Imprimitive Q-polynomial Association Schemes

It is well known that imprimitive P-polynomial association schemes with are either bipartite or antipodal, i.e., intersection numbers satisfy either for all for all . In this paper, we show that imprimitive -polynomial association schemes with are either dual bipartite or dual antipodal, i.e., dual intersection numbers satisfy either .     

Minihypers and Linear Codes Meeting the Griesmer Bound: Improvements to Results of Hamada, Helleseth and Maekawa

This article improves results of Hamada, Helleseth and Maekawa on minihypers in projective spaces and linear codes meeting the Griesmer bound.In [10,12],it was shown that any -minihyper, with , where , is the disjoint union of points, lines,..., -dimensional subspaces. For q large, we improve on this result by increasing the upper bound on non-square, to non-square, square, , and (4) for square, p prime, p<3, to . In the case q non-square, the conclusion is the same as written above; the minihyper is the disjoint union of subspaces. When q is square however, the minihyper is either the disjoint union of subspaces, or the disjoint union of subspaces and one subgeometry . For the coding-theoretical problem, our results classify the corresponding codes meeting the Griesmer bound.     

On the Uniqueness of the Recovery of Parameters of the Maxwell System from Dynamical Boundary Data

The paper deals with the problem of recovering the parameters (functions) and of the Maxwell dynamical system

On the Nonexistence of q-ary Linear Codes of Dimension Five

There do not exist codes over the Galois field GF attaining the Griesmer bound for for andfor for .     

Path-Integral Calculations for the First Excited State of Hydrogen Atom

Consider a path-integral which is the solution to a diffusion version of the generalized Schro¨dinger's equation . Here , where A is an infinitesimal generator of a strongly continuous Markov Semigroup corresponding to the diffusion process . For and V replaced by one obtains , which represents a quantum mechanical Hamiltonian corresponding to a particle of mass 1 (in atomic units) subject to interaction with potential V. This paper is concerned with computer calculations of the second eigenvalue of by generating a large number of trajectories of an ergodic diffusion process.     

A Criterion for Contiguity of Quasiconcave Functions

Quasiconcave functions and belong to the same scale if there exist quasiconcave functions and and numbers such that and . We establish a criterion for such functions to belong to the same scale up to equivalence. This criterion is obtained in terms of nodes of the corresponding linear-constant step-functions. It turns out that nodes must be equivalent to sequences.     

On Plane Maximal Curves

The number N of rational points on an algebraic curve of genus g over a finite field satisfies the Hasse–Weil bound . A curve that attains this bound is called maximal. With and , it is known that maximalcurves have . Maximal curves with have been characterized up to isomorphism. A natural genus to be studied is and for this genus there are two non-isomorphic maximal curves known when . Here, a maximal curve with genus g ₂ and a non-singular plane model is characterized as a Fermat curve of degree .     

Sharp Conditions for the CLT of Linear Processes in a Hilbert Space

In this paper we study the behavior of sums of a linear process associated to a strictly stationary sequence with values in a real separable Hilbert space and are linear operators from H to H. One of the results is that satisfies the CLT provided are i.i.d. centered having finite second moments and . We shall provide an example which shows that the condition on the operators is essentially sharp. Extensions of this result are given for sequences of weak dependent random variables under minimal conditions.     

Intersections of Convex Bodies

Let be nonempty convex bodies in . Let be vectors in , let , and let . Then is a convex set, and the family of sets is concave. Let . Then for the mean cross-sectional measures W_v (\Phi (\rho )), , the functions are concave on D. (Note that % MathType!MTEF!2!1!+-% feaafiart1ev1aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn% hiov2DGi1BTfMBaeXafv3ySLgzGmvETj2BSbqefm0B1jxALjhiov2D% aebbnrfifHhDYfgasaacH8srps0lbbf9q8WrFfeuY-Hhbbf9v8qqaq% Fr0xc9pk0xbba9q8WqFfea0-yr0RYxir-Jbba9q8aq0-yq-He9q8qq% Q8frFve9Fve9Ff0dmeaabaqaciGacaGaaeqabaWaaeaaeaaakeaaca% WGxbWaaSbaaSqaaiaaicdaaeqaaOGaaiikaiabfA6agjaacIcacqaH% bpGCcaGGPaGaaiykaiabg2da9iaabAfacaqGVbGaaeiBamaaBaaale% aatCvAUfKttLearyqr1ngBPrgaiuGacqWFRbWAaeqaaOGaeuOPdyKa% aiikaiabeg8aYjaacMcaaaa!4EE7!\[W_0 (\Phi (\rho )) = {\text{Vol}}_k\Phi (\rho )\] is the k-volume.) Bibliography: 2 titles.     

Absolute Continuity of the Spectrum of a Periodic Schrödinger Operator

We prove the absolute continuity of the spectrum of the Schrödinger operator in , , with periodic (with a common period lattice ) scalar and vector potentials for which either , , or the Fourier series of the vector potential converges absolutely, , where is an elementary cell of the lattice , for , and for , and the value of is sufficiently small, where and otherwise, , and .     

