bluuebunny/crossref_metadata_2025_split huggingface dataset:
Block-Finite Orthomodular Lattices
Authors: Bruns Günter 
Published: December 2010

Introduction. Every orthomodular lattice (abbreviated : OML) is the union of its maximal Boolean subalgebras (blocks). The question thus arises how conversely Boolean algebras can be amalgamated in order to obtain an OML of which the given Boolean algebras are the blocks. This question we deal with in the present paper.The problem was first investigated by Greechie [6, 7, 8, 9]. His technique of pasting [6] will also play an important role in this paper. A case solved completely by Greechie [9] is the case that any two blocks intersect either in the bounds only or have the bounds, an atom and its complement in common. This is, of course, a very special situation. The more surprising it is that Greechie's methods, if skillfully applied, yield considerable insight into the structure of OMLs and provide a seemingly unexhaustible source for counter-examples.
On the Extreme Rays of the Metric Cone
Authors: Avis David 
Published: December 2010

A classical result in the theory of convex polyhedra is that every bounded polyhedral convex set can be expressed either as the intersection of half-spaces or as a convex combination of extreme points. It is becoming increasingly apparent that a full understanding of a class of convex polyhedra requires the knowledge of both of these characterizations. Perhaps the earliest and neatest example of this is the class of doubly stochastic matrices. This polyhedron can be defined by the system of equationsBirkhoff [2] and Von Neuman have shown that the extreme points of this bounded polyhedron are just the n × n permutation matrices. The importance of this result for mathematical programming is that it tells us that the maximum of any linear form over P will occur for a permutation matrix X.
Sylvester's Problem for Spreads of Curves
Authors: Watson Kym S. 
Published: December 2010

Spreads of curves were introduced by Grunbaum in [1]. A spread of curves is a continuous family of simple arcs in the real plane, every two of which intersect in exactly one point. A spread is the continuous analogue of a finite arrangement of pseudolines in the plane. Sylvester's problem for finite arrangements of pseudolines asks if every non-trivial arrangement has a simple vertex, that is a point contained in exactly two pseudolines of the arrangement. This question was answered in the affirmative by Kelly and Rottenberg [5]. One interesting feature of this result is that it does not depend on the pseudolines being straight lines.Here we settle Sylvester's problem for spreads. We show that every nontrivial spread of line segments has uncountably many simple vertices. But we also give examples of non-trivial spreads with no simple vertices.
Topological Reflection Groups
Authors: Djoković Dragomir Ž. 
Published: December 2010

Let G be a closed subgroup of one of the classical compact groups 0(n), U(n), Sp(n). By a reflection we mean a matrix in one of these groups which is conjugate to the diagonal matrix diag (–1, 1, …, 1). We say that G is a topological reflection group (t.r.g.) if the subgroup of G generated by all reflections in G is dense in G.It was shown recently by Eaton and Perlman [5] that, in case of 0(n), the whole group 0(n) is the unique infinite irreducible t.r.g. In this paper we solve the analogous problem for U(n) and Spin). Our method of proof is quite different from the one used in [5]. We treat simultaneously all the three cases.
The Inductive Step of the Second Brauer-Thrall Conjecture
Authors: Smalø Sverre O. 
Published: December 2010

In this paper we are going to use a result of H. Harada and Y. Sai concerning composition of nonisomorphisms between indecomposable modules and the theory of almost split sequences introduced in the representation theory of Artin algebras by M. Auslander and I. Reiten to obtain the inductive step in the second Brauer-Thrall conjecture.Section 1 is devoted to giving the necessary background in the theory of almost split sequences.As an application we get the first Brauer-Thrall conjecture for Artin algebras. This conjecture says that there is no bound on the length of the finitely generated indecomposable modules over an Artin algebra of infinite type, i.e., an Artin algebra such that there are infinitely many nonisomorphic indecomposable finitely generated modules. This result was first proved by A. V. Roiter [8] and later in general for Artin rings by M. Auslander [2] using categorical methods.
An Inclusion Relation for Abel, Borel, and Lambert Summability
Authors: Gawronski W. , Siebert H. , Trautner R. 
Published: December 2010

In this paper a new type of inclusion theorem concerning Abel, Borel and Lambert summability is established. To state our results we need some definitions and notations. With a formal series ∑k=0∞ak, ak∈ C, and its partial sums snwe associate the seriesThen ∑k=0∞ ak is said to be summable to the value s(a) by Abel's method, if (1.1) is convergent for |v| > 1 and limv→1+A(v)= s,(b) by Lambert's method, if (1.2) is convergent for |v| > 1 and limv→1+L(v)= s,(c) by Borel's method, if (1.3) is convergent for all x ∈ R and limx→+∞B(x)= s,
The Bergman Projection on Weighted Norm Spaces
Authors: Burbea Jacob 
Published: December 2010

