bluuebunny/crossref_metadata_2025_split huggingface dataset:
A characterization of minimal prime ideals
Authors: Birkenmeier Gary F. , Kim Jin Yong , Park Jae Keol 
Published: May 2009

AbstractLet P be a prime ideal of a ring R, O(P) = {a ∊ R | aRs = 0, for some s ∊ R/P} | and Ō(P) = {x ∊ R | xn ∊ O(P), for some positive integer n}. Several authors have obtained sheaf representations of rings whose stalks are of the form R/O(P). Also in a commutative ring a minimal prime ideal has been characterized as a prime ideal P such that P= Ō(P). In this paper we derive various conditions which ensure that a prime ideal P = Ō(P). The property that P = Ō(P) is then used to obtain conditions which determine when R/O(P) has a unique minimal prime ideal. Various generalizations of O(P) and Ō(P) are considered. Examples are provided to illustrate and delimit our results.
Free elasticae and Willmore tori in warped product spaces
Authors: Barros Manuel 
Published: May 2009

AbstractWe use the principle of symmetric criticality to connect the Willmore variational problem for surfaces in a warped product space with base a circle, and the free elastica variational problem for curves on its fiber. In addition we obtain a rational oneparameter family of closed helices in the anti De Sitter 3-space which are critical points of the total squared curvature functional. This means they are free elasticae. Also they are spacelike; this allows us to construct a corresponding family of spacelike Willmore tori in a certain kind of spacetime close to the Robertson-Walker spaces.
On the fourth-powerfree part of x2 + 2
Authors: de Weger Benjamin M. M. 
Published: May 2009

AbstractWe show that x = 59 is the largest positive integer for which the fourth-powerfree part of x2 + 2 is at most 100. This implies the solution of the problem, posed recently by J. H. E. Cohn, to prove that (x, y) = (1, 1) is the only solution in nonnegative integers to the diophantine equation x2 – 3y4 = –2, as well as a new solution to the problem, posed a long time ago by the same J. H. E. Cohn and solved before by R. Bumby and N. Tzanakis, to prove that (x, y) = (1, 1), (11, 3) are the only solutions in nonnegative integers to the diophantine equation 2x2 – 3y4 = – 1.
A semi-lumped microstrip UWB bandpass filter
Authors: Kaddour Darine , Arnould Jean-Daniel , Ferrari Philippe 
Published: May 2009

In this paper, a miniaturized bandpass filter for ultra-wide-band applications is proposed. It is based on the embedding of high-pass structures in a low-pass filter. A semi-lumped technology combining surface-mounted capacitors and transmission lines has been used. The filter design rules have been carried out. Furthermore, two filters having a 3-dB fractional bandwidth of 142 and 150%, centered at 0.77 and 1 GHz, respectively, have been realized for a proof of concept. Measured characteristics, in good agreement with simulations, show attractive properties of return loss (|S11| <−18 dB), insertion loss (<0.3 dB), and a maximum group delay and group delay variation of 2 and 1.3 ns, respectively. A distributed filter based on the same low-pass/high-pass approach has been also realized and measured for comparison. The size reduction reaches 85% for the semi-lumped filter, and its selectivity is improved with a shape factor of 1.3:1 instead of 1.5:1. The semi-lumped filter's drawback is related to a smaller rejection bandwidth compared to the distributed one. To improve the high-frequency stopband, an original technique for spurious responses suppression based on capacitively loaded stubs has been proposed. Even if the performances do not reach that obtained for the distributed approach, with this technique spurious responses are pushed until eight times the center frequency. A sensitivity study vs. critical parameters has also been carried out, showing the robustness of the design.
On Neumann's Formula for the Legendre Functions
Authors: Macrobert T. M. 
Published: May 2009

§1. Introductory. The formulawhere w is zero or a positive integer and | ζ | > 1, was given by F. E. Neumann “Crelle's Journal, XXXVII (1848), p. 24”. In § 2 of this paper some related formulae are given; the extension to the case when n is not integral is dealt with in § 3; while in § 4 the corresponding formulae for the Associated Legendre Functions when the sum of the degree and the order is a positive integer are established.
Propagation of a Boundary of Fusion
Authors: Paterson Stewart 
Published: May 2009

We consider a volume of material, divided into two regions 1 and 2. each of density ρ, by a moving surface S. On S a change of phase occurs, at a definite temperature (which we may take to be zero) and with absorption or liberation of a latent heat L per unit mass. If θl, kl, K1 are the temperature, thermal conductivity and diffusivity of phase 1, and θ2, k2, K2 corresponding quantities for phase 2, the surface S is the isothermaland the boundary condition on this surface isSubscript letters denote partial differentiation.
Contiguous Hypergeometric Functions of the Type 3F2(1)
Authors: Bailey W. N. 
Published: May 2009

