bluuebunny/crossref_metadata_2025_split huggingface dataset:
A semilinear elliptic eigenvalue problem, II. The plasma problem
Authors: Keady Grant , Norbury John 
Published: November 2011

SynopsisThis paper continues the study of the boundary value problem, for (λ, ψ)Here δ denotes the Laplacian,kis a given positive constant, and λ1will denote the first eigenvalue for the Dirichlet problem for −δ on Ω. For λ ≦ λ1, the only solutions are those with ψ = 0. Throughout we will be interested in solutions (λ, ψ) with λ > λ1and with ψ > 0 in Ω.In the special case Ω =B(0,R) there is a branch ℱe, of explicit exact solutions which bifurcate from infinity at λ = λ1and for which the following conclusions are valid, (a) The setAψ,is simply-connected, (b) Along ℱe, ψm→k, ‖ψ‖1→ 0 and the diameter ofAψtends to zero as λ → ∞, whereHere it is shown that the above conclusions hold for other choices of Ω, and in particular, for Ω = (−a, a)×(−b, b). (Existence is settled in Part I, and elsewhere.)The results of numerical and asymptotic calculations when Ω = (−a, a)×(−b, b) are given to illustrate both the above, and some limitations in the conclusions of our analysis.
An index theorem and Bendixson's negative criterion for certain differential equations of higher dimension
Authors: Smith Russell A. 
Published: November 2011

SynopsisPoincaré's theorem on the sum of the indices of a plane autonomous differential equation at its critical points inside a periodic orbit is here extended to the periodic orbits of higher-dimensional equations under certain conditions. Under the same conditions, higher-dimensional extensions are obtained of some theorems of Bendixson and others which exclude periodic orbits from regions in which the differential equation haspositive divergence. The application of these results to feedback control equations is also considered.
Naturally ordered regular semigroups with a greatest idempotent
Authors: Blyth T. S. , McFadden R. 
Published: November 2011

SynopsisWe consider ordered regular semigroups in which the order extends the natural order on the idempotents, and which are graced with the presence of a greatest idempotent. This implies that every element has a greatest inverse. An investigation into the properties ofthese special elements allows a description of Green's relations on the subsemigroup generated by the idempotents. This in turn leads to a complete description of the structure of idempotent-generated naturally ordered regular semigroups having a greatest idempotent. The smallest such semigroup that is not orthodox is also described. These results lead us to obtain structure theorems in the general case with the added condition that Green's relations be regular. Finally, necessary and sufficient conditions for such a semigroup to be a Dubreil-Jacotin semigroup are found.
Necessary and sufficient conditions for asymptotic decay of oscillations in delayed functional equations
Authors: Chen Lu-San , Yeh Cheh-Chih 
Published: November 2011

SynopsisThis paper studies the equationwhere the differential operator Ln is defined byand a necessary and sufficient condition that all oscillatory solutions of the above equation converge to zero asymptotically is presented. The results obtained extend and improve previous ones of Kusano and Onose, and Singh, even in the usual case wherewhere N is an integer with l≦N≦n–1.
The lattice of congruences on direct products of cyclic semigroups and certain other semigroups
Authors: Trueman D. C. 
Published: November 2011

SynopsisLet W be a semigroup with W\W2 non-empty, such that if ρ is a congruence on W with xpy for all x, y= W\W2, then zpw for all z, w= W2. We prove that the lattice of congruences on W is directly indecomposable, and conclude that a direct product of cyclic semigroups, with at least two non-group direct factors, has a directly indecomposable lattice of congruences. We find that the lattice of congruences on a direct product S1×S2×V of two non-trivial cyclic semigroups S1 and S2, one not being a group, and any other semigroup V, is not lower semimodular, and hence, not modular. We then prove that any finite ideal extension of a group by a nil semigroup has an upper semimodular lattice of congruences, and conclude that a finite direct product of finite cyclic semigroups has an upper semimodular lattice of congruences.
Proof of a conjecture of Race
Authors: Niessen Heinz-Dieter 
Published: November 2011

SynopsisThe following conjecture of Race will be proved: if τ is a formally J-symmetric quasi-differential expression on a real interval I, such that for some λ = ℂ all solutions of τy = τy belong to L2(I), then λ belongs to the regularity field of the minimal operator To generated by τ in L2(l).
On a class of evolution problems
Authors: Fichera Gaetano 
Published: November 2011

