bluuebunny/crossref_metadata_2025 huggingface dataset:
Some characterizations of semiprime Goldie rings
Authors: López-Permouth S. R. , Rizvi S. Tariq , Yousif M. F.
Published: May 2009

The notation in this paper will be standard and it may be found in [3], for example. In particular, the notation A ⊂′ B stands for the statement “A is an essential submodule of B”. As is customary, we say that a ring R is a Goldie ring when R is both left and right Goldie. Similarly, a ring is noetherian if and only if it is both right and left noetherian, etc.
Units of group rings of groups of order 16
Authors: Jespers E. , Parmenter M. M.
Published: May 2009

LetGbe a finite group,(ZG) the group of units of the integral group ring ZGand1(ZG) the subgroup of units of augmentation 1. In this paper, we are primarily concerned with the problem of describing constructively(ZG) for particular groupsG.This has been done for a small number of groups (see [11] for an excellent survey), and most recently Jespers and Leal [3] described(ZG) for several 2-groups. While the situation is clear for all groups of order less than 16, not all groups of order 16 were discussed in their paper. Our main aim is to complete the description of(ZG) for all groups of order 16. Since the structure of the unit group of abelian groups is very well known (see for example [10]), we are only interested in the non-abelian case.
An identity for the Fibonacci and Lucas numbers
Authors: Jennings Derek
Published: May 2009

In this paper we prove an identity between sums of reciprocals of Fibonacci and Lucas numbers. The Fibonacci numbers are defined for all n ≥ 0 by the recurrence relation Fn + 1 = Fn + Fn-1 for n ≥ 1, where F0 = 0 and F1 = 0. The Lucas numbers Ln are defined for all n ≥ 0 by the same recurrence relation, where L0 = 2 and L1 = 1 We prove the following identify.
Pythagorean ratios in arithmetic progression, part i. three Pythagorean ratios
Authors: Leech John
Published: May 2009

Let {a, b} designate the Pythagorean ratio (a2 - b2)/2ab between the sides of a rational right angled triangle. This paper studies the circumstances in which Pythagorean ratios can occupy consecutive places in an arithmetic progression. Part I deals with sets of three such ratios, while Part II discusses sets of four ratios.
On frattini-like subgroups
Authors: Beidleman James C. , Smith Howard
Published: May 2009

Theorem 3 of the paper, published in the Glasgow Mathematical Journal 35 (1993), 95–98, is stated incorrectly.

The subgroup G′ ∩ L(G) is nilpotent but not, in general, finitely generated (a suitable counterexample being provided by the group whose presentation is given n the Introduction). In groups with the property σ the Fitting radical is itself finitely generated and so the conclusion of Theorem 3 holds in this special case. The words “finitely generated” should be deleted from the paragraph preceding the statement of Theorem 4, but both this theorem and its proof are correct.
Lacunarity of Dedekind η-products
Authors: Gordon Basil , Robins Sinai
Published: May 2009

The Dedekind η-function is defined by

where τ lies in the upper half plane ℋ = {tau;|Im(τ) > 0}, and x = e2πiτ. It is a modular form of weight ½ with a multiplier system. We define an η-product to be a function f (τ) of the form

where rδ ε ℤ. This is a modular form of weight with a multiplier system. The Fourier coefficients of η-products are related to many well-known number-theoretic functions, including partition functions and quadratic form representation numbers. They also arise from representations of the “monster” group [3] and the Mathieu group M24 [13]. The multiplicative structure of these Fourier coefficients has been extensively studied. Recent papers include [1], [4], [5] and [6]. Here we study the connections between the density of the non-zero Fourier coefficients of f(τ) and the representability of f(τ) as a linear combination of Hecke character forms (defined in Section 4 below). We first make the following definition.
Comparison of complexes of modules of generalized fractions and generalized Hughes complexes
Authors: Sharp R. Y. , Tousi M.
Published: May 2009

Let R be a commutative ring (with non-zero identity) and let M be an R-module.
Construction of semiabelian Galois extensions
Authors: Stoll Michael
Published: May 2009

This paper shows how to construct Galois field extensions of Hilbertian fields with a given group out of some subclass (called ‘semiabelian groups’ by Matzat [2]) of all soluble groups as Galois group. This is done in a fairly explicit way by constructing polynomials whose Galois groups are universal in the sense that every group in the above subclass is obtained as a quotient of some of them.
A note on locally soluble, normal closures of cyclic subgroups
Authors: Smith Howard
Published: May 2009

This brief note has the threefold purpose of improving on an earlier theorem of the author [4], gathering together some results on normal closures (with rank restrictions) which are more or less implicit in the literature and providing a few examples which indicate the impossibility of improving these results in one way or another. The proofs are mostly routine and usually omitted. Most of the relevant background material can be found in [3], and references to these results will often indicate that minoradditional details (an easy induction, for example) are required. Throughout, 〈x〉G will denote the normal closure of the subgroup 〈x〉 of the group G. The usual notation is used for upper central and derived series.
Extension of completely bounded A-B bimodule maps
Authors: Muhly Paul S. , Na Qiyuan
Published: May 2009

In this paper, we present an “order” characterization of completely bounded bimodule maps for bimodules over unital operator algebras. We use this result to prove a bimodule generalization of Wittstock's generalized Hahn-Banach theorem. Our proofs simplify and unify some of Wittstock's arguments.
Remarks on the range of a vector measure
Authors: Castilo Jesús M. F. , Sánchez Fernando
Published: May 2009