In a paper published recently in this Journal, Watson obtained a reduction formul for the integralHe showed that this reduction formula could be written in the form:Ifthenwhereand 2σ = α + β + γ + δ, 2θ3 = α − β − γ + δ.
The Closest Packing of Spherical Caps in n Dimensions
Authors: Rankin R. A. 
Published: May 2009

Let Sn denote the “surface” of an n-dimensional unit sphere in Euclidean space of n dimensions. We may suppose that the sphere is centred at the origin of coordinates O, so that the points P(x1, x2, …, xn) of Sn satisfyWe suppose that n≥2.
Completely continuous movements in topological vector spaces
Authors: Michael J. H. 
Published: May 2009

Let A be a closed subset of a topological space X and f a continuous mapping of A into X with the following two properties:1.1. f {Fr (A)} & f {Int (A)} are disjoint.1.2. The mapping f* = f | Fr (A) is 1–1.It is proved in [5], that if X is the euclidean n–sphere Sn = {x; x e Rn+1 and ― x ― = 1}, then1.3. f {Fr(A)} = Fr {f(A)}.[ Hence f{Int (A)} = Int {f(A)}].
On a problem of Rankin about the Epstein zeta-function
Authors: Cassels J. W. S. 
Published: May 2009

Letbe a positive definite quadratic form with determinant αβ−X2= 1. A special form of this kind isWe consider the Epstein zeta-functionthe series converging fors> 1. Fors≥ 1·035 Rankin [1] proved the followingSTatementR.The sign of equality is needed only when h is equivalent to Q.
Further Duals of a verbal Subgroup
Authors: Moran S. 
Published: May 2009

In a previous paper [3] we gave two methods for constructing subgroups which in certain senses may be considered to be dual to a verbal subgroupVf(G) of an arbitrary groupG.Associated with a wordh(u, v) in the two symbolsuandv, we have (i) the first dual subgroupwhich is defined as the minimal subgroup of G containing all elements ξ of G for whichfor all values ofx1,x2, …, inxninG, and (ii), the second dual subgroupwhich is defined as the minimal subgroup ofGcontaining all elementszofGfor whichfor all values of x1, x2, …, xninG.Below we introduce slight variations to these definitions, which give rise to the concepts of the third and the fourth dual subgroups respectively. For certain values ofh(u, v) we obtain concepts which also arise fromand, namely, the marginal subgroup, the invariable subgroup and the centralizer of a verbal subgroup. We also obtain the new concepts of elemental subgroups and commutal subgroups and briefly sketch some of their properties. Finally we conclude by showing that MacLane's dual for the centralizer of a verbal subgroup is a closely related verbal subgroup.
On Differences of Unitarily Equivalent Self-Adjoint Operators
Authors: Putnam C. R. 
Published: May 2009

1. All operators considered in this paper are bounded operators on a Hilbert space. In case A and B are self-adjoint, certain conditions on A, B and their differenceassuring the unitary equivalence of Aand B,have recently been obtained by Rosenblum [6] and Kato [2]. The present paper will consider the problem of investigating consequences of an assumed relation of type (2) for some unitary U together with an additional hypothesis that the difference H of (1) be non-negative, so thatFirst, it is easy to see that if only (2) and (3) are assumed, thereby allowing H = 0, relation (2) can hold for A arbitrary with U = I (identity) and B = A. If H = 0 in (3) is not allowed, however (an impossible assumption in the finite dimensional case, incidentally, since then the trace of H is zero and hence H = 0), it will be shown, among other things, that any unitary operator U for which (2) and (3) hold must have a spectrum with a positive measure (as a consequence of (i) of Theorem 2 below). Moreover A (hence B) cannot differ from a completely continuous operator by a constant multiple of the identity (Theorem 1). In case 0 is not in the point spectrum of H, then U is even absolutely continuous (see (iv) of Theorem 2). In § 4, applications to semi-normal operators will be given.
The elementary solution of dual integral equations
Authors: Sneddon Ian N. 
Published: May 2009

