bluuebunny/crossref_metadata_2025 huggingface dataset:
Strongly omnipresent operators: general conditions and applications to composition operators
Authors: Bernal-González L. , Calderón-Moreno M. C. , Grosse-Erdmann K.-G.
Published: April 2009

This paper studies the concept of strongly omnipresent operators that was recently introduced by the first two authors. An operator T on the space H(G) of holomorphic functions on a complex domain G is called strongly omnipresent whenever the set of T-monsters is residual in H(G), and a T-monster is a function f such that Tf exhibits an extremely ‘wild’ behaviour near the boundary. We obtain sufficient conditions under which an operator is strongly omnipresent, in particular, we show that every onto linear operator is strongly omnipresent. Using these criteria we completely characterize strongly omnipresent composition and multiplication operators.
Compact semilattices with open principal filters
Authors: Gutik Oleg V. , Rajagopalan M. , Sundaresan K.
Published: April 2009

A locally compact semilattice with open principal filters is a zero-dimensional scattered space. Cardinal invariants of locally compact and compact semilattices with open principal filters are investigated. Structure of topological semilattices on the one-point Alexandroff compactification of an uncountable discrete space and linearly ordered compact semilattices with open principal filters are researched.
Vector valued mean-periodic functions on groups
Authors: Devaraj P. , Rana Inder K.
Published: April 2009

LetGbe a locally compact Hausdorif abelian group andXbe a complex Banach space. LetC(G, X)denote the space of all continuous functionsf: G → X, with the topology of uniform convergence on compact sets. LetX′ denote the dual ofXwith the weak* topology. LetMc(G, X′)denote the space of allX′-valued compactly supported regular measures of finite variation onG. For a functionf ∈ C(G, X)and μ ∈Mc(G, X′), we define the notion of convolutionf* μ. A functionf ∈ C(G, X)is called mean-periodic if there exists a non-trivial measure μ ∈Mc(G, X′)such thatf* μ = 0. For μ ∈Mc(G, X′), letM P(μ) = {f ∈ C(G, X): f * μ = 0}and letM P(G, X) = ∪μM P(μ). In this paper we analyse the following questions: IsM P(G, X)≠ 0? IsM P(G, X) ≠ C(G, X)? IsM P(G, X)dense inC(G, X)? IsM P(μ) generated by ‘exponential monomials’ in it? We answer these questions for the groupsG= ℝ, the real line, andG= T, the circle group. Problems of spectral analysis and spectral synthesis forC(ℝ,X) andC(T,X) are also analysed.
Discrete series of fusion algebras
Authors: Srinivasan R. , Sunder V. S. , Wildberger N. J.
Published: April 2009

We show that the left regular representation of a countably infinite (discrete) group admits no finite-dimensional invariant subspaces. We also discuss a consequence of this fact, and the reason for our interest in this statement.

We then formally state, as a ‘conjecture’, a possible generalisation of the above statement to the context of fusion algebras. We prove the validity of this conjecture in the case of the fusion algebra arising from the dual of a compact Lie group.

We finally show, by example, that our conjecture is false as stated, and raise the question of whether there is a ‘good’ class of fusion algebras, which contains (a) the two ‘good classes’ discussed above, namely, discrete groups and compact group duals, and (b) only contains fusion algebras for which the conjecture is valid.
Recognizing powers in nilpotent groups and nilpotent images of free groups
Authors: Baumslag Gilbert
Published: April 2009

An element in a free group is a proper power if and only if it is a proper power in every nilpotent factor group. Moreover there is an algorithm to decide if an element in a finitely generated torsion-free nilpotent group is a proper power.
The block structure of complete lattice ordered effect algebras
Authors: Jenča Gejza
Published: April 2009

We prove that every for every complete lattice-ordered effect algebra E there exists an orthomodular lattice O(E) and a surjective full morphism øE: O(E) → E which preserves blocks in both directions: the (pre)imageofa block is always a block. Moreover, there is a 0, 1-lattice embedding : E → O(E).
On the asymptotic behaviour of associated primes of generalized local cohomology modules
Authors: Khashyarmaneshs Kazem , Abbasi Ahmad
Published: April 2009

LetMandNbe finitely generated and graded modules over a standard positive graded commutative Noetherian ringR, with irrelevant idealR+. Letbe thenth component of the graded generalized local cohomology module. In this paper we study the asymptotic behavior of AssfR+() as n → –∞ wheneverkis the least integerjfor which the ordinary local cohomology moduleis not finitely generated.
Large doubly transitive orbits on a line
Authors: Montinaro Alessandro
Published: April 2009

Projective planes of ordernwith a coUineation group admitting a 2-transitive orbit on a line of length at leastn/2 are investigated and new examples are provided.
Stable perturbation in Banach algebras
Authors: Xue Yifeng
Published: April 2009

Let be a unital Banach algebra. Assume that a has a generalized inverse a+. Then is said to be a stable perturbation of a if . In this paper we give various conditions for stable perturbation of a generalized invertible element and show that the equation is closely related to the gap function . These results will be applied to error estimates for perturbations of the Moore-Penrose inverse in C*–algebras and the Drazin inverse in Banach algebras.
Multipliers from spaces of test functions to amalgams
Authors: De Squire Maria Torres
Published: April 2009

