Bounds on convex reliability functions with known first moments

In this paper, upper and lower bounds are derived for convex reliability functions (or survival functions) with known first n moments. The case where the mean and the variance are given (n = 2) is discussed in details and explicit expressions are provided. Extensions for n ? 3 moments are described. Comparisons with existing bounds are performed.     

On the integral equation formulations of some 2D contact problems

Two integral equations, representing the mechanical response of a 2D infinite plate supported along a line and subject to a transverse concentrated force, are examined. The kernels of the integral operators are of the type (x−y)ln|x−y| and (x−y)²ln|x−y|. In spite of the fact that these are only weakly singular, the two equations are studied in a more general framework, which allows us to consider also solutions having non-integrable endpoint singularities. The existence and uniqueness of solutions of the equations are discussed and their endpoint singularities detected.Since the two equations are of interest in their own right, some properties of the associated integral operators are examined in a scale of weighted Sobolev type spaces. Then, new results on the existence and uniqueness of integrable solutions of the equations that in some sense are complementary to those previously obtained are derived.     

Planar unit-distance graphs having planar unit-distance complement

A graph G=(V,E) is called a unit-distance graph in the plane if there is an embedding of V into the plane such that every pair of adjacent vertices are at unit distance apart. If an embedding of V satisfies the condition that two vertices are adjacent if and only if they are at unit distance apart, then G is called a strict unit-distance graph in the plane. A graph G is a (strict) co-unit-distance graph, if both G and its complement are (strict) unit-distance graphs in the plane. We show by an exhaustive enumeration that there are exactly 69 co-unit-distance graphs (65 are strict co-unit-distance graphs), 55 of which are connected (51 are connected strict co-unit-distance graphs), and seven are self-complementary.     

Planes and processes

This article presented to Combinatorics 2006 is a survey of finite projective planes and the processes used to construct them. All non-translation planes are described, fundamental processes in translation planes are defined and some of these are used to connect semi-field flocks with symplectic spreads. Hermitian ovoids are connected to extensions of derivable nets, and three types of ‘lifting’ methods are discussed. Furthermore, hyperbolic fibrations and ‘regulus-inducing’ central collineation groups are connected to flocks of quadratic cones. Finally, hyper-reguli and multiple hyper-regulus replacement are considered.     

Finite-time boundedness and L2-gain analysis for switched delay systems with norm-bounded disturbance

Finite-time boundedness and finite-time weighted L₂-gain for a class of switched delay systems with time-varying exogenous disturbances are studied. Based on the average dwell-time technique, sufficient conditions which guarantee the switched linear system with time-delay is finite-time bounded and has finite-time weighted L₂-gain are given. These conditions are delay-dependent and are given in terms of linear matrix inequalities. Detail proofs are given by using multiple Lyapunov-like functions. An example is employed to verify the efficiency of the proposed method.     

On a signless Laplacian spectral characterization of -shape trees

Let M be an associated matrix of a graph G (the adjacency, Laplacian and signless Laplacian matrix). Two graphs are said to be cospectral with respect to M if they have the same M spectrum. A graph is said to be determined by M spectrum if there is no other non-isomorphic graph with the same spectrum with respect to M. It is shown that T-shape trees are determined by their Laplacian spectra. Moreover among them those are determined by their adjacency spectra are characterized. In this paper, we identify graphs which are cospectral to a given T-shape tree with respect to the signless Laplacian matrix. Subsequently, T-shape trees which are determined by their signless Laplacian spectra are identified.     

Finite difference schemes for the fourth-order parabolic equations with different boundary value conditions

In this paper, the fourth-order parabolic equations with different boundary value conditions are studied. Six kinds of boundary value conditions are proposed. Several numerical differential formulae for the fourth-order derivative are established by the quartic interpolation polynomials and their truncation errors are given with the aid of the Taylor expansion with the integral remainders. Effective difference schemes are presented for the third Dirichlet boundary value problem, the first Neumann boundary value problem and the third Neumann boundary value problem, respectively. Some new embedding inequalities on the discrete function spaces are presented and proved. With the method of energy analysis, the unique solvability, unconditional stability and unconditional convergence of the difference schemes are proved. The convergence orders of derived difference schemes are all O(τ² + h²) in appropriate norms. Finally, some numerical examples are provided to confirm the theoretical results.     

Characterization of mean transformations

The mean transformations M(A,?B) are linear mappings and they are analogues of the matrix means of A,?B?≥?0. They are defined by operator monotone functions. In this article several properties are described and a part of them characterize the concept.     

A determinantal approach to Sheffer–Appell polynomials via monomiality principle

In this article, the Sheffer and Appell polynomials are combined to introduce the family of Sheffer–Appell polynomials by using operational methods. The determinantal definition and other properties of the Sheffer–Appell polynomials are established. As particular cases of these polynomials, the Sheffer–Bernoulli and Sheffer–Euler polynomials are introduced and their determinantal definitions are obtained. The operational correspondence between the Appell and Sheffer–Appell polynomials is used to derive the results for the Sheffer–Appell polynomials. Certain results for the Hermite–Appell and Laguerre–Appell polynomials are also obtained.     

Monadic <Emphasis Type="Italic">GMV</Emphasis>-algebras

Monadic MV-algebras are an algebraic model of the predicate calculus of the Łukasiewicz infinite valued logic in which only a single individual variable occurs. GMV-algebras are a non-commutative generalization of MV-algebras and are an algebraic counterpart of the non-commutative Łukasiewicz infinite valued logic. We introduce monadic GMV-algebras and describe their connections to certain couples of GMV-algebras and to left adjoint mappings of canonical embeddings of GMV-algebras. Furthermore, functional MGMV-algebras are studied and polyadic GMV-algebras are introduced and discussed. The first author was supported by the Council of Czech Government, MSM 6198959214.     

