bluuebunny/crossref_metadata_2025 huggingface dataset:
A comparison theorem and the forced oscillation
Authors: Onose Hiroshi
Published: April 2009

Consider the n-th order delay differential equation

In the last few years, the oscillatory behavior of delay differential equations has been the subject of intensive investigations. But much less is known about the equation (A) with small forcing term q(t). The only papers devoted to this problem are by Kartsatos, Kusano, and the present author. The purpose of this paper is to prove some new oscillation theorems which contain the previous results.
On smoothness of the Banach space embedding
Authors: Giles J.R.
Published: April 2009

For a Banach space X, smoothness at a point of the natural embedding ◯ in X**, is characterised by a continuity property of the support mapping from X into X*. It then becomes clear that there are many non-reflexive Banach spaces with smooth embedding, a matter of interest raised by Ivan Singer [Bull. Austral. Math. Soc. 12 (1975), 407–416].
On the Sylow subgroups of a doubly transitive permutation group III
Authors: Praeger Cheryl E.
Published: April 2009

Let G be a 2-transitive permutation group of a set Ω of n points and let P be a Sylow p-subgroup of G where p is a prime dividing |G|. If we restrict the lengths of the orbits of P, can we correspondingly restrict the order of P? In the previous two papers of this series we were concerned with the case in which all P–orbits have length at most p; in the second paper we looked at Sylow p–subgroups of a two point stabiliser. We showed that either P had order p, or G ≥ An, G = PSL(2, 5) with p = 2, or G = M11 of degree 12 with p = 3. In this paper we assume that P has a subgroup Q of index p and all orbits of Q have length at most p. We conclude that either P has order at most p2, or the groups are known; namely PSL(3, p) ≤ G ≤ PGL(3, p), ASL(2, p) ≤ G ≤ AGL(2, p), G = PΓL,(2, 8) with p = 3, G = M12 with p = 3, G = PGL(2, 5) with p = 2, or G ≥ An with 3p ≤ n < 2p2; all in their natural representations.
The construction of diagrams for abelian groups
Authors: Ackermann Ernest C.
Published: April 2009

Christine W. Ayoub has defined diagrams for abelian groups and has shown that the structure of an abelian group A is determined by certain subgroups Ti of A which arise naturally from a given diagram for A. In this paper it is shown that a given diagram for A is formed from certain elementary diagrams for the Ti.
Splitting torsion theories over commutative rings
Authors: Fuelberth John D. , Kuzmanovich James , Shores Thomas S.
Published: April 2009

The purpose of this paper is to completely characterize splitting torsion theories over commutative rings. In particular, if (T, F) is a torsion theory for which T(R) = 0, then (T, F) is a splitting theory if and only if T contains only a finite number of nonisomorphic simple modules and every module in T is semisimple injective. In addition, an ideal theoretic characterization of splitting torsion theories is given, of which one consequence is that splitting torsion theories are TTF; furthermore, if R is also noetherian, then such torsion theories are centrally splitting. The known theorems concerning the splitting of the Goldie and simple torsion theories (for commutative rings) are derived from our theorem.
A class of modules over a locally finite group III
Authors: Hartley B.
Published: April 2009

Let G be a locally finite group, k a field of characteristic p ≥ 0 and V a right kG-module. We say that V is an -module over kG, if each p′-subgroup H of G contains a finite subgroup F with the same fixed points as H in V. (By convention, 0′ is taken as the set of all primes.) Such modules arise as elementary abelian section of -groups, a class of locally finite groups similar in many ways to the class of finite soluble groups.

The main theorem is that if V is an -module over kG with trivial Frattini submodule, and G is almost abelian, then every composition factor of V is complemented. This is a crucial ingredient in Tomkinson's theory of prefrattini subgroups in a certain subclass of . An example is given to show that the theorem breaks down for metabelian G. This leads to an example of a -group in which there are no analogues of prefrattini subgroups - the first situation where one of the standard conjugacy classes of subgroups of finite soluble groups has no decent analogue in the whole class
The K-functional of certain pairs of rearrangement invariant spaces
Authors: Arazy Jonathan
Published: April 2009

Let X, Y be rearrangement invariant spaces and let M = M(Y, X) be the space of all multipliers of Y into X. It is shown that if X = YM and some technical conditions are satisfied, then the K-functional K(t, f, X, Y) is equivalent to the expression

where ψ is the inverse of the fundamental function ϕM of M, defined by
Perturbation of nodes and poles in certain rational interpolants
Authors: Bokhari M.A.
Published: April 2009

Recently, E.B. Saff and A. Sharma proved a result on Walsh's type equiconvergence for certain sequences of rational interpolants having uniformly distributed poles and nodes of interpolation. Here we examine the sensitivity of this result to a slight perturbation of the poles and nodes. Some problems related to our work are also formulated.
A note on immersing manifolds in euclidean spaces
Authors: Beng Ng Tze
Published: April 2009

Let M be a closed, connected smooth and 3-connected mod 2 (that is Hi(M;ℤ2) = 0, 0 < i ≤ 3) manifold of dimension n = 7 + 8k. Using a combination of cohomology operations on certain cohomology classes of M and on the Thom class of the stable normal bundle of M we show that under certain conditions M immerses in R2n−8. This extends previously known results for such a general manifold when the number of 1's in the dyadic expansion of n is less than 8.
Fixed point theory and complementarity problems in Hilbert space
Authors: Isac G.
Published: April 2009

