The purpose of this chapter is to put in perspective the accumulating molecular data on Y chromosomal X chromosomal, and autosomal spermatogenesis genes, and their transmission to ICSI offspring. The current gene search on the Y chromosome is just a starting point for locating many other spermatogenesis genes that are widespread throughout the genome. Now that the Y has been sequenced, many mor...

In this paper we study evaluation codes arising from plane quotients of the Hermitian curve, defined by affine equations of the form yq + y = xm, q being a prime power and m a positive integer which divides q+ 1. The dual minimum distance and minimum weight of such codes are studied from a geometric point of view. In many cases we completely describe the minimum-weight codewords of their dual c...

In this paper, the partial derivatives Bp,q(x, y) = ∂ ∂xp∂yq B(x, y) of the Beta function B(x, y) are expressed in terms of a finite number of the Polygamma function, where p and q are non-negative integers, x and y are complex numbers. In particular, Bp,q(x, y) can be expressed by the Riemann zeta function if x is equal to n or n + 1 2 and y is equal to m or m + 1 2 , where n and m are integer...

This formula is not satisfactory under a computing point of view because it introduces more algebraic quantities than necessary. The number P(a)/Q'(a) is called the residue of the root a of Q. We introduce the notion of multiplicity of a residue b that is the number of roots a having b as a residue. Trager (1976) introduced a new formula involving less algebraic numbers: let S(y) be the resulta...

The interaction of mercury vacancies with dopant indium atoms in Hg0,7&d0.t,Te was studied using the perturbed ‘y”/ angular correlation (PAC) technique+ Two dominant PAC signals, characterized by quadrupole interaction strengths YQ~ = 83 MHz and yoL = 91 MHz and asymmetry parameters v1 = r/2 = 0.08, were observed and attributed to one or more In-Vu, complexes. The complexes appeared after annea...

In this paper, we will prove that the quantum ring of the quasi-homogeneous polynomial X p + XYq(p ≥ 2, q > 1) with some admissible symmetry group G defined by Fan-Jarvis-Ruan-Witten theory is isomorphic to the Milnor ring of its mirror dual polynomial X pY + Yq. We will construct an concrete isomorphism between them. The construction is a little bit different in case (p − 1, q) = 1 and case (p...

We describe a criterion for showing that the equation s2+y2p = α3 has no non-trivial proper integer solutions for specific primes p > 7. This equation is a special case of the generalized Fermat equation xp + yq + zr = 0. The criterion is based on the method of Galois representations and modular forms together with an idea of Kraus for eliminating modular forms for specific p in the final stage...

A preference system $$\mathcal {I}$$ is an undirected graph where vertices have preferences over their neighbors, and admits a master list if all can be derived from single ordering vertices. We study the problem of deciding whether given close to admitting based on three different distance measures. determine computational complexity following questions: modified by (i) k swaps in preferences,...

spinal muscular atrophy (sma) is an autosomal recessive neuromuscular disorder characterized by degeneration of spinal cord anterior horn cells, leading to muscular atrophy. sma is clinically classified into three sub-groups based on the age of onset and severity. the majority of patients with sma have homozygous deletions of exons 7 and 8 of the survival motor neuron (smn) gene. the purpose of ...

background: y chromosomal microdeletion is an important genetic disorder, which may arise due to intrachromosomal recombination between homologous sequences in the male specific region of the human y chromosome. it is frequently associated with the quantitative reduction of sperm. the screening for y chromosomal microdeletions has a great clinical value. objective: to develop a sequence tagged ...