bluuebunny/crossref_metadata_2025_split huggingface dataset:
The structure of solutions to the pseudo-conformally invariant nonlinear Schrödinger equation
Authors: Cazenave Thierry , Weissler Fred B. 
Published: November 2011

SynopsisWe study solutions in ℝn of the nonlinear Schrödinger equation iut + Δu = λ |u|γu, where γ is the fixed power 4/n. For this particular power, these solutions satisfy the “pseudo-conformal” conservation law, and the set of solutions is invariant under a related transformation. This transformation gives a correspondence between global and non-global solutions (if λ < 0), and therefore allows us to deduce properties of global solutions from properties of non-global solutions, and vice versa. In particular, we show that a global solution is stable if and only if it decays at the same rate as a solution to the linear problem (with λ = 0). Also, we obtain an explicit formula for the inverse of the wave operator; and we give a sufficient condition (if λ < 0) that the blow up time of a non-global solution is a continuous function on the set of initial values with (for example) negative energy.
A note on the homotopy type of certain gauge groups
Authors: Kono Akira 
Published: November 2011

SynopsisLet Gk be the gauge group of Pk, the principal SU(2) bundle over S4 with c2(Pk) = k. In this paper we show that Gk ≃ Gk. if and only if (12, k) = (12, k′) where (12, k) is the GCD of 12 and k.
On Saint-Venant's problem for an elastic strip
Authors: Mielke Alexander 
Published: November 2011

SynopsisThe equilibrium equations for elastic deformations of an infinite strip are considered. Under the assumption of sufficiently small strains along the whole body, it is shown that all solutions lie on a six-dimensional manifold. This is achieved by rewriting the field equations as a differential equation in a function spaceover the cross-section, the axial variable taken as time. Then the theory of centre manifolds for elliptic systems applies. Thus the local Saint-Venant's problem is solved. Moreover, the structure of the finite-dimensional solution space is analysed to reveal exactly the two-dimensional rod equations of Kirchhoff. The constitutive relations for this rod model are calculated in a mathematically rigorous way out of the constitutive law of the material forming the strip.
On binary differential equations and umbilics
Authors: Bruce J.W. , Fidal D.L. 
Published: November 2011

SynopsisIn this paper we give the local classification of solution curves of bivalued direction fields determined by the equationwhere a and b are smooth functions which we suppose vanish at 0 ∈ ℝ2. Such fields arise on surfaces in Euclidean space, near umbilics, as the principal direction fields, and also in applications of singularity theory to the structure of flow fields and monochromatic-electromagnetic radiation. We give a classification up to homeomorphism (there are three types) but the methods furnish much additional information concerning the fields, via a crucial blowing-up construction.
On an index law and a result of Buschman
Authors: McBride Adam C. 
Published: November 2011

SynopsisA result for the Erdélyi-Kober operators, mentioned briefly by Buschman, is discussed together with a second related result. The results are proved rigorously by means of an index law for powers of certain differential operators and are shown to be valid under conditions of great generality. Mellin multipliers are used and it is shown that, in a certain sense, the index law approach is equivalent to, but independent of, the duplication formula for the gamma function. Various statements can be made concerning fractional integrals and derivatives which produce, as special cases, simple instances of the chain rule for differentiation and changes of variables in integrals.
Interpolatory and variation-diminishing properties of generalized B-splines
Authors: Goodman T. N. T. , Lee S. L. 
Published: November 2011

SynopsisWe consider classes of functions satisfying certain simple criteria of sign and smoothness and a decomposition property. It is known that these properties are possessed by Chebysheffian B-splines and it is shown here that they are also possessed by certain trigonometric B-splines. For such a class of functions, we derive a variation-diminishing property and analyse interpolation both on a finite set of nodes and on an infinite, periodically spaced set of nodes. The results are also applied to interpolation by complex polynomial splines on the circle.
Existence conditions for eigenvalue problems generated by compact multiparameter operators
Authors: Binding Paul , Browne Patrick J. , Turyn Lawrence 
Published: November 2011

SynopsisLet T, V1,…, Vk denote compact symmetric linear operators on a separable Hilbert space H, and write W(λ) = T + λ1V1 + … + λkVk, λ = (λ1, …, λk) ϵ ℝk. We study conditions on the conerelated to solubility of the multiparameter eigenvalue problemwith W(λ)−I nonpositive definite. The main result is as follows.Theorem. If 0 ∉ V, then (*) is soluble for any T. If 0 ∈ V, then there exists T such that (*) is insoluble.We also deduce analogous results for problems involving self-adjoint operators with compact resolvent.
Singular first order perturbations of the heat equation
Authors: Avrin Joel 
Published: November 2011

