bluuebunny/crossref_metadata_2025_split huggingface dataset:
Another positivity result for determinantal operators
Authors: Binding Paul 
Published: November 2011

SynopsisLet Vrs, s = 1 … k, be Hermitian operators on separable Hilbert spaces Hr, r = 1 … k. For x⊗ = x1⊗ … ⊗ xk ∈ H = H1⊗…Δx⊗ by the formal determinantal expansion ⊗ det [Vrsxr Δ is then extended by linearity and continuity to H. It is shown that a positive definiteness condition on Δ need be checked only for decomposable tensors like x⊗. Applications are given to several conditions in the multiparameter eigenvalue literature.
Application to magnetohydrodynamic duct flows of a singular elliptic problem associated with a rectangle
Authors: Nye V. A. 
Published: November 2011

SynopsisThe analysis developed by the author in a previous paper is used to discuss two magnetohydrodynamic duct flows for which the boundary conditions are not of Dirichlet type. To the accuracy stated, the results obtained confirm those obtained by previous authors who used different approaches to the problems. A feature of the present analysis is that it yields the magnitude of the error entailed by the use of approximate forms for flow quantities. This has been lacking in previous analyses.
On oscillations in a compressible laminar boundary layer
Authors: Gribben R. J. 
Published: November 2011

SynopsisThe behaviour of heat transfer and skin friction is analysed in a compressible laminar boundary layer with external velocity Ue(x)(l + α sin ωt The Mach number M is assumed small but finite so that high frequency flows (s ≫1) in which c =αγM2s/2 = O(1) are considered. Solutions, obtained by matching in the Stokes and Prandtl layers, involve summation of Fourier-like series to give the dominant terms in the heat transfer and skin friction. Results, for c =½, verify that a previous approximate method gives a reasonable description of unsteady heat transfer and skin friction; forc =1 there is a substantial increase in amplitude of heat transfer but little change of phase.
Existence conditions for two-parameter eigenvalue problems
Authors: Binding Paul , Browne Patrick J. , Turyn Lawrence 
Published: November 2011

SynopsisWe discuss necessary and sufficient conditions for the existence of eigentuples λ=(λl,λ2) and eigenvectors x1≠0, x2≠0 for the problem Wr(λ)xr = 0, Wr(λ)≧0, (*), where Wr(λ)= Tr + λ1Vr2, r=1,2. Here Tr and Vrs are self-adjoint operators on separable Hilbert spaces Hr. We assume the Vrs to be bounded and the Tr bounded below with compact resolvent. Most of our conditions involve the conesWe obtain results under various conditions on the Tr, but the following is typical:THEOREM. If (*) has a solution for all choices ofT1, T2then (a)0∉ V1UV2,(b)V1∩(—V2) =∅ and (c) V1⊂V2∪{0}, V2⊈V1∪{0}. Conversely, if (a) and (b) hold andV1⊈V2∪∩{0}, V2⊈ then (*) has a solution for all choices ofT1, T2.
Integral representation of functionals defined on curves ofW1,p
Authors: Amar Micol , Bellettini Giovanni , Venturini Sergio 
Published: November 2011

LetI⊂ ℝ be a bounded open interval,(I) be the family of all open subintervals ofIand letp> 1. The aim of this paper is to give an integral representation result for abstract functionalsF:W1,p(I;ℝn) ×(I) → [0, + ∞) which are lower semicontinuous and satisfy suitable properties. In particular, we prove an integral representation theorem for the Г-limit of a sequence {Fh}h, of functionals of the formwhere eachfhis a Borel function satisfying proper growth conditions.
A description of E-unitary inverse semigroups
Authors: Wilkinson Ross 
Published: November 2011

SynopsisAn E-unitary inverse semigroup, S, has the property that, if x=S, and e2 = e=S, then (xe)2 = xe implies that x2 = x. As a consequence of this, we can see that S is an extension of its semilattice of idempotents, E, by its maximal group morphic image, G. Thus, following McAlister (1974), we attempt to describe S in terms of E and G. If we extend the semilattice E to a larger semilattice F, we are able to describe S in terms of a semi-direct product of F and G, giving a new interpretation to the approach of Schein (1975).
Bounds for the best constant in Landau/s inequality on the line
Authors: Franco Z. M. , Kaper Hans G. , Kwong Man Kam , Zettl A. 
Published: November 2011

