bluuebunny/crossref_metadata_2025_split huggingface dataset:
Self-adjoint subspace extensions satisfying λ-linear boundary conditions
Authors: Röh Harald 
Published: November 2011

SynopsisLet S be a symmetric subspace in a Hilbert space ℋ2 with finite equal deficiency indices and let S* be its adjoint subspace in ℋ2. We consider those self-adjoint subspace extensions ℋ of S into some larger Hilbert spaces ℋ2 = (ℋ × ℂm)2 which satisfy H⋂({0} × ℂm)2 = {{0,0}}. These extensions H are characterized in terms of inhomogeneous boundary conditions for S*; they are associated with eigenvalue problems for S* depending on λ-linear boundary conditions, which we also characterize.
Jacobi-type polynomials under an indefinite inner product
Authors: Mingarelli Angelo B. , Krall Allan M. 
Published: November 2011

SynopsisThe polynomials which are orthogonal with respect towhen α> – 1, M>0 are considered when α<–1 and/or M<0. The Cauchy regularization of 〈·, ·〉 provides orthogonality and generates a Pontrjagin (Krein) space spanned by the polynomials. The polynomials are eigenfunctions associated with a self-adjoint, fourth order differential operator.
Some classes of linear bornological spaces
Authors: Canela Miguel A. 
Published: November 2011

SynopsisIn this paper, two classes of linear bornological spaces are considered, the Kolmogorov spaces and the spaces of type b. These spaces satisfy conditions which are weakenings of the definition of infratopological linear bornological spaces. Various properties of these spaces are proved, and two examples are given, showing the independence of the two conditions introduced.
On the swirling flow between rotating coaxial disks, asymptotic behaviour, I
Authors: Kreiss Heinz Otto , Parter Seymour V. 
Published: November 2011

SynopsisConsider solutions 〈H(x, ε), G(x, ε)〉 of the von Kármán equations for the swirling flow between two rotating coaxial disksandWe also assume that |H(x, ε)|≦B√(ε) while |G(x, ε)|≦B. This work considers the shapes and asymptotic behaviour as ε→0+. We consider the kind of limit functions that are permissible. The only possible limits (interior) for G(x, ε) are constants. If that limit constant is not zero, then ε−½H(x, ε) will also tend to a constant.
Periodic and constant solutions of matrix Riccati differential equations: n = 2
Authors: Sánchez David A. 
Published: November 2011

SynopsisSeveral formulas are developed which can be used to determine constant solutions and the possible periods of periodic solutions (if any) of autonomous homogeneous matrix Riccati differential equations. These formulas are used to analyse some 2 × 2 cases, as well as to discuss the existence of periodic solutions under weak periodic forcing.
Some properties of periodic B-spline collocation matrices
Authors: Lee S. L. , Micchelli C. A. , Sharma A. , Smith P. W. 
Published: November 2011

SynopsisIn three recent papers by Cavaretta et al., progress has been made in understanding the structure of bi-infinite totally positive matrices which have a block Toeplitz structure. The motivation for these papers came from certain problems of infinite spline interpolation where total positivity played an important role.In this paper, we re-examine a class of infinite spline interpolation problems. We derive new results concerning the associated infinite matrices (periodic B-spline collocation matrices) which go beyond consequences of the general theory. Among other things, we identify the dimension of the null space of these matrices as the width of the largest band of strictly positive elements.
On the number of simple eigenvalues of a graph
Authors: Rowlinson Peter 
Published: November 2011

SynopsisLet Γ be a graph with n points, and let G be the group of automorphisms of Γ. An orbit of G on which G acts as an elementary abelian 2-group is said to be exceptional. It is shown that the number of simple eigenvalues of Γ is at most (5n+4t)/9, where t is the number of points of Γ lying in exceptional orbits of G.
On the existence of nodal domains for elliptic differential operators
Authors: Müller-Pfeiffer E. 
Published: November 2011

SynopsisWe prove that the selfadjoint elliptic differential equation (1) has rectangular nodal domains if the quadratic form of the equation takes on negative values. The existence of nodal domains is closely connected with the position of the smallest point of the spectrum of the corresponding selfadjoint operator (Friedrichs extension). If the smallest point of a second order selfadjoint differential operator with Dirichlet boundary conditions is an eigenvalue, then this eigenvalue is strictly increasing when the (possibly unbounded) domain, where the coefficients of the differential operator are denned, is shrinking (Theorem 4).
A fixed point theorem for α-condensing maps on a sphere
Authors: Massatt Paul 
Published: November 2011

