bluuebunny/crossref_metadata_2025 huggingface dataset:
Evaluation of two convolution sums involving the sum of divisors function
Authors: Lemire Mathieu , Williams Kenneth S.
Published: April 2009

The convolution sumsandare evaluated for alln∈ ℕ.
Pseudo-Einstein real hypersurfaces in complex two-plane Grassmannians
Authors: Suh Young Jin
Published: April 2009

In this paper we give a complete classification of -invariant or Hopf pseudo-Einstein real hypersurfaces in complex two-plane Grassmannians G2(ℂm+2).
Products of composition and differentiation between Hardy spaces
Authors: Ohno Shûichi
Published: April 2009

We shall discuss boundedness and compactness of the products of composition and differentiation between Hardy spaces.
Reverse inequalities for the numerical radius of linear operators in Hilbert spaces
Authors: Dragomir S. S.
Published: April 2009

Some elementary inequalities providing upper bounds for the difference of the norm and the numerical radius of a bounded linear operator on Hilbert spaces under appropriate conditions are given.
On powerful andp-central restricted Lie algebras
Authors: Siciliano S. , Weigel Th.
Published: April 2009

In this note we analyse the analogy betweenm-potent andp-central restricted Lie algebras andp-groups. For restricted Lie algebras the notion ofm-potency has stronger implications than forp-groups (Theorem A). Every finite-dimensional restricted Lie algebra  is isomorphic tofor some finite-dimensionalp-central restricted Lie algebra(Proposition B). In particular, for restricted Lie algebras there does not hold an analogue of J.Buckley's theorem. Forpodd one can characterise powerful restricted Lie algebras in terms of the cup product map in the same way as for finitep-groups (Theorem C). Moreover, thep-centrality of the finite-dimensional restricted Lie algebra  has a strong implication on the structure of the cohomology ringH•(,) (Theorem D).
A deformation of the Alexander polynomials of knots yielding lens spaces
Authors: Kadokami Teruhisa , Yamada Yuichi
Published: April 2009

For a knotKin a homology 3-sphere Σ, by Σ(K;p/q), we denote the resulting 3-manifold ofp/q-surgery alongK. We say that the manifold or the surgery isof lens typeif Σ(K;p/q) has the same Reidemeister torsion as a lens space.

We prove that, for Σ(K;p/q) to be of lens type, it is a necessary and sufficient condition that the Alexander polynomialΔK(t)ofKis equal to that of an (i, j)-torus knotT(i, j)modulo (tp– 1).

We also deduce two results: If Σ(K;p/q) has the same Reidemeister torsion asL(p, q')then (1)(2) The multiple of ΣK(tk) overk∈ (i) is ±tmmodulo (tp– 1), where (i) is the subgroup in (Z/pZ)×/{±1} generated byi. Conversely, if a subgroupHof (Z/pZ)×/{±l} satisfying that the product of ΣK(tk) (k∈H) is ±tmmodulo (tp– 1), thenHincludesiorj.

Here,i, jare the parameters of the torus knot above.
On recent congruence results of Andrews and Paule for broken k-diamonds
Authors: Hirschhorn Michael D. , Sellers James A.
Published: April 2009

In one of their most recent works, George Andrews and Peter Paule continue their study of partition functions via MacMahon's Partition Analysis by considering partition functions associated with directed graphs which consist of chains of hexagons. In the process, they prove a congruence related to one of these partition functions and conjecture a number of similar congruence results. Our first goal in this note is to reprove this congruence by explicitly finding the generating function in question. We then prove one of the conjectures posed by Andrews and Paule as well as a number of congruences not mentioned by them. All of our results follow from straightforward generating function manipulations.
Some remarks on the number of points on elliptic curves over finite prime field
Authors: He Saiying , McLaughlin J.
Published: April 2009

Let p ≥ 5 be a prime and for a, b ε p, let Ea, b denote the elliptic curve over p with equation y2 = x3 + ax + b. As usual define the trace of Frobenius ap, a, b by

We use elementary facts about exponential sums and known results about binary quadratic forms over finite fields to evaluate the sums and for primes p in various congruence classes.

As an example of our results, we prove the following: Let p ≡ 5 (mod 6) be prime and let b ε *p. Then
On the Dirichlet problem of elliptic type
Authors: Galewski Marek
Published: April 2009

We investigate the existence of solutions and their stability for elliptic Dirichlet problems with nonlinearity of a convex-concave type. By relating the primal action and the dual action functionals on certain subsets of their domains we get the existence of solutions which are further stable with respect to a numerical parameter. We allow also for the differential operator to depend on a numerical parameter.
Transformations for complex discrete linear Hamiltonian and symplectic systems
Authors: Wang Yi , Shi Yuming , Ren Guojing
Published: April 2009

This paper is concerned with transformations for complex discrete linear Hamiltonian systems and complex discrete linear symplectic systems. A general complex discrete trigonometric system is studied and a criterion for it is established. Based on these results, the Prüfer and trigonometric transformations for complex discrete linear Hamiltonian systems and complex discrete linear symplectic systems are formulated. The relative existing results in real cases are extended.
Orlicz–Pettis Theorem for λ-multiplier convergent operator series
Authors: Yuanhong Tao , Ronglu Li
Published: April 2009

We show that the λ-multiplier convergence of operator series depends completely upon the AK property of the sequence space λ, and thus present a lot of new important theorems.
Finite groups in which some property of two-generator subgroups is transitive
Authors: Delizia Costantino , Moravec Primoz , Nicotera Chiara
Published: April 2009

