Showing papers in "Journal of Mathematical Sciences in 1998"
120 citations
TL;DR: In this article, a trace formula expressing the mean values of the form (k = 2,3,...) is derived, where the sum is taken over a normalized orthogonal basis in the space of holomorphic cusp forms of weight 2k.
Abstract: A trace formula expressing the mean values of the form (k=2,3,...)
$$\frac{{\Gamma (2k - 1)}}{{(4\pi )^{2k - 1} }}\sum\limits_f {\frac{{\lambda _f (d)}}{{\left\langle {f,f} \right\rangle }}H_f^{(x)} (s_1 )\frac{{}}{{H_f^{(x)} (\bar s_2 )}}}$$
via certain arithmetic means on the group Г0(N1) is proved. Here the sum is taken over a normalized orthogonal basis in the space of holomorphic cusp forms of weight 2k with respect to Г0(N1). By Hf(x)(s) we denote the Hecke series of the form f, twisted with the primitive character χ (mod N2), and λf(d), (d, N1N2)=1, are the eigenvalues of the Hecke operators
$$T_{2k} (d)f(z) = d^{k - 1/2} \sum\limits_{d_1 d_2 = d} {d_2^{ - 2k} } \cdot \sum\limits_{m(\bmod d_2 )} {f\left( {\frac{{d_1 z + m}}{{d_2 }}} \right)}$$
. The trace formula is used for obtaining the estimate
$$\frac{{d^l }}{{dt^l }}H_f^{(x)} \left( {\frac{1}{2} + it} \right) \ll _{\varepsilon ,k,l,N_1 } (1 + \left| t \right|)^{1/2 + \varepsilon } N_2^{1/2 - 1/8 + \varepsilon }$$
for the newform f for all e>0, l=0,1,2,.... This improves the known result (Duke-Friedlander-Iwaniec, 1993) with upper bound (1+|t|)2N21/2−1/22+e on the right-hand side. As a corollary, we obtain the estimate
$$c(n) \ll _\varepsilon n^{1/4 - 1/16 + \varepsilon }$$
for the Fourier coefficients of holomorphic cusp forms of weight k+1/2, which improves Iwaniec' result (1987) with exponent 1/4–1/28+e. Bibliography: 25 titles.
68 citations
61 citations
TL;DR: In this article, the Sugawara construction is used to obtain representations of Krichever-Novikov vector field algebras of affine type via a higher genus affine Kac-Moody algebra.
Abstract: We show how to obtain from highest weight representations of Krichever-Novikov algebras of affine type (also called higher genus affine Kac-Moody algebras) representations of centrally extended Krichever-Novikov vector field algebras via the Sugawara construction. This generalizes classical results where one obtains representations of the Virasoro algebra. Relations between the weights of the corresponding representations are given and Casimir operators are constructed. In an appendix the Sugawara construction for the multi-point situation is done.
50 citations
TL;DR: In this article, a modification of a test for independence based on the empirical characteristic function is investigated, which makes the test always consistent and asymptotically distribution free, and is based on a special transformation of the data.
Abstract: A modification of a test for independence based on the empirical characteristic function is investigated. The initial test is not consistent in the general case. The modification makes the test always consistent and asymptotically distribution free. It is based on a special transformation of the data.
48 citations
TL;DR: In this paper, it was shown that every positive operator has the polynomial property and the kernel and co-kernel of the corresponding operator are described in terms of a finite-dimensional lineal P of vector-valued polynomials.
Abstract: The formally self-adjoint boundary-value problem possesses the polynomial property if the corresponding sesquilinear form degenerates only on a finite-dimensional lineal P of vector-valued polynomials. A problem with the polynomial property is elliptic. The kernel and co-kernel of the corresponding operator are described in terms of P. It is shown that every formally positive operator has the polynomial property. Bibliography: 22 titles.
43 citations
TL;DR: In this paper, a new solution of the Yang-Baxter equation with spectral parameter is found, and the resulting R-matrix R(x) is an operator inH⊗H, whereH=L2(ℝ).
Abstract: A new solution of the Yang-Baxter equation with spectral parameter is found. The resulting R-matrix R(x) is an operator inH⊗H, whereH=L2(ℝ). This R-matrix is required to justify the solution of the sine-Gordon model on the discrete space-time. Bibliography: 18 titles.