In this paper we study both the implicit and the explicit complementarity problem using some special and interesting connections between the complementarity problem and fixed point theory in Hilbert space.
Remarks on generalised power sums
Authors: Rumely Robert S. , van der Poorten A.J.
Published: April 2009

We give a description of factorisation in the ring of generalised power sums (the sequence of Taylor coefficients of rational functions regular at infinity) with a view to giving detailed bounds on the order of generalised power sum factors and roots of such sums.
Fourth-order boundary value problems at nonresonance
Authors: Yang Yisong
Published: April 2009

We establish under nonuniform nonresonance conditions an existence and uniqueness theorem for a linear, and the solvability for a nonlinear, fourth-order boundary value problem which occurs frequently in plate deflection theory.
Extreme values for divisor functions
Authors: MacLeod R.A.
Published: April 2009

Maximum and minimum values are obtained for some sums invovling the divisor functions of number theory.
A diophantine inequality with prime variables
Authors: Srinivasan S.
Published: April 2009

Let λ1, λ2, λ3 be non-zero reals, not all of the same sign and such that at least one ratio λi/λj is irrational. Then it is proved that for any given integer k ≥ 1 and real η, the inequaltiy

is solvable for every ε > 0. More general and sharper results are also proved.
A geometrically aberrant Banach space with uniformly normal structure
Authors: Yu Xin Tai
Published: April 2009

A geometrically aberrant Banach space with uniformly normal structure, a modification of Brown's example, is given.
On the lattice of right ideals of the endomorphism ring of an abelian group
Authors: Faticoni Theodore G.
Published: April 2009

Let A be an abelian group, let ∧ = End (A), and assume that A is a flat left ∧-module. Then σ = { right ideals I ⊂ ∧ | IA = A} generates a linear topology oil ∧. We prove that Hom(A,·) is an equivalence from the category of those groups B ⊂ An satisfying B = Hom(A, B)A, onto the category of σ-closed submodules of finitely generated free right ∧-modules. Applications classify the right ideal structure of A, and classify torsion-free groups A of finite rank which are (nearly) isomorphic to each A-generated subgroup of finite index in A.
Maximal coplanar sets of intersection points
Authors: Halpern Richard P. , Hobby David , Silberger Donald M.
Published: April 2009

Let F be any set of five points in R3 so situated that no four of the points are coplanar, and that the line xy through any two x and y of the points has a unique intersection point xy* with the plane determined by the other three. Let F^ denote the family of all such xy*. Let S(F) denote the set of all X ⊆ F^ which are maximal with respect to the property that X is a subset of a plane in R3. For k > 2 an integer, let S(k; F) denote the family of all k-membered elements in S(F).

A family 𝒟 of sets is said to be uniformly deep of depth d if and only if for every x ∈ ∪ 𝒟 there are exactly d distinct 𝒜 ∈ 𝒟 for which x ∈ 𝒜.

We establish the following result, and extend our ideas to general Euclidean spaces.
A natural proof of the cyclotomic identity
Authors: Taylor D.E.
Published: April 2009

The cyclotomic identity

where and μ is the classical Möbius function, is shown to be a consequence of a natural isomorphism of species.
The differentiability of convex functions on topological linear spaces
Authors: Sharp Bernice
Published: April 2009

In this paper topological linear spaces are categorised according to the differentiability properties of their continuous convex functions. Mazur's Theorem for Banach spaces is generalised: all separable Baire topological linear spaces are weak Asplund. A class of spaces is given for which Gateaux and Fréchet differentiability of a continuous convex function coincide, which with Mazur's theorem, implies that all Montel Fréchet spaces are Asplund spaces. The effect of weakening the topology of a given space is studied in terms of the space's classification. Any topological linear space with its weak topology is an Asplund space; at the opposite end of the topological spectrum, an example is given of the inductive limit of Asplund spaces which is not even a Gateaux differentiability space.
On a general nonlinear variational inequality
Authors: Bose Ramendra Krishna
Published: April 2009

Variational inequality theory provides techniques for solving a variety of applied problems in science and engineering. Recently Noor considered some interesting general nonlinear and linear variational inequalities in a series of papers and proved the existence and uniqueness of solutions by a fixed point technique developed by Glowinski, Lions and Tremolieres and also by a fixed point technique of Lions and Stampacchia. But there are several inaccuracies in his proofs and here they have been removed and correct formulation of the theorems are stated and proved and relationships are clearly shown. The existence of solution necessitates an additional condition in one case, and less condition in the other, but uniqueness can be proved without the condition that the operator be antimonotone.
Homothetic maps of distinguishing space-times
Authors: Kim Jin-Hwan
Published: April 2009

We show that if (M, g) is a distinguishing space-time, then any distance homothetic map from (M, g) onto arbitrary space-time (M′, g′) is a homothetic map; in particular, every distance preserving map is an isometry.
Oscillations for first order neutral differential equations with variable coefficients
Authors: Ruan Shigui
Published: April 2009

In this paper, sufficient conditions for oscillations of the first order neutral differential equation with variable coefficients

are obtained, where c, τ, σ and µ are positive constants, p, q ∈ C ([t0, ∞), R+).
A law of the iterated logarithm for martingales
Authors: Voit Michael
Published: April 2009

Using a slight generalisation of Brown's inequality, we show that for martingales the existence of a weak nonuniform bound on the rate of convergence in the central limit theorem yields the usual upper bound part of the law of the iterated logarithm.
On quasi-monotone sequences and their applications
Authors: Bor Hüseyin
Published: April 2009

