bluuebunny/crossref_metadata_2025_split huggingface dataset:
A note on reductions of ideals relative to an Artinian module
Authors: Taherizadeh A.-J. 
Published: May 2009

The concept of reduction and integral closure of ideals relative to Artinian modules were introduced in [7]; and we summarize some of the main aspects now.Let A be a commutative ring (with non-zero identity) and let a, b be ideals of A. Suppose that M is an Artinian module over A. We say that a is a reduction of b relative to M if a ⊆ b and there is a positive integer s such that)O:Mabs)=(O:Mbs+l).An element x of A is said to be integrally dependent on a relative to M if there exists n y ℕ(where ℕ denotes the set of positive integers) such thatIt is shown that this is the case if and only if a is a reduction of a+Ax relative to M; moreoverᾱ={x ɛ A: xis integrally dependent on a relative to M}is an ideal of A called the integral closure of a relative to M and is the unique maximal member of℘ = {b: b is an ideal of A which has a as a reduction relative to M}.
Representation of primes by binary quadratic forms of discriminant –256q and –128q
Authors: Halter-Koch Franz 
Published: May 2009

Recently, P. Kaplan and K. S. Williams [10] considered (as an example) the representation of primes by binary quadratic forms of discriminant –768. These forms fall into 4 genera, each consisting of two classes. In particular, they considered the formsF=3X2+642 and G = 12X2+12XY+19Y2.It follows from genus theory (as explained in [10]) that every prime p ≡ 19 mod 24 is represented by exactly one of the forms F and G. Based on numerical data, they conjectured that a prime p ≡ 19 mod 24 is represented bywhereVo = 2, V1 = -4, Vn+2=-4Vn+1 -Vn (n∨0).
Metacyclic p-groups and their conjugacy classes of subgroups
Authors: Brandl Rolf , Verardi Libero 
Published: May 2009

Let G be a group and let ℓ(G) be the set of all conjugacy classes [H] of subgroups H of G, where a partial order ≤ is defined by [H1] ≤ [H2] if and only if H1, is contained in some conjugate of H2.A number of papers (see for example [1] and the references mentioned there) deal with the question of characterizing groups G by the poset ℓ(G). For example, in [1] it was shown that if ℓ(G) and ℓ(H) are order-isomorphic and G is a noncyclic p-group then |G| = |H|. Moreover, if G is abelian, then G = H, and if G is metacyclic then H is metacyclic.
On the idempotence and stability of kernel functors
Authors: Teply Mark L. 
Published: May 2009

A kernel functor (equivalently, a left exact torsion preradical) is a left exact subfunctor of the identity on the category R-mod of left R-modules over a ring R with identity. A kernel functor is said to be idempotent if, in addition, σ satisfies σ(M / σ(M)) = 0 for every M ∊ R-mod. To every kernel functor / there corresponds a unique topologizing filter ℒσ = {I Ⅰ σ (R/I) = R/I} of left ideals and a unique class ℱσ = {M ∊ R-mod Ⅰ σ(M) = M} that is closed under homomorphic images, submodules, and direct sums. The idempotence of σ is characterized by either of the following additional conditions:(1) if I ∊ ℒσ, K ⊆ I, and (K:x) = {r ∊ R ∣ rx ∊ K} ∊ ℒσ for each x ∊ I, then K ∊ ℒ or(2) ℱσ is closed under extensions of one member of ℱσ by another member of ℱσ Idempotent kernel functors are important since they are the tool used to construct localization functors. For M∊ R-mod, let E(M) denote the injective hull of M. A kernel functor σ is called stable if Mℱ implies that E(M) ∊ ℱσ For more information about kernel functors, see [6], [7], [14], and [15].
On reducibility of ultrametric almost periodic linear representations
Authors: Diarra Bertin 
Published: May 2009

