bluuebunny/crossref_metadata_2025 huggingface dataset:
Primes of the form [pc] and related questions
Authors: Harman Glyn , Rivat Joël
Published: May 2009

Much interest has been shown in determining the range of values of c for which the sequence [n]c contains infinitely many primes. The result is an elementary deduction from the prime number theorem, of course, of 0<c≤l. In 1953, Piatetski–Shapiro [9] showed that

for 1<c<12/11, where xc(X) stands for the number of primes in the set {[nc]n≤x}.
Semigroup-graded rings with finite support
Authors: Clase M. V. , Jespers E. , Del Río A.
Published: May 2009

Let S be a semigroup and let be an S-graded ring. Rs = 0 for all but finitely many elements s ∈ S1, then R is said to have finite support. In this paper we concern ourselves with the question of whether a graded ring R with finite support inherits a given ring theoretic property from the homogeneous subrings Re corresponding to idempotent semigroup elements e.
Equality of essential spectra of quasisimilar operators with property (δ)
Authors: Miller T. L. , Miller V. G.
Published: May 2009

A Banach space operator has property (δ) if and only if it is the quotient of a decomposable operator, equivalently, if and only if its adjoint has Bishop's property (β). Within this class of operators, it is shown that quasisimilarity preserves essential spectra.
A spectral mapping theorem for the Weyl spectrum
Authors: Lee Woo Young , Lee Sang Hoon
Published: May 2009

Suppose H is a Hilbert space and write ℒ(H) for the set of all bounded linear operators on H. If T ∈ ℒ(H) we write σ(T) for the spectrum of T; π0(T) for the set of eigenvalues of T; and π00(T) for the isolated points of σ(T) that are eigenvalues of finite multiplicity. If K is a subset of C, we write iso K for the set of isolated points of K. An operator T ∈ ℒ(H) is said to be Fredholm if both T−1(0) and T(H)⊥ are finite dimensional. The index of a Fredholm operator T, denoted by index(T), is defined by
Mean curvature and shape operator of isometric immersions in real-space-forms
Authors: Chen Bang-Yen
Published: May 2009

According to the well-known Nash's theorem, every Riemannian n-manifold admits an isometric immersion into the Euclidean space En(n+1)(3n+11)/2. In general, there exist enormously many isometric immersions from a Riemannian manifold into Euclidean spaces if no restriction on the codimension is made. For a submanifold of a Riemannian manifold there are associated several extrinsic invariants beside its intrinsic invariants. Among the extrinsic invariants, the mean curvature function and shape operator are the most fundamental ones.
On linear recurrence sequences with polynomial coefficients
Authors: van der Poorten A. J. , Shparlinski I. E.
Published: May 2009

We consider sequences (Ah)defined over the field ℚ of rational numbers and satisfying a linear homogeneous recurrence relation

with polynomial coefficients sj;. We shall assume without loss of generality, as we may, that the sj, are defined over ℤ and the initial values A0A]…, An−1 are integer numbers. Also, without loss of generality we may assume that S0 and Sn have no non-negative integer zero. Indeed, any other case can be reduced to this one by making a shift h → h – l – 1 where l is an upper bound for zeros of the corresponding polynomials (and which can be effectively estimated in terms of their heights)
An extension of the Kegel–Wielandt theorem to locally finite groups
Authors: Franciosi Silvana , de Giovanni Francesco , Sysak Yaroslav P.
Published: May 2009

A famous theorem of Kegel and Wielandt states that every finite group which is the product of two nilpotent subgroups is soluble (see [1], Theorem 2.4.3). On the other hand, it is an open question whether an arbitrary group factorized by two nilpotent subgroups satisfies some solubility condition, and only a few partial results are known on this subject. In particular, Kegel [6] obtained an affirmative answer in the case of linear groups, and in the same article he also proved that every locally finite group which is the product of two locally nilpotent FC-subgroups is locally soluble. Recall that a group G is said to be an FC-group if every element of G has only finitely many conjugates. Moreover, Kazarin [5] showed that if the locally finite group G = AB is factorized by an abelian subgroup A and a locally nilpotent subgroup B, then G is locally soluble. The aim of this article is to prove the following extension of the Kegel–Wielandt theorem to locally finite products of hypercentral groups.
Some remarks on regular Banach spaces
Authors: Leung Denny H.
Published: May 2009

A Banach space E is said to be regular if every bounded linear operator from E into E′ is weakly compact. This property was studied in [7, 9] under the name Property (w). In [7], using James type spaces as constructed in [4], examples were given of regular Banach spaces which fail to have weakly sequentially complete duals, answering a question raised in [9]. In this paper, we present some more results concerning the regularity of James type spaces.
Automorphic forms on nondiscrete Möbius groups
Authors: Beardon A. F.
Published: May 2009

If Г is a discrete Möbius group acting on the upper half-plane ℋ of the complex plane, the quotient space ℋ/Г is a Riemann surface ℛ and the automorphic functions on Г correspond to meromorphic functions on ℛ. If Г is a nondiscrete Möbius group acting on ℋ, then ℋ/Г is no longer a Riemann surface, and it is obvious that in this case there are no nonconstant automorphic functions on Г. The situation for automorphic forms is quite different. Automorphic forms of integral dimension for a discrete group Г correspond to meromorphic differentials on ℛ, but even if Г is nondiscrete it may still support nontrivial automorphic forms. The problem of classifying those nondiscrete Möbius groups which act on ℋ and which support nonconstant automorphic forms of arbitrary real dimension was raised and solved (rather indirectly) in [2] where, roughly speaking, function-theoretic methods are used to analyse all possible polynomial automorphic forms of integral dimension, and the results obtained then used to analyse the more general situation.
Specht modules for finite reflection groups
Authors: HalicioǦlu S.
Published: May 2009