SynopsisThis paper shows that ifSis a sphere in a Banach space andf:S→Sis an α-contraction, thenfhas a fixed point. The paper generalizes a result of R. D. Nussbaum which holds for α-contractions only. The proof uses the Browder nonrepulsive fixed point theorem and is motivated by recent work of M. Martelli and G. D. Cooperman.
A two point boundary value problem for neutral functional differential equations
Authors: Sficas Y. G. , Ntouyas S. K. 
Published: November 2011

SynopsisThis paper is concerned with the existence of solutions of a two point boundary value problem for neutral functional differential equations. We consider the problemwhere M and N are n × n matrices. This is examined by using the “shooting method”. Also, an example is given to illustrate how our result can be applied to yield the existence of solutions of a periodic boundary value problem.
Solvability of cardinal spline interpolation problems
Authors: Goodman T. N. T. 
Published: November 2011

SynopsisWe consider interpolation by piecewise polynomials, where the interpolation conditions are on certain derivatives of the function at certain points of a periodic vector x, specified by a periodic incidence matrix G. Similarly, we allow discontinuity of certain derivatives of the piecewise polynomial at certain points of x, specified by a periodic incidence matrix H. This generalises the well-known cardinal spline interpolation of Schoenberg. We investigate conditions on G, H and x under which there is a unique bounded solution for any given bounded data.
On left quasinormal orthodox semigroups
Authors: Gomes Gracinda M. S. 
Published: November 2011

SynopsisThe existence of a smallest inverse congruence on an orthodox semigroup is known. It is also known that a regular semigroupSis locally inverse and orthodox if and only if there exists a local isomorphism fromSonto an inverse semigroupT.In this paper, we show the existence of a smallestR-unipotent congruence ρ on an orthodox semigroupSand give its expression in the case whereSis also left quasinormal. Finally, we prove that a regular semigroupSis left quasinormal and orthodox if and only if there exists a local isomorphism fromSonto anR-unipotent semigroupT.
Towers of submanifolds of Grassmannians
Authors: Rees Elmer 
Published: November 2011

SynopsisThere is a conjecture that a tower of smooth subvarieties V(n) with fixed codimension l in Gk(ℂn) must be a standard example. It is shown that even under topological hypotheses, all cohomological invariants of such a tower must coincide with those of standard examples.
A non-probabilistic approach to Poisson spaces
Authors: Paterson Alan L. T. 
Published: November 2011

SynopsisUsing techniques from probability theory, it has been established that if μ is a probability measure on a separable, locally compact group, then the space of μ-harmonic functions on the group can be identified with C(X) for some compact, Hausdorff space X. The space X is known as the Poisson space of μ. We generalise this result in the context of a measure μ on a locally compact semigroup S, in particular establishing the existence of a Poisson space for non-separable groups. The proof is non-probabilistic, and depends on properties of projections on C(K)(K compact Hausdorff). We then show that if S is compact and the support of μ generates S, then the Poisson space associated with μ, is X, where X×G×Y is the Rees product representing the kernel of S.
Admissibility criteria for shock wave solutions of a system of conservation laws of mixed type
Authors: Shearer Michael 
Published: November 2011

SynopsisThe following system of conservation laws is considered:where σ: ℝ→ℝ is a smooth function monotonically increasing except in an interval. Two criteria for the admissibility of shocks are shown to be independent in the sense that there are shocks satisfying each and violating the other. This contrasts with the corresponding situation for strictly hyperbolic systems (σ'(u)>0 for all u), for which the two criteria are equivalent.
A congruence-free semigroup associated with an infinite cardinal number
Authors: Marques M. Paula O. 
Published: November 2011

SynopsisLet X be a set with infinite cardinality m and let Qm be the semigroupof balanced elements in ℐ(X), as described by Howie. If I is the ideal{αεQm:|Xα|<m} then the Rees factor Pm = Qm/I is O-bisimple and idempotent-generated. Its minimum non-trivial homomorphic image has both these properties and is congruence-free. Moreover, has depth 4, in the sense that [E()]4 = , [E()]3≠
Continuous data dependence in linear elastodynamics on unbounded domains without definiteness conditions on the elasticities
Authors: Galdi Giovanni P. , Rionero Salvatore 
Published: November 2011