In this paper we study the space of multipliers M(r, s: p, q) from the space of test functions Φrs(G), on a locally compact abelian group G, to amalgams (Lp, lq)(G); the former includes (when r = s = ∞) the space of continuous functions with compact support and the latter are extensions of the Lp(G) spaces. We prove that the space M(∞: p) is equal to the derived space (Lp)0 defined by Figá-Talamanca and give a characterization of the Fourier transform for amalgams in terms of these spaces of multipliers.
Geometric and arithmetic postulation of the exponential function
Authors: Pila J.
Published: April 2009

This paper presents new proofs of some classical transcendence theorems. We use real variable methods, and hence obtain only the real variable versions of the theorems we consider: the Hermite-Lindemann theorem, the Gelfond-Schneider theorem, and the Six Exponentials theorem. We do not appeal to the Siegel lemma to build auxiliary functions. Instead, the proof employs certain natural determinants formed by evaluating n functions at n points (alternants), and two mean value theorems for alternants. The first, due to Pólya, gives sufficient conditions for an alternant to be non-vanishing. The second, due to H. A. Schwarz, provides an upper bound.
The fixed point property in banach spaces whose characteristic of uniform convexity is less than 2
Authors: Falset J. García
Published: April 2009

We prove that every Banach space X with characteristic of uniform convexity less than 2 has the fixed point property whenever X satisfies a certain orthogonality condition.
Quasi-linear parabolic partial differential equations with delays in the highest order spatial derivatives
Authors: Yong Jiongmin , Pan Liping
Published: April 2009

A class of functional differential equations in some Hilbert space are studied. The results are applicable to many quasi-linear parabolic paratial differential equations with (possibly) countably many discrete delays and finitely many distributed delays in the highest order spatial derivatives. For the linear case, an evolution operator on the underline space H is introduced, via which a variation of constant formula for the solution of the equation in the underline space H is derived. Some spectral properties of the generator of the solution semigroup defined on some appropriate space are discussed as well.
Crossed products of C*-algebras by *-endomorphisms
Authors: Stacey P. J.
Published: April 2009

Crossed products of C*-algebras by *-endomorphisms are defined in terms of a universal property for covariant representations implemented by families of isometries and some elementary properties of covariant representations and crossed products are obtained.
Rosenthal sets and the Radon-Nikodym property
Authors: Dowling Patrick N.
Published: April 2009

Let X be a complex Banach space, G a compact abelian metrizable group and Λ a subset of Ĝ, the dual group of G. If X has the Radon-Nikodym property and is separable then has the Radon-Nikodym property. One consequence of this is that CΛ(G, X) has the Radon-Nikodym property whenever X has the Radon-Nikodym property and the Schur property and Λ is a Rosenthal set. A partial stability property for products of Rosenthal sets is also obtained.
Generalized Emden-Fowler equations of subcritical growth
Authors: Rother Wolfgang
Published: April 2009

The existence of positive solutions, vanishing at infinity, for the semilinear eigenvalue problem Lu = λ f(x, y) in RN is obtained, where L is a strictly elliptic operator. The function f is assumed to be of subcritical growth with respect to the variable u.
Gevrey spaces and their intersections
Authors: Ter Elst A. F. M.
Published: April 2009

For unbounded operators A1, …, Ad, Gevrey spaces Sλ1, …, λd (A1, …, Ad) of order (λ1, …, λd) are introduced, where the orders λ1, …, λd need not be equal. These extend the notion of Gevrey space defined by Goodman and Wallach where λ1 = … = λd. Several mild conditions on the operators A1, … Ad and the orders λ1, …, λd are presented such that the equality is valid. Examples are included.
The locally convex topology on the space of meromorphic functions
Authors: Grosse-Erdmann Karl-Goswin
Published: April 2009

We give a positive answer to a question of Horst Tietz. A theorem of his that is related to the Mittag-Leffler theorem looks like a duality restult under some locally convex topology on the space of meromorphic functions. Tietz has posed the problem of finding such a topology. It is shown that a topology introduced by Holdguün in 1973 solves the problem. The main tool in the study of this topology is a projective description of it that is derived here. We also argue that Holdgrün's topology is the natural locally convex topology on the space of meromorphic functions.
A mean value theorem for exponential sums
Authors: Huxley M. N.
Published: April 2009

The exponential sum S(x) = Σe(f(m + x)) has mean square size O(M), when m runs through M consecutive integers, f(x) satisfies bounds on the second and third derivatives, and x runs from 0 to 1.
On diameters of orbits of compact groups in unitary representations
Authors: Deutsch Annabel , Valette Alain
Published: April 2009

For a compact group G, we compute the Kazhdan constants κ(G, G) obtained by taking G itself as a generating subset. We get κ(G, G) = if G is finite of order n, and κ(G, G) = if G is infinite.
Categorical compactness for rings
Authors: Fay Temple H. , Joubert Stephan V.
Published: April 2009

In this paper we study categorical compactness with respect to a class of objects F being motiveated by examples arising from modules, abelian groups, and various classes of non-abelian groups. This theory is then applied to the category of not necessarily associative rings. In particular, we study the example arising from the class of all torsion-free rings. This work extends some recent results of B. J. Gardner for associative rings and radical classes.
Bounds for the separations of real zeros of polynomials
Authors: Walker Peter
Published: April 2009

We measure the separation of the zeros of the polynomial f(x) = by δ(f) = mini(ai+1 − ai). We establish a bound for the amount by which the ratio δ(f′ − kf)/δ(f) exceeds 1.
On the uniform Kadec-Klee property with respect to convergence in measure
Authors: Sukochev F. A.
Published: April 2009

