bluuebunny/crossref_metadata_2025_split huggingface dataset:
Smooth conjugacy of centre manifolds
Authors: Burchard Almut , Deng Bo , Lu Kening 
Published: November 2011

SynopsisIn this paper, we prove that for a system of ordinary differential equations of classCr+1,1,r≧0 and two arbitrary Cr+1, 1local centre manifolds of a given equilibrium point, the equations when restricted to the centre manifolds areCrconjugate. The same result is proved for similinear parabolic equations. The method is based on the geometric theory of invariant foliations for centre-stable and centre-unstable manifolds.
A monotone method for a system of nonlinear parabolic differential equations
Authors: Chandra Jagdish , Dressel Francis G. , Norman Paul Dennis 
Published: November 2011

SynopsisA monotone iteration scheme for the solution of the initial boundary problems associated with a system of semilinear parabolic differential equations has been developed that does not require the nonlinearities to be quasimonotone. The class of equations to which this scheme applies includes physical models that describe combustion processes involving Arrhenius reaction terms.
On the structure of the set of solutions of certain holomorphic two-point boundary value problems
Authors: Hassan H. S. , Lloyd N. G. 
Published: November 2011

SynopsisSuppose that f: ℝ×ℂN→ℂN is holomorphic in z and continuous in t, and that Φ: ℂN×ℂN→ℂN is holomorphic. Boundary value problems of the formare considered. The particular interest is in the structure and topological properties of the set of solutions. The paper is motivated by the corresponding properties of the set of periodic solutions of ż = f(t, z) when f is periodic in t. Consideration of this complex equation gives information about the periodic solutions of the real equation ẋ = f(t, x).
Global regularity and formation of singularities of solutions to first order quasilinear hyperbolic systems
Authors: Da-tsin(Li Ta-tsien) Lee 
Published: November 2011

SynopsisFor the Cauchy problem for strictly hyperbolic systems with general eigenvalues, we obtain existence of global smooth solutions under certain conditions on the composition of the eigenvalues and the initial data; on the other hand, we give a sufficient condition which guarantees that singularities of the solution must occur in a finite time and describe certain applications. The present paper includes the corresponding results in earlier papers by several authors as special cases.
Orthogonal polynomials satisfying fourth order differential equations
Authors: Krall Allan M. 
Published: November 2011

SynopsisThese polynomials, which are intimately connected with the Legendre, Laguerre and Jacobi polynomials, are orthogonal with respect to Stieltjes weight functions which are absolutely continuous on (− 1, 1), (0, ∞) and (0, 1), respectively, but which have jumps at some of the intervals' ends. Each set satisfies a fourth order differential equation of the form Ly = λny, where the coefficients of the operator L depends only upon the independent variable. The polynomials also have other properties, which are usually associated with the classical orthogonal polynomials.
A note on linear hyperbolic evolution equations
Authors: Grabmüller Hans 
Published: November 2011

SynopsisGiven the linear hyperbolic evolution equation (P0) on a reflexive Banach space, we present a new method for an existence proof of unbounded solutions admitting an exponential growth rate as time tends to infinity. Utilizing abstract Wiener—Hopf techniques, an operational calculus is developed for the construction of the resolving operator associated with the problem under consideration. The results are based upon the fundamental hypothesis that the spectral set of the time-independent mapping A is contained in the interior of a parabola. The distance of the focus from the vertex of this parabola turns out to be a measure for the growth rate. Applicability of the results is shown in the case where A is a non-symmetric perturbation of a self-adjoint partial differential operator.
The assimilation of a strong, two-dimensional laminar jet into an aligned uniform stream
Authors: Wilks Graham , Hunt Roland 
Published: November 2011

SynopsisA comprehensive appraisal of the title problem is presented in terms of a characterizing nondimensional co-ordinate ξ which is based upon the half excess of the momentum of the jet, J. Perturbation features of the problem appear as regular and singular boundary conditions in ξ upstream and downstream respectively. The conservation of momentum excess provides a monitor on the consistency of regular and singular perturbation series solutions. In particular the conservation constraint on the downstream singular perturbation solution confirms the inadequacy of expansions in inverse half powers of ξ and justifies formally the introduction of logarithmic terms.The formulation provides the basis for a complete numerical integration over the semi-infinite region. Accordingly detailed knowledge of velocity excess along the axis of the jet is obtained and an undetermined coefficient in the asymptotic downstream perturbation solution may be estimated.
On the spectra of non-self-adjoint realisations of second-order elliptic operators
Authors: Evans W. D. 
Published: November 2011