Time shifted aliasing error upper bounds for truncated sampling cardinal series

Time shifted aliasing error upper bound extremals for the sampling reconstruction procedure are fully characterized. Sharp upper bounds are found on the aliasing error of truncated cardinal series and the corresponding extremals are described for entire functions from certain specific Lp, p>1, classes. Analogous results are obtained in multidimensional regular sampling. Truncation error analysis is provided in all cases considered. Moreover, sharpness of bounding inequalities, convergence rates and various sufficient conditions are discussed.     

Spherical symmetric solutions for the motion of relativistic membranes and null membranes in the reissner-nordström space-time

In this article, we concern the motion of relativistic membranes and null membranes in the Reissner-Nordström space-time. The equation of relativistic membranes moving in the Reissner-Nordström space-time is derived and some properties are discussed. Spherical symmetric solutions for the motion are illustrated and some interesting physical phenomena are discovered. The equations of the null membranes are derived and the exact solutions are also given. Spherical symmetric solutions for null membranes are just the two horizons of Reissner-Nordström space-time.     

Functions of a matrix and Krylov matrices

For a given nonderogatory matrix A, formulas are given for functions of A in terms of Krylov matrices of A. Relations between the coefficients of a polynomial of A and the generating vector of a Krylov matrix of A are provided. With the formulas, linear transformations between Krylov matrices and functions of A are introduced, and associated algebraic properties are derived. Hessenberg reduction forms are revisited equipped with appropriate inner products and related properties and matrix factorizations are given.     

Generalized canonical analysis for time series

Canonical correlation analysis is shown to be equivalent to the problem of estimating a linear regression matrix, B₀, of less than full rank. After reparameterizing B₀ some estimates of the new parameters, obtained by solving an eigenvalue problem and closely related to canonical correlations and vectors, are found to be consistent and efficient when the residuals are mutually independent. When the residuals are generated by an autocorrelated, stationary time series these estimates are still consistent and obey a central limit theorem, but they are no longer efficient. Alternative, more general estimates are suggested which are efficient in the presence of serial correlation. Asymptotic theory and iterative computational procedures for these estimates are given. A likelihoodratio test for the rank of B₀ is seen to be an extension of a familiar test for canonical correlations.     

Channel flow of a Maxwell fluid with chemical reaction

This work is concerned with the two-dimensional boundary layer flow of an upper-convected Maxwell (UCM) fluid in a channel with chemical reaction. The walls of the channel are porous. Employing similarity transformations the governing non-linear partial differential equations are reduced into non-linear ordinary differential equations. The resulting ordinary differential equations are solved analytically using homotopy analysis method (HAM). Expressions for series solutions are derived. The convergence of the obtained series solutions are shown explicitly. The effects of Reynold’s number Re, Deborah number De, Schmidt number Sc and chemical reaction parameter γ on the velocity and the concentration fields are shown through graphs and discussed.     

Achievable sets, brambles, and sparse treewidth obstructions

One consequence of the graph minor theorem is that for every k there exists a finite obstruction set Obs(TW?k). However, relatively little is known about these sets, and very few general obstructions are known. The ones that are known are the cliques, and graphs which are formed by removing a few edges from a clique. This paper gives several general constructions of minimal forbidden minors which are sparse in the sense that the ratio of the treewidth to the number of vertices n does not approach 1 as n approaches infinity. We accomplish this by a novel combination of using brambles to provide lower bounds and achievable sets to demonstrate upper bounds. Additionally, we determine the exact treewidth of other basic graph constructions which are not minimal forbidden minors.     

Spherically symmetric random permutations

We consider random permutations which are spherically symmetric with respect to a metric on the symmetric group S_n and are consistent as n varies. The extreme infinitely spherically symmetric permutation‐valued processes are identified for the Hamming, Kendall‐tau and Cayley metrics. The proofs in all three cases are based on a unified approach through stochastic monotonicity.     

Flow equivalence and orbit equivalence for shifts of finite type and isomorphism of their groupoids

We give conditions for when continuous orbit equivalence of one-sided shift spaces implies flow equivalence of the associated two-sided shift spaces. Using groupoid techniques, we prove that this is always the case for shifts of finite type. This generalises a result of Matsumoto and Matui from the irreducible to the general case. We also prove that a pair of one-sided shift spaces of finite type are continuously orbit equivalent if and only if their groupoids are isomorphic, and that the corresponding two-sided shifts are flow equivalent if and only if the groupoids are stably isomorphic. As applications we show that two finite directed graphs with no sinks and no sources are move equivalent if and only if the corresponding graph $C^{?}$-algebras are stably isomorphic by a diagonal-preserving isomorphism (if and only if the corresponding Leavitt path algebras are stably isomorphic by a diagonal-preserving isomorphism), and that two topological Markov chains are flow equivalent if and only if there is a diagonal-preserving isomorphism between the stabilisations of the corresponding Cuntz–Krieger algebras (the latter generalises a result of Matsumoto and Matui about irreducible topological Markov chains with no isolated points to a result about general topological Markov chains). We also show that for general shift spaces, strongly continuous orbit equivalence implies two-sided conjugacy.     

Szeg? type polynomials and para-orthogonal polynomials

Szeg? type polynomials with respect to a linear functional M for which the moments M[tn]=μ−n are all complex, μ−n=μn and Dn≠0 for n?0, are considered. Here, Dn are the associated Toeplitz determinants. Para-orthogonal polynomials are also studied without relying on any integral representation. Relation between the Toeplitz determinants of two different types of moment functionals are given. Starting from the existence of polynomials similar to para-orthogonal polynomials, sufficient conditions for the existence of Szeg? type polynomials are also given. Examples are provided to justify the results.