bluuebunny/crossref_metadata_2025_split huggingface dataset:
Weyl functions and the Ap condition on compact lie groups
Authors: Travaglini Giancarlo 
Published: April 2009

AbstractLet G be a compact, simple, simply connected Lie group. The Lp-norm of a central trigonometric polynomial reduces naturally to a weighted Lp-norm of a trigonometric polynomial on a maximal torus T. The weight is | Δ |2-p, where Δ is the usual Weyl function. If p ≥ 2, we prove that | Δ |2-p satisfies Muckenhoupt's Ap condition if and only if the Lp-norms of the irreducible characters of G are uniformly bounded.
Initial and relative limiting behaviour of temperatures on a strip
Authors: Watson N. A. 
Published: April 2009

AbstractLet u be a solution of the heat equation which can be written as the difference of two non-negative solutions, and let v be a non-negative solution. A study is made of the behaviour of u(x, t)/v(x, t) as t → 0+. The methods are based on the Gauss-Weierstrass integral representation of solutions on Rn × ]0, a[ and results on the relative differentiation of measures, which are employed in a novel way to obtain several domination, non-negativity, uniqueness and representation theorems.
A central limit theorem for empirical processes
Authors: Pollard David 
Published: April 2009

AbstractThe empirical measure Pn for independent sampling on a distribution P is formed by placing mass n−1 at each of the first n sample points. In this paper, n½(Pn − P) is regarded as a stochastic process indexed by a family of square integrable functions. A functional central limit theorem is proved for this process. The statement of this theorem involves a new form of combinatorial entropy, definable for classes of square integrable functions.
Some results concerning quasiperfect numbers
Authors: Hagis Peter , Cohen Graeme L. 
Published: April 2009

AbstractNew methods are introduced here to show that if n is a quasiperfect number and ω(n) the number of its distinct prime factors, then ω(n) ≥ 7 and n > 1035, and if further 3 ∤ n then ω(n) ≥ 9 and n > 1040.
Toeplitz operators on certain weakly pseudoconvex domains
Authors: Crocker David , Raeburn Iain 
Published: April 2009

AbstractLet Ω be the weakly pseudoconvex domainand let ∂Ω be its boundary. If ϕ ∈ L∞ (∂Ω), we denote by Tϕ, the Toephtz operator with symbol ϕ acting on the Hardy space H2(∂Ω), and by J(∂Ω) the C*-subalgebra of B(H2(∂Ω)) generated by the Toeplitz operators with continuous symbol. Our main theorem asserts that J(∂Ω) contains the ideal K of all compact operators on H2(∂Ω), and that the symbol map ϕ→Tϕ induces an isomorphism of C(∂Ω) onto the quotient C*-algebra ℑ(∂Ω)/K. Similar results have been established before for other domains, and in particular when Ω is strongly pseudoconvex. The main interest of our results lies in their proofs: ours are elementary, whereas those used in the strongly pseudoconvex case depend heavily on the theory of the tangential Cauchy-Riemann operator.
The proximally continuous integrals
Authors: Sarkhel D. N. , De A. K. 
Published: April 2009

AbstractThis paper introduces certain generalization of the notions of approximate limit, continuity and derivative and of absolute continuity, of real functions, leading to generalized integrals of Perron and Denjoy types comprising the AP-integral of Burkill (1931) and Sonouchi and Utagawa (1949) and the AD-integral of Kubota (1963), respectiely. The generalizations are all substantiated by appropriate examples.
Subordinate semigroups and order properties
Authors: Kishimoto Akitaka , Robinson Derek W. 
Published: April 2009

AbstractLetSt= exp{−tH},Tt= exp{−tK}, beC0-semigroups on a Banach space. For appropriatefone can define subordinate semigroupsSft= exp{−tf(H)},Ttf= exp{−tf(K)}, onand examine order properties of the pairsS, T, andSf,Tf. If, =Lp(X;dv)we defineSt≽Tt≽ 0 ifSt−TtandTtmap non-negative functions into non-negative functions. Then forpfixed in the range 1 >p> ∞ we characterize the functions for whichSt≽Tt≽ 0 impliesSft≽Tft≽ 0 for eachLp(X;dv)and the converse is true for allLp(X;dv). Further we give irreducibility criteria for the strict ordering of holomorphic semigroups. This extends earlier results forL2-spaces.
The lateral completion of a completely distributive lattice-ordered group (revisited)
Authors: Davis Gary , McCleary Stephen H. 
Published: April 2009