AbstractLet G be a group and K be a complete ultrametric valued field. Let AP(G, K) be the algebra of the generalized almost periodic functions of G in K. We have shown in a previous paper that when AP(G, K) has an invariant mean, then any almost periodic linear representation is quasi-reducible. Here, we show that with the same hypothesis, any topologically irreducible almost periodic linear representation is finite dimensional; also, any almost periodic linear representation is the topological sum of irreducible representations. Furthermore, we obtain a Peter-Weyl theorem for the algebra AP(G, K).We use the technical tools of Hopf algebra theory.
On the nilpotent ranks of certain semigroups of transformations
Authors: Garba G. U. 
Published: May 2009

Let Pn be the semigroup of all partial transformations on the set Xn = {1,…, n}. As usual, we shall say that an element α in Pn is of type (k, r) or belongs to the set [k, r] if |dom α|=k and |lim α|. The completion α* of an element α ∈ [n − 1, n − 1] is an element in [n, n] defined bywhere {i} = Xn∖dom α and {j} = Xn∖im α.
Classification of tensor product immersions which are of 1-type
Authors: Chen Bang-Yen 
Published: May 2009

Let V and W be two vector spaces over the field of real numbers R. Then we have the notion of the tensor product V ⊗ W. If V and W are inner product spaces with their inner products given respectively by «,»v and «,» w, then V ⊗ W is also an inner product space with inner product denned byLet Em denote the m-dimensional Euclidean space with the canonical Euclidean inner product. Then, with respect to the inner product defined above, Em ⊗Em is isometric to Em. By applying this algebraic notion, we have the notion of tensor product mapf ⊗h: M→ E: M ⊗= Em; associated with any two maps f: M→Em and h:M→E of a given Riemannian manifold (M, g) defined as follows:Denote by R(M) the set of all transversal immersions from an n-dimensional Riemannian manifold (M, g) into Euclidean spaces; i. e., immersions f:M→Em with f(p) ∉T*(TPM) for p ∈ M. Then ⊗ is a binary operation on R(M). Hence, if f: Mm and h: M→Em are immersions belonging to R(M), then their tensor product map f ⊗ h: M→ Em ⊗ Em ≡ Emm is an immersion in R(M), called the tensor product immersionof f and h.
Capitulation in unramified quadratic extensions of real quadratic number fields
Authors: Benjamin E. , Sanborn F. , Snyder C. 
Published: May 2009

Letkbe an algebraic number field andCkits ideal class group (in the wider sense). SupposeKis a finite extension ofk. Then we say that an ideal class ofk capitulatesinKif this class is in the kernel of the homomorphisminduced by extension of ideals fromktoK(See Section 2 below). In [4], Iwasawa gives examples of real quadratic number fields,with distinct primesPi≡ 1 (mod 4), for which all the ideal classes of the 2-class group,Ck,2(the 2-Sylow subgroup ofCk), capitulate in an unramified quadratic extension ofk. In these examples,Ck,2is abelian of type (2,2), i.e. isomorphic to ℤ/2ℤ×ℤ/2ℤ and so all four ideal classes capitulate.
On the endomorphism semigroup of an ordered set
Authors: Blyth T. S. 
Published: May 2009

M. E. Adams and Matthew Gould [1] have obtained a remarkable classification of ordered sets P for which the monoid End P of endomorphisms (i.e. isotone maps) is regular, in the sense that for every f є End P there exists g є End P such that fgf = f. They show that the class of such ordered sets consists precisely of(a) all antichains;(b) all quasi-complete chains;(c) all complete bipartite ordered sets (i.e. given non-zero cardinals α β an ordered set Kα,β of height 1 having α minimal elements and β maximal elements, every minimal element being less than every maximal element);(d) for a non-zero cardinal α the lattice Mα consisting of a smallest element 0, a biggest element 1, and α atoms;(e) for non-zero cardinals α, β the ordered set Nα,β of height 1 having α minimal elements and β maximal elements in which there is a unique minimal element α0 below all maximal elements and a unique maximal element β0 above all minimal elements (and no further ordering);(f) the six-element crown C6 with Hasse diagramA similar characterisation, which coincides with the above for sets of height at most 2 but differs for chains, was obtained by A. Ya. Aizenshtat [2].
Polynomial Grothendieck properties
Authors: González Manuel , Gutiérrez Joaquí M. 
Published: May 2009

