bluuebunny/crossref_metadata_2025 huggingface dataset:
Weakly prime left ideals in general rings
Authors: France-Jackson Halina
Published: April 2009

A.P.J. van der Walt introduced the concept of a weakly prime left ideal of an associative ring with unity. It is the purpose of the present paper to extend to general, that is not necessarily with unity associative rings, this concept as well as almost all results of van der Walt for rings with unity.
A Strengthened topological cardinal inequality
Authors: Shu-Hao Sun , Yan-Ming Wang
Published: April 2009

A new cardinal inequality, |K (X)| ≤ 2L∗(X) · psw (X), is proved in this paper. It strengthens the result of D.K. burke and R. Hodel the |K (X)| ≤ 2e (X) · psw (X).
Finite groups with large centralizers
Authors: Bertram Edward A. , Herzog Marcel
Published: April 2009

It is known that a finite non-abelian group G has a proper centralizer of order if, for example, |G| is even and |Z(G)| is odd, or whenever G is solvable. Often the exponent can be improved to , for example when G is supersolvable, or metabelian, or |G = pαqβ. Here we show more generally that this improvement is possible in many situations where G is factorizable into the product of two subgroups. In particular, much more evidence is presented to support the conjecture that some proper centralizer has order whenever G is a finite non-abelian solvable group.
Global dimensions of right coherent rings with left Krull dimension
Authors: Teply Mark L.
Published: April 2009

The weak global dimension of a right coherent ring with left Krull dimension α ≥ 1 is found to be the supremum of the weak dimensions of the β-critical cyclic modules, where β < α. If, in addition, the mapping I → assl gives a bijection between isomorphism classes on injective left R-modules and prime ideals of R, then the weak global dimension of R is the supremum of the weak dimensions of the simple left R-modules. These results are used to compute the left homological dimension of a right coherent, left noetherian ring. Some analogues of our results are also given for rings with Gabriel dimension.
A variational-like inequality problem
Authors: Parida J. , Sahoo M. , Kumar A.
Published: April 2009

Given a closed and convex set K in Rn and two continuous maps F: K → Rn and η: K × K → Rn, the problem considered here is to find ε K such that

.

We call it a variational-like inequality problem, and develop a theory for the existence of a solution. We also show the relationship between the variational-like inequality problem and some mathematical programming problems.
A note on subnormal defect in finite soluble groups
Authors: Bryce R.A.
Published: April 2009

It is shown that for every positive integernthere exists a finite group of derived lengthnin which all Sylow subgroups are abeian and in which the defect of subnormal subgroups is at most 3.
Every chaotic interval map has a scrambled set in the recurrent set
Authors: Du Bau-Sen
Published: April 2009

Let I denote a compact real interval and let f ∈ C0(I, I). In this note we show that if f chaotic in the sense of Li and Yorke, then there is an uncountable perfect δ-scrambled set S for f in the recurrent set of f. Furthermore, the ω-limit set of every x ∈ S under f contains S and contains infinitely many periodic points of f with arbitrarily large periods.
Invariant quadratic forms on finite dimensional lie algebras
Authors: Hofmann Karl H. , Keith Verena S.
Published: April 2009

Trace forms have been well studied as invariant quadratic forms on finite dimensional Lie algebras; the best known of these forms in the Cartan-Killing form. All those forms, however, have the ideal [L, L] ∩ R (with the radical R) in the orthogonal L⊥ and thus are frequently degenerate. In this note we discuss a general construction of Lie algebras equipped with non-degenerate quadratic forms which cannot be obtained by trace forms, and we propose a general structure theorem for Lie algebras supporting a non-degenerate invariant quadratic form. These results complement and extend recent developments of the theory of invariant quadratic forms on Lie algebras by Hilgert and Hofmann [2], keith [4], and Medina and Revoy [7].
Generalised Gaussian Fibonacci numbers
Authors: Pethe S. , Horadam A.F.
Published: April 2009

In this paper, generalised Gaussian Fibonacci numbers are defined and, using the recurrence relation satisfied by them, we obtain a number of summation identities involving the products of combinations of Fibonacci, Pell and Chebyshev polynomials.
A family of Hurwitz groups with non-trivial centres
Authors: Conder Marston
Published: April 2009

In this paper a new family of quotients of the triangle group < x, y, z | x2 = y3 = z7 = xyz = 1 > is obtained. It is shown that for every positive integer m divisible by 3 there is a Hurwitz group of order 504m6 having a centre of size 3, and as a consequence there is a Riemann surface of genus 6m6 + 1 with the maximum possible number of automorphisms.
A new proof of Laguerre's theorem about the zeros of polynomials
Authors: Aziz Abdul
Published: April 2009

An elementary new, simple and purely analytic proof of Laguerre's theorem about the zeros of the polar derivative of a polynomial P(z) with respect to the point α, is given. The proof is based on a lemma which is also of independent interest.
Automorphisms of homogeneous C*-algebras
Authors: Thomsen Klaus
Published: April 2009

For a homogeneous C*-algebra we identify the quotient of the automorphism group by the locally unitary automorphisms as a subgroup of the homeomorphisms of the spectrum. We sharpen a known criterion on the spectrum that ensures that all locally unitary automorphisms of the algebra are inner.
Extensions of Jensen's inequality on the unit circle
Authors: Nakazi Takahiko
Published: April 2009

