bluuebunny/crossref_metadata_2025_split huggingface dataset:
Coloring a Dodecahedron with Four Colors(1)
Authors: Ballard David 
Published: December 2010

The purpose of this note is to show that there is one and only one coloring of the sides of a dodecahedron with four colors, under the condition that no two adjacent sides share the same color.In [1] Busacker and Saaty give a graphical solution to the game known as “Instant Insanity”.
Quasigroups Orthogonal to a Given Abelian Group
Authors: Lindner Charles C. 
Published: December 2010

In this note we prove the following theorem, which does not seem to appear explicitly in the literature.Theorem. Let A be a finite abelian group and p the smallest prime which divides |A|. Then there are p—1 mutually orthogonal quasigroups of order |A|, one of which is A.
Sets of Generators of a Commutative and Associative Algebra(1)
Authors: Djoković D. Ž. 
Published: December 2010

AbstractLet A be a finite dimensional commutative and associative algebra with identity, over a field K. We assume also that A is generated by one element and consequently, isomorphic to a quotient algebra of the polynomial algebra K[X]. If A=K[a] and bi=fi(A), fi(X) ∊ K[X], 1≤i≤r we find necessary and sufficient conditions which should be satisfied by fi(X) in order that A = K[b1, …, br].The result can be stated as a theorem about matrices. As a special case we obtain a recent result of Thompson [4].In fact this last result was established earlier by Mirsky and Rado [3]. I am grateful to the referee for supplying this reference.
The Ring Scheme Fg
Authors: Connell Ian G. 
Published: December 2010

Let A be a ring and s2(A) the set of idempotents in A. It is a familiar fact that s2(A) becomes a ring if we define 0, 1 and multiplication as in A, and a new negative and new addition by1R. A. Melter [3] made the surprising observation that s3(A), where in general sq(A)={x∈A:xq=x}, is a ring if 2 is a unit in A and we define 0,1 minus and multiplication as in A, and a new addition by2The nonobvious facts are that s3(A) is closed under ⊕ and that ⊕ is associative when applied to the elements of s3(A). The ⊕ in (1) is actually a formal group over A, and so is associative when applied to any elements of A. However in (2) (and similarly in other cases we shall define) the ⊕ is not a formal group, and the associative law depends on the fact that the elements involved are in s3(A).
On Transportable Forms
Authors: Klemola Tapio 
Published: December 2010

In the theory of deformations of compact complex manifolds, the hypothesis of constancy of the dimension of diverse structural cohomology groups pertaining to a fibre plays an important role (see, for instance, [3, Propositions 2.5 and 2.7, Theorems 2.2 and 2.3, and Definition 6.1]). This paper is the first of two devoted to the investigation of conditions under which constancy of the dimension of given cohomology groups is assured, and more generally, to the study of the variation of that dimension.In [2] Griffiths introduces extendible forms in a holomorphic deformation. We consider in this paper a differentiate family, and besides extendible, also co-extendible and transportable forms (see §5), and deduce from their existence conclusions about the variation of the dimension of the corresponding structural cohomology groups. It is left to a subsequent paper to give more explicit conditions by means of cohomology operations, and to deal with some applications.
An Inequality for Elementary Symmetric Functions
Authors: Menon K. V. 
Published: December 2010

Let Er denote the rth elementary symmetric function on α1 α2,…,αm which is defined by1E0 = 1 and Er=0(r>m).We define the rth symmetric mean by2where denote the binomial coefficient. If α1 α2,…,αm are positive reals thenwe have two well-known inequalities3and4In this paper we consider a generalization of these inequalities. The inequality (4) is known as Newton's inequality which contains the arithmetic and geometric mean inequality.
Local Group Rings
Authors: Nicholson W. K. 
Published: December 2010