SynopsisWe exhibit dimension-independent conditions under which the formal operator A = −Δ + a.∇ + V can be defined on such that its closure Ā in L2(Rs, dx) is quasi-m-accretive. Here, a is real so that Ā is nonselfadjoint. the method of proof is a generalized version of the argument employed in the portion of the author's thesis where term a.∇ was originally considered. Specifically, we construct exp (−tĀ) as a limit of approximating semigroups. Since the thesis appeared, Kato has also dealt with the term a. ∇ his conditions on a and V are similar to, but more general than, the conditions that appear here; in addition, he considers magnetic vector potentials. Of interest here is the semigroup method itself, the conciseness of the arguments thereby produced, and a relaxed condition on div a.
Full- and partial-range eigenfunction expansions for Sturm-Liouville problems with indefinite weights
Authors: Kaper Hans G. , Kwong Man Kam , Lekkerkerker C. G. , Zettl A. 
Published: November 2011

SynopsisThis article is concerned with eigenvalue problems of the form Au = λTu in a Hilbert space H, where Ais a selfadjoint positive operator generated by a second-order Sturm-Liouville differential expression and T a selfadjoint indefinite multiplicative operator which is one-to-one. Emphasis is on the full-range and partial-range expansionproperties of the eigenfunctions.
Well-posedness, control and computation of a one-phase Stefan problem with Neumann condition*
Authors: Chen Goong , Sun Shunhua , Zheng Quan 
Published: November 2011

SynopsisA one-phase Stefan problem can be reduced to an equivalent variational inequality by using the Baiocchi-Duvaut transformation. In this paper, we study the variational inequality by formulating it as a set-valued partial differential equation. The existence of solutions is proved by applying a generalized Schauder fixed fixed point theorem for set-valued mappings. Uniqueness and regularity of solutions are also obtained. In §3, we regard the boundary value Neumann data as boundary controls and combine both the variational inequality and the classical approaches to study the effects of controls on the free boundary and the state (i.e. temperature). In §4, we further use the theory to study an optimal “ice-melting” problem. Our results show that if the controls have fixed total input heat flux and are constrained in magnitude, then the optimal control is “bang-bang”. If the admissible controls are not constrained in magnitude, then the optimal control is a Dirac delta type distribution which is no longer admissible. In the last section, our existence theory is combined with the finite difference method and non-linear programming techniques to obtain numerical solutions.
The global Hölder-continuous solution of isentropic gas dynamics
Authors: Lu Yun-Guang 
Published: November 2011

SynopsisThis paper considers the Cauchy problem for the isentropic equations of gas dynamics in Euler coordinates ρt + (ρu)x = 0, (ρu)t + (ρu)2 + P(ρ))x=0 and gives the Hölder-continuous solution by applying the method of vanishing viscosity.
On the blow-up of solutions of a convective reaction diffusion equation
Authors: Aguirre J. , Escobedo M. 
Published: November 2011

SynopsisWe study the blow-up of positive solutions of the Cauchy problem for the semilinear parabolic equationwhere u is a scalar function of the spatial variable x ∈ ℝN and time t > 0, a ∈ ℝV, a ≠ 0, 1 < p and 1 ≦ q. We show that: (a) if p > 1 and 1 ≦ q ≦ p, there always exist solutions which blow up in finite time; (b) if 1 < q ≦ p ≦ min {1 + 2/N, 1 + 2q/(N + 1)} or if q = 1 and 1 < p ≦ l + 2/N, then all positive solutions blow up in finite time; (c) if q > 1 and p > min {1 + 2/N, 1 + 2q/N + 1)}, then global solutions exist; (d) if q = 1 and p > 1 + 2/N, then global solutions exist.
Hyperbolic phase change problems in heat conduction with memory
Authors: Colli Pierluigi , Grasselli Maurizio 
Published: November 2011