A long-standing problem is the characterization of subsets of the range of a vector measure. It is known that the range of a countably additive vector measure is relatively weakly compact and, in addition, possesses several interesting properties (see [2]). In [6] it is proved that if m: Σ → Χ is a countably additive vector measure, then the range of m has not only the Banach–Saks property, but even the alternate Banach-Saks property. A tantalizing conjecture, which we shall disprove in this article, is that the range of m has to have, for some p > 1, the p-Banach–Saks property. Another conjecture, which has been around for some time (see [2]) and is also disproved in this paper, is that weakly null sequences in the range of a vector measure admit weakly-2-summable sub-sequences. In fact, we shall show a weakly null sequence in the range of a countably additive vector measure having, for every p < ∞, no weakly-p-summable sub-sequences.
Associate subgroups of orthodox semigroups
Authors: Blyth T. S. , Giraldes Emília , Marques-Smith M. Paula O.
Published: May 2009

A unit regular semigroup [1, 4] is a regular monoid S such that H1 ∩ A(x) ≠ Ø for every xɛS, where H1, is the group of units and A(x) = {y ɛ S; xyx = x} is the set of associates (or pre-inverses) of x. A uniquely unit regular semigroupis a regular monoid 5 such that |H1 ∩ A(x)| = 1. Here we shall consider a more general situation. Specifically, we consider a regular semigroup S and a subsemigroup T with the property that |T ∩ A(x) = 1 for every x ɛ S. We show that T is necessarily a maximal subgroup Hα for some idempotent α. When Sis orthodox, α is necessarily medial (in the sense that x = xαx for every x ɛ 〈E〉) and αSα is uniquely unit orthodox. When S is orthodox and α is a middle unit (in the sense that xαy = xy for all x, y ɛ S), we obtain a structure theorem which generalises the description given in [2] for uniquely unit orthodox semigroups in terms of a semi-direct product of a band with a identity and a group.
Finite metacyclic groups acting on bordered surfaces
Authors: May Coy L.
Published: May 2009

A group is called metacyclic in case both its commutator subgroup and commutator quotient group are cyclic. Thus a metacyclic group is a cyclic extension of a cyclic group, and metacyclic groups are among the best understood of the nonabelian groups. Many interesting groups are metacyclic. For instance, the dihedral groups and the “odd” dicyclic groups are metacyclic; see [4, pp. 9–11] for more examples. Here we shall consider the actions of these groups on bordered Klein surfaces.
A weaker condition for normality
Authors: Doust Ian
Published: May 2009

One of the most important results of operator theory is the spectral theorem for normal operators. This states that a normal operator (that is, a Hilbert space operator T such that T*T= TT*), can be represented as an integral with respect to a countably additive spectral measure,

Here E is a measure that associates an orthogonal projection with each Borel subset of ℂ. The countable additivity of this measure means that if x Eℋ can be written as a sum of eigenvectors then this sum must converge unconditionally.
On the non-albelian tensor square of a nilpotent group of class two
Authors: Bacon Michael R.
Published: May 2009

The nonabelian tensor square G⊗G of a group G is generated by the symbols g⊗h, g, h ∈ G, subject to the relations

,

for all g, g′, h, h′ ∈ G, where The tensor square is a special case of the nonabelian tensor product which has its origins in homotopy theory. It was introduced by R. Brown and J. L. Loday in [4] and [5], extending ideas of Whitehead in [6].
Automorphism groups of complex doubles of Klein surfaces
Authors: Bujalance E. , Costa A. F. , Gromadzki G. , Singerman D.
Published: May 2009

In this paper we consider complex doubles of compact Klein surfaces that have large automorphism groups. It is known that a bordered Klein surface of algebraic genus g > 2 has at most 12(g − 1) automorphisms. Surfaces for which this bound is sharp are said to have maximal symmetry. The complex double of such a surface X is a compact Riemann surface X+ of genus g and it is easy to see that if G is the group of automorphisms of X then C2 × G is a group of automorphisms of X+. A natural question is whether X+ can have a group that strictly contains C2 × G. In [8] C. L. May claimed the following interesting result: there is a unique Klein surface X with maximal symmetry for which Aut X+ properly contains C2 × Aut X (where Aut X+ denotes the group of conformal and anticonformal automorphisms of X+).
Modulus of nearly uniform smoothness and Lindenstrauss formulae
Authors: Benavides Tomás Domínguez
Published: May 2009

The Lindenstrauss formula

which states a strong relationship between the (Clarkson) modulus of uniform convexity δx of a Banach space X and the modulus of uniform smoothness px* of the conjugate space X*, is well known. Following the idea of the definitions of nearly uniform smooth space by S. Prus and modulus of uniform smoothness we define a modulus of nearly uniform smoothness and prove some Lindenstrauss type formulae concerning this modulus and the modulus of nearly uniform convexity for some measures of noncompactness.
Right fully idempotent rings need not be left fully idempotent
Authors: Andruszkiewicz R. R. , Puczyłowski E. R.
Published: May 2009

All rings in this paper are associative but not necessarily with an identity. The ring R with an identity adjoined will be denoted by R#.

To denote that I is an ideal (right ideal, left ideal) of a ring R we write I ◃ R (I <rR, I <1R).

A ring R is called right (left) fully idempotent if for every I <rR (I<1R), I = I2.

At the conference “Methoden der Modul und Ringtheorie” in Oberwolfach, Germany in 1993, J. Clark raised the question as to whether every right fully idempotent ring is left fully idempotent (see also [3]). A similar question was raised by S. S. Page in [5]. In this note we answer the questions in the negative.