SynopsisLet τ denote the second-order elliptic expressionwhere the coefficients bj and q are complex-valued, and let Ω be a spherical shell Ω = {x:x ∈ ℝn, l <|x|<m} with l≧0, m≦∞. Under the conditions assumed on the coefficients of τ and with either Dirichlet or Neumann conditions on the boundary of Ω, τ generates a quasi-m-sectorial operator T in the weighted space L2(Ω;w). The main objective is to locate the spectrum and essential spectrum of T. Best possible results are obtained.
On the swirling flow between rotating coaxial disks, asymptotic behaviour, II
Authors: Kreiss Heinz Otto , Parter Seymour V. 
Published: November 2011

SynopsisConsider solutions 〈H(x, ε), G(x, ε)〉 of the von Kármán equations for the swirling flow between two rotating coaxial disksandWe assume that |H(x, ε)| + |Hʹ(x, ε)| + |G(x, ε)|≦B. This work considers shapes and asymptotic behaviour as ε→0+. We consider the type of limit functions 〈H(x), G(x)〉 that are permissible. In particular, if 〈H(x, ε), G(x, ε)〉 also satisfy the boundary conditions H(0, ε)=H(1, ε)=0, Hʹ(0, ε)=Hʹ(1, ε)=0 then H(x) has no simple zeros. That is, there does not exist a point Z ε [0, 1] such that H(x)=0, Hʹ(z)≠0. Moreover, the case of “cells” which oscillate is studied in detail.
Almost-periodic forcing for a wave equation with a nonlinear, local damping term
Authors: Haraux Alain 
Published: November 2011

SynopsisLet Ω⊂ℝnbe a bounded open domain and T = ∂Ω. It β is a maximal monotone graph in ℝ×ℝ with 0ϵβ(0), and f: ℝ×Ω→ℝ is measurable with t→ f(t,.) S2-almost periodic as a function ℝ→L2(Ω), we consider the nonlinear hyperbolic equationWe show that:(i) if ゲ is strictly increasing and (1) has a solution ω on ℝ with [ω, Əω/Ət] almost periodic: , for any solution of (1) there exists with u(t,.)–ω(t,.)—ξin (ii) if β is single valued and everywhere defined, the existence of ω as above implies that, for every solution of (1), there exists Ϛ(t, x) with ә2Ϛ/әt2–0△Ϛ = in ℝ×Ω and u(t,.)–ω(t,.)—0 in as t → +∞(iii) if β–1 is uniformly continuous and ゲ satisfies some growth assumption (depending on N), for every f as above, there exists ω solution of (1) on ℝ with [ω, Əω/Ət] almost periodic: ℝ → .
The distribution of the values of a random power series in the unit disk
Authors: Jakob Matthias , Offord A. C. 
Published: November 2011

SynopsisThis is a study of the family of power series where Σ αnZn has unit radius of convergence and the εn are independent random variables taking the values ±1 with equal probability. It is shown that ifthen almost all these power series take every complex value infinitely often in the unit disk.
Remarks on the singularity indices of Arnol'd and Berry
Authors: Chillingworth David , Romero-Fuster Carmen 
Published: November 2011

SynopsisWe give a coordinate-free algebraic interpretation for singularity indices of quasihomogeneous functions and their unfoldings, as first exploited systematically by Berry in statistical optics. We also make some observations on geometric interpretation, on formulae for indices, and on the difficulties of rigorous treatment for non-quasihomogeneous functions.
Regular solutions of wave equations containing nonlinearities of the type L Φ L
Authors: Weyer Jürgen 
Published: November 2011

SynopsisRegular solutions of the forced nonlinear wave equation uu + L4u + LΦLu = r are studied in Hilbert spaces. L is a linear, positive, selfadjoint operator and the nonlinear nucleus Φ(u) = f(|u|2)u is generated by a C1-function f, such that LΦ(Lu) = f(|Lu|2)L2u. If the initial value data u(0) = ϕ and u1(0) = ψ belong to the domain D(Lk+4) and D(Lk+2), respectively, and if rεD(Lk), then there is a (global) solution u(t) such that u ε D(Lk+4), ut ε D(Lk+2) and uuε D(Lk) for all times t. The abstract result is applied to examples in nonlinear elasticity theory.
Subvarieties of the class of MS-algebras
Authors: Blyth T. S. , Varlet J. C. 
Published: November 2011