The purpose of this note is to give extensions of an inequality of Jensen for analytic functions in an unit disc. We investigate functions which satisfy equalities in the inequalities.
On adjoints of non-linear mappings
Authors: Pombo Dinamérico P.
Published: April 2009

Amply boundedness of collections of analytic mappings is proved to be equivalent to equicontinuity of the corresponding collections of adjoints, for certain classes of locally convex spaces which have good analytic properties.
A preemptive priority queue with a general bulk service rule
Authors: Sivasamy R.
Published: April 2009

In this paper a single server preemptive priority queueing system, consisting of two types of units, with unlimited Poisson inputs and exponential service time distributions, is studied. The higher priority units are served in batches according to a general bulk service rule and they have preemptive priority over lower priority units. Steady state queue length distributions, stability condition and the mean queue lengths are obtained.
Simple groups of small Engel depth
Authors: Brandl Rolf , Nikolova Daniela B.
Published: April 2009

It is proved that the simple group PSL (2,q) satisfies a law [x,3y] = [x, sy], s > 3, if and only if q = 4, 5, 8.
A note on the coefficients of mixed normed spaces
Authors: Kwon E. G.
Published: April 2009

For 0 < P,q < ∞, α> −1, Ap,q,α denotes the space of all holomorphic functions in the unit disc satisfying

where

In this paper, we find a sufficient condition for the multipliers from AP,q,α into ls, 1 ≤ s ≤ ∞, 1 ≤ q ≤ 2, which interpolates the results of Patrick Ahern and Miroljub Jevtic. As a corollary, we can calculate

for q′ ≤ s ≤ ∞, 1/q + 1/q′ = 1. Also, we can find a sharp coefficient condition for HP functions.
Weighted function algebras on groups and semigroups
Authors: Dzinotyiweyi Heneri A. M.
Published: April 2009

For a locally compact topological group admitting a weight function, we establish necessary and sufficient criteria for all the weighted continuous functions to be weakly almost periodic. Among other results, we show that weak almost periodicity of all ω-weighed continuous functions on a discrete semigroup S, can be very different drom the phenomenon of regularity of multiplication in the weighted algebra ℓ1 (S, w).
Properties of axial diameters
Authors: Scott Paul R.
Published: April 2009

Λ is a lattice and K a bounded, open, convex set in En. An axial diameter of K is the maximal length Xi, of chords of K parallel to the ith lattice basis vector (1 ≤ i ≤ n). A number of properties of the axial diameters are developed. For sets K containing just one lattice point, an inequality is established; when Λ is the integral lattice, this inequality takes the form .
Uniformisation of the twice–punctured disc - problems of confluence
Authors: Hempel Joachim A. , Smith Simon J.
Published: April 2009

For the twice-punctured unit disc Ωp = {z: |z| < 1, z ≠ ±p}, where 0 < p < 1, we obtain precise descriptions for p near 0 of various parameters associated with the uniformisation of Ωp by the upper half-plane U = {τ: Im τ > 0}. These parameters include the hyperbolic length of the geodesic surrounding ±p, the so-called “accessory parameters”, and the “proximity parameter” which determines the behaviour of the hyperbolic density near the punctures of Ωp.
The bisection width of cubic graphs
Authors: Clark L.H. , Entringer R.C.
Published: April 2009

For a graph G, define the bisection width bw(G) of G as min { eG(A,B): {A,B} partitions V(G) with ‖A| − |B‖ ≤ 1 } where eG(A, B) denotes the number of edges in G with one end in A and one end in B. We show almost every cubic graph G of order n has bw(G) ≥ n/11 while every such graph has bw(G) ≤ (n + 138)/3. We also show that almost every r-regular graph G of order n has bw(G) ≥ crn where cr → r/4 as r → ∞. Our last result is asymtotically correct.
Property preserving operators
Authors: Silvia Evelyn M.
Published: April 2009

Let S denote the class of functions of the form that are analytic and univalent in |z| < 1. Given f ∈ S and a, b, c, real numbers other than 0, −1, −2,…, let Ω(a, b, C; f) = F(a, b, C; z)* f(z) where is a hypergeometric Gauss function with (a)0 = 1 and (a)k = a(a + 1) … (a + k − 1) and * denotes the Hadamard product. For qn(z) = z + a2z2 + … + anzn (an ≠ 0, n = 5,6) in S, it is shown that , is univalent in |z| < 1. This extends the result previously known for n = 3 and n = 4. Also, we obtain a necessary and sufficient condition involving a, b, and c such that Ω(a, b, c;·) preserves the subclass of S consisting of starlike functions of order α, 0 ≤ α ≤ 1, with ak 0.
Compactness and convexity of cores of targets for neutral systems
Authors: Eke Anthony N.
Published: April 2009

In this paper we prove the convexity and the compactness of the cores of targets for neutral control systems. We make use of a weak compactness argument; but in the crucial part where we establish the boundeduess of the cores of the target we make use of the notion of asymptotic direction from convex Set Theory. Let En be n-dimensional Euclidean space. We prove that the core of the target H = L + E (where L = {x ∈ En | Mx = 0}, M is a constant in m × n matrix and E is a compact, convex set containing 0) of the neutral system

is convex, and is compact if, and only if, the system

is Euclidean controllable.
On Witt's dimension formula for free Lie algebras and a theorem of Klyachko
Authors: Blessenohl D. , Laue H.
Published: April 2009