We start with some general observations most of which are perhaps well known. We include their simple proofs for completeness.
On group graded rings satisfying polynomial identities
Authors: Kelarev A. V. , Okniński J.
Published: May 2009

A number of classical theorems of ring theory deal with nilness and nilpotency of the Jacobson radical of various ring constructions (see [10], [18]). Several interesting results of this sort have appeared in the literature recently. In particular, it was proved in [1] that the Jacobson radical of every finitely generated PI-ring is nilpotent. For every commutative semigroup ringRS, it was shown in [11] that ifJ(R) is nil thenJ(RS) is nil. This result was generalized to all semigroup algebras satisfying polynomial identities in [15] (see [16, Chapter 21]). Further, it was proved in [12] that, for every normal bandB, ifJ(R) is nilpotent, thenJ(RB) is nilpotent. A similar result for special band-graded rings was established in [13, Section 6]. Analogous theorems concerning nilpotency and local nilpotency were proved in [2] for rings graded by finite and locally finite semigroups.
Minimum topological genus of compact bordered Klein surfaces admitting a prime-power automorphism
Authors: Bujalance E. , Gamboa J. M. , Maclachlan C.
Published: May 2009

In the nineteenth century, Hurwitz [8] and Wiman [14] obtained bounds for the order of the automorphism group and the order of each automorphism of an orientable and unbordered compact Klein surface (i. e., a compact Riemann surface) of topological genus g s 2. The corresponding results of bordered surfaces are due to May, [11], [12]. These may be considered as particular cases of the general problem of finding the minimum topological genus of a surface for which a given finite group G is a group of automorphisms. This problem was solved for cyclic and abelian G by Harvey [7] and Maclachlan [10], respectively, in the case of Riemann surfaces and by Bujalance [2], Hall [6] and Gromadzki [5] in the case of non-orientable and unbordered Klein surfaces. In dealing with bordered Klein surfaces, the algebraic genus—i. e., the topological genus of the canonical double covering, (see Alling-Greenleaf [1])—was minimized by Bujalance- Etayo-Gamboa-Martens [3] in the case where G is cyclic and by McCullough [13] in the abelian case.
On the generators of elementary subgroups of general linear groups
Authors: Mason A. W.
Published: May 2009

Let R be a ring with identity and let Eij ∈ Mn(R) be the usual n X n matrix units, where n ≥ 2 and 1≤i, j≤N. Let En(R) be the subgroup of GLn(R) generated by all Tij(q where r ∈ R and i ≄ j. For each (two-sided) R-ideal q let En(R, q) be the normal subgroup of En(R) generated by Tij(q), where q ∈ q. The subgroup En(R, q) plays an important role in the theory of GLn(R). For example, Vaserˇstein has proved that, for a larger class of rings (which includes all commutative rings), every subgroup S of GLn(R), when R ∈ and n≥3, contains the subgroup En(R, q0), where q0 is the R-ideal generated by αij, rαij-αjjr (i ≄ j, r ∈ R), for all (αij) ∈ S. (See [13, Theorem 1].) In addition Vaseršstein has shown that, for the same class of rings, En(R, q) has a simple set of generators when n ≥ 3. Let Ên(R, q) be the subgroup of En(R, q) generated by Tij(r)Tij(q)Tij(−r), where r ∈ R, q ∈ q. Then Ên(R, q) = En(R, q), for all q, when R ∈ and n ≥ 3.(See [13, Lemma 8].)
Normal structure and fixed point property
Authors: García-Falset J. , Lloréns-Fuster E.
Published: May 2009

The most classical sufficient condition for the fixed point property of non-expansive mappings FPP in Banach spaces is the normal structure (see [6] and [10]). (See definitions below). Although the normal structure is preserved under finite lp-product of Banach spaces, (1<p≤∞), (see Landes, [12], [13]), not too many positive results are known about the normal structure of an l1,-product of two Banach spaces with this property. In fact, this question was explicitly raised by T. Landes [12], and M. A. Khamsi [9] and T. Domíinguez Benavides [1] proved partial affirmative answers. Here we give wider conditions yielding normal structure for the product X1⊗1X2.
Orders in power semigroups
Authors: Easdown David , Gould Victoria
Published: May 2009

In this paper we consider examples of orders in restricted power semigroups, where for any semigroup Sthe restricted power semigroup is given by with multiplication XY = {xy:x ∈ X, y ∈ Y} for all X, Y ∈ . We use the notion of order introduced by Fountain and Petrich in [2] which first appears in the form used here in [3]. If S is a subsemigroup of Q then S is an order in Q and Q is a semigroup of quotients of S if any q ∈ Q can be written as q = a*b = cd* where a, b, c, d ∈ S is the inverse of a(d) in a subgroup of Q, and in addition, all elements of S satisfying a weak cancellability condition called square-cancellability lie in a subgroup of Q.
Quasidistinguished countable enlargements of normed spaces
Authors: Saxon S. A. , Ruiz L. M. Sànchez
Published: May 2009

If E is a Hausdorff locally convex space and M is an -dimensional subspace of the algebraic dual E* that is transverse to the continuous dual E′, then, according to [7], the Mackey topology τ(E, E′ + M) is a countable enlargement (CE) of τ(E, E′) [or of E]. Much is still unknown as to when CEs preserve barrelledness (cf. [14]). E is quasidistinguished (QD) if each bounded subset of the completion Ê is contained in the completion of a bounded subset of E [12]. Clearly, each normed space is QD, and Tsirulnikov [12] asked if each CE of a normed space must be a QDCE, i.e., must preserve the QD property. Since CEs preserve metrizability (but not normability), her question was whether metrizable spaces so obtained must be QD, and was moderated by Amemiya's negative answer (cf. [5, p. 404]) to Grothendieck's query, who had asked if all metrizable spaces are QD, having proved the separable ones are [4].
On the diophantine equations x2 + 74 = y5 and x2 + 86 = y5
Authors: Mignotte Maurice , de Weger Benjamin M. M.
Published: May 2009

