Hamiltonian Tri-Integrable Couplings of the AKNS Hierarchy

We propose a systematic approach for generating Hamiltonian tri-integrable couplings of soliton hierarchies. The resulting approach is based on semi-direct sums of matrix Lie algebras consisting of 4 × 4 block matrix Lie algebras. We apply the approach to the AKNS soliton hierarchy, and Hamiltonian structures of the obtained tri-integrable couplings are constructed by the variational identity.     

Complex brain networks: From topological communities to clustered dynamics

Recent research has revealed a rich and complicated network topology in the cortical connectivity of mammalian brains. A challenging task is to understand the implications of such network structures on the functional organisation of the brain activities. We investigate synchronisation dynamics on the corticocortical network of the cat by modelling each node of the network (cortical area) with a subnetwork of interacting excitable neurons. We find that this network of networks displays clustered synchronisation behaviour and the dynamical clusters closely coincide with the topological community structures observed in the anatomical network. The correlation between the firing rate of the areas and the areal intensity is additionally examined. Our results provide insights into the relationship between the global organisation and the functional specialisation of the brain cortex.      

Quasiperiodic Solutions of the Heisenberg Ferromagnet Hierarchy

We present quasi-periodic solutions in terms of Riemann theta functions of the Heisenberg ferromagnet hierarchy by using algebro-geometric method. Our main tools include algebraic curve and Riemann surface, polynomial recursive formulation and a special meromorphic function.     

A Direct Method of Hamiltonian Structure

A direct method of constructing the Hamiltonian structure of the soliton hierarchy with self-consistent sources is proposed through computing the functional derivative under some constraints. The Hamiltonian functional is related with the conservation densities of the corresponding hierarchy. Three examples and their two reductions are given.     

LCZ族发展方程的换位表示

本文给出LCZ族非线性发展方程的换位表示。     

Thermodynamics and Hydrodynamics (Statistical Foundations): 1. The Problem Setup

Analyzing the physical foundations of statistical mechanics, we show that it can only be local. This means that the structure of matter and all its macroscopic parameters (except the density , the velocity of the liquid, and the temperature ) must be determined by what occurs inside a correlation sphere of the radius R10^–7cm; the values of , , and , which play the role of fixed parameters for the BBGKY hierarchy, must be found by solving hydrodynamic equations with macroscopic boundary and initial conditions taken into account.     

A model for standardizing human decisions concerning service-contracts management

Increased expectations of today’s customers are causing businesses to offer a variety of warranty contracts for their products. Because of the intense customer contact that takes place during the process of supporting a contract, the planning for contracts has to not only contend with the unpredictable and low demands of the service parts, but must also rely on human decision-making concerning a number of subjective factors. These subjective factors, which are related to the customer, the contract and the contracted product, have seldom been considered in the literature on inventory planning. Moreover, the evaluation of subjective factors often becomes non-standardized and non-coordinated among the geographically dispersed decision-makers of an organization, as was the situation with a Fortune 100 company’s case that motivated this paper. We propose a combination of a heuristic procedure along with the Analytical Hierarchy Process technique that has not been applied in the inventory-planning setting. We also demonstrate how a Web-based information system can be used to standardize the decision process, and discuss the implications of the system on the motivational case. Computational results are also provided to show the effectiveness of the heuristics.     

AN INTEGRABLE HIERARCHY AND ITS EXPANDING LAX INTEGRABLE MODEL

In general, Liouville integrable hierarchies of evolution equations were obtained by choosing proper U in zero curvature frame Ut - Vx + [U, V] = 0 first. But in the present paper, a new Liouville integrable hierarchy possessing bi-Hamiltonian structure is obtained by choosing V with derivatives in x and spectral potentials. Then integrable coupling, i.e. expanding Lax integrable model of the hierarchy obtained is presented by constructing a subalgebra of loop algebra A2.     

LEVELS OF IMPLICATION AND TYPE FREE THEORIES OF CLASSIFICATIONS WITH APPROXIMATION OPERATOR

We investigate a theory of Frege structures extended by the Myhill-Flagg hierarchy of implications. We study its relation to a property theory with an approximation operator and we give a proof theoretical analysis of the basic system involved. MSC: 03F35, 03D60.     

New properties of a class of generalized kinetic equations

We give some properties of a new class of hard-sphere kinetic equations of great generality, introduced earlier by Polewczak. The assumptions used to obtain the general class are very weak, and the equations include not only the standard and revised Enskog equations, but also generalizations thereof that can be expected to yield essentially exact transport coefficients. In particular, there is a natural two-particle realization that is obtained from maximizing the information entropy subject to prescribed two-particle and one-particle probability distribution functions;k-particle analogs fork > 2 also naturally follow. We obtain Liapunov functionals for the whole class of equations under consideration and discuss the question of which of these functionals can be expected to play the role ofH-functions. We also obtain several more special results that include new lower bounds on the potential part of theH-function for the revised Enskog equation. The bounds are instrumental in obtaining global existence theorems and also imply that the necessary condition for invertibility of the nonequilibrium extension of local activity as a functional of local density is satisfied.