AbstractThe lateral completion of a completely distributive lattice-ordered permutation group is investigated via various completions, obtained by adjoining permutations which match some elements of the given group in various ways. This makes known results on the lateral completion of a completely distributive lattice-ordered group both transparent and easy.
Locally trivial homotopy functors and their domain of representation
Authors: Alder Michael D. 
Published: April 2009

AbstractThe well known theorem of E. H. Brown on the representation of Homotopy Functors is extended to a larger domain category. This is accomplished by requiring the functor to satisfy a further condition, that of being locally trivial: the condition is both necessary and sufficient for the extension and is satisfied by functors arising from locally trivial fibre bundles such as K-theory.
Compatible tight Riesz orders on ordered permutation groups
Authors: Davis G. , Loci E. 
Published: April 2009

AbstractThe pointwise order makes the group A(Ω) of order-preserving permutations of a totally-ordered set Ω a lattice-ordered group. We give some criteria for determining the compatible tight Riesz orders on A(Ω) in the case of Ω being a totally-ordered field, and then obtain various adjunctionshellip one between tight Riesz orders on A(Ω) and certain ideals of the fixed point lattice Φ(Ω), and a second between maximal tangents and certain filters of Φ(Ω). We also establish a correspondence between tight Riesz orders and first-order properties. Finally, we make use of our results to say what we can in the case of the automorphisms of the real field, and to pose several open problems.
On the Stone-Weierstrass theorem
Authors: Ng Kung-Fu 
Published: April 2009

AbstractLet M be a vector subspace of the Banach space C(Ω) of all real-valued continuous functions on a compact space Ω, and suppose that M contains a subset L and the constant functions. Then in order that L be dense in M it is necessary and sufficient that L, M satisfy a filtering property and that each m in M can be approximated on every two points of Ω by functions in L.
On the compatibility of algebraic equations with extensions
Authors: Hule Harald , Müller Winfried B. 
Published: April 2009

AbstractIn this paper we investigate the following problem proposed by Lausch and Nöbauer: Let be a variety of universal algebras, B an algebra of and A a subalgebra of B. If a system of algebraic equations over A is solvable in , is it then solvable over B? We show that the answer is affirmative in certain varieties but negative in the general case.
Rings with dual continuous right ideals
Authors: Mohamed Saad 
Published: April 2009

AbstractIn this paper the structure of rings with dual continuous right ideals is discussed. The main result is the following: If R is a ring with (Jacobson) radical nil, and all of its finitely generated right ideals are dual continuous, then where S is a finite direct sum of local rings each of which has its radical square zero, or is a right valuation ring, T is semiprimary right semihereditary ring, and M is an (S, T)-bimodule such that all of its finitely generated T-submodules are projective. A partial converse of this result is obtained: any matrix ring of the above type with M = 0 has all of its finitely generated right ideals dual continuous.
Abelian 2-subgroups of finite symplectic groups in characteristic 2
Authors: Barry M. J. J. , Wong W. J. 
Published: April 2009

AbstractIf Sp(V) is the symplectic group of a vector space V over a finite field of characteristic p, and r is a positive integer, the abelian p-subgroups of largest order in Sp(V) whose fixed subspaces in V have dimension at least r were determined in the preceding paper, in the case p ≠ 2. Here we deal with the case p = 2. Our results also complete earlier work on the orthogonal groups.
On Modular Representation Algebras and a Class of Matrix Algebras
Authors: Renaud J-C. 
Published: April 2009

AbstractLet G be a cyclic group of prime order p and K a field of characteristic p. The set of classes of isomorphic indecomposable (K, G)-modules forms a basis over the complex field for an algebra p (Green, 1962) with addition and multiplication being derived from direct sum and tensor product operations.Algebras n with similar properties can be defined for all n ≥ 2. Each such algebra is isomorphic to a matrix algebra Mn of n × n matrices with complex entries and standard operations. The characters of elements of n are the eigenvalues of the corresponding matrices in Mn.
The degree of approximation by positive operators on compact connected abelian groups
Authors: Bloom Walter R. , Sussich Joseph F. 
Published: April 2009

AbstractIn 1953 P. P. Korovkin proved that if (Tn) is a sequence of positive linear operators defined on the space C of continuous real 2 π-periodic functions and lim Tnf = f uniformly for f = 1, cos and sin, then lim Tnf = f uniformly for all f ∈ C. Quantitative versions of this result have been given, where the rate of convergence is given in terms of that of the test functions 1, cos and sin, and the modulus of continuity of f. We extend this result by giving a quantitative version of Korovkin's theorem for compact connected abelian groups.
Attainable bounds for expectations
Authors: Seneta E. , Weber N. C. 
Published: April 2009

