bluuebunny/crossref_metadata_2025_split huggingface dataset:
Spreadable arrays and martingale structures
Authors: Ivanoff B. Gail , Weber N. C. 
Published: April 2009

AbstractKallenberg has introduced the concept of conditional spreadability for random sequences and has developed characterizations of this property in terms of one dimensional martingales and optional times, and as well has proven a predictable sampling theorem. This paper investigates the relationship between planar martingale structures and the natural analogues of conditional spreadability when extended to arrays of random elements. Analogues of the predictable sampling theorem are also established for spreadable arrays.
Maximal transference and summability of multilinear Fourier series
Authors: Grafakos Loukas , Honzík Petr 
Published: April 2009

AbstractWe obtain a maximal transference theorem that relates almost everywhere convergence of multilinear Fourier series to boundedness of maximal multilinear operators. We use this and other recent results on transference and multilinear operators to deduce Lp and almost everywhere summability of certain m–linear Fourier series. We formulate conditions for the convergence of multilinear series and we investigate certain kinds of summation.
Some completely monotonic functions involving the gamma and polygamma functions
Authors: Qi Feng , Guo Bai-Ni , Chen Chao-Ping 
Published: April 2009

AbstractThe function [Γ(x + 1)]1/x(1 + 1/x)x/x is strictly logarithmically completely monotonic in (0, ∞). The function ψ″ (x + 2) + (1 + x2)/x2(1 + x)2 is strictly completely monotonic in (0, ∞).
On p-adic L-functions and elliptic units
Authors: Coates J. , Wiles A. 
Published: April 2009

AbstractThe aim of the paper is to prove an elliptic analogue of a deep theorem of Iwasawa on cyclotomic fields.Subject classification(Amer. Math. Soc. (MOS) 1970): primary 12 A 35, 12 A 65.
A commutator identity for basic p-groups
Authors: Weichsel Paul M. 
Published: April 2009

AbstractThe consequences of the law (Ga(1), hellip, Ga(n)) = 1 in a basic p-group are examined. The principal tools are a combinatorial analysis of the lattice of n-tuples of positive integers and a theorem of the author about higher-commutator subgroups.Subject classification (Amer. Math. Soc. (MOS) 1970): 20 D 15.
Hamiltonian cycles in certain graphs
Authors: Heinrich Katherine , Wallis W. D. 
Published: April 2009

AbstractIt is observed that arrays which arise in the scheduling of tournaments exist if and only if there are Hamiltonian cycles in certain graphs. The graphs are generalizations of those which arise in the “Footballers of Croam” problem. It is proven that such Hamiltonian cycles exist in infinite classes of the graphs.Subject classification (Amer. Math. Soc. (MOS) 1970): 05 C 35, 05 B 30.
Chebyshev subspaces of finite codimension in spaces of continuous functions
Authors: Brown A. L. 
Published: April 2009

AbstractA. L. Garkavi in 1967 characterized those compact metric spaces X with the property that the space C(X) of real-valued continuous functions possesses Chebyshev subspaces of fine codimension ≥ 2. Here compact Hausdorif spaces with the same property are characterized in terms of certain standard subspaces of the space [0, 1] × {0, 1} equipped with a lexicographic order topology. Garkavi's result for metric spaces is exhibited as a corollary. The proof depends upon a simplification of a characterization by Garkavi of the Chebyshev subspaces of finite codimension in C(X).Subject classification (Amer. Math. Soc. (MOS) 1970): primary 41 A 65, 46 E 15; secondary 54 G 99.
On Fan's extensions of Browder's fixed point theorems for multi-valued inward mappings
Authors: Lee Cheng-Ming , Tan Kok-Keong 
Published: April 2009

AbstractSome fixed point theorems are obtained for weekly inward mappings which extend or generalize those results by K. Fan, B. Halpern or S. Reich. Various formulations of inward and outward concepts are also briefly discussed.
Rigid cohomology of topological groupoids
Authors: MacKenzie K. A. 
Published: April 2009

AbstractA cohomology theory for locally trivial, locally compact topological groupoids with coefficients in vector bundles is constructed, generalizing constructions of Hochschild and Mostow (1962) for topological groups and Higgins (1971) for discrete groupoids. It is calculated to be naturally isomorphic to the cohomology of the vertex groups, and is thus independent of the twistedness of the groupoid. The second cohomology space is accordingly realized as those “rigid” extensions which essentially arise from extensions of the vertex group; the cohomological machinery now yields the unexpected result that in fact all extensions, satisfying some natural weak conditions, are rigid.
On semigroups of endomorphisms of biregular algebras
Authors: Yzung Fu-Chien 
Published: April 2009