The purpose of this note is to generalize a result of Gulliksen, Ribenboim and Viswanathan which characterized local group rings when both the ring and the group are commutative.We assume throughout that all rings are associative with identity. If R is a ring we call R local if R/J(R) is a division ring where J(R) denotes the Jacobson radical of R. It is well known that R is local if and only if each element of R\J(R) is a unit. We need the following.
Higher Derivations and the Jordan Canonical Form of the Companion Matrix
Authors: Roberts Leslie G. 
Published: December 2010

The purpose of this note is to give a basis with respect to which the companion matrix of an equation (over a field of any characteristic) is in Jordan canonical form.Let k be a field. Define a k-linear map Di:k[X]→k[X] by where the integer is the binomial coefficient n!;/i!;(n —i)!;. We adopt the usual convention that if i>9 or j<0. Then D=(D0, D1D2,…) is a higher derivation (see [1, p. 192]).
Explicit Solutions of Pyramidal Diophantine Equations
Authors: Bernstein Leon 
Published: December 2010

Let Pm, k denote the set of pyramidal numbers1.1The question has been asked whether there exist elements p, q, r in Pm, k such that p+q = r or, as the problem is usually posed,1.2The case k=2 has been studied by Sierpinski [6] and Khatri [3]; the case k=3 by Oppenheim [4] and Segal [5]; recently Fraenkel [2] has generalized (1.1) to the larger set1.3
The Slimming Number and Genus of Graphs
Authors: Guy Richard K. 
Published: December 2010

J. Ch. Boland suggested, and Mrs. Sheehan named, the idea of the slimming number of a graph G, i.e. the minimum number, s(G), of edges, e1e2,…, es, which must be removed from G in order that G—∪ ei be planar.For the complete graph, Kn (n≥3), it may be seen by Euler's formula that a planar subgraph contains at most 3n—6 edges; moreover one may construct such a subgraph inductively, starting from K3, and adding points successively, joining them to the three vertices of the region in which they lie, so1
Noetherian Tensor Products
Authors: Magarian E. A. , Motto J. L. 
Published: December 2010

Relatively little is known about the ideal structure of A⊗RA' when A and A' are R-algebras. In [4, p. 460], Curtis and Reiner gave conditions that imply certain tensor products are semi-simple with minimum condition. Herstein considered when the tensor product has zero Jacobson radical in [6, p. 43]. Jacobson [7, p. 114] studied tensor products with no two-sided ideals, and Rosenberg and Zelinsky investigated semi-primary tensor products in [9].All rings considered in this paper are assumed to be commutative with identity. Furthermore, R will always denote a field.
Positive Definite Sequence of Operators and a Fixed Point Theorem
Authors: Dash A. T. 
Published: December 2010

The purpose of this note is to prove the following:Theorem. Let {An} be a positive definite sequence of operators on a Hilbert space H with A0=1. If A1f=f for some f in H, then Anf=f for all n.Note that a bilateral sequence of operators {An:n = 0, ±1, ±2,…} on H is positive definite iffor every finitely nonzero sequence {fn} of vectors in H [1].
Integral Functionals in the Duals of Lλ-Spacesc(1)
Authors: Ellis H. W. , Hiscocks J. D. 
Published: December 2010

Luxemburg and Zaanen [5] call an element φ of the topological dual of a normed or seminormed vector space V an integral ifWe denote the space of integrals by VI, For the Lλ function spaces introduced by Ellis and Halperin [2] another Banach subspace of the dual emerges, namely the conjugate space Lλ* which is the Lλ space determined by the conjugate length function λ*-Lλ* is contained in (Lλ)I but need not coincide with it.
On a Question of Colin Clark Concerning Three Properties of Convex Sets(1)
Authors: Klee Victor 
Published: December 2010

Let C be a convex subset of a normed linear space E. The following properties of C were studied by Clark [2]:(1)C is of finite width/ that is, C lies between two parallel closed hyperplanes;(2)C is of finite width in some direction; that is, for some line L in E there is a finite upper bound for the lengths of C's intersections with lines parallel to L;(3)C is partially bounded; that is, there is a finite upper bound for the radii of balls contained in C.
On a Class of Nonparametric Tests for Independence—Bivariate Case(1)
Authors: Srivastava M. S. 
Published: December 2010

