Hereditary Upper Radical Properties and Dual Supplementing Radicals of Hereditary Radicals of Groups

One aim of this paper is to prove that for any hereditary radical property 𝒫, there exists a radical property 𝒫′ supplementing 𝒫. Certain hereditary upper radical properties of groups are constructed, and some of them are applied to formulate the necessary and sufficient condition for a hereditary radical 𝒫 and its supplementing radical 𝒫′ forming a dual pair.     

On minimal forbidden subgraph characterizations of balanced graphs

A graph is balanced if its clique-matrix contains no edge–vertex incidence matrix of an odd chordless cycle as a submatrix. While a forbidden induced subgraph characterization of balanced graphs is known, there is no such characterization by minimal forbidden induced subgraphs. In this work, we provide minimal forbidden induced subgraph characterizations of balanced graphs restricted to graphs that belong to one of the following graph classes: complements of bipartite graphs, line graphs of multigraphs, and complements of line graphs of multigraphs. These characterizations lead to linear-time recognition algorithms for balanced graphs within the same three graph classes.     

Boyle’s conjecture and perfect localizations

ABSTRACT

In this article we study the behavior of left QI-rings under perfect localizations. We show that a perfect localization of a left QI-ring is a left QI-ring. We prove that Boyle’s conjecture is true for left QI-rings with finite Gabriel dimension such that every hereditary torsion theory in the Gabriel filtration is perfect. As corollary, we get that Boyle’s conjecture is true for left QI-rings which satisfy the restricted left socle condition, a result proved by Faith in [6 Faith, C. (1976). On hereditary rings and Boyle’s conjecture. Arch. Math. 27(1):113–119.[Crossref] , [Google Scholar]].     

On Formation Generalization of Some Local Theorems

In this paper we give formation generalizations of some results of the theory of finite groups concerning the normalizers of p-subgroups.     

Capillary electrophoresis for the detection of PMP22 gene duplication: study in Mexican patients

Charcot-Marie-Tooth (CMT) disease is the most common inherited disorder of the human peripheral nerve, with an estimated overall prevalence of 17-40/10 000 [1]. The typical phenotype presents peroneal muscular atrophy and pes cavus [2]. CMT is usually divided into two large types, about two-thirds of the patients have CMT type 1 (CMT1), that affects the layer of myelin (demyelination). In type 2 (CMT2) the nerve fibers are affected (axonal). CMT diseases have autosomal dominant, autosomal recessive, and X-linked inheritance [1]. The most frequent subtype is 1A (CMT1A) with autosomal dominant transmission, secondary in most cases to a tandem duplication of a 1.5 Mb DNA fragment on chromosome 17p11.2-p12 [4-7]. In this region, the codification of the peripheral myelin protein 22 (PMP22) takes place. The severity of the disease varies among patients, even within the same family, from almost no symptoms to severe foot-drop and sensory loss. The PMP22 gene has four exons and is regulated by two promoters located toward the extreme 5'. The origin of the duplication that causes the disease is an uneven exchange of the chromatids during the meiosis. This unequal recombination occurs between two regions that limit the PMP22 gene, described as REP places of 24 kb, proximal and distal [3, 4].     

Some super systems with local bi-Hamiltonian operators

For a class of super skew-symmetric operators with eight parameters, two kinds of super Hamiltonian operators are identified by the method of functional multi-vectors. Appropriate decompositions of these operators lead to compatible super Hamiltonian pairs which in turn produce nonlinear super bi-Hamiltonian systems from the trivial x-translation flow. As examples, besides the super Korteweg–de Vries equations and other known ones, new super generalizations are obtained for the Riemann equation, the Hunter–Saxton equation and the Camassa–Holm equation, all of them admit two compatible local super Hamiltonian operators.     

The telescope conjecture for hereditary rings via Ext-orthogonal pairs

For the module category of a hereditary ring, the Ext-orthogonal pairs of subcategories are studied. For each Ext-orthogonal pair that is generated by a single module, a 5-term exact sequence is constructed. The pairs of finite type are characterized and two consequences for the class of hereditary rings are established: homological epimorphisms and universal localizations coincide, and the telescope conjecture for the derived category holds true. However, we present examples showing that neither of these two statements is true in general for rings of global dimension 2.     

The Proof of Inseparable Prime AW^＊—Algebras Being Primitive C^＊—Algebras

The relation between the inseparable prime C^*-algebras and primitive C^*-algebras is studied,and we prove that prime AW^*-algebras are all primitive C^*-algebras.     

Rapid mutation detection in complex genes by heteroduplex analysis with capillary array electrophoresis

Mutational analysis of large multiexon genes without prevalent mutations is a laborious undertaking that requires the use of a high-throughput scanning technique. The Human Genome Project has enabled the development of powerful techniques for mutation detection in large multiexon genes. We have transferred heteroduplex analysis (HA) by conformation-sensitive gel electrophoresis of the two major breast cancer (BC) predisposing genes, BRCA1 and BRCA2, to a multicapillary DNA sequencer in order to increase the throughput of this technique. This new method that we have called heteroduplex analysis by capillary array electrophoresis (HA-CAE) is based on the use of multiplex-polymerase chain reaction (PCR), different fluorescent labels and HA in a 16-capillary DNA sequencer. To date, a total of 114 different DNA sequence variants (19 insertions/deletions and 95 single-nucleotide substitutions - SNS) of BRCA1 and BRCA2 from 431 unrelated BC families have been successfully detected by HA-CAE. In addition, we have optimized the multiplex-PCR conditions for the colorectal cancer genes MLH1 and MSH2 in order to analyze them by HA-CAE. Both genes have been amplified in 13 multiplex groups, which contain the 35 exons, and their corresponding flanking intronic sequences. MLH1 and MSH2 have been analyzed in nine hereditary nonpolyposis colorectal cancer patients, and we have found six different DNA changes: one complex deletion/insertion mutation in MLH1 exon 19 and another five SNS. Only the complex mutation and one SNS may be classified as cancer-prone mutations. Our experience has revealed that HA-CAE is a simple, fast, reproducible and sensitive method to scan the sequences of complex genes.