bluuebunny/crossref_metadata_2025_split huggingface dataset:
Nondassical eigenvalue distribution of one-dimensional Schrödinger operators
Authors: Klaus M. 
Published: November 2011

SynopsisWe consider differential operators of the form H = −d2/dx2 + q(x) acting on u ∈ L2(0,∞) with boundary condition u(0) = 0. The potential q(x) is such that H has essential spectrum [0,∞) and an infinite sequence of negative eigenvalues converging to zero. Let n(E) denote the number of eigenvalues of H which are less than E. Under certain conditions on q(x), the well-known formula n(E)∼(2φ)−1 vol {x, p | p2 + q(x)<E}, E↑0, holds. We shall study the validity of this formula for potentials which show oscillatory behaviour as x →∞, like e.g. q(x) = −(1 + x)−α(a + b sin x) with 0<α <2, a≧0, b≠0. We shall obtain the leading-order behaviour of both n(E) and vol n(E)∼(2φ)−1 vol {x, p | p2 + q(x)<E} as E↑0 for a certain class of q's, and we shall see that the classical formula fails in most cases, but there are some noteworthy exceptions.
Symmetry sets
Authors: Bruce J. W. , Giblin P. J. , Gibson C. G. 
Published: November 2011

SynopsisFor a smooth manifold M ⊆ ℝn, the symmetry set S(M) is defined to be the closure of the set of points u∈ℝn which are centres of spheres tangent to M at two or more distinct points. (The idea has its origin in the theory of shape recognition.) The connexion with singularities is that S(M) can be described alternatively as the levels bifurcation set of the family of distance-squared functions on M. In this paper a multi-germ version of the standard uniqueness result for versal unfoldings of potential functions is used to obtain a complete list of local normal forms (up to diffeomorphism) for the symmetry sets of generic plane curves, generic space curves, and generic surfaces in 3-space. For these cases the authors verify that M can be recovered as the envelope of a family of spheres centred at smooth points of S(M).
A general monotone scheme for elliptic systems with applications to ecological models
Authors: Korman Philip , Leung Anthony W. 
Published: November 2011

SynopsisWe consider weakly-coupled elliptic systems of the typewith each fi being either an increasing or a decreasing function of each uj. Assuming the existence of coupled super- and subsolutions, we prove the existence of solutions, and provide a constructive iteration scheme to approximate the solutions. We then apply our results to study the steady-states of two-species interaction in the Volterra–Lotka model with diffusion.
Minimum action solutions of non-linear elliptic equations in unbounded domains containing a plane
Authors: Kavian Otared 
Published: November 2011

SynopsisLet d ≧ 1 be an integer and ω ⊂ℝd a smooth bounded domain and consider the elliptic equation − Δu = g(u) on Ω = ℝ2 × ω. We prove that under (almost) necessary and sufficient conditions on the continuous function g: ℝm→ ℝm the above equation has a minimum-action solution.
A nilpotent-generated semigroup associated with a semigroup of full transformations
Authors: Howie John M. , Marques-Smith M. Paula O. 
Published: November 2011

SynopsisLet X be a set with infinite regular cardinality m and let ℱ(X) be the semigroup of all self-maps of X. The semigroup Qm of ‘balanced’ elements of ℱ(X) plays an important role in the study by Howie [3,5,6] of idempotent-generated subsemigroups of ℱ(X), as does the subset Sm of ‘stable’ elements, which is a subsemigroup of Qm if and only if m is a regular cardinal. The principal factor Pm of Qm, corresponding to the maximum ℱ-class Jm, contains Sm and has been shown in [7] to have a number of interesting properties.Let N2 be the set of all nilpotent elements of index 2 in Pm. Then the subsemigroup (N2) of Pm generated by N2 consists exactly of the elements in Pm/Sm. Moreover Pm/Sm has 2-nilpotent-depth 3, in the sense that
Lattice isomorphisms of Malcev algebras
Authors: Elduque Alberto 
Published: November 2011

SynopsisThe lattice of subalgebras of a Malcev algebra determines to a great extent the structureof the algebra. It is shown that conditions such as nilpotency, solvability or semisimplicity are almost characterised by means of conditions on this lattice. This enables us to study the relationship between Malcev algebras with isomorphic lattices of subalgebras.
Almost-everywhere injectivity in nonlinear elasticity
Authors: Qi Tang 
Published: November 2011