Finite groups in which a given property of two-generator subgroups is a transitive relation are investigated. We obtain a description of such groups and prove in particular that every finite soluble-transitive group is soluble. A classification of finite nilpotent-transitive groups is also obtained.
On the Nonlinear Dirichlet Problem withP(x)-Laplacian
Authors: Galewski Marek , Płócienniczak Marek
Published: April 2009

Using a dual variational method which we develop, we show the existence and stability of solutions for a family of Dirichlet problemsk= 0, 1,… in a bounded domain in ℝNand with the nonlinearity satisfying some general growth conditions. The assumptions put onvare satisfied byp(x)-Laplacian operators.
On 2-absorbing ideals of commutative rings
Authors: Badawi Ayman
Published: April 2009

Suppose that R is a commutative ring with 1 ≠ 0. In this paper, we introduce the concept of 2-absorbing ideal which is a generalisation of prime ideal. A nonzero proper ideal I of R is called a 2-absorbing ideal of R if whenever a, b, c ∈ R and abc ∈ I, then ab ∈ I or ac ∈ I or bc ∈ I. It is shown that a nonzero proper ideal I of R is a 2-absorbing ideal if and only if whenever I1I2I3 ⊆ I for some ideals I1,I2,I3 of R, then I1I2 ⊆ I or I2I3 ⊆ I or I1I3 ⊆ I. It is shown that if I is a 2-absorbing ideal of R, then either Rad(I) is a prime ideal of R or Rad(I) = P1 ⋂ P2 where P1,P2 are the only distinct prime ideals of R that are minimal over I. Rings with the property that every nonzero proper ideal is a 2-absorbing ideal are characterised. All 2-absorbing ideals of valuation domains and Prüfer domains are completely described. It is shown that a Noetherian domain R is a Dedekind domain if and only if a 2-absorbing ideal of R is either a maximal ideal of R or M2 for some maximal ideal M of R or M1M2 where M1,M2 are some maximal ideals of R. If RM is Noetherian for each maximal ideal M of R, then it is shown that an integral domain R is an almost Dedekind domain if and only if a 2-absorbing ideal of R is either a maximal ideal of R or M2 for some maximal ideal M of R or M1M2 where M1,M2 are some maximal ideals of R.
On a new singular direction of algebroid functions
Authors: Wang Songmin , Gao Zongsheng
Published: April 2009

In this paper, we prove that for an algebroid function w (z) with finite lower order, satisfying , there exists a T direction dealing with multiple values.
Sign-variations of solutions of nonlinear discrete boundary value problems
Authors: Ma Ruyun
Published: April 2009

In this paper, we study two-point boundary value problems for the nonlinear second order difference equation

We establish the relationship between the number of sign-variation of f on {0,…, T + 2} and the one of the solution u of the above problem.
Finite matrix model of quantum hall fluids on S2
Authors: Chen Yi-Xin , Gould Mark D. , Zhang Yao-Zhong
Published: April 2009

Based on Haldane's spherical geometrical formalism of the two-dimensional quantum Hall fluids, the relation between the noncommutative geometry of S2 and the two-dimensional quantum Hall fluids is exhibited. A finite matrix model on the two-sphere is explicitly constucted as an effective description of the fractional quantum Hall fluids of finite extent, and the complete sets of physical quantum states of this matrix model are determined. We also describe how the low-lying excitations in the model are constructed in terms of the quasi-particle and quasi-hole excitations. It is shown that there exists a Haldane hierarchical structure in the two-dimensional quantum Hall fluid states of the matrix model. These hierarchical fluid states are generated by the parent fluid state by condensing the quasi-particle and quasi-hole excitations level by level.
A question on McCoy rings
Authors: Lei Zhen , Chen Jianlong , Ying Zhiling
Published: April 2009

Nelsen [J. Algebra 298 (2006) 134–141] asked whether there is a natural class of McCoy rings which includes all reversible rings and all rings R such that R[X] is semi-commutative. In this paper, some new equivalent conditions of McCoy rings are given. One of them is used to answer this question in the affirmative. Finally, an example is given which is McCoy and semi-commutative, but it is not reversible and does not have the property that R[x] is semi-commutative.
Surjectivity of linear operators from a Banach space into itself
Authors: Drivaliaris Dimosthenis , Yannakakis Nikos
Published: April 2009

We show that linear operators from a Banach space into itself which satisfy some relaxed strong accretivity conditions are invertible. Moreover, we characterise a particular class of such operators in the Hilbert space case. By doing so we manage to answer a problem posed by B. Ricceri, concerning a linear second order partial differential operator.
A note on bounded variation and heat semigroup on Riemannian manifolds
Authors: Carbonaro A. , Mauceri G.
Published: April 2009

In a recent paper Miranda Jr., Pallara, Paronetto and Preunkert have shown that the classical De Giorgi's heat kernel characterisation of functions of bounded variation on Euclidean space extends to Riemannian manifolds with Ricci curvature bounded from below and which satisfy a uniform lower bound estimate on the volume of geodesic balls of fixed radius. We give a shorter proof of the same result assuming only the lower bound on the Ricci curvature.
Existence results for semilinear differential inclusions
Authors: Fan Zhenbin , Li Gang
Published: April 2009

In this paper we study the existence of mild solutions for Cauchy problem

We derive conditions under which the mild solutions exist, and also get the relative compactness of the solution set, which extend and improve some existing results in this area.
Exponential attractors for abstract parabolic systems with bounded delay
Authors: Pražák Dalibor
Published: April 2009

We show that a suitable adaptation of the so-called method of trajectories can be used to construct an exponential attractor for a very general class of nonlinear reaction-diffusion systems with a bounded delay.