SynopsisIn a previous publication (1983), we defined a class of algebras, denoted by MS, which generalises both de Morgan algebras and Stone algebras. Here we describe the lattice of subvarieties of MS. This is a 20-element distributive lattice. We then characterise all the subvarieties of MS by means of identities. We also show that some of these subvarieties can be described in terms of three important subsets of the algebra. Finally, we determine the greatest homomorphic image of an MS-algebra that belongs to a given subvariety.
Linearization stability and Signorini Series for the traction problem in elastostatics
Authors: Marsden J. E. , Wan Y. H. 
Published: November 2011

SynopsisThis paper uses previous results of Chillingworth, Marsden and Wan on symmetry and bifurcation for the traction problem in three dimensional elastostatics to establish new results on the Signorini expansion. We show that the Signorini compatibility conditions are necessary and sufficient for linearization stability and analogies with results known for other field theories are pointed out. Under an explicit non-degeneracy condition, a new series expansion is given in which successive terms are inductively determined in pairs rather than singly. Our results include as special cases, classical results of Signorini, Tolotti and Stoppelli.
On Schauder bases in Hardy spaces
Authors: Oswald P. 
Published: November 2011

SynopsisIt is proved that in the case ½<p<l the periodic Franklin system forms a Schauder basis for the real Hardy space Hp(T) defined on the one-dimensional torus.In this note we prove the followingTheorem. The periodic Franklin system forms a Schauder basis in the real Hardyspace Hp(T) defined on the one-dimensional torus if ½<p< l.
On integral transformations with G-function kernels
Authors: Rooney P. G. 
Published: November 2011

SynopsisIntegral transformations T of the formal formwhere G is a Meijer-G function are studied on the spaces ℐμ,r of functions f such thatResults are obtained on the boundedness, representation and range of the transformations, and on when they have an inverse of the same formal form.
The breadth of the lattice of those varieties of inverse semigroups which contain the variety of groups
Authors: Reilly Norman R. 
Published: November 2011

SynopsisThe relations v1 and v2 defined on the lattice ℒ of varieties of inverse semigroups by v1 if and only if and v2 if and only if , where denotes tie variety of groups, are both congruences on ℒ the class v1, is simply the lattice of varieties of grcups and is therefore known to have cardinality .The class v2 is precisely the sublattice of ℒ consisting of those varieties containing . Each v1-class contains preciselyone element of v2. The main result of this paper establishes that the sublattice v2 of ℒ has breadth . From this it follows that the lattice ℒ/v1 also has breadth . Some consequences concerning varieties generated by fundamental inverse semigroups are also considered.
Qualitative theory for hyperbolic characteristic initial value problems
Authors: Kreith Kurt , Pagan Gordon 
Published: November 2011

SynopsisCharacteristic initial value problems associated with hyperbolic equations of the form uxy + g(x, y)u = 0 are considered for (x, y)∈ℝ+× ℝ+. New criteria for the existence of a nodal line asymptotic to the axes are established, as are criteria for the existence of a zero beyond such a nodal line. Some numerical solutions are presented in graphical form and discussed relative to what is known about oscillation properties of such problems.
A perturbation method and the limit-point case of even order symmetric differential expressions
Authors: Mergler Bernhard , Schultze Bernd 
Published: November 2011

SynopsisWe give a new perturbation theorem for symmetric differential expressions (relatively bounded perturbations, with relative bound 1) and prove with this theorem a new limit-point criterion generalizing earlier results of Schultze. We also obtain some new results in the fourth-order case.
The Rothe method for the wave equation in several space dimensions
Authors: Martensen Erich 
Published: November 2011

SynopsisThe interior initial-boundary value problem for the wave equation in m ≧ 1 space dimension is considered for vanishing boundary values. Certain regularity, dependent on m, is required for the solution and additionalboundary conditions, the number of which being also dependent on m, are imposed on the given right hand side. Emphazising the case m = 3, the Rothe method is applied after the problem has been rewritten as a hyperbolic first order evolution problem for m + 1 unknown functions. The sequence of discrete solutions obtained is shown to be discretely convergent to the continuous solution in the sense of uniform convergence if the solution of the continuous problem is assumed to exist. A priori estimates are derived both for the discrete solutions and the continuous solution.
On diffracted wave fronts
Authors: Wolfe Peter 
Published: November 2011