SynopsisThis paper gives a sufficient condition for almost-everywhere injectivity for nonlinear three dimensional elasticity similar to that of Claret-Necas [8], namely.We prove that this relation is maintained under the weak convergence of minimising sequences for nonlinear elasticity problems. The existence and partial regularity of an “inverse” function are proved.
Painlevé analysis of the damped, driven nonlinear Schrödinger equation
Authors: Clarkson Peter A. 
Published: November 2011

SynopsisIn this paper we apply the Painlevé tests to the damped, driven nonlinear Schrödinger equationwhere a(x, t) and b(x, t) are analytic functions of x and t, todetermine under what conditions the equation might be completely integrable. It is shown that (0.1) can pass the Painlevé tests only ifwhere α0(t),α1(t) and β(t) are arbitrary, real analytic functions of time. Furthermore, it is shown that in this special case, (0.1) may be transformed into the original nonlinear Schrödinger equation, which is known to be completely integrable.
Local existence and blow-up criterion for the Boussinesq equations
Authors: Chae Dongho , Nam Hee-Seok 
Published: November 2011

SynopsisIn this paper, we prove local existence and uniqueness of smooth solutions of the Boussinesq equations. We also obtain a blow-up criterion for these smooth solutions. This shows that the maximum norm of the gradient of the passive scalar controls the breakdown of smooth solutions of the Boussinesq equations. As an application of this criterion, we prove global existence of smooth solutions in the case of zero external force.
Positive definite temperature functions and a correspondence to positive temperature functions
Authors: Chung Soon-Yeong 
Published: November 2011

SynopsisPositive definite temperature functionsu(x, t) in ℝn+1= {(x, t)|x∈ ℝn,t> 0} are characterised bywhere μ is a positive measure satisfying that for every ℰ > 0,is finite. A transformis introduced to give an isomorphism between the class ofall positive definite temperature functions and the class of all possible temperature functions inThen correspondence given bygeneralises the Bochner–Schwartz Theorem for the Schwartz distributions and extends Widder's correspondence characterising some subclass of the positive temperature functions by the Fourier-Stieltjes transform.
A perturbed Hopf bifurcation with reflection symmetry
Authors: Nagata Wayne 
Published: November 2011

SynopsisWe study the effects of a small symmetry breaking perturbation on a system of differential equations at a coupled Hopf bifurcation with O(2) symmetry, where the perturbation breaks the continuous rotation symmetry, but retains a reflection (Z2) symmetry. It is shown that for a large range of parameter values, the invariant manifolds of the unperturbed bifurcation persist and that for some values of normal form coefficients there are secondary bifurcations of nonsymmetric periodic standing wave solutions.
A global existence theorem for the Cauchy problem of nonlinear wave equations
Authors: Gao Jianmin , Xu Lichen 
Published: November 2011

SynopsisIn this paper we consider the global existence (in time) of the Cauchy problem of the semilinear wave equation utt – Δu = F(u, Du), x ∊ Rn, t > 0. When the smooth function F(u, Du) = O((|u| + |Du|)k+1) in a small neighbourhood of the origin and the space dimension n > ½ + 2/k + (1 + (4/k)2)½/2, a unique global solution is obtained under suitable assumptions on initial data. The method used here is associated with the Lorentz invariance of the wave equation and an improved Lp–Lq decay estimate for solutions of the homogeneous wave equation. Similar results can be extended to the case of “fully nonlinear wave equations”.
On smooth solutions to the initial value problem for the mixed nonlinear Schrödinger equations
Authors: Boling Guo , Shaobin Tan 
Published: November 2011

SynopsisSolutions to the initial value problem for the mixed nonlinear Schrödinger equationare considered. Conditions on the constants α,β, γ, function g(·) and initial data u(x, 0) are given so that, for this problem, the unique existence of smooth solutions is proved. In addition, the decay behaviours of the smooth solutions as |x|→+∞ are discussed.
Nilpotent local automorphisms of an independence algebra
Authors: Lima Lucinda M. 
Published: November 2011

Let A be a strong independence algebra of infinite rank m. Let ℒ(A) be the inverse monoid of all local automorphisms of A. The Baer–Levi semigroup B over the algebra A is defined to be the subsemigroup of ℒ(A) consisting of all the elements α with dom α = A and corank im α = m. Let Km be the subsemigroup of ℒ(A) generated by B−1B. Then Km is inverse and it is generated (as a semigroup) by N2, the subset of ℒ(A) consisting of all nilpotent elements of index 2. The 2-nilpotent depth, Δ2(Km) of Km is defined to be the smallest positive integer t such that Km = N2∪…∪(N2)t. In fact, Δ2(Km) is either 2 or 3 and a criterion is found which distinguishes between the two cases.If N denotes the set of all nilpotents in ℒ(A), then the subsemigroup generated by N is also Km. In fact, Km is proved to be exactly N2.
A necessary and sufficient condition for nonattainment and formation of microstructure almost everywhere in scalar variational problems
Authors: Friesecke Gero 
Published: November 2011