In this paper using δ-quasi-monotone sequences a theorem on summability factors of infinite series, which generalises a theorem of Mazhar [7] on |C, 1|k summability factors of infinite series, is proved. Also we apply the theorem to Fourier series.
Hyperbolic flows are topologically stable
Authors: Choi Sung Kyu , Park Jong Suh
Published: April 2009

We show that any hyperbolic flow (X, π) on a metric space X is topologically stable by showing that it is expansive and has the chain-tracing property.
Orthonormal expansions and the principle of uniform boundedness
Authors: Husain S.A. , Sehgal V.M.
Published: April 2009

Let {φν: ν ∈ N (non-negative integers)} ⊆ C[0, 1] be a complete orthonormal sequence of complex-valued functions in L2[0, 1], {λν: ν ∈ N} and {λνμ: ν, μ ∈ N} be sequences of complex numbers. In this paper, the necessary and sufficient conditions are developed for the series to converge and also to exist, in C[0, 1] for each f ∈ L1[0, 1] where .
Monochromatic solutions to equations with unit fractions
Authors: Brown Tom C. , Rödl Voijtech
Published: April 2009

Our main result is that if G(x1, …, xn) = 0 is a system of homogeneous equations such that for every partition of the positive integers into finitely many classes there are distinct y1,…, yn in one class such that G(y1, …, yn) = 0, then, for every partition of the positive integers into finitely many classes there are distinct Z1, …, Zn in one class such that

In particular, we show that if the positive integers are split into r classes, then for every n ≥ 2 there are distinct positive integers x1, x1, …, xn in one class such that

We also show that if [1, n6 − (n2 − n)2] is partitioned into two classes, then some class contains x0, x1, …, xn such that

(Here, x0, x2, …, xn are not necessarily distinct.)
Generalised retract semigroups
Authors: Auinger Karl
Published: April 2009

We give a description of the structure of the semigroups for which each principal ideal is a retract. The globally idempotent case is solved quickly using a—suitably modified—construction which has been developed by Tully for the study of semigroups in which each ideal is a retract. The general case can be treated by a naturally obtained semigroup of subsets of the semigroup constructed for the globally idempotent case.
On metric regularity of multifunctions
Authors: Jourani A.
Published: April 2009

The aim of this paper is to give a metric regularity theorem for multifunctions between metric spaces involving some known results for multifunctions by using the notion of strict (G, δ)-differentiability of multifunctions and a simple convergence procedure.
Fractions of the period of the continued fraction expansion of quadratic integers
Authors: van der Poorten A.J.
Published: April 2009

The elementary nature and simplicity of the theory of continued fractions is mostly well disguised in the literature. This makes one reluctant to quote sources when making a remark on the subject and seems to necessitate redeveloping the theory ab initio. That had best be done succinctly. That is done here and allows the retrieval of some amusing results on pattern in the period of the continued fraction expansion of quadratic integers.
A fixed point theorem and existence of equilibrium for abstract economies
Authors: Rim Dong Il , Kim Won Kyu
Published: April 2009

In this paper, we shall prove a generalisation of Himmelberg's fixed point theorem and as applications, the existence of equilibrium points for abstract economies given by preference correspondences and utility functions have been established.
On the monotone convergence of general Newton-like methods
Authors: Argyros Ioannis K. , Szidarovszky Ferenc
Published: April 2009

This paper examines conditions for the monotone convergence of general Newton-like methods generated by point-to-point mappings. The speed of convergence of such mappings is also examined.
Lower bounds for the norms of projections with small kernels
Authors: Franchetti Carlo
Published: April 2009

Popov has recently introduced a class of subspaces of Lp(μ) (μ nonatomic) which generalise the finite codimensional ones, and proved that for p ≠ 2 any projection onto such a subspace has a norm strictly greater than one. In this paper we give the quantitative version of Popov's result computing the best possible lower bound for the norms of the considered projections.
On the metric theory of the optimal continued fraction expansion
Authors: Nair R.
Published: April 2009

Suppose kn denotes either φ(n) or φ(rn) (n = 1, 2, …) where the polynomial φ maps the natural numbers to themselves and rk denotes the kth rational prime. Let denote the sequence of convergents to a real numbers x for the optimal continued fraction expansion. Define the sequence of approximation constants by

In this paper we study the behaviour of the sequence for all most all x with respect to Lebesgue measure. In the special case where kn = n (n = 1, 2, …) these results are due to Bosma and Kraaikamp.
A characterisation of cyclic subnormal separated A-groups of nilpotent length three
Authors: Makarfi Muhammad Umar
Published: April 2009

The paper gives a detailed description of all those finite A-groups of nilpotent length three that satisfy the cyclic subnormal separation condition. It is shown that every monolithic group under discussion is an extension of its Fitting subgroup P, which is a homocyclic p-group, by a p′ metabelian subgroup H, where p is a prime. The centraliser of P in H is trivial while the monolith W is equal to ω1(P) and the action of H on W is faithful and irreducible. H is further shown to have non trivial centre and is an extension of its derived subgroup M by a subgroup L such that

for all primes q where Mq and Lq are the respective Sylow q-subgroups of M and L. The Fitting subgroup of F of H is shown to be M × Z(H), while Z(H) = F ∩ L and every element of L of prime order is in Z(H). Finally it is shown that if ql(q) is the exponent of Mq then every element of order dividing ql(q) in L belongs to Z(H).
Smoothness of the solution of the trivial Monge-Ampère equation
Authors: Ushakov Vitaly
Published: April 2009

