bluuebunny/crossref_metadata_2025_split huggingface dataset:
A further instability theorem for a certain fifth-order differential equation
Authors: Ezeilo J. O. C. 
Published: November 2008

In our previous consideration in (1) of the constant-coefficient fifth-order differential equation:an attempt was made to identify (though not exhaustively) different sufficient conditions on a1,…,a5 for the instability of the trivial solution x = 0 of (1·1). It was our expectation that the conditions so identified could be generalized in some form or other to equations (1·1) in which a1,…,a5 were not necessarily constants, thereby giving rise to instability theorems for some non-linear fifth-order differential equations; and this turned out in fact to be so except only for the case:with R0 = R0(a1, a2, a3, a4) > 0 sufficiently large, about which we were unable at the time to derive any worthwhile generalization to any equation (1·1) in which a1, …,a5 are not all constants.
On the equations defining tangent cones
Authors: Robbiano Lorenzo , Valla Giuseppe 
Published: November 2008

This paper treats the local study of singularities by means of their tangent cones, more specifically the study of graded rings associated to an ideal of a local ring. We recall some basic facts: let (R,) be a local ring,I, Jideals ofR, such thatJ⊆I; thenGR/J(I/J), the graded ring associated toI/J, is canonically isomorphic to the quotient ofGR(I) modulo a homogeneous ideal, which is calledJ*, and which is generated by the so-called ‘initial forms’ of the elements ofJ. Let us consider the following example: Letkbe a field,R=k[X, Y, Z](x, y, Z),I= (X, Y, Z)R, Jthe prime ideal generated byfl,f2wheref1=Y3−Z2,f2=YZ−X4. Thenand it is easily seen thatJ*properly contains the ideal generated by the initial formsf*1f*2off1,f2; namelyf*1= −Z2,f*2=YZand (Yf1+Zf2)* =Y4∉ (−Z2,YZ).
Radiation fields and hyperbolic scattering theory
Authors: Friedlander F. G. 
Published: November 2008

Let u(x, t), where x ∈ 3, t ∈ , be a C∞ solution of the wave equation on {|x| > a} × for some a > 0, and suppose that u = 0 for |x|> a, t < 0. One then also has u = 0 for |x| > a + t, t > 0, so that u(.,t) can be thought of as a wave expanding into a previously undisturbed medium. One can now ask for a description of the asymptotic behaviour of u as |x| → ∞. It turns out that there is a v0(θ, τ) ∈ C∞ (S2 × ) such thatin the topology of C∞ (S2 × ). This limit may be called the radiation field of the expanding wave u. (See (2) and the earlier papers quoted there.)
Orthomorphisms of archimedean vector lattices
Authors: Bernau S. J. 
Published: November 2008

AbstractA linear operator T on a vector lattice L preserves disjointness if Tx ⊥ y whenever x ⊥ y. If such a T is positive it is automatically order bounded. An ortho-morphism is an order bounded disjointness preserving linear operator on L. In this note we show that the theory of orthomorphisms on archimedean vector lattices admits a totally elementary exposition. Elementary methods are also effective in duality considerations when the order dual separates points of L. For the Jordan decomposition T = T+ − T− with T+x = (Tx+)+ − (Tx−)+ we can dtrop the order boundedness assumption if we assume either that T preserves ideals or that L is normed and T is continuous. Alternatively we may keep order boundedness and assume only |Tx| ⊥ |Ty| whenever x ⊥ y. The main duality results show: T preserves ideals if and only if T** does; T is an orthomorphism if and only if T* is; T is central (|T| is bounded by a multiple of the identity) if and only if T* is central if and only if T and T* preserve ideals.
Asymptotic formula for the capacitance of two oppositely charged discs
Authors: Chew W. C , Kong J. A 
Published: November 2008

AbstractAsymptotic formulae for the capacitances of two oppositely charged, identical, circular, coaxial discs and two identical, infinite parallel strips separated by dielectric slabs are derived from the dual integral equations approach. The formulation in terms of dual integral equations using transforms gives rise to relatively simple Green's functions in the transformed space and renders the derivation of the asymptotic formulae relatively easy. The solution near the edge of the plates, a two-dimensional problem previously thought not solvable by the Wiener-Hopf technique, is solved indirectly using the method. Solution of the Helmholtz wave equation is first sought, and the solution to Laplace's equation is obtained by letting the wavenumber go to zero. The solution away from the edge is obtained by solving the dual integral equations approximately. The total charge on the plate is obtained by matching the solution near the edge and away from the edge giving the capacitance.
Convergence of spatial birth-and-death processes
Authors: Lotwick H. W. , Silverman B. W. 
Published: November 2008