SynopsisBy suitably coupling convexity and weight function methods, we prove uniqueness and continuous dependence theorems in linear elastodynamics in unbounded domains without definiteness conditions on the elasticities. The class of solutions considered allows the “growth” at large spatial distances.
Parameterization of the M(λ) function for a Hamiltonian system of limit circle type
Authors: Hinton D. B. , Shaw J. K. 
Published: November 2011

SynopsisThe authors continue their study of Titchmarch-Weyl matrix M(λ) functions for linear Hamiltonian systems. A representation for the M(λ) function is obtained in the case where the system is limit circle, or maximum deficiency index, type. The representation reduces, in a special case, to a parameterization for scalar m-coefficients due to C. T. Fulton. A proof that matrix M(λ) functions are meromorphic in the limit circle case is given.
The Hilbert boundary value problem for nonlinear elliptic systems
Authors: Begehr Heinrich , Hsiao George C. 
Published: November 2011

SynopsisThe Hilbert boundary value problem for a first order nonlinear elliptic system in the plane with linear boundary conditions of nonnegative index is (under suitable side conditions uniquely) solved by use of the Newton imbedding method. This constructive method is based on an a priori estimate which arises from an integral representation formula for C1-functions first developed by Haack and Wendland. The approximation procedure yields an error estimate too.
Cardinal interpolation by Dm-splines
Authors: Goodman T. N. T. , Lee S. L. 
Published: November 2011

SynopsisDuchon (1978) considered interpolation in ℝn by “Dm-splines”, which are interpolating functions having, in a sense, minimum energy. The purpose of this paper is to consider the analogous interpolation at the lattice of points in ℝn with integer co-ordinates, generalising aspects of Schoenberg's (1973) theory of cardinal spline interpolation. Following Schoenberg, we prove that higher order “basic” splines can be written as convolutions of lower order ones, using a new notion of convolution due to Jones (1982).
Operators of minimal norm via modified Green's functions
Authors: Kleinman R. E. , Roach G. F. 
Published: November 2011

SynopsisThe exterior Dirichlet and Neumann problems can be treated very satisfactorily by using a fundamental solution which is modified by adding radiating spherical wave functions. It has been shown [3], that the coefficients of these added terms can be chosen to ensure that the associated boundary integral equation formulation of the problem was uniquely solvable and, in addition, that the modified Green's function was a least squares best approximation to the exact Green's function for the problem. Here we show that the coefficients can be chosen to ensure not only unique solvability but also minimization of the norm of the modified integral operator. This leads to a constructive method of solution. The theory is illustrated when the boundary is a sphere and when it is a perturbation of a sphere.
Cohen elements in Banach algebras
Authors: Sinclair Allan M. 
Published: November 2011

SynopsisThe definition of Cohen elements in a commutative Banach algebra with a countable bounded approximate identity given by Esterle is modified slightly to be more analogous to the invertible elements in a unital Banach algebra. With the modified definition the n1-Cohen factorization results that were proved by Esterle are shown tohold in the semigroup of Cohen elements. If is the algebra of continuous complex valued functions vanishing at infinity on a σ-compact locally compact Hausdorff space X, then the Cohen elements in are identified and a natural quotient of a subsemigroup of Cohen elements is shown to be a group, isomorphic to the abstract index group of C(X∪{∞}).
Non-linear functional differential equations and abstract integral equations
Authors: Kappel F. , Schappacher W. 
Published: November 2011