AbstractLet A be a finite dimensional algebra over a field F. Let R and S be biregular algebras over F such that 1R ∈ R and 1S ∈ S. We show that if R/P≃A≃ S/M for each primitive ideal P in A and each primitive ideal M in S then End FR≃ End S implies R≃S.
Radicals related to the Brown-McCoy radical in some varieties of algebras
Authors: Gardner B. J. 
Published: April 2009

AbstractThe Brown-McCoy radical is the upper radical defined by the class of simple rings with identities. For associative or alternative rings the Brown-McCoy radical is hereditary, and its semi-simple class consists of all subdirect products of simple rings with identities. In this paper we present some classes of simple non-associative algebras whose upper radicals behave similarly. Classifications are then obtained of ‘most’ semi-simple radical classes of (γ, δ) and right alternative rings.
Special pairs of semi-bilogic and bilogic tetrahedra
Authors: Mandan Sahib Ram 
Published: April 2009

AbstractLet (A), (B) be a special pair of perspective tetrahedra such that the 4 joins of their corresponding vertices are perpendicular to their plane of perspectivity. It has been already established (Mandan (1977a), p. 573) that they are, in general, skew-orthologic such that the perpendiculars from the vertices of one to the corresponding opposite faces of the other lie in a regulus. Here we give a construction of a special pair of semi-orthologic and orthologic tetrahedra, the said regulus degenerating into 2 pairs of intersecting lines and 4 concurrent lines respectively. Following Thébault ((1952), p. 25; (1955), p. 67), we call them semi-bilogic and bilogic respectively.
Certain generalizations of presetarlike functions
Authors: Al-Amiri H. S. 
Published: April 2009

AbstractThe classes of prestarlike functionsRα, α ≧ – 1, were studied recently by St. Ruscheweyh. The author generalizes and extends these classes. In particular the author obtains the radius ofRa+1for the classRα, α ≧ –1.
Inertial subalgebras of algebras possessing finite automorphism groups
Authors: Ford Nicholas S. 
Published: April 2009

AbstractLet R be a commutative ring with identity, and let A be a finitely generated R-algebra with Jacobson radical N and center C. An R-inertial subalgebra of A is a R-separable subalgebra B with the property that B+N=A. Suppose A is separable over C and possesses a finite group G of R-automorphisms whose restriction to C is faithful with fixed ring R. If R is an inertial subalgebra of C, necessary and sufficient conditions for the existence of an R-inertial subalgebra of A are found when the order of G is a unit in R. Under these conditions, an R-inertial subalgebra B of A is characterized as being the fixed subring of a group of R-automorphisms of A. Moreover, A ⋍ B ⊗R C. Analogous results are obtained when C has an R-inertial subalgebra S ⊃ R.
Radical properties defined locally by polynomial identities I
Authors: Gardner B. J. 
Published: April 2009

AbstractBijective correspondences are established between the radical classes R (in a variety W of rings) with the property that a ring A is in R exactly when its finitely generated subrings are all in R, and certain filters of ideals in a free W-ring. It follows that such classes are determined by the polynomial identities satisfied by the finite subsets of their members. Analogous considerations are applied to radical classes R which, for a fixed integer n, have the property that a ring is in R if and only if its subrings generated by at most n elements are in R.
Flat spots on unit spheres
Authors: Van Dulst D. 
Published: April 2009

AbstractA flat spot in a Banach space X is an element x ∈ Sx = {x ∈ X: ‖x‖ = 1} with the property that the infimum m(x) of the lengths of all curves in Sx joining x to −x is 2. Flat spots occur in every non-superreflexive space when suitably renormed. A study is made of the geometric implications of the existence of flat spots. Connections with other notions such as differentiability, decomposition constants and Kadec-Klee norms are explored and some renorming results for non-superreflexive spaces are proved.
Multidimensional Volterra integral equations of convolution type
Authors: Laird P. G. 
Published: April 2009

AbstractIn this article, it is shown that the Volterra integral equation of convolution type w − w⊗g = f has a continuous solution w when f, g are continuous functions on Rx and ⊗ denotes a truncated convolution product. A similar result holds when f, g are entire functions of several complex variables. Also simple proofs are given to show when f, g are entire, f⊗g is entire, and, if f⊗g=0, then f = 0 or g = 0. Finally, the set of exponential polynomials and the set of all solutions to linear partial differential equations are considered in relation to this convolution product.
Residual finiteness and ‘free’ distributively generated near-rings
Authors: John David J. 
Published: April 2009

