The axino dark matter hypothesis in RSII brane model is studied. Within the framework of CMSSM we assume that the lightest neutralino or stau is the NLSP, and that the axino production has a single contribution from the NLSP decay. It is found that the axino can play the role of dark matter in the universe and we determine what the axino mass should be for different values of the five-dimensional Planck mass. An upper bound is obtained for the latter.

A model suitable for simulating lyotropic polymer liquid crystals (PLCs) is described. By varying the persistence length between infinity and 25, the effect of increasing flexibility on the nematic-smectic transition of a PLC with a length-to-width ratio L/D = 6 is investigated. It is found that increasing flexibility shifts the formation of a smectic phase to higher densities. Comparison is made with a recent theory of the nematic-smectic transition of slightly flexible rods.

Nonspecific aortoarteritis is a systemic disease, which has been referred to the group of vasculitis affecting elastic and muscular arteries oflarge and medium calibre with the inflammatory processlocalized in the media and adventitia. The article presents the history of development of ideas about clinical manifestations, morphological changes and the course of the disease from 1761 to the present day, the timeline of medical advances in this disease studies. The genuine interest in nonspecific aortoarteritis arose at the beginning of thelast century, when the Japanese ophthalmologist Mikito Takayasu reported unusual changes in the retinal vessels of a 21-year-old Japanese girl suffering from recurrent bouts of syncope. The first publications dealt with clinical manifestations in the patients, who had only brachiocephalic arterial involvement. In the early 60s, it was found that nonspecific aortoarteritis (Takayasu's disease) can affect not only the branches of the aortic arch, but also the thoracic aorta, renal and visceral arteries. It was the mosaic clinical manifestations in patients with various forms of Takayasu's disease that caused the presentation of the disease in theliterature until the mid-1970s under various terms such as “pulseless disease”, “arteritis of young women”, “brachiocephalic arteritis”, “atypical coarctation of aorta”, “Martorell's syndrome”, “syndrome of obliteration of the supra-aortic trunks”, “panaortitis” or “panarteritis”, “aortitis syndrome”, “mid-aortic syndrome”, “occlusive thromboarteriopathy”. The review details the epidemiology and prevalence of this disease. Views not only on the etiology and pathogenesis, but also on the methods of treating this disease have changed since M. Takayasu's publication in 1908. Much attention is paid to the historical aspect of the first surgical procedures. Starting in 1951, the surgical method has firmly taken the lead in the treatment of stenosis of the carotid arteries, thoracic aorta, renal and visceral arteries. Surgical concepts changed, but the literature data indicate the sustainability of the basic principle of treatment: combination of surgical interventions and various antiinflammatory therapy regimens.

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The article considers nondegenerate quadrics in C n+1 with codimension 2 that are of the form M={zEC.,weC':Im wj=(z, zb;i=l,2}, where (z,z) ~=~,~=~z.~ v are Hermitian forms, and thje stability groups Aut x M that preserve the point x. It is proved that if the matrix ml is stable and the matrix (ml)-im2 has more than two different eigenvalues, all automorphisms of Aut x M are linear transformations.Let z e C n (n > i, ~ e C 2, and let W c C n+2 be a neighborhood of a point w 0 = (Zo,~0). Let U c C n and V c C a be neighborhoods of the points z 0 and G0, respectively, andare linearly independent Hermitian forms in U, where one of them is nondegenerate. Let ~ be a locally biholomorphic automorphism of M that leaves the point w 0 e M in place. We denote the set of all such automorphisms by the symbol Autw0 M and call it the stability group of M at the point wo (see [i]). We wish to describe Autw0 M.Quadrics of the form M={(z, ~)~C~+k: Im ~=(e~z, z); j=J,..., k} were discussed in [2]. There it was conjectured that the automorphisms of Autw0 M are rational; this conjecture was later proved by A. E. Tumanov [3].In this paper, the following theorem strengthens this result for k = 2 (i.e., for M of the form (i)). THEOREM.Let ml and ~2 be Hermitian linear operators defined by the forms (2) that map C n into C n, where ml is invertible and A = (~i)-i~2.If A has more than two different eigenvalues, all of the automorphisms of Autw0 M are linear.The condition on the number of different eigenvalues in this theorem is essential, as the following examples show. Nizhegorod State University.