Let E(0, ∞) be a separable symmetric function space, let M be a semifinite von Neumann algebra with normal faithful semifinite trace μ, and let E(M, μ) be the symmetric operator space associated with E(0, ∞). If E(0, ∞) has the uniform Kadec-Klee property with respect to convergence in measure then E(M, μ) also has this property. In particular, if LΦ(0, ∞) (ϕ(0, ∞)) is a separable Orlicz (Lorentz) space then LΦ(M, μ) (Λϕ (M, μ)) has the uniform Kadec-Klee property with respect to convergence in measure on sets of finite measure if and only if the norm of E(0, ∞) satisfies G. Birkhoff's condition of uniform monotonicity.
Commutators in pseudo-orthogonal groups
Authors: Arlinghaus F. A. , Vaserstein L. N. , You Hong
Published: April 2009

We study commutators in pseudo-orthogonal groups O2nR (including unitary, symplectic, and ordinary orthogonal groups) and in the conformal pseudo-orthogonal groups GO2nR. We estimate the number of commutators, c(O2nR) and c(GO2nR), needed to represent every element in the commutator subgroup. We show that c(O2nR) ≤ 4 if R satisfies the ∧-stable condition and either n ≥ 3 or n = 2 and 1 is the sum of two units in R, and that c(GO2nR) ≤ 3 when the involution is trivial and ∧ = R∈. We also show that c(O2nR) ≤ 3 and c(GO2nR) ≤ 2 for the ordinary orthogonal group O2nR over a commutative ring R of absolute stable rank 1 where either n ≥ 3 or n = 2 and 1 is the sum of two units in R.
A generalization of Evans' Theorem: embedding partial tricycle systems
Authors: Lindner C. C. , Rodger C. A.
Published: April 2009

In 1960, Trevor Evans gave a best possible embedding of a partial latin square of order n in a latin square of order t, for any t ≥ 2n. A latin square of order n is equivalent to a 3-cycle system of Kn, n, n, the complete tripartite graph. Here we consider a small embedding of partial 3k-cycle systems of Kn, n, n of a certain type which generalizes Evans' Theorem, and discuss how this relates to the embedding of patterned holes, another recent generalization of Evans' Theorem.
The uniform Kadec-Klee property for the Lorentz spaces Lw,1
Authors: Dilworth S. J. , Hsu Yu-Ping
Published: April 2009

In this paper we show that the Lorentz space Lw, 1(0, ∞) has the weak-star uniform Kadec-Klee property if and only if inft>0 (w(αt)/w(t)) > 1 and supt>0(φ(αt) / φ(t))< 1 for all α ∈ (0, 1), where φ(t) = ∫t0 w(s) ds.
Discrete coactions on C*-algebras
Authors: Ng Chi-Keung
Published: April 2009

We will consider coactions of discrete groups on C*-algebras and imitate some of the results about compact group actions on C*-algebras. In particular, the crossed product of a reduced coaction ∈ of a discrete amenable group G on A is liminal (respectively, postliminal) if and only if the fixed point algebra of ∈ is. Moreover, we will also consider ergodic coactions on C*-algebras.
On non-homogeneous canonical third-order linear differential equations
Authors: Parhi N.
Published: April 2009

In this paper sufficient conditions have been obtained for non-oscillation of non-homogeneous canonical linear differential equations of third order. Some of these results have been extended to non-linear equations.
Existence results for differential equations with reflection of the argument
Authors: O'Regan Donal
Published: April 2009

Existence principles are given for systems of differential equations with reflection of the argument. These are derived using fixed point analysis, specifically the Nonlinear Alternative. Then existence results are deduced for certain classes of first and second order equations with reflection of the argument.
Injective endomorphisms of 𝒢x-normal semigroups: finite defects
Authors: Levi Inessa
Published: April 2009

A semigroup of transformations of an infinite set X is called 𝒢x-normal if S is invariant under conjugations by permutations of X. In this paper we describe injective endomorphisms of 𝒢x-normal semigroups of total one-to-one transformations f such that the range of f has a finite non-empty complement in X.
Flat functors and free exact categories
Authors: Hu Hongde
Published: April 2009

Let C be a small category with weak finite limits, and let Flat(C) be the category of flat functors from C to the category of small sets. We prove that the free exact completion of C is the category of set-valued functors of Flat (C) which preserve small products and filtered colimits. In case C has finite limits, this gives A. Carboni and R. C. Magno's result on the free exact completion of a small category with finite limits.
A group variety defined by a semigroup law
Authors: Ol'shanskii A. Yu. , Storozhev A.
Published: April 2009

A group variety defined by one semigroup law in two variables is constructed and it is proved that its free group is not a periodic extension of a locally soluble group.
Partitions into distinct large parts
Authors: Freiman Gregory A. , Pitman Jane
Published: April 2009

An asymptotic estimate is obtained for the number of partitions of the positive integer n into distinct parts, each of which is at least m. The estimate holds uniformly with respect to positive m such that m = o(n(log n)−9), as n → ∞.
genus theory for function fields
Authors: Bae Sunghan , Koo Ja Kyung
Published: April 2009

We study the genus theory for function fields which is the analogue of the classical genus theory developed by Hasse and Fröhlich.
On products of almost strong liftings
Authors: Macheras N. D. , Strauss W.
Published: April 2009

