bluuebunny/crossref_metadata_2025_split huggingface dataset:
The critical coupling of modes in a tapered earth-ionosphere wave guide
Authors: Budden K. G. 
Published: November 2008

AbstractIn a stratified wave guiding system, it is often possible to adjust parameters, such as the wave frequency or some dimension of the guide, so that the propagation constants of two modes become equal. These modes are then said to be degenerate. In a tapered guide some of the parameters are slowly varying functions of distance x measured along the guide, and the conditions of degeneracy can be satisfied for some value x0 of x, possibly complex. Here the two modes are said to be critically coupled, and x0 is called a ‘coupling point’ in the complex x-plane. Cases are known where two modes in the earth-ionosphere wave guide could approach critical coupling in the twilight region of the earth, where the guide is tapered. The x dependence of the composite field for the two modes can then be expressed in terms of an Airy Integral function. The theory is closely analogous to that used for studying critical coupling of Ordinary and Extraordinary radio waves within a horizontally stratified ionosphere.
Positive-moment problems in abstract measure spaces
Authors: Rogosinski H. P. 
Published: November 2008

In this paper we continue the investigation of positive-moment problems, begun in (4). For an arbitrary index set A we consider a family (fα)α ∈ A of measurable real-valued functions on a measure-space (X, µ). We suppose throughout thatwhere (Xm) is an increasing sequence of measurable subsets of X and where, for each α in A and each m, fα is µ-integrable over Xm. Let (сα)α ∈ A be a given family of real numbers. We consider the following restricted positive-moment problem: does there exist a measurable function g on X such that 0 ≤° g ≤° 1 and such thatfor every α in A? (Here the symbol ‘≤°’ indicates that the relation ≤ holds almost everywhere with respect to µ on X. Symbols ‘ = °, <°, …’ are used similarly.) If such a g exists we call (сα)α ∈ A a moment family for the problem:
Vector lattices freely generated by distributive lattices
Authors: Beynon W. M. 
Published: November 2008

In this paper, the duality theory for vector lattices developed by the author in (2) is applied to the study of vector lattices freely generated by distributive lattices.If L is a finite distributive lattice defined by a set of generators X, subject to a finite set of relations R, then the vector lattice FVL(L) freely generated by the elements of L subject to the relations governing intersection and union in L is a finitely generated projective vector lattice, being a quotient of the vector lattice freely generated by elements of X by the principal ideal generated by the relations R. Thus, there is a polyhedron Q, such that FVL(L) is isomorphic with the vector lattice of real valued polyhedral functions on Q, under pointwise operations, and the isomorphism class of FVL(L) determines and is determined by the polyhedral type of Q. The principal result of this paper shows that the polyhedral class to which Q belongs can be simply characterised in terms of the nerve of the poset P of join-irreducible elements of L. Explicitly, up to polyhedral equivalence, Q is a suspension of the nerve of P.
On null cone preserving mappings
Authors: Lester J. A. , McKiernan M. A. 
Published: November 2008

Alexandrov (1), Zeeman (3) and others after them have investigated at length the problem of characterizing as Lorentz transformations those mappings f of Minkowski space M which ‘preserve cones’, i.e. if C(a) denotes the null-cone in M with vertex a ∈ M, thenfor all a ∈ M.
Some unexpectedly non-singular orbit spaces
Authors: Morton H. R. 
Published: November 2008

The orbit space of a manifold under the smooth action of a compact Lie group is typically a ‘manifold with singularities’. The orbits of a given type each form a mani-fold, but these ‘strata’ generally do not give a manifold when pieced together. For example, the orbit space of S3 under the action of given by the matrix.is the suspension of P(2), which fails to be a manifold at the suspension points.In this paper I shall give examples where, in spite of having many orbit types, the orbit space is a manifold, with or without boundary.
On nonlinear perturbations of linear second order elliptic boundary value problems
Authors: Fitzpatrick P. M. 
Published: November 2008

AbstractLet Ω ⊆ n be open and bounded, with ∂Ω smooth. Sufficient conditions on f are given in order that for p > n, the equationhas a solution for every h ∈ Lp; L is a second order symmetric elliptic operator and B represents either the first, second or third boundary value problems. These conditions are in terms of the asymptotic behaviour of f, in its second variable, in relation to those λ for which there is a nontrivial solution of
On polycyclic groups with isomorphic finite quotients
Authors: Grunewald Fritz , Segal Daniel 
Published: November 2008