SynopsisA class of evolution problems is investigated [see (1.5), (1.6), (1.7) of the present paper] which includes, as a particular case, an evolution problem previously considered by a different author. Existence and uniqueness theorems are given in several function spaces. It is shown that, when the solution is required to belong to spaces of smooth functions, the problem becomes overdetermined. The necessary and sufficient integro-differential equations, to be satisfied by the datum, for the existence of a smooth solution, are given.
Estimates for the state density for ordinary differential operators with white gaussian noise potential
Authors: Moscatelli V. B. , Thompson M. 
Published: November 2011

SynopsisThe present paper is concerned with developing the existence and asymptotic properties of the state density N(λ) associated with certain higher order random ordinary differential operators A of the formwhere Ao has homogeneous and ergodic coefficients with respect to the σ-algebra generated by the Wiener process q(ω, x). The analysis uses the Weyl min-max principle to determine rough upper and lower bounds for N(λ).
On a conjecture related to the number of solutions of a nonlinear Dirichlet problem
Authors: Lazer A. C. , McKenna P. J. 
Published: November 2011

SynopsisIn an earlier paper (1981), the present authors made a conjecture about the number of solutions of a semilinear elliptic boundary value problem which has been investigated extensively in the past decade. The conjecture is proved in the one-dimensional case.
The linear growth of localized disturbances in unstable compressible flows
Authors: Candler S. , Craik A. D. D. 
Published: November 2011

SynopsisAccurate computation of the evolution of initially localized disturbances in compressible parallel flows is a tedious task requiring superposition of a large number of Fourier modes with differing temporal growth rates. An alternative approximate method, similar to that developed by Craik (1981, 1982) for viscous incompressible flows, is presented here. This involves asymptotic evaluation, by the saddle point method, of a double Fourier integral representation of the disturbance, with the actual dispersion relation replaced by a simpler analytic expression containing several parameters which may be adjusted to approximate the flow under investigation. Limiting cases yield informative results in simple closed form: these exemplify the possible shapes into which the disturbance may evolve. In particular, ‘splitting’ of the disturbance into two dominant regions is demonstrated.
Uniqueness of positive solutions for a class of elliptic boundary value problems
Authors: Castro Alfonso , Shivaji Ratnasingham 
Published: November 2011

SynopsisUniqueness of non-negative solutions conjectured in an earlier paper by Shivaji is proved. Our methods are independent of those of that paper, where the problem was considered only in a ball. Further, our results apply to a wider class of nonlinearities.
On the topological structure of the set of generalized solutions of the catenary problem
Authors: Alexander J. C. , Reeken Michael 
Published: November 2011

SynopsisThe global topological structure of the space of configurations of a non-rotating elastic string under compression and tension is studied. The part of the string under tension is specified by a measurable subset of the interval. The set of such intervals, with the Hausdorff topology, is considered a parameter space for the equation satisfied by the string, and the solutions are shown to form an infinitedimensional continuum over this parameter space. A new global topological theorem is needed, since the parameter space is not Euclidean. The topological theorem is based on the fixed-point transfer.
On normal families and a result of Drasin
Authors: Langley J. K. 
Published: November 2011

SynopsisWe prove the following: suppose that a and b are complex numbers, with a non-zero, and that n is an integer not less than 5. Then, if F is a family of functions meromorphic in a plane domain Dsuch that, for each f in F, the equationhas no solutions in D, then F is normal in D.
Large time estimates for solutions to the porous medium equation with nonintegrable data via comparison
Authors: Alikakos Nicholas D. , Rostamian Rouben 
Published: November 2011

SynopsisWe consider the Cauchy problem for the porous medium equation in one space dimension, with initial data which are locally integrable. We measure the asymptotic behaviour of the initial data near infinity in an integral sense and relate this to the pointwise rate of growth or decay of solution for large time. The emphasis is on a novel comparison method wherein the initial data are rearranged on the ×-axis to form a sequence of Dirac δ-masses. By using the explicit solution in the latter case, we derive upper and lower bounds for the solution to the original problem by comparisons.
On the periodic solution of the Van der Pol oscillator with large damping
Authors: El-Abbasy E. M. 
Published: November 2011