Let(X1, Y1), (X2, Y2),…, (Xn, Yn) benmutually independent pairs of random variables with absolutely continuous (hereafter, a.c.)pdfgiven by(1)where f(ρ)denotes the conditionalpdfofXgivenY, g(y)the marginalpdfofY, e(ρ)→ 1andb(ρ)→0as ρ→0 and,(2)We wish to test the hypothesis(3)against the alternative(4)For the two-sided alternative we take — ∞< b < ∞. A feature of the model (1) is that it covers both-sided alternatives which have not been considered in the literature so far.
On the Diophantine Equation x(x + d)(x + 2d) +y(y + d)(y + 2d) = z(z + d)(z + 2d)
Authors: Bernstein Leon 
Published: December 2010

AbstractA previous result of the author concerning the parametric representation of infinitely many solutions of the title equation is strongly improved. New classes each containing infinitely many solutions of the equation for specified values of d are stated explicitly. The method of solution hinges heavily on solving the generalized Pell’s equation x2—Dy2=c.
Orbital Lattices of SL+(2, Z)
Authors: Rankin S. A. 
Published: December 2010

The results described in this paper were obtained in the study of analytic maps between flat two-tori. It is felt that analogous results will be obtained from a similar study of the analytic maps between higher-dimensional flat tori.It is well-known that the multiplicative group GL+(2, Q) acts on the upper halfplane as a group of linear fractional transformations, i.e. for each element
A Short Proof of an Interpolation Theorem
Authors: Hughes Edward 
Published: December 2010

In this note we give a simple proof of an operator-interpolation theorem (Theorem 2) due originally to Donoghue [6], and Lions-Foias [7].Let be the complex plane, the open upper half-plane, the real line, ℛ+ and ℛ- the non-negative and non-positive axes. Denote by the class of positive functions on which extend analytically to —ℛ-, and map into itself. Denote by ’ the class of functions φ such that φ(x1/2)2 is in .
Self-Complementary Generalized Orbits of a Permutation Group
Authors: Frucht Roberto , Harary Frank 
Published: December 2010

AbstractA permutation groupAof degree n acting on a setXhas a certain number of orbits, each a subset ofX. More generally, A also induces an equivalence relation onX(k)the set of allksubsets ofX, and the resulting equivalence classes are calledkorbits ofA, orgeneralized orbits. Aself-complementary k-orbitis one in which for everyk-subsetSin it,X—Sis also in it. Our main results are two formulas for the numbers(A)of self-complementary generalized orbits of an arbitrary permutation group A in terms of its cycle index. We show that self-complementary graphs, digraphs, and relations provide special classes of self-complementary generalized orbits.
Some Fixed and Common Fixed Point Theorems in Metric Spaces
Authors: Sehgal V. M. 
Published: December 2010

Let (X, d) be a metric space and Ti(i=l, 2) be self mappings of X. The purpose of this paper is to investigate the fixed and common fixed points of Ti, when the pair Ti(i=l, 2) satisfies a condition of the following type:(1)
The Local Growth of Power Series: A Survey of the Wiman-Valiron Method
Authors: Hayman W. K. 
Published: December 2010

Suppose that1.1is a transcendental integral function. In this article we develop the theory initiated by Wiman [22, 23] and deepened by other writers including Valiron [18, 19, 20], Saxer [15], Clunie [4, 5] and Kövari [10, 11], which describes the local behaviour off(z), near a point where |f(z) | is large, in terms of the power seriesf off(z).
On the Minimum Order of Graphs with Given Group
Authors: Babai László 
Published: December 2010