AbstractSome models for spatial point processes are difficult to simulate directly and are most easily realized as the equilibrium distribution of certain spatial-temporal Markov processes. This paper examines the convergence of such processes, concentrating mainly on the ‘hard core’ case when the points represent the centres of non-overlapping discs. Coupling methods from the theory of Markov chains are used to establish sufficient conditions for the processes to converge to the required equilibrium, and to give a lower bound on the rate of convergence. One technique used is to couple processes when they become close in a suitable metric.
Threshold functions for small subgraphs
Authors: Bollobás Béla 
Published: November 2008

In this note we shall study random labelled graphs. Denote bythe set of all graphs with n given labelled vertices andM(n)edges. As usual, we turn(M(n))into a probability space by giving all graphs the same probability. The question we address ourselves to is the following. Given a graphHand a constant p, 0 < p < 1, for what functionsM(n)is it true that the probability PM(n)(H ⊂ G) that a graphG∈(M(n))containsHtends topas n∞→? This question was posed by Erdös and Rényi (3), (4), who also proved several beautiful and surprising theorems. In order to state the main general result of Erdös and Rényi in this direction, and for our use later, we introduce some definitions.
Asymptotic estimates of the eigenvalues of certain positive Fredholm operators
Authors: Little G. 
Published: November 2008

1. Introduction. Suppose that K is a continuous function on the square Q = [ – 1, 1] x [– 1,1] satisfying , for – 1 ≤ s, t ≤ 1; then the Fredholm operator T on L2(-1,1)is compact and symmetric. Suppose also that T is a positive operator, i.e.then there is an eigenfunction expansionwhere (λn) is a sequence of non-negative real numbers which decreases to 0 and (φn) is an orthonormal sequence in L2( – 1,1). In this paper we shall find asymptotic estimates for λn when K takes certain specific analytic forms. In all cases K will be real-valued on Q and analytic in a neighbourhood of Q in complex 2-space; for example
Indefinite binary forms representing the same numbers
Authors: Delang Li 
Published: November 2008

It is an old problem whether two binary quadratic forms representing the same numbers are equivalent. Legendre asserted without proof that two positive definite forms representing the same numbers are equivalent. In 1895, Bauer(1) proved Legendre's assertion for primitive forms with the same discriminant. In 1938 Delone (2) proved that two positive definite binary forms with real coefficients are equivalent if they represent the same numbers, with the sole exception of the pair equivalent toand their scalings. Watson (3) rediscovered this result in 1979 and asked the same question for indefinite binary forms.
On the rank of horizontal maps
Authors: Rawnsley J. H. 
Published: November 2008

Let M, N be smooth manifolds and ℋ ⊂ TN a smooth sub-bundle. A smooth map φ:M → N will be called horizontal ifAt points where φ(M) is a submanifold of N, the tangent spaces to φ(M) will be sub-spaces of the fibres of ℋ. In other words where φ(M) is a submanifold it is an integral submanifold of ℋ. If ℋ is not integrable it will follow that the rank of Æ must be less than dim ℋx. But we can often place much stricter bounds on the rank of φ by examining the integrability tensor of ℋ. This we shall do in this note.
The order of the approximation to a Wiener process by its Fourier series
Authors: Hall Peter 
Published: November 2008

AbstractLetFbe a distribution function with support confined to ( − π, π),Wa Wiener process on (0, 1), andW0a Brownian bridge. We examine the order of the approximation toW(F)andW0(F)by their Fourier series. The results we obtain are of theoretical interest since the Wiener process possesses the unusual property of satisfying a Lipschitz condition of order ∝ for each 0 < ∝ < ½, but not one of order ∝. = ½. The classical results on the rate of convergence of Fourier series are not sufficiently specific to provide an exact rate in the case of the Wiener process. The work also has practical significance because many statistical procedures can be closely approximated by functions of a Wiener process, and several procedures rely heavily on Fourier series methods. Thus, some of our results may be applied to obtain limit theorems for quantities such as trigonometric series estimates of density and distribution functions.
Homothetic ellipsoids
Authors: Goodey P. R. 
Published: November 2008