In particular, we assume that the dependence on the past history is controlled via convolution with a possibly singular measure. Assuming a priori that the solutions are bounded, a simple proof of the existence of an exponential attractor is given under very little regularity requirements.
Analysis of a periodic bacteria-immunity system with delayed quorum sensing
Authors: Zhang Zhonghua , Zhang Juan , Peng Jigeng
Published: April 2009

Based on the work of Fergola, Zhang and Cerasuolo, a bacteria-immunity model with the mechanism of periodic quorum sensing is formulated, which describes the competition between bacteria and immune cells. A discrete delay is introduced to characterise the time between when bacteria receive signal molecules and then combat with immune cells. In this paper, we focus on a subsystem of the bacteria-immunity model and investigate the existence of a positively periodic solution, and then study its global stability.
A sequential quadratic programming algorithm for nonlinear minimax problems
Authors: Hu Qing-Jie , Hu Ju-Zhou
Published: April 2009

In this paper, an active set sequential quadratic programming algorithm with non-monotone line search for nonlinear minmax problems is presented. At each iteration of the proposed algorithm, a main search direction is obtained by solving a reduced quadratic program which always has a solution. In order to avoid the Maratos effect, a correction direction is yielded by solving the reduced system of linear equations. Under mild conditions without the strict complementarity, the global and superlinear convergence can be achieved. Finally, some preliminary numerical experiments are reported.
Semi-classical solutions for a nonlinear coupled elliptic-parabolic problem
Authors: Choquet Catherine
Published: April 2009

We give an existence result for a fully nonlinear system consisting of a parabolic equation strongly coupled with an elliptic one. It models in particular miscible displacement in porous media. To this aim, we adapt the tools of Ladyzenskaja, Solon-nikov and Uralćeva [27, 28] to the coupled nonlinear setting. Under some reasonable assumptions on the data, we state the existence of semi-classical solutions for the problem. We also give an existence result of weak solutions for a degenerate form of the problem.
The 2-epistasis of fitness functions
Authors: Iglesias M. T. , Peñaranda V. S. , Vidal C. , Verschoren A.
Published: April 2009

In this note about Genetic Algorithms(GA-), we study the2-epistasisof a fitness function over a search space. This concept is a natural generalisation of that ofepistasis, previously considered by Davidor in 1991 Suys and Verschoren in 1996 and Van Hove and Verschoren in 1994 for example. We completely characterise fitness functions whose 2-epistasis is minimal: these are exactly the second order functions. The validity of 2-epistasis as a measure of hardness with respect to genetic algorithms is checked over some classical laboratory functions. Finally, we obtain an upper bound of the maximal value of the 2-epistasis when we restrict attention to non-negative functions.
On Existence and Stability of Solutions to Elliptic Systems with Generalised Growth
Authors: Galewski Marek , Plócienniczak Marek
Published: April 2009

We are concerned with existence and stability of solutions for system of equations with generalisedp(x)andm(x)—Laplace operators and where the nonlinearity satisfies some local growth conditions. We provide a variational approach that is based on investigation of the primal and the dual action functionals. As a consequence we consider the dependence of the the system on functional parameters.
Group closures of one-to-one transformations
Authors: Levi Inessa
Published: April 2009

For a semigroup S of transformations of an infinite set X let Gs be the group of all the permutations of X that preserve S under conjugation. Fix a permutation group H on X and a transformation f of X, and let 〈f: H〉 = 〈{hfh−1: h ∈ H}〉 be the H-closure of f. We find necessary and sufficient conditions on a one-to-one transformation f and a normal subgroup H of the symmetric group on X to satisfy G〈f:H〉 = H. We also show that if S is a semigroup of one-to-one transformations of X and GS contains the alternating group on X then Aut(S) = Inn(S) ≅ GS.
Abelian groups that are torsion over their endomorphism rings
Authors: Hill J. , Hill P. , Ullery W.
Published: April 2009

Using Lambek torsion as the torsion theory, we investigate the question of when an Abelian group G is torsion as a module over its endomorphism ring E. Groups that are torsion modules in this sense are called ℒ-torsion. Among the classes of torsion and truly mixed Abelian groups, we are able to determine completely those groups that are ℒ-torsion. However, the case when G is torsion free is more complicated. Whereas no torsion-free group of finite rank is ℒ-torsion, we show that there are large classes of torsion-free groups of infinite rank that are ℒ-torsion. Nevertheless, meaningful definitive criteria for a torsion-free group to be ℒ-torsion have not been found.
Coprime actions and degrees of primitive inducers of invariant characters
Authors: Moretó Alexander , Sanus Lucía
Published: April 2009

Let a finite group A act coprimely on a finite group G and χ ∈ Irr A(G). Isaacs, Lewis and Navarro proved that if G is nilpotent then the degrees of any two A-primitive characters of A-invariant subgroups of G inducing χ coincide. In this note we aim at extending this result by weakening the hypothesis on G.
Macmahon's partition analysis IX:K-gon partitions
Authors: Andrews George E. , Paule Peter , Riese Axel
Published: April 2009

