In this note, we consider the parabolic Anderson model on R+×R, driven by a Gaussian noise which is fractional in time with index H0>1∕2 and space 03∕4. Under general condition initial data, prove existence uniqueness of mild solution obtain its exponential upper bounds for all p-th moments p≥2.

Let denote by Fk,n the nth k-Fibonacci number where Fk,n = kFk,n−1+Fk,n−2 for n 2 with initial conditions Fk,0 = 0, Fk,1 = 1, we may derive a functionalequation f(k, x) = kf(k, x − 1) + f(k, x − 2). In this paper, we solve thisequation and prove its Hyere-Ulam stability in the class of functions f : N×R ! X,where X is a real Banach space.

In the paper the relation is given between linear difference equations with constant coefficients those obtained via the application of forward and backward differences. Relation is also established between input-output difference equations and state-space difference equations, which define the state of inner quantities of a discrete system. In conclusion, the state-space representation of a di...

This paper examines the recently developed p-shift iterative unbiased Kalman-like algorithm intended for filtering (p = 0), prediction (p > 0), and smoothing (p < 0) of linear discrete time-varying state-space models in non Gaussian environment with uncertainties. The algorithm is designed to have no requirements for noise and initial conditions and becomes optimal on large averaging intervals....

We examined the effect of goal specificity on a search in two problem spaces: a hypothesis space and an instance space. Two hypotheses were considered: 1) a nonspecific goal facilitates a search in a hypothesis space more than a specific goal, and 2) as a hypothesis space is searched more, the performance in discovering the target rule improves. We also defined an initial hypothesis space consi...

0

0

ABS methods are direct iterative methods for solving linear systems of equations, where the i-th iteration satisfies the first i equations. Thus, a system of m equations is solved in at most m ABS iterates. In 2004 and 2007, two-step ABS methods were introduced in at most [((m+1))/2] steps to solve full row rank linear systems of equations. These methods consuming less space, are more compress ...

A model of the equations of two dimensional problems in a half space, whose surface in free of micropolar thermoelastic medium possesses cubic symmetry as a result of a Mode-I Crack is studied. There acts an initial magnetic field parallel to the plane boundary of the half- space. The crack is subjected to prescribed temperature and stress distribution. The formulation in the context of the Lor...