For scalar variational problemssubject to linear boundary values, we determine completely those integrandsW: ℝn→ ℝ for which the minimum is not attained, thereby completing previous efforts such as a recent nonexistence theorem of Chipot [9] and unifying a large number of examples and counterexamples in the literature.As a corollary, we show that in case of nonattainment (and providedWgrows superlinearly at infinity), every minimising sequence converges weakly but not strongly inW1,1(Ω) to a unique limit, namely the linear deformation prescribed at the boundary, and develops fine structure everywhere in Ω, that is to say every Young measure associated with the sequence of its gradients is almost-nowhere a Dirac mass.Connections with solid–solid phase transformations are indicated.
The direct and inverse problem in Newtonian scattering
Authors: Astaburuaga M. A. , Fernández Claudio , Cortés Víctor H. 
Published: November 2011

SynopsisIn this paper we study the direct and inverse scattering problem on the phase space for a classical particle moving under the influence of a conservative force. We provide a formula for the scattering operator in the one-dimensional case and we settle the properties of the potential that can be deduced from it. We also study the question of recovering the shape of the barriers which can be seen from −∞ and ∞. An example is given showing that these barriers are not uniquely determined by the scattering operator.
Geometry related to the key del Pezzo surface and the associated mapping of plane cubics
Authors: Edge W. L. 
Published: November 2011

SynopsisWhen the points of a projective space [9] map ternary cubics the maps of perfect cubes are the points of a del Pezzo surface F. Several manifolds linked with F are listed and the cubics mapped on these are noted. A new approach leads to the first of Aronhold's two invariants.
Rees matrix covers for a class of abundant semigroups
Authors: Lawson Mark V. 
Published: November 2011

SynopsisRecently considerable attention has been paid to the study of locally inverse regular semigroups. McAlister [14] obtained a description of such semigroups as locally isomorphic images of regular Rees matrix semigroups over an inverse semigroup. The class of abundant semigroups originally arose from ‘homological’ considerations in the theory of S-systems: they are the semigroup theoretic analogue of PP-rings. Cancellative monoids, full subsemigroups of regular semigroups as well as the multiplicative semigroups of PP rings are abundant. The aim of this paper is to show how the structure theory described above for regular semigroups may be generalised to a class of abundant semigroups.
Linear equations in B(ℤ)*
Authors: Filali M. 
Published: November 2011

SynopsisLet B(ℤ)* be the Banach dual of the space of all bounded complex-valued functions on ℤ. For each n ε ℤ, let Ln be the translation operator on B(ℤ) and Tn be its adjoint operator on B(ℤ)*. This paper concerns itself with equations of the formwhere (an)nεℤ is a sequence of complex numbers.
Sharp uniform bounds for steady potential fluid-Poisson systems
Authors: Gamba Irene M. 
Published: November 2011

We consider steady potential hydrodynamic-Poisson systems with a dissipation term (viscosity) proportional to a small parametervin a two- or three-dimensional bounded domain. We show here that for any smooth solution of a boundary value problem which satisfies that the speed, denoted by |∇φv|, has an upper coarse bound, uniform in the parameterv, then a sharper, correct uniform bound is obtained: the viscous speed |∇φv| is bounded pointwise, at pointsx0in the interior of the flow domain, by cavitation speed (given by Bernoulli's Law at vacuum states) plus a term ofthat depends on. The exponent is β = 1 for the standard isentropic gas flow model and β = 1/2 for the potential hydrodynamic Poisson system. Both cases are considered to have a γ-pressure law with 1<γ<2 in two space dimensions and 1 < γ< 3/2 in three space dimensions. These systems have cavitation speeds which take not necessarily constant values. In fact, for the potential hydrodynamic-Poisson systems, cavitation speed is a function that depends on the potential flow function and also on the electric potential.In addition, we consider a two-dimensional boundary value problem which has been proved to have a smooth solution whose speed is uniformly bounded. In this case, we show that the pointwise sharper bound can be extended to the section of the boundary ∂Ω\∂3Ω, where ∂3Ω is called the outflow boundary. The exponent β varies between 1 and 1/8 depending on the location ofx0at the boundary and on the curvature of the boundary atx0. In particular, our estimates apply to classical viscous approximation to transonic flow models.
Limit analysis for a class of nonconvex problems
Authors: Buttazzo Giuseppe , Faina Loris 
Published: November 2011