SynopsisExplicit formulae and numerical values for upper and lower bounds for the best constant in Landau/s inequality on the real line are given. For p > 3, the value of the upper bound is less than the value of the best constant conjectured by Gindler and Goldstein (J. Analyse Math. 28 (1975), 213–238).
Generic space curves and secants
Authors: Bruce J. W. 
Published: November 2011

SynopsisIn this paper, we study the local structure of the secant mapping of a pair of disjoint curves. We show that for generic curves, the secant map and unit secant maps are locally stable. If we allow our curves to coincide, we can define anew unit secant map to be the natural unit tangent map near the diagonal. This is, for a generic curve, a locally stablemap away from the diagonal. Along the diagonal, it is locally stable as a ℤ2 symmetric germ (the ℤ2 symmetry originating with reflection in the diagonal).
A Titchmarsh-Weyl matrix function for symmetric differential equations of order 2n with an indefinite weight function
Authors: Daho Karim 
Published: November 2011

SynopsisA Titchmarsh-Weyl matrix function W(λ) is defined for the differential equation of order 2nwith po>0, pk≧0, k = 1, 2, …, n on 005B;0, b), λєℂ and an indefinite weight function r. It is shown that this function W(λ) belongs to some class and that some operators associated with the above equation are definitizable in the Krein space . In the particular case n = 1, these results are contained in an earlier paper by the present author and H. Langer.
The reciprocal variational approach to the Signorini problem with friction. Approximation results
Authors: Haslinger J. , Panagiotopoulos P. D. 
Published: November 2011

SynopsisIn this paper, a new variational formulation of the Signorini problem with friction is given in terms of the contact stresses. The method corresponds to the direct integral equation approach in classical elastostatic problems. First the displacement and mixed problems are briefly described together with some numerical results. Next the displacements are eliminated by the use of Green's function, and a constrained minimum problem with respect to the normal and tangential tractions on the contact boundary is derived. Then the resulting approximation procedure is studied and certain convergence results are proved. Finally, some remarks on the Signorini problem with Coulomb friction are presented. Numerical results illustrate the theory.
Gradient estimates for semilinear elliptic equations
Authors: Lieberman Gary M. 
Published: November 2011

SynopsisEstimates on the gradient of solutions to the Dirichlet problem for a semilinear elliptic equation are given when the nonlinearity in the equation is quadratic with respect to the gradient of the solution. These estimates extend results of F. Tomi to less smooth boundary data and results of the author to the full quadratic growth.
Energy decay for the wave equation with a degenerate dissipative term
Authors: Nakao Mitsuhiro 
Published: November 2011

SynopsisDecay estimates for the energy are derived for the initial boundary value problem of the wave equation with a degenerate dissipative term:where Ω is a bounded domain in Rn, a(×) is a nonnegative function such that a1 ∊Lp(Ω) for some p > 0 and f is a function tending to 0 rapidly as t → ∞
Inverse multi-parameter eigenvalue problems for matrices
Authors: Browne Patrick J. , Sleeman B. D. 
Published: November 2011

SynopsisWe study the possibility of perturbing a matrix A by a diagonal matrix so that an eigenvalue problem with leading matrix A has specifiedeigenvalues when A is replaced by A+D. The particular cases presented are the one-parameter generalized eigenvalue problem (A× = λB μ×, a two-parameter eigenvalue problem (A + λB + μC)× = 0, a linked system ofsuch two-parameter problems and a quadratic eigenvalue problem (A + λB + λ2C)× = 0. The work extends results of Hadeler for the classical problem A× = λ×.
A classification of the solutions of a differential equation according to their behaviour at infinity, II
Authors: Elias Uri 
Published: November 2011

SynopsisThe solutions of the differential equation Lny + p(×)y = 0, where Ln is a disconjugate operator, are classified according to their behaviour as × →∞. The solution space is decomposed into disjoint sets. We study the dominance properties of the solutions which belong to different sets.
Best constants in norm inequalities for derivatives on a half-line
Authors: Franco Z. M. , Kaper Hans G. , Kwong Man Kam , Zettl A. 
Published: November 2011