It is shown that Witt's basic dimension formula and a more recent result of Klyachko imply each other. Then Klyachko's identities between certain idempotents in the group ring of Sn are supplemented by identities involving Wever's classical idempotent. This leads to a direct proof of Klyachko's theorem (and hence Witt's formula), avoiding any commutator collecting process. Furthermore, this approach explains why the Witt dimensions are numbers which otherwise occur when “counting necklaces”.
Degenerate critical points, homotopy indices and morse inequalities III
Authors: Dancer E.N.
Published: April 2009

This paper contains two main types of results. Firstly, we discuss what sort of critical points are obtained in various direct and dual minimax principles. The techniques we apply are widely applicable. Secondly, we obtain “best possible” results on which critical points of a function on Rn are removable.
A note on the fixed subring of an FPF ring
Authors: Clark John
Published: April 2009

An associative ring R with identity is called a left (right) FPF ring if given any finitely generated faithful left (right) R-module A and any left (right) R-module M then M is the epimorphic image of a direct sum of copies of A. Faith and Page have asked if the subring of elements fixed by a finite group of automorphisms of an FPF ring need also be FPF. Here we present examples showing the answer to be negative in general.
Convergence in neighbourhood lattices
Authors: Prokop Frank P.
Published: April 2009

A consideration of the separation properties of pre-neighbourhood lattices, leads to the definition and characterisation ofT1-neighbourhood lattices in terms of the properties of the neighbourhood mapping, independently of points. It is then shown that if net convergence is defined in neighbourhood lattices as a consequence of replacing ‘point’ by ‘set’ in topological convergence, then the limits of convergent nets are unique. The relationship between continuity and convergence is established with the proof of the statement that a residuated function between conditionally completeT1-neighbourhood lattices is continuous if and only if it preserves the limit of convergent nets. IfP(X)denotes the power set ofX, then the observation that a filter in a topological space (X, T) is a net inP(X)leads to a discussion of the net convergence of a filter as a special case of net convergence. Particular attention is paid to maximal filters, Fréchet filters and to the filter generated by the limit elements of a net. Further, if the ‘filter’ convergence of a filterFin a topological space (X, T) is given by, if η(x) ⊆F, then the relationship between ‘filter’ convergence and the net convergence of a filter inP(X) is established. Finally, it is proved that, in the neighbourhood system ‘lifted’ from a topological space toP(P(X)), the continuous image of a filter which converges to a singleton set is a convergent filter with the appropriate image set as the limit.
Tensor products of function algebras
Authors: Kyriazis Athanasios
Published: April 2009

For appropriate topclogical spaces X, Y, Z the algebra Cc(X xZY) of ℂ-valued continuous functions on the fibre product X xZY in the compact-open topology, describes the completed biprojective Cc(Z)-tensor product of Cc(X), Cc(Y).
On the Stone-Čeck compactification of an orbit space
Authors: Srivastava Kavita
Published: April 2009

By extending the given action of a discrete group G on a Tychonoff space X to βX, it is proved that the Stone-Čech compactification of the orbit space of X is the orbit space of the Stone-Čech compactification βX of X, when G is finite. The notion of G-retractive spaces is introduced and it is proved that the orbit space of a G-retractive space with G finite, is G-retractive.
Two remarks on amalgams of locally finite groups
Authors: Maier Berthold J.
Published: April 2009

We construct non amalgamation bases in the class of locally finite groups, and we present necessary and sufficient conditions for the embeddability of an amalgam into a locally finite group in the case that the common subgroup has finite index in both constituents.
A remark on projective modules
Authors: Kucharz Wojciech
Published: April 2009

Let R denote the field of real numbers and let A be the ring of regular functions on Rn, that is the localization of R[T1 …, Tn] with respect to the set of all polynomials vanishing nowhere on Rn. Let X be an algebraic subset of Rn and let I(X) be the ideal of A of all functions vanishing on X. Assume that X is compact and nonsingular and k = codim X = 1, 2, 4 or 8. we prove here that if the A/I(X)-module I(X)/I(X)2 can be generated by k elements, then there exist a projective A-module P of rank k and a homomorphism from P onto I(X).
Similarity between Kleinecke-Shirokov theorem and Fuglede-Putnam theorem
Authors: Furuta Takayuki
Published: April 2009

Recently in this journal we have shown the similarity between the Kleinecke-Shirokov theorem for subnormal operators and the Fuglede-putnam theorem. The purpose of this paper is to show that this similarity can be generalized to operators which belong to some classes of non-normal operators wider than the class of subnormal operators.
Sets of constant width, the spherical intersection property and circumscribed balls
Authors: Sallee G. T.
Published: April 2009

It is well-known that if W is a set of costant width λ then the circumsphere and the insphere of W are concentric and their radii sum to λ. Here this fact is generalized to sets of constant relative width and it is shown that the result does not depend no W being of constant width, but rather on W satisfying the spherical intersection property; that is, W = ∩{ω + λB:ω ɛ W}.
Quasi-codivisible covers
Authors: Bland Paul E.
Published: April 2009

In this paper quasi-codivisible covers are defined and investigated relative to a torsion theory (T, F) on Mod R. It is shown that if (T, F) is cohereditary, then a right R-module M has a quasi-codivisible cover whenever it has a codivisible cover. Moreover, it is shown that if (T, F) is cohereditary, then the universal existence of quasi-codivisible covers implies that the ring R/T (R) must be right perfect. The converse holds when (T, F) is pseudo-hereditary.
Kneser's theorem for differential equations in Banach spaces
Authors: Papageorgiou Nikolaos S.
Published: April 2009