AbstractWe let K1 and K2 be two convex bodies in Ed (d ≥ 3) and consider translates of K2 for which ∂K1 ∩ ∂ ≠ ø and K1 ≠ . We show that if, for all such translates,∂K1 ∩ is contained in a hyperplane then K1 and K2 are homothetic ellipsoids.If K1 and K2 are two planar non-coincident convex sets whose interiors intersect we define α(K1, K2) to be the number of connected components of ∂K1 ∩ ∂K2. The starting point for our investigations is the result of Fujiwara(S) and Bol(2) to the effect that K is a circular disc if and only if α(K, K′) = 2 for all congruent copies K′ of K. An easy extension of this result is the observation that K1 and K2 are congruent circular discs if and only if for all congruent copies of K2. When working with such results it is natural to look for analogues in the situation where only translates are allowed rather than all possible congruences. The appropriate analogue was obtained in (7) and we state it here for completeness.
Oriented percolation in dimensions d ≥ 4: bounds and asymptotic formulas
Authors: Cox J. Theodore , Durrett Richard 
Published: November 2008

AbstractLet pc(d) be the critical probability for oriented percolation in ℤd and let μ(d) be the time constant for the first passage process based on the exponential distribution. In this paper we show that as d → ∞,dpc(d) and dμ,(d) → γ where γ is a constant in [e−1, 2−1] which we conjecture to be e−1. In the case of pc(d) we have made some progress toward obtaining an asymptotic expansion in powers of d−1. Our results showThe left hand side agrees, up to O(d−3), with a (nonrigorous) series expansion of Blease (1, 2):
Families of smooth hypersurfaces on certain compact homogeneous complex manifolds
Authors: Borcea Ciprian 
Published: November 2008

Let X be a compact connected homogeneous complex manifold, which is Kāhlerian and has the second Betti number equal to one: b2(X) = 1; dimcX ≥ 3.It is known that these conditions imply the following: X is a projective-rational homogeneous manifold (see (3)); X has an ‘algebraic cell-decomposition’: the 2s-dimensional closed cells are s-dimensional irreducible algebraic sets in X and they form a basis for the 2s-homology group of X, s = 1, 2, …, dimcX (see (1)); there are no holomorphic maps of X on lower dimensional (normal) analytic spaces except constants (see (9)).
Inhomogeneous minimum of indefinite quadratic forms in six variables: A conjecture of Watson
Authors: Raka Madhu 
Published: November 2008

The famous conjecture of Watson(11) on the minima of indefinite quadratic forms in n variables has been proved for n ≤ 5, n ≥ 21 and for signatures 0 and ± 1. For the details and history of the conjecture the reader is referred to the author's paper(8). In the succeeding paper (9), we prove Watson's conjecture for signature ± 2 and ± 3 and for all n. Thus only one case for n = 6 (i.e. forms of type (1, 5) or (5, 1)) remains to he proved which we do here; thereby completing the case n = 6. This result is also used in (9) for proving the conjecture for all quadratic forms of signature ± 4. More precisely, here we prove:Theorem 1. Let Q6(x1, …, x6) be a real indefinite quadratic form in six variables of determinant D ( < 0) and of type (5, 1) or (1, 5). Then given any real numbers ci, 1 ≤ i ≤ 6, there exist integers x1,…, x6such that
A new proof for the residual set dimension of the apollonian packing
Authors: Tricot Claude 
Published: November 2008

AbstractLet (Dn) be the apollonian packing of a curvilinear triangle T, ρn the radius of Dn, E = T—U Dn the residual set, dim (E) its Hausdorff dimension. In this paper we give a new proof of the equality dim proved by Boyd [2]. Our technique is to construct a sequence of regular triangles covering E, and suitable measures μkcarried by E which allow us to apply a density theorem.
Minimal projections in Lp-spaces
Authors: Halton E. J. , Light W. A. 
Published: November 2008

Let X be a normed linear space and let W be a proper subspace of X. A projection is a surjective linear map P: X → W such that P is idempotent. It is immediately clear that P has norm at least unity. Thus the problem of calculating the numberhas some interest. The number λ(W, X) is often called the relative projectiion constant of W in X. If the infimum is attained, any attaining projection is called a minimal projection. The problems of calculating λ(W, X) for a fixed X and W or finding a minimal projection turn out to be very dificult. For example, if X = C [0, 1] with the usual supremem norm and W is the subspace of polynominals of degree at most two then λ(W, X) remains unknown as does any example of a minimal projection. One of the few places where the problem shows much tractability is the case
Residual finiteness of certain 1-relator groups: extensions of results of Gilbert Baumslag
Authors: Allenby R. B. J. T. , Tang C. Y. 
Published: November 2008

