It was conjectured by Černý in 1964, that a synchronizing DFA on n states always has a shortest synchronizing word of length at most (n− 1), and he gave a sequence of DFAs for which this bound is reached. Until now a full analysis of all DFAs reaching this bound was only given for n ≤ 4, and with bounds on the number of symbols for n ≤ 10. Here we give the full analysis for n ≤ 6, without bound...

ABSTRACT—Software Engineering plays a vital role in software development process. Software effort Estimation usually takes place in early stage of software life cycle. Estimation relies upon previous experience. Software development based on accurate estimates because badly chosen estimate causes problems during the performance of software development process. A linear Regression model with exp...

The star-clique transformation (SCT) is a simple reformulation of the star-delta transformation known in resistor networks. Under action of SCT, links of the original network are transformed to nodes of the new network. Links are transformed into linked nodes if they shared a node in the original network. SCT converts a node of degree k to a k-clique, i.e. to a fully connected cluster of k node...

Abstract: Theory and methodology for nonparametric regression have been particularly well developed in the case of additive homoscedastic Gaussian noise. Inspired by asymptotic equivalence theory, there have been ongoing efforts in recent years to construct explicit procedures that turn other function estimation problems into a standard nonparametric regression with Gaussian noise. Then in prin...

We study a tensorial exponential transformation of a three-dimensional metric of space-like hypersurfaces embedded in a four-dimensional space-time, γij = e ikmmekejknn , where φk are logarithms of the eigenvalues of γij , θk are rotation angles, and ǫijk is a fully antisymmetric symbol. Evolution part of Einstein’s equations, formulated in terms of φk and θk, describes time evolution of the me...

Transformations are a common technique used to linearize data so that simple linear regression can be applied. A common transformation used is the logarithmic transformation. This transforms data that follows an exponential pattern so that a straight line can be fit to it. In this study human chorionic gonadotropin (hCG) levels in women with gestational trophoblastic disease (GTD), which are kn...

In a recent study, we found that newly isolated clones of NIH 3T3 mouse cells undergo neoplastic transformation more readily than uncloned cultures from which they were derived. After eleven low-density passages (LDPs), most of the 29 clones produced lightly stained early-stage transformed foci when grown to confluence in a primary assay for transformation, and one of them consistently produced...

We study the limiting behavior of the zeros of the Euler polynomials. When linearly scaled, they approach a definite curve in the complex plane related to the Szegö curve which governs the behavior of the roots of the Taylor polynomials associated to the exponential function. Further, under a conformal transformation, the scaled zeros are uniformly distributed.

By means of generalized Riccati transformation techniques and generalized exponential functions, we give some oscillation criteria for the nonlinear dynamic equation (p(t)x ∆ (t)) ∆ + q(t)(f • x σ) = 0, on time scales. We also apply our results to linear and nonlinear dynamic equations with damping and obtain some sufficient conditions for oscillation of all solutions.

A class of Cohen-Grossberg-type BAM neural networks with distributed delays and impulses are investigated in this paper. Sufficient conditions to guarantee the uniqueness and global exponential stability of the periodic solutions of such networks are established by using suitable Lyapunov function, the properties of M-matrix, and some suitable mathematical transformation. The results in this pa...