AbstractA Banach space sE has the Grothendieck property if every (linear bounded) operator from E into c0 is weakly compact. It is proved that, for an integer k > 1, every k-homogeneous polynomial from E into c0 is weakly compact if and only if the space (kE) of scalar valued polynomials on E is reflexive. This is equivalent to the symmetric A>fold projective tensor product of £(i.e., the predual of (kE)) having the Grothendieck property. The Grothendieck property of the projective tensor product EF is also characterized. Moreover, the Grothendieck property of E is described in terms of sequences of polynomials. Finally, it is shown that if every operator from E into c0 is completely continuous, then so is every polynomial between these spaces.
Null 2-type Chen surfaces
Authors: Li Shi-Jie 
Published: May 2009

Let M be an n-dimensional connected submanifold in an mdimensional Euclidean space Em. Denote by δ the Laplacian of M associated with the induced metric. Then the position vector x and the mean curvature vector H of Min Em satisfyThis yields the following fact: a submanifold M in Em is minimal if and only if all coordinate functions of Em, restricted to M, are harmonic functions. In other words, minimal submanifolds in Emare constructed from eigenfunctions of δ with one eigenvalue 0. By using (1. 1), T. Takahashi proved that minimal submanifolds of a hypersphere of Em are constructed from eigenfunctions of δ with one eigenvalue δ (≠0). In [3, 4], Chen initiated the study of submanifolds in Em which are constructed from harmonic functions and eigenfunctions of δ with a nonzero eigenvalue. The position vector x of such a submanifold admits the following simple spectral decomposition:for some non-constant maps x0and xq, where A is a nonzero constant. He simply calls such a submanifold a submanifold of null 2-type.
The 3-local cohomology of the Mathieu group M24
Authors: Green David John 
Published: May 2009

In this paper we calculate the localisation at the prime 3 of the integral cohomology ring of the Mathieu group M24, together with its mod-3 cohomology ring. The main results areTheorem 1. The ring H*(M24, Z)(3)is the commutative graded Z(3)-algebra with generatorsand relations v2 = 0 and βθ = 0. The Chern classes of the Todd representation in GL11F2
The range of non-surjective convolution operators on Beurling spaces
Authors: Bonet José , Galbis Antonio 
Published: May 2009

AbstractLet μ ≠ 0 be an ultradistribution of Beurling type with compact support in the space . We investigate the range of the convolution operator Tμ on the space of non-quasianalytic functions of Beurling type associated with a weight w, in the case the operator is not surjective. It is proved that the range of TM always contains the space of real-analytic functions, and that it contains a smaller space of Beurling type for a weight σ ≥ ω if and only if the convolution operator is surjective on the smaller class.
On a hyperlogistic delay equation
Authors: Yu Jianshe , Wu Jianhong , Zou Xingfu 
Published: May 2009

Consider the following hyperlogistic equationwherer, K, τj∈ (0, ∝), and αj=pj/qjare rational numbers withqjodd,pjandqj, are co-prime, 1 ≤j≤m, and.
An integral formula for hypersurfaces in space forms
Authors: Vlachos Theodoros 
Published: May 2009

Let be an n+ 1-dimensional, complete simply connected Riemannian manifold of constant sectional curvature c and We consider the function r(·) = d(·, P0) where d stands for the distance function in and we denote by grad r the gradient of The position vector (see [1]) with origin P0 is defined as where ϕ(r)equalsr, if c = 0, c< 0 or c <0 respectively.
Normal curvature of minimal submanifolds in a sphere
Authors: Deshmukh Sharief 
Published: May 2009

