Valence-weightings are considered for shortest-path distance moments, as well as related weightings for the so-called “Wiener” polynomial. In the case of trees the valence-weighted quantities are found to be expressible as a combination of unweighted quantities. Further the weighted quantities for a so-called “thorny” graph are considered and shown to be related to the weighted and unweighted q...

The Weiner index is considered one of the basic descriptors fixed interconnection networks because it provides average distance between any two nodes network. Many methods have been used by researchers to calculate value Wiener index. starting from brute force method invention an algorithm without calculating matrix. application found in molecular structure organic compounds, especially benzeno...

We describe a strategy for finding small modular and integer roots of multivariate polynomials using lattice-based Coppersmith techniques. Applying our strategy, we obtain new polynomial-time attacks on two RSA variants. First, we attack the Qiao-Lam scheme that uses a Chinese Remaindering decryption process with a small difference in the private exponents. Second, we attack the so-called Commo...

In this paper the identification of SISO Wiener models in presence of bounded output noise is considered. A three stage procedure based on the inner signal estimation, outlined in a previous contribution, has been proposed. Results and algorithms for the computation of inner-signal bounds through the design of a suitable input sequence have been provided for the case of polynomial without inver...

Let G be a graph of order n and let Λ(G, λ) = ∑n k=0(−1)ckλ be the characteristic polynomial of its Laplacian matrix. Zhou and Gutman recently proved that among all trees of order n, the kth coefficient ck is largest when the tree is a path, and is smallest for stars. A new proof and a strengthening of this result is provided. A relation to the Wiener index is discussed.

We study optimal approximation of stochastic processes by polynomial splines with free knots. The number of free knots is either a priori fixed or may depend on the particular trajectory. For the s-fold integrated Wiener process as well as for scalar diffusion processes we determine the asymptotic behavior of the average Lp-distance to the splines spaces, as the (expected) number k of free knot...

This paper, apart from the polynomial estimation technique based on the statespace model, examines to develop an estimation method for the quadratic estimation problem by applying the multivariate RLS Wiener estimator to the quadratic estimation of a stochastic signal in linear discrete-time stochastic systems. The augmented signal vector includes the signal to be estimated and its quadratic qu...

Capability to manage the performance of a shared resources environment relies on the model estimation of all dynamics in the system. The main challenge is to capture the nonlinear characteristic which inherently exists in software system applications. Hammerstein-Wiener block structural model is widely regarded as a basis for description of nonlinear systems. This paper extends the existing wor...

In this article, we present a complex baseband model for a wideband power amplifier that incorporates carrier frequency dependent amplitude modulation (AM) and phase modulation (PM) (i.e., AM/AM and AM/PM) characteristics in the design process. The structure used to implement the amplifier model is a Wiener system which accounts for memory effects caused by the frequency selective nature of the...

We present a generalized polynomial chaos algorithm for the solution of transient heat conduction subject to uncertain inputs, i.e. random heat conductivity and capacity. The stochastic input and solution are represented spectrally by the orthogonal polynomial functionals from the Askey scheme, as a generalization of the original polynomial chaos idea of Wiener [Am. J. Math. 60 (1938) 897]. A G...