SynopsisLittlewood showed that the forced Van der Pol oscillator with 0<b<⅔ and k large normally has subharmonic solutions of order 2n + l where n ≅ O([⅔−b]k). Numerical experiments suggest that n ≅ (⅔ –b)k/3 as k →∞. A refinement of Littlewood's calculation is given which leads to this result.
Asymptotic solutions to linear differential equations with coefficients of the power order of growth, 1
Authors: Lantsman M. H. 
Published: November 2011

SynopsisWe consider a method for determining the asymptotic solution to a sufficiently wide class of ordinary linear homogeneous differential equations in a sector of a complex plane or of a Riemann surface for large values of the independent variable z. The main restriction of the method is the condition that the coefficients in the equation should be analytic and single-valued functions in the sector for | z | ≫ 1 possessing the power order of growth for |z| → ∞. In particular, the coefficients can be any powerlogarithmic functions. The equationcan be taken as a model equation. Here ai are complex numbers, aij are real numbers (i = 1,2,…, n; j = 0, 1, …, m) and ln1 Z≡ln z, lnsz= lnlnS−1z = S = 2, … It has been shown that the calculation of asymptotic representations for solution to any equation in the class considered may be reduced to the solution of some algebraic equations with constant coefficients by means of a simple and regular procedure. This method of asymptotic integration may be considered as an extension (to equations with variable coefficients) of the well known integration method for linear differential equations with constant coefficients. In this paper, we consider the main case when the set of all roots of the characteristic polynomial possesses the property of asymptotic separability.
Deficiency zero presentations for certain perfect groups
Authors: Campbell C. M. , Robertson E. F. , Kawamata T. , Miyamoto I. , Williams P. D. 
Published: November 2011

SynopsisIn this paper we give two generator, two relation presentations for the following perfect groups which were not previously known to have deficiency zero: SL(2, 32), SL(2, 64), SL(2, 27), SL(2, 49), Â7, Ŝz(8), SL(2, 5) × SL(2, 5), SL(2, 5) × SL(2, 25). We also give two generator, two relation presentations for three other finite perfect groups, two having SL(2, 7) as an image and one having SL(2, 5) as an image. We also discuss presentations for certain other perfect groups which were known to have deficiency zero and find some neat new presentations for them.
Boundary conditions and the Cayley transform
Authors: Zahreddine Z. 
Published: November 2011

SynopsisSelf-adjoint operators in L2(0, 1) associated with a formally symmetric differential operator regular in [0, 1] can be determined by boundary conditions or as extensions of the minimal operator. These extensions are determined by extensions of the Cayley transform of the minimal operator. This paper establishes an explicit expression for the extension of the Cayley transform in terms of the boundary conditions and vice versa.
The Steiner system S(5,8, 24) constructed from dual affine planes
Authors: Kadir G. A. , Key J. D. 
Published: November 2011

SynopsisWe construct firstly a single tactical configuration which has the structure of the dual of the affine plane of order 4, and show how to obtain a further set of 3 such dual planes which, together with , satisfy a certain set of intersection properties. This set of 4 dual planes is used to extend the 20 points of to the Steiner system = S(5, 8, 24). The construction leads to the production of involutions of the type which fix the points of an octad. It is shown that 3 involutions each of this type suffice to generate M24, each of the simple Mathieu groups inside M24, the Todd group, and all the intransitive maximal subgroups of M24.
Dynamical modelling of phase transitions by means of viscoelasticity in many dimensions
Authors: Rybka Piotr 
Published: November 2011

SynopsisWe study the equations of viscoelasticity in a multidimensional setting for the ‘no-traction’ boundary data. For the sake of modelling phase transitions we do not assume elliptieity of the stored energy function W. We construct dynamics in W1,2(Ωℝn) globally in time. Next, we study the question of stability for a class of equilibria. Moreover, we show a certain kind of decay in time of solutions for arbitrary initial conditions.
Positive perturbations of self-adjoint Schrödinger operators
Authors: Kappeler Th. 
Published: November 2011

SynopsisIn this paper, we prove that a positive perturbation T = T0 + q (q ≧ 0 and in ) of an essentially self-adjoint Schrödinger operator T0 = −Δ + q0 on is again essentially self-adjoint if T is relatively bounded with respect to T0. An application of the method of the proof to positive approximations of elements u ≧ 0 in D(T) by a positive sequence in is given.
Nonlinear problems with strong resonance at infinity: an abstract theorem and applications
Authors: Capozzi A. , Salvatore A. 
Published: November 2011