Following P. F. Pickel (5) we write (G) for the set of isomorphism classes of finite quotients of a group G. One of the outstanding problems in the theory of polycyclic groups is to determine whether there can be infinitely many non-isomorphic polycyclic groups G with a given (G). We solve a special case of this problem with our first main result:Theorem 1. Let G be an abelian-by-cyclic polycyclic group. Then the polycyclic-by-finite groups H withlie in only finitely many isomorphism classes.
Path node-covering constants for certain families of trees
Authors: Meir A. , Moon J. W. 
Published: November 2008

1. introduction. A set P of disjoint paths in a graph G is a node-covering of G if every node of G is in a path in P. (For definitions not given here see (5) or (11).) The path (node-covering) number of G is the smallest possible number p(G) of paths in such a node-covering of G. The problem of determining the path number of a graph was considered in (1) and (4) for undirected graphs and in (2) for directed graphs. In particular, an algorithm for determining the path number of a tree was given in (1) and (4). If ℱ denotes some family of trees, let μ(n) = μℱ(n) denote the average value of p(T) over all trees T in ℱ with n nodes. Our object here is to show the existence and to determine the value of the path (node-covering) constantfor certain families ℱ of trees. The arguments are similar to those used in (7), (8), and (9), where some other parameters, associated with families of trees, were investigated.
On dichotomy of Riesz products
Authors: Ritter G. 
Published: November 2008

Background. Riesz products are very useful for the construction of singular measures on compact, Abelian groups. Under some circumstances, two Riesz products are either equivalent or singular in the measure-theoretic sense. Exact knowledge of these circumstances has been of major interest ever since the 1930s, when Riesz's famous example (8) was recognized as a fertile source of examples of singular continuous measures. Zygmund(11) showed that any Riesz product over a Hadamard dissociate subset of ℕ is either a square integrable function or singular with respect to Lebesgue measure. Hewitt–Zuckerman(4) generalized these products to all compact, Abelian groups, introducing the notion of a dissociate subset. They extended Zygmund's result in certain cases. The next major step was taken by Brown–Moran(3) and Peyrière(6), (7), who showed that two Riesz productsare mutually singular ifThe author (9) has improved another result of Brown–Moran (3) by showing that µa and µb are equivalent if
Multiple points of codimension one immersions of oriented manifolds
Authors: Eccles Peter John 
Published: November 2008

Work by L.S.Pontrjagin(18) and M.W.Hirsch(7) allows us to identify the stablen-stemwith the bordism group of oriented compact closed smoothn-manifolds immersed in ℝn+1. In a recent paper (11), U. Koschorke discusses invariants thereby defined onby analysing the self-intersections of immersed manifolds. In particular he discusses the homomorphismdefined by assigning to a generic immersionMn→ ℝn+1number (modulo 2) of its (n+ 1)-fold points.
Conditions for the local existence of metric in a generic affine manifold
Authors: Cheng Kuo-Shung , Ni Wei-Tou 
Published: November 2008

AbstractFor a manifold with a generic symmetric affine connection, explicit necessary and sufficient conditions for the local existence of metric compatible with the connection are obtained in terms of the Riemann tensor and its first-order covariant derivatives. If these conditions are satisfied, the solutions for metric are unique up to a constant scale factor and the absolute value of the signature is uniquely determined. Explicit formulae for the solutions are given in terms of integrals.
Completeness properties inL2of the eigenfunctions of two semi-linear differential operators
Authors: Fraenkel L. E. 
Published: November 2008

This paper concerns the boundary-value problemsin which λ is a real parameter,uis to be a real-valued function inC2[0, 1], and problem (I) is that with the minus sign. (The differential operatorsare called semi-linear because the non-linearity is only in undifferentiated terms.) If we linearize the equations (for ‘ small’ solutionsu) by neglecting, there result the eigenvalues λ =n2π2(withn= 1,2,…) and corresponding normalized eigenfunctionsand it is well known ((2), p. 186) that the sequence {en} iscompletein that it is an orthonormal basis for the real Hilbert spaceL2(0, 1). We shall be concerned with possible extensions of this result to the non-linear problems (I) and (II), for which non-trivial solutions (λ,u) bifurcate from the trivial solution (λ, 0) at the points {n2π2,0) in the product space×L2(0, 1). (Heredenotes the real line.)
Normal modes for Green's functions and the method of theta functions
Authors: Terras Riho 
Published: November 2008