When the theory of Hankel transforms is applied to the solution of certain mixed boundary value problems in mathematical physics, the problems are reduced to the solution of dual integral equations of the typewhere α and ν are prescribed constants and f(ρ) is a prescribed function of ρ [1]. The formal solution of these equations was first derived by Titchmarsh [2]. The method employed by Titchmarsh in deriving the solution in the general case is difficult, involving the theory of Mellin transforms and what is essentially a Wiener-Hopf procedure. In lecturing to students on this subject one often feels the need for an elementary solution of these equations, especially in the cases α = ± 1, ν = 0. That such an elementary solution exists is suggested by Copson's solution [3] of the problem of the electrified disc which corresponds to the case α = –l, ν = 0. A systematic use of a procedure similar to Copson's has in fact been made by Noble [4] to find the solution of a pair of general dual integral equations, but again the analysis is involved and long. The object of the present note is to give a simple solution of the pairs of equations which arise most frequently in physical applications. The method of solution was suggested by a procedure used by Lebedev and Uflyand [5] in the solution of a much more general problem.
Note on a conjecture of Coxeter
Authors: Leech John , Mennicke Jens 
Published: May 2009

Coxeter [1] has studied groups defined by the relationsand gives lists of finite groups known to be completely defined by such sets of relations. In a later paper [2] he shows that G3, n, p is finite if n, p are both even and satisfyand expresses the conjecture that the restriction to even values may be removed. The only case satisfying this inequality and not already known to be finite is G3, 7, 16. In this note we show that G3, 7, 16 is indeed finite, being of order 21504 = 210.3.7, by showing that its subgroupof index 2 is finite and of order 10752. Thus we add one entry to each of the lists of finite groups in Coxeter [1].
Upon A Second Confluent Form of the Ɛ-Algorithm
Authors: Wynn P. 
Published: May 2009

In two previous papers [1], [2] the confluent formof the δ-algorithm [3]was established, and various properties which the confluent form of the algorithm possesses were discussed. It was shown, among other things, that if in (1)and the notationis used, then (1) is satisfied byand further that under certain conditions, and for a certainn,identically. It is the purpose of this note to derive another confluent form of the Ɛ-algorithm and to discuss its properties.
Some definitions of Klein's simple group of order 168 and other groups
Authors: Leech John 
Published: May 2009

In a previous note [3], Mennicke and I showed that the relations(8, 7|2, 3): A8=B7=(AB)2=(AB)2=(A-1B)2=(A-1B)3=Edefine a group of order 10752. As we remarked, the results of §§ 2, 3 of that note are not restricted in their application to this group; they apply to the group[3, 7]+: B7=(AB)2=(A-1B)3=Eand to any factor group of this group which in turn has Klein's simple group of order 168, defined by(4,7|2, 3): A4=B7=(AB)2=(A-1B)3=E,as a factor group. In this note I use these results to establish alternative “weaker” definitions for Klein's group and for two groups discussed by Sinkov [4], namely (8, 7|2, 3) defined above and a factor group of this group of order 1344. These latter groups are eloquently discussed by Coxeter [1].
Integrals involving E-functions
Authors: Macrobert T. M. 
Published: May 2009

1. Introductory. The following two integrals will be established in § 2.If m is a positive integer, if p ≧ q + 1 and if R(ar+kt) > 0 (r = 1, 2,…, p, t = 1, 2,…, m),where co is 1 or e±in according as m is even or odd, the dash denotes that the factor sin (k,–k,)π does not appear and the asterisk that the parameter kt–kt + 1 is omitted. If pp ≧ qthe result holds if the integral is convergent.
On harmonic continuation
Authors: Eastham M. S. P. 
Published: May 2009

Let D be a bounded, closed, simply-connected domain whose boundary C consists of a finite number of analytic Jordan curves. Let γ be any analytic arc of C. Then we shall prove the following theorem.Theorem 1. Let u(x, y) be harmonic in the interior of D and continuous on γ, and let ϱu(x, y)/ϱn=g(s) when (x, y) is on γ, where g(s) is an analytic function of arc-length s along γ. Then u(x, y) can be harmonically continued across γ.
A generalisation of Divinsky's radical
Authors: Bostock F. A. , Patterson E. M. 
Published: May 2009

Let A be an associative ring. Given a ∊ A, an element b ∊ A is called a left identity for a ifGiven a subset S of A, an element b ∊ A is, called a left identity for S if (1) is satisfied for all a ∊ S. An element of A need not have a left identity; for example, if A is nilpotent then no non-zero element of A has a left identity. If a does have a left identity, the latter need not be unique; if every element of a subset S of A has a left identity, then it is not necessarily true that S has a left identity.
A note on principal sequences
Authors: Rotman B. 
Published: May 2009