ForGa, finite group letα(G) denote the minimum number of vertices of the graphsXthe automorphism groupA(X) of which is isomorphic toG.G. Sabidussi proved [1], thatα(G)=0(nlogd) wheren=\G\anddis the minimum number of generators ofG.As0(log n) is the best possible upper bound ford,the result established in [1] implies thatα(G)=0(nlog logn).
Hausdorff Compactifications as Epireflections
Authors: Hunsaker W. N. , Naimpally S. A. 
Published: December 2010

AbstractWe answer the following problem posed by Herrlich in the affirmative: “Can the Freudenthal compactification be regarded as a reflection in a sensible way?” This is accomplished by exploiting the one-to-one correspondence between proximities compatible with a given Tihonov space and compactifications of that space. We give topological characterizations of proximally continuous functions for the proximities associated with the Freudenthal and Fan-Gottesman compactifications.
On Semiperfect Modules
Authors: Nicholson W. K. 
Published: December 2010

AbstractSandomierski (Proc. A.M.S. 21 (1969), 205–207) has proved that a ring is semiperfect if and only if every simple module has a projective cover. This is generalized to semiperfect modules as follows: If P is a projective module then P is semiperfect if and only if every simple homomorphic image of P has a projective cover and every proper submodule of P is contained in a maximal submodule.
On the Extension of Uniformly Continuous Functions(1)
Authors: Gardner L. T. , Milnes P. 
Published: December 2010

AbstractA theorem of M. Katětov asserts that a bounded uniformly continuous function f on a subspace Q of a uniform space P has a bounded uniformly continuous extension to all of P. In this note we give new proofs of two special cases of this theorem: (i) Q is totally bounded, and (ii) P is a locally compact group and Q is a subgroup, both P and Q having the left uniformity.
On Certain Problems in the Theory of Sequences
Authors: Higgins Rada 
Published: December 2010

We are well-acquainted with the theorem about sequences which states that, the existence of(1)is sufficient to imply limk→∞ak = 0. Partially out of a growing interest in the theory of regularly varying sequences ([1]), and probably as an interesting problem, in and of itself, some mathematicians have tried to find conditions weaker than (1) that would guarantee limk→∞ak = 0.
Relations Between Boundary Value Functions for a Nonlinear Differential Equation and its Variational Equations*
Authors: Spencer James D. 
Published: December 2010

We consider here the nonlinear differential equation(1.1)where x ∊l= [a, ∞). We will make the following assumptions(A)f is continuous on [a, ∞) × Rn,(B)solutions of initial value problems (I.V.P.'s) are unique and extend throughout [a, ∞).(C)
Extension of a Semigroup Embedding Theorem to Semirings
Authors: Karyellas Paul H. 
Published: December 2010

It is well known [1,3] that a commutative semigroup (S, +) can be embedded in a semigroup which is a union of groups if and only if S is separative (2a = a + b = 2b implies a = b). We extend this result to additively commutative semirings.A semiring (S, +, ⋅) is a set S with associative addition (+) and multiplication (⋅), the latter distributing over addition from left and right. In what follows (S, +, ⋅) will denote a semiring in which the additive semigroup (S, +) is commutative. An element 0 can be adjoined, where s = s + 0, 0 = 0 ⋅ s = s ⋅ 0 for all s in S, to form S°.
On Second-Order Differential Operators With Bohr-Neugebauer Type Property
Authors: Rao Aribindi Satyanarayan 
Published: December 2010

AbstractLet B be a bounded linear operator having domain and range in a Banach space. If the second-order differential operator d2/dt2–B has a Bohr-Neugebauer type property for Bochner almost periodic functions, then any Stepanov-bounded solution of the differential equation (d2/dt2)u(t) – Bu(t) = g(t) is Bochner almost periodic, with g(t) being a Stepanov-almost periodic continuous function.
La 7e Conférence Jeffery-Williams Présentée le 7 Juin 1974 à L'université Laval à L'occasion de la 28e Réunion Annuelle de la Société Mathématique
Authors: Zassenhaus Hans J. 
Published: December 2010

