Maeda-type Decomposition of CJ-generated Algebraic Lattices

We prove necessary and sufficient conditions for the decomposition of an arbitrary CJ-generated algebraic lattice into a direct product of subdirectly irreducible lattices. We generalize earlier results due to F. Maeda, T. Katriák and the present author. New structure theorems for two classes of CJ-generated algebraic lattices are also obtained.AMS Subject Classification (1991) 06B05 06B10Research partially supported by Hungarian National foundation for Scientific Research, Grant No. T029525 and T030243 and by János Bolyai Grant of Hungarian Academy of Science.     

The multi-soliton solutions of the CH-γ equation

This paper solves the integrable CH-γ equation for analytical multiple soliton solutions with the Darboux transformation method. Some properties of the soliton solutions are different from the CH equation. This work was partially supported by the National Natural Science Foundation of China (Grant No. 10401022) and the Research Grants Council of Hong Kong     

Orthogonal separable Hamiltonian systems on <Emphasis Type="Italic">T</Emphasis><Superscript>2</Superscript>

In this paper we characterize the Liouvillian integrable orthogonal separable Hamiltonian systems on T ² for a given metric, and prove that the Hamiltonian flow on any compact level hypersurface has zero topological entropy. Furthermore, by examples we show that the integrable Hamiltonian systems on T ² can have complicated dynamical phenomena. For instance they can have several families of invariant tori, each family is bounded by the homoclinic-loop-like cylinders and heteroclinic-loop-like cylinders. As we know, it is the first concrete example to present the families of invariant tori at the same time appearing in such a complicated way. This work is partially supported by the National Natural Science Foundation of China (Grant Nos. 10671123, 10231020), “Dawn” Program of Shanghai Education Comission of China (Grant No. 03SG10) and Program for New Century Excellent Tatents in University of China (Grant No. 050391)     

Finite equational bases for congruence modular varieties

In this paper it is proved that a variety generated by a finite algebraic system with finitely many operations is finitely axiomatizable, provided that the variety is congruence modular and residually small. This result is an extension to congruence modular varieties of a well known theorem for congruence distributive varieties, due to K. A. Baker. Also, under somewhat less restrictive hypotheses, (which are satisfied by finite groups and rings) it is proved that a finite algebraic system belongs to a finitely axiomatizable locally finite variety.Research supported by National Science Foundation Grant No. DMS-8302295.Presented by George Gratzer.     

Structure of commutative cancellative integral residuated lattices on (0, 1]

ΠMTL-algebras were introduced as an algebraic counterpart of the cancellative extension of monoidal t-norm based logic. It was shown that they form a variety generated by ΠMTL-chains on the real interval [0, 1]. In this paper the structure of these generators is investigated. The results illuminate the structure of cancellative integral commutative residuated chains, because every such algebra belongs to the quasivariety generated by the zero-free subreducts on (0, 1] of all ΠMTL-chains on [0, 1]. The work of the author was partly supported by the grant No. A100300503 of the Grant Agency of the Academy of Sciences of the Czech Republic and partly by the Institutional Research Plan AV0Z10300504.     

Quantum volterra model and the universalR-matrix

We prove that an integrable system solved by the quantum inverse scattering method can be described by a purely algebraic object (universal R-matrix) and a proper algebraic representation. For the quantum Volterra model, we construct the L-operator and the fundamental R-matrix from the universal R-matrix for the quantum affine algebra U_q(ŝl₂) and the q-oscillator representation for it. Thus, there is an equivalence between an integrable system with the symmetry algebra A and the representation of this algebra. Translated from Teoreticheskaya i Matematicheskaya Fizika, Vol. 113, No. 3, pp. 384–396, December, 1997.     

Weakly symmetric spaces and spherical varieties

Weakly symmetric homogeneous spaces were introduced by A. Selberg in 1956. We prove that, for a real reductive algebraic group, they can be characterized as the spaces of real points of affine spherical homogeneous varieties of the complexified group. As an application, under the same assumption on the transitive group, we show that weakly symmetric spaces are precisely the homogeneous Riemannian manifolds with commutative algebra of invariant differential operators.Supported by the Alexander von Humboldt Foundation and Russian Foundation for Basic Research, Grant No. 95-01-01263.Supported by the U. S. Civilian Research and Development Foundation, Award No. 206, Russian Foundation for Basic Research, Grant No. 98-01-00598, and the Alexander von Humboldt Foundation.     

