background and aims: this research aimed to study a possible link between endometriosis and polymorphism of the progesterone receptor gene. materials and methods: the control group consisted of 86 women without endometriosis and the case group comprised 86 patients with a diagnosis of endometriosis by laparoscopy. genotypes for alu insertion polymorphisms (a1/a1, a1/a2 and a2/a2) were described...

gbss protein, that is the product of waxy gene (wx) is one of the major enzyme in starch biosynthesis that controls the proportion of amylose to amylopechtine and its absence leads to production of starch with low amylose and higher amylopechtine content, called waxy starch.wx-a1, wx-b1, wx-d1 are three locuses in bread wheat (triticum aestivum) genome that encodes gbss protein and waxy starch ...

let r be a commutative ring with identity and m be a unitary r-module. let : s(m) −! s(m) [ {;} be a function, where s(m) is the set of submodules ofm. suppose n  2 is a positive integer. a proper submodule p of m is called(n − 1, n) − -prime, if whenever a1, . . . , an−1 2 r and x 2 m and a1 . . . an−1x 2p(p), then there exists i 2 {1, . . . , n − 1} such that a1 . . . ai−1ai+1 . . . an−1x...

Let ∆(a1, a2, · · · , an) be an n-dimensional real simplex with vertices at (a1, 0, · · · , 0), (0, a2, · · · , 0), · · · , (0, 0, · · · , an). Let P(a1,a2,··· ,an) be the number of positive integral points lying in ∆(a1, a2, · · · , an). In this paper we prove that n!P(a1,a2,··· ,an) ≤ (a1 − 1)(a2 − 1) · · · (an − 1). As a consequence we have proved the Durfee conjecture for isolated weighted ...

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In addition to A1 in the crystal lattice of clay minerals, A1 in soils can be divided into two major groups viz., exchangeable and non-exchangeable. The A1 equilibrium in soils is controlled by the solubility of the solid phase A1 compounds on the one hand and the adsorption characteristics of the adsorption phase on the other. Thus for a given soil the amount of exchangeable A1 will depend on ...

For finite subsets A1, . . . , An of a field, their sumset is given by {a1+ · · ·+an : a1 ∈ A1, . . . , an ∈ An}. In this paper we study various restricted sumsets of A1, . . . , An with restrictions of the following forms: ai − aj 6∈ Sij , or αiai 6= αjaj , or ai + bi 6≡ aj + bj (mod mij). Furthermore, we gain an insight into relations among recent results on this area obtained in quite differ...

The mixed discriminant of an n-tuple of n×n matrices A1, . . . , An is defined as D(A1, A2, . . . , An) = 1 n! ∑ σ∈S(n) det(A (1) σ(1), A (2) σ(2), . . . , A (n) σ(n)), where A denotes the ith column of the matrix A and S(n) denotes the group of permutations of 1, 2, . . . , n. For n matrices A1, ..., An and indeterminates λ1, . . . , λn, set Φλ1,...,λn(A1, ..., An) = D(λ1I −A1, ..., λnI −An). ...