Local deformations of positive-definite quadratic forms

Бондаренко, В. М.; Бондаренко, В. В.; Pereguda, Yu. N.

doi:10.1007/s11253-012-0696-z

Cited by 2 publications

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“…To date, the influence of various external and internal environmental factors has been widely studied, both on the pineal gland (of antipsychotic therapy and neuroleptics [4], electromagnetic radiation [5,6], light and radiation in the experiment [7,8], etc. ), and parathyroid glands.…”

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confidence: 99%

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Hryntsova¹,

Tymakova²,

Romaniuk³

2020

PEP

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An important environmental problem is the pollution of the environment with heavy metal salts, which are in various combinations depending on the region and cause adverse effects on public health. The endocrine system together with the immune and nervous system maintains homeostasis in the body. In order to study the morphofunctional rearrangements of the epiphyseal-parathyroid axis structural components in rats during 30 days of readaptation after 90 days of exposure to heavy metal salts (zinc (ZnSO4 · 7H2O) — 5 mg/l, copper (CuSO4 · 5H2O) — 1 mg/l, iron (FeSO4 ) — 10 mg/l, manganese (MnSO4 · 5H2O) — 0.1 mg/l, lead (Pb(NO3 ) 2 ) — 0.1 mg/l and chromium K2Cr2O7) — 0.1 mg/l) an experiment was performed on 24 white sexually mature male rats weighing 250–300 g, aged 7–8 months. The animals of the experimental group consumed ordinary drinking water for 30 days. Morphological, statistical, immunohistochemical and biochemical research methods were used. The 30-day period of readaptation after 90 days of heavy metal salts intake is insufficient to completely restore homeostasis in the epiphyseal-parathyroid system, which is at the stage of chronic stress «subcompensation». Significant morphological changes on the part of the vascular bed of the pineal gland and parathyroid glands (blood stasis, erythrocyte aggregation, sludge phenomenon) were determined, an active glial reaction was formed in the pineal gland, and the structure of the epithelial trabeculae of the glands was disturbed. The levels of parathyroid hormone and calcium in the blood of experimental animals were significantly lower than those of experimental animals. There is a greater vulnerability and faster dynamics of the regenerative processes in the parathyroid glands to the action of salts of heavy metals in comparison with the pineal gland. The development of hypofunction of the parathyroid glands, of course, has a negative effect on the overall calcium metabolism in the body, the development of compensatory and adaptive processes and the course of the general adaptation syndrome in response to the damaging agent.

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confidence: 99%

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Hryntsova¹,

Tymakova²,

Romaniuk³

2020

PEP

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Strengthening of a theorem on Coxeter–Euclidean type of principal partially ordered sets

Бондаренко

Styopochkina

2018

BKNUPhM

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Among the quadratic forms, playing an important role in modern mathematics, the Tits quadratic forms should be distinguished. Such quadratic forms were first introduced by P. Gabriel for any quiver in connection with the study of representations of quivers (also introduced by him). P. Gabriel proved that the connected quivers with positive Tits form coincide with the Dynkin quivers. This quadratic form is naturally generalized to a poset. The posets with positive quadratic Tits form (analogs of the Dynkin diagrams) were classified by the authors together with the P-critical posets (the smallest posets with non-positive quadratic Tits form). The quadratic Tits form of a P-critical poset is non-negative and corank of its symmetric matrix is 1. In this paper we study all posets with such two properties, which are called principal, related to equivalence of their quadratic Tits forms and those of Euclidean diagrams. In particular, one problem posted in 2014 is solved.

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Local deformations of positive-definite quadratic forms

Cited by 2 publications

References 1 publication

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Strengthening of a theorem on Coxeter–Euclidean type of principal partially ordered sets

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