In the last two decades the Inverse Spectral Transform (IST) method has been generalized and successfully applied to various (2 + 1)-dimensional nonlinear evolution equations such as Kadomtsev–Petviashvili, Davey–Stewardson, Nizhnik–Veselov–Novikov, Zakharov–Manakov system, Ishimory, two dimensional integrable sine-Gordon and others (see books [1, 2, 3, 4] and references therein). The nonlocal ...

We s tudy the u n i f i c a t i o n and match ing problems in the s igned b i n a r y t r ees t h e o r y . We show t h a t any equa t i on tl1=t2 can be t rans formed i n t o an e q u i v a l e n t one x = t . I f x does not occur in t then (x > t) i s the unique most genera l u n i f i e r i n the theory (up to an isomorph ism) . We apply t h i s technique to f i n d recur rence r e l a t i o...

Fur pi-riodit input u(l.). a liTu r i pi i si nt all on L (t) foi t lit clipptr is obtaint-d such tliat llu output \(t) = *(t) u(l). Th» Fourier LOef f ic ii-nt s oi y(t) are obtaimd in Ltrms ol tin Foui i t r coefficients of both e (t ) and u(t). Fei light > lipping, tin Fournr coef f ici ents of y (t ) equa 1 the Feurii i ei t I f ii i eiil s ol u(t ) plus j .s ma 1 1 correct ion fac tor of t...

The DI methods for directly solving a system of a general higher order ODEs are discussed. The convergence of the constant stepsize and constant order formulation of the DI methods is proven first before the convergence for the variable order and stepsize case. 1. INTRODUCTION Many problems in engineering and science can be formulated in terms of such a system. The general system of higher orde...

This paper considers MAP/G/1 queueing systems under the following two situations: (1) At the end of a busy period, the server is turned off and inspects the queue length every time a customer a,rrives. When the queue length reaches a pre-specified value N , the server turns on and serves customers continuously until the system becomes empty. (2) At the end of a busy period, the server takes a s...

Since gravitational wave spacetimes are time-varying vacuum solutions of Einstein’s field equations, there is no unambiguous means to define their energy content. However, Weber and Wheeler had demonstrated that they do impart energy to test particles. There have been various proposals to define the energy content but they have not met with great success. Here we propose a definition using “sli...

We present the Isabelle/HOL formalisation of some key equa-tional properties of the untyped λ-calculus with one-sorted variable names. Existing machine formalisations of λ-calculus proofs typically rely on alternative representations and/or proof principles to facilitate mechanization and we briefly account for these works. Our own development remains faithful to the standard textbook presentat...

Undoubtedly, minimum-fuel and -time orbit transfer are the two major goals of the op timal orbit maneuver. This paper considers two coplanar elliptic orbits when the apsidal l ines coincide. We analytically find the conditions for the two-impulse minimum-time tra nsfer orbit using Lambert’s theorem. In the minimum-time transfer, the transfer time is a decreasing function of a variable related t...

CONSTRUCTION OF EFFECTIVE ELECTROMAGNETIC CURRENTS FOR TWO BODY QUASIPOTENTIAL EQUATIONS Dmitri Krioukov Old Dominion University Director Dr J W Van Orden A systematic algebraic approach for the construction of e ective electro magnetic currents consistent with relativistic two body quasipotential equa tions is presented This approach generalizes the Mandelstam formalism and applies it to a gen...

M~crobial processes are now perceived to be an important component of the marlne food chaln Mathematical models present a quantltatlve means of analys~ng lnterspecles lnteract~ons within food webs Although detalled models of i n d ~ v ~ d u a l components of the m~crobial food web (bacteria, phytoplankton, protozoan predators) have been denved, t hen incorporation into large-scale food web mode...