SynopsisThe aim of this paper is to formulate and study phase transition problems in materials with memory, based on the Gurtin–Pipkin constitutive assumption on the heat flux. As different phases are involved, the internal energy is allowed to depend on the phase variable (besides the temperature) and to take its past history into account. By considering the standard equilibrium condition at the interface between two phases, we deal with a hyperbolic Stefan problem reckoning with memory effects. Then, substituting this equilibrium condition with a relaxation dynamics, we represent some dissipation phenomena including supercooling or superheating. The application of a fixed point argument helps us to show the existence and uniqueness of the solution to the latter problem (still of hyperbolic type). Hence, by introducing a suitable regularisation and taking the limit as a kinetic parameter goes to zero, we prove an existence result for the former Stefan problem. Moreover, its uniqueness is deduced by contradiction.
Asymptotics of Sturm-Liouville eigenvalues for problems on a finite interval with one limit-circle singularity, I
Authors: Atkinson F. V. , Fulton C. T. 
Published: November 2011

SynopsisAsymptotic formulae for the positive eigenvalues of a limit-circle eigenvalue problem for –y” + qy = λy on the finite interval (0, b] are obtained for potentials q which are limit circle and non-oscillatory at x = 0, under the assumption xq(x)∈L1(0,6). Potentials of the form q(x) = C/xk, 0<fc<2, are included. In the case where k = 1, an independent check based on the limit-circle theory of Fulton and an asymptotic expansion of the confluent hypergeometric function, M(a, b; z), verifies the main result.
Comparison functions for a model problem related to nonlinear elasticity
Authors: Stredulinsky E. W. 
Published: November 2011

SynopsisComparison functions are constructed for the problem of minimizingover maps u: D(⊆ℝ2)→ℝ2 with det≥0, subject to the constraint u= f on ∂D, D the unit disk. This is accomplished for maps / which are reparameterizations of ∂D or which are “graph-like” maps. Estimates involving half derivative boundary norms are obtained.
Level and index in the modular group
Authors: Stothers W. W. 
Published: November 2011

SynopsisIt is shown that the index of a congruence subgroup of the modular group cannot be less than the level of the subgroup. This allows a number of existence theorems about non-congruence subgroups.The level of a subgroup of the modular group can be defined in terms of the action on Q ∪ {∞}. We define a similar action to get information on congruence subgroups. In fact, we get a more powerful result, but this appears to be the most useful version.
Multipliers for vector valued functions
Authors: Torrea José Luis 
Published: November 2011

SynopsisLet G be a locally compact abelian group and let Γ be the dual of G. Let A, B be Banach spaces and Lp(G,A) the Bochner-Lebesgue spaces. We prove that the space of bounded linear translation invariant operators from L1(G, A) to LX(G, B) can be identified with the space of bounded convolution invariant (in some sense) operators and also with the space of a(A, B)-valued “weak regular” measures with the relation Tf = f *μ. (A. The existence of a function m∈ L∞ (Γ,α(A,B)), such that is also proved.
Inverse semigroups generated by nilpotent transformations
Authors: Howie John M. , Marques-Smith M. Paula O. 
Published: November 2011

SynopsisLet X be a set with infinite cardinality m and let B be the Baer-Levi semigroup, consisting of all one-one mappings a:X→X for which ∣X/Xα∣ = m. Let Km=<B 1B>, the inverse subsemigroup of the symmetric inverse semigroup ℐ(X) generated by all products β−γ, with β,γ∈B. Then Km = <N2>, where N2 is the subset of ℐ(X) consisting of all nilpotent elements of index 2. Moreover, Km has 2-nilpotent-depth 3, in the sense that Let Pm be the ideal {α∈Km: ∣dom α∣<m} in Km and let Lm be the Rees quotient Km/Pm. Then Lm is a 0-bisimple, 2-nilpotent-generated inverse semigroup with 2-nilpotent-depth 3. The minimum non-trivial homomorphic image of Lm also has these properties and is congruence-free.
RP-dominated regular semigroups
Authors: Blyth T. S. , Hickey J. B. 
Published: November 2011

SynopsisWe describe the structure of regular semigroups in which each element is dominated, in the Nambooripad order, by a unique maximal element that is ℋ-equivalent to a mididentity. These are precisely direct products of a rectangular band and a uniquely unit regular semigroup.
Sums and products of quasi-nilpotent operators
Authors: Fong C. K. , Sourour A. R. 
Published: November 2011