Quite recently Bekollé and Bonami [1] have characterized the weighted measures λ on the unit disk Δ for which the Bergman projection is bounded on Lp(Δ : λ), 1 < p < ∞. Our methods in [4] can be applied to even extend their result by replacing the unit disk with multiply connected domains. This is done via a rather interesting identity between the Bergman kernel and its “adjoint” [2]. As a corollary of our result we obtain a generalization of a result due to Shikhvatov [7].Let D be a bounded plane domain and let λ be a positive locally integrate function in D. λ is said to belong to Mp(D) (1 < p < ∞) if it satisfies the Muckenhoupt condition:where the supremum is taken over all sectors V ⊂ D, dσ is the area Lebesgue measure and |V| = σ(V).
Divisible Properties and the Stone-Čech Compactification
Authors: Glasner S. 
Published: December 2010

Let T be an abelian infinite countable group. We say that a property of subsets of T is divisible if it satisfies the following requirements. (We identify with the set of all subsets of T which satisfy .)(i) ∅ ∉ and T ∈ (ii) A ∈ and B ⊃ A implies B ∈ (iii) A ∈ and A = B1 ∪ B2 implies that either B1 or B2 is in
On the and Transformations
Authors: Rooney P. G. 
Published: December 2010

Denote by C0 the collection of complex-valued functions which are continuous and compactly supported on (0, ∞). The transformations of the title are defined on C0 by1.1and1.2respectively, where Yv(x) is the Bessel function of the second kind, and Hv(x) is the Struve function; see [1; 7.5.4(55)]. The two transformations are studied briefly in [6; §8.4]; tables of transform pairs are given in [2; Chapters IX and XI], where it is also stated that, for – , each of the transformations is the inverse of the other.
The Two-Sided Factorization of Ordinary Differential Operators
Authors: Browne Patrick J. , Nillsen Rodney 
Published: December 2010

Throughout this paper we shall use I to denote a given interval, not necessarily bounded, of real numbers and Cn to denote the real valued n times continuously differentiable functions on I and C0 will be abbreviated to C. By a differential operator of order n we shall mean a linear function L:Cn → C of the form1.1where pn(x) ≠ 0 for x ∊ I and pi ∊ Cj 0 ≦ j ≦ n. The function pn is called the leading coefficient of L.It is well known (see, for example, [2, pp. 73-74]) thai a differential operator L of order n uniquely determines both a differential operator L* of order n (the adjoint of L) and a bilinear form [·,·]L (the Lagrange bracket) so that if D denotes differentiation, we have for u, v ∊ Cn,1.2
Translation Planes of Dimension Two with Odd Characteristic
Authors: Ostrom T. G. 
Published: December 2010

A translation plane of dimension d over its kernel K = GF(q) can be represented by a vector space of dimension 2d over K. The lines through the zero vector form a “spread”; i.e., a class of mutually independent vector spaces of dimension d which cover the vector space.The case where d = 2 has aroused the most interest. The more exotic translation planes tend to be of dimension two; a spread in this case can be interpreted as a class of mutually skew lines in projective three-space.The stabilizer of the zero vector in the group of collineations is a group of semi-linear transformations and is called the translation complement. The subgroup consisting of linear transformations is the linear translation complement.
Some Generalizations of Ramanujan's Sum
Authors: Ramanathan K. G. , Subbarao M. V. 
Published: December 2010

Ramanujan's well known trigonometrical sum C(m, n) denned bywhere x runs through a reduced residue system (mod n), had been shown to occur in analytic problems concerning modular functions of one variable, by Poincaré [4]. Ramanujan, independently later, used these trigonometrical sums in his remarkable work on representation of integers as sums of squares [6]. There are various generalizations of C(m, n) in the literature (some also to algebraic number fields); see, for example, [9] which gives references to some of these. Perhaps the earliest generalization to algebraic number fields is due to H. Rademacher [5]. We here consider a novel generalization involving matrices.
The Poincaré Series Of Stretched Cohen-Macaulay Rings
Authors: Sally Judith D. 
Published: December 2010

