The contributors use zeta functions to factor polynomials over finite fields, determine the canonical models of arithmetic curves, obtain an expression for the

probability density function of the distribution of the trace function on Lie group G, and compute the weight enumerators of Reed-Muller codes.

In this paper we will discuss the

probability density function of [[tau].sub.r.sup.([??])], for which we write [p.sub.r.sup.([??])] (.; x) in the case when d [greater than or equal to] 2.

It should be noted that the borders of the interval can be displayed in the parameters of the distribution law explicitly (for example, the boundaries of the interval in the case of the law of equal

probability density) or indirectly as the area of definition of this law.

Individual clearances are randomly generated, following a particular

probability density function (PDF), such that the sum of these random numbers is equal to the total clearance H.

Ideally, the solution to data uncertainty is establishing corresponding

probability density function by collected data and putting it into LCA.

The criteria included mean annual data, standard deviation, annual climate cycle, normalized root mean square error (NRMSE), spatial distribution, climate change trend, empirical orthogonal function (EOF), and

probability density function (PDF); these criteria are listed in Table 1.

A random matrix is a probability law on a space of matrices, usually given by the joint

probability density on its entries:

The

probability density function of the correlated log-normal especially is carried out to propose various approximations of the sum distribution.

As it is customary for brittle materials, the strength data are interpreted statistically by assuming that specimen strength obeys a

probability density function.

such that [y.sub.i] ~ Gamma([alpha], P) is with

probability density function

However, the generation of a

probability density functions as proposed by the authors required a large amount of training data that were different from the actual test data.