AbstractLet V be a variety of groups in which the free group is residually finite, and let S be a residually finite semigroup. Let Nv(S) be the ‘free’ distributively generated near-ring constructed from S and V. Theorem; Nv(S) is residually finite.
Nilpotents and units in skew polynomial rings over commutative rings
Authors: Rimmer M. , Pearson K. R. 
Published: April 2009

AbstractLet R be a commutative ring with an automorphism ∞ of finite order n. An element f of the skew polynomial ring R[x, α] is nilpotent if and only if all coefficients of fn are nilpotent. (The case n = 1 is the well-known description of the nilpotent elements of the ordinary polynomial ring R[x].) A characterization of the units in R[x, α] is also given.
Completions of certain nilpotent groups
Authors: Moran Siegfried , Williams Janet 
Published: April 2009

AbstractThe completions of certain nilpotent groups with respect to some ascending sequences of integral domains are constructed. These completions are generalizations of Lazard completions for the groups under consideration and they are Lie algebras over the first integral domain in the sequence. The construction is possible in particular for finite p-groups of exponent p and class < p.
A one-step method for the numerical solution of ordinary non-linear second-order differential equations based upon lobatto four-point quadrature formula
Authors: Sharma K. D. , Gupta R. G. 
Published: April 2009

AbstractThis paper describes a one-step method besed upon the Lobatto four-point quadreture formula for the numerical integration of differential: y″(x) = f(x, y(x), y'(x)); y(x0)=y0, y'(x0)=y'0. The method has a local truncation error 0(h6) in y(x) and 0(h5) in y′(x). In the case of linear second-order differential equation, a stability criterion has been developed. Theoretical and computational comparisons of the new method existing method is discussed.
On semiprime segments of rings
Authors: Mazurek R. , Törner G. 
Published: April 2009

AbstractA semiprime segment of a ring R is a pair P2 ⊂ P1 of semiprime ideals of R such that ∩ In ⊆ P2 for all ideals I of R with P2 ⊂ I ⊂ P1. In this paper semiprime segments with P1 a comparizer ideal are classified as either simple, exceptional, or archimedean, extending to several classes of rings a classification known for right chain rings. These three types of semiprime segments are also characterized in terms of the pseudo-radical.
On transitive commutative idempotent quasigroups
Authors: Neumaier Arnold 
Published: April 2009

AbstractCommutative idempotent quasigroups with a sharply transitive automorphism group G are described in terms of so-called Room maps of G. Orthogonal Room maps and skew Room maps are used to construct Room squares and skew Room squares. Very general direct and recursive constructions for skew Room maps lead to the existence of skew Room maps of groups of order prime to 30. Also some nonexistence results are proved.
On groups with all subgroups almost subnormal
Authors: Detomi Eloisa 
Published: April 2009

AbstractIn this paper we consider groups in which every subgroup has finite index in the nth term of its normal closure series, for a fixed integer n. We prove that such a group is the extension of a finite normal subgroup by a nilpotent group, whose class is bounded in terms of n only, provided it is either periodic or torsion-free.
On the orders of conjugacy classes in group algebras ofp-groups
Authors: Bovdi A. , Kovács L. G. , Mihovski S. 
Published: April 2009

AbstractLetpbe a prime,a field ofpnelements, andGa finitep-group. It is shown here that ifGhas a quotient whose commutator subgroup is of orderpand whose centre has indexpk, then the group of normalized units in the group algebrahas a conjugacy class ofpnkelements. This was first proved by A. Bovdi and C. Polcino Milies for the casek= 2; their argument is now generalized and simplified. It remains an intriguing question whether the cardinality of the smallest noncentral conjugacy class can always be recognized from this test.
On the chromatic number of plane tilings
Authors: Coulson D. 
Published: April 2009

AbstractIt is known that 4 ≤ x(ℝ2) ≤ 7, where x(ℝ2) is the number of colour necessary to colour each point of Euclidean 2-space so that no two points lying distance 1 apart have the same colour. Any lattice-sublattice colouring sucheme for R2 must use at least 7 colour to have an excluded distance. This article shows that at least 6 colours are necessary for an excluded distance when convex polygonal tiles (all with area greater than some positive constant) are used as the colouring base.
Some regularity estimates for convolution semigroups on a group of polynomial growth
Authors: Dungey Nick 
Published: April 2009