We consider the Cauchy problem x (t) = f (t,x (t)), x (O) = xO defined in a nonreflexive Banach space and with the vector field f: T × X → X being weakly uniformly continuous. Using a compactness hypothesis that involves the weak measure of noncompactness, we prove that the solution set of the above Cauchy problem is nonempty, connected and compact in .
A note on periodic points of expanding maps of the interval
Authors: Du Bau-Sen
Published: April 2009

We sharpen a result of Byers on the existence of periodic points for some continuous expanding maps of the interval and generalize it to some classes of continuous maps of the interval which are not necessarily expanding. We then use these results to construct one-parameter families of continuous maps of the interval which have a bifurcation form fixed points directly to period 3 points together with a series of reverse bifurcations from period 3 points back to fixed points. Consequently, our results also provide examples of one-parameter families of continuous maps of the interval whose topological entropy jumps form zero to some positive number and then changes back to zero as the parameter varies.
Integration by parts for some general integrals
Authors: Das U. , Das A.G.
Published: April 2009

The present work is concerned with an integration by parts formula for the Pk-integral of De Sarkar and Das, and of the equivalent Pk-integral of Bullen. The process involves a simpler and updated version of that for the Zk−1-integral of Bergin. If f is Pk – (Zk−1)-integrable and G is of bounded kth variation, then fG is Pk – (Zk−1)-integrable.
Some representation formulae for entire functions of exponential type
Authors: Frappier Clément
Published: April 2009

We obtain some explicit formulae for series of the type

where f is an entire function of exponential type τ, bounded on the real exis (and satisfying in the first case). These series are expressed in terms of the derivatives of f and Bernoulli numbers. We examine the case where f is a trigonometric polynomial which lead us, in particular, to a new representation of the associated Fejér mean.
Demicontinuity of Nemitsky operators on Orlicz-Sobolev spaces
Authors: Hardy Grahame
Published: April 2009

We give an extension, to Orlicz-Sobolev spaces, of a theorem of Marcus and Mizel on the demicontinuity of Nemitsky operators on Sobolev spaces.
Injectivity and injective hulls of Abelian groups in a localic topos
Authors: Bhutani Kiran R.
Published: April 2009

We prove the analogue of the Baer Criterion for injectivity in the category AbShℒ of abelian groups in a topos of sheaves on a locale, that is, we show A is injective in AbShℒ if and only if it is injective relative to all S ↣ Zℒ where Zℒ is the group of integers in Shℒ. for a well-ordered locale we describe the injective hulls in AbShℒ in terms of injective hulls in Ab. Further we show that the global functor A → AE preserves injective hulls if and only if ℒ is a finite boolean locale. Finally We characterise injectives in AbShℒ for some special locales.
Groups with a nilpotent triple factorisation
Authors: Amberg Bernhard , Franciosi Silvana , de Giovanni Francesco
Published: April 2009

In the investigation of factorised groups one often encounters groups G = AB = AK = BK which have a triple factorisation as a product of two subgroups A and B and a normal subgroup K of G. It is of particular interest to know whether G satisfies some nilpotency requirement whenever the three subgroups A, B and K satisfy this same nilpotency requirement. A positive answer to this problem for the classes of nilpotent, hypercentral and locally nilpotent groups is given under the hypothesis that K is a minimax group or G has finite abelian section rank. The results become false if K has only finite Prüfer rank. Some applications of the main theorems are pointed out.
On single-law definitions of groups
Authors: Tasić Vladimir
Published: April 2009

It will be proved that any mononomic variety of groups can be considered as a variety of (ρ ε) or (ρ, τ) or (ν, ε)-algebras, or as a variety ofn-groupoids—which satisfy a single law, where:xyρ =x.y−1=xτ =x−1,xyν =x−1.y−1, ε is the identity, and for certain interpretations of then-ary operation. The problem is discussed for Ω-groups, too.
A dual characterisation of the existence of small combinations of slices
Authors: Deville Robert
Published: April 2009

We characterise, by a property of roughness, the norms of a Banach space X such that the dual unit ball has no small combination of ω*-slices. Among separable Banach spaces, the existence of an equivalent norm for this new property of roughness characterises spaces which contain an isomorphic copy of ℓ1(N).
A higher order approximation technique for restricted linear least-squares problems
Authors: Engl Heinz W. , Groetsch C.W.
Published: April 2009

An essential limitation for the method of weighting for equality constrained linear least-squares problems is the sub-optimality of the attainable convergence rate. In this paper, we propose a method, related to the method of iterated Tikhonov regularisation, that (under suitable conditions) gives rise to convergence rates which are arbitrarily near the optimal rate. As a by-product, we develop the theory of iterated Tikhonov regularisation for equations with unbounded linear operators.
Newton-like methods under mild differentiability conditions with error analysis
Authors: Argyros Ioannis K.
Published: April 2009

We apply Newton-like methods to operator equations where the operator has Hölder continuous derivatives. Our results reduce to the ones obtained by Rockne when the ordinary Newton method is applied to find solutions of nonlinear operator equations.
Embedding and representation theorems for clones and varieties
Authors: Evans Trevor
Published: April 2009

We use the theory of clones to prove that a countably presented variety of algebras can be embedded in a variety of groupoids.
Third Engel groups
Authors: Gupta N. D. , Newman M. F.
Published: April 2009

We present some new results on third Engel groups which are motivated by computer calculations but are not dependent on them. They include:

• for n > 2 every n-generator third Engel group is nilpotent of class at most 2n – 1;

