We use a path integral representation to solve the Eigen and Crow-Kimura molecular evolution models for the case of multiple fitness peaks with arbitrary fitness and degradation functions. In the general case, we find that the solution to these molecular evolution models can be written as the optimum of a fitness function, with constraints enforced by Lagrange multipliers and with a term accoun...

In the evolutionary computation research community, the performance of most evolutionary algorithms (EAs) depends strongly on their implemented coordinate system. However, the commonly used coordinate system is fixed and not well suited for different function landscapes, EAs thus might not search efficiently. To overcome this shortcoming, in this paper we propose a framework, named ACoS, to ada...

Relational learning has received extensive attentions in recent years since a huge amount of data is generated every day in the cyber-space andmost of them is organized by the relations between entities. Themain tasks of the relational learning include discovering the communities of entities, classifying the entities, and make predictions of possible new relations. Since the graph is a natural ...

In the present paper a method is proposed to investigate the free vibration of a partially liquid-filled cylindrical tank. The mechanical properties of the container are assumed to change continuously along the thickness according to volume fraction Power-law, Sigmoid or Exponential distribution. The liquid is supposed to be incompressible and in viscid and its velocity potential is formulated ...

In this work, we prove the existence of a spectral function for singular q-Sturm-Liouville operator. Further, we establish a Parseval equality and expansion formula in eigenfunctions by terms of the spectral function.

In this paper, one of the numerical solution method of one- particle, one dimensional timeindependentSchrodinger equation are presented that allows one to obtain accurate bound state eigenvalues and functions for an arbitrary potential energy function V(x).For each case, we draw eigen functions versus the related reduced variable for the correspondingenergies. The paper ended with a comparison ...

For the free vibrations of multi-degree mechanical structures appeared in structural dynamics, we solve quadratic eigenvalue problem either by linearizing it to a generalized or directly treating developing iterative detection methods for real and complex eigenvalues. To problem, impose nonzero exciting vector into eigen-equation, nonhomogeneous linear system obtain response curve, which consis...

Molecular dynamics simulations using a dissociative water potential were applied to study transport of excess protons in water and determine the applicability of this potential to describe such behavior. While originally developed for gas-phase molecules and bulk liquid water, the potential is transferrable to nanoconfinement and interface scenarios. Applied here, it shows proton behavior consi...

mathematics or on quantum mechanics. List of All Articles 16 4.3 General Solution to Wave Equation Mukul Agrawal Noticing that f j t (t) forms an orthonormal set of functions, we get ( ∂ 2 ∂x2 + ∂ 2 ∂y2 + ∂ 2 ∂ z2 ) f j xyz(x,y,z) =−εμ0ωj f j xyz(x,y,z) (15) Hence the space dependent separable part of the eigen function of the operator i ∂ ∂ t , i.e. the f j xyz(x,y,z), should be an eigen funct...

The so-called ”acoustic revival mechanism” of core-collapse supernova proposed recently by the Arizona group is an interesting new possibility. Aiming to understand the elementary processes involved in the mechanism, we have calculated the eigen frequencies and eigen functions for the g-mode oscillations of a non-rotating proto neutron star. The g-modes have relatively small eigen frequencies. ...