AbstractThe eigenfunctions for four types of bounded plane domains are constructed by a group-theoretic method. The group theory is then used to prove a completeness theorem and to derive a theta function transformation formula. Rapidly convergent series for the Green's functions of the Laplace operator on these domains are then constructed. Final formulas are summarized without reference to group theory.
The determination of thermal stresses in dissimilar media
Authors: Aderogba K. 
Published: November 2008

AbstractIt is shown that if, in an infinite homogeneous unbounded elastic heat-conducting solid, we are given the thermal stresses which arise when any arbitrarily shaped subregion of the upper half-space z > 0 is emitting any quantity of heat into the surrounding, then on introducing a different heat-conducting material into the half-space z < 0, the new thermal stresses in z >0 and in z < 0 are explicitly expressible in an invariant form in terms of the known thermal stresses in the homogeneous infinite solid. Specialization of the derived dependence shows that the physically interesting interfacial discontinuities inherent in the problem admit the representationwhile the traction transmitted across the interface takes the formwhere αi and βi are constants. An application is then made to the case when the region emitting heat into the surrounding is ellipsoidal, since this is a fundamental shape of practical importance. Applications can however be made to any shape of the region emitting heat, provided that the corresponding harmonic and biharmonic potentials are available.The paper may be considered to have its origin in the half-space theorem of Lorentz in hydrodynamics.
Lipschitz classes and convolution approximation processes
Authors: Ditzian Z. 
Published: November 2008

For a continuous function f(x) on the reals or on the circle T (continuous and 2π periodic) we say that f(x) belongs to the generalized Lipschitz class, denoted by f ∈ Lip* α, ifwhere and Δhf(x) = f(x + ½h)−f(x−½h). For a convolution approximation process given bywherewe shall investigate equivalence relations between the asymptotic behaviour of (d/dx)rAn(f, x) and f ∈ Lip* α.
An acceleration condition for b-incomplete timelike curves
Authors: Dodson C. T. J. , Sulley L. J. , Williams P. M. 
Published: November 2008

AbstractThe b-completion of a smooth manifold with linear connection was introduced by Schmidt (6). He pointed out that, in a spacetime, an inextensible timelike curve of finite proper length and bounded acceleration has an endpoint on the b-boundary. However, it is not clear in what sense boundedness was meant. Geroch(1) suggested that any acceptable method of completing a spacetime should have this property with boundedness interpreted through the Lorentz norm. This result for the b-completion was given by Rosso(4), based on his earlier paper (3), which, however, contains some arguments that we do not accept. We give another proof of the result and improve it by weakening the condition of boundedness of the acceleration.
Achromatic numbers of random graphs
Authors: McDiarmid Colin 
Published: November 2008

AbstractThe achromatic number ψ(G) of a graph G is the greatest number of colours in a proper colouring of the vertices of G such that for every pair of colours some vertex of the first colour and some vertex of the second colour are adjacent. We prove that almost all graphs Gn with n vertices satisfy n/(k+l) < ψ(Gn) < n/(k–1), where k = k(n) = (log2n)½. We show also that the achromatic number is a ‘global’ invariant.
A lifting result for local cohomology of graded modules
Authors: Brodmann M. 
Published: November 2008

In this paper we prove a lifting result for local cohomology. As a special case we get the following result for the Serre-cohomology over a projective variety:Proposition (1·1). Let ℱ be a coherent sheaf over X, where X is a projective variety over an algebraically closed field k. Let i ≽ 0 and assume that there is a pencil P of hyper-plane sections which is in general position with respect to ℱ (which means that x ∉ H, ∀x ∈ Ass(ℱ), ∀H∈p), and such that for each H ∈ P Hi(X, ℱ│H(n)) = 0, ∀n ≪ 0. Then Hi + 1(X, ℱ) = 0, ∀n ≪ 0.
Representing 3-manifolds by a universal branching set
Authors: Montesinos José María 
Published: November 2008

