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