Characterization and structure of Finsler spaces with constant flag curvature

The geometric characterization and structure of Finsler manifolds with constant flag curvature (CFC) are studied. It is proved that a Finsler space has constant flag curvature 1 (resp. 0) if and only if the Ricci curvature along the Hilbert form on the projective sphere bundle attains identically its maximum (resp. Ricci scalar). The horizontal distributionH of this bundle is integrable if and only ifM has zero flag curvature. When a Finsler space has CFC, Hilbert form’s orthogonal complement in the horizontal distribution is also integrable. Moreover, the minimality of its foliations is equivalent to given Finsler space being Riemannian, and its first normal space is vertical Project supported by Wang KC Fundation of Hong Kong and the National Natural Science Foundation of China (Grant No. 19571005).     

On decoupling,series expansions,and tail behavior of chaos processes

Some important aspects of chaos random variables such as decoupling, an almost sure representation (a Karhunen-Loeve expansion) and integrability are discussed here, the first being a tool for, and the third as a consequence of, the second. The main goal in this note is to learn about the structure of the limit laws ofU-processes.Research partially supported by National Science Foundation Grant No. DMS-9000132 and University of Connecticut Grant No. G12-913501.     

Minimal circumscribed Hermitian ellipsoid of Hartogs domains and an application to an extremal problem

In this paper we construct circumscribed Hermitian ellipsoids of Hartogs domains of least volume and as an application, we obtain the Carath′eodory extremal mappings between the Hartogs domains and the unit ball, and also give an explicit formula for calculating the extremal values.     

Efficient implementation of heuristics for the continuous network design problem

In this paper, we present an efficient implementation of heuristic procedures for solving the continuous network design problem where network users behave according to Wardrop's first principle of traffic equilibrium. Numerical results involving a standard benchmark problem are given. Also, it is shown that the cost mapping arising in the Iterative-Optimization-Assignment algorithm is integrable if and only if the volume-delay function is of either the BPR or some logarithmic form.Research supported by the National Sciences and Engineering Research Council of Canada (Grant A5789) and the Academic Research Program of the Department of National Defense (Grant FUHBP).     

Convergence rates for probabilities of moderate deviations for moving average processes

The present paper first shows that, without any dependent structure assumptions for a sequence of random variables, the refined results of the complete convergence for the sequence is equivalent to the corresponding complete moment convergence of the sequence. Then this paper investigates the convergence rates and refined convergence rates （or complete moment convergence） for probabilities of moderate deviations of moving average processes. The results in this paper extend and generalize some well-known results.     

Use of dynamic trees in a network simplex algorithm for the maximum flow problem

Goldfarb and Hao (1990) have proposed a pivot rule for the primal network simplex algorithm that will solve a maximum flow problem on ann-vertex,m-arc network in at mostnm pivots and O(n ² m) time. In this paper we describe how to extend the dynamic tree data structure of Sleator and Tarjan (1983, 1985) to reduce the running time of this algorithm to O(nm logn). This bound is less than a logarithmic factor larger than those of the fastest known algorithms for the problem. Our extension of dynamic trees is interesting in its own right and may well have additional applications.Research partially supported by a Presidential Young Investigator Award from the National Science Foundation, Grant No. CCR-8858097, an IBM Faculty Development Award, and AT&T Bell Laboratories.Research partially supported by the Office of Naval Research, Contract No. N00014-87-K-0467.Research partially supported by the National Science Foundation, Grant No. DCR-8605961, and the Office of Naval Research, Contract No. N00014-87-K-0467.     