SynopsisIt is proved that a bounded operator on Hilbert space is the sum of two quasi-nilpotent operators if and only if it is not a non-zero scalar plus a compact operator. Necessary conditions and sufficient conditions for an operator to be the product of two quasi-nilpotent operators are given.
A note on linear ordinary quasi-differential equations
Authors: Everitt W. N. 
Published: November 2011

SynopsisThe theory of differential equations is largely concerned with properties of solutions of individual, or classes of, equations. This paper is given over to the converse problem - that of seeking properties of functions which require them to be, in some respect, solutions of a differential equation, and to determining all possible such differential equations.From this point of view this paper discusses only linear ordinary quasi-differential equations of the second order. However, the methods can be extended to quasi-differential equations of general order.
On a discrete-time version of a problem of A. J. Pritchard and J. Zabczyk
Authors: Przyłuski K. Maciej 
Published: November 2011

SynopsisIt is shown that every weakly l1-stable linear and bounded operator (which represents a linear discrete-time system) on a Hilbert space is power stable. It solves (at least partially) a discrete-time version of a problem posed by A. J. Pritchard and J. Zabczyk for strongly continuous semigroups of bounded linear operators.
On the automorphism group of the integral group ring of the infinite dihedral group
Authors: Wallace D. A. R. 
Published: November 2011

SynopsisLet ℤ(G) be the integral group ring of the infinite dihedral groupG; the aim is to calculate Autℤ(G), the group of Z-linear automorphisms of ℤ(G). It is shown that Aut ℤ(G), the subgroup of Aut *ℤ(G) consisting of those automorphisms that preserve elementwise the centre of ℤ(G), is a normal subgroup of Aut *ℤ(G) of index 2 and that Aut*ℤ(G) may be embedded monomorphically intoM2(ℤ[t]), the ring of 2 × 2 matrices over a polynomial ring ℤ[t]From this embedding and by the Noether—Skolem Theorem it is shown that Inn (G), the group of inner automorphisms of ℤ(G) induced by the units of ℤ(G), is a normal subgroup of Aut*ℤ(G)/ such that Aut*ℤ(G)/Inn (G) is isomorphic to the Klein four-group.
Oscillation criteria of Nehari-type for Sturm–Liouville operators and elliptic differential operators of second order and the lower spectrum
Authors: Fiedler F. 
Published: November 2011

SynopsisSufficient oscillation criteria of Nehari-type are established for the differential equation−uʺ(t) + q(t)u(t) = 0, 0<t<∞, with and without sign restrictions onq(t), respectively. These results are extended to Sturm-Liouville equations and elliptic differential equations of second order.In Section 7 we present conclusions for the lower spectrum of elliptic differential operators and also for the discreteness of the spectrum of certain ordinary differential operators of second order.
Limit cycles of a class of polynomial systems
Authors: Carbonell Marc , Llibre Jaume 
Published: November 2011

SynopsisWe study the class of polynomial vector fields of the form = αx — y + Pn(x, y), = x + αy + Qn(x, y), where Pn and Qn are homogeneous polynomials of degree n. If we define the functions f(x, y) = xPn(x, y) + yQn(x, y) and g(x, y) = xQn(x, y)−yPn(x, y), we characterise the number of limit cycles for this class when the function g(αg − f) does not change sign.
A combinatorial procedure for finding isolating neighbourhoods and index pairs
Authors: Szymczak Andrzej 
Published: November 2011

SynopsisWe present a purely combinatorial procedure for finding an isolating neighbourhood and an index pair contained in a given set, being a finite union of cubes in Rs. It is applied for a computer-assisted computation of the Conley index of an isolated invariant subset of the Hénon attractor. As a corollary, it is shown that the Hénon attractor contains periodic orbits of all principal periods except for 3 and 5.
On the KOℤ/2-Euler class, II
Authors: Crabb M. C. 
Published: November 2011

SynopsisLet ξ be an oriented n-dimensional real vector bundle over an oriented closed m-manifold X. An r-field on ξ defined outside a finite subset of X has an index in the homotopy group πm−l(Vn,r) of the Stiefel manifold of r-frames in ℝn. The principal theorems of this paper relate the d and e-invariants of an associated ℝ/2-equivariant stable homotopy class, in certain cases, to computable cohomology characteristic numbers. Results of this type were first obtained by Atiyah and Dupont [5].
Jacobi matrices and transversality
Authors: Fusco Giorgio , Oliva Waldyr Muniz 
Published: November 2011

