In this thesis, three methods are investigated to express context-free tree languages by regular tree grammars. The first method is a characterization. We show restrictions to context-free tree grammars such that, for each restricted context-free tree grammar, a regular tree grammar can be constructed that induces the same tree language. The other two methods are approximations. An arbitrary co...

Time evolving networks tend to have an element of regularity. This regularity is characterized by existence repetitive patterns in the data sequences graph metrics. As per our research, relevance such regular network has not been adequately explored. Such certain are indicative properties like popularity, activeness etc. which vital significance for any network. These closely indicated metrics ...

Inverse weighted estimators are commonly used in econometrics (and statistics). Some examples include: 1) The binary response model under mean restriction introduced by Lewbel(1997) and further generalized to cover endogeneity and selection. The estimator in this class of models is weighted by the density of a special regressor. 2) The censored regression model under mean restrictions where the...

In this paper, we address the problem of curve and surface reconstruction from sets of points. We introduce regular interpolants, which are polygonal approximations of curves and surfaces satisfying a new regularity condition. This new condition, which is an extension of the popular notion of r-sampling to the practical case of discrete shapes, seems much more realistic than previously proposed...

Let H = −∆+V , where V is a real valued potential on R satisfying |V (x)| . 〈x〉−3−. We prove that if zero is a regular point of the spectrum of H = −∆ + V , then ‖wePacf‖L∞(R2) . 1 |t| log(|t|) ‖wf‖L1(R2), |t| > 2, with w(x) = log(2 + |x|). This decay rate was obtained by Murata in the setting of weighted L spaces with polynomially growing weights.

In this paper, we study some systems of integral equations, including those related to Hardy-Littlewood-Sobolev (HLS) inequalities. We prove that, under some integrability conditions, the positive regular solutions to the systems are radially symmetric and monotone about some point. In particular, we established the radial symmetry of the solutions to the Euler-Lagrange equations associated wit...