AbstractWe study a convolution semigroup satisfying Gaussian estimates on a groupGof polynomial volume growth. IfQis a subgroup satisfying a certain geometric condition, we obtain high order regularity estimates for the semigroup in the direction ofQ. Applications to heat kernels and convolution powers are given.
Relative amenability and the non-amenability of B(l1)
Authors: Read C. J. 
Published: April 2009

AbstractIn this paper we begin with a short, direct proof that the Banach algebraB(l1) is not amenable. We continue by showing that various direct sums of matrix algebras are not amenable either, for example the direct sum of the finite dimensional algebrasis no amenable for 1 ≤p≤ ∞,p≠ 2. Our method of proof naturally involves free group algebras, (by which we mean certain subalgebras ofB(X)for some spaceXwith symmetric basis—not necessarilyX = l2) and we introduce the notion of ‘relative amenability’ of these algebras.
Valuated Butler groups of finite rank
Authors: Fuchs L. , Rangaswamy K. M. 
Published: April 2009

AbstractValuated Butler groups of finite rank are investigated. The valuated B2-groups are both epic images and pure subgroups of completely decomposable valuated groups of finite rank (Theorem 3.1). However, there are fundamental changes in the theory of Butler groups when valuations are involved. We introduce valuated B1-groups and show that they are valuated B2-groups. Surprisingly, valuated B2-groups of rank greater than 1 need not be valuated B1 -groups, unless they carry a special kind valuation, see Theorem 7.1. Theorem 6.5 gives a full characterization of valuated B1 -groups of finite rank, generalizing Bican's characterization of Butler groups.
Characterizing rings by a direct decomposition property of their modules
Authors: Huynh Dinh Van , Rizvi S. Tariq 
Published: April 2009

AbstractA module M is said to satisfy the condition (℘*) if M is a direct sum of a projective module and a quasi-continuous module. In an earlier paper, we described the structure of rings over which every (countably generated) right module satisfies (℘*), and it was shown that such a ring is right artinian. In this note some additional properties of these rings are obtained. Among other results, we show that a ring over which all right modules satisfy (℘*) is also left artinian, but the property (℘*) is not left-right symmetric.
Omitted rays and wedges of fractional Cauchy transforms
Authors: Hibschweiler R. A. , Macgregor T. H. 
Published: April 2009

AbstractFor α > 0 let α denote the set of functions which can be expressed where μ is a complex-valued Borel measure on the unit circle. We show that if f is an analytic function in Δ = {z ∈ : |z| < 1} and there are two nonparallel rays in /f(Δ) which do not meet, then f ∈ α where απ denotes the largest of the two angles determined by the rays. Also if the range of a function analytic in Δ is contained in an angular wedge of opening απ and 1 < α < 2, then f ∈ α.
Free algebras in varieties of BL-algebras generated by a BLn-chain
Authors: Busaniche Manuela , Cignoli Roberto 
Published: April 2009

AbstractFree algebras with an arbitrary number of free generators in varieties of BL-algebras generated by one BL-chain that is an ordinal sum of a finite MV-chain Ln, and a generalized BL-chain B are described in terms of weak Boolean products of BL-algebras that are ordinal sums of subalgebras of Ln, and free algebras in the variety of basic hoops generated by B. The Boolean products are taken over the Stone spaces of the Boolean subalgebras of idempotents of free algebras in the variety of MV-algebras generated by Ln.2000 Mathematics subject classification: primary 03G25, 03B50, 03B52, 03D35, 03G25, 08B20.
A note on upper radicals in rings
Authors: Leavitt W. G. 
Published: April 2009

AbstractA class (calledc-radicals) is defined such that, given ac-radicalP, there is in any classM′ a certain internal criterion that its upper radicalUM′ =P, ForPa non-c-radical (called aq-radical) there exists no smallest classMsuch thatUM=P, andPis aq-radical if and only if for someMwithP=UMthere exists 0 ≠R∈Msuch that when an image¯ ofRhas a non-zero image inMthere exists an infinite chain of epimorphisms¯ →R1→R2→ … with allR1∈Mand noRi, the image of anyRj, withj>i. Several examples of such rings are constructed including a ring all of whose images are primitive. Thus all radicals contained in the Jacobson radical areq-radicals.
Oscillatory and asymptotic properties of homogeneous and nonhomogeneous delay differential equations of even order
Authors: Terry Raymond D. 
Published: April 2009