SynopsisLet K be the class of all operators T in a Banach space × which have the property that, for any pair of integers (n, k) with n ≧2 and l≦ k ≦ n – l, there exists a constant Cnk such thatfor all fϵdom Tn. If T ϵ K, then the best possible constant for the norm inequality (*) is the smallest non-negative value of the constant Cnk in (*). Any operator T which is the adjoint of a maximal symmetric operator in a Hilbert space belongs to the class K, as was shown by Ljubič [Izv. Akad. Nauk SSSR, Ser. Mat. 24 (1960), 825–864].This article is concerned with the computation of the best possible constant for the differentiation operator Tf=if′ on the maximal domain in L2(0, ∞). Three algorithms, proposed by Ljubič [ibid.] and Kupcov [Trudy Mat. Inst. Steklov. 138 (1975)], are discussed and related to one another, asymptotic expressions (valid for large n) and numerical values of the best possible constant are presented, and the extremals (i.e. the elements / ∈ dom Tn for which equality holds in (*) with the best possible constant) are given.
Products of idempotent linear transformations
Authors: Reynolds M. A. , Sullivan R. P. 
Published: November 2011

SynopsisIn 1966, J. M. Howie characterised the transformations of an arbitrary set that can be written as a product (under composition) of idempotent transformations of the same set. In 1967, J. A. Erdos considered the analogous problem for linear transformations of a finite-dimensional vector space and in 1983, R. J. Dawlings investigated the corresponding idea for bounded operators on a separable Hilbert space. In this paper we study the case of arbitrary vector spaces.
Generalizations of Hardy's Integral Inequality
Authors: Love E. R. 
Published: November 2011

SynopsisExtensions of the integral version of Hardy's Inequality were given by Kadlec and Kufner (1967) and by Copson (1976). This paper provides several levels of further generalization of their results, obtained mostly by specializing four main inequalities. Most of the inequalities have the form ∥Kf∥ ≤C∥f∥, whereKis an integral transform and ∥.∥ is a generalizedLp-norm; some have the inequality sign reversed. Best possible constantsCare obtained in several cases, under mild extra hypotheses.
The asymptotic form of the spectral functions associated with a class of Sturm–Liouville equations
Authors: Harris B. J. 
Published: November 2011

SynopsisWe use a modified form of the Stieltjes inversion formula due to Atkinson together with some recent results on the asymptotic form of Titchmarch–Weyl m-functions to obtain an asymptotic expression for the spectral functions τ(t) associated with the differential equation
Minimax methods for open-loop equilibria in N-person differential games. Part I: Linear quadratic games and constrained games
Authors: Chen Goong , Zheng Quan , Zhou Jian-Xin 
Published: November 2011

SynopsisIn [13], Nikaido and Isoda generalised von Neumann's symmetrisation method for matrix games. They showed that N-person noncooperative games can be treated by a minimax method.We apply this method to N-person differential games. Lukes and Russell [11] first studied N-person nonzero sum linear quadratic games in 1971. Here we have reproduced and strengthened their results. The existence and uniqueness of equilibria are completely determined by the invertibility of the decision operator, and the nonuniqueness of equilibrium strategies is only up to a finite dimensional subspace of the space of all admissible strategies.In the constrained case, we have established an existence result for games with a much weaker convexity assumption subject to compact convex constraints. We have also derived certain results for games with noncompact constraints. Several examples of quadratic and non-quadratic games are given to illustrate the theorem.Numerical computations are also possible and are given in the sequel [3].
On the stability of the limit-point property of “Kauffman expressions” under relatively bounded perturbations
Authors: Mergler Bernhard , Schultze Bernd 
Published: November 2011

SynopsisIn this paper we show that for the whole class of differential expressions in the limit-point case considered by Kauffman in [2], the perturbation theory yields a limit-point criterion for a much wider class of ordinary differential expressions. More general coefficients are admitted which may be eventually negative provided they are “dominated” by some other positive coefficients. This generalises results in [4], [5] and [6].
Kinetic conditions for the existence of wave fronts in reaction-diffusion systems
Authors: Fraile José M. , Sabina José 
Published: November 2011

SynopsisThis paper deals with the existence of bounded plane wave fronts of reaction-diffusion systems. The main result ensures the partial invariance of a certain region, under kinetic conditions commonly used in the literature. This allows us to construct bounded plane wave fronts taking their values in that domain. We also give an estimate of the minimum permissible value of the propagation velocity of those plane wave fronts. Some examples are given.
Remarks on complemented subspaces of von Neumann algebras
Authors: Pisier G. 
Published: November 2011