SynopsisIn this paper, we consider the equationwhere A is a linear operator, N = ψ′ with ψ ∈ C1(E, R), and E is an Hilbert space. We suppose that N has a derivative at infinity N′(∞) and that 0 belongs to the spectrum of A–N′(∞). We prove an abstract theorem for multiplicity of solutions for the above equation. We then apply this theorem to the study of periodic solutions of Hamiltonian systems and of semilinear wave equations when the period is prescribed.
On the sign of the solutions to some semilinear Dirichlet problems
Authors: Cafagna Vittorio , Donati Flavio 
Published: November 2011

SynopsisWe study the sign of solutions to a class of semilinear Dirichlet problems when the nonlinearity is, for instance, a concave-convex function which interacts with the spectrum of the linear part. We are able to prove, in some cases, exact multiplicity results for positive and negative solutions. For the proofs we employ a device which splits the given problem into two others satisfying a suitable version of the Ambrosetti–Prodi result.
Extension and amalgamation in rings
Authors: Renshaw J. 
Published: November 2011

SynopsisIt is proved that if a ringRhas theextension propertyin containing ringSi, then the amalgam [R; Si,] is strongly embeddable. Using a result of P. M. Cohn, a necessary and sufficient condition for a ring to be an amalgamation base is then given. It is also shown thatRis alevelsubring of a ringSif and only ifS/Ris flat. From this, a classical result of P. M. Cohn on flat amalgams is proved.
Singularities of the inverses of Fredholm operators
Authors: Ramm A. G. 
Published: November 2011

SynopsisLet B(k) be a linear bounded mapping of a Banach space X into a Banach space Y meromorphic in the parameter k on a connected domain of the complex plane. Under certain assumptions on B(k), more general than previously considered, the singularities of the inverse operator are described.
Bubble growth in porous media and Hele–Shaw cells
Authors: Howison S. D. 
Published: November 2011

SynopsisWe consider the characterisation of a class of free boundary problems arising in the flow of a viscous liquid in a porous medium (or, in two dimensions, a Hele–Shaw cell). Injected air forms a bubble which grows as time increases; it is shown that three kinds of behaviour can occur. Firstly, the solution may cease to exist in finite time; secondly, the solution may exist for all time and the free boundary may have one or more limit points as t tends to infinity; and thirdly, the bubble may exist for all time and fill the whole space as t tends to infinity. Two-dimensional explicit examples arc given of all three types of behaviour, and it is proved that the only solutions of the third kind are those in which the bubble is always elliptical; the proof uses the theory of null quadrature domains. It is shown that solutions for ellipsoidal bubbles exist in three dimensions and it is conjectured that the only three-dimensional null quadrature domains with finite complement are those whose complement is an ellipsoid.
Ck centre unstable manifolds
Authors: Chow Shui-Nee , Lu Ke ning 
Published: November 2011

SynopsisWe consider the existence and smoothness of global centre unstable manifolds for finite and infinite dimensional flows or maps. We show that every global centre unstable manifold can be expressed as a graph of a Ck map, provided that the nonlinearities are Ck smooth. The proofs are based on a lemma by D. Henry on a necessary and sufficient condition for a Lipschitz map to be continuously differentiable.
On the maximum of solutions for a semilinear elliptic problem
Authors: Sweers Guido 
Published: November 2011

SynopsisIn this paper we study some properties of a semilinear elliptic eigenvalue problem with nondefinite right-hand side. In the first part we show that every solution will have its maximum in some specified interval J. If the domain is inside a cone in ℝN with N > 1, then J is strictly smaller than in the one-dimensional case. In the second part we show, for bounded domains, that if the maximum is inside some subinterval of J, then for any eigenvalue there will be at most one solution.
Maximal smoothness of solutions to certain Euler–Lagrange equations from nonlinear elasticity
Authors: Bauman Patricia , Phillips Daniel , Owen Nicholas C. 
Published: November 2011

SynopsisWe investigate the maximal smoothness of stationary states for the multiple integral = Such variational problems are motivated by the study of nonlinear elasticity. Assuming certain structure conditions for γ and given a stationary state , we derive an a priori LP estimate for for any p < ∞ in terms of and where . As a consequence, we show that a C1,β stationary state necessarily satisfies det and is of class C2, β in Ω. Nevertheless, singular stationary states do exist: we construct a nonsmooth C1 solution for a particular γ in two dimensions such that det in Ω and det vanishes at precisely one point in Ω.
Lower semicontinuity and continuity of functions of measures with respect to the strict convergence
Authors: Delladio S. 
Published: November 2011