A new proof of <Emphasis Type="Italic">L</Emphasis><Superscript><Emphasis Type="Italic">p</Emphasis></Superscript> estimates for the parabolic polyharmonic equations

In this paper we obtain local L ^p estimates for the parabolic polyharmonic equations by a straightforward approach. Yao was supported by the Innovation Foundation of Shanghai University (Grant No. A10-0101-08-905), Shanghai Leading Academic Discipline Project (Grant No. J50101) and Key Disciplines of Shanghai Municipality (Grant No. S30104). Zhou was supported by the National Basic Research Program of China (Grant No. 2006CB705700), National Natural Science Foundation of China (Grant No. 60532080), and the Key Project of Chinese Ministry of Education (Grant No. 306017)     

On (2<Superscript><Emphasis Type="Italic">m</Emphasis></Superscript> + 1)-variable symmetric Boolean functions with submaximum algebraic immunity 2<Superscript><Emphasis Type="Italic">m</Emphasis>−1</Superscript>

All (2 ^m + 1)-variable symmetric Boolean functions with submaximal algebraic immunity 2 ^m−1 are described and constructed. The total number of such Boolean functions is 3² · 2^2m−3 +3 ^m−2 · 2⁴ − 2 for m ⩾ 2. This work was supported by the Major State Basic Research Development Program of China (Grant No. 2004CB3180004) and National Natural Science Foundation of China (Grant No. 60433050)     

An adaptive numerical method for solving linear Fredholm integral equations of the first kind

A general procedure is presented for numerically solving linear Fredholm integral equations of the first kind. The approximate solution is expressed as a continuous piecewise linear (spline) function. The method involves collocation followed by the solution of an appropriately scaled stabilized linear algebraic system. The procedure may be used iteratively to improve the accuracy of the approximate solution. Several numerical examples are given.Supported in part by the Office of Naval Research under Contract No. NR 044-457.Supported in part by the National Science Foundation under Grant No. GJ-31827.     

Algebraic integrability: The Adler-Van Moerbeke approach

In this paper, I present an overview of the active area of algebraic completely integrable systems in the sense of Adler and van Moerbeke. These are integrable systems whose trajectories are straight line motions on abelian varieties (complex algebraic tori). We make, via the Kowalewski-Painlevé analysis, a study of the level manifolds of the systems. These manifolds are described explicitly as being affine part of abelian varieties and the flow can be solved by quadrature, that is to say their solutions can be expressed in terms of abelian integrals. The Adler-Van Moerbeke method’s which will be used is devoted to illustrate how to decide about the algebraic completely integrable Hamiltonian systems and it is primarily analytical but heavily inspired by algebraic geometrical methods. I will discuss some interesting and well known examples of algebraic completely integrable systems: a five-dimensional system, the Hénon-Heiles system, the Kowalewski rigid body motion and the geodesic flow on the group SO(n) for a left invariant metric.     

Extensions of nilpotent blocks over arbitrary fields

In this paper, with a suitable condition, we describe the algebraic structure of block extensions of nilpotent blocks over arbitrary fields, thus generalize the main result of B. Külshammer and L. Puig on block extensions of nilpotent blocks over algebraically closed fields. Supported by NSFC (Grant No.: 10501016).     

The Paley-Wiener theorem in the non-commutative and non-associative octonions

The Paley-Wiener theorem in the non-commutative and non-associative octonion analytic function space is proved. This work was supported by the National Basic Research Program of China (Grant No. 1999075105), the National Natural Science Foundation of China (Grant No. 10471002) and Research Foundation for Doctoral Programm (Grant No. 20050574002)     

Real zeros of the zero-dimensional parametric piecewise algebraic variety

The piecewise algebraic variety is the set of all common zeros of multivariate splines. We show that solving a parametric piecewise algebraic variety amounts to solve a finite number of parametric polynomial systems containing strict inequalities. With the regular decomposition of semi-algebraic systems and the partial cylindrical algebraic decomposition method, we give a method to compute the supremum of the number of torsion-free real zeros of a given zero-dimensional parametric piecewise algebraic variety, and to get distributions of the number of real zeros in every n-dimensional cell when the number reaches the supremum. This method also produces corresponding necessary and sufficient conditions for reaching the supremum and its distributions. We also present an algorithm to produce a necessary and sufficient condition for a given zero-dimensional parametric piecewise algebraic variety to have a given number of distinct torsion-free real zeros in every n-cell in the n-complex. This work was supported by National Natural Science Foundation of China (Grant Nos. 10271022, 60373093, 60533060), the Natural Science Foundation of Zhejiang Province (Grant No. Y7080068) and the Foundation of Department of Education of Zhejiang Province (Grant Nos. 20070628 and Y200802999)