Dedicated to George Szekeres on the occasion of his 90th birthday

MacMahon devoted a significant portion of Volume II of his famous bookCombinatory Analysisto the introduction of Partition Analysis as a computational method for solving combinatorial problems in connection with systems of linear diophantine inequalities and equations. In a series of papers we have shown that MacMahon's method turns into an extremely powerful tool when implemented in computer algebra. In this note we explain how the use of the package Omega developed by the authors has led to a generalisation of a classical counting problem related to triangles with sides of integer length.
Some metric properties of Lüroth expansions over the field of Laurent series
Authors: Kristensen Simon
Published: April 2009

J. Knopfmacher and A. Knopfmacher have previously produced some metric results concerning the coefficients of the Lüroth expansions of elements in the field of Laurent series with coefficients from a finite field. In this paper, we obtain analogous metric results for subsequences of the coefficients of the expansions.
Rigid sets
Authors: Guerrini Luca , Papini Pier Luigi
Published: April 2009

The term “rigid set” appears often in the literature in different contexts and with different meanings. In many cases the notions are unrelated, while in other they refer to related facts. Here we study infinite sets which are rigid according to [2] and analyse the relationship with the notion of rigidity used in [1]. We make several remarks, summarise different results in the area and prove a few new results.
Topological sequence entropy and topologically weak mixing
Authors: Li Simin
Published: April 2009

A charactersiation of topologically weak mixing is given by using the topological sequence entropy.
Characterisations of derivations on some operator algebras
Authors: Jing Wu , Lu Shijie , Li Pengtong
Published: April 2009

Some conditions under which a derivation on some operator algebras can be completely determined by the action on operators of zero product are given.
A subdifferential characterisation of Banach spaces with the Radon–Nikodym property
Authors: Giles J. R.
Published: April 2009

A Banach space has the Radon–Nikodym Property if and only if every continuous weak* lower semi–continuous gauge on the dual space has a point of its domain where its subdifferential is contained in the natural embedding.
Commuting of Toeplitz operators on the Bergman spaces of the bidisc
Authors: Lu Yufeng
Published: April 2009

In this paper we describe when two Toeplitz operators Tf and Tg on the Bergman space of the bidisc commute, where f = f1 + f̅2, g = g1 + ḡ2, fi, gi ∈ H∞(D2)(i = 1, 2).
Average normalisations of elliptic curves
Authors: Banks William D. , Shparlinski Igor E.
Published: April 2009

Ciet, Quisquater, and Sica have recently shown that every elliptic curve E over a finite field 𝔽p is isomorphic to a curve y2 = x3 + ax + b with a and b of size O (p¾). In this paper, we show that almost all elliptic curves satisfy the stronger bound O (p⅔). The problem is motivated by cryptographic considerations.
1-perfect codes in Sierpiński graphs
Authors: Klavžar Sandi , Milutinović Uroš , Petr Ciril
Published: April 2009

Sierpiński graphs S (n, κ) generalise the Tower of Hanoi graphs—the graph S (n, 3) is isomorphic to the graph Hn of the Tower of Hanoi with n disks. A 1-perfect code (or an efficient dominating set) in a graph G is a vertex subset of G with the property that the closed neighbourhoods of its elements form a partition of V (G). It is proved that the graphs S (n, κ) possess unique 1-perfect codes, thus extending a previously known result for Hn. An efficient decoding algorithm is also presented. The present approach, in particular the proposed (de)coding, is intrinsically different from the approach to Hn.
On boundedness of the weighted Bergman projections on the Lipschitz spaces
Authors: Cho Hong Rae , Lee Jinkee
Published: April 2009

In this paper we study the boundedness of the weighted Bergman projections on the weighted subspaces of Bergman spaces and the Lipschitz spaces on the unit ball and the unit polydisc.
Topology of four-manifolds with special homotopy groups
Authors: Cavicchioli Alberto , Spaggiari Fulvia
Published: April 2009

We study the homotopy type and thes—cobordism class of a closed connected topological 4-manifold with vanishing second homotopy group. Our results are related to problem 4.53 of Kirby inGeometric Topology, Studies in Advanced Math.2(1997), and give a partial answer to a question stated by Hillman inBull. London Math. Soc.27(1995) 387–391.
On strong convex compactness property of spaces of nonlinear operators
Authors: Song Xueli , Peng Jigen
Published: April 2009

The strong convex compactness property is important for property persistence of operator semigroups under perturbations. It has been investigated in the linear setting. In this paper, we are concerned with the property in the nonlinear setting. We prove that the following spaces of (nonlinear) operators enjoy the strong convex compactness property: the space of compact operators, the space of completely continuous operators, the space of weakly compact operators, the space of conditionally weakly compact operators, the space of weakly completely continuous operators, the space of demicontinuous operators, the space of weakly continuous operators and the space of strongly continuous operators. Moreover, we prove the property persistence of operator semigroups under nonlinear perturbation.
Indépendance algébrique de logarithmes en caractéristique P
Authors: Denis Laurent
Published: April 2009

Let k be the rational function field over the field with q elements with characteristic p. Since the work of Carlitz we know in this situation the function ζ analog of the Riemann zeta function and the function Logφ analog of the usual logarithm. We will show two main results. Firstly, if ξ denotes the fundamental period of Carlitz module, we prove that ξ, ζ(1),…, ζ(p – 2) are algebraically independent over k. Secondly if α1,…, αn are rational elements (of degree less than q/(q − 1) to ensure convergence of the logarithm) such that Logφ α1,…, Logφ αn are linearly independent over k then they are algebraically independent over k. The point is to find suitable functions taking these values and for which Mahler's method can be used.
Four-fold torsion theories
Authors: Rutter Edgar A.
Published: April 2009

