Let be a finite-dimensional local commutative algebra over , dim. In this work we consider compact manifolds over , and prove that the real part of an -differentiable function is constant. Also we find estimates for the dimensions of some spaces of 1-form

A method is proposed in this paper to assess the local influence of minor perturbation for a nonlinear structural equation model with missing data that are missing at random. The main idea is to apply Zhu and Lee's (2001) approach to the conditional expectation of the complete-data...

By ( ± 1) ± 1 mod and by the lattice structure of Z(.) mod for = ± 1 (odd prime p) all idempotents taken as naturals < are shown to have distinct −1 mod , and all divisors r of p − 1 (resp. + 1) have distinct −1 mod p. Moreover 2 / 2 mod p for prime p, related to W ieferich primes [4] and case. It is conjectured that for prime > 2 some | ± 1 is semi primitive root of 1 mod ( > 2), with units group {−1, }

We present a simple proof of the Clarke-Ledyaev multidirectional mean value inequality on smooth Banach space. As application we establish a formula for the Clarke-Rockafellar directional derivative of lower semicontinuous function

Exact, limiting distributions along with their rates of convergence of exceedance statistics for both order statistics and record statistics are provided when the underlying distribution may have points of discontinuity. Furthermore the exact distribution of record statistics for arbitrary...

A new class of bivariate and trivariate discrete distributions with binomial and multinomial marginals are studied. This class of distributions are obtained by the natural way using probabilistic properties of the considered sampling model. The applications in exceedance models for order...

This paper study generalized Serre problem proposed by Lin zhiping and N. K. Bose in multidimensional system theory context [5], [7]. This problem is stated as follows. Let be a full row rank matrix, and be the greatest common divisor of all the minors of . Assume that the reduced minors of...

An enlargement of the domain of multiindex regular Hausdorff matrices is constructed. Its elements can be viewed as multiindex and multidiagonal regular Hausdorff-like matrices. The above matrices are subordinated to sequences of finite variation functions on [0,1] satisfying a boundary...

The driving idea of this work is that the test-and-branch operation familiar to computer programmers draws new information into a computation. This idea is used to justify an information-theoretic/probabilistic approach to some problems in the prime numbers. We use it here against the Riemann...