The use of the term \landscape" is increasing rapidly in the eld of evolutionary computation, yet in many cases it remains poorly, if at all, deened. This situation has perhaps developed because everyone grasps the imagery immediately, and the questions that would be asked of a less evocative term do not get asked. This paper presents an important consequence of a new model of landscapes. The m...

The second-order partial differential wave Equation (Cauchy’s first equation of motion), derived from Newton’s force equilibrium, describes a standing field consisting two waves propagating in opposite directions, and is, therefore, “two-way equation”. Due to the second order differentials analytical solutions only exist few cases. “binomial factorization” linear two-way operator into first-ord...

let a be a bounded linear operator on a banach space x. we investigate the conditions of existing rank-one operator b such that i+f(a)b is invertible for every analytic function f on sigma(a). also we compare the invariant subspaces of f(a)b and b. this work is motivated by an operator method on the banach space ell^2 for solving some pdes which is extended to general operator space under some ...

let h be a finite dimensional complex hilbert space, b(h)+ be the set of all positive semi-definite operators on h and phi is a (not necessarily linear) unital map of b(h) + preserving the entropy-gibbs transformation. then there exists either a unitary or an anti-unitary operator u on h such that phi(a) = uau* for any b(h) +. thermodynamics, a branch of physics that is concerned with the study...