A fundamental problem in the theory of ordinals is the assignation of principal sequences to limit numbers of the second number class.It is our main object here to show that a certain class of methods, which are a natural generalisation of those used in the solution of the corresponding problem for the real numbers (the description of which we omit), must fail to solve the problem. The methods are those which rest on the following assumption: the principal sequence assigned to any limit number of the second number class is determined once the first i terms of that sequence are known.
On polylogarithms
Authors: Eastham M. S. P. 
Published: May 2009

The nth order polylogarithm Lin(z) is defined for |z| ≦ 1 by([4, p. 169], cf. [2, §1. 11 (14) and § 1. 11. 1]). The definition can be extended to all values of zin the z-plane cut along the real axis from 1 to ∝ by the formula[2, §1. 11(3)]. Then Lin(z) is regular in the cut plane, and there is a differential recurrence relation [4, p. 169]It is convenient to extend the sequence Lin(z) backwards in the manner suggested by (2) and defineThen Li1(z)= – log(l–z), and Lin(z) is a rational function of z for n= 0, – 1, – 2,…. Formula (2) now holds for all integers n.
Inequalities involving the genus of a graph and its thicknesses
Authors: Beineke Lowell W. , Harary Frank 
Published: May 2009

Let G be a graph with p points and q lines, and genus γ. The thicknesst(G) has been introduced as the minimum number of planar subgraphs whose union is G. This topological invariant of a graph has been studied by Battle, Harary and Kodama [1], Tutte [7], Beineke, Harary and Moon [3], and Beineke and Harary [2].It is natural to generalise this concept of the thickness of a graph to the union of graphs with a specified genus. We say that the n-thickness of G is the minimum number of subgraphs of genus at most n whose union is G. Denoting the n-thickness of G by tn, we write in particular t0 the 0-thickness, i.e., the thickness.
On minimal n-universal graphs
Authors: Moon J. W. 
Published: May 2009

A graph Gn consists of n distinct vertices x1x2, …, xn some pairs of which are joined by an edge. We stipulate that at most one edge joins any two vertices and that no edge joins a vertex to itself. If xi, and xj are joined by an edge, we denote this by writing xi ∘ xj.Consider a second graph HN, where n ≦ N. Following Rado [1], we say that a one-to-one mapping/of the vertices of Gn into the vertices of HN defines an embedding if xi ∘ xj implies f(xi) ∘ f(xj), and conversely, for all i, j = 1, 2,…, n. If there exists an embedding of Gn into HN, we denote this by writing Gn <HN. The particular graph HN is said to be n-universal if Gn < HN for every graph Gn with n vertices.
The Reissner-Sagoci problem
Authors: Sneddon Ian N. 
Published: May 2009

The statical Reissner-Sagoci problem [1, 2, 3] is that of determining the components of stress and displacement in the interior of the semi-infinite homogeneous isotropic elastic solid z ≧ 0 when a circular area (0 ≦ p ≦ a, z = 0) of the boundary surface is forced to rotate through an angle a about an axis which is normal to the undeformed plane surface of the medium. It is easily shown that, if we use cylindrical coordinates (p, φ, z), the displacement vector has only one non-vanishing component uφ (p, z), and the stress tensor has only two non-vanishing components, σρπ(p, z) and σπz(p, z). The stress-strain relations reduce to the two simple equationswhere μ is the shear modulus of the material. From these equations, it follows immediately that the equilibrium equationis satisfied provided that the function uπ(ρ, z) is a solution of the partial differential equationThe boundary conditions can be written in the formwhere, in the case in which we are most interested, f(p) = αρ. We also assume that, as r → ∞, uπ, σρπ and σπz all tend to zero.
A Group-Theoretic Proof of a Theorem of MacLagan-Wedderburn
Authors: Zassenhaus Hans J. 
Published: May 2009

The purpose of this paper is to present a proof of the following theorem of Maclagan-Wedderburn.*Every finite skew-field† is a field.The proof depends on group theory and on the properties of Galois fields. As an introduction, §§1–4 are devoted to a systematic and self-contained account of the theory of Galois fields.
Integral of an E-function expressed as a Sum of two E-functions
Authors: Macrobert T. M. 
Published: May 2009

§ 1. Introductory. The formula to be proved iswhere ρq+1 – αp+1 > 0, αr – ρq+1 > 0, r = 1,2, …, p, and p≧q + 1.
Arteriovenous malformation as a consequence of a scar pregnancy
Authors: RYGH ASTRID B. , GREVE OLE J. , FJETLAND LARS , BERLAND JANNICKE M. , EGGEBØ TORBJØRN M. 
Published: May 2009