SynopsisThe equivalence between solutions of functional differential equations and an abstract integral equation is investigated. Using this result we derive a general approximation result in the state space C and consider as an example approximation by first order spline functions. During the last twenty years C1-semigroups of linear transformations have played an important role in the theory of linear autonomous functional differential equations (cf. for instance the discussion in [9, Section 7.7]). Applications of non-linear semigroup theory to functional differential equations are rather recent beginning with a paper by Webb [17]. Since then a considerable number of papers deal with problems in this direction. A common feature of the majority of these papers is that as a first step with the functional differential equation there is associated a non-linear operator A in a suitable Banach-space. Then appropriate conditions are imposed on the problem such that the conditions of the Crandall-Liggett-Theorem [5] hold for the operator A. This gives a non-linear semigroup. Finally the connection of this semigroup tothe solutions of the original differential equation has to be investigated [c.f. 8, 15, 18]. To solve thislast problem in general is the most difficult part of this approach.In the present paper we consider the given functional differential equation as a perturbation of the simple equationx = 0. The solutions of this equation generate a very simple C1-semigroup. The solutions of the original functional differential equation generate solutions of an integral equation which is the variation of constants formula for the abstract Cauchy problem associated with the equation x = 0. Under very mild conditions we can prove a one-to-one correspondence between solutions of the given functional differential equation and solutions of the integral equation in the Lp-space setting. In the C-space setting the integral equation inthe state space has to be replaced by a ‘pointwise’ integral equation. Using the pointwise integral equation together with a theorem which guarantees continuous dependence of fixed points on parameters we show under rather weak hypotheses that the original functional differential equation can be approximated by a sequence of ordinary differential equations. Using 1st order spline functions we finally get results which are very similar to those obtained in [1 and 11] in the L2-space setting.
Effects of a sharp pressure rise on a compressible laminar boundary layer, when the Prandtl number is σ = 0.72
Authors: Curle N. 
Published: November 2011

SynopsisFollowing an earlier paper (Curle 1978) we consider a compressible laminar boundary layer with uniform pressure when the distance x along the wall satisfies x < x0 and a prescribed large adverse pressure gradient when x > x0. The viscosity and absolute temperature are again taken to be proportional, but the Prandtl number is no longer assumed to be unity. After applying the Illingworth-Stewartson transformation, the transformed external velocity u1(x) is chosen so thatis large and constant, where Ts is the stagnation temperature, Tw is the (constant) Wall temperature and u0 is the upstream value of u1(x).The flow reacts to this sharp pressure rise mainly in a thin inner sublayer, so inner and outer asymptotic expansions are derived and matched for functions F and S which determine the stream function and the temperature.The skin friction, heat transfer, displacement thickness and momentum thickness are determined as functions of , andinvolve two parameters B1, B2, which depend upon the Mach number and the walltemperature. Detailed numerical calculations are presented here for σ = 0.72. In particular, it is seen that the heat transfer rate varies roughly like σ⅓ except near to separation, where it varies like σ¼.
On the deficiency indices of a fourth order singular differential operator
Authors: Wood Alastair D. 
Published: November 2011

SynopsisWe consider the operatorL[y] =y(4)+ ((ax2+bx+c)y′)′ +dyon the half-line [0, ∞). This paper shows that the deficiency indices are independent of the real numbersb, canddwhena≠ 0. They depend only on the sign ofaand are (2,2) ifa< 0 and (3, 3) ifa> 0. In the casea=0 the sign ofbmust be considered.
The point-continuous spectrum of second-order, ordinary differential operators
Authors: Thurlow Christine 
Published: November 2011

SynopsisGiven any countably infinite set of isloated points on the ℷ -axis, it is shown that there is a continuous q(x) such that these points constitute exactly the point-continuous spectrum for the equation yn″(x) + (ℷ —q(x))y(x) = 0(0≦x<∞) with some homogenous boundary condition at x = 0. This extends a result given by Eastham and McLeod for countably infinite sets of isolated points on the positive ℷ-axis.
Comportement à l'infini pour certains systèmes dissipatifs non linéaires
Authors: Haraux A. 
Published: November 2011

SynopsisIn the Hilbert space framework, we give some results concerning the behaviour when t goes to infinity for solutions of equations of the form:A is assumed to be a maximal monotone operator and F(t) is a periodic function.When F = 0, under a compactness assumption for trajectories of (1), we give the complete description of the asymptotic behaviour, e.g. every trajectory is asymptotic to an almost-periodic solution of (1). When F ≠ cst, the compactness hypothesis being too restrictive, we concentrate our efforts on the case of the equation:with Dirichlet boundary condition) and get weak convergence to particular solutions of the equation when β is either univalued or strictly monotone. The methods used in these cases seem of general interest for hyperbolic equations of dissipative type with periodic forcing term.
Stability theory for quasi-linear wave equations with linear damping
Authors: Dickey R. W. 
Published: November 2011