There are relatively few classes of local rings (R, m) for which the question of the rationality of the Poincaré serieswhere k = R/m, has been settled. (For an example of a local ring with non-rational Poincaré series see the recent paper by D. Anick, “Construction of loop spaces and local rings whose Poincaré—Betti series are nonrational”, C. R. Acad. Sc. Paris 290 (1980), 729-732.) In this note, we compute the Poincaré series of a certain family of local Cohen-Macaulay rings and obtain, as a corollary, the rationality of the Poincaré series of d-dimensional local Gorenstein rings (R, m) of embedding dimension at least e + d – 3, where e is the multiplicity of R. It follows that local Gorenstein rings of multiplicity at most five have rational Poincaré series.
On The Center Of Quasi-Central Banach Algebras With bounded Approximate Identity
Authors: Takahasi Sin-Ei 
Published: December 2010

Let A be a quasi-central complex Banach algebra with a bounded approximate identity and Prim A the structure space of A. In [15], we have shown that every central double centralizer T on A can be represented as a bounded continuous complex-valued function ΦT on Prim A such that Tx + P = ΦT(P)(x + P) for all x ∈ A and P ∈ Primal when the center Z(A) of A is completely regular. Here x + P for P ∈ Prim A denotes the canonical image of x in A/P. In particular, in the case of quasi-central C*-algebras, this result is equivalent to the Dixmier's representation theorem of central double centralizers on C*-algebras (see [3, Section 2] and [9, Theorem 5]).In this paper, it is shown that if Z(A) is completely regular then the space Prim A is locally quasi-compact and for each element z of Z(A), ΦLz vanishes at infinity, where Lz for z ∊ Z(i) is the central double centralizer on A defined by Lz(x) = zx for all x ∊ A.
A Localization of R[x]
Authors: Huckaba James A. , Papick Ira J. 
Published: December 2010

Throughout this paper, R will be a commutative integral domain with identity and x an indeterminate. If ƒ ∈ R[x], let CR(ƒ) denote the ideal of R generated by the coefficients of ƒ. Define SR = {ƒ ∈ R[x]: cR(ƒ) = R} and UR = {ƒ ∈ R(x): cR(ƒ)– 1 = R}. For a,b ∈ R, write . When no confusion may result, we will write c(ƒ), S, U, and (a:b). It follows that both S and U are multiplicatively closed sets in R[x] [7, Proposition 33.1], [17, Theorem F], and that R[x]s ⊆ R[x]U.The ring R[x]s, denoted by R(x), has been the object of study of several authors (see for example [1], [2], [3], [12]). An especially interesting paper concerning R(x) is that of Arnold's [3], where he, among other things, characterizes when R(x) is a Priifer domain. We shall make special use of his results in our work.
Variational Methods for One and Several Parameter Non-Linear Eigenvalue Problems
Authors: Binding Paul 
Published: December 2010

We shall consider a multiparameter eigenvalue problem of the form(1.1)where λ ∈ Rk while Tn and Vn(λ) are self-adjoint linear operators on a Hilbert space Hn. If λ = (λ1, …, λk) ∈ Rk and satisfy (1.1) then we call λ an eigenvalue, x an eigenvector and (λ, x) an eigenpair. While our main thrust is towTards the general case of several parameters λn, the method ultimately involves reduction to a sequence of one parameter problems. Our chief contributions are (i) to generalise the conditions under which this reduction is possible, and (ii) to develop methods for the one parameter problem particularly suited to the multiparameter application. For example, we give rather general results on the magnitude and direction of the movement of non-linear eigenvalues under perturbation.
Term by Term Dyadic Differentiation
Authors: Powell Charles H. , Wade William R. 
Published: December 2010

Let ψ0, ψ1, … denote the Walsh-Paley functions and let ∔ denote the group operation which Fine [5] defined on the interval [0, 1). Thus, if k ≧ 0 is an integer and if u, t are points in the interval [0, 1) then(where αk = 0 or 1 represents the kth coefficient of the binary expansion of t), andA real-valued function ƒ, is said to be dyadically differentiable at a point x ∈ [0, 1) if ƒ is defined at x and at x ∔ 2–n–1, n = 0, 1, …;, and if the sequence(1)converges as N → ∞.
Algebraic Homotopy Theory
Authors: Jardine J. F. 
Published: December 2010

Kan and Miller have shown in [9] that the homotopy type of a finite simplicial set K can be recovered from its R-algebra of 0-forms A0K, when R is a unique factorization domain. More precisely, if is the category of simplicial sets and is the category of R-algebras there is a contravariant functorwiththe simplicial set homomorphisms from X to the simplicial R-algebra ∇, whereand the faces and degeneracies of ∇ are induced byandrespectively.
Irregularity of the Rate of Decrease of Sequences of Powers in the Volterra Algebra
Authors: Esterle J. 
Published: December 2010