40 citations
TL;DR: In this paper, a new class of tests for testing the homogeneity of two independent polynomial samples is proposed, which are a natural extension of those based on Jaccard's index of similarity.
Abstract: A new class of tests for testing the homogeneity of two independent polynomial samples is proposed Our tests are a natural extension of those based on Jaccard's index of similarity The theory of separable statistics is applied We investigate asymptotic powers of these tests The results of numerical analysis allow us to select the asymptotically optimal test of similarity within this class
36 citations
TL;DR: New determinant representations for the simplest correlation functions of the Heisenberg XY spin chain were obtained for the first time in this article, where the determinant function is defined as a function of the correlation function.
Abstract: New determinant representations are obtained for the simplest correlation functions of the Heisenberg XY spin chain. Bibliography: 8 titles.
35 citations
TL;DR: The class of functions which are analytic in |z| β,Re α>0, β 0, 0 0, δ > 0, is convex or starlike as discussed by the authors.
Abstract: Let A denote the class of functions which are analytic in |z| β,Re α>0, β 0, 0 0, δ>0, is convex or starlike. Bibliography: 16 titles.
31 citations
TL;DR: Pre preconditioning of linear algebraic systems with symmetric positive-definite coefficient matrices by deflation is considered and the possibility of using the extreme Ritz vectors of the coefficient matrix for deflation is analyzed.
Abstract: In this paper, preconditioning of linear algebraic systems with symmetric positive-definite coefficient matrices by deflation is considered. The twofold deflation technique for simultaneously deflating largest s and smallest s eigenvalues using an appropriate deflating subspace of dimension s is suggested. The possibility of using the extreme Ritz vectors of the coefficient matrix for deflation is analyzed. Bibliography: 15 titles.
TL;DR: The main aim of as discussed by the authors is to describe all positive measures on the unit circle such that all continuous functions f ∈ H2⊖θH2 can be expressed as
Abstract: Let θ be an inner function. The main aim of this paper is to describe all positive measures on the unit circle
$$\mathbb{T}$$
such that
$$\int\limits_\mathbb{T} {\left| f \right|^2 } d\mu = \left\| f \right\|_{H^2 }^2 $$
for all continuous functions f∈H2⊖θH2. Bibliography: 8 titles.
TL;DR: In this paper, an upper estimate for the topological entropy of a dynamical system defined by a system of ODEs is obtained, which involves the Lyapunov functions and Losinskii's logarithmic norm.
Abstract: An upper estimate for the topological entropy of a dynamical system defined by a system of ODE is obtained. The estimate involves the Lyapunov functions and Losinskii’s logarithmic norm. The proof uses the known fact that the topological entropy of a mapping acting in a compact space K can be estimated via the fractal dimension of K. Bibliography: 28 titles.
TL;DR: In this paper, conditions for unique determination of an unknown source in a parabolic equation for the case of general boundary conditions and overdetermined conditions were established for both general and over-specified conditions.
Abstract: We establish conditions for unique determination of an unknown source in a parabolic equation for the case of general boundary conditions and overdetermined conditions.
TL;DR: An approach to solving the following multiparameter algebraic problems is suggested: spectral problems for singular matrices polynomially dependent on q≥2 spectral parameters and the solution of systems of linear algebraic equations with multiparameters polynomial matrices and the construction of inverse and pseudoinverse matrices.
Abstract: An approach to solving the following multiparameter algebraic problems is suggested: (1) spectral problems for singular matrices polynomially dependent on q≥2 spectral parameters, namely: the separation of the regular and singular parts of the spectrum, the computation of the discrete spectrum, and the construction of a basis that is free of a finite regular spectrum of the null-space of polynomial solutions of a multiparameter polynomial matrix; (2) the execution of certain operations over scalar and matrix multiparameter polynomials, including the computation of the GCD of a sequence of polynomials, the division of polynomials by their common divisor, and the computation of relative factorizations of polynomials; (3) the solution of systems of linear algebraic equations with multiparameter polynomial matrices and the construction of inverse and pseudoinverse matrices. This approach is based on the so-called ΔW-q factorizations of polynomial q-parameter matrices and extends the method for solving problems for one- and two-parameter polynomial matrices considered in [1–3] to an arbitrary q≥2. Bibliography: 12 titles.
