We compute all irregular primes less than 163 577 856. For all of these primes we verify that the Kummer–Vandiver conjecture holds and that the λ-invariant is equal to the index of irregularity.

We study invariants of Calabi-Yau varieties in positive characteristic, especially the height of the Artin-Mazur formal group. We illustrate these results by Calabi-Yau varieties of Fermat and Kummer type. 2000 Mathematics Subject Classification: 14J32, 14L05, 14F

We introduce a notion of highly Kummer-faithful fields and study its relationship with the fields. also give some examples For example, if $k$ is number field finite degree over \mathbb{Q}, $g$ an integer $> 0$ $\mathbf{m}=(m_p)_p$ family non-negative integers, where $p$ ranges all prime numbers, then extension $k_{g,\mathbf{m}}$ obtained by adjoining to coordinates elements $p^{m_p}$-torsion s...

Treating number of customers and time as random variables and taking into account binary behaving of customers in shopping, the general expression for marketing distribution is formulated. Binary probabilities are averaged by means of beta distribution. On the basis of the general formula and some of its specifications, the ways of marketing advantages are proposed. Among the advantage approach...

Identifying and counting the total number of biological species observed, when plotted against a measure of the effort used to record them, gives rise to a species accumulation curve. We investigate estimation of the total number of species and other relevant properties of accumulation by elaborating on the multinomial model (Nakamura and Peraza, 1998, Journal of Agricultural, Biological, and E...

We introduce in this paper a new four-parameter generalized version of the linear failure rate distribution which is called Beta-linear failure rate distribution. The new distribution is quite flexible and can be used effectively in modeling survival data and reliability problems. It can have a constant, decreasing, increasing and bathtub-shaped failure rate function depending on its parameter...

We propose an exact method for generating random deviates from continuous order statistics. This versatile method that generates Beta deviates as a middle step can be applied to any density function without resorting to numerical inversion. We also conduct an exhaustive investigation to document the merits of our method in generating deviates from any Beta distribution.

Abstract: The mathematical properties of a family of generalized beta distribution, including beta-normal, skewed-t, log-F, beta-exponential, betaWeibull distributions have recently been studied in several publications. This paper applies these distributions to the modeling of the size distribution of income and computes the maximum likelihood estimation estimates of parameters. Their performan...