In this note 4-fold torsion theories (for categories of modules) are classified by means of orthogonal pairs of comaximal ideals. Among the applications are results of Kurata concerning lengths of n-fold torsion theories and an upper bound for the number of 4-fold torsion theories over a semiperfect ring.
Nonoscillation of third order retarded equations
Authors: Singh Bhagat , Dahiya R.S.
Published: April 2009

The third order delay equation

y‴(t) + a(t)yτ(t) = 0

is studied for its nonoscillatory nature under the general condition in which a(t) has been allowed to oscillate. It is shown by way of a differential inequality that if g(t) is a thrice differentiable and eventually positive function then

g‴(t) + t2|a(t)|g(t) ≤ 0

is sufficient for this equation to have bounded nonoscillatory solutions.
Jackson's Theorem for locally compact abelian groups
Authors: Bloom Walter R.
Published: April 2009

If f is a p–th integrable function on the circle group and ω(p; f; δ) is its mean modulus of continuity with exponent p then an extended version of the classical theorem of Jackson states the for each positive integer n, there exists a trigonometric polynomial tn of degree at most n for which

‖f-tn‖p ≤(p; f; 1/n).

In this paper it will be shewn that for G a Hausdorff locally compact abelian group, the algebra L1(G) admits a certain bounded positive approximate unit which, in turn, will be used to prove an analogue of the above result for Lp(G).
Sabidussi-type theorems for stability
Authors: Grant Douglas D. , Holton D.A. , McAvaney K.L.
Published: April 2009

In this note we give details of a method by which we can produce an index-0 graph from any unstable graph and use it to show that given any finite group there exists an index-0 graph whose automorphism group is isomorphic, as an abstract group, to the given group. We proceed to construct two infinite families of connected index-0 graphs with connected complements whose automorphism group contains a transposition. This enables us to produce, for any finite group G, an index-0 graph whose automorphism group, isomorphic as an abstract group to C2 × G, contains a transposition.
On the associativity of the torsion functor
Authors: Clark John
Published: April 2009

Let R be a commutative ring with identity. We say that tor is associative over R if for all R-modules A, B, C there is an isomorphism Our main results are that (1) tor is associative over a noetherian ring R if and only if R is the direct sum of a finite number of Dedekind rings and uniserial rings, and (2) tor is associative over an integral domain R if and only if R is a Prüfer ring.
On groups of exponent four with generators of order two
Authors: Gupta Narain D. , Mochizuki Horace Y. , Weston Kenneth W.
Published: April 2009

The largest group of exponent 4 generated by n elements of order 2 has nilpotency class n + 1 when n ≥ 3.
Partially well-ordered sets of infinite matrices and closed classes of abelian groups
Authors: Bang C.M.
Published: April 2009

We give a necessary and sufficient condition for a class of row-decreasing infinite matrices to be partially well-ordered with regard to the component-wise ordering. Then, using these matrices, we determine all the classes of abelian groups, closed under taking subgroups, direct limits, and isomorphic groups.
Submartingales and stochastic stability
Authors: Diamond Phil
Published: April 2009

Sufficient conditions, involving the existence of a Lyapunov function which is a submartingale of special type, are given for the instability of stochastic discrete time systems.
Some remarks on coherent soluble groups
Authors: Lennox John C. , Wiegold James
Published: April 2009

An example of Wehrfritz is pointed out to show that GL(4, Q) is not coherent. This answers a question of Serre. It is shown that finitely generated soluble coherent subgroups of GL(2, Q) need not be polycyclic, in sharp contrast to the fact that all soluble subgroups of GL(n, Z) are polycyclic and so automatically coherent.
A new definition of discrete analytic functions
Authors: Harman C.J.
Published: April 2009

The concept of a tetradiffric function is introduced. This new scheme for defining discrete analytic functions is shown to retain the algebraic simplicity of monodiffric functions, while introducing to the theory a symmetry similar to the Schwarz Reflection Principle.
Diffraction of planetary waves by an infinite strip
Authors: Asghar S. , Rashid M.A.
Published: April 2009

In this paper we construct the Wiener-Hopf equation for diffraction of a planetary wave by an infinite strip and obtain its solution in the form of an integral representation. We also discuss the asymptotic character of the diffracted wave using the saddle point method.
Adders for the patterned starter in some non-abelian groups
Authors: Leonard Philip A.
Published: April 2009

Starters with adders in abelian groups of odd order have been used extensively in the construction and study of Room squares. It is possible to define these concepts in non-abelian groups, with similar applicability to Room squares. Examples are given of adders for the “patterned starter” in the non-abelian groups of order pq, p and q primes larger than 3, p ≡ q ≡ 3 (mod 4), q ≡ 1 (mod p).
On rational approximations of the exponential function at rational points
Authors: Mahler Kurt
Published: April 2009

Letp, q, u, andvbe any four positive integers, and let further δ be a number in the interval 0 < δ ≤ 2. In this note an effective lower bound forqwill be obtained which insures thatIn the special case whenu=v= 1, it was shown by J. Popken,Math. Z. 29 (1929), 525–541, thatHerecandCare two positive absolute constants which, however, were not determined explicity. A similarly non-effective result was given in my paper,J. reine angew. Math. 166 (1932), 118–150.