Dealing with a problem posed by Kupka we give results concerning the permanence of the almost strong lifting property (respectively of the universal strong lifting property) under finite and countable products of topological probability spaces. As a basis we prove a theorem on the existence of liftings compatible with products for general probability spaces, and in addition we use this theorem for discussing finite products of lifting topologies.
Endomorphisms of type II1-factors and Cuntz algebras
Authors: Enomoto Masatoshi , Watatani Yasuo
Published: April 2009

Any unital *-endomorphism of a type II1-factor is implemented by isometries of a Cuntz algebra outside the factor. If the Jones index of the range of the *-endomorphism is an integer and the algebras act on the standard space, the Jones index must agree with the number of the generators of the Cuntz algebra. We also study (outer) conjugacy of *-endomorphisms using Cuntz algebras.
Bialgebraic contexts from dualities
Authors: Kearnes Keith A. , Vogt Frank
Published: April 2009

In this paper we show that a bialgebraic context which arises from a duality in a fairly general way must arise from a duality between categories of modules. To show this, we give an elementary proof of Mitchell's Embedding Theorem for prevarieties.
On the L1-convergence of Fourier transforms
Authors: Giang Dᾰng Vũ , Móricz Ferenc
Published: April 2009

We study cosine and sine Fourier transforms defined by F(t):= (2/π) and (t):= (2/π), where f is L1-integrable over[0, ∞]. We also assume than F are locally absolutely continuous over [0, ∞). In particular, this is the case if both f(x) and xf(x) are (L1-integrable over [0, ∞). Motivated by the inversion formulas, we consider the partial integras Sν (f, x):= and ν(f, x):= , the modified partial integrals uν (f, x):= sν(f, x) - F(ν)(sin νx)/x and ũν(f, x):= ν(f, x) + (ν) (cos νx)/x, where ν > 0. We give necessary and sufficient conditions for(L1 [0, ∞)-convergence of uν (f) and ũν (f) as well as for the L1 [0, X]-convergence of sν (f) and ν(f) to f as ν← ∞, where 0 < X < ∞ is fixed. On the other hand, in certain cases we conclude that sν(f) and ν(f) cannot belong to (L1 [0,∞). Conequently, it makes no sense to speak of their (L1 [0, ∞)-convergence as ν ← ∞.

As an intermediate tool, we use the Cesàro means of Fourier transforms. Then we prove Tauberian type results and apply Sidon type inequalities in order to obtain Tauberian conditions of Hardy-Karamata kind.

We extend these results to the complex Fourier transform defined by G(t):= , where g is L1- integrable over (−∞, ∞).
Weighted composition operators on Orlicz-Sobolev spaces
Authors: Arora Subhash C. , Datt Gopal , Verma Satish
Published: April 2009

For an open subset Ω of the Euclidean space Rn, a measurable non-singular transformation T: Ω → Ω and a real-valued measurable function u on Rn, we study the weighted composition operator uCτ: f ↦ u · (f º T) on the Orlicz-Sobolev space W1·Ψ (Ω) consxsisting of those functions of the Orlicz space LΨ (Ω) whose distributional derivatives of the first order belong to LΨ (Ω). We also discuss a sufficient condition under which uCτ is compact.
On finite generation and presentability of Schützenberger products
Authors: Gallagher Peter , Ruškucs Nik
Published: April 2009

The finite generation and presentation of Schützenberger products of semigroups are investigated. A general necessary and sufficient condition is established for finite generation. The Schützenberger product of two groups is finitely presented as an inverse semigroup if and only if the groups are finitely presented, but is not finitely presented as a semigroup unless both groups are finite.
Permutable functions concerning differential equations
Authors: Hua X. , Vaillancourt R. , Wang X. L.
Published: April 2009

Let f and g be two permutable transcendental entire functions. Assume that f is a solution of a linear differential equation with polynomial coefficients. We prove that, under some restrictions on the coefficients and the growth of f and g, there exist two non-constant rational functions R1 and R2 such that R1 (f) = R(g). As a corollary, we show that f and g have the same Julia set: J(f) = J(g). As an application, we study a function f which is a combination of exponential functions with polynomial coefficients. This research addresses an open question due to Baker.
Characterization of left Artinian algebras through pseudo path algebras
Authors: Li Fang
Published: April 2009

In this paper, using pseudo path algebras, we generalize Gabriel's Theorem on elementary algebras to left Artinian algebras over a field k when the quotient algebra can be lifted by a radical. Our particular interest is when the dimension of the quotient algebra determined by the nth Hochschild cohomology is less than 2 (for example, when k is finite or char k = 0). Using generalized path algebras, a generalization of Gabriel's Theorem is given for finite dimensional algebras with 2-nilpotent radicals which is splitting over its radical. As a tool, the so-called pseudo path algebra is introduced as a new generalization of path algebras, whose quotient by ken is a generalized path algebra (see Fact 2.6).

The main result is that

(i) for a left Artinian k–algebra A and r = r(A) the radical of A. if the quotient algebra A/r can be lifted then A ≅ PSEk (Δ, , ρ) with Js ⊂ (ρ) ⊂ J for some s (Theorem 3.2);

(ii) If A is a finite dimensional k–algebra with 2-nilpotent radical and the quotient by radical can be lifted, then A ≅ k(Δ, , ρ) with 2 ⊂ (ρ) ⊂ 2 + ∩ ker (Theorem 4.2),

where Δ is the quiver of A and ρ is a set of relations.

