On C*-algebras generated by pairs of q-commuting isometries

We consider the C*-algebras O_2^q and A_2^q generated, respectively, by isometries s_1, s_2 satisfying the relation s_1^* s_2 = q s_2 s_1^* with |q| < 1 (the deformed Cuntz relation), and by isometries s_1, s_2 satisfying the relation s_2 s_1 = q s_1 s_2 with |q| = 1. We show that O_2^q is isomorphic to the Cuntz-Toeplitz C*-algebra O_2^0 for any |q| < 1. We further prove that A_2^{q_1} is isomorphic to A_2^{q_2} if and only if either q_1 = q_2 or q_1 = complex conjugate of q_2. In the second part of our paper, we discuss the complexity of the representation theory of A_2^q. We show that A_2^q is *-wild for any q in the circle |q| = 1, and hence that A_2^q is not nuclear for any q in the circle.Comment: 18 pages, LaTeX2e "article" document class; submitted. V2 clarifies the relationships between the various deformation systems treate

Cosmological Production of Vector Bosons and Cosmic Microwave Background Radiation

The intensive cosmological creation of vector W, Z- bosons in the cosmological model with the relative units is considered. Field theoretical models are studied, which predict that the CMB radiation and the baryon matter in the universe can be products of decay and annihilation processes of these primordial bosons.Comment: 31 pages, 1 figur

Intellectual development disorder syndrome with congenital anomalies of type 99, faceted female (OMIM: 300968), updated mutation in the USP9X gene

The syndrome of mental retardation with congenital anomalies of type 99, limited to the female sex (OMIM: 300968) is an X-linked dominant disorder of the development of the central nervous system, characterized by delayed psychomotor development and mild or moderate mental retardation.In the article, a clinical case of a 2-year-old 8-month-old patient with mental retardation syndrome and type 99 congenital anomalies characteristic only of the female sex (OMIM: 300968) is presented. Due to the heterozygous carriage of a previously undescribed pathogenic variant with a reading frame shift in the X-linked USP9X gene associated with a type 99 developmental disorder with dominant inheritance, in chrX:41196714AATTG&gt;A, ENST00000378308, C.4214_4217delATT.P.Asp1405fs. The pathogenic variant was confirmed in the child in the study of the trio by Sanger. It is absent from the parents (a new pathogenic variant). Along with cognitive impairments, the patient revealed congenital anomalies, some of which coincided with those previously described. There were also some special features: the asymmetry of the skull in the described patient was expressed in the parietal part of the skull, and not the facial one, as described in previous publications. Secondary mitochondrial disorders were revealed during the study of the activity of mitochondrial enzymes in peripheral blood lymphocytes, which are an “enzymatic mirror” of tissues, which is an indication for the appointment of energotropic drugs (succinic acid and carnitine)