• the fifth term of the lower central series of a third Engel group has exponent dividing 20;

• the subgroup generated by fifth powers of elements in a third Engel group is nearly centre-by-metabeliami;

and a normal form theorem for freest third Engel groups without elements of order 2.
Oscillation conditions in scalar linear delay differential equations
Authors: Győri István
Published: April 2009

Sufficient conditions are obtained for all solutions of a general scalar linear functional differential equation to be oscillatory. Our main theorem concerns some particular cases of a conjecture of Hunt and Yorke.
Commutator of two projections in prediction theory
Authors: Nakazi Takahiko
Published: April 2009

Let w be a nonnegative weight function in L1 = L1 (dθ/2π). Let Q and P denote the orthogonal projections to the closed linear spans in L2(wdθ/2π) of {einθ: n ≤ 0} and {einθ: n > 0}, respectively. The commutator of Q and P is studied. This has applications for prediction problems when such a weight arises as the spectral density of a discrete weakly stationary Gaussian stochastic process.
On zero-trace commutators
Authors: Kittaneh Fuad
Published: April 2009

We present some results concerning the trace of certain trace class commutators of operators acting on a separable, complex Hilbert space. It is shown, among other things, that if X is a Hilbert-Schmidt operator and A is an operator such that AX − XA is a trace class operator, then tr (AX − XA) = 0 provided one of the following conditions holds: (a) A is subnormal and A*A − AA* is a trace class operator, (b) A is a hyponormal contraction and 1 − AA* is a trace class operator, (c) A2 is normal and A*A − AA* is a trace class operator, (d) A2 and A3 are normal. It is also shown that if A is a self - adjoint operator, if f is a function that is analytic on some neighbourhood of the closed disc{z: |z| ≥ ||A||}, and if X is a compact operator such that f (A) X − Xf (A) is a trace class operator, then tr (f (A) X − Xf (A))=0.
Eventually regular semigroups that are group-bound
Authors: Edwards P. M.
Published: April 2009

Necessary and sufficient conditions are given for certain classes of eventually regular semigroups to the group-bound or even periodic.
Absolute values in orthogonally decomposable spaces
Authors: Yamamuro Sadayuki
Published: April 2009

In an ordered Banach space which is orthogonally decomposable, we define the absolute value and its general properties are given. The results are used to study the properties of linear operators which satisfy Kato's inequality and the locality condition.
Antipodal coincidence sets and stronger forms of connectedness
Authors: Harmse J.E.
Published: April 2009

A new notion of α-connectedness (α-path connectedness) in general topological spaces is introduced and it is proved that for a real-valued function defined on a space with this property, the cardinality of the antipodal coincidence set is at least as large as the cardinal number α. In particular, in linear topological spaces, the antipodal coincidence set of a real-valued function has cardinality at least that of the continuum. This could be regarded as a treatment of some Borsuk-Ulam type results in the setting of general topology.
A note on spaces related to Namioka spaces
Authors: Lee J.P. , Piotrowski Z.
Published: April 2009

Namioka proved that the following condition (*) given below holds, if X is Čech-complete and Y is a locally compact, σ-compact space.

(*) Let X and Y be spaces, Z be a metric space and let f: X × Y → Z be separately continuous. Then there is a dense, Gδ set A in X such that A × Y ⊂ C(f).

Following Christensen a space X is called Namioka if (*) is true for any compact space Y. In this paper we introduce and study a new class of spaces which is closely related to Namioka spaces. Namely, we say that a space Y is co-Namioka if (*) holds for any Namioka space X.
On complete reducibility of module bundles: Corrigendum
Authors: Prema G. , Kiranagi B.S.
Published: April 2009

In Theorem 3.5 ([1], p. 407), we need the base space X to be compact Hausdorff, so that it has a finite partition of unity.
On equicontinuous transformation groups
Authors: Elaydi Saber
Published: April 2009

It is shown that, under certain conditions, a transformation group is pointwise equicontinuous if and only if it is P-equicontinuous for some replete semigroup P in the phase group.
Embedding group amalgams
Authors: Fitzpatrick Patrick , Wiegold James
Published: April 2009

A classof groups is said to have the small embedding property if every amalgam of two groups fromamalgamating a normal subgroup embeds into a group not generating the varietyof all groups. Very few large classes have the small embedding property. For example, the minimal non-abelian varieties containing non-abelian finite groups do not; neither does any class of groups containing; but the set of finitely generated groups in a nilpotent variety not containingdoes have the small embedding property.
A radius of convexity problem
Authors: Mogra M.L. , Juneja O.P.
Published: April 2009

The authors determine the sharp radius of convexity for functions analytic and starlike in the unit disc having power series representation of the form where an+1 is fixed. The estimate obtained is an improvement over the corresponding fixed second coefficient result. It is expected that this approach will lead to sharpening and improvement of a number of earlier known results.
Representation of Boolean hypolattices
Authors: Miller John Boris
Published: April 2009

The principal result is a representation theorem for relatively-distributive, relatively complemented hypolattices with zero, generalizing the Stone representation theorem for a Boolean lattice. It uses the small product of a family of Boolean lattices which are maximal sublattices of the hypolattice. The paper also characterizes the maximal sublattices when the hypolattice is coherent; and it gives several examples of hypolattices, including hypolattices of subgroups and of ideals by direct sum, and examples from relative convexity, relative closure, and cofinality.
On the normaliser of a group in the Cayley representation
Authors: Bhattacharya Prabir
Published: April 2009

