The main purpose of this paper is to study the functional equation arising in dynamic programming of multistage decision processes f x opty∈Dopt{p x, y , q x, y f a x, y , r x, y f b x, y , s x, y f c x, y } for all x ∈ S. A few iterative algorithms for solving the functional equation are suggested. The existence, uniqueness and iterative approximations of solutions for the functional equation ...

f0(v) log f0(v)dv for all t ≥ 0. Assume that in a dilute gas or plasma, particles collide by pairs, due to a repulsive force proportional to 1/r, where r stands for the distance between the two particles. Then if s ∈ (2,∞), the velocity distribution solves the corresponding Boltzmann equation [14, 15]. But if s = 2, the Boltzmann equation is meaningless [14] and is often replaced by the Landau ...

Given a nonlinear It^ o equation dx(t)=f(x(t);t)dt+ug(x(t);t)dw(t), suppose that the equation is almost surely exponentially stable provided the noise intensity u is large enough. We show that if u is replaced by u= R t 0 jr(s)x(s)j p ds, then the equation stabilizes itself in the sense that R 1 0 jr(t)x(t)j p dt<1 a.s. Moreover, if u is replaced by u=sup 0t jr(s)x(s)j, then the equation stabil...

A new equation for microbial growth has been proposed and its implications discussed. The proposed equation has a distinct advantage over B e r t a l a n f f y ' s in being an explicit relationship between growth parameter and time. Attempt has been made to read the proposed equation in the light of H i n s h e 1 w o o d's auto-synthetic model. The constants occurring in the proposed equation h...

SNOW 2.0, a software oriented stream cipher proposed by T. Johansson and P. Ekdahl in 2002 as an enhanced version of the NESSIE finalist SNOW 1.0, is usually considered as one of the strongest stream ciphers designed so far. This paper investigates the resistance of SNOW 2.0 against algebraic attacks. This is motivated by the fact that the main source of non-linearity in SNOW 2.0 comes from a p...

Differentially 4-uniform permutations on F22k with high nonlinearity are often chosen as Substitution boxes in both block and stream ciphers. Recently, Qu et al. introduced a class of functions, which are called preferred functions, to construct a lot of infinite families of such permutations [21]. In this paper, we propose a particular type of Boolean functions to characterize the preferred fu...

Block and stream ciphers are widely used to protect the privacy of digital informa-tion. A variety of attacks against block and stream ciphers exist; the most recentbeing the algebraic attacks. These attacks reduce the cipher to a simple algebraicsystem which can be solved by known algebraic techniques. These attacks havebeen very successful against a variety of stream ciphers a...

Nekrasov's integral equation describing water waves of permanent form, determines the angle φ (s) that the wave surface makes with the horizontal. The independent variable s is a suitably scaled velocity potential, evaluated at the free surface, with the origin corresponding to the crest of the wave. For all waves, except for amplitudes near the maximum, φ (s) satisfies the inequality |φ (s) | ...