A solution of the equation must be C2 smooth, need not be C3 smooth, but at the same time the ratio zxy: zxx is C1 (provided zxx ≠ 0). An analytical proof of this fact is given; the underlying geometrical interpretation is discussed.
Generalised solutions of Hessian equations
Authors: Colesanti Andrea , Salani Paolo
Published: April 2009

We introduce a definition of generalised solutions of the Hessian equation Sm(D2u) = f in a convex set ω ⊂ ℝn, where Sm(D2u) denotes the m-th symmetric function of the eigenvalues of D2u, f ∈ Lp(ω), p ≥ 1, and m ∈ {1, …, n}. Such a definition is given in the class of semi-convex functions, and it extends the definition of convex generalised solutions for the Monge-Ampère equation. We prove that semiconvex weak solutions are solutions in the sense of the present paper.
A note on the permutation behaviour of the Dickson polynomials of the second kind
Authors: Henderson M.
Published: April 2009

In this note known factorisation results for the Dickson polynomials of the second kind, fk(X, a), are used to obtain simple restrictions on those k for which fk(X, a) is a permutation polynomial over Fq.
On the size of integer solutions of elliptic equations
Authors: Bugeaud Yann
Published: April 2009

We improve upon earlier effective bounds for the magnitude of integer points on an elliptic curve ε defined over a number field K. We slightly refine the dependence on the discriminant of K. In most of the previous papers, the estimates obtained are exponential in the height of ε. In this work, taking also into consideration the prime ideals dividing the discriminant of ε, we provide a totally explicit bound which is only polynomial in the height.
Functional means and harmonic functional means
Authors: Chung Soon-Yeong
Published: April 2009

For a continuous function f(t) on (0, ∞) which is strictly monotone and a probability measure μ on [0, 1] we introduce the functional mean and the harmonic functional mean of x > 0 and y > 0 with respect to μ by

which gives a unified approach to various famous means.

Moreover, functional means and harmonic means in n variables are also given and applied to get many interesting properties, such as

where
Class numbers of real quadratic fields
Authors: Kim Jae Moon
Published: April 2009

Letbe a real quadratic field. It is well known that if 3 divides the class number ofk, then 3 divides the class number of, and thus it dividesB1,χω−1, where χ and ω are characters belonging to the fieldskandrespectively. In general, the main conjecture of Iwasawa theory implies that if an odd primepdivides the class number ofk, thenpdividesB1,χω−1, where ω is the Teichmüller character forp.

The aim of this paper is to examine its converse whenpsplits ink. Letk∞be the ℤp-extension ofk=k0andhnbe the class number ofkn, thenth layer of the ℤp-extension. We shall prove that ifp|B1,χω−1, thenp|hnfor alln≥ 1. In terms of Iwasawa theory, this amounts to saying that ifM∞/k∞, is nontrivial, thenL∞/k∞is nontrivial, whereM∞andL∞are the maximal abelianp-extensions unramified outsidepand unramified everywhere respectively.
On non-linear elliptic equations and the stability of soap film
Authors: Truong Công Nghê
Published: April 2009

We use an Inverse Mapping Theorem for Sobolev chains to obtain a number of existence theorems for non-linear elliptic partial differential equations with general order. We then apply one of these theorems to prove the stability of a soap film.
On approximation measures of q-logarithms
Authors: Matala-Aho Tapani , Väänänen Keijo
Published: April 2009

Using Padé approximations of the q-logarithmic series we obtain new approximation measures for values of q-logarithms and for the series , k = 1, 2, …, where (un) is a recurrence sequence, satisfying
Lattice basis reduction, Jacobi sums and hyperelliptic cryptosystems
Authors: Buhler Joe , Koblitz Neal
Published: April 2009

Using the LLL-algorithm for finding short vectors in lattices, we show how to compute a Jacobi sum for the prime field Fp in Q(e2πi/n) in time O(log3p), where n is small and fixed, p is large, and p = 1 (mod n). This result is useful in the construction of hyperelliptic cryptosystems.
An interpolation by successive derivatives at a finite set
Authors: Chung Soon-Yeong
Published: April 2009

For an n-times differentiable function f(x) whose derivatives f(j)(xj) at x = xj, j = 0, 1, …, n are specified, we introduce a sequence of fundamental polynomials to interpolate f(x) with a remainder as

The remainder R(x|x0, x1,… xn) is given in an integral form and Lagrange's form.

In addition, by introducing orthogonality of Sobolev type we verify the best optimality of the approximations and interpret the fundamental polynomials as a kind of Sobolev orthogonal polynomial.
Automorphic pseudodifferential operators, Poincaré series and Eisenstein series
Authors: Lee Min Ho
Published: April 2009

We construct Poincaré series and Eisenstein series for automorphic pseudodifferential operators, and show that the space of automorphic pseudodifferential operators associated to cusp forms is generated by Poincaré series. We also obtain explicit formulas for such Poincaré series and Eisenstein series.
A generalisation of the lower radical class
Authors: McDougall Robert
Published: April 2009

In this work we demonstrate that the lower radical class construction on a homomorphically closed class of associative rings generates a radical class for any class of associative rings. We also give a new description of the upper radical class using the construction on an appropriate generating class.
Circumradius-diameter and width-inradius relations for lattice constrained convex sets
Authors: Awyong Poh Wah , Scott Paul R.
Published: April 2009