Let be the class of groups which can be presented in the formwhere u, v are positive words on the generators g, h, …, k and where each generator appears in uv−1 with zero exponent sum. Let be the class of groups which can be presented in the formwhere u, v are words (not necessarily positive) on the disjoint sets of generators c1, …, cm and d1, …, dn and where [u, v] = u−1v−1uv.
An infinite family of non-Haken hyperbolic 3-manifolds with vanishing Whitehead groups
Authors: Nicas Andrew J. 
Published: November 2008

A manifold M is said to be aspherical if its universal covering space is contractible. Farrell and Hsiang have conjectured [3]:Conjecture A. (Topological rigidity of aspherical manifolds.) Any homotopy equivalence f: N → M between closed aspherical manifolds is homotopic to a homeomorphism,and its analogue in algebraic K-theory:Conjecture B. The Whitehead groups Whj(π1M)(j ≥ 0) of the fundamental group of a closed aspherical manifold M vanish.
Bipartite completely positive matrices
Authors: Berman Abraham , Grone Robert 
Published: November 2008

A non-zero n-by-n matrix A is said to be completely positive if there exist non-negative vectors b1,…, bk, such thatThe smallest such integer k is called the factorization index of (completely positive) A, and is denoted by ø(A). Completely positive matrices are important in the study of block designs [4], statistics and modelling of energy demand [3].
Almost convergence of double sequences and strong regularity of summability matrices
Authors: Móricz F. , Rhoades B. E. 
Published: November 2008

A double sequence x = {xjk: j, k = 0, 1, …} of real numbers is called almost convergent to a limit s ifthat is, the average value of {xjk} taken over any rectangle {(j, k): m ≤ j ≤ m + p − 1, n ≤ k ≤ n + q − 1} tends to s as both p and q tend to ∞, and this convergence is uniform in m and n. The notion of almost convergence for single sequences was introduced by Lorentz [1].
Uniform bounds for the number of solutions to Yn = f(X)
Authors: Evertse J.-H. , Silverman J. H. 
Published: November 2008

Let K be an algebraic number field and f(X) ∈ K[X]. The Diophantine problem of describing the solutions to equations of the formhas attracted considerable interest over the past 60 years. Siegel [12], [13] was the first to show that under suitable non-degeneracy conditions, the equation (+) has only finitely many integral solutions in K. LeVeque[7] proved the following, more explicit, result. Letwhere a ∈ K* and αl,…,αk are distinct and algebraic over K. Then (+) has only finitely many integral solutions unless (nl,…,nk) is a permutation of one of the n-tuples
Constructions of arcbodies
Authors: Lozano María Teresa 
Published: November 2008

The concept of arcbody was introduced in [4] as a generalization of prime tangles used by Lickorish[3] and Bleiler[l]. The pair (A, l), where A is a compact 3-manifold with boundary ∂A, and l is a 1-submanifold properly embedded in A, is an arcbody if:(i) the inclusion ∂ A – l ↪ A – l is monic, i.e. A – l has incompressible boundary;(ii) no component of (A, l) is homeomorphic to (D2, 0) × I or (D2, 0) × S1; and(iii) every sphere of ∂A intersects l.
A many-variable Landau-Kolmogorov inequality
Authors: Boyadzhiev Khristo N. 
Published: November 2008

The Landau–Kolmogorov inequalitywhere ‖.‖ is the ‘sup’ norm, is well known and has many interesting applications and generalizations (see [1, 4–7, 13, 16]). Its study was initiated by Landau[10] and Hadamard [8] (the case n = 2). Kolmogorov [9] succeeded in finding in explicit form the best possible constants K(n, k) = Cn, k in (1) for functions on the whole real line R. The best constants for the half line R+ are not known in explicit form except for n = 2, 3, 4, but an algorithm exists for their computation (Schoenberg and Cavaretta [15]).
On the ranks of certain finite semigroups of transformations
Authors: Gomes Gracinda M. S. , Howie John M. 
Published: November 2008

It is well-known (see [2]) that the finite symmetric group Sn has rank 2. Specifically, it is known that the cyclic permutationsgenerate Sn,. It easily follows (and has been observed by Vorob'ev [9]) that the full transformation semigroup on n (< ∞) symbols has rank 3, being generated by the two generators of Sn, together with an arbitrarily chosen element of defect 1. (See Clifford and Preston [1], example 1.1.10.) The rank of Singn, the semigroup of all singular self-maps of {1, …, n}, is harder to determine: in Section 2 it is shown to be ½n(n − 1) (for n ≽ 3). The semigroup Singn it is known to be generated by idempotents [4] and so it is possible to define the idempotent rank of Singn as the cardinality of the smallest possible set P of idempotents for which <F> = Singn. This is of course potentially greater than the rank, but in fact the two numbers turn out to be equal.
The Artin–Rees equations
Authors: Caruth A. 
Published: November 2008