SynopsisIn this note we include two remarks about bounded (not necessarily contractive) linear projections on a von Neumann algebra. We show that if M is a von Neumann subalgebra of B(H) which is complemented in B(H) and isomorphic to M⊗M, then M is injective (or equivalently M is contractively complemented). We do not know how to get rid of the second assumption on M. In the second part, we show that any complemented reflexive subspace of a C*-algebra is necessarily linearly isomorphic to a Hilbert space.
Stochastic reinforcement problems and ergodic theory
Authors: Balzano M. , Paderni G. 
Published: November 2011

SynopsisWe study the asymptotic behaviour of Dirichlet problems in domains of R2 bounded by thin layers whose thickness is given by means of an assigned ergodic random function. Using a capacitary method together with ergodic theorems for additive and superadditive processes, we are able to characterise the limit problem precisely.
Exponential length and exponential rank in C*-algebras
Authors: Ringrose J. R. 
Published: November 2011

SynopsisIn an operator algebra, the general element of the connected component of the unitary group can beexpressed as a finite product of exponential unitary elements. The recently introduced concept of exponential rank is defined in terms of the number of exponentials required for this purpose. The present paper is concerned with a concept of exponential length, determined not by the number of exponentials but by the sum of the norms of their self-adjoint logarithms. Knowledge of the exponential length of an algebra provides an upper bound for its exponential rank (but not conversely). This is used to estimate the exponential rank of certain algebras of operator-valued continuous functions.
Fundamental semigroups
Authors: Edwards P. M. 
Published: November 2011

SynopsisAn idempotent-separating congruence μ is studied further in this paper. It is shown to satisfy special properties with respect to regular elements and to group-bound elements. It is shown that for any semigroup S, μ is the identity congruence on S/μ. From this, it can be shown that S/μ is fundamental for any semigroup S. Some alternative characterizations of μ are given and applied to yield sufficient conditions for a subsemigroup T of S to satisfy μ (T) = μ (S) ∩ (T × T), whence T is fundamental if S is fundamental.
A distributional theory of fractional calculus
Authors: Lamb W. 
Published: November 2011

SynopsisIn this paper, a theory of fractional calculus is developed for certain spacesD′p,μof generalised functions. The theory is based on the construction of fractionalpowers of certain simple differential and integral operators. With the parameter μ suitably restricted, these fractional powers are shown to coincide with the Riemann-Liouville and Weyl operators of fractional integration and differentiation. Standard properties associated with fractional integrals and derivatives follow immediately from results obtained previously by the author on fractional powers of operators; see [6], [7]. Some spectral properties are also obtained.
The algebra of a commutative semigroup over a commutative ring with unity
Authors: Munn W. D. 
Published: November 2011

SynopsisA new description is provided for the nil radical of the algebra RS of a commutative semigroup S over a commutative ring R with a 1. It is shown that the Jacobson radical of RS is nil if the Jacobson radical of R is nil and that the converse holds in the case where S is periodic.
Remarks on a non-well posed problem
Authors: Medeiros L. A. 
Published: November 2011

SynopsisIn this paper, it is proved that the problem (∂2u/∂t2) + ∆xu = v, u(x, 0) = u0(x), ut(x, 0) = u1(x), with homogeneous Dirichlet conditions on the boundary, is well posed provided v, u0, u1 belong to a suitable space of functions.
On the zeros of (f″ + αf)f and a result of Steinmetz
Authors: Langley J. K. 
Published: November 2011

SynopsisWe characterise all functions f meromorphic of finite order in the plane such that fF has only finitely many zeros, where F = f″ + αf for some constant α. The problem is related to results of N. Steinmetz and others.
Dynamics near a symmetric Hopf bifurcation
Authors: Nagata Wayne 
Published: November 2011

SynopsisWe consider the effects of a small symmetry breaking perturbation on a system of differential equations near a Hopf bifurcation point, where the unperturbed system has O(2) symmetry. We show that there exist secondary bifurcations of invariant two-tori of solutions and that the flow on the tori can be quasiperiodic or weakly resonant (phase locked), depending on the size of the perturbation.
Steady symmetric vortex pairs and rearrangements
Authors: Burton G. R. 
Published: November 2011

SynopsisWe prove an existence theorem for a steady planar flow of an ideal fluid, containing a bounded symmetric pair of vortices, and approaching a uniform flow at infinity. The data prescribed are the rearrangement class of the vorticity field, and either the momentum impulse of the vortex pair, or the velocity of the vortex pair relative to the fluid at infinity. The stream function ψ for the flow satisfies the semilinear elliptic equationin a half-plane bounded by the line of symmetry, where φ is an increasing function that is unknown a priori. The results are proved by maximising the kinetic energy over all flows whose vorticity fields are rearrangements of a specified function.
The order and level of a subgroup of GL2 over a Dedekind ring of arithmetic type
Authors: Mason A. W. 
Published: November 2011

