Let X, X1, X2, . . . be i.i.d. random variables, and set Sn = X1 + . . . + Xn, Mn = maxk≤n |Sk|, n ≥ 1. Let an = o( √ n/ log n). By using the strong approximation, we prove that: if EX = 0, VarX = σ > 0 and E|X|2+2 < ∞ for some 2 > 0, then for any r > 1, lim 2↗1/√r−1 [2−2 − (r − 1)] ∞ ∑ n=1 nr−2P { Mn ≤ 2σ √ π2n/(8 log n) + an } = 4 π . We also show that the widest an is o( √ n/ log n).

We consider the .n; p/ boundary value problem y C 1⁄2H .t; y/ D 1⁄2K .t; y/; n 1⁄2 2; t 2 .0; 1/; y.1/ D y.0/ D 0; 0 i n 2; where 1⁄2 > 0 and 0 p n 1 is fixed. We characterize the values of 1⁄2 such that the boundary value problem has a positive solution. For the special case 1⁄2 D 1, we also offer sufficient conditions for the existence of positive solutions of the boundary value problem.

Over the past years, the development of technology applications for elderly people has increased, creating new possibilities for treatment. These applications are usually identified as successful solutions for mental health but usability limitations may influence their effective deployment in clinical use. The objective of this study was to examine the usability aspects of a cognitive and physi...

Intercultural communication is now a crucial part of our globalizing lives; however, not everyone has an opportunity to engage in an intercultural interaction with people from different cultures. Computer-based technologies are promising in creating environments for people to communicate with people from diverse cultures. This qualitative synthesis of quantitative and qualitative research there...

A system or family (A. : y E N) of sets A y , indexed by the elements of a set N, is called an (a, b)-system if I N I = a and I A,, I = b for y c-N. Expressions such as "(a, < b)-system" are self-explanatory. The system (A,, : y c N) is called a A-system [1] if A,, n A,, = Ap n A Q whenever p, y, p, c c N ; p 7~ y ; p =A a. If we want to indicate the cardinality I NJ of the index set N then we ...

We consider the following Gierer-Meinhardt system in R 1 : A 0 (?1) = A 0 (1) = H 0 (?1) = H 0 (1) = 0; where (p; q; r; s) satisses 1 < qr (s + 1)(p ? 1) < +1; 1 < p < +1: We rigorously show that the existence and stability of symmetric and asymmetric N?peaked steady-states can be reduced to computing two matrices in terms of the coeecients D; N; p; q; r; s. The main techniques are the Liapunov...

Previous studies have shown that after being trained on A-B and A-C match-to-sample tasks, adults match not only same-class Band C stimuli (equivalence) but also BC compounds with sameclass elements and with different-class elements (BC-BC) . The assumption was that the BC-BC performances are based on matching equivalence and nonequivalence relations (equivalenceequivalence) . The present study...

Hartman I.B.-A., I. Newman and R. Ziv, On grid intersection graphs, Discrete Mathematics 87 (1991) 41-52. A bipartite graph G = (X, Y; E) has a grid representation if X and Y correspond to sets of horizontal and vertical segments in the plane, respectively, such that (xi, y,) E E if and only if segments x, and y, intersect. We prove that all planar bipartite graphs have a grid representation, a...

A b s t r a c t A t o m a t o p d u c t a s e) a r e e n z y m e s t h a t m a y a c c e p t a b r o a d r a n g e o f s u b s t r a t e s i n v i t r o b u t t h d e t h a t t a r g e t t h e m t o t h e s e c r e t o r y p a t h w a y [ a n u t [ 8 ] , t o b a c c o [ 9 ] a n d t o m a t o [ 1 0 ] .

It is well known that if a scalar second order hyperbolic partial differential equation in two independent variables is Darboux integrable, then its local Cauchy problem may be solved by ordinary differential equations. In addition, such an equation has infinitely many non-trivial conservation laws. Moreover, Darboux integrable equations have properties in common with infinite dimensional compl...