TL;DR: In this paper, the same authors obtained holdover estimates for weak solutions of doubly nonlinear parabolic equations of the type of fast diffusion with coefficients satisfying natural growth conditions and the monotonicity requirement.
Abstract: Holder estimates for weak solutions of doubly nonlinear parabolic equations of the type of fast diffusion with coefficients satisfying only natural growth conditions and the monotonicity requirement are obtained. Bibliography: 17 titles.
TL;DR: In this article, the Gauss decomposition of quantum groups related to classical Lie groups and supergroups is considered by the elementary algebraic and R-matrix methods, and commutation relations between the generators of the new basis introduced by the decomposition are described in detail.
Abstract: The Gauss decompositions of quantum groups related to classical Lie groups and supergroups are considered by the elementary algebraic and R-matrix methods. The commutation relations between the generators of the new basis introduced by the decomposition are described in detail. It is shown that it is possible to reduce a number of independent generators to the dimension of the related classical group. The symplectic quantum group Spq(2) and supergroups GLq(1, 1) and GLq(2, 1) are considered as examples. Bibliography: 73 titles.
TL;DR: In this article, explicit bounds for the deviation of the distribution of the state probabilities of a perturbed birth-and-death process from that of a nonperturbed one are obtained.
Abstract: Explicit bounds for the deviation of the distribution of the state probabilities of a perturbed birth-and-death process from that of a nonperturbed one are obtained. These bounds appear to be exact in time.
TL;DR: In this article, the spectral properties of polynomial matrices with respect to one or several parameters have been investigated and a method for linearizing such matrices by passing to the accompanying pencils has been proposed.
Abstract: Spectral problems for multiparameter polynomial matrices are considered. The notions of the spectrum (including those of its finite, infinite, regular, and singular parts), of the analytic multiplicity of a point of the spectrum, of bases of null-spaces, of Jordan s-semilattices of vectors and of generating vectors, and of the geometric and complete geometric multiplicities of a point of the spectrum are introduced. The properties of the above characteristics are described. A method for linearizing a polynomial matrix (with respect to one or several parameters) by passing to the accompanying pencils is suggested. The interrelations between spectral characteristics of a polynomial matrix and those of the accompanying pencils are established. Bibliography: 12 titles.
TL;DR: In this paper, the authors investigated a queueing system with geometrically distributed interarrival and service times in which the service of a request may be started upon arrival (in the case of a free system) or at moments differing from it by multiples of the cycle time.
Abstract: On the basis of a real problem connected with the landing of airplanes, the paper investigates a queueing system with geometrically distributed interarrival and service times in which the service of a request may be started upon arrival (in the case of a free system) or (in the case of a busy server, a queue, or noncorresponding position of the request) at moments differing from it by multiples of the cycle time For the service discipline the FIFO rule is assumed Using the embedded-Markov-chain technique (considering the system at moments just before starting the service of a request), the generating function of ergodic probabilities is found and the condition of existence of an ergodic distribution is established
TL;DR: In this paper, the Cauchy-Dirichlet problem for quasilinear parabolic systems of second-order equations is considered in the case of two spatial variables.
Abstract: The Cauchy-Dirichlet problem for quasilinear parabolic systems of second-order equations is considered in the case of two spatial variables. Under the condition that the corresponding elliptic operator has variational structure, the global in time solvability is established. The solution is smooth almost everywhere and the number of singular points is finite. Sufficient conditions that guarantee the absence of singular points are given. Bibliography: 23 titles.
TL;DR: In this article, the authors consider homotopy invariants of ornaments and construct explicity two large series of such invariants and establish some new algebraic structures in the space of invariants.
Abstract: Anornament is a collection of oriented closed curves in a plane, no three of which intersect at the same point. We consider homotopy invariants of ornaments. Thefinite-order invariants of ornaments are a natural analog of the Vassiliev invariants of links. The calculation of them is based on the homological study of the corresponding space of singular objects. We perform the “local” part of these calculations and a part of the “global” one, which allows us to estimate the dimensions of the spaces of invariants of any order. We also construct explicity two large series of such invariants and establish some new algebraic structures in the space of invariants.
