In this paper, we obtain a direct result and Voronovskaya type asymptotic formula for the exponential-type operators in simultaneous approximation with polynomial growth. In the end, we obtain the recurrence formulae for the central moments, direct results and Voronovskaya type asymptotic formulae for the various mixed summation-integral type operators. 2000 AMS Subject Classification. 41A28, 4...

Consider a time series with missing observations but a known final point. Using control theory ideas we estimate/predict these missing observations. We obtain recurrence equations which minimize sum of squares of a control sequence. An advantage of this method is in easily computable formulae and flexibility of its application to different structures of missing data.

In this work, we use the generalized Riccati transformation and the inequality technique to establish some new oscillation criteria for the second-order nonlinear delay dynamic equation p t xΔ t γ Δ q t f x τ t 0, on a time scale T, where γ is the quotient of odd positive integers and p(t) and q(t) are positive right-dense continuous rd-continuous functions on T. Our results improve and extend ...

This paper is concerned with oscillation of the second-order halflinear delay dynamic equation (r(t)(x)) + p(t)x(τ(t)) = 0, on a time scale T, where γ ≥ 1 is the quotient of odd positive integers, p(t), and τ : T → T are positive rd-continuous functions on T, r(t) is positive and (delta) differentiable, τ(t) ≤ t, and limt→∞ τ(t) = ∞. We establish some new sufficient conditions which ensure that...

Abstmct--We consider the convergence properties of certain algorithms arising in storhastie, discrete-time, adaptive estimation problems and operating in random environments of engineering d@hnce. We demonstrate that the algorithms operating mder ideal conditions are d e s d i l e by homogeneous time-varying linear difference equations with dependent random coefficients, while in praclical use,...

The model theory of fields with operators has proven to be very useful in applications of model theory to problems outside logic. Differentially closed fields and separably closed fields were instrumental in Hrushovski’s proof of the conjecture of Mordell-Lang ([39]), and in work of Hrushovski and Pillay on counting the number of transcendental points on certain varieties ([44]). Let me also me...

The problem of global asymptotic stability of a time-variant mth-order difference equation is addressed. Stable regions in the parameter space will be derived for two cases: the case of a time-invariant parameter region, and the case of a time-variant parameter region. These results find applications in the area of adaptive digital filters.

This paper deals with two concepts of polynomial dichotomy for linear difference equations which are defined in a Banach space and whose norms can increase not faster than exponentially. Some illustrating examples clarify the relations between these concepts. Our approach is based on the extension of techniques for exponential dichotomy to the case of polynomial dichotomy. The obtained results ...

In this paper the definition of Hermite-Hermite matrix polynomials is introduced starting from the Hermite matrix polynomials. An explicit representation, a matrix recurrence relation for the Hermite-Hermite matrix polynomials are given and differential equations satisfied by them is presented. A new expansion of the matrix exponential for a wide class of matrices in terms of Hermite-Hermite ma...