For all the cases we discuss in this paper, we prove the uniqueness of such quivers Δ and the generalized path algebras/pseudo path algebras satisfying the isomorphisms when the ideals generated by the relations are admissible (see Theorem 3.5 and 4.4).
The limiting distribution of a recursive resampling procedure
Authors: Zukang Zheng , Lipeng Wu
Published: April 2009

A recursive resampling method is discussed in this paper. Let X1, X2,…, Xn, be i.i.d. random variables with distribution function F and construct the empirical distribution function Fn. A new sample Xn+1 is drawn from Fn and the new empirical distribution function 1 in the wide sense, is computed from X1, X2,…, Xn, Xn+1. Then Xn+2 is drawn from 1 and 2 is obtained. In this way, Xn+m and m are found. It will be proved that m converges to a random variable almost surely as m goes to infinity and the limiting distribution is a compound beta distribution. In comparison with the usual non-recursive bootstrap, the main advantage of this procedure is a reduction in unconditional variance.
Hyperbolic linear invariance and hyperbolic k-convexity
Authors: Ma Wancang , Minda David
Published: April 2009

Pommerenke initiated the study of linearly invariant families of locally schlicht holomorphic functions defined on the unit disk The concept of linear invariance has proved fruitful in geometric function theory. One aspect of Pommerenke's work is the extension of certain results from classical univalent function theory to linearly invariant functions. We propose a definition of a related concept that we call hyperbolic linear invariance for locally schlicht holomorphic functions that map the unit disk into itself. We obtain results for hyperbolic linearly invariant functions which generalize parts of the theory of bounded univalent functions. There are many similarities between linearly invariant functions and hyperbolic linearly invariant functions, but some new phenomena also arise in the study of hyperbolic linearly invariant functions.
On commutator laws in groups, 3
Authors: Macdonald I. D. , Neumann B. H.
Published: April 2009

In this final contribution to the investigation of commutator laws in groups, we answer some of the questions left open in the previous two papers. The principal result is the independence of the Jacobi-Witt-Hall type laws from the so-called standard set of laws. The main results of the earlier papers are summarised. An interlude corrects some of the numerous printing errors in the second of our papers.
On different types of cleavability of topological spaces
Authors: Arhangel'skii A. V. , Cammaroto F.
Published: April 2009

The notion of pointwise cleavability is introduced. We clarify those results concerning cleavability which can be or can not be generalized to the case of pointwise cleavability.

The importance of compactness in this theory is shown. Among other things we prove that t, ts, πx, the property to be Fréchet-Urysohn, radiality, biradiality, bisequentiality and so on are preserved by pointwise cleavability on the class of compact Hausdorff spaces.
Characterization of lipschitz spaces on compact Lie groups
Authors: Fan Dashan , Xu Zengfu
Published: April 2009

Lipschitz spaces are important function spaces with relations to Hp spaces and Campanato spaces, the other two important function spaces in harmonic analysis. In this paper we give some characterizations for Lipschitz spaces on compact Lie groups, which are analogues of results in Euclidean spaces.
Complex extreme measurable selections
Authors: Mupasiri Douglas
Published: April 2009

We give a characterization of complex extreme measurable selections for a suitable set-valued map. We use this result to obtain necessary and sufficient conditions for a function to be a complex extreme point of the closed unit ball of Lp (ω, Σ, ν X), where (ω, σ, ν) is any positive, complete measure space, X is a separable complex Banach space, and 0 < p < ∞.
Some trace inequalities for operators
Authors: Yang Xinmin
Published: April 2009

In this paper, we obtain some trace inequalities for arbitrary finite positive definite operators. Finally an open question is presented.
The number of trees with large diameter
Authors: Łuczak Tomasz
Published: April 2009

In the paper we study the asymptotic behaviour of the number of trees with n vertices and diameter k = k(n), where k/√n → ∞ as n → ∞ but k = o(n).
Duality in fractional minimax programming
Authors: Chandra S. , Kumar Viveka
Published: April 2009

Certain omissions in the recently introduced dual for fractional minimax programming problem ‘minimize max y ∈ Y f(x, y) / h(x, y), subject to g(x) ≤ 0’, are indicated and two modified duals for this problem are presented. Various fractional programming and generalized fractional programming duals are shown to be special cases of this study.
The class L(log L)α and some lacunary sets
Authors: Gupta Sanjiv Kumar , Madan Shobha , Tewari U. B.
Published: April 2009

A well-known result of Zygmund states that if f ∈ L (log+L) ½ on the circle group T and E is a Hadamard set of integers, then . In this paper we investigate similar results for the classes on an arbitrary infinite compact abelian group G and Sidon subsets E of the dual Γ. These results are obtained as special cases of more general results concerning a new class of lacunary sets Sαβ, 0 < α ≤ β, where a subset E of Γ is an Sα β set if . We also prove partial results on the distinctness of the Sαβ sets in the index β.
Right inverses of vector fields
Authors: Virsik George
Published: April 2009

D. Przeworska-Rolewicz developed an algebra-based theory around linear, not necessarily continuous, operators D: X → X which admit a right inverse, the elementary example being D = d/dt or, more generally, where ai are constants. We give conditions for the right invertibility of D in the case where ai are functions, or more generally, where D is the Lie or convariant derivative associated with a vector field on a (Banach) manifold M.
The parabolicity of Brelot's harmonic spaces
Authors: Imai Hideo
Published: April 2009

The parabolicity of Brelot's harmonic spaces is characterized by the fact that every positive harmonic function is of minimal growth at the ideal boundary.
Extensions of regular orthogroups by groups
Authors: Szendrei Mária B.
Published: April 2009