TL;DR: In this article, the authors characterized smooth vector fields g on ∂Ω which annihilate all harmonic vector fields f in Ω continuous up to ∂∩, with respect to the pairing.
Abstract: Let Ω⊂ℝN be a smooth bounded domain. We characterize smooth vector fields g on ∂Ω which annihilate all harmonic vector fields f in Ω continuous up to ∂Ω, with respect to the pairing\(\left\langle {f,g} \right\rangle = \int\limits_{\partial \Omega } {f \cdot gd\sigma } \) (dσ denotes the hypersurface measure on ∂Ω). In addition, we extend these results to differential forms with harmonic vector fields being replaced by harmonic fields, i.e., forms f satisfying df=0, δf=0. A smooth form g on ∂Ω is an annihilator if and only if suitable extensions, u and v, into Ω of its normal and tangential components on ∂Ω, satisfy the generalized Cauchy-Riemann system du=δv, δu=0, dv=0 in Ω. Finally, we prove that the described smooth annihilators are weak* dense among all annihilators. Bibliography: 12 titles.
TL;DR: In this paper, the authors studied the effect of the model describing the stress-strain state of plates on the type of integral equations and the structure of their solutions, and showed that taking account of reducing turns the problem into a Volterra integral equation of second kind, which has a unique solution that is continuous and agrees quite well with the results obtained from the three-dimensional theory.
Abstract: We reduce the solution of contact problems in the interaction of rigid bodies (dies) with thin-walled elements (one-dimensional problems) to Volterra integral equations. We study the effect of the model describing the stress-strain state of plates on the type of integral equations and the structure of their solutions. It is shown that taking account of reducing turns the problem into a Volterra integral equation of second kind, which has a unique solution that is continuous and agrees quite well with the results obtained from the three-dimensional theory. In the case of a theory of Timoshenko type the problem is reduced to a Volterra three-dimensional theory. In the case of a theory of Timoshenko type the problem is reduced to a Volterra integral equation of first kind that has a unique continuous solution; but for dies without corners the Herz condition does not hold (p(a) ≠ 0), and the contact pressure assumes its maximal value at the end of the zone of contact. For thin-walled elements, whose state can be described by the classical Kirchhoff-Love theory, the integral equation of the problem (a Volterra equation of first kind) has a solution in the class of distributions. The contact pressure is reduced to concentrated reactions at the extreme points of the contact zone. We give a comparative analysis of the solutions in all the cases just listed (forces, normal displacements, contact pressures). Three figures, 1 table. Bibliography: 5 titles.
TL;DR: In this article, it was shown that for every interior point O of a convex compact set in ℝ3, there exists a two-dimensional section through O circumscribed about an affine image of a regular octagon.
Abstract: Five theorems on polygons and polytopes inscribed in (or circumscribed about) a convex compact set in the plane or space are proved by topological methods. In particular, it is proved that for every interior point O of a convex compact set in ℝ3, there exists a two-dimensional section through O circumscribed about an affine image of a regular octagon. It is also proved that every compact convex set in ℝ3 (except the cases listed below) is circumscribed about an affine image of a cube-octahedron (the convex hull of the midpoints of the edges of a cube). Possible exceptions are provided by the bodies containing a parallelogram P and contained in a cylinder with directrix P. Bibliography: 29 titles.
TL;DR: In this article, an explicit formula for the contractive zero divisor is given for a zero set that consists of two points of arbitrary multiplicities, and a simple one-to-one correspondence between contractive divisors and reproducing kernels for certain weighted Bergman spaces is established.
Abstract: In the Hardy spaces Hp of holomorphic functions, Blaschke products are applied to factor out zeros. However, for Bergman spaces, the zero sets of which do not necessarily satisfy the Blaschke condition, the study of divisors is a more recent development. Hedenmalm proved the existence of a canonical contractive zero-divisor which plays the role of a Blascke product in the Bergman space\(L_\alpha ^2 \left( \mathbb{D} \right)\). Duren, Khavinson, Shapiro, and Sundberg later extended Hedenmalm's result to\(L_\alpha ^p \left( \mathbb{D} \right)\), 0