SynopsisThe problemis considered, where X is a normed space, F: X →] –∞, + ∞] is a (possibly non-convex) functional and L ∈ X'. We look for the values of γy for which the infimum above is attained. Applications to nonconvex functionals denned on measures and on the BV space are given.
On the continuity of the polyconvex, quasiconvex and rank-oneconvex envelopes with respect to growth condition
Authors: Gangbo Wilfrid 
Published: November 2011

SynopsisLetCf, Pf, QfandRfbe respectively the convex, polyconvex, quasi-convex and rank-one-convex envelopes of a given functionf. If fp: RNxM→R andfq(ξ) behaves as |ξ|qat infinityq∈ (1, ∞), we show that. This is the case for (Pfp)pprovided thatq≠1,…, min (N, M), otherwise. In the last part of this work, we show thatf(ξ) = g(|ξ|) does not imply in generalPf = Qf.
Generalised characteristics in hyperbolic systems of conservation laws with special coupling
Authors: Dafermos C. M. , Geng X. 
Published: November 2011

SynopsisUsing the theory of generalised characteristics, we study the structure of BV solutions of genuinely nonlinear systems of two conservation laws whose shock and rarefaction wave curves of the first family are straight lines. We also establish a priori estimates on the variation of the solution similar to those obtained earlier by Glimm and Lax.
Symmetry breaking and multiple solutions for a Neumann problem in an exterior domain
Authors: Zelati Vittorio Coti , Esteban Maria J. 
Published: November 2011

SynopsisIn this paper we prove existence of multiple positive solutions for a Neumann problem in ℝN/(0, R), R large, with a superquadratic and odd nonlinearity. The proof is based on the fact that in such a situation the minimum of the corresponding energy functional (which is achieved) is not an even function and that there is quite a large gap (for large R) between such a minimum and the minimum of the same functional on even functions. In the set of functions whose energy lies in such a gap, we can apply index theory to prove the desired multiplicity result.
Bifurcation of steady-state solutions in predator-prey and competition systems
Authors: Blat J. , Brown K. J. 
Published: November 2011

SynopsisWe discuss steady-state solutions of systems of semilinear reaction-diffusion equations which model situations in which two interacting species u and v inhabit the same bounded region. It is easy to find solutions to the systems such that either u or v is identically zero; such solutions correspond to the case where one of the species is extinct. By using decoupling and global bifurcation theory techniques, we prove the existence of solutions which are positive in both u and v corresponding to the case where the populations can co-exist.
Sur les sous-groupes planaires des groupes des dispersions des équations difiérentielles linéaires du deuxième ordre
Authors: Borůvka O. 
Published: November 2011

SynopsisA group consisting of real continuous functions of one real variable on the interval j = (−∞, ∞) is called planar if through each point of the plane j × j there passes just one element s ∈ .Every differential oscillatory equation (Q): y″ = Q(t)y (t ∈ j = (−∞, ∞), Q ∈ C(0)) admits functions, called the dispersions of (Q), that transform (Q) into itself. These dispersions are integrals of Kummer's equation (QQ): −{X, t} + Q(X)X′2(t) = Q(t) and form a three-parameter group , known as the dispersion group of (Q). The increasing dispersions of (Q) form a three-parameter group invariant in . The centre of the group is an infinite cyclic group , whose elements, the central dispersions of (Q), describe the position of conjugate points of (Q).The present paper contains new results concerning the algebraic structure of the group . It provides information on the following: (1) the existence and properties of planar subgroups of a given group and (2) the existence and properties of the groups containing a given planar group . The results obtained are: the planar subgroups of a given group form a system depending on two constants, SQ, such that for all ∈SQ. The equations (Q) whose groups contain the given planar group form a system dependent on one constant, QS, such that for all (Q)∈QS.
Lower bounds for the spectrum of a second order linear differential equation with a coefficient whose negative part is p-integrable
Authors: Harris B. J. 
Published: November 2011

SynopsisWe consider ihe differential expression M[y]: = −y″ + qy on [0, ∞) where q_∈ Lp [0, ∞) for some p ≧ 1. It is known that M, together with the boundary conditions y(0) = 0 or y′(0) = 0, defines linear operators on L2 [0, ∞). We obtain lower bounds for the spectra of these operators. Our bounds depend on the Lp norm of q_ and extend results of Everitt and Veling.
On the limit-n classification of powers of positive coefficient ordinary differential expressions
Authors: Kauffman Robert M. 
Published: November 2011