AbstractA simple technique for obtaining bounds in terms of means and variances for the expectations of certain functions of random variables in a given class is examined. The bounds given are sharp in the sense that they are attainable by at least one random variable in the class. This technique is applied to obtain bounds for moment generating functions, the coefficient of skewness and parameters associated with branching processes. In particular an improved lower bound for the Malthusian parameter in an age-dependent branching process is derived.
Omega-Polish spaces and measurable selections
Authors: Tu Le Van 
Published: April 2009

AbstractIn this paper, the author introduces the notion of Ω-Polish spaces (which includes the Polish spaces and a large class of Banach spaces) and extends Castaing's selection theorem (1966) for closed-valued measurable thin multifunctions from a measurable space into an Ω-Polish space. He also extends Robertson's theorem (1974) in the same way.
Combinatorial solution of certain systems of linear equations involving (0,1) matrices
Authors: Longstaff W. E. 
Published: April 2009

AbstractIf m and n are natural numbers satisfying 1 ≦ m < n let denote the least integer k such that the statement: ‘Every (0,1) matrix with n columns, with constant row-sum m, and with at least k distinct rows, has rank n’ is true. Then = +1 for m ≧ 2, n ≧ m2 + 2. Further, for 1 ≦ m < n.
Note on monoidal monads
Authors: Day B. J. 
Published: April 2009

AbstractThe representation theory of categories is used to embed each promonoidal monad in a monoidal biclosed monad. The existence of a promonoidal structure on the ordinary Eilenberg- Moore category generated by a promonoidal monad is examined. Several results by previous authors (notably A. Kock and F. E. J. Linton) are reproved and extended.
The bichromaticity of a lattice-graph
Authors: Harary Frank , Hsu Derbiau , Miller Zevi 
Published: April 2009

AbstractThe bichromaticity β(B) of a bipartite graph B has been defined as the maximum order of a complete bipartite graph onto which B is homomorphic. This number was previously determined for trees and even cycles. It is now shown that for a lattice-graph Pm × Pm the cartesian product of two paths, the bichromaticity is 2 + {mn/2}.
On transposes of nilpotent matrices over arbitrary rings
Authors: Kezlan Thomas P. 
Published: April 2009

AbstractIt is shown that if every nilpotent 2 × 2 matrix over a ring has nilpotent transpose, then the commutator ideal must be contained in the Jacobson radical, thus generalizing a result of R. S. Gupta, who considered the division ring case. Moreover, if the nilpotent elements form an ideal or if the ring satisfies a polynomial identity, then the above property of the transpose implies that in fact the commutator ideal must be nil.
Finite groups with short nonnormal chains
Authors: Spencer Armond E. 
Published: April 2009

This note is a continuation of the author's work [6], describing the structure of a finite group given some information about the distribution of the subnormal subgroups in the lattice of all subgoups.DEFINITION. An upper chain of length n in the finite group G is a sequence of subgroups of G; G = Go > G1 > … > Gn, such that for each i, Gi is a maximal subgroup of Gi-1. Let h(G) = n if every upper chain in G of length n contains a proper ( ≠ G) subnormal entry, and there is at least one upper chain in G of length (n – 1) which contains no proper subnormal entry.
Uniformly weak differentiability of the norm and a condition of Vlasov
Authors: Giles J. R. 
Published: April 2009

AbstractIn determining geometrical conditions on a Banach space under which a Chebychev set is convex, Vlasov (1967) introduced a smoothness condition of some interest in itself. Equivalent forms of this condition are derived and it is related to uniformly weak differentiability of the norm and rotundity of the dual norm.
On the fixed points of Sylow subgroups of transitive permutation groups
Authors: Herzog Marcel , Praeger Cheryl E. 
Published: April 2009

AbstractLet G be a transitive permutation group on a set Ω of n points, and let P be a Sylow p-subgroup of G for some prime p dividing ∣G∣. If P has t long orbits and f fixed points in Ω, then it is shown that f ≦ tp − ip(n), where ip(n) = p – rp(n), rp(n) denoting the residue of n modulo p. In addition, groups for which f attains the upper bound are classified.
Stability of line graphs
Authors: Grant Douglas D. 
Published: April 2009