Let G be a p-group of order n and embed G into Sn by the Cayley representation. If X is a group such that G≨X≤Sn and CX(G) = G, then it is proved that G is properly contained in NX(G).
Serre classes for toposes
Authors: Adelman M. , Johnstone P.T.
Published: April 2009

We prove first that a logical fraction functor from a topos to a topos must be a filter-power functor, then we prove that such functors can have adjoints only when the filter is principal. Finally we refine this so that we are able to prove that the filter-power of a Grothendieck topos is Grothendieck if and only if the filter is principal.
On Hering's flag transitive plane of order 27
Authors: Rao M.L. Narayana , Rao K. Kuppuswamy , Satyanarayana K.
Published: April 2009

The full collineation group of the flag transitive plane of order 27 constructed by Hering is determined. It is shown that the stabilizer of the origin of this plane is of order 2184.
Growth of functions in Hp
Authors: Wang Hwai-Chiuan
Published: April 2009

There are two Hardy and Littlewood theorems which describe the rate of growth of functions in Hp on the unit circle T. In this paper we first establish their analogues on Euclidean space Rn and then apply them to solve multiplier and factorization problems on Hp(Rn).
Does mathematics have elements?
Authors: Halmos P.R.
Published: April 2009

For Empedocles, a little over 2400 years ago, there were four chemical elements, fire, water, earth, and air, and they were continually brought together and torn apart by two opposing forces, harmony and discord. For Aristotle, a hundred years later, two binary classification schemes took the place of one: instead of harmony-discord, he had wet-dry and hot-cold. The serious alchemists of the middle ages found that nature was even more complicated than that; they classified matter by its luster, heaviness, combustilibity, solubility, and so on. Boyle, in the 1600's, offered a definition similar to that of a prime number – an element is a substance from which other substances can be made but which cannot be separated into different substances – and analytical chemistry was off and running. A hundred years later Lavoisier (inspired in part by Newton's insight into the paramount importance of weight) could formulate a modified definition that led for the first time to quantitative tables of chemical elements similar to our modern ones.
On randomly 3-axial graphs
Authors: Alavi Yousef , Anderson Sabra S. , Chartrand Gary , Kapoor S.F.
Published: April 2009

A graph G, every vertex of which has degree at least three, is randomly 3-axial if for each vertex v of G, any ordered collection of three paths in G of length one with initial vertex v can be cyclically randomly extended to produce three internally disjoint paths which contain all the vertices of G. Randomly 3-axial graphs of order p > 4 are characterized for p ≢ 1 (mod 3), and are shown to be either complete graphs or certain regular complete bipartite graphs.
On locally weakly almost periodic transformation groups
Authors: Elaydi Saber
Published: April 2009

It is shown that a transformation group with a locally compact Hausdorff phase space and an abelian phase group is locally weakly almost periodic if and only if it is P-locally weakly almost periodic for some replete semigroup P in the phase group.
Maximum principle for non-linear degenerate equations of the parabolic type
Authors: Chabrowski Jan , Výborný Rudolf
Published: April 2009

This paper establishes a weak maximum principle for the difference u − v of solutions to nonlinear degenerate parabolic differential inequality
A theorem on abstract Segal algebras over some commutative Banach algebras
Authors: Tewari U.B. , Parthasarathy K.
Published: April 2009

Let B be a commutative, semi-simple, regular, Tauberian Banach algebra with noncompact maximal ideal space Δ(B). Suppose B has the property that there is a constant C such that for every compact subset K of Δ(B) there exists a f ∈ B with = 1 on K, ‖f‖B ≤ C and has compact support. We prove that if A is a proper abstract Segal algebra over B then for every positive integer n there exists f ∈ B such that fn ∉ A but fn+1 ∈ A. As a consequence of this result we prove that if G is a nondiscrete locally compact abelian group, μ a positive unbounded Radon measure on Γ (the dual group of G), 1 ≤ p < q < ∞ and , then .
Weight functions which admit Tchebycheff quadrature
Authors: Peherstorfer Franz
Published: April 2009

We describe a class of weight functions, which admit Tchebycheff quadrature.
On the essentially-algebraic theory generated by a sketch
Authors: Kelly G.M.
Published: April 2009

By a sketch we here mean a small category S together with a small set φ of projective cones in S, each cone φ ∈ φ being indexed by a small category Lφ. A model of S in any category B is a functor G: S → B such that each Gφ is a limit-cone. Let F be any small set of small categories containing all the Lφ. A small category T admitting all F-limits (that is, an F-complete small T ) is called an F-theory; it is considered as a sketch in which the distinguished cones are all the F-limit-cones. It is an important result of modern universal algebra, due originally to Ehresmann, that each sketch S = (S, φ) with every Lφ ∈ F determines an F-theory T, with a generic model M: S → T of S, such that composition with M induces an equivalence M* between the category of T-models in B and that of S-models in B, whenever B is F-complete. We give a simple proof of this result – one which generalizes directly to the case of enriched categories and indexed limits; and we make the new observation that the inverse to M* is given by (pointwise) right Kan extension along M.
A theorem on power-open LCA groups and its consequences
Authors: Khan M.A.
Published: April 2009

An LCA group G is called largely open if every large subgroup (that is, subgroup of finite index) of G is open. G is power-open if the continuous endomorphism, g → ng, g ∈ G, takes open sets of G onto open sets of G for every integer n > 1.
On Measures of Polynomials in Several Variables: Corrigendum
Authors: Myerson Gerald , Smyth C.J.
Published: April 2009