SynopsisThe paper deals with smooth nonlinear ODE systems in ℝn, ẋ = f(x), such that the derivative f′(x) has a matrix representation of Jacobi type (not necessarily symmetric) with positive off diagonal entries. A discrete functional is introduced and is discovered to be nonincreasing along the solutions of the associated linear variational system ẏ = f′(x(t))y. Two families of transversal cones invariant under the flow of that linear system allow us to prove transversality between the stable and unstable manifolds of any two hyperbolic critical points of the given nonlinear system; it is also proved that the nonwandering points are critical points. A new class of Morse–Smale systems in ℝn is then explicitly constructed.
Piecewise continuous solutions of nonlinear pseudoparabolic equations in two space dimensions*
Authors: Dai Dao-Qing , Lin Wei 
Published: November 2011

SynopsisAn initial boundary value problem of Riemann type is solved for the nonlinear pseudoparabolic equation with two space variablesThe complex functionHis measurable on ℂ ×I × ℂ5, withIbeing an interval of the real line ℝ, Lipschitz continuous with respect to the last five variables, with the Lipschitz constant for the last variable being strictly less than one (ellipticity condition). No smallness assumption is needed in the argument.
On multiple solutions for Berman's problem
Authors: Hwang Tzy-Wei , Wang Ching-An 
Published: November 2011

SynopsisWe study Berman's problemsubjects to the conditions f(0) =f″(0) = f′(1) = f(1)− 1 = 0, which arises from the study of laminar flows in channels with porous walls. Positive (negative) Re denotes the case of suction (injection) flows. Preliminary numerical studies indicated the existence of three different types of solutions and a small portion of mathematical evidence was provided. In this paper, we are able to show that there exist connected sets in the Re-K plane on which different types of solutions occur. In particular, our result verifies that the problem possesses all three types of suction solutions for sufficiently large Re. Moreover, the limiting injection solution is also obtained.
Uniform asymptotic expansions for oblate spheroidal functions I: positive separation parameter λ
Authors: Dunster T. M. 
Published: November 2011

SynopsisUniform asymptotic expansions are derived for solutions of the spheroidal wave equation, in the oblate case where the parameter µ is real and nonnegative, the separation parameter λ is real and positive, and γ is purely imaginary (γ = iu). As u →∞, three types of expansions are derived for oblate spheroidal functions, which involve elementary, Airy and Bessel functions. Let δ be an arbitrary small positive constant. The expansions are uniformly valid for λ/u2 fixed and lying in the interval (0,2), and for λ / u2when 0<λ/u2 < 1, and when 1 = 1≦λ/u2 < 2. The union of the domains of validity of the various expansions cover the half- plane arg (z)≦ = π/2.
Robustness of a feedback control scheme for one-dimensional diffusion equations: perturbation to the Sturm-Liouville operator
Authors: Nambu Takao 
Published: November 2011

SynopsisWe study the stabilisation of a one-dimensional diffusion equation by means of static feedback. The equation contains the so-called Sturm-Liouville operator (S-L operator). A perturbation, often interpreted as an error in modelling physical systems, enters the principal part and the boundary condition of the S-L operator. Since the perturbation is not subordinate to the operator, the classical perturbation theory is no longer available. We show, however, that the feedback stabilisation scheme for the unperturbed equation is effective also for the perturbed equation as long as the perturbation is small in an adequate topology. The key idea is to show the strong continuity of the eigenfunctions for the S-L operator relative to the coefficients of the operator.
The Lavrentieff phenomenon for quadratic functionals
Authors: De Arcangelis Riccardo 
Published: November 2011

The paper provides an example of an integral functional in more than two dimensions, with a symmetric and positively defined quadratic integrandq, exhibiting the Lavrentieff phenomenon on a ballBand on a linear boundary datumu0, i.e. for whichThe example is also utilised to discuss nonidentity between some relaxation procedures for a quadratic integral functional and to provide a weighted Sobolev space in the Hilbert case in which smooth functions are not dense.
Quadratic systems having a parabola as an integral curve
Authors: Christopher Colin 
Published: November 2011

SynopsisThe class of quadratic systems having a parabola composed of integral curves is examined. Canonical forms are found for the members of this class, and conditions are obtained, using the Bendixson's Criterion and the Poincaré–Bendixson Theorem, for the existence or non-existence of limit cycles, in the case where there is a limit cycle “inside” the parabola (that is, in the convex component of its compliment).