SynopsisIn this paper we study the wave equation, in particular the propagation of discontinuities. Two problems are considered: diffraction of a normally incident plane pulse by a plane screen and diffraction of a spherical wave by the same screen. It is shown that when an incident wave front strikes the edge of the screen a diffracted wave front is produced. The discontinuities are precisely computed in a neighbourhood of the edge for a small time interval after the arrival of the incident wave front and a theorem of Hörmander on the propagation of singularities is used to obtain a globalresult.
Some loci in S5 associated with systems of conics in a plane
Authors: Knight A. J. 
Published: November 2011

SynopsisIf the conic α, a0x2 + a1y2 + a2z2 + 2a3yz + 2a4zx + 2a5xy=0, is represented by the point (a0, a1, a2, a3, a4, a5) of S5, the transforms of α by projectivities that fix a second conic ω will generally be represented by points of a threefold in S5 containing (a0, a1,…, a5). It is shown that this threefold is in general a rational sextic belonging to an ∞2 family, that is composed of ∞1 sets of projectively equivalent threefolds. Special, exceptional members of the family are discussed.Equations for the threefold are found in terms of the mutual projection invariants of ω and α.
A multiplicity result for a class of elliptic boundary value problems
Authors: Amann Herbert , Hess Peter 
Published: November 2011

SynopsisWe consider a mildly nonlinear elliptic boundary value problem depending on a parameter. Given appropriate hypotheses concerning the asymptotic behaviour of the nonlinearity, we derive lower bounds on the number of solutions. The results complement an earlier theorem due to Kazdan and Warner [6].
A simpler proof of two inequalities of Brodlie and Everitt
Authors: Beesack P. R. 
Published: November 2011

SynopsisIn 1975 K. W. Brodie and W. N. Everitt dealt with integral inequalities of the formin the two casesT= ℝ,T= ℝ+, and obtained the best possible constantsKT(μ)for all μ ε ℝ. The proof was not elementary, but an elementary proof was given in 1977 by E. T. Copson. This note shows how Copson's method can be greatly simplified so as to obtain the results in a more straightforward manner.
Bounds for the point spectra of separated Dirac operators
Authors: Evans W. D. , Harris B. J. 
Published: November 2011

SynopsisIn this paper real numbers A1, A2 are obtained which are such that for λ > A1 or λ < A2 there are no non-trivial solutions of the equationwhich are in L2(a,∞) for some a>0. Precise values for A1 and A2 are obtained in certain cases.
Existence and multiplicity result for a class of second order elliptic equations
Authors: Hofer Helmut 
Published: November 2011

SynopsisSome second order semilinear elliptic boundary value problems of the Ambrosetti-Prodi-type are studied. Existence and multiplicity of solutions is proved in dependence on a parameter. Constructing a global strongly increasing fixed point operator in a suitable function space, observing - under appropriate conditions, which are in some sense optimal–that the fixed point operator has some properties similar to a strongly positive linear endomorphism, one unifies and improves the treatment of such problems, whether the nonlinearity is dependent on the gradient or not, and obtains some new results.
Groups of units of zero ternary quadratic forms
Authors: Maclachlan Colin 
Published: November 2011

SynopsisThe groups of units of indefinite ternary quadratic forms with rational integer coefficients contain subgroups of index two which are isomorphic to Fuchsian groups and which, for zero forms, are commensurable with the classical modular group. This is used to obtain a family of forms whose groups are representatives of the conjugacy classes of maximal groups associated with zero forms. The signatures of the groups of the forms in this family are determined and it is shown that the group associated to any zero form is isomorphic to a subgroup of finite index in the group of one of three particular forms. This last result should be compared with the corresponding result by Mennicke on non-zero forms.
A class of bisimple, idempotent-generated congruence-free semigroups
Authors: Howie J. M. 
Published: November 2011