Il me fait un très grand plaisir de vous présenter aujourd'hui la conférence Jeffrey-Williams nommée ainsi en l'honeur des distingués fondateurs de la Société Mathématique du Canada.Il y a beaucoup d'évidences indirectes d'un vif échange d'idées entre Herman Minkowski et David Hilbert, pendant la période de temps entre la soutenance de thèse de Hilbert (décembre 1884) et la mort prématurée de Minkowski (le 12 janvier 1909).
An N-Parameter Chebyshev Set which is not a Sun
Authors: Braess Dietrich 
Published: December 2010

Recently, Dunham has given examples for 1-parameter and 2-parameter Chebyshev sets which are not suns. In this note 2-parameter sets with these properties are described.When studying the old problem whether Chebyshev sets are always convex, Klee [10] introduced certain sets which were called suns by Efimov and Stechkin [7]. Recently, in two shorts notes Dunham [4, 5] has given examples of 1-parameter- and 2-parameter-sets which are Chebyshev sets but not suns (cf. also [3]). The examples refer to Chebyshev sets in containing an isolated point.
Some Results on Spiral-Like Functions
Authors: Bagşöze Türkân 
Published: December 2010

We begin with the following definitions.Let f(z) be regular near z=0 and let f(0)=0, f'(0)≠0. Let α and λ be two real numbers such that |α|<π/2 and 0≤λ1. Then Rα,λ is the largest value of r such that the following conditions are satisfied for |z|<r
A Proof of Jacobson’s Theorem
Authors: Dolan S. W. 
Published: December 2010

AbstractLet R be a ring such that, for each element a of R, there exists a positive integer n(a) > 1, depending on a, such that an(a)=a. Jacobson proved that such a ring R is necessarily commutative and the purpose of this paper is to give a proof of Jacobson’s Theorem that does not involve the use of the axiom of choice.We take this opportunity to point out that all rings are assumed to be associative and that nothing beyond elementary ring theory is assumed in the proof to follow. Such ring theory can be found, for example, in [1].
A Characterization of the Commutator Subgroup of a Group
Authors: Thierrin G. 
Published: December 2010

AbstractAn element a of a semigroup S is n-potent if there exist a1, a2,..., ak∈S such that a = a1a2...ak and If S is a group, the set of n-potent elements is a normal subgroup of S and the set of 1-potent elements is the commutator subgroup of S.
1-Cohomology and Splitting of Group Extensions
Authors: Pandya G. N. , Bercov R. D. 
Published: December 2010

The object of this note is to give simpler proofs of a splitting theorem of Gaschütz [1] and a related theorem for groups with operators by using cross-homomorphisms (1-cocycles) instead of 2-cohomology.We recall that a cross-homomorphism or 1-cocycle from a group E to an abelian normal subgroup N of E is a map f from E to N such that f(ab)=(f(a))bf(b) for all a, b ∈ E where superscript denotes conjugation. Cocycles f and h are equivalent if for some n ∈ N have h(e)=nef(e)n-1 for all e ∈ E.
The Set of Julia Points for Functions Omitting Two Values
Authors: Gauthier P. M. , Hwang J. S. 
Published: December 2010

Let f be a function denned in the unit disk D(|z| < 1). For each point eiθ on the unit circle C(|z| = 1) and each subset S of D, we denote by Cs(f, eiθ) the cluster set of f at eiθ relative to s, i.e.where N(eiθ, j) = {z∈D:|z-eiθ| <1/j}.
Note on Burde's Rational Biquadratic Reciprocity Law
Authors: Williams Kenneth S. 
Published: December 2010

A short proof is given of a biquadratic reciprocity law proved by Burde in 1969.Let p and q be primes ≡1 (mod 4) such that (p | q) = (q | p) = 1. Then there are integers a, b, c, d withSet
On Spanning and Dominating Circuits in Graphs
Authors: Lesniak-Foster L. , Williamson James E. 
Published: December 2010