SynopsisLet R be a commutative ring and let q be an R-ideal. Let En(R) be the subgroup of GLn(R) generated by the elementary matrices and let En(R, q) be the normal subgroup of En(R) generated by the q-elementary matrices. For each subgroup S of GLn(R) the order of S, o(S), is the R-ideal generated by xij, xii − xjj (i ≠ j), where (xij) ∈ S, and the level of S, l(S), is the largest R-ideal q0 with the property that En (R, q0) ≦ S. It is known that when n ≧ 3, the subgroup S is normalised by En(R) if and only if o(S) = l(S). It is also known that this result does not hold when n = 2. For example, there are uncountably many normal subgroups S of SL2(ℤ) such that o(S) ≠ {0} and l(S) = {0}, where ℤ is the ring of integers. In this paper we prove that, when A is a Dedekind ring of arithmetic type containing infinitely many units, the order q and level q′ of a subgroup S of GL2(A), normalised by E2(A), are closely related. It is proved that Ψ(q)≦q′, where ≦(q) = 12uq, with u the A-ideal generated by u2 − 1 (u ∈ A*), when A is contained in a number field, and Ψ(q) = q3, when A is contained in a function field.
Remarks on a paper of Olver
Authors: Fairlie D. B. 
Published: November 2011

SynopsisSome disparate ideas in the literature are drawn together. The work of P. J. Olver and his associates on Lagrangians which vanish for arbitrary variations, the so-called null Lagrangians, is viewed as a parallel development to Witten's study of topological field theories. A theorem of Olver, that all hyperjacobians are expressible as divergences, and are thus candidates for the construction of null Lagrangians, is shown to follow directly from the observation that such entities appear in a power series development of the general associative product, and this technique facilitates the construction of multi-dimensional examples.
Conjugacy classes in Sylow p-subgroups of GL(n,q), II
Authors: Vera-López A. , Arregi J. M. 
Published: November 2011

SynopsisIn this paper, we find the canonical matrices of the conjugacy classes of the Sylow p-subgroup of GL(n, pt) consisting of all upper unitriangular matrices, whose cardinality is one of the two maximal possible values, that is, pt(n−1)(n−2)/2 and ptn(n−3)/2, as well as their number.
Existence of positive entire solutions for weakly coupled semilinear elliptic systems
Authors: Furusho Yasuhiro 
Published: November 2011

SynopsisWeakly coupled semilinear elliptic systems of the formare considered in RN, N≧2, where k = 1, 2, …, M, u = (u1, …, uM) and λ is a real constant. The aim of this paper is to give sufficient conditions for (*) to have entire solutions whose components are positive in RN and converge to non-negative constants as |x| tends to ∞. For this purpose a new supersolution-subsolution method is developed for the system (*) without any hypotheses on the monotonicity of the non-linear terms fk with respect to u.
On a result of Petersson concerning the modular group
Authors: Stothers W. W. 
Published: November 2011

SynopsisLet N(u, g, h) denote the number of subgroups of index u, genus g and parabolic class number h in the classical modular group. In 1974, Petersson proved that, for g = 0 and h = 1, 2, N(u, g, h) grows exponentially with u. We obtain a formula valid for all g and h. From this we derive an asymptotic estimate, showing that Petersson's result gives the correct type of growth. The proofs use coset diagrams.
The principle of limiting absorption for Laplacians on two-point homogeneous spaces
Authors: Thompson M. 
Published: November 2011

SynopsisThe present note is concerned to develop the principle of limiting absorption for the Laplacian Δ on a two-point homogeneous noncompact space M = G/H subject to a real-valued potential perturbation V. Such a property depends on the detailed structure of the Laplacian in a suitable coordinate system while V is assumed to satisfy a short-range condition.
Commuting linear differential expressions
Authors: Giertz M. , Kwong M. K. , Zettl A. 
Published: November 2011

SynopsisWe consider the question: When do two ordinary linear differential expressions commute? It turns out that the set of all expressions which commute with a given one form a commutative ring. Here we study the algebraic structure of these rings. As an application a complete characterization of normal differential expressions is obtained.