Over fields of characteristic zero, there are well known constructions of the irreducible representations, due to A. Young, and of irreducible modules, called Specht modules, due to W. Specht, for the symmetric groupsSnwhich are based on elegant combinatorial concepts connected with Young tableaux etc. (see, e.g. [13]). James [12] extended these ideas to construct irreducible representations and modules over an arbitrary field. Al-Aamily, Morris and Peel [1] showed how this construction could be extended to cover the Weyl groups of typeBn. In [14] Morris described a possible extension of James' work for Weyl groups in general. Later, the present author and Morris [8] gave an alternative generalisation of James' work which is an extended improvement and extension of the original approach suggested by Morris. We now give a possible extension of James' work for finite reflection groups in general.
A class of groups rich in finite quotients
Authors: Walter Vonn
Published: May 2009

If X is a class of groups, the class of counter-Xgroups is defined to consist of all groups having no non-trivial X-quotients. The counter-abelian groups are the perfect groups and the counter-counter-abelian groups are the imperfect groups studied by Berrick and Robinson [2]. This paper is concerned with the class of counter-counterfinite groups. It turns out that these are the groups in which any non-trivial quotient has a non-trivial representation over any finitely generated domain (Theorem 1.1), so we shall call these groups highly representable or HR-groups.
Khinchin's inequality for operators
Authors: Jameson G. J. O.
Published: May 2009

Let be either a C*-algebra (with norm ∥ ∥) or a symmetric ideal of operators on a Hilbert space (with norm denoted by σ). Let a1…, an be self-adjoint elements, and let a0 = .
Co-Cohen-Macaulay Artinian modules over commutative rings
Authors: Denizler I. H. , Sharp R. Y.
Published: May 2009

In [7], Z. Tang and H. Zakeri introduced the concept of co-Cohen-Macaulay Artinian module over a quasi-local commutative ring R (with identity): a non-zero Artinian R-module A is said to be a co-Cohen-Macaulay module if and only if codepth A = dim A, where codepth A is the length of a maximalA-cosequence and dimA is the Krull dimension of A as defined by R. N. Roberts in [2]. Tang and Zakeriobtained several properties of co-Cohen-Macaulay Artinian R-modules, including a characterization of such modules by means of the modules of generalized fractions introduced by Zakeri and the present second author in [6]; this characterization is explained as follows.
Extensions of semilattices by left type-A semigroups
Authors: Billhardt Bernd
Published: May 2009

On a semigroup S let the relation ℛ*, sometimes denoted by ℛ, be defined by xℛ*y[(sx = txsy = ty]. A semigroup S is called left type-A, iff the set Es of idempotents of S forms a semilattice under multiplication, each element x of Sis ℛ* related to a (necessarily unique) idempotent x+, and xe = (xe)+x for all x ∈ S, е ∈ Es.
Strongly simply connected Auslander algebras
Authors: Assem Ibrahim , Brown Peter
Published: May 2009

Letkbe an algebraically closed field. By an algebra is meant an associative finite dimensionalk-algebra A with an identity. We are interested in studying the representation theory of Λ, that is, in describing the category mod Λ of finitely generated right Λ-modules. Thus we may, without loss of generality, assume that Λ is basic and connected. For our purpose, one strategy consists in using covering techniques to reduce the problem to the case where the algebra is simply connected, then in solving the problem in this latter case. This strategy was proved efficient for representation-finite algebras (that is, algebras having only finitely many isomorphism classes of indecomposable modules) and representation-finite simply connected algebras are by now well-understood: see, for instance [5], [7],[8]. While little is known about covering techniques in the representation-infinite case, it is clearly an interesting problem to describe the representation-infinite simply connected algebras. The objective of this paper is to give a criterion for the simple connectedness of a class of (mostly representationinfinite) algebras.
Automorphisms fixing every subnormal subgroup of a finite group
Authors: Cossey John
Published: May 2009

We denote by Autsn(G) the set of all automorphisms that fix every subnormal subgroup of G setwise. In a recent paper [7] Robinson showed that the structure of Autsn(G) is quite restricted for a finite group G. Our aim in this paper is to show that more detailed information about the structure of Autsn(G) can be obtained by focussing on its action on F*(G), the generalised Fitting subgroup of G.
Mixed Hilbert modular forms and families of abelian varieties
Authors: Lee Min Ho
Published: May 2009

In [18] Shioda proved that the space of holomorphic 2-forms on a certain type of elliptic surface is canonically isomorphic to the space of modular forms of weight three for the associated Fuchsian group. Later, Hunt and Meyer [6] made an observation that the holomorphic 2-forms on a more general elliptic surface should in fact be identified with mixed automorphic forms associated to an automorphy factor of the form

for z in the Poincaré upper half plane ℋ, g = and χ(g) = , where g is an element of the fundamental group Γ⊂PSL(2, R) of the base space of the elliptic fibration, χ-Γ→SL(2, R) the monodromy representation, and w: ℋ→ℋ the lifting of the period map of the elliptic surface.
The modulus of near smoothness of the lp product of a sequence of Banach spaces
Authors: Olszowy Leszek
Published: May 2009

In the classical geometry of Banach spaces the notions of smoothness, uniform smoothness, strict and uniform convexity introduced by Day [1] and Clarkson [2] play a very important role and are used in many branches of functional analysis ([3,4,5], for example). In recent years a lot of papers have appeared containing interesting generalizations of these notions in terms of a measure of noncompactness. These new concepts investigated in this paper as near uniform smoothness, local near uniform smoothness and modulus of near smoothness have been introduced by Stachura and Sekowski [6] and Banaś [7] (see also [8,9]).
An estimate on the eigenvalues in bifurcation for gradient mappings
Authors: Chiappinelli Raffaele
Published: May 2009