J. H. E. Cohn solved the diophantine equations x2 + 74 = yn and x2 + 86 = yn, with the condition 5 ∤ n, by more or less elementary methods. We complete this work by solving these equations for 5 | n, by less elementary methods.
Congruences on orthodox semigroups with associate subgroups
Authors: Blyth T. S. , Giraldes Emília , Marques-Smith M. Paula O.
Published: May 2009

If Sis a regular semigroup then an inverse transversal of S is an inverse subsemigroup T with the property that |T ∩ V(x)| = 1 for every x ∈ S where V(x) denotes the set of inverses of x ∈ S. In a previous publication [1] we considered the similar concept of a subsemigroup T of S such that |T ∩ A(x)| = 1 for every x ∩ S where A(x) = {y∈ S;xyx = x} denotes the set of associates (or pre-inverses) of x ∈ S, and showed that such a subsemigroup T is necessarily a maximal subgroup Ha for some idempotent α ∈ S. Throughout what follows, we shall assume that S is orthodox and α is a middle unit (in the sense that xαy = xy for all x, y ∈ S). Under these assumptions, we obtained in [1] a structure theorem which generalises that given in [3] for uniquely unit orthodox semigroups. Adopting the notation of [1], we let T ∩ A(x) = {x*} and write the subgroup T as Hα = {x*;x ∈ S}, which we call an associate subgroup of S. For every x ∈ S we therefore have x*α = x* = αx* and x*x** = α = x**x*. As shown in [1, Theorems 4, 5] we also have (xy)* = y*x* for all x, y ∈ S, and e* = α for every idempotent e.
On the topological degree of real polynomial vector fields
Authors: Szafraniec Zbigniew
Published: May 2009

Let G: Rn → Rn be a continuous mapping such that the origin 0 ∈ Rn is isolated in G-1(0). Then deg0G will denote the local topological degree of G at the origin, i.e. the topological degree of the mapping

where Sr denotes a sphere in Rn centered at the origin with small radius r > 0.
The Jordan-Hölder theorem and prefrattini subgroups of finite groups
Authors: Ballester-Bolinches A. , Ezquerro L. M.
Published: May 2009

All groups considered are finite. In recent years a number of generalizations of the classic Jordan-Hölder Theorem have been obtained (see [7], Theorem A.9.13): in a finite group G a one-to-one correspondence as in the Jordan-Holder Theorem can be defined preserving not only G-isomorphic chief factors but even their property of being Frattini or non-Frattini chief factors. In [2] and [13] a new direction of generalization is presented: the above correspondence can be defined in such a way that the corresponding non-Frattini chief factors have the same complement (supplement).
Algebras of bounded finite dimensional representation type
Authors: Bell Allen D. , Goodearl K. R.
Published: May 2009

It is well known that for finite dimensional algebras, “bounded representation type” implies “finite representation type”; this is the assertion of the First Brauer-Thrall Conjecture (hereafter referred to as Brauer-Thrall I), proved by Roiter [26] (see also [23]). More precisely, it states that if R is a finite dimensional algebra over a field k, such that there is a finite upper bound on the k-dimensions of the finite dimensional indecomposable right R-modules, then up to isomorphism R has only finitely many (finite dimensional) indecomposable right modules. The hypothesis and conclusion are of course left-right symmetric in this situation, because of the duality between finite dimensional left and right R-modules, given by Homk(−, k). Furthermore, it follows from finite representation type that all indecomposable R modules are finite dimensional [25].
Commutants of Toeplitz operators on the ball and annulus
Authors: Čučković Željko , Fan Dashan
Published: May 2009

In this paper we study commutants of Toeplitz operators with polynomial symbols acting on Bergman spaces of various domains. For a positive integer n, let V denote the Lebesgue volume measure on ℂn. If ω is a domain in ℂn, then the Bergman space is defined to be the set of all analytic functions from ω into ℂ such that
Prime ideals of quantized Weyl algebras
Authors: Akhavizadegan M. , Jordan D. A.
Published: May 2009

The main object of study in this paper is the quantized Weyl algebra which arises from the work of Maltsiniotis [10] on noncommutative differential calculus. This algebra has been studied from the point of view of noncommutative ring theory by various authors including Alev and Dumas [1], the second author [9], Cauchon [3], and Goodearl and Lenagan [5]. In [9], it is shown that has n normal elements zi and, subject to a condition on the parameters, the localization obtained on inverting these elements is simple of Krull and global dimension n. It is easy to show that each of these normal elements generates a height one prime ideal and that these are all the height one prime ideals of . The purpose of this paper is to determine, under a stronger condition on the parameters, all the prime ideals of and to compare the prime spectrum with that of a related algebra . This algebra has more symmetric defining relations than those of but it shares the same simple localization which again is obtained by inverting n normal elements zi. Like the alternative algebra can be regarded as an algebra of skew differential (or difference) operators on the coordinate ring of quantum n-space.
Some remarks on the p-homotopy type of B∑p2
Authors: Brunetti Maurizio
Published: May 2009

Let G be a finite group, H a copy of its p-Sylow subgroup, and N the normalizer of H in G. A theorem by Nishida [10] states the p-homotopy equivalence of suitable suspensions of BN and BG when H is abelian. Recently, in [3] the authors proved a stronger result: let ΩkH be the subgroup of H generated by elements of order pk or less; if

then BN and BG are stably p-homotopy equivalent. The hypothesis above is obviously verified when H is abelian. In the same paper the authors recall that H does not verify such condition when p = 2 and G = SL2(Fq) for a suitable odd prime power q; in this case BG and BN are not stably 2-homotopy equivalent.
Characterization of affine ruled surfaces
Authors: Jelonek Włodzimierz
Published: May 2009