SynopsisLet X be a set with infinite regular cardinality m. Within the full transformation semigroup ℑ(X) a subsemigroup Sm is described which is bisimple and idempotent-generated. Its minimum non-trivial homomorphic image has both these properties and is also congruence-free. The semigroup contains an isomorphic copy of every semigroup having order less than m.
Boundary value problems for the vibrating string equation
Authors: Sleeman B. D. 
Published: November 2011

SynopsisDirichlet, Neumann and mixed boundary value problems for the equation uxx −uyy = 0 are considered for a variety of rectangular domains. Uniqueness of solutions to these non-well-posed problems is considered by separation of variables methods. The question of uniqueness is also discussed for domains other than rectangles.
Elliptic transmutation I
Authors: Carroll Robert 
Published: November 2011

SynopsisGiven and similar , modelled on radial Laplace-Beltrami operators (ρp = , in this paper we begin the study of transmutations which leads to elliptic equations Working with and transmutations Qm → −D2 for m > −½ and −D2 → for m < −½, we obtain a transmutation formulation and derivation of many results of generalized axially symmetric potential theory in the first case and in both cases generalized Hilbert transforms (different). Canonical generalizations are then automatic using general transmutation theory.
Gradient estimates for degenerate diffusion equations II
Authors: Alikakos Nicholas D. , Rostamian Rouben 
Published: November 2011

SynopsisWe establish upper and lower bounds for various norms of solutions and their gradients for the equation ut = div (|∇u|m−1 ∇u) in ℝN in terms of the norms of the initial data. Based on the L∞ estimate of ∇u, we conclude that u(x, t) is Lipschitz continuous in space-time, for all t>0, whenever u(x,0) is in L1(ℝN).
Analogues of the bicyclic semigroup in simple semigroups without idempotents
Authors: Jones Peter R. 
Published: November 2011

SynopsisBy an important theorem of Andersen, any semigroup, containing idempotents, which is simple but not completely simple contains a copy of the bicyclic semigroup B = 〈a, b | ab = 1〉. In this paper the semigroups A = 〈a, b | a2b = a〉 and C = 〈a, b | a2b = a, ab2 = b〉 are shown to play a similar role in various classes of simple semigroups without idempotents, particularly in those for which Green's relation is nontrivial. For example it is shown that every right simple semigroup without idempotents is a union of copies of A; every finitely generated simple semigroup without idempotents contains either A or C. In a generalisation of a different sort it is shown that the bicyclic semigroup divides every simple semigroup without idempotents.Similar results are obtained for 0-simple semigroups without nonzero idempotents.
Some second-order systems of partial differential equations of composite type
Authors: Wei Lin 
Published: November 2011

SynopsisThe Cauchy problem and the Dirichlet-Cauchy type problem of some second-order systems of partial differential equations of composite type of two unknown functions are investigated. Such systems possess some of the characteristics not only of elliptic but also of hyperbolic systems in the same domain. Representations of the solutions are found for the upper half plane. To this end, the composite systems are reduced to the canonical form by means of successive applications of three kinds of linear transformations. Function theoretic methods are used to obtain representation formulae. Furthermore, some composite systems of 2m-unknown function are also considered.
E-unitary regular semigroups
Authors: Szendrei Mária B. 
Published: November 2011

SynopsisLet S be an E-unitary regular semigroup and V a variety of bands. We prove that S can be embedded into a semidirect product of a band from V by a group if and only if S can be embedded in a canonical way into the semidirect product of the free band in V over a well-determined partial semigroup by the greatest group homomorphic image of S. Moreover, we show that every E-unitary regular semigroup with regular band of idempotents E can be embedded into a semidirect product of a band B by a group, where B belongs to the variety of bands generated by E.
Quasilinear Hamiltonian systems
Authors: Rogulski Jan S. 
Published: November 2011

SynopsisWe consider quasilinear systems of 2N partial differential equations with 2N unknown functions depending on n + 1 variables as evolution systems on the space L2(Rn, RN) × L2(Rns, RN) endowed with a symplectic form induced by the standard scalar product on L2(Rn, RN). The necessary and sufficient conditions for such a system to be a Hamiltonian system are derived. The main purpose of this paper is to propose a straightforward link between the symplectic approach formulated by Chernoff, Hughes and Marsden and the multisymplectic formulations of evolution systems created by Kijowski and developed by Gawedzki and Kondracki. A general method of constructing the multisymplectic form and the Hamiltonian form for these systems is given.