Let H be a real Hilbert space and let A: H→H be a nonlinear operator such that A(0) = 0. We consider the eigenvalue problem

Recall that λ0 ε ℝ is said to be a bifurcation point for (1.1) if every neighbourhood of (λ0, 0) in ℝ × H contains solutions of (1.1).
On the complexity of computing the 2-Selmer group of an elliptic curve
Authors: Siksek S. , Smart N. P.
Published: May 2009

In this paper we give an algorithm for computing the 2-Selmer group of an elliptic curve

which has complexityO(LD(0·5),c1)), whereDis the absolute discriminant of the curve. Our algorithm is unconditional but the complexity estimate assumes the GRH and a standard conjecture on the distribution of smooth reduced ideals. This improves on the corresponding algorithm of Birch and Swinnerton-Dyer, which has complexity ofO(√D).
On 2-class field towers for quadratic number fields with 2-class group of type (2,2)
Authors: Gerth Frank
Published: May 2009

LetKbe a quadratic number field with 2-class group of type (2,2). Thus ifSkis the Sylow 2-subgroup of the ideal class group ofK, thenSk= ℤ/2ℤ × ℤ/2ℤ Let

K ⊂ K1⊂ K2⊂ K3⊂…

the 2-class field tower ofK. ThusK1is the maximal abelian unramified extension ofKof degree a power of 2;K2is the maximal abelian unramified extension ofKof degree a power of 2; etc. By class field theory the Galois group Ga1 (K1/K) ≅Sk≅ ℤ/2ℤ × ℤ/2ℤ, and in this case it is known that Ga(K2/Kl) is a cyclic group (cf. [3] and [10]). Then by class field theory the class number ofK2is odd, and henceK2=K3=K4= …. We say that the 2-class field tower ofKterminates atK1if the class number ofK1is odd (and henceK1=K2=K3= … ); otherwise we say that the 2-class field tower ofKterminates atK2. Our goal in this paper is to determine how likely it is for the 2-class field tower ofKto terminate atK1and how likely it is for the 2-class field tower ofKto terminate atK2. We shall consider separately the imaginary quadratic fields and the real quadratic fields.
Gauss sums for U(2n, q2)
Authors: Kim Dae San
Published: May 2009

For a lifted nontrivial additive character λ' and a multiplicative character λ of the finite field with q2 elements, the “Gauss” sums Σ λ'(trg) over g ∈SU(2n, q2) and Σ λ (detg)λ'(trg) over g ∈ U(2n, q2) are considered. We show that the first sum is a polynomial in q with coefficients involving averages of “bihyperkloosterman sums” and that the second one is a polynomial in q with coefficients involving powers of the usual twisted Kloosterman sums. As a consequence, we can determine certain “generalized Kloosterman sums over nonsingular Hermitian matrices”, which were previously determined by J. H. Hodges only in the case that one of the two arguments is zero.
Totally complex submanifolds of the Cayley projective plane
Authors: Ximin Liu
Published: May 2009

Let h be the second fundamental form of a compact submanifold M of the Cayley projective plane CaP2. We determine all compact totally complex submanifolds of complex dimension n in CaP2 satisfying |h|2 ≤ n.
On Peiffer central series
Authors: Ellis Graham
Published: May 2009

Let G be a group. A precrossed G-module is a group homomorphism ∂: M → G together with a group action (g, m) ↦gm of G on M, such that ∂(gm) = g(∂m)g−1. The Peiffer commutator < m, m′ > of two elements m, m′ ∊ M is denned as

< m, m′ >= mm′ m−1(∂mm′)−1

If all Peiffer commutators are trivial, the precrossed G-module is said to be a crossed G-module. The subgroup < M, M > generated by all Peiffer commutators is called the Peiffer subgroup of M; it is the second term of a lower Peiffer central series (see below). The following table indicates how these concepts reduce to more standard concepts when restrictions are placed on ∂ and G.
On a class of operators
Authors: Yang Youngoh
Published: May 2009

In this paper we show that the Weyl spectrum of an operator of class W satisfies the spectral mapping theorem for analytic functions and give the equivalent conditions for an operator of the form normal + compact to be polynomially compact.
Periodic radical products of two locally nilpotent subgroups
Authors: Höfling Burkhard
Published: May 2009

A group G is the product of its subgroups A and B if G equals the set AB = (ab | a ∊ A, b ∊ B). A subgroup H of G is called prefactorized if it is the product of a subgroup of A and a subgroup of B; thus H is prefactorized if and only if H = (H ∩ A)(H ∩ B). A prefactorized subgroup H of G is factorized if it contains A ∩ B. if H is any subgroup of G = AB, then the intersection X ofall factorized subgroups of G containing H is itself factorized; see for example [2, Lemma 1.1.2]. This subgroup, which is evidently the smallest factorized subgroup of G which contains H, is called the factorizer of H in G = AB.
On joint essential spectra of doubly commuting n-tuples of p-hyponormal operators
Authors: Jeon In Ho
Published: May 2009