The aim of this paper is to give certain conditions characterizing ruled affine surfaces in terms of the Blaschke structure (∇, h, S) induced on a surface (M, f) in ℝ3. The investigation of affine ruled surfaces was started by W. Blaschke in the beginning of our century (see [1]). The description of affine ruled surfaces can be also found in the book [11], [3] and [7]. Ruled extremal surfaces are described in [9]. We show in the present paper that a shape operator S is a Codazzi tensor with respect to the Levi-Civita connection ∇ of affine metric h if and only if (M, f) is an affine sphere or a ruled surface. Affine surfaces with ∇S = 0 are described in [2] (see also [4]). We also show that a surface which is not an affine sphere is ruled iff im(S - HI) =ker(S - HI) and ket(S - HI) ⊂ ker dH. Finally we prove that an affine surface with indefinite affine metric is a ruled affine sphere if and only if the difference tensor K is a Codazzi tensor with respect to ∇.
Some results on Teichmüller spaces of Klein surfaces
Authors: Gastesi Pablo Arés
Published: May 2009

The deformation theory of nonorientable surfaces deals with the problem of studying parameter spaces for the different dianalytic structures that a surface can have. It is an extension of the classical theory of Teichmüller spaces of Riemann surfaces, and as such, it is quite rich. In this paper we study some basic properties of the Teichmüller spaces of non-orientable surfaces, whose parallels in the orientable situation are well known. More precisely, we prove an uniformization theorem, similar to the case of Riemann surfaces, which shows that a non-orientable compact surface can be represented as the quotient of a simply connected domain of the Riemann sphere, by a discrete group of Möbius and anti-Möbius transformation (mappings whose conjugates are Mobius transformations). This uniformization result allows us to give explicit examples of Teichmüller spaces of non-orientable surfaces, as subsets of deformation spaces of orientable surfaces. We also prove two isomorphism theorems: in the first place, we show that the Teichmüller spaces of surfaces of different topological type are not, in general, equivalent. We then show that, if the topological type is preserved, but the signature changes, then the deformations spaces are isomorphic. These are generalizations of the Patterson and Bers-Greenberg theorems for Teichmüller spaces of Riemann surfaces, respectively.
Compact Hankel operators on weighted harmonic Bergman spaces
Authors: Stroethoff Karel
Published: May 2009

We prove the compactness of certain Hankel operators on weighted Bergman spaces of harmonic functions on the unit ball in Rn.
Topological invariants of germs of real analytic functions
Authors: Dudziński Piotr
Published: May 2009

Let f: (ℝn, 0)→ (ℝ,0) be a germ of a real analytic function. Let L and F(f) denote the link of f and the Milnor fibre of fc respectively, i. e., L = {x ∈ Sn−1 | f(x) = 0}, , where 0 ≤ ξ ≪ r ≪ 1, . In [2] Szafraniec introduced the notion of an -germ as a generalization of a germ defined by a weighted homogeneous polynomial satisfying some condition concerning the relation between its degree and weights (definition 1). He also proved that if f is an -germ (presumably with nonisolated singularity) then the number χ(F(f)/d mod 2 is a topological invariant of f, where χ(F(f)) is the Euler characterististic of F(f), and gave the formula for χ(L)/2 mod 2 (it is a well-known fact that F(L) is an even number). As a simple consequence he got the fact that χ(F(f)mod 2 is a topological invariant for any f, which is a generalization of Wall's result [3] (he considered only germs with an isolated singularity).
Endomorphism regular Ockham algebras of finite Boolean type
Authors: Blyth T. S. , Silva H. J.
Published: May 2009

If (L; ƒ) is an Ockham algebra with dual space (X; g), then it is known that the semigroup of Ockham endomorphisms onLis (anti-)isomorphic to the semigroup Λ(X; g) of continuous order-preserving mappings onXthat commute withg. Here we consider the case whereLis a finite boolean lattice and ƒ is a bijection. We begin by determining the size of Λ(X;g), and obtain necessary and sufficient conditions for this semigroup to be regular or orthodox. We also describe its structure when it is a group, or an inverse semigroup that is not a group. In the former case it is a cartesian product of cyclic groups and in the latter a cartesian product of cyclic groups each with a zero adjoined.
Matched pairs of Lie algebroids
Authors: Mokri Tahar
Published: May 2009

We extend to Lie algebroids the notion variously known as a double Lie algebra (Lu and Weinstein), matched pair of Lie algebras (Majid), or twilled extension of Lie algebras (Kosmann-Schwarzbach and Magri). It is proved that a matched pair of Lie groupoids induces a matched pair of Lie algebroids. Conversely, we show that under certain conditions a matched pair of Lie algebroids integrates to a matched pair of Lie groupoids. The importance of matched pairs of Lie algebroids has been recently demonstrated by Lu.
Pietsch integral operators defined on injective tensor products of spaces and applications
Authors: Popa Dumitru
Published: May 2009

For X and Y Banach spaces, let X⊗εY, be the injective tensor product. If Z is also a Banach space and U ∊ L(X⊗εY,Z) we consider the operator

We prove that if U ∊ PI(X⊗εY, Z), then U# ∊ I(X, PI(Y,Z)). This result is then applied in the case of operators defined on the space of all X-valued continuous functions on the compact Hausdorff space T. We obtain also an affirmative answer to a problem of J. Diestel and J. J. Uhl about the RNP property for the space of all nuclear operators; namely if X* and Y have the RNP and Y can be complemented in its bidual, then N(X, Y) has the RNP.
Montel subspaces of Fréchet spaces of Moscatelli type
Authors: Albanese Angela A.
Published: May 2009

In this note we show that every complemented Montel subspace F of a Fréchet space E of Moscatelli type is isomorphic to ω or is finite–dimensional; the last case always occurs when E has a continuous norm. To do this, we first study the topology induced by E on its Montel subspaces, extending a result on Fr6chet-Montel spaces of Moscatelli type in [4].

