We investigate the convergence behavior of the normalized least mean square (NLMS) algorithm in the structure of a linear transversal filter. At the n-th iteration, the traditional NLMS transversal filter generates the n-th output signal by using linear convolution of the n-th input vector and the n-th coefficient vector. Based on this result, the n-th coefficient vector is updated to the n + 1...

semilinear stochastic evolution equations with multiplicative l'evy noise are considered‎. ‎the drift term is assumed to be monotone nonlinear and with linear growth‎. ‎unlike other similar works‎, ‎we do not impose coercivity conditions on coefficients‎. ‎we establish the continuous dependence of the mild solution with respect to initial conditions and also on coefficients. ‎as corollaries of ...

For self-dual codes with all weights divisible by an integer greater than one, the minimum distance is bounded by the Mallows-Sloane upper bounds and by their improvements due to Krasikov-Litsyn and Rains. We obtain the improved upper bounds from short relations with constant coefficients on suitable binomial moments of the codes. In this approach, the Mallows-Sloane bounds are analogues of the...

Let NR([k]) denote the set of words over the alphabet [k] = {1, . . . , k} with no consecutive repeated letters. Given a word w = w1 . . . wn ∈ NR([k]), or more generally in [k]∗, we say that a pair 〈wi, wj〉 matches the μ pattern if i < j, wi < wj, and there is no i < k < j such that wi ≤ wk ≤ wj. We say that 〈wi, wj〉 is a trivial μ-match if wi + 1 = wj and a nontrivial μ-match if wi + 1 < wj. ...

In this paper we study some aspects of a conjecture on the convolution of univalent functions in the unit disk D , which was recently proposed by Grünberg, Ronning, and Ruscheweyh (Trans. Amer. Math. Soc. 322 (1990), 377-393) and is as follows: let 3 := {/ analytic in D: \f"(z)\ < Ref'(z), z £ D} and g, h £ S? (the class of normalized univalent functions in D) . Then Ke(f*g*h)(z)/z > 0 in D . W...

In this study we consider further analysis on the classification problem of linear second order partial differential equations with non-constant coefficients. The equations are produced by using convolution with odd or even functions. It is shown that the patent of classification of new equations is similar to the classification of the original equations.

In this paper certain classes of meromorphic functions in punctured unit disk are defined. Some properties including coefficient inequalities, convolution and other interesting results are investigated.

By considering the famous identity on the convolution of the central binomial coefficients

Making use of the familiar convolution structure of analytic functions, in this paper we introduce and investigate two new subclasses of multivalently analytic functions of complex order. Among the various results obtained here for each of these function classes, we derive the coefficient inequalities and other interesting properties and characteristics for functions belonging to the class intr...

In this paper, involving Wgh operators W q ([α1]) and W p q ([α1 + 1]), a generalized class of k-uniformly starlike functions is defined. Some results on coefficient inequalities, inclusion and convolution properties for functions belonging to this class are derived. Our results generalize some of the previously obtained results as well as generate new ones.