G. R. Allan and A. M. Sinclair proved in [1] that if a commutative radical Banach algebra possesses bounded approximate identities then for every sequence (αn) of real numbers such that limn→∞αn = 0 there exists such thatIn the other direction it is shown in [6] that if is separable and if the nilpotents are dense in then for every sequence (βn) of positive reals there exists such that(This result was given in [2] for the Volterra algebra.)
Rankings and Ranking Functions
Authors: Walker W. J. 
Published: December 2010

Suppose that n competitors compete in r races and in each race they are awarded placings l, 2, 3, …, n – 1, n. After the r races each competitor has a result consisting of his r placings. Let such a result be written (αj)1≦j≦r where for convenience the positive integers αj are arranged in ascending order. For example, if n = 4 and r = 6 a typical result is (1, 2, 2, 3, 4, 4).A final ranking of the n competitors will be determined in all circumstances if a strict ordering is assigned to all possible results. In the next section it is shown that the number or results is . Of course only some strict orderings of this set of results will be feasible in that there are criteria which a final ranking should satisfy. For example, (1, 1, …, 1) should clearly be ranked first in any feasible ranking.
Hermitian Configurations in Odd-Dimensional Projective Geometries
Authors: Kestenband Barbu C. 
Published: December 2010

A t-cap in a geometry is a set of t points no three of which are collinear. A (t, k)-cap is a set of t points, no k + 1 of which are collinear.It has been shown in [3] that any Desarguesian PG(2n, q2) is a disjoint union of (q2n+l – l)/(q – 1) (q2n+l – l)/(q + l)-caps. These caps were obtained as intersections of 2n Hermitian Varieties of a certain kind; the intersection of 2n + 1 such varieties was empty. Furthermore, the caps in question constituted the ‘large points” of a PG(2n, q), with the incidence relation defined in a natural way.It seemed at the time that nothing similar could be said about odd-dimensional projective geometries, if only because |PG(2n – 1, q)| ∤ |PG(2n – l, q2)|.
The Quotient Problem for Noetherian Rings
Authors: Müller Bruno J. 
Published: December 2010

Our work was motivated by attempts to find a criterion for the existence of a classical quotient ring, for a noetherian ring, in analogy with the various known criteria for the existence of an artinian classical quotient ring ([9], [10], [13], [2]).We have restricted our attention to Krull symmetric noetherian rings R, and we make heavy use of the fact that all their Krull composition factors are non-singular (Proposition 7). The collection Kprime R of the associated primes of the Krull composition factors of R plays a central role, taking the place of the collection of the associated primes of R.
Co-Absolutes with Homeomorphic Dense Subspaces
Authors: Williams Scott W. 
Published: December 2010

Recall that the absolute ∈(X) of a regular space X is the unique (up to a homeomorphism) extremally disconnected space whose image is X under a perfect irreducible map. X and Y are co-absolute whenever ∈(X) and ∈(Y) are homeomorphic. Completely regular spaces X and Y are weakly co-absolute whenever βX and βY are co-absolute. For a survey of this area we suggest [6] and [8].In this paper we proveTHEOREM 1. Suppose, for i ∈ {0, 1};, X(i) is a compact connected linearly ordered space. Then X(0) and X(l) are co-absolute if, and only if, X(0) and X(l) have homeomorphic dense sets.Making use of Theorem 1 and a result from [7] we give Theorem 2, a cardinal generalization ofCOROLLARY 1. Suppose for each i ∈ {0, 1};, X(i) is a Čech-complete space with a Gδ-diagonal.
Unbounded Negative Definite Functions
Authors: Akemann Charles A. , Walter Martin E. 
Published: December 2010

Negative definite functions (all definitions are given in § 1 below) on a locally compact, σ-compact group G have been used in several different contexts recently [2, 5, 7, 11]. In this paper we show how such functions relate to other properties such a group may have. Here are six properties which G might have. They are grouped into three pairs with one property of each pair involving negative definite functions. We show that the paired properties are equivalent and, where possible, give counter-examples to other equivalences. We assume throughout that G is not compact.(1A) G does not have property T.(IB) There is a continuous, negative definite function on G which is unbounded.(2A) G has the (weak and/or strong) dual R-L property.(2B) For every closed, non-compact set Q ⊂ G there is a continuous, negative definite function on G which is unbounded on Q.
Generalization of the Hausdorff Moment Problem
Authors: Borwein David , Jakimovski Amnon 
Published: December 2010

