In this paper we prove the following result. LetH be a real or complex Hilbert space, let L(H) be the algebra of all bounded linear operators on H and let A(H) ⊆ L(H) be a standard operator algebra. Suppose we have an additive mapping D : A(H) → L(H) satisfying the relation D(An) = D(A)A∗n−1 + AD(An−2)A∗ + An−1D(A) for all A ∈ A(H) and some fixed integer n > 1. In this case there exists a uniqu...

(A) All rings in this announcement are commutative and with 1. For any ring K we denote by W(K) the Witt ring of nondegenerate symmetric bilinear forms over K. DEFINITION 1. A signature o of K is a ring homomorphism from W(K) to Z. REMARK 1. If K is a field, the signatures correspond uniquely with the orderings of K [3], [9]. Thus Theorem 1 below generalizes the main results of Artin-Schreier's...

With the rise of Internet Things, fog-to-cloud computing has emerged as a new cutting-edge approach (IoT). Except for cloud service provider, necessitates participation additional entities, such mobile sinks and fog nodes (CSP). As result, storage integrity audits will differ from standard auditing. Tian et al. completed first stage in developing public auditing system computing. However, becau...

We calculate the minimal surface bounded by four-sided figures whose projection on a plane is a rectangle, starting with the bilinear interpolation and using, for smoothness, the Chebyshev polynomial expansion in our discretized numerical algorithm to get closer to satisfying the zero mean curvature condition. We report values for both the bilinear and improved areas, suggesting a quantitative ...

We propose a differential difference equation in R × Z and study it by Hirota’s bilinear method. This equation has a singular continuum limit into a system which admits the reduction to the Davey-Stewartson equation. The solutions of this discrete DS system are characterized by Casorati and Grammian determinants. Based on the bilinear form of this discrete DS system, we construct the bilinear B...

One objective of this paper is to estimate the parameters p,d,q of an autoregressive fractionally integrated moving average ARFIMA(p,d,q) stochastic model by minimizing the squares of the residuals using a Bayesian global optimization techniques. We consider bilinear model, too because it is the simple extension of linear model, defined by adding a bilinear term to traditional ARMA model. There...