AbstractA scar pregnancy is an ectopic pregnancy implanted in a previous lower segment cesarean scar, and the incidence of this complication may be expected to rise along with increasing cesarean section rates. Arteriovenous malformation of the uterus may be congenital, associated with early pregnancy loss, trophoblastic disease, or surgical procedures. We describe a case of uterine arteriovenous malformation as a consequence of a scar pregnancy, complicated by recurrent, serious bleeding. The condition was diagnosed using three‐dimensional ultrasound with color Doppler and magnetic resonance imaging and appears not to have been described before. Selective embolization was performed, but eventually surgical intervention with resection of the affected uterine segment was necessary, and the patient recovered. The diagnosis was confirmed by pathologic‐anatomical diagnosis showing trophoblastic cells in the resected area. Because of collateral formation, non‐surgical options may be limited and not successful.
Efficacy of methylcellulose and loperamide in managing fecal incontinence
Authors: SZE EDDIE H.M. , HOBBS GERRY 
Published: May 2009

AbstractObjective. To evaluate the efficacy of methylcellulose (Citrucel®) and loperamide (Imodium®) in managing fecal incontinence by comparing cure rates with expectant management. Design. Prospective controlled study. Setting. Urogynecology clinic in a university hospital. Population. Sixty‐nine women with fecal incontinence. Methods. All incontinent women received one heaping tablespoon of methylcellulose twice a day, which was increased to two heaping tablespoons twice a day as needed. If the incontinence persisted after taking the maximum dose of methylcellulose for two weeks, loperamide, one capsule twice a day was added, which was increased to two capsules three times a day as needed. If both fecal urgency and incontinence resolved, the therapy was continued for a three‐month treatment period. Women, who declined the proposed treatment and did not undergo any other therapy during the subsequent eight weeks, served as controls. A subject or control was considered cured if she stated that her incontinence was cured, had zero Pescatori incontinence point, resolution of fecal urgency, and her incontinence did not affect her emotional, social, occupational, and physical functions during the three‐month treatment or eight‐week observation period. Main outcome measures. Difference in the cure rate between subjects and controls. Results. Fifty‐nine subjects were treated with methylcellulose. Forty (68%) also required loperamide. Ten women served as controls. Women treated with methylcellulose and loperamide had a higher cure rate than those managed expectantly (46% vs. 0%, p<0.01). Conclusion. Methylcellulose and loperamide are an effective treatment for fecal incontinence, at least on a short‐term basis.
Value of sonographically guided needle sampling of cystic versus solid components in the diagnosis of complex cystic breast masses
Authors: Lin Wen-Chiung , Hsu Giu-Cheng , Yu Cheng-Ping , Yu Jyh-Cherng , Lee Hsiu-Nan , Hsu Hsian-He , Chang Tsun-Hou , Chen Tom , Li Chao-Shiang , Huang Guo-Shu 
Published: May 2009

Background: The common practice for diagnosis of complex cystic breast masses (CCBM) may be imaging-guided aspiration or biopsy of cystic or solid components. Purpose: To assess the diagnostic value of sonographically guided needle sampling of cystic and solid components for CCBM. Material and Methods: Twenty patients with 20 CCBM underwent sonographically guided fine-needle aspiration biopsy (FNAB) for cystic components, followed by core needle biopsy (CNB) for residual solid components. The diagnostic results of each were evaluated. Excisional biopsy or mastectomy served as a reference standard. Results: Fourteen (70%) masses were malignant. Needle sampling for cystic components of the 14 malignant tumors showed malignancy in one (7%), atypia in four (29%), benign findings in four (29%), and insufficient samples in five (36%). Needle sampling for residual solid components showed malignancy in 11 (79%), atypia in two (14%), and insufficient sample in one (7%). The diagnostic yield of needle sampling of solid components was significantly higher than that of cystic components for malignant CCBM ( P<0.05). Sixteen (80%) of 20 CCBMs showed bloody fine-needle aspirates. There was no significant difference between the rates of bloody aspirates of malignant and benign CCBM (86% vs. 67%, P=0.55). Conclusion: Sonographically guided needle sampling of solid components may help to identify most malignant CCBMs, and the aspirated fluid may be discarded due to low diagnostic value.
Cellular Mechanisms of Memory: Complex Circuits
Authors: Eichenbaum Howard 
Published: May 2009

AbstractThis chapter reviews recent progress toward a full characterization of one particular form of synaptic plasticity observed in the mammalian brain called long-term potentiation (LTP). LTP can be induced in many brain structures that are involved in memory, and there is substantial evidence that the same cellular mechanisms that mediate LTP are required for lasting memory.