A New Critical Behavior for Nonlinear Wave Equations

We study the inhomogeneous semilinear wave equations on with initial values and ,where is a noncompact, complete manifold. We founda new critical behavior in the following sense. There exists ap* > 0. When 1 < p p*, the above problem hasno global solution for any nonnegative not identicallyzero and for any and ; when the problem has a global solution for some and some and . If , which is equipped with the Euclideanmetric, then . If we show that belongs to the blow upcase. Although homogeneous semilinear wave equations are known to exhibit acritical behavior for a long time, this seems to be the first result oninhomogeneous ones.     

Split Orthogonal Arrays and Maximum Independent Resilient Systems of Functions

A system of (Boolean) functions in variables is called randomized if the functions preserve the property of their variables to be independent and uniformly distributed random variables. Such a system is referred to as -resilient if for any substitution of constants for any variables, where 0 i t, the derived system of functions in variables will be also randomized. We investigate the problem of finding the maximum number of functions in variables of which any form a -resilient system. This problem is reduced to the minimization of the size of certain combinatorial designs, which we call split orthogonal arrays. We extend some results of design and coding theory, in particular, a duality in bounding the optimal sizes of codes and designs, in order to obtain upper and lower bounds on . In some cases, these bounds turn out to be very tight. In particular, for some infinite subsequences of integers they allow us to prove that , , , , . We also find a connection of the problem considered with the construction of unequal-error-protection codes and superimposed codes for multiple access in the Hamming channel.     

Effects Connected with the Coincidence of Velocities in the Two-Velocity Dynamical System

The paper deals with the system

Two New Infinite Families of 3-Designs from Kerdock Codes over Z4

In this paper we show that the support of the codewords of each type in the Kerdock code of length 2^m over Z₄ form 3-designs for any odd integer . In particular, twonew infinite families of 3-designs are obtained in this constructionfor any odd integer . In particular, twonew infinite families of 3-designs are obtained in this constructionfor any odd integer , whose parameters are ,and .     

Automorphisms of Aschbacher Graphs

If a regular graph of valence and diameter has vertices, then , which was proved by Moore (cf. [1]). Graphs for which this non-strict inequality turns into an equality are called Moore graphs. Such have an odd girth equal to . The simplest example of a Moore graph is furnished by a -triangle. Damerell proved that a Moore graph of valence has diameter 2. In this case , the graph is strongly regular with and , and the valence is equal to 3 (Peterson's graph), to 7 (Hoffman–Singleton's graph), or to 57. The first two graphs are of rank 3. Whether a Moore graph of valence exists is not known; yet, Aschbacher proved that the Moore graph with will not be a rank 3 graph. We call the Moore graph with the Aschbacher graph. Cameron showed that such cannot be vertex transitive. Here, we treat subgraphs of fixed points of Moore graph automorphisms and an automorphism group of the hypothetical Aschbacher graph for the case where that group contains an involution.     

On Complete Arcs Arising from Plane Curves

We point out an interplay between -Frobenius non-classical plane curves and complete -arcs in . A typical example that shows how this works is the one concerning an Hermitian curve. We present some other examples here which give rise to the existence of new complete -arcs with parameters and being a power of the characteristic. In addition, for q a square, new complete -arcs with either and or and are constructed by using certain reducible plane curves.     

On a Jacobian Identity Associated with Real Hyperplane Arrangements

For the mapping is onto R. It was shown by G. Boole in the 1850's that We give an n-dimensional analogue of this result. The proof makes use of the Griffiths–Harris residue theorem from algebraic geometry.     

The Maximum Size Of Graphs With A Unique<Emphasis Type="Italic">k</Emphasis>- Factor

For suitable positive integers n and k let m(n, k) denote the maximum number of edges in a graph of order n which has a unique k-factor. In 1964, Hetyei and in 1984, Hendry proved for even n and , respectively. Recently, Johann confirmed the following conjectures of Hendry: for and kn even and for n = 2kq, where q is a positive integer. In this paper we prove for and kn even, and we determine m(n, 3).     

Uniform Convergence of Trigonometric Series with Rarely Changing Coefficients

We consider the series and whose coefficients satisfy the condition for , where the sequence can be expressed as the union of a finite number of lacunary sequences. The following results are obtained. If as , then the series is uniformly convergent. If for all , then the sequence of partial sums of this series is uniformly bounded. If the series is convergent for and as , then this series is uniformly convergent. If the sequence of partial sums of the series for is bounded and for all , then the sequence of partial sums of this series is uniformly bounded. In these assertions, conditions on the rates of decrease of the coefficients of the series are also necessary if the sequence is lacunary. In the general case, they are not necessary.     

Simultaneous Preservation of Orthogonality of Polynomials by Linear Operators Arising from Dilation of Orthogonal Polynomial Systems

For an orthogonal polynomial system and a sequence of nonzero numbers,let be the linear operator defined on the linear spaceof all polynomials via for all .We investigate conditions on and under which can simultaneously preserve the orthogonality ofdifferent polynomial systems. As an application, we get that for , a generalized Laguerre polynomial system, no can simultaneously preserve the orthogonality of twoadditional Laguerre systems, and , where and . On the other hand, for ,the Chebyshev polynomial system and , simultaneously preserves the orthogonality of uncountablymany kernel polynomial systems associated with p. We study manyother examples of this type.