and Applied Analysis 3 Affine transformation element to b set a = In t+1 Mapping from a a b X = {I1 t+1, I2 t+1, . . . , In t+1} I = {I1 (t+1)(x0,y0), . . . , I 1 (t+1)(xn,yn), . . . , I n (t+1)(xn,yn)} b = {I1 (t+1)(x,y), . . . , I1 (t+1)(x,y)} Figure 2: Affine transformation from X to I. the transfer of the probability state of the affine transformation parameters is obtained, the function of...

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An affine invariant point on the class of convex bodies Kn in R, endowed with the Hausdorff metric, is a continuous map from Kn to R which is invariant under one-to-one affine transformations A on R, that is, p ` A(K) ́ = A ` p(K) ́ . We define here the new notion of dual affine point q of an affine invariant point p by the formula q(K) = p(K) for every K ∈ Kn, where K denotes the polar of K with...

We prove that the well-known 3/2 stability condition established for the Wright equation (WE) still holds if the nonlinearity p(exp(−x)−1) in WE is replaced by a decreasing or unimodal smooth function f with f (0) < 0 satisfying the standard negative feedback and below boundedness conditions and having everywhere negative Schwarz derivative.

The Boolean expression of an analogical proportion, i.e., a statement of the form “a is to b as c is to d”, expresses that “a differs from b as c differs from d, and vice-versa. This is the basis of an analogical inference principle, which is shown to be a particular instance of the analogical “jump”: from P (s), P (t), and Q(s), deduceQ(t). Roughly speaking, an analogical proportion sounds lik...

Affine point pattern matching (APPM) is an integral part of many pattern recognition problems. Given two sets P and Q of points with unknown assignments pi → qj between the points, no additional information is available. The following task must be solved: – Find an affine transformation T such that the distance between P and the transformed set Q′ = TQ is minimal. In this paper, we present a ne...

The genetic architecture of a phenotype consists of the genes, the interactions among them (epistasis), and the interactions among genes and environments (G · E) that affect the phenotype’s expression (Wade et al., 2001). For a phenotype with a ‘complex’ genetic architecture, epistasis and G · E play significant roles as opposed to a phenotype with a ‘simple’ architecture, in which interactions...

Abstract. The object of the present paper is to establish an integral formula involving Wright generalized Bessel function (or generalized Bessel-Maitland function) J ν,q (z) defined by Singh et al. [21], which is expressed in the terms of generalized (Wright) hypergeometric functions. Some interesting special cases involving Bessel functions, generalized Bessel functions, generalized Mittag-Le...

We present an algorithm computing, for any first order differential equation L over the affine line and any (Berkovich) point t of this affine line, the p-adic radius of convergence RL(t) of the solutions of L near t. We do explicit computations for the equation (0.1) L(f) def = xf ′ − π(px + ax)f = 0 (πp−1 = −p). where a lies in some valued extension of Qp. For a = −1 and t = 0, a solution of ...