Simons [5] has proved a pinching theorem for compact minimal submanifolds in a unit sphere, which led to an intrinsic rigidity result. Sakaki [4] improved this result of Simons for arbitrary codimension and has proved that if the scalar curvature S of the minimal submanifold Mn of Sn+P satisfiesthen either Mn is totally geodesic or S= 2/3 in which case n = 2 and M2 is the Veronese surface in a totally geodesic 4-sphere. This result of Sakaki was further improved by Shen [6] but only for dimension n=3, where it is shown that if S>4, then M3 is totally geodesic (cf. Theorem 3, p. 791).
A family of conformally asymmetric Riemann surfaces
Authors: Everitt Brent 
Published: May 2009

AbstractWe give explicit examples of asymmetric Riemann surfaces (that is, Riemann surfaces with trivial conformal automorphism group) for all genera g ≥ 3. The technique uses Schreier coset diagrams to construct torsion-free subgroups in groups of signature (0; 2,3,r) for certain values of r.
Two exponential Diophantine equations
Authors: Dofs Erik 
Published: May 2009

In [3], two open problems were whether either of the diophantine equationswith n ∈ Z and f a prime number, is solvable if ω > 3 and 3 √ ω, but in this paper we allow f to be any (rational) integer and also 3 | ω. Equations of this form and more general ones can effectively be solved [5] with an advanced method based on analytical results, but the search limits are usually of enormous size. Here both equations (1) are norm equations in K (√–3): N(a + bp) = fw with p = (√–1 + –3)/2 which makes it possible to treat them arithmetically.
On Hankel convolutors on certain Hankel transformable function spaces
Authors: Betancor Jorge J. , Rodíguez-Mesa Lourdes 
Published: May 2009

AbstractIn this paper we introduce the spaces of Hankel convolutors. We characterize the dual spaces of certain Hankel transformable function spaces as spaces of Hankel convolutors. Here the Hankel convolution and the Hankel transformation play an important role.
Bilinear forms on vector Hardy spaces
Authors: Blower Gordon 
Published: May 2009

AbstractLet φ: ℋ → be a bilinear form on vector Hardy space. Introduce the symbol φ of Φ by (φ (Z1, Z2), a ⊗ b) = Φ (K21 ⊗ a, K22 ⊗ b ), where Kw is the reproducing kernel for w ∈ D. We show that Φ extends to a bounded bilinear form on provided that the gradient defines a Carleson measure in the bidisc D2. We obtain a sufficient condition for Φ to extend to a Hilbert space. For vectorial bilinear Hankel forms we obtain an analogue of Nehari's Theorem.
Almost-Bieberbach groups with (in)finite outer automorphism group
Authors: Malfait Wim , Szczepański Andrzej 
Published: May 2009

AbstractIf we investigate symmetry of an infra-nilmanifoldM, the outer automorphism group of its fundamental group (an almost-Bieberbach group) is known to be a crucial object. In this paper, we characterise algebraically almost-Bieberbach groupsEwith finite outer automorphism group Out(E). Inspired by the description of Anosov diffeomorphisms onM, we also present an interesting class of infinite order outer automorphisms. Another possible type of infinite order outer automorphisms arises when comparing Out(E) with the outer automorphism group of the underlying crystallographic group ofE.
Commutator length of abelian-by-nilpotent groups
Authors: Akhavan-Malayeri Mehri , Rhemtulla Akbar 
Published: May 2009

AbstractLet G be a group and C = [G, G] be its commutator subgroup. Denote by c(G) the minimal number such that every element of G′ can be expressed as a product of at most c(G) commutators. The exact values of c{G) are computed when G is a free nilpotent group or a free abelian-by-nilpotent group. If G is a free nilpotent group of rank n>2 and class c>2, c(G) = [n/2] if c = 2 and c(G) = n if c>2. If G is a free abelian-by-nilpotent group of rank n > 2 then c(G) = n.
The normal curvature of totally real submanifolds ofS6(1)
Authors: De Smet P. J. , Dillen F. , Verstraelen L. , Vrancken L. 
Published: May 2009