AbstractWe present in this paper a discussion on some stability properties of line graphs. After relating the semi-stability properties of the line graph of a graph to a concept of Sheehan, we proceed to deduce that, with fully characterised lists of exceptions, the line graphs of trees and unicyclic graphs are semi-stable. We then discuss the problem of deciding which line graphs are stable. Via a discovery of the finite number of graphs G such that both G and its complement have stable line graphs, we show that P4 is the only self-complementary graph whose line graph is stable.
The chromatic number of the sphere
Authors: Simmons Gustavus J. 
Published: April 2009

AbstractErdös, Harary and Tutte have defined the chromatic number of the plane to be the least number of sets partitioning the plane such that no set contains two points at unit distance apart. By analogy, the chromatic number χ(S1), of the sphere, Sr of radius r is defined to be the least number of sets partitioning the surface of Sr such that no set contains two points at unit chordal distance apart. In this paper it is proven that and that this bound is best possible since .
On the boundedness of multiplicative and positive functionals
Authors: Husain Taqdir , Ng Shu-Bun 
Published: April 2009

AbstractLet A be a complex sequentially complete, locally convex (not necessarily commutative) topological algebra with the defining family {pα}α∈D of seminorms in which (*): for each sequence xn → 0 there exists xm ∈ {xn} such that xmk → 0 as k → ∞. Then each multiplicative linear functional on a Fréchet algebra satisfying the above condition (*) is Continuous.These results answer open questions (1) and (2) (Mem. Amer. Math. Soc. 11, 1953) in the affirmative for Fréchet algebras in which (*) holds. It is also shown that a positive linear functional on such algebras with identity and continuous involution is continuous, thus partially generalizing Shah's result (1959).
Dirichlet-finite outer functions
Authors: Yamashita Shinji 
Published: April 2009

AbstractGiven a measurable function k non-negative a.e. on the circle |z| = 1, when is the outer function Tk (see(1.3)) continuous on the disk |z| < 1 and further, Dirichlet-finite: We shall show, among other results, that the answer is in the positive if , with ess inf k > 0.
Imperfect bifurcation and Banach space singularity theory
Authors: Arkeryd Leif 
Published: April 2009

AbstractThis paper generalizes the theory of imperfect bifurcation via singularity theory as developed by M. Golubitsky and D. Schaeffer to a Banach space setting. Like the parameter-free potential catastrophe theory, where similar generalizations have been discussed in the literature, Banach control spaces allow useful uniform control of function parameters through the universal unfolding. Among the results are tests for various germ properties and discussion of their reducibility under a Liapunov—Schmidt type splitting, as well as a generalization of the finite dimensional unfolding and germ classification theory.
A congruence-free inverse semigroup associated with a pair of infinite cardinals
Authors: Howie J. M. 
Published: April 2009

AbstractLet m, n be infinite cardinals such that m < n, and let X be a set of cardinality m. Within the symmetric inverse semigroup on X the elements whose domain and range have complements of cardinality m form an inverse semigroup T. The closure Eω of the semilattice E of idempotents of T is a fundamental bismple inverse semigroup. Its maximum congruence is described. The quotient of Eο by this maximum congruence is a bisimple, congruence is a bisimple, congruence-free inverse semigroup.
The Boolean ring universal over a meet semilattice
Authors: Evans Elliot 
Published: April 2009

AbstractThe Boolean ring B{M} universal over a meet semilattice M is examined. It is the vector space over the two element field Z2 with base M\{0}. The Z2 linear independence of a meet subsemilattice of a Boolean ring is characterized in order theoretic terms and some ramifications of this on B[M] are considered. The space (ℱpM) of proper filters of M is shown homeomorphic to the Stone space S(B[M]) of B[M] if M has no least element, with ℱP(M) ∪ {M} and S(B[M]) homeomorphic otherwise. The congruence lattice θ(M) of M is compared to the ideal lattice ℱ(B [M]) of B [M] with best results coming if M is a tree with zero when θ (M) = ℐ (B [M]).
Random semigroup acts on a finite set
Authors: Högnäs Göran 
Published: April 2009

AbstractLetXbe a finite set andSa semigroup of transformations ofX. We investigate the trace onXof a random walk onS. We relate the structure of the trace process, which turns out to be a Markov chain, to that of the random walk. We show, for example, that all periods of the trace process divide the period of the random walk.
Rearranging measures
Authors: Brown G. , Williamson J. H. 
Published: April 2009