Let K be a planar, compact, convex set with circumradius R, diameter d, width w and inradius r, and containing no points of the integer lattice. We generalise inequalities concerning the ‘dual’ quantities (2R − d) and (w − 2r) to rectangular lattices. We then use these results to obtain corresponding inequalities for a planar convex set with two interior lattice points. Finally, we conjecture corresponding results for sets containing one interior lattice point.
The range of the Helgason-Fourier transformation on homogeneous trees
Authors: Cowling Michael , Setti Alberto G.
Published: April 2009

Let be a homogeneous tree, o be a fixed reference point in , and be the closed ball of radius N in centred at o. In this paper we characterise the image under the Helgason–Fourier transformation ℋ of , the space of functions supported in , and of , the space of rapidly decreasing functions on . In both cases our results are counterparts of known results for the Helgason–Fourier transformation on noncompact symmetric spaces.
Boundary two-parameter eight-state supersymmetric fermion model and Bethe ansatz solution
Authors: Bracken Anthony J. , Ge Xiang-Yu , Zhang Yao-Zhong , Zhou Huan-Qiang
Published: April 2009

The recently introduced two-parameter eight-state Uq [gl(3|1)] supersymmetric fermion model is extended to include boundary terms. Nine classes of boundary conditions are constructed, all of which are shown to be integrable via the graded boundary quantum inverse scattering method. The boundary systems are solved by using the coordinate Bethe ansatz and the Bethe ansatz equations are given for all nine cases.
Note on U-closed semigroup rings
Authors: Matsuda Ryûki
Published: April 2009

Let D be an integral domain with quotient field K. If α2 − α ∈ D and α3 − α2 ∈ D imply α ∈ D for all elements α of K, then D is called a u-closed domain. A submonoid S of a torsion-free Abelian group is called a grading monoid. We consider the semigroup ring D[S] of a grading monoid S over a domain D. The main aim of this note is to determine conditions for D[S] to be u-closed. We shall show the following Theorem: D[S] is u-closed if and only if D is u-closed.
Pointwise chain recurrent maps of the space Y
Authors: Guo Wenjing , Zeng Fanping , Hu Qiying
Published: April 2009

Let Y = {z ∈ C: z3 ∈ [0, 1]} (equipped with subspace topology of the complex space C) and let f: Y → Y be a continuous map. We show that if f is pointwise chain recurrent (that is, every point of Y is chain recurrent under f), then either f12 is the identity map or f12 is turbulent. This result is a generalisation to Y of a result of Block and Coven for pointwise chain recurrent maps of the interval.
On sums of certain trigonometric series
Authors: Eie Minking , Ong Yao Lin
Published: April 2009

Let N be a fixed positive integer. In this paper, we apply a newly developed method of Eie and Lai to the evaluation of certain infinite trigonometric series. Indeed, we are able to express the sums of these series in terms of Bernoulli polynomials. That is, we obtain several new Bernoulli identities. A similar method leads to Ramanujan's identities.
A spectral problem in ordered Banach algebras
Authors: Mouton S.
Published: April 2009

We recall the definition and properties of an algebra cone C of a complex unital Banach algebra A. It can be shown that C induces on A an ordering which is compatible with the algebraic structure of A, and A is then called an ordered Banach algebra. The Banach algebra ℒ(E) of all bounded linear operators on a complex Banach lattice E is an example of an ordered Banach algebra, and an interesting aspect of research in ordered Banach algebras is that of investigating in an ordered Banach algebra-context certain problems that originated in ℒ(E). In this paper we investigate the problems of providing conditions under which (1) a positive element a with spectrum consisting of 1 only will necessarily be greater than or equal to 1, and (2) f (a) will be positive if a is positive, where f (a) is the element defined by the holomorphic functional calculus.
Finite groups with two p-regular conjugacy class lengths
Authors: Beltrán Antonio , Felipe María José
Published: April 2009

Let G be a finite p-solvable group for a fixed prime p. We determine the structure of G when the set of p-regular conjugacy class sizes of G is {1, m} for an arbitrary integer m > 1.
Nonlinear filtering of a system of logistic equations
Authors: Ahlip Rehez , Anh Vo
Published: April 2009

This paper is concerned with the filtering problem for a nonlinear stochastic system of prey-predator logistic equations. Based on the innovations approach, we establish the Zakai equation for the unnormalised conditional distribution and the adjoint Zakai equation for the unnormalised conditional density of the nonlinear filter. Using a perturbation technique, we obtain the appropriate expressions for the unnormalised conditional distribution and density of stochastic integrals with respect to the observation processes.
Invariant analytic hypersurfaces in complex Lie groups
Authors: Gilligan Bruce
Published: April 2009

Suppose G is a complex Lie group and H is a closed complex subgroup of G. Let G′ denote the commutator subgroup of G. If there are no nonconstant holomorphic functions on G/H and H is not contained in any proper parabolic subgroup of G, then Akhiezer [2] asked whether every analytic hypersurface in G which is invariant under the right action of H is also invariant under the right action of G′. In this paper we answer a related question in two settings. Under the assumptions stated above we show that the orbits of the radical of G in G/H cannot be Cousin groups, provided G/H is Kähler. We also introduce an intermediate fibration of G/H induced by the holomorphic reduction of the radical orbits and resolve the related question in a situation arising from this fibration.
Bounds for the distance to finite-dimensional subspaces
Authors: Dragomir S. S.
Published: April 2009

