Two well-known q-Hermite polynomials are the continuous and discrete q-Hermite polynomials. In this paper we consider a new family of q-Hermite polynomials and prove several curious properties about these polynomials. One striking property is the connection with q-Fibonacci and q-Lucas polynomials. The latter relation yields a generalization of the Touchard-Riordan formula.

But these experiments [2] will not give us any information about the dependence or independence of the two factors, namely study habit and home environment. In such cases, we resort to Factorial ANOVA which not only helps us to study the effect of two or more factors but also gives information about their dependence or independence in the same experiment. There are many types of factorial desig...

in this paper, a practical review of the adomian decomposition method, to extend the procedure to handle the strongly nonlinear problems under the mixed conditions, is given and the convergence of the algorithm is proved. for this respect, a new and simple way to generate the adomian polynomials, for a general nonlinear function, is proposed. the proposed procedure, provides an explicit formula...

the main purpose of this article is to present an approximate solution for the two-dimensional nonlinear volterra integral equations using legendre orthogonal polynomials. first, the two-dimensional shifted legendre orthogonal polynomials are defined and the properties of these polynomials are presented. the operational matrix of integration and the product operational matrix are introduced. th...

In this paper we consider the dynamics of the real polynomials of degree d + 1 with a fixed point of multiplicity d ≥ 2. Such polynomials are conjugate to fa,d(x) = axd(x−1)+x, a ∈ R{0}, d ∈ N. Our aim is to study the dynamics fa,d in some special cases.

Design of crystal-like lattices can be achieved by using some net operations. Hypothetical networks, thus obtained, can be characterized in their topology by various counting polynomials and topological indices derived from them. The networks herein presented are related to the Dyck graph and described in terms of Omega polynomial and PIv polynomials.

It has been suggested that sensory information processing makes use of a factorial code. It has been shown that the major components of the hippocampal-entorhinal loop can be derived by conjecturing that the task of this loop is forming and encoding independent components (ICs), one type of factorial codes. However, continuously changing environment poses additional requirements on the coding t...

Received (to be inserted Revised by Publisher) We investigate the consequences of maximizing information transfer in a simple neural network, with bounded and invertible transfer functions. In the case of a vanishing additive output noise, and an even smaller input noise, the main result is that maximization of information (over receptive elds and transfer functions) leads to a factorial code-h...

In this study, a relationship between scanner response (RGB) and CIE tristimulus values (XYZ) is established by regression technique with different polynomials for colored polyester fabrics. The results showed that the transformation process is material dependent and higher order polynomials will fit the experimental data better than lower polynomials. The results also showed that the way the c...

In this study, a relationship between scanner response (RGB) and CIE tristimulus values (XYZ) is established by regression technique with different polynomials for colored polyester fabrics. The results showed that the transformation process is material dependent and higher order polynomials will fit the experimental data better than lower polynomials. The results also showed that the way the c...