Let A be an operator on a Hillbert space with polar decomposition A = |A|, let Â = |A|½U|A|½ and let Â = V|Â| be the polar decomposition of Â. Write Ã for the operatorÃ = |Â|½V|Â|½. If = (A1,…,AN) is a doubly commuting n-tuple of p-hyponormal operators on a Hillbert space with equal defect and nullity, then = (Ã1,…,Ãn) is a doubly commuting n-tuple of hyponormal operators. In this paper we show that

where σ* denotes σTe (Taylor essential spectrum), σTw (Taylor-Weyl spectrum) and σTb (Taylor-Browder spectrum), respectively.
Norm Attaining Bilinear Forms on Spaces of Continuous Functions
Authors: Alaminos J. , Choi Y. S. , Kim S. G. , Payá R.
Published: May 2009

We show that continuous bilinear forms on spaces of continuous functions can be approximated by norm attaining bilinear forms.
n-Reflexivity for linear spaces of operators
Authors: Choi Kun Wook
Published: May 2009

We discuss the relationship between then-reflexivity of a linear sub-spaceSinB(H), property (A1/n), ClassCoand strictlyn-separating vectors. We also show that every algebraic operator with property (A2) is hyperreflexive.
A metrical result on the discrepancy of (nα)
Authors: Schoissengeier J.
Published: May 2009

In the following let Ω be the set of irrational numbers in the interval [0,1] and let λ be Lebesgue measure restricted to Ω. For any real number x, let {x} = x - [x] be the fractional part of x. Let N be anatural number and let α e Ω. Then

is known as the discrepancy of the sequence (nα)n>1 modulo 1; here c[x, y) denotes the characteristic function of the interval [x, y).
Corrigendum
Authors: Nicholson W. K. , Yousif M. F.
Published: May 2009

Proposition 3.1 of the paper Annihilators and the CS-condition, Glasgow Math. J. 40 (1998), 213–222, is incorrect as stated, and consequently the note added in proof is incorrect. Hence the question of Faith and Menal whether every strongly right Johns ring is quasi- Frobenius remains open. The problem is that the assumption that the left socle S1 and the right socle Sr are equal is not established. All we know is that Si⊆Sr = r(J) = l(J) by [8, Lemma 2.2]. We can prove the following result.
Comparison of the activity of human and bovine milk on two cell lines
Authors: Pocoví Coloma , Conesa Celia , Barbana Chockry , D Pérez María , Calvo Miguel , Sánchez Lourdes
Published: May 2009

The activity of human milk on cell growth has been evaluated on two cell lines, MDCK and Caco-2. The proportion of human milk samples that reduced by half the growth of MDCK cells was of 36%. This inhibitory activity was associated with casein and not the whey fraction. Great variability was found in the degree of inhibitory activity depending on the milk sample. The susceptibility of Caco-2 cells to milk inhibitory activity was lower than that of MDCK. Bovine milk did not have any effect on cell growth, either as skimmed milk or as whey or casein. Morphology of cells incubated with active human casein showed abnormal features, such as chromatin condensation, reduced cellular volume and apoptotic bodies, and also fragmented DNA, which are all features of apoptosis.
Comparison of the level of residual coagulant activity in different cheese varieties
Authors: Bansal Nidhi , Fox Patrick F , McSweeney Paul L H
Published: May 2009

The coagulant retained in cheese curd is a major contributor to proteolysis during ripening. The objective of this study was to quantify residual coagulant in 9 cheese varieties by measuring its activity on a synthetic heptapeptide (Pro-Thr-Glu-Phe-[NO2-Phe]-Arg-Leu) assayed using reversed-phase HPLC. The level of residual coagulant activity was highest in Camembert cheese, probably due to its low pH at whey drainage and the high moisture content of the cheese, followed in order by Feta=Port du Salut=Cheddar>Gouda>Emmental=Parmigiano Reggiano=low-moisture part-skim Mozzarella=Mozzarella di Bufala Campana. The high cooking temperature (50–54°C) used during the manufacture of Emmental and Parmigiano Reggiano cheeses and the cooking and stretching step in hot water during the manufacture of Mozzarella cheese may be the reasons for the lowest residual coagulant activity in these cheeses. The level of residual coagulant activity was higher in Feta cheese made from milk concentrated by ultrafiltration than in conventional Feta.
Conjugated linoleic acid (CLA) and fatty acid composition of milk, curd and Grana Padano cheese in conventional and organic farming systems
Authors: Prandini Aldo , Sigolo Samantha , Piva Gianfranco
Published: May 2009

CLA levels and fatty acid composition were measured to compare the fat composition in organic bulk milk, destined to the production of Grana Padano cheese, with those produced by conventional system. The curds and Grana Padano cheeses were also analysed to evaluate the effects of the production technology on the CLA content. All analysed organic samples were characterized by higher annual means of CLA, vaccenic acid (TVA) and linolenic acid (LNA) in comparison with conventional samples (with P<0·05). Nevertheless, no particular effect of the production technology was seen on the CLA content. The animal diet appears to be the factor which has the highest effect on the CLA concentration in milk and milk products and an organic diet based on fresh or dried forage, that is rich in CLA precursory fatty acids, may improve the yield of fatty acids with beneficial effects on health.
Effect of high-pressure homogenisation on rheological properties of rennet-induced skim milk and standardised milk gels
Authors: Lodaite Kristina , Chevalier François , Armaforte Emanuele , Kelly Alan L.
Published: May 2009