In [2], it was asserted in Theorem 3 that the measure M(x0 + … + xx) is asymptotically , where c was an explicit constant. The value of c given was incorrect, and should be e-½γ where γ is Euler's constant. This was pointed out by the first author. In fact

where we have tried to make amends by improving the error term.
An average distance result in Euclidean n-space
Authors: Strantzen John
Published: April 2009

The following result has been established by Stadje and Gross:

THEOREM. If 〈X, d〉 is a compact connected metric space, then there is a unique positive real number a(〈X, d〉) with the property that for each natural number n, and for all {x1, x2, …, xn} ⊂ X, there exists y ∈ X for which
On a class of polynomials associated with the subgraphs of a graph and its application to chromatic and dichromatic polynomials
Authors: Farrell E.J.
Published: April 2009

Let G be a graph. With every connected subgraph of G, let us associate a weight (Wα and with every spanning subgrapha or cover) C of G, a weight

where αi (i = 1, 2, …, n) are the components of C. The subgraph polynomial of G is

where the summation is taken over all the spanning subgraphs in G.

The basic properties of subgraph polynomials are given, expressions for the subgraph polynomials of multigraphs and pseudographs are derived, and the chromatic and dichromatic polynomials are shown to be special cases of the subgraph polynomial.
On some Gelfand-Mazur like theorems in p-normed algebras
Authors: Srinivasan V.K. , Shaing Hu
Published: April 2009

The main theorem of this paper shows that a complex p-normed algebra which is a pre-Bezout domain is isomorphic to the field of complex numbers, if it is a generalized unique factorization domain. This theorem generalizes the previous result of the authors proved by them in their paper Bull. Austral. Math. Soc. 20 (1979), 247–252. Some applications are then given.
On certain group ring problems
Authors: Karpilovsky G.
Published: April 2009

Recent developments on the isomorphism and other group ring problems are amply reviewed in Sehgal's book,Topics in group rings. The aim of this expository paper is to complement the content of Sehgal's book. Our main emphasis is the presentation of some results due to Saksonov which are published in Russian and do not seem well-known to the English reader. We also draw the reader's attention to some unpublished results of Higman.
A nonlinear complementarity problem in Banach space
Authors: Nanda Sribatsa , Nanda Sudarsan
Published: April 2009

Existence and uniqueness theorems for the nonlinear complementarity problem over closed convex cones in a reflexive real Banach space are established.
On one-sided boundedness of normed partial sums
Authors: Maller R. A.
Published: April 2009

This paper gives a very general sufficient condition for the existence of constants B(n), C(n) for which either almost surely or almost surely, where Sn = X1 + X2 + … + Xn and Xi are independent and identically distributed random variables. The theorem is closely connected with results of Klass and Teicher on the one-sided boundedness of Sn, with the relative stability of Sn, and with a generalised law of the iterated logarithm due to Kesten. For non negative Xi the sufficient condition is shown to be necessary, and the results are partially generalised to the case when Xi form a stationary m-dependent sequence. Some connections with a generalised type of regular variation and with domains of partial attraction are also noted.
An extension of kesten's generalised law of the iterated Logarithm
Authors: Maller R. A.
Published: April 2009

Let Xi be independent and identically distributed random variables with Sn = X1 + X2 + … + Xn. We extend a classic result of Kesten, by showing that if Xiare in the domain of partial attraction of the normal distribution, there are sequences αn and B(n) for which

almost surely, and the almost sure limit points of (sn−αn)/b(n) coincide with the interval [−1, l]. The norming sequence B(n) is slightly different to that used by Kesten, and has properties that are less desirable. The converse to the above result is known to be true by results of Heyde and Rogozin.
Two-generator groups II
Authors: Brenner J.L. , Wiegold James
Published: April 2009

Let n be an odd integer greater than 9. It is proved that the alternating group An has spread 3 in the sense that for any non-trivial elements x1, x2, x3 of An, there is an element y in An such that 〈xi, y〉 = An for i = 1, 2, 3.
An ordered sheaf representation of subresiduated lattices
Authors: Cornish William H.
Published: April 2009

Kennison's concept of an ordered sheaf is used to show that any member of the variety of subresiduated lattices is canonically isomorphic to the algebra of all ordered sections in a certain ordered sheaf, whose base is the Priestley space of the residuating sublattice.
On solutions of parabolic equations in regions with edges
Authors: Azzam A. , Kreyszig E.
Published: April 2009

In this paper, smoothness properties of solutions of the initial-Dirichlet problem for parabolic equations in regions with edges are considered. We obtain bounds for solutions and derivatives, and prove the Hölder continuity of the first derivatives and of the second derivatives multiplied by a suitable power of the distance from the edges.
On generalized Nörlund methods of summability II
Authors: Tanaka Minoru
Published: April 2009

The object of this paper is to establish some inclusion relations between two generalized Nörlund methods of summability. Our results are generalizations of Das's Theorem and one of them is also a generalization of a theorem of the author. They include the well-known fact that the Cesàro method (C, α) is weaker than (C, β) for β > α > 0.
The relative Schoenflies theorem
Authors: Gauld David
Published: April 2009

The relative Schoenflies theorem says that a locally flat embedding e: Sn−1 → Rn for which e−1(Rk) = Sk−1 extends to homeomorphism of the pair (Rn, Rk) provided the local collars respect Rk. In this note it is shown that the proviso is essential, at least when k = 3.
On the generalized Hadamard product and the Jordan-Hadamard product
Authors: Chuan Jen-chung , Chuan Wai-fong
Published: April 2009