AbstractA churning transformation can be defined on probability measures by an infinite sequence of finite permutations of mass. Continuity and absolute continuity of measures are invariants for such transformations but it is shown that certain probability measures whose Fourier-Stieltjes transforms fail to vanish at infinity may be churned into measures whose transforms do vanish in this sense.
Strictly positive and strongly positive semigroups
Authors: Majewski Adam , Robinson Derek W. 
Published: April 2009

AbstractWe examine positive semigroups acting on Banach lattices and operator algebras. In the lattice framework we characterize strict positivity and strict ordering of holomorphic semigroups by irreducibility criteria. In the algebraic setting we derive ergodic criteria for irreducibility and discuss various aspects of strict positivity. Finally we examine invariant states of a C*-dynamical system in which the automorphism group is replaced by a strongly positive semigroup. We demonstrate that ergodic states are characterized by a cluster property despite the absence of a covariant implementation law for the semigroup.
Elementary abelian operator groups and admissible formations
Authors: Gross Fletcher 
Published: April 2009

AbstractSuppose the elementary abelian group A acts on the group G where A and G have relatively prime orders. If CG(a) belongs to some formation F for all non-identity elements a in A, does it follow that G belongs to F? For many formations, the answer is shown to be yes provided that the rank of A is sufficiently large.
The distributive lattice free product as a sublattice of the abelianl-group free product
Authors: Powell Wayne B. , Tsinakis Constantine 
Published: April 2009

AbstractThis paper establishes an important link between the class of abelianl-groups and the class of distributive lattices with a distinguished element. This is accomplished by describing the distributive lattice free product of a family of abelianl-groups as a naturally generated sublattice of their abelianl-group free product.
Best Diophantine approximations to a set of linear forms
Authors: Lagarias J. C. 
Published: April 2009

AbstractWe define the notion of a best Diophantine approximation vector to a set of linear forms. This generalizes definitions of a best approximation vector to a single linear form and of a best simultaneous Diophantine approximation vector. We derive necessary and sufficient conditions for the existence of an infinite set of best Diophantine approximation vectors. Finally, we prove that such approximation vectors are spaced far apart in an appropriate sense.
On primitive abundant numbers
Authors: Cohen Graeme L. 
Published: April 2009

AbstractLetnbe a natural with largest componentsd. We prove that ifxσ(n) =yn+z(x, y, zgiven positive integers),nis not primitive (y/x)-abundant andn/sis not (y/x)-perfect, thenn< 4(z+ ½)3/27y(ifz≥ 175). All solutions are tabled for the equationxσ(n) -ynwhenx= 1,y≥ 2, 1 ≤z≤ 210, andnis not primitivey-abundant. We also prove that ifnis primitive (y/x)-abundant, thens3d< (yn/2)2. A number of results are proved concerning the range of σ(n)/nwhennis primitive αabundant, for any real number α > 1. For example, then α(n/n< α + min {½ 3 αe-5a/9/2) and σ(n)/n< α /1.6α/logn. All primitive abundant numbersnwith α(n)/ ≥ 2.05 are listed.
The number of solutions to an equation arising from a problem on latin squares
Authors: Goulden I. P. , Vanstone S. A. 
Published: April 2009

AbstractA recent article of G. Chang shows that an n × n partial latin square with prescribed diagonal can always be embedded in an n × n latin square except in one obvious case where it cannot be done. Chang's proof is to show that the symbols of the partial latin square can be assigned the elements of the additive abelian group Zn so that the diagonal elements of the square sum to zero. A theorem of M. Halls then shows this to be embeddable in the operation table of the group. In this paper, we show that when n is a prime one can determine exactly the number of distinct ways in which this assignment can be made. The proof uses some graph theoretic techniques.
Ordinary differential equations
Authors: Coppel W. A. 
Published: April 2009

This is the text and invited lecture given at the 20th Annual Meeting of the Australian Mathematical Society in Perth, May 1976.In this talk I want to give a survey of some of the areas of research in ordinary differential equations. In view of the vastness of the field, the limited thime available and may own inadequacies I will restrict attention to problems in which I have been involved in some way, although I won't be speaking about my own work. Even with this restriction it will be necessary to be somewhat superficial. However, in spite of all these drawbacks, I thought it would assist communication among mathematicians simply to have an idea of what other people are doing. Since this is my purpose I will not mention the quite mild smoothness hypotheses in the statements of some results.