We establish upper bounds for the distance to finite-dimensional subspaces in inner product spaces and improve some generalisations of Bessel's inequality obtained by Boas, Bellman and Bombieri. Refinements of the Hadamard inequality for Gram determinants are also given.
Similarity invariant semigroups generated by non-Fredholm operators
Authors: Kavkler Iztok
Published: April 2009

Let A ∈ B(H) be a bounded non-compact operator that is not semi-Fredholm. The similarity invariant semigroup generated by A is shown to consist of all operators that are not semi-Fredholm and satisfy obvious inequalities for the nullity and co-nullity.
Principal groupoids with continuous weak multiplication
Authors: Amiri H. , Bami M. Lashkarizadeh
Published: April 2009

In the present paper by extending the original multiplication of a principal groupoid to a weak multiplication and introducing a notion of semitopological semigroupoid compactification we have proved that every principal groupoid with a continuous weak multiplication has a semitopological semigroupoid compactification.
Characterisation of the sub-Riemannian isometry groups of theH-type groups
Authors: Tan Kang-Hai , Yang Xiao-Ping
Published: April 2009

For aH-type groupG, we first give explicit equations for its shortest sub-Riemannian geodesics. We use properties of sub-Riemannian geodesics inGto characterise the isometry groupISO(G) with respect to the Carnot-Carathéodory metric. It turns out thatISO(G) coincides with the isometry group with respect to the standard Riemannian metric ofG.
On the Boas-Bellman inequality in inner product spaces
Authors: Dragomir S. S.
Published: April 2009

New results related to the Boas–Bellman generalisation of Bessel' inequality in inner product spaces are given.
On Bessel and Grüss inequalities for orthonormal families in inner product spaces
Authors: Dragomir S. S.
Published: April 2009

A new reverse of Bessel's inequality for orthornormal families in real or complex inner product space is obtained. Applications for some Grüss type results are also provided.
On the existence of premixed laminar flames
Authors: Razani Abdolrahman
Published: April 2009

In this article, the existence of travelling wave solutions for premixed laminar flames in a model of slow, “constant density” combustion is studied. The model is governed by a simple system of an exothermic chemical reaction in a gas, via the reaction rate function, which is very natural, as we do not impose the assumption of its continuity. The existence of travelling waves is demonstrated and they are shown to be specific heteroclinic orbits of a three dimensional system of ordinary differential equations, connecting the unburned state points to a burned state point. The existence of these solutions is based on some general topological arguments in ordinary differential equations.
Witt kernels of bi-quadratic extensions in characteristic 2
Authors: Ahmad Hamza
Published: April 2009

Let κ be a field of characteristic 2. The author's previous results (Arch. Math. (1994)) are used to prove the excellence of quadratic extensions of κ. This in turn is used to determine the Witt kernel of a quadratic extension up to Witt equivalence. An example is given to show that Witt equivalence cannot be strengthened to isometry.
Finite normal edge-transitive Cayley graphs
Authors: Praeger Cheryl E.
Published: April 2009

An approach to analysing the family of Cayley graphs for a finite group G is given which identifies normal edge-transitive Cayley graphs as a sub-family of central importance. These are the Cayley graphs for G for which a subgroup of automorphisms exists which both normalises G and acts transitively on edges. It is shown that, for a nontrivial group G, each normal edge-transitive Cayley graph for G has at least one homomorphic image which is a normal edge-transitive Cayley graph for a characteristically simple quotient group of G. Moreover, given a normal edge-transitive Cayley graph ΓH for a quotient group G/H, necessary and sufficient conditions are obtained for the existence of a normal edge-transitive Cayley graph Γ for G which has ΓH as a homomorphic image, and a method for obtaining all such graphs Γ is given.
On rings of invariants of non-modular Abelian groups
Authors: Campbell H.E.A. , Harris J.C. , Wehlau D.L.
Published: April 2009

We study the ring of invariant Laurent polynomials associated to the action of a finite diagonal group G on the symmetric algebra of a vector space over a field F. Here the characteristic p of the field F necessarily does not divide the order q = |G| of the group, so G is said to be non-modular. For certain representations of such groups, we can characterise generators of the ring of invariant polynomials in the original symmetric algebra, extending results of Campbell, Hughes, Pappalardi and Selick. In particular we obtain a recursive formula for the number of minimal generators for these rings of invariants.
On incidence rings of group automata
Authors: Kelarev A. V.
Published: April 2009

For all finite p-groups, we describe the Jacobson radicals of incidence rings of group automata.
Interior regularity of the degenerate Monge-Ampère equation
Authors: Błocki Zbigniew
Published: April 2009

We study interior C1,1 regularity of generalised solutions of the Monge-Ampére equation det D2u = ψ, ψ ≥ 0, on a bounded convex domain Ω in ℝn with u = ϕ on ∂Ω. We prove in particular that u ∈ C1,1(Ω) if either i) ϕ = 0 and ψ1/(n − 1) ∈ C1,1 (Ω) or ii) Ω is C1,1 strongly convex, ϕ ∈ C1,1 (Ω̅), ψ1/(n − 1) ∈ C1,1(Ω̅) and ψ > 0 on U ∩ Ω, where U is a neighbourhood of ∂Ω. The main tool is an improvement of Pogorelov's well known C1,1 estimate so that it can be applied to the degenerate case.
On numbers which are differences of two conjugates over Q of an algebraic integer
Authors: Zaimi T.
Published: April 2009