AbstractWe prove the pointwise inequality 0 ≥ρ+ρ⊥– 1 involving the normalized scalar curvatureρand normal scalar curvatureρ⊥of a totally real 3-dimensional submanifold of the nearly Kaehler 6-sphere. Further we classify submanifolds realizing the equality in this inequality.
On M-harmonic Bloch functions and their Carleson measures
Authors: Choe Boo Rim , Lee Young Joo 
Published: May 2009

AbstractOn the setting of the unit ball of the complex n-space, some characterizations of M-harmonic Bloch functions are obtained. As an application, Carleson measures are characterized by means of Berezin type integrals of M-harmonic Bloch functions. As one may expect, these results carry over to M-harmonic little Bloch functions and vanishing Carleson measures.
Convolution operators associated with vector measures
Authors: Robdera Mangatiana A. , Saab Paulette 
Published: May 2009

AbstractInthis note, we present a thorough investigation of convolution operators that are naturally associated to vector measures. We characterize those convolution operators that are weakly compact and compact on Ll(G) and C(G) as well as those that are p summing, (1 ≤ p ≤ ∞) and nuclear on C(G).
On Certain Types of Solution of the Equation of Heat Conduction
Authors: Paterson Stewart 
Published: May 2009

Let f(x, y, z, t) satisfy the equationFor certain purposes, particularly in connection with the propagation of a boundary of fusion etc., it is of interest to discover solutions of (1) which permit the equation:to be solved explicitly in the form:This suggests the examination of solutions of the typewhereand f, ϕ, ψ are functions to be determined. To save repetition, Roman capitals denote arbitrary constants throughout.
Integrals Involving E-Functions and Modified Bessel Functions of the Second Kind
Authors: Ragab F. M. 
Published: May 2009

The two following formulae are to be established.If R (m ± n) > 0, | amp z | < π,If p ≧ q + 1, R(k ± n + 2αr) > 0, r = 1, 2, …, p, | amp z | < π,For other values of p and q the formula holds if the integral is convergent.
On Packings of Spheres in Hilbert Space
Authors: Rankin R. A. 
Published: May 2009

A point x in real Hilbert space is represented by an infinite sequence (x1, x2, x3, …) of real numbers such thatis convergent. The unit “sphere“ S consists of all points × for which ‖x‖ ≤ 1. The sphere of radius a and centre y is denoted by Sa(y) and consists of all points × for which ‖x−y‖ ≤ a.
A Theorem in Operational Calculus and some Integrals involving Legendre, Bessel and E-Functions
Authors: Rathie C. B. 
Published: May 2009

In this paper we prove a theorem in Operational Calculus and use it to evaluate a few infinite integrals involving Legendre, Bessel and E-functions. We writewhenandwhen(2) is a generalisation of (1) as given by Meijer [2] and it reduces to (1) when v = ±½ by virtue of the relation
Some Bessel Function Integrals
Authors: MacRobert T. M. 
Published: May 2009

The basic formula to be proved iswhere p≧q + 1, z ≠0; | amp z | < π, R(n)>0, r = 1, 2,…,p. For other values of pand qthe result holds if the integral converges. From this formula some results, involving Bessel functions and Confluent Hypergeometric functions, will be deduced.
On a Conjecture of Hanna Neumann
Authors: Neumann B. H. 
Published: May 2009

In what follows, groups are written additively, and commutators are denoted by brackets:A group is metabelian if it satisfies the lawIt is conceivable, though not plausible, that this law is equivalent to a law, or a set of laws, in only three variables, or even two. The present note shows that this is not the case.
Certain expansions involving E-functions
Authors: Singh V. N. 
Published: May 2009

The E-functions were defined by MacRobert [3] in 1937; they are denoted by E (p; αr: q; ps. z).In § 3 of this paper, I prove a new expansion for E(p; αr: q; ps: z) which is similar to an expansion due to MacRobert [2], viz.,where
On stratifications of Mittag-Leffler's transcendents
Authors: Wintner Aurel 
Published: May 2009