A common generalization of the author's embedding theorem concerning the E-unitary regular semigroups with regular band of idempotents, and Billhardt's and Ismaeel's embedding theorem on the inverse semigroups, the closure of whose set of idempotents is a Clifford semigroup, is presented. We prove that each orthodox semigroup with a regular band of idempotents, which is an extension of an orthogroup K by a group, can be embedded into a semidirect product of an orthogroup K′ by a group, where K′ belongs to the variety of orthogroups generated by K. The proof is based on a criterion of embeddability into a semidirect product of an orthodox semigroup by a group and uses bilocality of orthogroup bivarieties.
Radial functions and maximal estimates for solutions to the Schrödinger equation
Authors: Sjölin Per
Published: April 2009

Maximal estimates are considered for solutions to an initial value problem for the Schrödinger equation. The initial value function is assumed to be radial in ℝn, n≥2.
The continuous Diophantine approximation mapping of Szekeres
Authors: Lagarias Jeffrey C. , Pollington Andrew D.
Published: April 2009

Szekeres defined a continuous analogue of the additive ordinary continued fraction expansion, which iterates a map T on a domain which can be identified with the unit square [0, 1]2. Associated to it are continuous analogues of the Lagrange and Markoff spectrum. Our main result is that these are identical with the usual Lagrange and Markoff spectra, respectively; thus providing an alternative characterization of them.

Szekeres also described a multi-dimensional analogue of T, which iterates a map Td on a higherdimensional domain; he proposed using it to bound d-dimensional Diophantine approximation constants. We formulate several open problems concerning the Diophantine approximation properties of the map Td.
A problem on growth sequences of groups
Authors: Erfanian A.
Published: April 2009

The aim of this paper is to consider Problem 1 posed by Stewart and Wiegold in [6]. The main result is that if G is a finitely generated perfect group having non-trivial finite images, then there exists a finite image B of G such that the growth sequence of B is eventuallly faster than that of every finite image of G. Moreover we investigate the growth sequences of simple groups of the same order.
An application of Lyapunov's direct method to the study of oscillations of a delay differential equation of even order
Authors: Terry Raymond D.
Published: April 2009

The direct method of Lyapunov is utilized to obtain a variety of criteria for the nonexistence of certain types of positive solutions of a delay differential equation of even order. Previous results of Terry (Pacific J. Math. 52 (1974), 269–282) are seen to be corollaries of the more general results of this paper.
On generalizations of C*-embedding for wallman rings
Authors: Bentley H. L. , Taylor B. J.
Published: April 2009

Biles (1970) has called a subring A of the ring C(X), of all real valued continuous functions on a topological space X, a Wallman ring on X whenever Z(A), the zero sets of functions belonging to A, forms a normal base on X in the sense of Frink (1964). Previously, we have related algebraic properties of a Wallman ring A to topological properties of the Wallman compactification w(Z(A)) of X determined by the normal base Z(A). Here we introduce two different generalizations of the concept of “a C*-embedded subset” and study relationships between these and topological (respectively, algebraic) properties of w(Z(A)) (respectively, A).
The Stone-Weierstrass theorem for wallman rings
Authors: Bentley H. L. , Taylor B. J.
Published: April 2009

Biles has called a subring A of the ring C(X) a Wallman ring on X whenever Z(A), the zero sets of function belonging to A, forms a normal base on X in the sense of Frink (1964). In the following, we are concerned with the uniform topology of C(X). We formulate and prove some generalizations of the Stone–Weierstrass theorem in this setting.
Nikolskii-type inequalities for trigonometric polynomials and entire functions of exponential type
Authors: Nessel R. J. , Wilmes G.
Published: April 2009

Nikolskii-type inequalities, thus inequalities between different metrics of a function, are established for trigonometric polynomials and pth power integrable functions, 0<p<∞, of several variables having Fourier transform with compact support. It is shown that certain gaps in the spectra of the functions involved may be taken into account. As an immediate consequence it follows that the general results cover the classical inequalities which are concerned with functions of rectangular type. But at the same time one may give applications to functions of type K where K is a symmetric body in Euclidean n–space.
Finite groups as automorphism groups of orthocomplemented projective planes
Authors: Greechie Richard J.
Published: April 2009

A construction is given for a non-desarguesian projective plane P and an absolute-point free polarity on P such that the group of collineations of P which commute with the polarity is isomorphic to an arbitrary preassigned finite group.
A property of hereditarily locally connected continua related to arcwise accessibility
Authors: Simone Joseph N.
Published: April 2009

A continuum (that is, a compact connected Hausdorff space) is hereditarily locally connected if each of its subcontinua is locally connected. It is shown that a continuumXis hereditarily locally connected if and only if for each connected open setUinXand each pointpin the boundary ofU, U∪ {p} is locally connected. This result is used to prove that ifXis an hereditarily locally connected continuum,Uis a connected open subset ofX, pis an element of the boundary ofUandXis first countable atp, thenpis arcwise accessible fromU.
Existence of finite groups with classical commutator subgroup
Authors: Miller Michael D.
Published: April 2009

Given a group G, we may ask whether it is the commutator subgroup of some group G. For example, every abelian group G is the commutator subgroup of a semi-direct product of G x G by a cyclic group of order 2. On the other hand, no symmetric group Sn(n>2) is the commutator subgroup of any group G. In this paper we examine the classical linear groups over finite fields K of characteristic not equal to 2, and determine which can be commutator subgroups of other groups. In particular, we settle the question for all normal subgroups of the general linear groups GLn(K), the unitary groups Un(K) (n≠4), and the orthogonal groups On(K) (n≧7).
Splitting theorems in abelian-by-hypercyclic groups
Authors: Tomkinson M. J.
Published: April 2009