We continue the investigation started by A. Dubickas of the numbers which are differences of two conjugates of an algebraic integer over the field Q of rational numbers. Mainly, we show that the cubic algebraic integers over Q with zero trace satisfy this property and we give a characterisation for those for which this property holds in their normal closure. We also prove that if a normal extension K/Q is of prime degree, then every integer of K with zero trace is a difference of two conjugates of an algebraic integer in K if and only if there exists an integer of K with trace 1.
The generalised Hadamard inequality, g-convexity and functional Stolarsky means
Authors: Neuman E. , Pearce C. E. M. , Pečarić J. , Šimić V.
Published: April 2009

We explore the role of weighted functional Stolarsky means in providing bounds in generalised Hadamard-type inequalities for g-convex functions. Refinements are given for Levinson's inequality and the generalised Hadamard inequality. Applications are made to multivariate weighted functional Stolarsky means.
Differential equations in spaces of Hilbert space valued distributions
Authors: Alshansky Maxim
Published: April 2009

A Gaussian measure is introduced on the space of Hilbert space valued tempered distributions. It is used to define a Hilbert space valued Q-Wiener process and a white noise process with a nuclear covariance operator Q. The proposed construction is used for solving operator-differential equations with additive noise with the operator coefficient generating an n-times integrated exponentially bounded semigroup.
Universality on higher order Hardy spaces
Authors: Bernal-González L. , Bonilla A. , Calderón-Moreno M. C.
Published: April 2009

We prove a Seidel-Walsh-type theorem about the universality of a sequence of derivation-composition operators generated by automorphisms of the unit disk in the setting of the higher order Hardy spaces. Moreover, some related positive or negative assertions involving interpolating sequences and sequences between two tangent circles are established for the class of bounded functions in the unit disk. Our statements improve earlier ones due to Herzog and to the first and third authors.
On the cohomology of extensions by a Heisenberg Lie algebra
Authors: Pouseele Hannes
Published: April 2009

This article describes the cohomology spaces of any Lie algebra containing a Lie algebra of Heisenberg type (whose cohomology was studied by Santharoubane) as an ideal of codimension 1. For instance, the twisted standard filiform Lie algebras are of this kind. We give an explicit formula for the Betti numbers of this Lie algebra, and use this to describe new families of algebras whose Betti numbers do not behave unimodally.
Some extensions of additive properties of general sequences
Authors: Tang Min
Published: April 2009

Let A = {a1, a2,…}(a1 < a2 < …) be an infinite sequence of positive integers. Let k ≥ 2 be a fixed integer and denote by Rk(n) the number of solutions of . Erdős, Sárközy and Sós studied the boundness of |R2(n + 1) − R2(n)| and the monotonicity property of R2(n). In this paper, we extend some results to k > 2.
The discontinuity point sets of quasi-continuous functions
Authors: Maslyuchenko Oleksandr V.
Published: April 2009

It is proved that a subsetEof a hereditarily normal topological spaceXis a discontinuity point set of some quasi-continuous functionf:X→ ℝ if and only ifEis a countable union of setsEn=Ān⋂Bdash abovenwhereĀn⋂Bn=An⋂Bdash aboven= φ
An analytic extension of a spacelike maximal surface
Authors: Koh Sung-Eun
Published: April 2009

It is shown that a spacelike maximal surface in the three dimensional Lorentz-Minkowski space can be extended analytically if it meets a spacelike plane at a constant hyperbolic angle.
Completely continuous elements of Banach algebras related to locally compact groups
Authors: Mehdipour M. J. , Nasr-Isfahani R.
Published: April 2009

Let G be a locally compact group and be the Banach space of all essentially bounded measurable functions on G vansihing an infinity. Here, we study some families of right completely continuous elements in the Banach algebra equipped with an Arens type product. As the main result, we show that has a certain right completely continuous element if and only if G is compact.
A Remark on minimal Lagrangian diffeomorphisms and the Monge-Ampère equation
Authors: Urbas John
Published: April 2009

We construct a counterexample to a theorem of Jon Wolfson concerning the existence of globally smooth solutions of the second boundary value problem for Monge-Ampère equations in two dimensions, or equivalently, on the existence of minimal Lagrangian diffeomorphisms between simply connected domains in R2.
Decomposability of finite rank operators in certain subspaces and algebras
Authors: Li Jiankui
Published: April 2009

Let  be either a reflexive subspace or a bimodule of a reflexive algebra in B (H), the set of bounded operators on a Hilbert space H. We find some conditions such that a finite rank T ∈  has a rank one summand in  and  has strong decomposability. Let (ℒ) be the set of all operators on H that annihilate all the operators of rank at most one in alg ℒ. We construct an atomic Boolean subspace lattice ℒ on H such that there is a finite rank operator T in (ℒ) such that T does not have a rank one summand in (ℒ). We obtain some lattice-theoretic conditions on a subspace lattice ℒ which imply alg ℒ is strongly decomposable.
Non-periodic continued fractions in hyperelliptic function fields
Authors: van der Poorten Alfred J.
Published: April 2009

Dedicated to George Szekeres on his 90th birthday

We discuss the exponential growth in the height of the coefficients of the partial quotients of the continued fraction expansion of the square root of a generic polynomial.
Steady vortex flows obtained from an inverse problem
Authors: Emamizadeh B. , Bahrami F.
Published: April 2009