The effects of high-pressure homogenisation (HPH) in the pressure range 100–300 MPa on the gel formation and rheological properties of rennet-induced skim milk (0·08%, fat, w/w) and standardised milk (3·60% fat, w/w) gels at pH 6·60 were studied. The average casein micelle size in skim milk was significantly reduced and the gel formation time decreased when skim milk was subjected to the pressures of 200 and 300 MPa. The storage modulus of rennet-induced skim milk gels at 2700 s after rennet addition was higher for samples homogenised at higher pressures, which contained smaller casein particles. HPH had little effect on the large deformation properties of rennet-induced skim milk gels. The gel formation time of renneted standardised milk was significantly reduced as a result of HPH, while the storage modulus of rennet-induced milk gels 2700 s after rennet addition increased with increasing homogenising pressure. The apparent fracture stress was slightly higher for standardised milk gels formed from HPH-treated milk, whereas the apparent strain at fracture was lower, than that of unhomogenised milk. In conclusion, HPH treatment influenced gel formation processes of skim milk and its small-deformation rheological properties, mainly through modification of casein micelles. HPH also significantly affected the gel formation process of standardised milk gels and its rheological properties as a result of an increase in volume fraction of aggregating particles, while the particle size was of lesser importance.
Excitation of electrostatic ion-cyclotron-like modes by the electron density ripple in dusty magnetoplasmas
Authors: SHUKLA P. K.
Published: May 2009

It is shown that electrostatic ion-cyclotron (EIC)-like modes can be excited by the pre-existing electron density ripple across the external magnetic field in a dusty magnetoplasma. For this purpose, we use the ion continuity and momentum equations, together with the Boltzmann-distributed electrons, and derive the standard Mathieu equation. The latter admits unstable solutions, demonstrating that the EIC-like modes in dusty magnetoplasmas can be driven due to the free energy in the electron density ripple.
The spread of computer-assisted language learning
Authors: Chapelle Carol A.
Published: May 2009

This paper argues that the vertical spread of computer-assisted language learning (CALL), i.e., a spread throughout language materials and curricula, makes it difficult to draw a clear distinction between CALL and other language materials. In view of the emphasis that teachers, researchers, and administrators have placed on evaluating CALL, I argue that some valuable lessons about materials evaluation can be drawn from reflection on issues in CALL evaluation. In particular, I discuss the opportunities for professionals to reconsider assumptions held about comparative research, draw upon research perspectives and methods from applied linguistics in materials evaluation, and include critical perspectives which examine the opportunities that materials offer language learners to engage in language and culture learning.
First among equals: why some habitats should be considered more important than others during marine reserve planning
Authors: HARBORNE ALASTAIR R.
Published: May 2009

Reserve selection algorithms (RSAs) are a powerful tool for marine conservation, but need biological realistic constraints. A common constraint is that the RSA aims to include the same percentage area of each habitat in the reserve network. The example of Caribbean reefs is used to argue that there is significant additional scope to set specific areal targets for each habitat type, as in many terrestrial case studies. Ten Caribbean habitats are weighted by data on their biodiversity, functional value to ecosystem processes and ecosystem services. These weightings vary depending on the criteria used, and are particularly distinct for ecosystem services. Furthermore, a percentage goal for a habitat can be achieved in multiple ways by including different combinations of habitat patches from across a seascape. RSAs may treat these combinations equally, but some habitat patches are more ‘valuable’ than others because, for example, high abundances of grazers make the benthic community resilient. Incorporating some of these considerations into RSAs is relatively easy, while others are more difficult. However, establishing how to integrate patterns of biodiversity, and ecological processes, functions, goods and services across seascapes into RSAs offers opportunities to improve the design of networks of reserves.
Piezo-controlled microwave devices
Authors: Poplavko Yuriy M. , Molchanov Vitally I. , Yakimenko Yuriy I.
Published: May 2009

At present, millimeter wave fast tunable components are required for telecommunication systems, car collision prevention radar, etc. The only mechanical way of control inserts practically no loss in the frequency agile system. That is why micro-electromechanical systems devices are being studied intensively. In an overview, an alternative way – piezo-electromechanical tuning of microwave components – is reported.
The Double Six of Lines and a Theorem in Euclidean Plane Geometry
Authors: Dougall John
Published: May 2009

The object of the present paper is to establish the equivalence of the well-known theorem of the double-six of lines in projective space of three dimensions and a certain theorem in Euclidean plane geometry. The latter theorem is of considerable interest in itself for two reasons. In the first place, it is a natural extension of Euler's classical theorem connecting the radii of the circumscribed and the inscribed (or the escribed) circles of a triangle with the distance between their centres. Secondly, it gives in a geometrical form the invariant relation between the circle circumscribed to a triangle and a conic inscribed in the triangle. For a statement of the theorem, see § 13 (4).
An Integral Involving the Product of a Bessel Function and an E-Function
Authors: Ragab Fouad M.
Published: May 2009

The formula

where αp+1 = 1/2(m + n), αp+2 = 1/2(m-n), R(m±n)>0 and x is real and positive, was given by MacRobert (Phil. Mag., Ser. 7, XXXI, p. 258). From it the formula (6) below will be deduced.
Note on the Strong Summability of Series
Authors: Hyslop J. M.
Published: May 2009

Given the series ,the n-th Casáro sum of order k is defined by the relation

where is the binomial coefficient . Let Then Σan is said to be summable (C; K) to the sum s if, as n → ∞, The series is said to be absolutely summable (C; k), or summable | is convergent. The series is said to be strongly summable (C; k) with index p, or summable [Ck, p], to the sum s if

It is assumed that k and p are positive.
Cohomology Theory for Non-Normal Subgroups and Non-Normal Fields
Authors: Adamson Iain T.
Published: May 2009