Let R denote a commutative Noetherian ring with an identity element and N a finitely generated R -module. When K is a submodule of N and A an ideal of R the Artin–Rees lemma states that there is an integer q ≥ 0 such that AnN ∩ K = An−q(AqN ∩ K) for all n ≥ q (Rees[4]; Northcott [3], theorem 20, p. 210; Atiyah and Macdonald [1], proposition 10·9, p. 107; Nagata [2], theorem (3·7), p. 9). The above equation belongs to the family of module equations involving A and K which is considered below. We characterize, in terms of A and K, the set of submodules X of N for which there is an integer q = q(X) ≥ 0 satisfying the equationEquation (1), which we call the Artin–Rees equation related to A and K, gets its maximal force when X is largest and we determine the best possible solution in this sense. Notice that for any submodule X satisfying (1), X ⊆ K:NAn for all n ≥ q(X). Since N is a Noetherian R-module ([3], proposition 1 (corollary), p. 177), there is an integer t ≥ 1 such that K:NAt = K:NAt+n for all n ≥ 0. We define M = K:NAt and prove, in Theorem 1, that X = Q satisfies equation (1), for a suitable integer q(Q) ≥ 0, if and only if K ⊆ Q:NAυ ⊆ M for some integer υ ≥ 0. In topological terms, the A-adic topology of K coincides with the topology induced by the A-adic topology of N on the subspace Q if the inequality K ⊆ Q:NAυ ⊆ M is satisfied. It follows that the solution set of equation (1) includes every submodule of N of the form An−rK when n ≥ r = q(K) as well as every submodule lying between K and M. Hence, X = M is the strongest solution, in the sense that M is the largest such submodule contained in An−s (AsN ∩ K): NAn for all n ≥ s = q(M). Recall that M is strictly larger than K if and only if A is contained in at least one prime ideal of R belonging to K ([3], theorem 14 (corollary 1), p. 193). Thus, equation (1) has a unique solution (necessarily X = K) if and only if A is not contained in any prime ideal of R belonging to any solution.
Quasi-standard C*-algebras
Authors: Archbold R. J. , Somerset D. W. B. 
Published: November 2008

AbstactA necessary and sufficient condition is given for a separable C*-algebra to be *-isomorphic to a maximal full algebra of cross-sections over a base space such that the fibre algebras are primitive throughout a dense subset. The condition is that the relation of inseparability for pairs of points in the primitive ideal space should be an open equivalence relation.
A stochastic calculus approach to the shape distribution induced by a complex normal model
Authors: Le Huiling 
Published: November 2008

AbstractAn approach via stochastic calculus was given by Kendall in [7] to the Mardia–Dryden shape distribution of three labelled independent -random points (j = 1, 2, 3). We give here the analogous approach for the general case discussed in [3] in which k labelled random points have a complex normal distribution.
On exchanges between convective modes in a slightly tilted porous cavity
Authors: Impey M. D. , Riley D. S. 
Published: November 2008

AbstractWe use Liapunov–Schmidt reduction and singularity-theory methods to investigate the bifurcation structure of steady free convection in a finite two-dimensional saturated porous cavity heated from below. In particular, we develop a qualitative model describing the modal exchanges that occur as the aspect ratio of a slightly tilted cavity varies. ℤ2-symmetry breaking bifurcations are involved in these exchanges and the mechanism is significantly different from those in previously studied physical systems. The work is akin to, but distinct from, that of Schaeffer's on the Taylor–Couette problem. We also derive and clearly state conditions for the application of this model to modal exchange in other systems.
Generators and relations for metabelian Lie algebras
Authors: Wisliceny Jürgen , Zerck Rainer 
Published: November 2008

The aim of this paper is to prove an inequality of Golod-Shafarevich type for metabelian Lie algebras and to show that this inequality is best possible up to a constant factor. Investigations of this kind were started in [4] in connection with the solution of the class field tower problem. It was shown that if there is a finite p-group which may be presented as a pro-p-group with d ≥ 2 generators and r relations then the inequality r > ¼(d − 1)2 holds; and Vinberg [8] improved this result by showingThe inequality (1) also holds for presentations of nilpotent Lie algebras (see [6]) (with the exception (d, r) = (2, 1)) and nilpotent associative algebras (see [4, 8, 6]). If the relations have of degree at least m ≥ 3 then more relations are needed. More precisely, Koch [5] has shown that the inequalityholds for finite p-groups, and the corresponding results hold for associative algebras and Lie algebras.