Throughout this paper, R will denote a commutative ring with identity and M is a unitary R- module and Z will denote the ring of integers. We introduce the graph Ω(M) of module M with the set of vertices contain all nontrivial non-essential submodules of M. We investigate the interplay between graph-theoretic properties of Ω(M) and algebraic properties of M. Also, we assign the values of natura...

We prove that the number of non-isomorphic face 2-colourable triangulations of the complete graph Kn in an orientable surface is at least 2 n2/54−O(n) for n congruent to 7 or 19 modulo 36, and is at least 2 2/81−O(n) for n congruent to 19 or 55 modulo 108.

Kabanov and Kramkov introduced the notion of "large nancial markets". Instead of considering{as usual in mathematical nance{a stochastic stock price process S based on a ltered probability space ( ;F ; (Ft)t2I ;P) one considers a sequence (Sn)n 1 of such processes based on a sequence ( ;F; (F t )t2In ;P n)n 1 of ltered probability spaces. The interpretation is that an investor can invest not on...

Randomized complete block designs are common in agricultural and other experiments. In this manuscript, we derive asymptotic procedures as well as finite approximations, for the analysis of data arising from series of such experiments. We do not assume normality of the data, and the within-block covariance structures can be arbitrary (no restriction to compound symmetry). The methods are specif...

This note deals with the structure of the class NPR introduced by L. Blum, M. Shub, and S. Smale (1989, Bull. Amer. Math. Soc. 21, 1 46). It is shown that, assuming NPR 3 PR poly, there exists a problem NPR"(PR poly) which is not NPR-complete (w.r.t PR poly reductions). It also clarifies the scope of a padding technique used in a former similar result by R. Ladner (1975, J. Assoc. Comput. Mach....

For theorem proving in non-classical logics two similar approaches have been established: a matrix characterization of Wallen and Ohlbach’s resolution calculus. In both cases the essential extension of the classical calculi is a need for unifying the so-called prefixes of atomic formulae or so-called world-paths respectively. We present a specialized string-unification algorithm which computes ...

Uterine inversion is shortly described as the indentation and depression of the fundic area extending downwards up to the different levels of the birth canal till vaginal opening. Clinical diagnosis of uterine inversion is difficult due to its non-specific symptoms and physical examination. Ultrasonography is the most practical modality for radiological evaluation, but it is inadequate to deter...