Let G be a finite group, H an arbitrary subgroup (i.e., not necessarily normal); we decompose G as a union of left cosets modulo H:

choosing fixed coset representatives v. In this paper we construct a “coset space complex” and assign cohomology groups; Hr([G: H], A), to it for all coefficient modules A and all dimensions, -∞<r<∞. We show that if

is an exact sequence of coefficient modules such that H1U, A')= 0 for all subgroups U of H, then a cohomology group sequence

may be defined and is exact for -∞<r<∞. We also provide a link between the cohomology groups Hr([G: H], A) and the cohomology groups of G and H; namely, we prove that if Hv(U, A)= 0 for all subgroups U of H and for v = 1, 2, …, n–1, then the sequence

is exact, where the homomorphisms of the sequence are those induced by injection, inflation and restriction respectively.
On Homogeneous Ideals
Authors: Northcott D. G.
Published: May 2009

The modern algebraic treatment of geometry in projective spaces focuses attention on the properties of homogeneous ideals in polynomial and power-series rings. This inevitably raises questions concerning how far ordinary ideal theory needs to be modified if only homogeneous ideals are to be regarded as significant. In practice, one can usually answer any particular question of this type without undue difficulty when it arises but, it seems to the author, the topic has enough intrinsic interest to merit a connected discussion by itself.
The minimum discriminants of quintic fields
Authors: Hunter John
Published: May 2009

Let D be the discriminant of an algebraic number field F of degree n over the rational field R. The problem of finding the lowest absolute value of D as F varies over all fields of degree n with a given number of real (and consequently of imaginary) conjugate fields has not yet been solved in general. The only precise results so far given are those for n = 2, 3 and 4. The case n = 2 is trivial; n = 3 was solved in 1896 by Furtwangler, and n = 4 in 1929 by J. Mayer [6]. Reference to Furtwangler's work is given hi Mayer's paper. In this paper the results for n = 5, that is, for quintic fields, are obtained.
Infinite integrals involving products of Legendre functions
Authors: Sharma K. C.
Published: May 2009

In this paper we evaluate a few infinite integrals involving products of Legendre functions. The results obtained herein are quite general and include, as particular cases, some known results.
Semigroups satisfying minimal conditions
Authors: Munn W. D.
Published: May 2009

In his fundamental paper, “On the structure of semigroups” [6], J. A. Green has examined certain important minimal conditions which may be satisfied bya semigroup S.We say that S satisfies the minimal condition on principal left ideals if every set of principal left ideals of S contains a minimal member with respect to inclusion:this condition is denoted by ℳ1. The corresponding conditions on principal rightideals and principal two-sided ideals are denoted by ℳr and ℳ1 respectively. The purpose of the present paper is to give some further results concerning these three conditions.Extensive use is made of the work of A. H. Clifford ([3] and [4]) onminimal ideals.
On Tauberian theorems for Abel-Cesàro summability
Authors: Rajagopal C. T.
Published: May 2009

For a series Σanwith partial sumsAn=a0+a1+ … +an(n ≥ 0), supposed to be real in this note, we define, in a generally accepted notation ([2], pp. 7, 9, 94–98), the following transforms:

(C, α) sequence-transform,

(H,k)sequence-transform (k = 0, 1, 2, …):

(A:C, α)fnunction-transform,
Infinite Series of E-Functions
Authors: Macrobert T. M.
Published: May 2009

In § 2 a number of infinite series of E-functions are summed by expressing the E-functions as Barnes integrals and interchanging the order of summation and integration.

The Barnes integral employed is

where | amp z | < π and the integral is taken up the η;-axis, with loops, if necessary, to ensure that the origin lies to the left of the contour and the points α1, α2,… αp to the right of the contour. Zero and negative integral values of the α's and p's are excluded, and the α's must not differ by integral values. When p < q + 1 the contour is bent to the left at each end.
Dual Trigonometrical Series
Authors: Tranter C. J.
Published: May 2009

In a recent joint paper with J. C. Cooke [1], we have given a method of determining the coefficients an in the “dual” Fourier-Bessel series

where −1 ≤p≤, F(r) is specified and αn is a positive root of Jv(αnα) = 0. This method reduced the problem to the solution of an infinite set of algebraical equations and it was shown that, under certain circumstances, numerical values for the coefficients could be obtained fairly readily.
On Trace Bilinear Forms on Lie-Algebras
Authors: Zassenhaus Hans
Published: May 2009

To what extent is the structure of a Lie-algebra L over a field F determined by the bilinear form

on L that is derived from a matrix representation

of L with finite degree d(Δ) by forming the trace of the matrix products

Such a bilinear form is a function with two arguments in L, values in F and the properties:
Abstract theory of packings and coverings. I.
Authors: Macbeath A. M.
Published: May 2009

The aim of this note is to examine the basic ideas underlying Minkowski's theorem on lattice points in a symmetrical convex body and related results of Blichfeldt, and to indicate how these can be generalized. Theorems analogous to Minkowski's, on the automorphisms of quadratic forms and other linear groups and on Fuchsian groups of transformations in the complex plane, have been obtained by Siegel [6] and Tsuji [7], Generalizations which include these are due to Chabauty [2] and Santalo [5].
Generalisation of an embedding theorem for groups
Authors: Chehata C. G.
Published: May 2009

Let G be a given group and A, B be two subgroups of G which may or may not coincide. A homomorphism μ which maps A onto B is called a partial endomorphism of G. When A coincides with G then we call μ a total endomorphism or as it is usually called an endomorphism of G. If μ* is a partial (or total) endomorphism of a supergroup G* ⊇ G, then we say that μ* extends, or continues, μ when μ* is defined for at least all the elements a ∈ A and moreover aμ = aμ* for all a ∈ A If the partial endomorphism μ is an isomorphic mapping then we speak of a partial automorphism of G.
Some Integrals Involving E-Functions
Authors: Saxena R. K.
Published: May 2009

In this paper we evaluate some integrals involving U-functions by the methods of the Operational Calculus. The results obtained are quite general and many of them include, as particular cases, some known results.

