Many problems in computation can be specified in terms of computing the inverseof an easily constructed function. However, studies on how to derive an algorithm froma problem specification involving inverse functions are relatively rare. The aim of thisthesis is to demonstrate, in an example-driven style, a number of techniques to do the job.The techniques are based on the frame...

Abstract In this article, we define the following: Let N 0 {{\mathbb{N}}}_{0} be set of all nonnegative integers and D = ( d i ) ∈ D={\left({d}_{i})}_...

The basic Schema Theorem for genetic algorithms is modiied for a grammatically-based learning system. A context-free grammar is used to deene a language in which each sentence is mapped to a tness value. The derivation trees associated with these sentences are used to deene the structure of schemata. The eeect of crossover and mutation on schemata is described. A schema theorem is developed whi...

A unital $C^*$ -- algebra $mathcal A,$ endowed withthe Lie product $[x,y]=xy- yx$ on $mathcal A,$ is called a Lie$C^*$ -- algebra. Let $mathcal A$ be a Lie $C^*$ -- algebra and$g,h:mathcal A to mathcal A$ be $Bbb C$ -- linear mappings. A$Bbb C$ -- linear mapping $f:mathcal A to mathcal A$ is calleda Lie $(g,h)$ -- double derivation if$f([a,b])=[f(a),b]+[a,f(b)]+[g(a),h(b)]+[h(a),g(b)]$ for all ...

A simple derivation of the effective spin-wave Hamiltonian for a double-exchange system with infinitely large Hund’s-rule coupling is demonstrated. The formalism can be applied to models with arbitrary range of hopping as well as those with randomness. The result shows that, within the leading order of the 1/S expansion, one magnon excitation spectrum can be described by the Heisenberg model.

We tabulate angularly reduced fourth-order many-body corrections to matrix elements for univalent atoms, derived in [A. Emmons, Phys. Rev. A 65 , 052115 (2002)]. In particular we focus on practically important diagrams complementary to those included cluster method truncated at single and double excitations. Derivation and angular reduction of a large number of diagrams have the help of symboli...

In this paper we revisit several recent results on monotone and strictly monotone Hurwitz numbers, providing new proofs. In particular, we use various versions of these numbers to discuss methods of derivation of quantum spectral curves from the point of view of KP integrability and derive new examples of quantum curves for the families of double Hurwitz numbers.

The main results of the combinatorial theory of maximal biprefix codes of words (Ckari, Perrin, Schtitzenberger) are extended to the codes of paths in a graph in this paper: degree and decoding of double-infinite paths, finiteness of codes of a given degree, the CCsari-Schiitzenberger algorithm, derivation and integration of codes will be discussed.

We show that  higher derivations on a Hilbert$C^{*}-$module associated with the Cauchy functional equation satisfying generalized Hyers--Ulam stability.  

We show that the BRST Lagrangian double copy construction of $\mathcal{N}=0$ supergravity as `square' Yang-Mills theory finds a natural interpretation in terms homotopy algebras. significantly expand on our previous work arguing validity at loop level, and we give detailed derivation copied operator. Our constructions are very general can be applied to vast set examples.