In [30] a class of quasi-cyclic LDPC codes has been proposed, whose information rate is 1/2. We generalize that construction to arbitrary rates l-1/l and we provide a Grobner basis for their dual codes, in some generic cases.

Using the notion of the generalized external semidirect product of two GROUPs we investigate the structure of some known deficiency zero GROUPs and also construct some new deficiency zero GROUPs having specified properties. In particular, for any integers i, j with 1 ≤ i ≤ j, we construct a 2-generator 2-relation GROUP of order 33i+j+1 and nilpotency class 2i + 1.

For every integer n³1 and every odd prime p, an efficient presentation is given for the wreath product Zp Zpn which, is of nilpotency class (p-1) n+1. Moreover, the Fibonacci length is proved to be 8x3n when p=3, and in general, k (p)xpn, where k (p) is the period of Fibonacci length modulo p (the Wall number of p).

Giving a condition for the amenability of GROUPs, Rosenblatt and Willis first introducedthe concept of configuration. In this paper, we investigate the relationship between ping-pong lemma and configuration sets, and show that only one configuration set is enough to ensure that several elements in a GROUP generates a free subGROUP of that GROUP. Using only one two-sided configuration sets, we give, in a sense, a generalization of this result to polycyclic or FC-GROUPs. Finiteness and paradoxical decompositions of GROUPs, are other properties which can be characterized with only one configuration set.

In using faithful complex representations of CYCLICALLY pinched and conjugacy pinched one-relator GROUPs we proved that any limit GROUP has a faithful representation in PSL (2, C). Further this representation can be e effectively constructed using the JSJ decomposition. In this note we show that any hyperbolic CYCLICALLY pinched one-relator GROUP with maximal amalgamated subGROUPs in each factor has a 2-dimensional faithful real representation.

The subject of 4NF, but not 5NF, relation is introduced in the textbooks, but no theoretical study is achieved on their decomposition algorithm. In this kind of normal relation, there exists a special semantic constraint so called "cyclic nature constraint" which needs yet a theoretical analysis. On the other hand, in the practice of database design it is sometimes necessary to decompose a relation into two or more relations. In this paper, we f11st mention the reason for decomposing a relation, and then give a rigorous defmition of CYCLICALLY constraint relation. Then by providing five Lemmas and their proofs, we describe in detail the characteristics of this kind of relation. We also introduce tow theorems and their proofs and provide the algorithms, based on these theorems to decompose the CYCLICALLY constrained relation, with a very high degree of flexibility. Finally, we discuss the results of this research.

The infinite family of GROUPs defined by the presentation $G_p=\langle x, y|x^p=y^p,\; xyx^my^n=1\rangle$, in which $p$ is a prime in $\{2,3,5\}$ and $m,n\in\mathbb{N}_0$, will be considered and finite and infinite GROUPs in the family will be determined. For the primes $p=2,3$ the GROUP $G_p$ is finite and for $p=5$, the GROUP is finite if and only if $m\equiv n\equiv1\pmod5$ is not the case.

Within the framework of plasticity-based constitutive laws, a plastic-damage model is developed in a complete form for analysis of damaged structures under large tensile strains which is suitable for concrete subjected to cyclic loadings. This is based on the plastic-damage model proposed by Lee and Fenves, which utilizes two separate damage variables for tension and compression and also a scalar degradation simulating damage on stiffness. Implementation of the model is coded for three-dimensional space in a special purpose finite element program to analyze the behavior of concrete subjected to large tensile cracking, which is inevitable in plain concrete structures. In order to include large crack opening/closing displacements in the model, the excessive increase in plastic strain causing unrealistic results in cyclic behaviors is prevented when the tensile plastic-damage variable controlling the evolution of tensile damage is larger than a critical value. To expedite the convergence rate for the overall equilibrium iterations, the consistent algorithmic tangent stiffness tensor is also derived, in detail, for large cracking states. The paper is completed with some numerical examples demonstrating the capability of the extended model in reproducing the behavior of CYCLICALLY loaded plain concrete subjected to large tensile strains.

Disseminated tuberculosis (DTB) refers to the concurrent involvement of at least two nonadjacent organs or sites of the body, or involvement of the blood or bone marrow by tuberculosis.Splenic invasion in TB can occur in either disseminated form or miliray tuberculosis. Occurrence of hypersplenism in TB is very rare. In this article, a case of DTB with hypersplenism is PRESENTED.A 23 years old man citizen of Kashan was admitted complaining of fever, night sweats, anorexia, headache, weakness, shortness of breath and early satiety since 10 days ago. He was well until 9 months ago, when early satiety developed for the first time. Physical examination and ultrasonography of the abdomen revealed huge splenomegaly. The results of his blood tests showed pancytopenia but the X-ray and CT-scan of his chest were normal. Abdominal CT-scan revealed a mild hepatomegaly, huge splenomegaly, para-aortic, retroperitoneal and left inguinal lymphadenopathy. The patient underwent splenectomy. Pathologic examination of his liver, spleen and lymph node biopsies revealed caseous necrosis and granuloma formation due to TB. Finally, he was classified as a tuberculosis patient. After beginning the anti-tuberculosis treatment, all of his signs and symptoms disappeared. At the present time, his general condition is very good and he has no problem.Huge splenomegaly and hypersplenism may occur during DTB. DTB can mimic lymphoma, so it should be considered in differential diagnosis of a huge spleen.