SynopsisLet , with each pi a finite sum of real multiples of real powers of x, and with D = d/dx. Suppose that pi≧0, pN > 0, and p0≧ε > 0 on the interval [1, ∞). Suppose that there exists a j such that degree pi − 2j > degree pi−2i for all i ≠ j. We compute the deficiency index d(Ln) in L2[l, ∞) of any power of L. It is known that d(L) = N. We give an exact formula for d(Ln) which, if degree pi − 2j > 0, shows that d(Ln) = nN for all n if and only if j = 0, and that the limit as n approaches infinity of d(Ln)/n is N + j. We show in addition that if degree pi − 2i ≦ 0 for all i, d(Ln) = nN for all n.
Uniqueness of positive solutions of some semilinear Sturm–Liouville problems on the half line
Authors: Toland J. F. 
Published: November 2011

SynopsisThis note gives a simple proof of uniqueness for positive solutions of certain non-linear boundary value problems on ℝ+ which are typified by the equationwith boundary conditions u′(0) = u(+∞) = 0. In the autonomous case (r ≡ 1), this is easy to see, by quadrature. The proof here supposes r to be non-increasing on ℝ+.
p-Summing operators on injective tensor products of spaces
Authors: Montgomery-Smith Stephen , Saab Paulette 
Published: November 2011

SynopsisLet X, Y and Z be Banach spaces, and let Πp (Y, Z) (1 ≦ p < ∞) denote the space of p-summing operators from Y to Z. We show that, if X is a ℒ∞-space, then a bounded linear operator is 1-summing if and only if a naturally associated operator T#: X → Πl (Y, Z) is 1-summing. This result need not be true if X is not a ℒ∞-space. For p > 1, several examples are given with X = C[0, 1] to show that T# can be p-summing without T being p-summing. Indeed, there is an operator T on whose associated operator T# is 2-summing, but for all N ∈ N, there exists an N-dimensional subspace U of such that T restricted to U is equivalent to the identity operator on . Finally, we show that there is a compact Hausdorff space K and a bounded linear operator for which T#: C(K) → Π1 (l1, l2) is not 2-summing.
Cauchy problem for an extended model of combustion
Authors: Lu Yun-guang 
Published: November 2011

SynopsisThis paper considers the Cauchy problem for an extended model of combustion (u + qz)t + f(u)x = 0, zt + kg(u)z = 0 with Lp bounded initial data, where g(u) is a piecewise Lipschitz continuous function and its discontinuous points have no finite limit point. The integral representation gives a definition of a weak solution in Lp space. Some existence results are obtained based on a simplified method of compensated compactness in which the weak continuity theorem of 2 * 2 determinants plays a more important role, but the idea of Young measures has been avoided.
On singular differential operators with positive coefficients
Authors: Schultze Bernd 
Published: November 2011

SynopsisA class of singular real formally self-adjoint differential expressions M on I = [a, = ∞) (a ∈ ℝ), i.e. expressions of the form My = with pj ≧ 0 (j = 0, …, n – 1), pn > 0 is constructed with the following property: For every integer k with 0 ≦ k < n/2 there exists an expression M in this class such that the deficiency index of T0(M) – the minimal operator associated with M – is n + 2k. This generalises a result in [3] and proves part of the McLeod's conjecture.
On the spectrum of the periodic Dirac operator
Authors: Harris B. J. 
Published: November 2011

SynopsisIn an earlier paper we considered periodic Dirac operators and obtained criteria for them to be self-adjoint and for their spectra to be devoid of eigenvalues of finite multiplicity. The question of the existence of eigenvalues of infinite multiplicity was left open. In this article we obtain further criteria for self-adjointness and show that under these conditions periodic Dirac operators do not possess eigenvalues of infinite multiplicity. We also obtain a spectral gap result.
Proximate topology and shape theory
Authors: Čerin Zvonko 
Published: November 2011

Most of the development of shape theory was in the so-called outer shape theory, where the shape of spaces is described with the help of some outside objects.This paper belongs to the so-called inner shape theory, in which the shape of spaces is described intrinsically without the use of any outside gadgets. We give a description of shape theory that does not need absolute neighbourhood retracts. We prove that the category ℋN whose objects are topological spaces and whose morphisms are proximate homotopy classes of proximate nets is naturally equivalent to the shape category h. The description of the category ℋN for compact metric spaces was given earlier by José M. R. Sanjurjo. We also give three applications of this new approach to shape theory.