We give explicit lower bounds on the modular degree of a rational elliptic curve. The technique is via a convolution-type formula involving the symmetric-square L-function, for which an analogue of “no Siegel zeros” is known due to a result of Goldfeld, Hoffstein, and Lieman; our main task...

This paper considers the problem of estimating conditional scale function from time series. We discuss an estimate obtained using kernel version of quantile regression objective function of Keonker and Bassett (1978) and prove its consistency by applying some results, on dependent observations,...

We use the generalization of the Laplacian matrix to hypergraphs to obtain several spectral-like results on partition problems in hyper-graphs which are computationally extremely difficult to solve (NP-hard or NP-complete). Therefore it is very important to obtain nontrivial bounds. More...

The problem explained in this paper is aimed to solve the following signal identification problemwhere and are inexact vectors using the SNTLNR (Structured Nonlinear Total Least Norm Regularization). Numerical experiments show that in most cases the problem to find exact values of vectors and is...

In this paper, we propose principle factor analysis method to reduce the dimensions of a high dimensional random vector in calculates portfolio's Value at Risk. The theoretical foundation, algorithm and numerical example of the method are given. This method outperforms the principle component...

A brief review of some of the most important features of the Extended Relativity theory in Clifford-spaces (-spaces) is presented whose ” point” coordinates are noncommuting Clifford-valued quantities and which incorporate the lines, areas, volumes,.... degrees of freedom associated with the...

The aim of this paper is to propose numerical models and methods for solving (nxn) linear equations, AX = b where parameters in the matrix A and the vector b are random and correlated. In case of a probabilistic b and a deterministic A, the amount of second order covariances computation is...

This distribution answers the question; If I had to wait m untill I saw an event what is the probability of seeing it again after time x.It is very similar to the geometric and exponential distributions but only works after one (and only one) observation to predict the next.It assumes that the...

The purpose of this paper is to solve the problem stated in [5, Pg. 139] of finding a necessary and sufficient condition for a stratified L–filter to be induced by a [latticetop]–filter in the sense of [5, Lemma 4.4.3]. This condition given is proved to be equivalent to the condition...

A formal linear vector field representation for scientific equations is developed to rationalize the intuitive methods that are constantly employed. It is shown that unlike mechanical units that appear in the basis of the space, the reduced temperature and Boltzmann parameter cannot be described...