The method of this note depends again on the classical formulae by Hermite which I applied alsoop. cit.
The hyper-archimedean kernel sequence of a lattice-ordered group
Authors: Martinez Jorge
Published: April 2009

Thehyper-archimedean kernel Ar(G)of a lattice-ordered group (hence forthl–group) is the largest hyper-archimedean convexl–subgroup of thel–groupG. One definesArσ(G), for an ordinal σ asif a is a limit ordinal, and as the uniquel–ideal with the property thatArσ(G)/Ar.σ–1(G)=Ar(G/Arσ–1(G)), otherwise. The resulting "Loewy"-like sequence of characteristicl–ideals,Ar(G)⊆Ar2(G) ⊆ … ⊆Arσ(G)⊆ …, is called thehyper-archimedean kernel sequence. The first result of this note says that eachArσ(G)⊆Ar(G)”.

Most of the paper concentrates on archimedeanl–groups; in particular, the hyper-archimedean kernels are identified for:D(X), whereXis a Stone space, a large class of free products of abelianl–groups, and certainl–subrings of a product of real groups.

It is shown that even for archimedeanl–groups the hyper-archimedean kernel sequence may proceed pastAr(G).
A generalized contraction principle
Authors: Reilly Ivan L.
Published: April 2009

This paper presents an extension of Banach's contraction mapping principle to Hausdorff spaces, in fact to the larger class of topological spaces in which convergent sequences have unique limits. This is achieved by considering topologies on X generated by families of quasi-pseudo-metrics on X. An extension of the concept of Cauchy sequence to this non-metric setting is given.
On common fixed points of mappings
Authors: Iséki Kiyoshi
Published: April 2009

The object of this paper is to study common fixed points of mappings of a complete metric space into itself. The results obtained are generalizations of Ray Theorems.
Countable vector lattices
Authors: Conrad Paul F.
Published: April 2009

In his paper “On the structure of ordered real vector spaces” (Publ. Math. Debrecen 4 (1955–56), 334–343), Erdös shows that a totally ordered real vector space of countable dimension is order isomorphic to a lexicographic direct sum of copies of the group of real numbers. Brown, in “Valued vector spaces of countable dimension” (Publ. Math. Debrecen 18 (1971), 149–151), extends the result to a valued vector space of countable dimension and greatly simplifies the proof. In this note it is shown that a finite valued vector lattice of countable dimension is order isomorphic to a direct sum of o–simple totally ordered vector spaces. One obtains as corollaries the result of Erdös and the applications that Brown makes to totally ordered spaces.
Nonoscillation of arbitrary order retarded differential equations of non-homogeneous type
Authors: Dahiya R.S.
Published: April 2009

The object of the present paper is to study the delay differential equation of arbitrary order namely
y(n)(t) + a(t)yτ(t) = f(t), n≥2 (an integer)
and prove a nonoscillation theorem under the general situation in which a(t) and f(t) are allowed to oscillate arbitrarily often on some positive half real line. This is accomplished by way of two differential inequalities of nth order.
The two generator restricted Burnside group of exponent five
Authors: Havas George , Wall G.E. , Wamsley J.W.
Published: April 2009

The two generator restricted Burnside group of exponent five is shown to have order 534and class 12 by two independent methods. A consistent commutator power presentation for the group is given.
On a new finite non–abelian simple group of Janko
Authors: Wong S. K.
Published: April 2009

Two new simple groups have recently been discovered by Z. Janko. One of these groups has order 50,232,960. As a first step in showing that there is precisely one (up to isomorphism) simple group of order 50,232,960, the author proves in this paper the following result: If G is a non-abelian simple group of order 50,232,960, then the structure of the centralizer of an element of order two in G is uniquely determined.

In a note added on 21 April 1969 to this paper, the author announces that he has proved the uniqueness of the simple group of order 50,232,960.
Optimal quadrature
Authors: Elhay S.
Published: April 2009

Certain Hilbert spaces of functions with known smoothness are considered. The weights and mesh of the quadrature formulae which have least estimate of error with respect to the norm for functions in these spaces are found and their properties are discussed.
An extension of the Krull-Schmidt theorem
Authors: Conlon S. B.
Published: April 2009

In the usual Krull-Schmidt-Azumaya theorem in abelian categories it is essential that each of the direct summands has a local ring of endomorphisms. A partial answer is given here to the case where this last condition is not satisfied by the indecomposable direct summands. It is found that those summands with local endomorphism rings are determined up to isomorphism and cardinality of occurrence.
On the lattice of congruences on a regular semigroup
Authors: Hall T. E.
Published: April 2009

A result of Reilly and Scheiblich for inverse semigroups is proved true also for regular semigroups. For any regular semigroup S the relation θ is defined on the lattice, Λ(S), of congruences on S by: (ρ, τ) ∈ θ if ρ and τ induce the same partition of the idempotents of S. Then θ is a congruence on Λ(S), Λ(S)/θ is complete and the natural homomorphism of Λ(S) onto Λ(S)/θ is a complete lattice homomorphism.
Varieties of topological groups II
Authors: Morris Sidney A.
Published: April 2009

This paper is a sequel to one entitled “Varieties of topological groups”. The variety V of topological groups is said to be full if it contains every group which is algebraically isomorphic to a group in V For any Tychonoff space X, the free group F of V on X exists, is Hausdorff and disconnected, and has X as a closed subset. Any subgroup of F which is algebraically fully invariant is a closed subset of F. If X is a compact Hausdorff space, then F is normal. Let V be a full Schreier variety and X a Tychonoff space, then all finitely generated subgroups of F are free in V.

A β-variety V is one for which the free group of V on each compact Hausdorff space exists and is Hausdorff. For any β-variety V and Tychonoff space X, the free group of V exists, is Hausdorff and has X as a closed subset. A necessary and sufficient condition for V to be a β-variety is given.