We recall that the Fréchet spaces of Moscatelli type were introduced and studied by J. Bonet and S. Dierolf in [4]; the general idea behind the construction of such spaces was due to V. B. Moscatelli [7].
Hilbert cusp forms and special values of Dirichlet series of Rankin type
Authors: Lee Min Ho
Published: May 2009

Let K be a totally real number field of degree nover ℚ and let c be an integral ideal of a maximal order of K. Given a nonnegative integer j and a Hecke character on the group of ideles of K, let denote the space of Hilbert cusp forms of holomorphic type on ℋn of weight j, level c and character ψ where ℋn is the n-th power of the Poincaré upper half plane ℋ.Let g be an element of , where 1 is the trivial character. If u ∈ Sk(c, ψ), then the product gu is an element of Sk+l (c, ψ), and therefore we can consider the linear map sending u to gu. Let be the adjoint of the linear map Φg with respect to the Petersson inner product.
Cleft extensions for a Hopf algebrakq[X,X−1, Y]
Authors: Chen Hui-Xiang
Published: May 2009

The concept of cleft extensions, or equivalently of crossed products, for a Hopf algebra is a generalization of Galois extensions with normal basis and of crossed products for a group. The study of these subjects was founded independently by Blattner-Cohen-Montgomery [1] and by Doi-Takeuchi [4]. In this paper, we determine the isomorphic classes of cleft extensions for a infinite dimensional non-commutative, non-cocommutative Hopf algebra kq[X, X–l, Y], which is generated by a group-like element X and a (1,X)-primitive element Y. We also consider the quotient algebras of the cleft extensions.
An equivalence induced by Ext and Tor applied to the finitistic weak dimension of coherent rings
Authors: Wilkins Elwood
Published: May 2009

Let R be a ring, see below for other notation. The functor categories (mod-R, Ab) and ((R-mod)op, Ab) have received considerable attention since the 1960s. The first of these has achieved prominence in the model theory of modules and most particularly in the investigation of the representation theory of Artinian algebras. Both [11, Chapter 12] and [8] contain accounts of the use (mod-R, Ab) may be put to in the model theoretic setting, and Auslander's review, [1], details the application of (mod-R, Ab) to the study of Artinian algebras. The category ((R-mod)op, Ab) has been less fully exploited. Much work, however, has been devoted to the study of the transpose functor between R-mod and mod-R. Warfield's paper, [13], describes this for semiperfect rings, and this duality is an essential component in the construction of almost split sequences over Artinian algebras, see [4]. In comparison, the general case has been neglected. This paper seeks to remedy this situation, giving a concrete description of the resulting equivalence between (mod-R, Ab) and ((R-mod)op, Ab) for an arbitrary ring R.
Spectral decomposition of spherical immersions with respect to the Jacobi operator
Authors: Arroyo J. , Barros M. , Garay O. J.
Published: May 2009

We study the spectral decomposition with respect to the Jacobi operator, J, of spherical immersions and characterize those with a simple decomposition in terms of the Finite Chen-type submanifolds. As a consequence, we give an application to the inverse problem for J.
Groups isomorphic to their non-nilpotent subgroups
Authors: Smith Howard , Wiegold James
Published: May 2009

We were concerned in [12] with groups G that are isomorphic to all of their non-abelian subgroups. In order to exclude groups with all proper subgroups abelian, which are well understood in the finite case [7] and which include Tarski groups in the infinite case, we restricted attention to the class X of groups G that are isomorphic to their nonabelian subgroups and that contain proper subgroups of this type; such groups are easily seen to be 2-generator, and a complete classification was given in [12, Theorem 2] for the case G soluble. In the insoluble case, G/Z(G) is infinite simple [12; Theorem 1], though not much else was said in [12] about such groups. Here we examine a property which represents a natural generalisation of that discussed above. Let us say that a group G belongs to the class W if G is isomorphic to each of its non-nilpotent subgroups and not every proper subgroup of G is nilpotent. Firstly, note that finite groups in which all proper subgroups are nilpotent are (again) well understood [9]. In addition, much is known about infinite groups with all proper subgroups nilpotent (see, in particular, [8] and [13] for further discussion) although, even in the locally nilpotent case, there are still some gaps in our understanding of such groups. We content ourselvesin the present paper with discussing finitely generated W-groups— note that a W-group is certainly finitely generated or locally nilpotent. We shall have a little more to say about the locally nilpotent case below.
A continuation theory for weakly inward maps
Authors: O'Regan Donal
Published: May 2009

Fixed point and random fixed point theorems are presented for weakly inward maps. Also a continuation theorem for weakly inward maps is presented.
On projective characters of the same degree
Authors: Higgs R. J.
Published: May 2009

All groups G considered in this paper are finite and all representations of G are defined over the field of complex numbers. The reader unfamiliar with projective representations is referred to [9] for basic definitions and elementary results. Let Proj (G, α) denote the set of irreducible projective characters of a group G with cocyle α. In previous papers (for exampe [2], [4], and [6]) numerous authors have considered the situation when Proj(G, α) = 1 or 2; such groups are said to be of α-central type or of 2α-central type, respectively. In particular in [4, Theorem A] the author showed that if Proj(G, α) = {ξ1, ξ2}, then ξ1(1)=ξ2(1). This result has recently been independently confirmed in [8, Corollary C].
Finite 3-groups acting on bordered surfaces
Authors: May Coy L.
Published: May 2009