AbstractIn this paper we consider the (non)oscillation properties of two general nonhomogeneous nonlinear delay differential equations of order 2n using as background and motivation the techniques previously applied to the associated homogeneous delay differential equations H+ and H−. The equations N+ and N− are each reduced to homogeneous form by the introduction of transformations u(t) = y(t) – R(t) and v(t) = R(t) — y(t), where R(t) is a solution of the associated nonhomogeneous differential equation (N). We first extend certain results for the equation H+ and then develop a classification of the positive solutions of equation H−. Using this classification and the one developed by Terry (1974) for H+ we develop a natural classification of the positive solutions of N+ and N− according to the sign properties of the derivatives of u(t) and v(t). For each choice of R(t), it is seen that there are 2n + 1 types of positive solutions of N+or N–. An intermediate Riccati transformation is employed to obtain integral criteriafor the nonexistence of some of these solutions. Analysis of the Taylor remainder results in sufficient conditions for the nonexistence of other such solutions.
A 4-chromatic graph with a special plane drawing
Authors: Wormald Nicholas 
Published: April 2009

AbstractA graph is found which is 4-chromatic, has girth 5, and can be obtained by taking a setSof points in the plane and joining two of the points whenever their distance is 1. The points inSare not found explicitly, but their existence is demonstrated by use of a computer.Subject classification (Amer. Math. Soc. (MOS) 1970): 05 C 15, 05 C 10.
Extremal graphs of diameter 3
Authors: Caccetta L. 
Published: April 2009

AbstractThis paper is concerned with graphs of order n and diameter at most 3 having the property that by deleting any s or fewer vertices (edges) the resulting subgraphs (partial graphs) have duameter at most. λ. A graph satisfying the above constraints and having minimum number of edges is said to be extramal. A characterization of extremal graphs is presented for the case s = 1.Subject classification (Amer. Math. Soc. (MOS) 1970): 05 C 35.
On product varieties of inverse semigroups
Authors: Bales J. L. 
Published: April 2009

AbstractThis paper extends results on product varieties of groups to inverse semigroups. We show that if is a variety of groups and any inverse semigroup variety, then ∘ is a variety. We give a characterization of the identities of∘in terms of the identities of and ofWe show that if does not contain the variety of all groups then it has uncountably many supervarieties. Finally we show that ifis another variety of groups then Subject classifiaction (Amer. Math. Soc. (MOS) 1970): 20 M 05.
The free centre-by-metabelian groups
Authors: Gupta Chander Kanta 
Published: April 2009

Let be the free centre-by-metabelian group of rank n. In this paper, our main result is the followingTheorem. For n ≧ 4, Gn has a finite elementary abelian subgroup Hn of rank . More precisely, Hn is a minimal fully invariant subgroup contained in the centre of Gn and Gn/Hn is isomorphic to a group of 3 x 3 matrices over a finitely generated integral domain of characteristic zero.
On the solubility of a product of permutable subgroups
Authors: Lennox John C. 
Published: April 2009

AbstractConditions are investigated under which a product G = HK of soluble subgroups H, K, each permutable in G, is soluble. It is shown in particular that this is true if one of the subgroups is nilpotent or if H ∩ K is subnormal in both H and K.
Heat Kernels on homogeneous spaces
Authors: Smulders C. M. P. A. 
Published: April 2009

AbstractLet a1… adbe a basis of the Lie algebragof a connected Lie groupGand letMbe a Lie subgroup of,G. Ifdxis a non-zero positive quasi-invariant regular Borel measure on the homogeneous spaceX = G/MandS: X × G→ C is a continuous cocycle, then under a rather weak condition ondxandSthere exists in a natural way a (weakly*) continuous representationUofGinLp(X;dx) for allp ε[1,].Let Aibe the infinitesimal generator with respect toUand the directionai, for alli∈ { 1… d}. We considern–th order strongly elliptic operatorsH= ΣcαAαwith complex coefficientscα. We show that the semigroupSgenerated by the closure ofHhas a reduced heat kernelKand we derive upper bounds forkand all its derivatives.
Decomposability of finite rings
Authors: Mainwaring Diane , Pearson K. R. 
Published: April 2009

AbstractLet p be a prime, let R be a finite p-ring with identity and suppose that the radical of R has pm elements. If R is indecomposable as a ring then there are at most m+1 minimal ideals in R/Rad R.1980 Mathematics subject classification (Amer. Math. Soc): 16 A 44.