Suppose throughout that {kn} is a sequence of positive integers, thatthat k0 = 1 if l0 = 1, and that {un(r)}; (r = 0, 1, …, kn – 1, n = 0, 1, …) is a sequence of real numbers. We shall be concerned with the problem of establishing necessary and sufficient conditions for there to be a function a satisfying(1)and certain additional conditions. The case l0 = 0, kn = 1 for n = 0, 1, … of the problem is the version of the classical moment problem considered originally by Hausdorff [5], [6], [7]; the above formulation will emerge as a natural generalization thereof.
On Some Twisted Chevalley Groups Over Laurent Polynomial Rings
Authors: Morita Jun 
Published: December 2010

We let Z denote the ring of rational integers, Q the field of rational numbers, R the field of real numbers, and C the field of complex numbers.For elements e and f of a Lie algebra, [e,f] denotes the bracket of e and f. A generalized Cartan matrix C = (cij) is a square matrix of integers satisfying cii = 2, cij ≦ 0 if i ≠ j, cij = 0 if and only if cji = 0. For any generalized Cartan matrix C = (cij) of size l × l and for any field F of characteristic zero, denotes the Lie algebra over F generated by 3l generators e1, …, el, h1, …, hl, f1, …, fl with the defining relationsfor all i, j,for distinct i, j.
On Block-Schematic Steiner Systems: S(t, t + 1, v)
Authors: Yoshizawa Mitsuo 
Published: December 2010

A Steiner system S(t, k, v) is a collection of k-subsets, called blocks, of a v-set of points with the property that any t-subset of points is contained in a unique block. We assume 1 < t < k < v. A Steiner system is called block-schematic if the blocks form an association scheme with the relations determined by size of intersection. Ito and Patton [3] proved that if S(4, 5, v) is block-schematic, then v = 11. The purpose of this paper is to extend this result, and we prove the following theorem.THEOREM. A Steiner system S(t, t + 1, v) is block-schematic if and only if one of the following holds: (i) t = 2, (ii) t = 3, v = 8, (iii) t = 4, v = 11, (iv) t = 5, v = 12.
Distinguished Domains
Authors: Heitmann Raymond C. , McAdam Stephen 
Published: December 2010

This paper introduces a class of domains which we hope to show merits some attention.Definition. The domain R is said to be a distinguished domain if for any 0 ≠ z ∈ K, the quotient field of R, (1 : z) does not consist entirely of zero divisors modulo (1 : z–l). (Note: Here we use the fact that a zero module has no zero divisors. Thus if z–l ∈ R, so that (1 : z–l) = R, then the condition holds trivially.)Section 1 of this paper gives numerous examples of distinguished domains, foremost among them being Krull domains and Prufer domains. In fact Prüfer domains are shown to be exactly those distinguished domains whose prime lattice forms a tree. Other distinguished domains can be constructed by the D + M construction. It is shown that distinguished domains are integrally closed but the converse fails.
Linear Isometries of Spaces of Absolutely Continuous Functions
Authors: Pathak V. D. 
Published: December 2010

Let X be an arbitrary compact subset of the real line R which has at least two points. For each finite complex valued function f on X we denote by V(f; X) (and call it the weak variation of f on X) the least upper bound of the numbers ∑i|f(bi) – f(ai)| where {[ai, bi]} is any sequence of non-overlapping intervals whose end points belong to X. A function f is said to be of bounded variation (BV) on X if V(f; X) < ∞. A function f is said to be absolutely continuous (AC) on X, if given any ∈ > 0 there exists an n > 0 such that for every sequence of non-overlapping intervals {[au bi]} whose end points belong to X, the inequalityimplies that([7], p. 221, 223).
Some Finiteness Conditions for Orthomodular Lattices
Authors: Bruns Günter , Greechie Richard 
Published: December 2010

Throughout this paper L will be an orthomodular lattice and the set of all maximal Boolean subalgebras, also called blocks [4], of L. For every x ∈ L, C(x) will be the set of all elements of L which commute with x. Let n ≧ 1 be a natural number. In this paper we consider the following conditions for L:An: L has at most n blocks,Bn: there exists a covering of L by at most n blocks,Cn: the set ﹛C(x)| x ∈ L﹜ has at most n elements,Dn: out of any n + 1 elements of L at least two commute.We also consider quantified versions of these statements, namely the statements A, B, C, D defined by: A ⇔ ∃ nAn, B ⇔ ∃ nBn, C ⇔ ∃ nCn and D ⇔ ∃ nDn.