In this paper all 3-manifolds will be supposed to be compact, connected, oriented and without 2-spheres in the boundary.Given a 3-manifold M we obtain a closed pseudomanifold M^ by capping off each boundary component of M with a cone. We prove that such an M^ is a covering of S3 branched over a subcomplex G of S3 which is independent of M, and such that S3 - G has free fundamental group on two generators. Hence M^ (and also M) can be represented by a transitive pair {σ, τ} of permutations in the symmetric group Σh on the set {1,2, …, h}, for some h. We show how to obtain {σ, τ} from a given Heegaard diagram of M.
Saturation results for a class of linear operators
Authors: Kuttner B. , Mohapatra R. N. , Sahney B. N. 
Published: November 2008

Let B denote the space of bounded measurable functions with period 2π. We will suppose throughout that f(x) ∈ B. All norms considered are essential sup norms. Let the Fourier series of f(x) be given byLet D = (dnk) (n, k = 0, 1, …) be an infinite matrix.Let Ln(f; x) be the D transform of the Fourier series of f(t) at t = x, i.e.where Sk(x) = A0(x) + A1(x) + … + Ak(x). Let us write
On a symbolic algebra for Hencky-Prandtl nets
Authors: Hill R. 
Published: November 2008

AbstractIn the classical theory of plane deformations in isotropic plastic media, the field equations are hyperbolic and the orthogonal families of characteristics are known as Hencky-Prandtl nets. Their distinctive geometry has been given symbolic expression by Collins (1968), in an algebra of infinite matrices associated with canonical series representations of the general solution. This has become the standard technique when investigating boundary-value problems, both analytically and numerically. The basic framework of the algebra is here reorganized and developed. A systematic approach then leads to new identities which are shown to be fundamental in the algebraic hierarchy.
Eigenvalues of smooth kernels
Authors: Reade J. B. 
Published: November 2008

Suppose is a symmetric square integrable kernel on the unit square [0, 1]2. Thenis a compact symmetric operator on the Hilbert space L2[0, 1]. H. Weyl (see [2]) has shown that, if then the eigenvaluesof T satisfy as n → ∞. We prove a related result. Let W12[0, 1]2 denote the space of all K(x, t) ε L2[0, 1]2 which are absolutely continuous in x for each t and absolutely continuous in t for each x, and the partial derivatives ∂K/∂x(x, t), ∂K/∂t(x, t) are both in L2[0, 1]2. We slow that the eigenvalues of any satisfy .
Poisson integrals of absolutely continuous and other measures
Authors: Madan Shobha , Sjögren Peter 
Published: November 2008

AbstractWe characterize absolutely continuous and continuous measures by means of the g-function and distribution function, respectively, of the Poisson integral in a half space. Some other ways of measuring the Poisson integral are found to make such measures indistinguishable. A variant of the Poisson integral is also studied.
Realcompact spaces and regular σ -frames
Authors: Gilmour Christopher R. A. 
Published: November 2008

AbstractWe show that there is an adjoint dual equivalence between realcompact Alexandroff spaces and the Alexandroff σ-frames. This gives a corresponding adjoint duality for realcompact Tychonoff spaces. Consequently we characterize lattice theoretically the cozero-sets of a topological space.
A sequence of Gamma-type approximation operators
Authors: Upreti Rita , Joshi J. M. C. 
Published: November 2008

AbstractA sequence of Gamma-type approximation operators n(f) (n = 1,2,…) (which reduce to the Gamma operators, Gn (n = 1,2,…), defined by Müller in a particular case) has been defined. Uniform convergence of n(f) towards f on fixed intervals [x1, x2] (0 ≦ x1 ≦ x2 < ∞) has been proved and a simple example has been given in support of the proof.
Scattering of surface waves obliquely incident on a fixed half immersed circular cylinder
Authors: Mandal B. N. , Goswami S. K. 
Published: November 2008

AbstractThe problem of scattering of surface water waves obliquely incident on a fixed half immersed circular cylinder is solved approximately by reducing it to the solution of an integral equation and also by the method of multipoles. For different values of the angle of incidence and the wave number the reflection and transmission coefficients obtained by both methods are evaluated numerically and represented graphically to compare the results obtained by the respective methods.
On the supports of Gauss measures on algebraic groups
Authors: McCrudden M. 
Published: November 2008

