The Asymptotic Equipartition Property (AEP) in information theory is the analog of the Law of Large Numbers in probability theory. Assume that the binary random variable X has a probability mass function defined by p(1) = 2/3, and p(0) = 1/3, where X1,X2,...,Xn are i.i.d. random variables according to p(x), and we want to observe a realization of the sequenceX1,X2,...,Xn, where n −→ ∞. We will ...

Building on symbolic self-completion theory, we conceptualize group identity as a goal toward which group members strive, using material symbols of that identity. We report four studies showing that the value placed on such material symbols (e.g., a building) depends on commitment to group identity, the extent to which a symbol can be used to represent in-group identity, and situational variabi...

Systematically derived equations for fluid-loaded thin poroelastic layers are presented for time-harmonic conditions. The layer is modeled according to Biot theory for both open and closed pores. Series expansion techniques in the thickness variable are used, resulting in separate symmetric and antisymmetric plate equations. These equations, which are believed to be asymptotically correct, are ...

In this paper we present a new exact schema theory for genetic programming and variable-length genetic algorithms which is applicable to the general class of homologous crossovers. These are a group of operators, including GP one-point crossover and GP uniform crossover, where the offspring are created preserving the position of the genetic material taken from the parents. The theory is based o...

We study a class of first-order theories whose complete quantifier-free types with one free variable either have a trivial positive part or are isolated by a positive quantifier-free formula—plus a few other technical requirements. The theory of vector spaces and the theory fields are examples. We prove the amalgamation property and the existence of a model-companion. We show that the model-com...

Let A be an n × n real matrix. An eigenvector of A is a vector such that Ax is parallel to x; in other words, Ax = λx for some real or complex number λ. This number λ is called the eigenvalue of A belonging to eigenvector v. Clearly λ is an eigenvalue iff the matrix A − λI is singular, equivalently, iff det(A − λI) = 0. This is an algebraic equation of degree n for λ, and hence has n roots (wit...

Abstract In view of strengthening reinforced PTFE/Al composite system, based on the fiber mechanism and cross-scale theory material, research about material component system design, mechanical property design microstructure optimization was carried out by means theoretical analysis numerical simulation. The properties with different carbon content aspect ratio were studied using short fiber.