡ ∩ {y < 0}, “Schneider's Condition”, where F(y) = 1 + 2(k/k′)′, and such that S = S(x, y) is integrable in G2, “Frankl's Condition”. Then the Tricomi Problem (T): L[u] = f with has a weak solution u ∈ L2(Ḡ) and the Adjoint Tricomi Problem (T+): L+[w] = f with has at most one semistrong solution.In this present paper we get the above result of Schneider in a much more generalized way, so that here our uniqueness theorem and existence results include cases where S(x, y) may be negative in G2.
On some Gelfand-Mazur like theorems in Banach algebras
Authors: Srinivasan V.K. 
Published: April 2009

The following Gelfand-Mazur like theorems are proved in this paper:(1) A complex Banach algebra which is locally finite, and which is also an integral domain, is isomorphic to the complex field .(2) A complex Banach algebra which is a noetherian domain is isomorphic to .(3) A complex Banach algebra which is a principal ideal domain is isomorphic to .An application is given to the algebra of all complex formal power series in several variables.
Ishikawa and Mann iteration methods for nonlinear strongly accretive mappings
Authors: Osilike M.O. 
Published: April 2009

Let X be a real Banach space with a uniformly convex dual, X*, and let C be a nonempty closed convex and bounded subset of X. Let T: C → C be a strongly accretive and a continuous mapping. For any f ∈ C, let S: C → C be defined by Sx = f + x – Tx for each x ∈ C. Then, the iteration process xo ∈ C,under suitable conditions on the real sequence converges strongly to a solution of the equation Tx = f in C. Furthermore, if T is strongly accretive and Lipschitz with Lipschitz constant L ≥ 1 then the iteration process x0 ∈ C,under suitable conditions on the real sequences and converges strongly to a solution of the equation Tx = f in C. Explicit error estimates are obtained.
Hecke groups and continued fractions
Authors: Rosen David , Schmidt Thomas A. 
Published: April 2009

The Hecke groupsare Fuchsian groups of the first kind. In an interesting analogy to the use of ordinary continued fractions to study the geodesics of the modular surface, the λ-continued fractions (λF) introduced by the first author can be used to study those on the surfaces determined by the Gq. In this paper we focus on periodic continued fractions, corresponding to closed geodesics, and prove that the period of the λF for periodic has nearly the form of the classical case. From this, we give: (1) a necessary and sufficient condition for to be periodic; (2) examples of elements of ℚ(λq) which also have such periodic expansions; (3) a discussion of solutions to Pell's equation in quadratic extensions of the ℚ(λq); and (4) Legendre's constant of diophantine approximation for the Gq, that is, γq such that < γq/Q2 implies that P/Q of “reduced finite λF form” is a convergent of real α ∉ Gq(∞).
Eigenvalue estimates and isoperimetric inequalities for cone-manifolds
Authors: Hodgson Craig , Tysk Johan 
Published: April 2009

This paper studies eigenvalue bounds and isoperimetric inequalities for Rieman-nian spaces with cone type singularities along a codimension-2 subcomplex. These “cone-manifolds” include orientable orbifolds, and singular geometric structures on 3-manifolds studied by W. Thurston and others.We first give a precise definition of “cone-manifold” and prove some basic results on the geometry of these spaces. We then generalise results of S.-Y. Cheng on upper bounds of eigenvalues of the Laplacian for disks in manifolds with Ricci curvature bounded from below to cone-manifolds, and characterise the case of equality in these estimates.We also establish a version of the Lévy-Gromov isoperimetric inequality for cone-manifolds. This is used to find lower bounds for eigenvalues of domains in cone-manifolds and to establish the Lichnerowicz inequality for cone-manifolds. These results enable us to characterise cone-manifolds with Ricci curvature bounded from below of maximal diameter.
Ramanujan's remarkable summation formula and an interesting convolution identity
Authors: Adiga S. Bhargava Chandrashekar , Somashekara D.D. 
Published: April 2009

In this note we obtain a convolution identity for the coefficients Bn(α, θ, q) defined byusing Ramanujan's 1Ψ1 summation. The identity contains as special cases convolution identities of Kung-Wei Yang and a few more interesting analogue.
Biconcave-function characterisations of UMD and Hilbert spaces
Authors: Lee Jinsik Mok 
Published: April 2009

Suppose that X is a real or complex Banach space with norm |·|. Then X is a Hilbert space if and only iffor all x in X and all X-valued Bochner integrable functions Y on the Lebesgue unit interval satisfying EY = 0 and |x − Y| ≤ 2 almost everywhere. This leads to the following biconcave-function characterisation: A Banach space X is a Hilbert space if and only if there is a biconcave function η: {(x, y) ∈ X × X: |x − y| ≤ 2} → R such that η(0, 0) = 2 andIf the condition η(0, 0) = 2 is eliminated, then the existence of such a function η characterises the class UMD (Banach spaces with the unconditionally property for martingale differences).
Small zeros of quadratic L-functions
Authors: Özlük Ali E. , Snyder C. 
Published: April 2009