SynopsisLarge time behaviour of solutions to a damped quasi-linear wave equation are studied. Conditions are obtained which guarantee the global existence of a classical solution. The asymptotic behaviour of this solution is studied in the case of a unique equilibrium solution and in the case of multiple equilibria. The results are applied to various special examples.
A differentiability property and its application to the spectral theory of differential operators
Authors: Kauffman Robert M. 
Published: November 2011

SynopsisFor an ordinary differential operation Lλ of order 2N which depends differentiably on a parameter λ, we study the differentiability with respect to λ of all solutions to Lλf = 0 which are in L2[a,∞). Applications to spectral theory are given, including a formula for the rate of change with respect to the end-point a of the spectrum of the weighted eigenvalue problem Lf = λwf, f∈L2[a,∞), f[i](a) = 0 for i ≦N − 1. The weight w may be a function or an operator. The formula seems new even when w = 1.
A variational inequality approach to Hele-Shaw flow with a moving boundary
Authors: Elliott C. M. , Janovský V. 
Published: November 2011

SynopsisThis paper is concerned with the study of a mathematical model of the injection of fluid into a finite Hele–Shaw cell. The mathematical problem is one of solving Laplace's equation in an unknown region whose boundary changes with time. By a transformation of the dependent variable, an elliptic variational inequality formulation of the moving boundary problem is obtained. The variational inequality is shown to have a unique solution up to the time at which the cell is filled. Regularity results for the solution of the inequality are obtained by studying a penalty approximation of the inequality.
Enumeration of smooth labelled graphs
Authors: Wright E. M. 
Published: November 2011

SynopsisAn (n,q) graph is a graph on n labelled points andqlines without loops or multiple lines. We write ν(n,q) for the number of smooth (n,q) graphs, i.e. connected graphs without end points, and ν =V(Z,Y) = ∑n,qν(n,q)ZnYq/n! for the exponential generating function of ν(n,q). We use the Riddell “core and mantle” method to find an explicit form forV(not, as usual with this method, only a functional equation). From this we deduce a partial differential equation satisfied byV.We interpret this equation in purely combinatorial terms. We writeVk= ∑nν(n,n+k)Xn/n! and find a recurrence formula forVkfor successivek.We use these and other results to find an asymptotic expansion for ν(n,q) asn→∞ when (q/n) −logn−log logn→ + ∞ and an asymptotic approximation to ν(n,n+k) when 0 <k=oand to log ν(n,n+k) whenk<(1−ε).
Linear evolution equations in two Banach spaces
Authors: Sauer Niko 
Published: November 2011

SynopsisWe consider the ordinary differential equation [Bu(t)]′ = Au(t) with A and B linear operators with domains in a Banach space X and ranges in a Banach space Y. The initial condition is that the limit as (t → 0 of Bu(t) is prescribed in Y. We study the properties of the “solution operator” S(t) which maps the initial state in Y to the solution u(t) at time t. The notion of infinitesimal generator A of S(t) is introduced and the relationships between S(t), an associated semi-group E(t), the operators A and B and some other operators are studied. In particular a pair of operators Ao and Bo, derived from A and B, determine the family S(t) of operators. These so-called “generating pairs” are characterized. The operators A and B and Ao and Bo need not be closed, but form so-called closed pairs which is a weaker condition. We also discuss two applications of the theory.
Oscillation of second-order hyperbolic equations with non-integrable coefficients
Authors: Hsiang Wu-Teh , Kwong Man Kam 
Published: November 2011

SynopsisSome sufficient conditions are obtained on the coefficient g and the initial values Φ and ψfor the solution ot the non-linear hyperbolic equationto change sign in the first quadrant. An example is given to show that is not sufficient in the linear case.
A perturbation theorem for exponential dichotomies
Authors: Palmer Kenneth J. 
Published: November 2011

SynopsisSuppose the linear equation x' = A(t)x has an exponential dichotomy and suppose B(t) is close to A(t) in the following sense: on any interval of length 2T, B(t) is close to some translate A(t + τ) of A(t) (actually the conditions in the paper are slightly weaker than this). Then if T is sufficiently large, the equation y' = B(t)y also has an exponential dichotomy. This generalises the usual roughness theorem for exponential dichotomies.