The generalized Hadamard product S * T and the Jordan-Hadamard product S ∘ T of two operator-matrices S and T are introduced. They coincide with the usual Hadamard product of two complex matrices when the underlying Hilbert spaces are one-dimensional. Some inequalities which hold true for the usual Hadamard product of positive definite complex matrices are shown to be true for these two new products of positive invertible operator-matrices.
The additive groups of subdirectly irreducible rings II
Authors: Feigelstock Shalom
Published: April 2009

The classification of strongly subdirectly irreducible rings, which was begun in a previous paper, is completed by showing that a mixed group G is strongly subdirectly irreducible if and only if G ⋍ Z(p∞) ⊕ H, H a rank one, p-divisible, torsion free nil group.
On measures of polynomials in several variables
Authors: Smyth C.J.
Published: April 2009

The measure of a polynomial is defined as the exponential of a certain intractable-looking integral. However, it is shown how the measures of certain polynomials can be evaluated explicitly: when all their irreducible factors are linear, and belong to one of two special classes. Asymptotic values for the measures of two sequences of polynomials in large numbers of variables are also found. The proof of this result uses a quantitative form of the central limit theorem.
Another single law for groups
Authors: Neumann B.H.
Published: April 2009

It has long been known that, in terms of right division, groups can be defined by a single law. In this paper a single law defining groups in terms of multiplication and inversion is proposed. This law is in 4 variables, and it is conjectured that no fewer than 4 variables will do, and that the proposed law is of minimal length as well. Some extensions of the result, and an alternative single law with the same length and number of variables, are also discussed. By contrast, groups in terms of multiplication, inversion, and a unit element can not be defined by a single law. Most of these results were stated by Tarski at the Logic Colloquium at Hannover in 1966, but apparently no proof has yet been published.
Finite potent groups
Authors: Poland John
Published: April 2009

A group is potent if for any element of the group and any prescribed positive integer (dividing its order if this order is finite) there corresponds a finite homomorphic image of the group in which the element has the prescribed integer as its order. The finite potent groups form a finite variety that contains all finite nilpotent groups, all finite metabelian groups, and precisely one simple group, A5.
Extensions of theorems of Gagliardo and Marcus and Mizel to Orlicz spaces
Authors: Hardy Grahame
Published: April 2009

In 1958, Gagliardo showed that if u is a locally integrable function on a domain Ω satisfying the cone condition, with all weak derivatives belonging to the Lebesgue space Lp (Ω) (1 ≤ p < ∞), then u belongs to Lp (Ω) also. We extend this result to Orlicz spaces, and use it to extend a result of Marcus and Mizel on Nemitsky operators between Sobolev spaces to Orlicz-Sobolev spaces.
Trees as commutative BCK-Algebras
Authors: Cornish William H.
Published: April 2009

A new method of constructing commutative BCK-algebras is given. It depends upon the notion of a valuation of a lower semilattice in a given commutative BCK-algebra. Any tree vith the descending chain condition has a valuation in the natural numbers, considered as a commutative BCK-algebra; the valuation is the height-function. Thus, any tree of finite height possesses a uniquely determined commutative BCK-structure. The finite trees with at most one atom and height at most n are precisely the finitely generated subdirectly irreducible (simple) algebras in the subvariety of commutative BCK-algebras which satisfy the identity (En): xyn = xyn+1. Due to congruence-distributivity, it is then possible to describe the associated lattice of subvarieties.
On a theorem of Brudno over non-Archimedian Fields
Authors: Somasundaram D.
Published: April 2009

A classical theorem of Brudno, dealing with the consistency of summability with regular matrices is shown by example not to hold over a non-archimedian field.
Characterizations of the sphere by the mean II-curvature
Authors: Stamou George
Published: April 2009

The notion of “mean II-curvature” of a C4-surface (without parabolic points) in the three-dimensional Euclidean space has been introduced by Ekkehart Glässner. The aim of this note is to give some global characterizations of the sphere related to the above notion.

In the three-dimensional Euclidean space E3 we consider a sufficiently smooth ovaloid S (closed convex surface) with Gaussian curvature K > 0 . The ovaloid S possesses a positive definite second fundamental form II, if appropriately oriented. During the last years several authors have been concerned with the problem of characterizations of the sphere by the curvature of the second fundamental form of S. In this paper we give some characterizations of the sphere using the concept of the mean II-curvatureHII (of S), defined by Ekkehart Glässner.
Weak ideal invariance and orders in Artinian rings
Authors: Beachy John A.
Published: April 2009

It Is known that a ring R with Krull dimension is an order in an Artinian ring if R is K-homogeneous and the prime radical N of R is weakly ideal invariant. The notion of weak ideal invariance can be interpreted in torsion theoretic terms, yielding a shorter and more conceptual proof of this result. In addition, it is shown that the orders in Artinian rings which arise in this fashion are precisely those for which R/N is K-homogeneous.
On interpolation polynomials of the Hermite-Fejér type II
Authors: Goodenough S.J. , Mills T.M.
Published: April 2009

Given a ŕeal-valued function f on [−1, 1], n ∈ N, and the following partition of [−1, 1[:

there exists a unique polynomial R4n−1(f; x) of degree not exceeding 4n − 1 such that

and, for j = 1, 2 and 3,