The concept of a projective (topological) group of a variety V is introduced. The projective groups of V are shown to be precisely the summands of the free groups of V. A finitely generated Hausdorff projective group of a Schreier variety V is free in V.
High Reynolds number flow between torsionally oscillating disks
Authors: Smith K.G. , Pillow A.F.
Published: April 2009

In this paper the problem solved is that of unsteady flow of a viscous incompressible fluid between two parallel infinite disks, which are performing torsional oscillations about a common axis. The solution is restricted to high Reynolds numbers, and thus extends an earlier solution by Rosenblat for low Reynolds numbers.

The solution is obtained by the method of matched asymptotic expansions. In the main body of the fluid the flow is inviscid, but may be rotational, and in the boundary layers adjacent to the disks the non-linear convection terms are small. These two regions do not overlap, and it is found that in order to match the solutions a third region is required in which viscous diffusion is balanced by steady convection. The angular velocity is found to be non-zero only in the boundary layers adjacent to the disks.
Quantum logic as an implication algebra
Authors: Finch P.D.
Published: April 2009

For the purpose of this paper a logic is defined to be a non-empty set of propositions which is partially ordered by a relation of logical implication, denoted by “≤”, and which, as a poset, is orthocomplemented by a unary operation of negation. The negation of the proposition x is denoted by NX and the least element in the logic is denoted by 0, we write NO = 1.

A binary operation “→” is introduced into a logic, the operation is interpreted as material implication so that “x → y” is a proposition of the logic and is read as “x materially implies y”. If material implication has the properties

11. (x → 0) = NX,
12. if x ≤ y then (z → x) ≤ (z → y),
13. if x ≤ y then x ≤ (y ≤ z)= x → z,
14. x ≤ {y → N(y → Nx)},
then the logic is an orthomodular lattice. The lattice operations of join and meet are given by
x ∨ y = Nx → N(Nx → Ny)
x ∧ y = N(X → N(x → y))
and, in terms of the lattice operations, the material implication is given by
(x → y) = (y ∧ x) ∨ NX.

Moreover the logic is a Boolean algebra if, and only if, in addition to the properties above, material implication satifies
15. (x → y) = (Ny → Nx).
Structure of perfect rings
Authors: Dlab Vlastimil
Published: April 2009

In the present note, we offer a simple characterization of perfect rings in terms of their components and socle sequences, which is subsequently used to establish a one-to-one correspondence between perfect rings and certain finite additive categories. This correspondence is effected by means of a matrix representation, which describes the way in which perfect rings are built from local perfect rings.
Orthogonality relations and orthomodularity
Authors: Finch P.D.
Published: April 2009

An abstract orthogonality relation is defined, a closure operation and a corresponding lattice of closed sets are associated with it. Necessary and sufficient conditions are obtained for the orthomodularity of a sub-ortholattice of the lattice of closed sets.
One variable equations over semigroups
Authors: Levin Frank
Published: April 2009

An analogue of the theorem on the existence of a primitive element for separable extensions of fields is presented for semigroups. This has two immediate consequences.

(i) A semigroup is algebraically closed with respect to equations in several variables if and only if it is closed with respect to equations in a single variable.

(ii) Any countable semigroup C is embedded in a two-generator semigroup, one of whose generators is in C.

Further, a proof is given that any free product of a semigroup of order one with one of order two is SQ–universal, that is, its factor semigroups embed all countable semigroups. The proofs are adaptations of one used by Trevor Evans, Proc. Amer. Math. Soc. 3 (1952), 614–620. to show that a free product of two infinite cyclic semigroups is SQ–universal.
Some group laws equivalent to the commutative law
Authors: Gandhi J. M.
Published: April 2009

In this paper we prove the Theorem: A group satisfying the law (1) [x, y] = [u, v, w], where u, v, w are the entries from the set {x, x-1, y, y-1} is always abelian. Earlier a few cases of this theorem were proved by Gupta. It is also proved that a group satisfying the law = [x, y, x] is always abelian.
Topologies generated by relations
Authors: Smithson Raymond E.
Published: April 2009

Let R be a relation on a set X, and if A ⊂ X set RA = {x ∣ (x, α) ∈ R for some α ∈ A} and AR = {x ∣ (α, x) ∈ R for some α ∈ A}. Also A is called an antiset in case no two distinct elements of A are related. If A is a collection of antisets, then we generate a topology T(A) by taking sets of the form RA or AR (or X or ø) as subbasic open sets. Then conditions are given under which this topology satisfies separation axioms, or is compact or connected. For example. Theorem: Let A contain the singletons. If for each x ∈ X and y ∈ X \ x, there is a z ∈ X such that (x, z) ∈ R ((z, x) ∈. R) and (y, z) ∉ R ((z, y) ∉ R), then T(A) is a T1-topology. The conditions used to obtain compactness or connectedness are analogous to the conditions used to get the same properties for the order topology on a totally ordered set. Finally, by modifying the definition of T(A) slightly, we obtain conditions so that if X is a tree and R the cutpoint order, then T(A) is the original topology.
Sasaki projections on orthocomplemented posets
Authors: Finch P.D.
Published: April 2009

It is proved that an orthocomplemented posetPis an orthomodular lattice if and only if it admits a suitable defined set of order preserving maps. These maps are called projections. They are, in fact, Just the projections of the Baer *-semigroup associated with the orthomodular lattice.
Certain graphs arising from Hadamard matrices
Authors: Wallis W.D.
Published: April 2009