Guided by an observation of Hausdorff ([4]; reproduced by Whittaker and Robinson [6, pp. 177–178]), I pointed out a long time ago [7] that his “Fourier“ treatment of certain products can be systematized so as to apply to an inclusive class of infinite convolutions. Recently I noticed [8] that an appropriate application of this method supplies the following curious result on gamma-quotients:Corresponding to every index θ on the range 0 < θ < 1, there exists on the line - ∞ < t < ∞ a monotone function μ = μθ = μθ(t) in terms of which the identityholds on the half-plane Re z > -1 and so, in particular, on the half-line z ≧0.
Expansion of an E-function in a series of products of E-functions
Authors: Ragab F. M. 
Published: May 2009

The formula to be established iswhere | amp z < π, z ≠ 0, R(α + β) > R(ς) > R(alpha;) > 0, R(ς - β) > 0.In proving (1) use will be m ade of the two following formulae.
On Square Roots and Logarithms of Self-Adjoint Operators
Authors: Putnam C. R. 
Published: May 2009

All operators considered in this paper are bounded and linear (everywhere defined) on a Hilbert space. An operator A will be called a square root of an operator B ifA simple sufficient condition guaranteeing that any solution A of (1) be normal whenever B is normal was obtained in [1], namely: If B is normal and if there exists some real angle θ for which Re(Aeιθ)≥0, then (1) implies that A is normal. Here, Re (C) denotes the real part ½(C + C*) of an operator C.
A Note on the Angles in an n-Dimensional Simplex
Authors: Guinand A. P. 
Published: May 2009

Three different sets of equations connecting the sums of angles in an n-dimensional simplex have been given by Sommerville [7], Höhn [5], and Peschl [6]. The equivalence of the first two sets of equations has been proved by Sprott [7].In the present note it is shown that results are simplified if we consider averages instead of sums, and that the averages form a sequence which is self-reciprocal with respect to the transformationThe equivalence of the sets of equations is then easily proved by symbolic methods.
Lattice-ordered groups having at most two disjoint elements
Authors: Conrad P. F. , Clifford A. H. 
Published: May 2009

Let L = L( +, v, ＾) be a lattice-ordered group, or l-group (Birkhoff [1, p. 214]). Two elements a and b of L will be called disjoint if a > 0, b > 0, and a ＾; b = 0. It is easily seen that if L does not contain two disjoint elements, then it is linearly ordered (and, of course, conversely). What can we say about Z-groups containing two but not more than two mutually disjoint elements?Let Aand B be linearly ordered groups (o-groups), and let A ⋏ B be the cardinal sum of A and B. That is, A ⋏ B is the direct sum of A and B, and (a, b) is positive in A + B if and only if a is positive in A and b is positive in B. An l-group L containing A ⋏ B as a convex normal subgroup (or Z-ideal) is called a lexico-extension of A ⋏ B if every positive element of L not in A ⋏ B exceeds every element of A ⋏ B. It then follows (subsection 2.9 below) that L/(A ⋏ B) is an o-group. Such an l-group L is easily seen to satisfy the following condition: (D)There exists a pair of disjoint elements in L, but no triple of pairwise disjoint elements exists in L.
Some recurrence relations and series for the generalised laplace transform
Authors: Bhonsle B. R. 
Published: May 2009

The Laplace transformhas been generalised by Varma [4] by the relationwhich reduces to (1.1) when k = -m + ½ by virtue of the identityWe shall define πk, m, λ (p) by the relationThe object of this paper is to obtain some recurrence formulae and series for πk, m, λ (p) and to use them to obtain recurrence formulae and series for MacRobert's E-function.
On Strong and Absolute Summability
Authors: Borwein D. 
Published: May 2009

Suppose throughout that λ > 0, κ > - l. γ is real and thatThe series is said to be(i) summable (C, k) to s if (ii) strongly summable (C, k + 1) with index λ, or summable |C, k + 1|λ, to s if(iii) absolutely summable (C, k) with indices γ, λ, or summable |C, k + 1|λ, if