We study the distribution of the imaginary parts of zeros near the real axis of quadratic L-functions. More precisely, let K(s) be chosen so that |K(1/2 ± it)| is rapidly decreasing as t increases. We investigate the asymptotic behaviour ofas D → ∞. Here denotes the sum over the non-trivial zeros p = 1/2 + iγ of the Dirichlet L-function L(s, χd), and χd = () is the Kronecker symbol. The outer sum is over all fundamental discriminants d that are in absolute value ≤ D. Assuming the Generalized Riemann Hypothesis, we show that for
Asymptotic equivalence of ordinary and operator-differential equations
Authors: Simeonov P. S. , Bainov D. D. 
Published: April 2009

The paper considers problems connected with the asymptotic equivalence of the system of ordinary differential equationsand the system of operator differential equationsThe generality of the operator At guarantees a number of its important implementations. By a specific choice of the operator At the system (2) can be one of the concentrated delay, a system of distributed delay, a system with maxima, etcetera.
On Hau's lemma
Authors: Loh W.K.A. 
Published: April 2009

Let f ∈ ℤ[X] and let q be a prime power pl(l ≥ 2). Hua stated and proved thatfor some unspecified constant C > 0 depending on the derivative f′ of f; M denoting the maximum multiplicity of the roots of the congruence
p−tf′(x) ≡ 0 (mod p),
where t is an integer chosen so that the polynomial p−tf′(x) is primitive. An explicit value for C was given by Chalk for p ≥ 3. Subsequently, Ping Ding (in two successive articles) obtained better estimates for p ≥ 2.This article provides a better result, based upon a more precise form of Hua's main lemma, previously overlooked.
A note on Ohm's rationality criterion for conics
Authors: Hajja Mowaffaq 
Published: April 2009

An irreducible quadratic polynomial P(X, Y) in two variables over a field k is called a conic over k. It is called rational if its function field is simple transcendental over k (equivalently if P is parameterisable by rational functions). Ohm's rationality criterion states that P is rational if and only if (i) the locus of P is non-empty and (ii) k is algebraically closed in the function field of P. To show the irredundancy of (ii), Ohm gives an example of a non-rational conic with a non-empty locus. That locus, however, consists of a single point.In this note, we show that a better example cannot exist by showing that if the locus of a conic contains more than one point then it is rational. We also show that the only rational conic whose locus consists of one point is the conic XY + 1 over the field of two elements.
Strange triangular maps of the square
Authors: Forti G.L. , Paganoni L. , Smítal J. 
Published: April 2009

We show that continuous triangular maps of the square I1, F: (x, y) → (f(x), g(x, y)), exhibit phenomena impossible in the one-dimensional case. In particular: (1) A triangular map F with zero topological entropy can have a minimal set containing an interval {a} × I, and can have recurrent points that are not uniformly recurrent; this solves two problems by S.F. Kolyada.(2) In the class of mappings satisfying Per(F) = Fix(F), there are non-chaotic maps with positive sequence topological entropy and chaotic maps with zero sequence topological entropy.
On weighted estimates for Stein's maximal function
Authors: Gunawan Hendra 
Published: April 2009

Let φ denote the normalised surface measure on the unit sphere Sn−1. We shall be interested in the weighted Lp estimate for Stein's maximal function Mφf, namelywhere w is an Ap weight, especially for 1 < p ≤ 2. Using the Mellin transformation approach, we prove that the estimate holds for every weight wδ where w ∈ Ap and 0 ≤ δ < (p(n − 1) − n)/(n(p − 1)), for n ≥ 3 and n/(n − 1) < p ≤ 2.
Existence and dimensionality of simple weight modules for quantum enveloping algebras
Authors: Shi Zhiyong 
Published: April 2009

We give sufficient and necessary conditions for simple modules of the quantum group or the quantum enveloping algebraUq(g) to have weight space decompositions, where g is a semisimple Lie algebra andqis a nonzero complex number. We show that(i) ifqis a root of unity, any simple module ofUq(g) is finite dimensional, and hence is a weight module;(ii) ifqis generic, that is, not a root of unity, then there are simple modules ofUq(g) which do not have weight space decompositions.Also the group of units ofUq(g) is found.
On semigroups with involution
Authors: Easdown D. , Munn W.D. 
Published: April 2009