If is a saturated formation of finite soluble groups and G is a finite group whose -residual A is abelian then it is well known that G splits over A and the complements are conjugate. Hartley and Tomkinson (1975) considered the special case of this result in which is the class of nilpotent groups and obtained similar results for abelian-by-hypercentral groups with rank restrictions on the abelian normal subgroup. Here we consider the super-soluble case, obtaining corresponding results for abelian-by-hypercyclic groups.
On the structure and existence of some amicable orthogonal designs
Authors: Robinson Peter J. , Seberry Jennifer
Published: April 2009

The structure is determined for the existence of some amicable weighing matrices. This is then used to prove the existence and non-existence of some amicable orthogonal designs in powers of two.
On the approximation of algebraic numbers by algebraic integers
Authors: Mahler K.
Published: April 2009

In his Topics in Number Theory, vol. 2, chapter 2 (Reading, Mass., 1956) W. J. LeVeque proved an important generalisation of Roth's theorem (K. F. Roth, Mathematika 2,1955, 1—20).

Let ξ be a fixed algebraic number, σ a positive constant, and K an algebraic number field of degree n. For κ∈K denote by κ(1), …, κ(n) the conjugates of κ relative to K, by h(κ) the smallest positive integer such that the polynomial has rational integral coefficients, and by q(κ) the quantity
Upper and Lower bounds for a certain class of constrained variational problems
Authors: Hanson M. A.
Published: April 2009

Certain optimization problems involving inequality constraints, known as optimal control problems have been extensively studied during recent years especially in relation to the calculation of optimal rocket thrusts and trajectories. A summary of these works is given by Berkovitz [1] who also establishes necessary conditions for the existence of solutions for a wide class of such problems.
Zumino's theorem in the quasi-chemical equilibrium theory
Authors: Matsubara Takeo , Thompson Colin J.
Published: April 2009

A theorem on the canonical form of an antisymmetric matrix, which we attribute to Zumino, is used to show how the derivations of the results of two earlier papers by Blatt on expectation values of operators can be considerably simplified.
On partial sums of Lagrange's series with application to the theory of queues
Authors: Finch P. D.
Published: April 2009

Lagrange's theorem on the reversion of power series may be stated in the following form (e.g. Whittker and Watson [3]).
Preemptive priority queues
Authors: Yeo G. F.
Published: April 2009

In this paper priority queues with K classes of customers with a preemptive repeat and a preemptive resume policy are considered. Customers arrive in independent Poisson processes, are served, within classes, in order of arrival, and have general requirements for service. Transforms of stationary waiting time and queue size distributions and busy period distributions are obtained for individual classes and for the system; the moments of the distributions are considered.
Extremally richC*-crossed products and the cancellation property
Authors: Jeong Ja A , Osaka Hiroyuki
Published: April 2009

A unitalC*-algebraAis called extremally rich if the set of quasi-invertible elementsA-1ex (A)A-1(= A-1q) is dense inA, where ex(A) is the set of extreme points in the closed unit ballA1ofA. In [7, 8] Brown and Pedersen introduced this notion and showed thatAis extremally rich if and only if conv(ex(A)) =A1. Any unital simpleC*-algebra with extremal richness is either purely infinite or has stable rank one (sr(A) = 1). In this note we investigate the extremal richness ofC*-crossed products of extremally richC*-algebras by finite groups. It is shown that ifAis purely infinite simple and unital thenAxα,Gis extremally rich for any finite groupG. But this is not true in general whenGis an infinite discrete group. IfAis simple with sr(A) =, and has the SP-property, then it is shown that any crossed productAxαGby a finite abelian groupGhas cancellation. Moreover if this crossed product has real rank zero, it has stable rank one and hence is extremally rich.
On special atoms
Authors: Jackson H. France
Published: April 2009

A characterization of all special atoms in the from of the upper radical generated by the class of all prime rings outside the smallest special class containing some prime ring is provided and prime rings for which the above mentioned upper radical coincides with the prime radical are investigated.
C*-actions of r-discrete groupoids and inverse semigroups
Authors: Quigg John , Sieben Nándor
Published: April 2009

Groupoid actions on C*-bundles and inverse semigroup actions on C*-algebras are closely related when the groupoid is r-discrete.
Boundedness of rough singular integral operators on homogeneous Herz spaces
Authors: Hu Guoen , Lu Shanzhen , Yang Dachun
Published: April 2009

The authors establish the boundedness on the Herz spaces and the weak Herz spaces for a large class of rough singular integral operators and their corresponding fractional versions. Applications are given to Fefferman's rough singular integral operators, their fractional versions, their commutators with BMO() functions and Ricci-Stein oscillatory singular integral operators. Some new results are obtained.
Involutions and commutators in orthogonal groups
Authors: Knüppel Frieder , Thomsen Gerd
Published: April 2009

Suppose we are given a regular symmetric bilinear from on a finite-dimensional vector space V over a commutative field K of characteristic ≠ 2. We want to write given elements of the commutator subgroup ω(V) (of the orthogonal group O(V)) and also of the kernel of the spinorial norm ker(Θ) as (short) products of involutions and as products of commutators
Amenability, lp-homologies and translation invariant functionals
Authors: Elek Gábor
Published: April 2009