A function ψ (p) is operationally related with another function f(t), if they satisfy the integral equation

2. Theorem. If

and

As usual, we shall denote (1) by the symbolic expression

provided that the integral is convergent. HereR(α) > 0, R(p) > 0, n = 2,3,4, …, andmeans that in the expression following it, i is to bee replaced by – i and the two expressions are to be added.
A Structure Theorem for Topological Lattices
Authors: Anderson L. W. , Ward L. E.
Published: May 2009

In the study of connected partially ordered spaces a problem of fundamental interest is to determine sufficient conditions to ensure the existence of chains (i.e., simply ordered subsets) which are connected. Recently [5] R. J. Koch proved that, if X is a compact Hausdorff space with continuous partial order (i.e., the partial order has a closed graph), if L(x) = {y: y ≦ x} is connected for each x ∈ X, and if X has a zero (i.e., an element 0 such that 0 ≦ x for all x ∈ X), then each element of X lies in a connected chain containing zero. It is easy to find simple examples which show that this result is false if X is assumed only to be locally compact. However, if it is assumed that the partial order is that of a topological lattice then the existence of such chains can be shown by elementary methods. This solves a problem which was proposed in [3].
A Basic Analogue of MacRobert's E-Function
Authors: Agarwal R. P.
Published: May 2009

MacRobert [2] in 1937 defined the E-function as

where the symbol denotes that to the expression following it, a similar expression with α and β interchanged is to be added. For (1) he also gave the integral representation

where Re β > 0, | arg z | < π.
On Certain Dual Integral Equations
Authors: Copson E. T.
Published: May 2009

In his book on Fourier Integrals, Titchmarsh [l] gave the solution of the dual integral equations

for the case α > 0, by some difficult analysis involving the theory of Mellin transforms. Sneddon [2] has recently shown that, in the cases v = 0, α = ±½, the problem can be reduced to an Abel integral equation by making the substitution

or

It is the purpose of this note to show that the general case can be dealt with just as simply by putting

The analysis is formal: no attempt is made to supply details of rigour.
The product of two ultraspherical polynomials
Authors: Carlitz L.
Published: May 2009

Let

It is familiar that

(1) In the addition theorem [3, p. 363]

where

take θ = π and replace v by v−½. Since

we get
On a Theorem of Hurwitz
Authors: Macbeath A. M.
Published: May 2009

By a theorem of Hurwitz [3], an algebraic curve of genus g ≧ 2 cannot have more than 84(g − l) birational self-transformations, or, as we shall call them, automorphisms. The bound is attained for Klein's quartic

of genus 3 [4]. In studying the problem whether there are any other curves for which the bound is attained, I was led to consider the universal covering space of the Riemann surface, which, as Siegel observed, relates Hurwitz's theorem to Siegel's own result [7] on the measure of the fundamental region of Fuchsian groups. Any curve with 84(g − 1) automorphisms must be uniformized by a normal subgroup of the triangle group (2, 3, 7), and, by a closer analysis of possible finite factor groups of (2, 3, 7), purely algebraic methods yield an infinite family of curves with the maximum number of automorphisms. This will be shown in a later paper.
The centre of a hereditary local ring
Authors: Northcott D. G.
Published: May 2009

The purpose of this note is to establish the following

Theorem. The centre of a (left) hereditary local ring is either afield or a one-dimensional regular local ring.

Before starting the proof, it is necessary to explain the terminology. A ring R with an identity element is called a left local ring if the elements of R which do not have left inverses form a left ideal I. In these circumstances (see [1, Proposition 2.1, p. 147]), I is necessarily a two-sided ideal and it consists precisely of all the elements of R which do not have right inverses. Furthermore, every element of R which is not in I possesses a two-sided inverse. Thus there is, in fact, no difference between a left local ring and a right local ring and therefore one speaks simply of a local ring. In addition, I contains every proper left ideal and every proper right ideal. We may therefore describe I simply as the maximal ideal of R.
Group Algebras With Central Radicals
Authors: Wallace D. A. R.
Published: May 2009

It is well known that when the characteristic p(≠ 0) of a field divides the order of a finite group, the group algebra possesses a non-trivial radical and that, if p does not divide the order of the group, the group algebra is semi-simple. A group algebra has a centre, a basis for which consists of the class-sums. The radical may be contained in this centre; we obtain necessary and sufficient conditions for this to happen.
Summation of a series of products of E-functions
Authors: Ragab F. M.
Published: May 2009

In previous papers [1, 2, 3] the sums of a number of series of products of E-functions have been found. For the definitions and properties of the E-functions the reader is referred to [4, pp. 348–358]. In § 3 a further series of this type is given. The proof is based on an integral of an E-function with respect to its parameters, to be established in § 2. Similar integrals were given in [5] and [6].
On a cyclic sum
Authors: Diananda P. H.
Published: May 2009

1. For any positive integralnand any positive realx1,…,xnwe write

clearly. It is known [1,2] that

forn≦ 6, and further [4, 5, 6] that (5) is false for evenn≧ 14 and for oddn≧ 53. Mordell [2] conjectured that (5) is false for alln≧ 7, but recently [3] stated that computations indicated that (5) is true forn= 7 and gave some calculations in support of (5) forn= 7.
The solution of a pair of dual integral equations
Authors: Lowengrub M. , Sneddon I. N.
Published: May 2009

We define two functions F(p), G(p) in terms of a third function ψ(ζ) by the equations