A semigroup S with an involution * is called a special involution semigroup if and only if, for every finite nonempty subset T of S,.It is shown that a semigroup is inverse if and only if it is a special involution semigroup in which every element invariant under the involution is periodic. Other examples of special involution semigroups are discussed; these include free semigroups, totally ordered cancellative commutative semigroups and certain semigroups of matrices. Some properties of the semigroup algebras of special involution semigroups are also derived. In particular, it is shown that their real and complex semigroup algebras are semiprimitive.
When are dense subgroups of LCA groups closed under intersections?
Authors: Khan M.A. 
Published: April 2009

Let G be a nondiscrete locally compact Hausdorff abelian group. It is shown that if G contains an open torsion subgroup, then every proper dense subgroup of G is contained in a maximal subgroup; while if G has no open torsion subgroup, then it has a dense subgroup D such that G/D is algebraically isomorphic to R, the additive group of reals. With each G, containing an open torsion subgroup, we associate the least positive integer n such that the nth multiple of every discontinuous character of G is continuous. The following are proved equivalent for a nondiscrete locally compact abelian group G:(1) The intersection of any two dense subgroups of G is dense in G.(2) The intersection of all dense subgroups of G is dense in G.(3) G contains an open torsion subgroup, and for each prime p dividing the positive integer associated with G, pG is either open or a proper dense subgroup of G.Finally, we construct a locally compact abelian group G with infinitely many dense subgroups satisfying the three equivalent conditions stated above.
On some geometry associated with a generalised Toda lattice
Authors: Vassiliou P.J. 
Published: April 2009

We define the notion of Darboux integrability for linear second order partial differential operators,.We then build on certain geometric results of E. Vessiot related to the theory of Monge characteristics to show that the Darboux integrable operators L can be used to obtain a solution of the A2 Toda field theory. This solution is parametrised by four arbitrary functions. The approach presented in this paper thereby represents an alternative means of linearising the A2 Toda equations and may be contrasted with the known linearisation via the Lax pair.
Representation of finite groups as short products of subsets
Authors: Jia Xingde 
Published: April 2009

Let M be a finite quasigroup of order n. For any integer k ≥ 2, let H(k, M) be the smallest positive integer h such that there exist h subsets Ai (i = 1, 2, …, h) such that Ai … Ah = M and |Ai| = k for every i = 1, 2, …, h. Define H(k, n) = max H(k, M). It is proved in this paper that.
The existence of bounded harmonic functions on C-H manifolds
Authors: Ding Qing , Zhou Detang 
Published: April 2009

Let M be a Cartan-Hadamard manifold of dimension n (n ≥ 2). Suppose that M satisfies for every x > M outside a compact set an inequality:where b, A are positive constants and A > 4. Then M admits a wealth of bounded harmonic functions, more precisely, the Dirichlet problem of the Laplacian of M at infinity can be solved for any continuous boundary data on Sn−1(∞).
Oblique derivative problem for quasilinear elliptic equations with VMO coefficients
Authors: Di Fazio Guiseppe , Palagachev Dian K. 
Published: April 2009

Strong solvability and uniqueness in the Sobolev space W2, q(Ω), q > n, are proved for the oblique derivative problemassuming the coefficients of the quasilinear elliptic operator to be Carathéodory functions, aij ∈ VMO∩L∞ with respect to x, and b to grow at most quadratically with respect to the gradient.
On almost additive functions
Authors: Brzdȩk Janusz 
Published: April 2009

Let (S, +) be a semigroup and (H, +) be a group (neither necessarily commutative). Suppose thatJ⊂ 2sis a proper ideal inSsuch thatand Ω(J) = {M⊂S2: there existsU(M)∈JwithM[x] ∈Jfor x ∈S/U(M)}, whereM[x] = {y∈S: (y, x) ∈M}. We show that iff:S→His a function satisfyingthen there exists exactly one additive functionF : S→HwithF(x) =f(x)J-almost everywhere inS.We also prove some results concerning regularity of the functionF.
Nilpotent-like fitting formations of finite soluble groups
Authors: Ballester-Bolinches A. , Pérez-Ramos M. D. , Martínez- Pastor A. 
Published: April 2009

Dedicated to Professor K. Doerk on his 60th Birthday.In this paper the subnormal subgroup closed saturated formations of finite soluble groups containing nilpotent groups are fully characterised by means of extensions of well-known properties enjoyed by the formation of all nilpotent groups.
Quadratic forms associated with planar endomorphisms
Authors: Prince G. E. 
Published: April 2009

Any linear operator A on 2 is shown to have two real quadratic form on S1 associated with it. They represent the expansion and rotation of the map and the eigenvalues of A can be described in a geometrically intrinsic way in therms of the eigenvalues of these two quadratic forms via the formula
.A number of theorems concerning these quadṙatic forms are presented.