Let G be a finite group. The real genus p(G) [8] is the minimum algebraic genus of any compact bordered Klein surface on which G acts. There are now several results about the real genus parameter. The groups with real genus p ≤ 5 have been classified [8,9,12], and genus formulas have been obtained for several classes of groups [8,9,10,11,12]. Most notably, McCullough calculated the real genus of each finite abelian group [13]. In addition, there is a good general lower bound for the real genus of a finite group [11].
A note on Saleh's paper ‘Almost continuity implies closure continuity’
Authors: Dontchev Julian , Noiri Takashi
Published: May 2009

Recently, Saleh [3] claimed to have solved ‘a long standing open question’ in topology; namely, he proved that every almost continuous function is clousure continuous (= θ = continuous). Unforunately, this problem was settled long time ago and even a better result is known. Consider the following implications: Cont. ⇒ Almost cont. ⇒ Almost α-cont.⇒ η-cont. ⇒.θ-cont. ⇒ Weakley cont.
Influence of somatic cell counts and breed on physico-chemical and sensory characteristics of hard ewes'-milk cheeses
Authors: Revilla Isabel , Lurueña-Martínez Miguel A , Vivar-Quintana Ana M
Published: May 2009

The aim of the present work was to perform a physico-chemical, descriptive quantitative and consumer-preference analysis of hard ewes'-milk cheeses that had been matured for one year and to determine the correlations between the variables studied. The cheeses were elaborated with milk from three breeds of sheep (Castellana, Churra and Assaf) with different somatic cell counts (lower than 500 000 cells ml−1; between 1 000 000 and 1 500 000 cells ml−1, and more than 2 500 000 cells ml−1). The results show that the cheeses elaborated with milk with high SCC had lower values of dry extract and fat and high values of pH and fat acidity and were described as pungent, granulose and less creamy. Regarding the effect of breed, the cheeses made with milk from the Churra breed had lower values for fat and those made with Assaf breed milk were significantly more rancid. The study of correlations showed that creaminess was positively correlated with the dry extract and total fat content and negatively correlated with ash and fat acidity, indeed grainy texture and pungency had the opposite sign in their correlation with these latter variables. The yellow colour was positively correlated with ash and negatively with protein. Finally, the consumer preferences reveals that the less accepted cheeses showed the higher values for rancidness and pungency and they were less likely to accept the cheeses made with Assaf breed milk.
Long-term effects on heifer performance of an enhanced-growth feeding programme applied during the preweaning period
Authors: Terré Marta , Tejero Carolina , Bach Alex
Published: May 2009

Sixty female dairy calves (body weight, BW, 43·2±0·58 kg and age 9·8±0·61 d) were arranged in two groups to compare the short-term and long-term effects of an enhanced-growth feeding programme (EF) with those of a conventional-growth feeding programme (CF). After 1 week of adaptation to a milk replacer (MR), CF calves were fed 4 l/d of MR (25% crude protein, CP; 19·2% ether extract) at 12% dry matter (DM) from days 1 to 27 and 2 l/d at 12% DM from days 28 to 34, and the EF calves were offered the same MR at 18% DM: 4 l/d from days 1 to 6, 6 l/d from days 7 to 13, 7 l/d from days 14 to 20, 6 l/d from days 21 to 27 and 3 l/d from day 28 to weaning at day 34 of the study (50 d of age). Individual calf starter (20·7% CP) intake was recorded daily from the beginning until day 41 of study (57 d of age). Then, calves were placed in groups of six and they received a total mixed ration (TMR) containing 18·5% CP until day 56 d of study (72 d of age). Then, heifers were moved to larger pens and were fed the same TMR in both treatments at each subsequent stage of growth throughout the study. Calves were weighed weekly until day 56 of study and before every pen change (days 94, 149, 200, 387 of study). When heifers were 400 d old and weighed >380 kg, they were moved to a breeding pen where oestruses were checked three times a day. Heifers were inseminated 12 h after the detection of oestrus. One month before calving, heifers were returned to their original farm and milk yield at 305 days in milk was recorded from 28 cows. Starter intake was greater (P<0·001) in CF than in EF calves (0·79 v. 0·29±0·043 kg/d, respectively) during the preweaning period, but TMR consumption was similar in both treatments from days 42 to 56 of study. BW of EF calves was greater (P<0·01) than that of CF calves at weaning (76·4 v. 71·6±1·10 kg, respectively), but BW was not different at day 387 of study (405 d of age) (406·3 v. 401·3±4·05 kg, respectively). There were numerical differences in age at first breeding, fertility at first artificial insemination, age at pregnancy, and milk yield but some of these differences might have reached statistical significance with more replication.
An Expansion in Terms of Associated Legendre Functions
Authors: Macrobert T. M.
Published: May 2009

If the right-hand side of the expansion

is integrated m times from 1 to µ, it becomes
Simultaneous Extension of Partial Endomorphisms of Groups
Authors: Chehata C. G.
Published: May 2009

Let μ be a homomorphic mapping of some subgroup A of the group G onto a subgroup Ḃ (not necessarily distinct from A) of G; then we call μ a partial endomorphism of G. If A coincides with G, that is, if the homomorphism is defined on the whole of G, we speak of a total endomorphism; this is what is usually called an endomorphism of G. A partial (or total) endomorphism μ*extends or continues a partial endomorphism μ if the domain of μ* contains the domain of μ, that is, μ* is defined for (at least) all those elements for which μ. is defined, and moreover μ* coincides with μ where μ is defined.
Further Integrals Involving E-Functions
Authors: Ragab F. M.
Published: May 2009

The formulae to be proved are

where m is a positive integer, p ≧ q + 1, R(mar + k) > 0, r = 1, 2, …, p, and | amp z |ππ. For other values of p and q the result holds if the integral is convergent.
An Integral Involving a Product of Two Modified Bessel Functions of the Second Kind
Authors: Ragab F. M.
Published: May 2009

The formula to be proved is

where R(z)>0.
Integrals Involving a Modified Bessel Function of the Second Kind and an E-Function
Authors: Macrobert T. M.
Published: May 2009

The first formula to be proved is

where p ≧ q + 1, | amp z | < л, R(k±n + αr)>0, r = l, 2, …, p. For other values of p and q the result is valid if the integral is convergent. A second formula is given in § 3.