We establish several infinite classes of regular graphs with the property that any two distinct vertices have a fixed number of other vertices joined to both of them. The graphs are found by constructing their incidence matrices, which correspond to certain Hadamard matrices.
Subdirectly irreducible rings–some pathology
Authors: Moore H.G.
Published: April 2009

Every ring is isomorphic to a subdirect sum of subdirectly irreducible rings. Unfortunately, however, as is shown, the property of being subdirectly irreducible is not preserved under homomorphisms. An example is given of a finite non-commutative subdirectly irreducible ring R with heart (= the intersection of all non-zero ideals) H, such that R/E is isomorphic with GF(2) + GF(2). (GF(2) is the two element Galois Field.) Some additional properties of the ring R are listed and contrasts are made with results for commutative subdirectly irreducible rings; for example, the zero divisors of R do not form an ideal.
An application of a theorem of Gaschütz
Authors: Lausch H.
Published: April 2009

A theorem of Gaschütz is used to prove: Let τ be a homomorphism of the distributively generated near-ring R with identity element and descending chain condition for left modules, τ have finite kernel, and U(R) be the group of units of R; then U(Rτ) = U(R)τ.

Furthermore it is shown that the finiteness condition for ker τ can be dropped in the case of R being a ring.
On algebraic rings
Authors: Chacron M.
Published: April 2009

A ring R is π-regular (periodic) if for each element x of R there is n = n(x) SO that xn = xn.a.xn (xn = xn.1.xn) (a depending on x). Let R be an algebraic algebra over a commutative ring F With identity. In this paper we prove that if every π-regular image of the ring F is periodic, then R is periodic. This result applies in particular to the algebraic rings R (over the integers) considered by Drazin and to the algebraic algebras R over algebraically prime fields. It extends a result of Drazin on torsin-free algebraic rings and a generalization by this author of Drazin's result.
An autonomous system of differential equations in the plane
Authors: Matlak R.F.
Published: April 2009

In the present note the equation yn = x1-m ym is reduced, under appropriate conditions, to a quadratic autonomous system of differential equations in the plane. In pursuance of this new approach, the main geometric features of this autonomous system are determined and a method of solving it is outlined.
Arithmetical properties of the digits of the multiples of an irrational number
Authors: Mahler Kurt
Published: April 2009

Little seems to be known about the digits or sequences of digits in the decimal representation of a given irrational number like √2 or π. There is no difficulty in constructing an irrational number such that in its decimal representation certain digits or sequences of digits do not occur. On the other hand, well known theorems by Tchebychef, Kronecker, and Weyl imply that some integral multiple of the given irrational number always has any given finite sequence of digits occuring at least once in its decimal representation: for the fractional parts of the multiplies of the number lie dense in the interval (0, 1).
A characterization of weak projectability
Authors: Miller J.B.
Published: April 2009

For a commutative l–group G with carrier lattice , G is weakly projectable iff the proper prime filters of are all maximal filters.
A Fritz John theorem in complex space
Authors: Craven B.D. , Mond B.
Published: April 2009

Necessary conditions of the Fritz John type are given for a class of nonlinear programming problems over polyhedral cones in finite dimensional complex space.

Consider the problem to

whereSis a polyhedral cone in, andCmandf:C2n→C,g:C2n→Cmare differentiable functions. A necessary condition for a feasible pointz0to be optimal is that there exist τ≥0, ν ∈S*, (τ, ν) ≠ 0, such that

and
On a class of diophantine inequalities
Authors: Mahler Kurt
Published: April 2009

As a special case of more general results, it is proved in this note that, if α is any real number and δ any positive number, then there exists a positive integer X such that the inequality

has infinitely many solutions in positive integers h and Yh.

The method depends on the study of infinite sequences of real linear forms in a fixed number of variables. It has relations to that used by Kronecker in the proof of his classical theorem and can be generalised.
The Jacobi-Perron algorithm and the algebra of recursive sequences
Authors: Shannon A.G. , Bernstein Leon
Published: April 2009

This paper shows the existence of a one-to-one correspondence between a certain class of square matrices of arbitrary order and a related extension field. The elements of these matrices are obtained from certain basic linear recursive sequences by means of a generalization of the euclidean algorithm.
On soluble groups which admit the dihedral group of order eight fixed-point-freely
Authors: Camina Alan R. , Lockett F. Peter
Published: April 2009

If the finite soluble group G admits the dihedral group of order eight as a fixed-point-free group of automorphisms then the nilpotent length of G is at most three.
Corrigendum: Block idempotents and the Brauer correspondence
Authors: Carlson Jon F.
Published: April 2009

Professor William F. Reynolds has discovered a mistake in the main theorem of [1]. The problem occurs with the first display on page 339 in that is only congruent modulo radZ(G) to . The theorem still holds if θ(radZ(G)) ⊆ radZ(H), but this is not the case in general.
Computation of the stationary distribution of an infinite Markov matrix
Authors: Golub G.H. , Seneta E.
Published: April 2009

An algorithm is presented for computing the unique stationary distribution of an infinite stochastic matrix possessing at least one column whose elements are bounded away from zero. Elementwise convergence rate is discussed by means of two examples.
A note on the lattice properties of the linear maps of finite rank
Authors: Chaney John W.
Published: April 2009

It is shown that if E is a barreled locally convex lattice and F is a quasi-complete and order complete locally convex lattice then E′ ⊗ F equipped with the cone of positive continuous linear maps of finite rank is a lattice if and only if E′ or F has finite dimensional order intervals.