We present a rigorous derivation of the flow at arbitrary time in a deterministic cellular automaton model of traffic flow. The derivation employs regularities in preimages of blocks of zeros, reducing the problem of preimage enumeration to a well-known lattice path counting problem. Assuming infinite lattice size and random initial configuration, the flow can be expressed in terms of generaliz...

Abstract. The underlying field is of characteristic p > 2. In this paper, we first use the method of computing the homogeneous derivations to determine the first cohomology of the so-called odd contact Lie algebra with coefficients in the even part of the generalized Witt Lie superalgebra. In particular, we give a generating set for the Lie algebra under consideration. Finally, as an applicatio...

In this article we introduce the notion of a generalized system of fundamental sequences and we define its associated slow-growing hierarchy. We claim that these concepts are genuinely related to the classification of the complexity—the derivation length— of rewrite systems for which termination is provable by a standard termination ordering. To substantiate this claim, we re-obtain multiple re...

We construct the states that are invariant under action of generalized squeezing operator $\exp{(z{a^{\dagger k}}-z^*a^k)}$ for arbitrary positive integer $k$. The given explicitly in number representation. find a value $k$ there such states. show behave as $n^{-k/4}$ when occupation $n\to\infty$. This implies any $k\geq3$ normalizable. For $k$, expectation values operators form $(a^{\dagger} a...

Stream X-machines are a general and powerful computational model. By coupling the control structure of a stream X-machine with a set of formal grammars a new machine called generalized stream X-machine with underlying distributed grammars, acting as a translator, is obtained. By introducing this new mechanism a hierarchy of computational models is provided. If the grammars are of a particular c...

In this report, generalized wave breaking equations are developed using three dimensional fully nonlinear extended Boussinesq equations to encompass rotational dynamics in wave breaking zone. The derivation for vorticity distributions are developed from Reynold based stress equations.

We present a derivation of Gosper's algorithm which permits generalization to higher-order recurrences with constant least and most significant coefficients. Like Gosper's algorithm, the generalized algorithm requires only 'rational' operations (such as gcd and resultant computations) but no factorization.

We discuss the generalized Touchard polynomials introduced recently by Dattoli et al. as well as their extension to negative order introduced by the authors with operationial methods. The connection to generalized Stirling and Bell numbers is elucidated and analogs to Burchnall’s identity are derived. A recursion relation for the generalized Touchard polynomials is established and it is shown t...

In this paper, we study the generalized derivation of a Lie sub-algebra algebra polynomial vector fields on $\mathbb{R}^n$ where $n\geq1$, containing all constant and Euler field, under some conditions sub-algebra.