The following formulae are required in the proof:

where R(z);>0, (1);

where R(α)>0, | amp z | < л, (2);

where the contour starts from -∞ on the ξ-axis, passes round the origin in the positive direction, and ends at -∞ on the ξ-axis, the initial value of amp ζ being - л, (3).
Elliptic Integrals in Terms of Legendre Polynomials
Authors: González M. O.
Published: May 2009

Consider the elliptic integral of the first kind

or, alternatively,

where x = sin ϕ. It is customary in the theory of elliptic integrals to let k = sin α, k' = cos α, sot that k'2 + k2 = 1. For convenience we shall also introduce the parameter
A Product of two E-Functions Expressed as a Sum of Two E-Functions
Authors: Ragab F. M.
Published: May 2009

The formula to be proved is

In proving (1) the following formulae are required:

where p≥q + 1, (1).
Two Integrals involving Modified Bessel Functions of the Second Kind
Authors: Conolly B. W.
Published: May 2009

In § 2 a product of two modified Bessel Functions of the Second Kind is expressed as an integral with a function of the same type as a factor of the integrand. In § 3 an integral involving a product of these functions, regarded as functions of their orders, is evaluated in terms of another function of this kind. These results were suggested by a study of Mellin's inversion formula.
A Few Infinite Integrals involvingE-Functions
Authors: Rathie C. B.
Published: May 2009

The object of this paper is to evaluate a few infinite integrals involvingE-functions by applying the Parseval-Goldstein [1] theorem of Operational Calculus; that, if

and

then

when the integrals are convergent.
Integrals allied to Airy's integrals
Authors: Macrobert T. M.
Published: May 2009

Airy's integrals

can be expressed ([1], [2]) in terms of Bessel functions. In this paper integrals of the types

are discussed. Various subsidiary formulae are given in § 2, some integrals of the type

are evaluated in § 3, and from these the integrals of the Airy type are derived in § 4.
Integration of E-Functions with regard to their parameters
Authors: Ragab F. M.
Published: May 2009

In integrating E-functions with respect to their parameters the contours are usually of the Barnes type, deformed if necessary to separate the increasing and decreasing sequences of poles of the integrands. Also the constants are taken to be such that the integrals converge. The following formulae are required in proving the theorems given in this paper.
A formula of Bateman
Authors: Carlitz L.
Published: May 2009

The formula

was stated by Bateman ([2], p. 457); a proof is sketched in [3], p. 144. Here

the Laguerre polynomial of degree
A note on Mathieu functions
Authors: Bell M.
Published: May 2009

The Mathieu functions of integral order [1] are the solutions with period π or 2π of the equation

The eigenvalues associated with the functions ceN and seN, where N is a positive integer, denoted by aN and bN respectively, reduce to

aN = bN = N2

when q is zero. The quantities aN and bN can be expanded in powers of q, but the explicit construction of high order coefficients is very tedious. In some applications the quantity of most interest is aN – bN, which may be called the “width of the unstable zone“. It is the object of this note to derive a general formula for the leading term in the expansion of this quantity, namely

Suppose first that N is an odd integer. Then there is an expansion

where

These functions π satisfy

and

On Substituting (3) in (1), one obtains the algebraic equation

where

Explicitly,

{11} = q

{lm} = 0 otherwise.
A note on semi-special permutations
Authors: Yacoub K. R.
Published: May 2009

In a recent paper [1], the theory of non-linear semi-special permutations has been developed. A method for describing such permutations, on a given range [n], is to be found in §§2, 3. This method consists in choosing a proper divisor s of n, determining all the semispecial permutations with principal number s, and then making stake all its possible values. In this way the totality of non-linear semi-special permutations on [n] may be obtained.
On rearrangements of infinite series
Authors: Robertson A. P.
Published: May 2009

If a convergent series of real or complex numbers is rearranged, the resulting series may or may not converge. There are therefore two problems which naturally arise.

(i) What is the condition on a given series for every rearrangement to converge?

(ii) What is the condition on a given method of rearrangement for it to leave unaffected the convergence of every convergent series?

The answer to (i) is well known; by a famous theorem of Riemann, the series must be absolutely convergent. The solution of (ii) is perhaps not so familiar, although it has been given by various authors, including R. Rado [7], F. W. Levi [6] and R. P. Agnew [2]. It is also given as an exercise by N. Bourbaki ([4], Chap. III, § 4, exs. 7 and 8).
Integrals involving hypergeometric functions and E-functions
Authors: Macrobert T. M.
Published: May 2009

In § 2 a number of integrals in which the integrand contains a product of a hypergeometric function and an E-function will be evaluated. The following formulae will be employed in the proofs.

If ρ +σ = α + β + γ + 1, and if α, β or γ is zero or a negative integer,

this is Sallschütz's theorem [1].

If R(γ - ½α - ½β)< - ½,

This theorem was given by Wastson [2] for negative integral values of α and later by Whipple [3] for general values α.

R(γ) > 0,

This formula was given by Whipple [3]

l is a positive integer,