In this paper, polynomial recurrence bounds for a class of stochastic differential equations with rotational symmetric gradient type drift and an additive Wiener process are established, as well certain priori moment inequalities solutions. The key feature paper is that the approach does not use Lyapunov functions because it clear how to construct them. method based on Dynkin’s (nonrandom) chai...

The correlations between the physico-chemical properties of a chemical structure and its molecular structure-properties are used in quantitative structure-activity property relationship studies (QSAR/QSPR) by using graph-theoretical analysis techniques. It is well known that some structure-property studies, eccentric distance sum, better than corresponding values obtained Wiener index. In this ...

Wiener’s famous attack on RSA with d < N shows that using a small d for an efficient decryption process makes RSA completely insecure. As an alternative, Wiener proposed to use the Chinese Remainder Theorem in the decryption phase, where dp = d mod (p − 1) and dq = d mod (q − 1) are chosen significantly smaller than p and q. The parameters dp, dq are called private CRT-exponents. Since Wiener’s...

Nonlinear approximation has usually been studied under deterministic assumptions and complete information about the underlying functions. In the present paper we assume only partial information, e.g., function values at some points, and we are interested in the average case error and complexity of approximation. We show that the problem can be essentially split into two independent problems rel...

In this article we prove a Wiener Tauberian theorem for L(SL2(R)), 1 ≤ p < 2. Let G be the group SL2(R) and K its maximal compact subgroup SO(2,R). Let M be {±I}. We show that if the Fourier transforms of a set of functions in L(G) do not vanish simultaneously on any irreducible Lp− -tempered representation for some > 0, where they are assumed to be defined, and if for each M-type at least one ...

Let W (G) and Sz(G) be the Wiener index and the Szeged index of a connected graph G. It is proved that if G is a connected bipartite graph of order n ≥ 4, size m ≥ n, and if ` is the length of a longest isometric cycle of G, then Sz(G) − W (G) ≥ n(m − n + ` − 2) + (`/2) − ` + 2`. It is also proved if G is a connected graph of order n ≥ 5 and girth g ≥ 5, then Sz(G) − W (G) ≥ PIv(G) − n(n − 1) +...

Abstract. In this paper Reverse Wiener index, Reverse Detour Wiener index, Reverse Circular Wiener index Reverse Harary index, Reverse Detour Harary index, Reverse Circular Harary index, Reverse Reciprocal Wiener index, Reverse Detour Reciprocal Wiener index, Reverse Circular Reciprocal Wiener index, Reverse Hyper Wiener index, Reverse, Detour Hyper Wiener index, Reverse Circular Hyper Wiener i...

Let Sz(G) and W (G) be the revised Szeged index and the Wiener index of a graph G. Chen, Li, and Liu [European J. Combin. 36 (2014) 237–246] proved that if G is a non-bipartite connected graph of order n ≥ 4, then Sz(G) −W (G) ≥ ( n + 4n− 6 ) /4. Using a matrix method we prove that if G is a non-bipartite graph of order n, size m, and girth g, then Sz(G)−W (G) ≥ n ( m− 3n 4 ) + P (g), where P i...

The notion of frequency response functions has been generalized to nonlinear systems in several ways. However, a relation between different approaches has not yet been established. In this paper, frequency domain representations for nonlinear systems are uniquely connected. Specifically, by means of novel analytical results, the generalized frequency response function (GFRF) and the higher orde...