A standard problem in the theory of dual integral equations is to determine the function ψ(ζ) such that

when the functions f(p), g(p) are prescribed.
On the solution of certain dual integral equations
Authors: Burlak J.
Published: May 2009

1. In this note we consider the formal solution of the dual integral equations

where f(x) and g(x) are given and χ(x) is to be found. The direct solution of these equations has been given by Noble [1] but we shall show that they may be solved more easily if they are first reduced to a form in which g(x) ≡ 0.
Arithmetics in Cayley's algebra
Authors: Lamont P. J. C.
Published: May 2009

Let C denote Cayley's algebra defined over the field of rational numbers. This paper contains a simple characterization of arithmetics of C in terms of a given basis i0 = 1, i1, i2, …, i7. We deduce that certain of the arithmetics of C are isomorphic. The result that the maximal arithmetics are isomorphic is also contained in the work of van der Blij and Springer [2].
On Gordon's method of solving dual integral equations
Authors: Burlak J.
Published: May 2009

1. Dual integral equations of the form

where f(x) and g(x) are given and Ψ(x) is the unknown, have been increasingly studied in recent years; the first solutions were given for the case g(x) ≡ 0 by Titchmarsh [1] (for 0 < α < 2) and Busbridge [2] (for — 2 < α < 0). An interesting and much simpler method of solving the equations in the same case, g ≡ 0, was given by Gordon [3]. He also showed that the problem of solving the general equations (1) and (2) can be reduced to a problem in which g ≡ 0. He did not pursue this idea as far as finding and simplifying the solution of (1) and (2) but this has been done recently (see [4]) and Noble [5] used a similar idea in treating the case f ≡ 0.
Integrals involving products of Bessel functions
Authors: Saxena R. K.
Published: May 2009

1. Introductory. In this paper certain infinite integrals involving products of four Bessel functions of different arguments are evaluated in terms of Appell's function F4 by the methods of the operational calculus. The results obtained are believed to be new.

As usual, the conventional notation will be used to denote the classical Laplace integral relation

In the proofs of the formulae the following results will be required [1, pp. 281, 284], [3, pp. 78, 79].
Some inclusion theorems
Authors: Maddox I. J.
Published: May 2009

1. A number of inclusion theorems have been given in connection with methods of summation which include the Riesz method (R, λ, κ). Lorentz [4, Theorem 10] gives necessary and sufficient conditions for a sequence to sequence regular matrix A = (an, v) to be such that A ⊃ (R, λ, 1)†. He imposes restrictions on the sequence { λn}, so that A does not include all Riesz methods of order 1. In Theorem 1 below, we generalize the Lorentz theorem by giving a condition without restriction on λn, If the matrix A is a series to sequence or series to function regular matrix, there do not appear to be any results concerning the general inclusion

A ⊃ (R, λ, κ).

However, when A is the Riemann method (ℜ, λ, μ), Russell [7], generalizing earlier results, has given sufficient conditions for (ℜ, λ, μ) ⊃ (R, λ, κ). Our Theorem 2 gives necessary and sufficient conditions for A ⊃ (R, λ, 1), where A satisfies the condition an, v → 1 (n →co, ν fixed). Thus Theorem 2 applies to any series to sequence regular matrix A. In Theorem 3 we give a further representation for matrices A which include (R, λ, 1), and finally make some remarks on the problem of characterizing matrices which include Riesz methods of any positive order κ.
On Lattice Complements
Authors: Bumcrot Robert
Published: May 2009

Let (L, ≦) be a distributive lattice with first element 0 and last element 1. If a, b in L have complements, then these must be unique, and the De Morgan laws provide complements for a ∧ b and a ∨ b. We show that the converse statement holds under weaker conditions.

Theorem 1. If(L, ≦) is a modular lattice with 0 and 1 and if a, b in L are such that a ≦b and a ≨ b have (not necessarily unique) complements, then a andb have complements.
Bisimple ω-Semigroups
Authors: Reilly N. R.
Published: May 2009

The structure of a bisimple inverse semigroup with an identity has been related by Clifford [2] to that of its right unit subsemigroup. In this paper we give an explicit structure theorem for bisimple inverse semigroups in which the idempotents form a simple descending chain

e0 > e1 > e2.…

We call such a semigroup a bisimple co-semigroup. The structure of a semigroup of this kind is shown to be determined entirely by its group of units and an endomorphism of its group of units.
Note on the region of overconvergence of Dirichlet series with Ostrowski gaps
Authors: Earl J. P. , Shackell J. R.
Published: May 2009

The main object of this note is to show that a proof given by A. J. Macintyre [2] of a result on the overconvergence of partial sums of power series works more easily in the context of Dirichlet series. Applying this observation to the particular Dirichlet series Σane−ns, we can remove certain restrictions which Macintyre finds necessary in the direct treatment of power series.
Generalisations of some Integrals Involving Bessel Functions and E-Functions
Authors: Ragab Fouad M.
Published: May 2009

§ 1. Introductory. In § 3 a generalisation of the formula [MacRobert, Phil. Mag., Ser. 7, XXXI, p. 258]

where αp+1 = ½m + ½n, αp+2 = ½m - ½n, R(m ± n) > 0, and x is real and positive, will be established. In the course of the proof Hardy's formula [Mess, of Maths., LVI, (1927), p. 190],

where R(b)>0, will be required. This was originally proved by an application of Mellin's Inversion Formula. An alternative proof is given in § 2, and some related formulae are deduced.
An Integral involving a Modified Bessel Function of the Second Kind and an E-function
Authors: Ragab Fouad M.
Published: May 2009

§ 1. Introductory. The formula to be established is

where m is a positive integer,

and the constants are such that the integral converges.