In this paper we prove the existence of solutions to an inverse semilinear elliptic partial differential equation. Physically, solutions represent stream functions of steady planar flows with bounded vortices. The kinetic energy functional is maximised over the set of rearrangements of a given function.
The weighted Turán type inequality for generalised Jacobi weights
Authors: Wang J. L. , Zhou S. P.
Published: April 2009

We study the weighted Turán type inequality for generalised Jacobi weights, and give a complete positive answer to Zhou's conjecture.
Quantities related to upper and lower semi-Fredholm type linear relations
Authors: Alvarez Teresa , Cross Ronald , Wilcox Diane
Published: April 2009

Certain norm related functions of linear operators are considered in the very general setting of linear relations in normed spaces. These are shown to be closely related to the theory of strictly singular, strictly cosingular, F+ and F− linear relations. Applications to perturbation theory follow.
Jacobi-like forms and power series bundles
Authors: Lee Min Ho
Published: April 2009

Jacobi-like forms are certain formal power series which generalise Jacobi forms in some sense, and they are closely linked to modular forms when their coefficients are holomorphic functions on the Poincaré upper half plane. We construct two types of vector bundles whose fibres are isomorphic to the space of certain formal power series and whose sections can be identified with Jacobi-like forms for a discrete subgroup of SL (2,ℝ).
Optimality conditions for vector optimisation with set-valued maps
Authors: Huang Yong Wei
Published: April 2009

In this paper, we establish a Farkas-Minkowski type alternative theorem under the assumption of nearly semiconvexlike set-valued maps. Based on the alternative theorem and some other lemmas, we establish necessary optimality conditions for set-valued vector optimisation problems with extended inequality constraints in a sense of weak E-minimisers.
On a boundary value problem arising in elastic deflection theory
Authors: Wang Xiuqin
Published: April 2009

In this paper, a finite-difference method for the determination of an approximate solution of a fourth-order two-point boundary value problem is presented under the nonresonance condition. The solution of this linear problem can be used to find approximate solutions of a broad range of nonlinear problems in applications.
A note on Hadamard arrays
Authors: Cooper Joan
Published: April 2009

Let V = mk + 1 be a prime power; we show for m even it is not possible to partition the Galois field GF(v) to give four (0, 1, −1) matrices X1, X2, X3, X4 satisfying:

(i) Xi * Xj = 0, i ≠ j, i, j = 1, 2, 3, 4;

(ii) is a (1, −1) matrix;

(iii) Thus this method of partitioning the Galois field GF(V), into four matrices satisfying the above conditions, cannot be used to find Baumert-Hall Hadamard arrays BH[4V] for v = 9, 11, 17, 23, 27, 29, ….
A two parameter eigenvalue problem
Authors: Rickard J.A.
Published: April 2009

An ordinary second order differential equation is considered in which the coefficients are dependent on two parameters ω and F as well as the independent variable μ. The equation arises in the study of free oscillations of incompressible inviscid fluid in global shells. An asymptotic technique is presented which estimates the eigenvaiues (that is the values of ω for which the solution is bounded for all |μ| ≤ 1) as functions of F, as F → ∞. The agreement of the results with numerical computations is also discussed.
Queuing and the provision of service facilities
Authors: Finch Peter D.
Published: April 2009

Results are obtained which enable one to assess the extent to which the waiting times of queuing customers depend on the number of servers which provide them with service.
A special property of the matrix Riccati equation
Authors: Stokes A.N.
Published: April 2009

In the domain of real symmetric matrices ordered by the positive definiteness criterion, the symmetric matrix Riccati differential equation has the unusual property of preserving the ordering of its solutions as the independent variable changes, Here is is shown that, subject to a continuity restriction, the Riccati equation is unique among comparable equations in possessing this property.
The CREAM conjecture for the subvarieties of certain abelian-by-nilpotent varieties
Authors: Leong Y.K.
Published: April 2009

It is proved that the subvarieties of the variety are CREAM in the sense of Higman when m, n are coprime and n is an odd integer not divisible by q4 for any prime q.
Metabelian groups and varieties
Authors: Bryce R. A.
Published: April 2009

Here we announce results which will appear in full in due course elsewhere. The aim is a study of varieties of metabelian groups. The technique is to study varieties of certain universal algebras, which are very similar to groups, called bigroups. For certain varieties of bigroups all the non-nilpotent join-irreducible subvarieties are determined, and this is used to reduce the same problem for varieties of metabelian groups to the case of prime-power exponent. Questions of distributivity of the lattice of metabelian varieties are also discussed.
Semifield metric spaces
Authors: Kleiber Martin , Pervin W. J.
Published: April 2009

Extending the results of An†onovskiĭ, Bol†janskiĭ, and Sarymsakov on semifield metric spaces, the authors define a regular semifield metric to be one in which the distance in the standard Tychonoff product representation of a point from a disjoint closed set is nonzero. It is shown that every completely regular topological space possesses a completely regular semifield metric and that there is an equivalent completely regular semifield metric for every semifield metric space. A normal semifield metric is defined to be one in which the distance between two disjoint closed sets is nonzero and it is shown that possessing a normal semifield metric is equivalent to being a normal topological space. Finally, Cauchy nets in semifield metric spaces are introduced leading to the notion of completeness. It is shown that a semifield metric space is complete iff every Cauchy net with the property that its directed set has cardinality less than or equal to the cardinality of the indexing set of the Tychonoff product representation of the semifield converges.