SynopsisLet Ω be an open subset of Rn. It is well known that, given a suitable real-valued function f on Ω × Rk and a Rk -valued Borel measure µ on Ω, then one can define a real-valued measurefµ on Ω. The object of this note is to define the Ψ-strict convergence of the Rk-valued Borel measures µj to the Rk-valued Borel measure µ, where Ψ: Ω × Rk → [0, + ∞] is a continuous function which is positively homogeneous and convex in the Rk-variable, and to investigate the lower semicontinuity and continuity of the map µ → fμ with respect to the Ψ-strict convergence; here f is positively homogeneous in the Rk-variable and satisfies one suitable convexity condition (related to Ψ).
Conical functions with one or both parameters large
Authors: Dunster T. M. 
Published: November 2011

SynopsisUniform asymptotic expansions are derived for conical functions, Legendre functions of order µ and degree −½ + iτ, where µ and τ are non-negative real parameters. As τ → ∞, expansions are furnished for the conical functions which involve Bessel functions of order µ. These expansions are uniformly valid for 0 ≦ µ ≦ Aτ (A an arbitrary positive constant), and are also uniformly valid for Re (z) ≧ 0 in the complex argument case, and 0 ≦ z < ∞ in the real argument case. The case µ → ∞ is also considered, and expansions are furnished which are uniformly valid in the same z regions for 0 ≦ τ ≧ Bµ (B an arbitrary positive constant); in the cases where Re(z) ≧ 0 and 1 ≦ z < ∞, the expansions involve Bessel functions of purely imaginary order iτ, and in the case where 0 ≦ z < 1 the expansions involve elementary functions.
Topologically nilpotent Banach algebras and factorisation
Authors: Dixon P. G. 
Published: November 2011

SynopsisA Banach algebra A is said to be topologically nilpotent if sup {‖x1x2…xn‖1/n: xi ∈ A, ‖xi‖ ≦ 1 (1 ≦ i ≦ n)} tends to zero as n → ∞. A Banach algebra A is uniformly topologically nil if sup {‖xn‖ 1/n: x ∈ A, ‖x‖ ≦ 1} tends to zero as n → ∞. These notions are equivalent for commutative algebras and a topological version of the Nagata-Higman Theorem gives a partial result for the non-commutative case. Topologically nilpotent algebras have a strong non-factorisation property and this yields theorems of the type “factorisation implies the existence of arbitrarily slowly decreasing powers”. Extensions of topologically nilpotent algebras by topologically nilpotent algebras are topologically nilpotent.
The Signorini perturbation scheme in an abstract setting
Authors: Chillingworth D. R. J. 
Published: November 2011

SynopsisThe Signorini perturbation scheme is a series expansion algorithm that locates solution branches for a class of symmetry-breaking bifurcation problems in nonlinear elastostatics. The relationship of the formal steps in the algorithm to geometric aspects of the problem is brought out in work of J. E. Marsden and Y.-H. Wan, where an abstract formulation is also considered. In this paper, the abstract algorithm and its geometry are explored further: the logical structure is clarified, and it is shown how the scheme adapts to the presence of additional symmetry constraints.
The group of homotopy self-equivalences of non-simply-connected spaces using Postnikov decompositions
Authors: Rutter J. W. 
Published: November 2011

SynopsisWe give here a group extension sequence for calculating, for a non-simply-connected space X, the group of self-homotopy-equivalence classes which induce the identity automorphism of the fundamental group, that is the kernel of the representation → aut (π1(X)). This group extension sequence gives in terms of , where Xn is the n-th stage of a Postnikov decomposition. As special cases, we calculate for non-simply-connected spaces having at most two non-trivial homotopy groups, in dimensions 1 and n, as the unit group of a semigroup structure on ; and we calculate up to extension for non-simply-connected spaces having at most three non-trivial homotopy groups. The group is, for nice spaces, isomorphic to the groups and of self-homotopy-equivalence classes of X in the categories top*M and top M, respectively, where X→M = K1(π1(X)) is a top fibration which determines an isomorphism of the fundamental group; and our results are obtained initially in topM.