We introduce a new homology theory for infinite graphs in order to generalize some results of Willis and Woodward on translation invariant functionals. We also extend some theorems of Gerl and Gromov.
A class of C-totally real submanifolds of Sasakian space forms
Authors: Defever Filip , Mihai Ion , Verstraelen Leopold
Published: April 2009

Recently, Chen defined an invariant δM of a Riemannian manifold M. Sharp inequalities for this Riemannian invariant were obtained for submanifolds in real, complex and Sasakian space forms, in terms of their mean curvature. In the present paper, we investigate certain C-totally real submanifolds of a Sasakian space form M2m+1(C)satisfying Chen's equality.
Stationarity in the simplex method
Authors: Cameron Neil
Published: April 2009

Degeneracies occur with increasing frequency in some large scale linear programming problems, but with a simple change to the (revised) simplex method, resulting stationarity of the algorithm can be reduced. The method introduced here may also prevent cycling; neither the lexicographic refinement of Dantzig, Orden and Wolfe nor the perturbation technique of Charnes may be required to prevent cycling.
An Experimental Investigation of Causal Attributions for the Political Behavior of Muslim Candidates: Can a Muslim Represent you?
Authors: Braman Eileen , Sinno Abdulkader H.
Published: April 2009

American Muslim representation in elected office has lagged behind that of other groups of comparable size. Muslims now make up 2% of the total United States population and enjoy much larger concentrations in some urban areas. American Muslims are also disproportionately educated and enjoy a higher average socio-economic status than members of groups with similar numbers that have made strides in terms of political representation in our democracy. Yet Muslims have not made similar advances in the political arena. There are a number of reasons that might account for this situation. Here, we look at one possible explanation that is especially intriguing — and perhaps a bit troubling: the idea that voters make different causal attributions for the behavior of Muslim candidates for office. We employ an experimental design to examine the attributions participants use to “explain” the behavior of hypothetical Muslim and non-Muslim candidates. We conduct two experiments involving distinct political offices: State Attorney General and United States Senator. We find that respondents generally do not attribute behavior differently in the case of Muslim and Christian candidates, except in the case of lax prosecution of a terrorism case. Politically sophisticated respondents assume that a Muslim prosecutor who does not have a large Muslim constituency is sympathetic to Muslim terrorists, but not one with a larger Muslim voting base. Non-sophisticates attribute his behavior to such motivations regardless of the concentration of Muslims in his district.
On the importance of the forward speed of hurricanes in storm surge forecasting: A numerical study
Authors: Rego João Lima , Li Chunyan
Published: April 2009

A systematic investigation of storm surge along the coast of Louisiana was conducted by using the fully nonlinear Finite‐Volume Coastal Ocean Model. FVCOM was first applied to Hurricane Rita and validated by in situ measurements. Experiments were conducted with different parameters to evaluate the impacts of each factor on inundation over a wide and shallow shelf. Results show that a hurricane's forward speed is a significant parameter which has been overlooked in previous studies. Resonance may occur for certain hurricane forward motion speeds: increasing this speed increases peak surge heights while decreasing inland volume of flood. The effects of wind intensity, Radius of Maximum Winds, tidal timing, amplitude, and wind inflow angle were also examined. It was concluded that varying a storm's forward motion may account for variations in flooded volumes equivalent to an upgrade or downgrade of about 1 category on the Saffir‐Simpson scale.
Giant vortices lead to ion escape from Venus and re‐distribution of plasma in the ionosphere
Authors: Pope S. A. , Balikhin M. A. , Zhang T. L. , Fedorov A. O. , Gedalin M. , Barabash S.
Published: April 2009

The interaction of the solar wind with Venus has a significant influence on the evolution of its atmosphere. Due to the lack of an intrinsic planetary magnetic field, there is direct contact between the fast flowing solar wind and the Venusian ionosphere. This leads to a number of different types of atmospheric escape process. Using Venus Express observations, we show that such contact leads to the formation of global vortices downstream of the Venusian bow shock. These vortices accelerate heavy ionospheric ions such as oxygen, leading to their escape. We argue that these vortices are the result of the Kelvin‐Helmholtz instability excited by the shear velocity profile at the boundary between the solar wind and ionospheric plasma. These vortices also help to repopulate the night‐side ionosphere during solar minimum, when the ionospheric flow from day to night is restricted by the lowered ionopause altitude at the terminator.
Aircraft and ground‐based observations of boundary layer CO2 concentration in anticyclonic synoptic condition
Authors: Saito Ryu , Tanaka Tomoaki , Hara Hiroshi , Oguma Hiroyuki , Takamura Tamio , Kuze Hiroaki , Yokota Tatsuya
Published: April 2009

Concentrations of atmospheric CO2 and aerosol were measured in a field campaign conducted in winter 2006 around Mt. Tsukuba, Japan using ground‐based CO2 analyzers, a lidar, and sky radiometers as well as CO2 analyzers onboard an aircraft. Vertical measurements revealed occasional similarity between the profiles of CO2 and aerosol concentrations, though their temporal variations are not always coordinated because of the effects of local sources or sinks. A sudden increase of downward winds, due to the approach of an anticyclonic synoptic flow, resulted in a rapid decrease in both the CO2 and aerosol concentrations in the boundary layer. These observation results have demonstrated that simultaneous measurements with airborne and ground‐based instruments set on the summit/foot of a mountain are useful for the study of variability of CO2 concentration in the boundary layer.