AbstractA set E of edges of a graph G is said to be a dominating set of edges if every edge of G either belongs to E or is adjacent to an edge of E. If the subgraph 〈E〉 induced by E is a trail T, then T is called a dominating trail of G. Dominating circuits are defined analogously. A sufficient condition is given for a graph to possess a spanning (and thus dominating) circuit and a sufficient condition is given for a graph to possess a spanning (and thus dominating) trail between each pair of distinct vertices. The line graph L(G) of a graph G is defined to be that graph whose vertex set can be put in one-to-one correspondence with the edge set of G in such a way that two vertices of L(G) are adjacent if and only if the corresponding edges of G are adjacent. The existence of dominating trails and circuits is employed to present results on line graphs and second iterated line graphs, respectively.
Some Generalizations of an Identity of Subhankulov
Authors: Suryanarayana D. , Walker David T. 
Published: December 2010

AbstractIn 1957, M. A. Subhankulov established the following identitywhere ; μ is the Môbius function and J2 is the Jordan totient function of order 2. Since the Ramanujan trigonometrical sum C(nr) = ∑d| (n, r)dμ(r/d), we rewrite the above identity using C(n, r).In this paper, we give a generalization of Ramanujan's sum, which generalizes some of the earlier generalizations mainly due to E. Cohen, and prove a theorem from which we deduce some generalizations of the above identity.
On Sheaf Representation of a Biregular Near-Ring
Authors: Szeto George 
Published: December 2010

AbstractIt is shown that R is a biregular near-ring if and only if it is isomorphic with the near-ring of sections of a sheaf of reduced near-rings over a Boolean space. Also, some ideal properties of a biregular near-ring are proved. These are considered as generalizations of some works of R. Pierce on biregular rings.
A Helly type Theorem for Convex Sets
Authors: Katchalski Meir 
Published: December 2010

AbstractA ray in Euclidean n-dimensional space Rn is a set of the form {a + λb: λ≥ 0 } where a and b are fixed points in Rn and b≠0.The subject of this paper is a Helly type theorem for convex sets in Rn.If is a finite family of at least 2n convex sets in Rn and if theintersection of any 2n members of contains a ray then containsa ray.
The Representation of (C, k) Summable Series in Fourier Form
Authors: Cross G. E. 
Published: December 2010

Several non-absolutely convergent integrals have been defined which generalize the Perron integral. The most significant of these integrals from the point of view of application to trigonometric series are the Pn- and pn-integrals of R. D. James [10] and [11]. The theorems relating the Pn -integral to trigonometric series state essentially that if the series1.1
Order Characterization of the Complex Field
Authors: Novoa Lino Gutierrez 
Published: December 2010

It is well known that the real number field can be characterized as an ordered field satisfied the “least upper bound” property.Using the idea of n -ordered set, introduced in [3], and generalizing the notion of l.u.b. in a suitable way, it is possible to give a similar categorical definition of the complex field.With these extended meanings, the main theorem of this paper (Theorem 7 in the text) is stated almost identically to the one for the real field. Any directly two-ordered field, in which the "supremum property" holds, is isomorphic to the complex field.
Applications of Variants of the Hölder Inequality and its Inverses: Extensions of Barnes, Marshall-Olkin, and Nehari Inequalities.
Authors: Wang Chung-Lie 
Published: December 2010

The primary aim of this paper is to extend Barnes [1], Marshall-Olkin [6], and Nehari [8] inequalities as applications of some results introduced in [10] by the author.Since several results from various sources are adopted here, a unified notation is required in order to simplify our subsequent arguments. To this end, let Lp = Lp(S, ∑, μ), p>0 (unless otherwise stated), be the space of all pth power non-negative integrable functions over a given finite measure space (S, ∑, μ) (where S may be regarded as a bounded subset of real numbers).