For any locally compact topological group G let M(G) denote the topological semigroup of all probability (Borel) measures on G, furnished with the weak topology and with convolution as the multiplication. A Gauss semigroup on G is a homomorphism t→ μt of the strictly positive reals (under addition) into M(G) such that(i) no μt is a point mesaure,(ii) for each neighbourhood V of 1 in G we have
On Λ-Ω-extendable distributions
Authors: Dierolf Peter 
Published: November 2008

AbstractLet Λ ⊂ Ω ⊂ ℝnbe open subsets. We construct a natural space of test functions on Λ such that the dual consists exactly of those distributions on Λ which can be extended to distributions on Ω. As an application of this representation we calculate the space of multiplication operators on as well as the space of absolutely regular extendable distributions.
On convergence and quasiconformality of complex planar spline interpolants
Authors: Dikshit H. P. , Ojha A. 
Published: November 2008

There appear to be two main approaches for developing complex splines. One of these, which has been in use for quite some time, consists in defining splines on the boundary of a given region which are then extended into the interior by Cauchy's integral formula (see e.g. [1]). The other approach, which is of a more recent origin, is motivated in spirit by the theory of finite elements (see e.g. [10], p. 320) and is contained in [8] and [9]. Observing that the foregoing extension into the interior is not easy to execute numerically, certain continuous piecewise non-holomorphic functions, called complex planar splines have been studied in [8] and [9]. The choice of non-holomorphic functions is justified, since if we take the pieces to be holomorphic functions like polynomials, then by the well known identity theorem ([5], p. 132, theorem 60) the continuity of such a piecewise function implies that all the pieces represent just one holomorphic function. Thus, we shall consider polynomials in z and its conjugate z¯ of the formwhich are generally non-holomorphic functions. The numberwill be called the degree of q. For simplicity we also write q(z) for q(z, z¯).
Cayley graphs and group presentations
Authors: Thomas Richard M. 
Published: November 2008

The aim of this paper is to prove the following result:Theorem. Let G be the group defined by the presentationwhere each ui is a word in the xj and , and suppose that there is a homomorphism σ such that the orders of the elements respectively. Let If G is finite, then α−d + 1 > 0 and .
Far field patterns and the inverse scattering problem for electromagnetic waves in an inhomogeneous medium
Authors: Colton David , Päivärinta Lassi 
Published: November 2008

AbstractWe consider the scattering of time harmonic electromagnetic waves by an inhomogeneous medium of compact support. It is first shown that the set of far field patterns of the electric fields corresponding to incident plane waves propagating in arbitrary directions is complete in the space of square-integrable tangential vector fields defined on the unit sphere. We then show that under certain conditions the electric far field patterns satisfy an integral identity involving the unique solution of a new class of boundary value problems for Maxwell's equations called the interior transmission problem for electromagnetic waves. Finally, it is indicated how this integral identity can be used to formulate an optimization scheme yielding an optimal solution of the inverse scattering problem for electromagnetic waves.
Star multigraphs with three vertices of maximum degree
Authors: Chetwynd A. G. , Hilton A. J. W. 
Published: November 2008

The graphs we consider here are either simple graphs, that is they have no loops or multiple edges, or are multigraphs, that is they may have more than one edge joining a pair of vertices, but again have no loops. In particular we shall consider a special kind of multigraph, called a star-multigraph: this is a multigraph which contains a vertex v*, called the star-centre, which is incident with each non-simple edge. An edge-colouring of a multigraph G is a map ø: E(G)→, where is a set of colours and E(G) is the set of edges of G, such that no two edges receiving the same colour have a vertex in common. The chromatic index, or edge-chromatic numberχ′(G) of G is the least value of || for which an edge-colouring of G exists. Generalizing a well-known theorem of Vizing [14], we showed in [6] that, for a star-multigraph G,where Δ(G) denotes the maximum degree (that is, the maximum number of edges incident with a vertex) of G. Star-multigraphs for which χ′(G) = Δ(G) are said to be Class 1, and otherwise they are Class 2.
Multiple points of singular maps
Authors: Szücs András 
Published: November 2008

In 1979 at the Siegen Topology conference Peter Eccles in his lecture asked and in most cases answered the followingQuestion. For which values of n does an immersion of a closed n-dimensional manifold into Rn+1 exist with a single (n + 1)-tuple point?The answer (see [3–5, 8]) implies the following:Proposition (Eccles). No immersion of an even dimensional orientable manifold Mn into Rn+1 has a single (n + l)-tuple point.