A relativistic model of the NN-dimensional singular oscillator

Exactly solvable $N$-dimensional model of the quantum isotropic singular oscillator in the relativistic configurational $\vec r_N$-space is proposed. It is shown that through the simple substitutions the finite-difference equation for the $N$-dimensional singular oscillator can be reduced to the similar finite-difference equation for the relativistic isotropic three-dimensional singular oscillator. We have found the radial wavefunctions and energy spectrum of the problem and constructed a dynamical symmetry algebra.Comment: 8 pages, accepted for publication in J. Phys.

Взаимосвязь биохимических показателей и авидности антител у больных сахарным диабетом типа 2

We evaluated some biochemical and immune parameters, such as IgA, IgM, IgG, CIC, phagocytic index, T-lymphocytes, as well as avidity of antibodies in type 2 diabetic patients.Avidity, high- and low-avid antibody ratio was determined by test-systems for express-diagnostics of clinical and preclinical forms of immunologic deficiency. All patients (n = 47), depending on the level of glycemia and disease duration were divided into 3 groups: in the stage of compensation, subcompensation and decompensation. Control group included 17 healthy subjects.Value of high-avid antibodies in diabetes mellitus patients decreased in 75, 57 and 26% respectively, whereas in healthy subjects it is 89%. Conversely, increased amount of low-avid antibodies was observed, respectively 25, 43, and 74% (11% in control).These parameters prove antibody-folding disorders in diabetes mellitus and show that, change of metabolic parameters affects antibody avidity: G class high-avid antibody level decreases and shows weak protective function. This indicates functional disorders in B-system immunity.Проведено исследование некоторых биохимических и иммунных показателей (иммуноглобулины A, M, G, циркулирующие иммунные комплексы, фагоцитарное число, Т-лимфоциты, авидность антител). Авидитет и соотношение высоко- и низкоавидных нормальных антител в сыворотке крови определяли с помощью тест-систем для экспресс-диагностики доклинических и клинически выраженных форм иммунологической недостаточности. Все больные (47 человек) в зависимости от уровня гликемии и продолжительности заболевания были разделены на три группы: находящиеся в стадии компенсации, субкомпенсации и декомпенсации. В качестве контроля служили 17 здоровых доноров. У больных сахарным диабетом (СД) наблюдалось снижение содержания высокоавидных антител до 75, 57 и 26% соответственно, тогда как у здоровых доноров этот показатель был равен 89%. Наоборот, содержание низкоавидных антител нарастает соответственно до 25, 43, 74% (в контроле 11%). У больных СД изменения метаболических показателей отрицательно влияют на авидность антител: происходит резкое снижение высокоавидных антител класса G с аномальной конформацией и низкой функциональной и протективной активностями, что свидетельствует о нарушении протективной системы функции В-системы иммунитета

Study on the role of tissue-specific and non-specific autoantibodies, matrix metalloproteinase-3 and neuron-specific enolase enzymes in the exacerbation of autoimmune thyroiditis

The aim of the study was to examine the involvement of tissue-specific and non-specific autoantibodies, matrix metalloproteinase-3 and neuron-specific enolase (NSE) enzymes in the development and exacerbation of autoimmune thyroiditis. Materials and methods. The study enrolled 170 patients with autoimmune thyroiditis (64 males and 106 females aged 18 to 64 years) to comprehensively examine their humoral immune response indicators (IgA, M, G), organ-specific (Ab-TG, Ab-TPO) and organ-non-specific antibodies (Ab-DNA), metalloproteinase-3 and NSE activity. The control group consisted of 65 individuals without thyroid pathologies or other autoimmune diseases, aged 20 to 65 years (26 males and 39 females). Results. The study has demonstrated changes in the levels of organ-specific and organ-nonspecific antibodies and statistically significantly increased metalloproteinase-3 activity in patients with autoimmune thyroiditis. Positive correlations have been found between elevated levels of IgG, Ab-TG, Ab-TPO, Ab-dsDNA and NSE activity. Negative correlations have been observed between NSE activity and IgA concentrations. Conclusions. Elevated titers of anti-DNA autoantibodies may indicate an aggravation of the autoimmune process due to cellular structure damage, resulting in gland dysfunction. The findings also suggest that metalloproteinase-3, a marker predicting thyroid tissue damage, may negatively impact the immune response induction, ultimately affecting the activity of neuron-specific enolase. The data have shown that studying biochemical indicators such as antinuclear antibodies (ANA), anti-DNA antibodies, metalloproteinase-3 and neurodegenerative indicators could provide informative markers to determine the nature of the disease development and worsening

On a global uniform pullback attractor of a class of PDEs with degenerate diffusion and chemotaxis in one dimension.

In this chapter, we deal with a class of nonautonomous degenerate parabolic systems that encompasses two different effects: porous medium and chemotaxis. Such classes of equations arise in the mesoscale level modeling of biomass spreading mechanisms via chemotaxis. Under certain "balance" conditions on the order of the porous medium degeneracy and the growth of the chemotactic function, we establish the existence of a strong uniform pull back attractor for the case of one spatial dimension, thus improving our previous study, where a weak attractor was constructed

On a 'balance' condition for a class of PDEs including porous medium and chemotaxis effect: Non-aoutonomous case.

In this article we deal with a class of degenerate parabolic systems that encompasses two different effects: porous medium and chemotaxis. Such classes of equations arise in the mesoscale level modeling of biomass spreading mechanisms via chemotaxis. We prove well-posedness under certain ”balance conditions” on the order of the porous medium degeneracy and the growth of the chemotactic functions

The relationship between biochemical parameters and antibody avidity in diabetes mellitus type 2 patients

We evaluated some biochemical and immune parameters, such as IgA, IgM, IgG, CIC, phagocytic index, T-lymphocytes, as well as avidity of antibodies in type 2 diabetic patients.Avidity, high- and low-avid antibody ratio was determined by test-systems for express-diagnostics of clinical and preclinical forms of immunologic deficiency. All patients (n = 47), depending on the level of glycemia and disease duration were divided into 3 groups: in the stage of compensation, subcompensation and decompensation. Control group included 17 healthy subjects.Value of high-avid antibodies in diabetes mellitus patients decreased in 75, 57 and 26% respectively, whereas in healthy subjects it is 89%. Conversely, increased amount of low-avid antibodies was observed, respectively 25, 43, and 74% (11% in control).These parameters prove antibody-folding disorders in diabetes mellitus and show that, change of metabolic parameters affects antibody avidity: G class high-avid antibody level decreases and shows weak protective function. This indicates functional disorders in B-system immunity.</jats:p

Local vs nonlocal models for mitochondria swelling.

In this paper, we consider deterministic, continuous, nonlocal models for the mitochondrial permeability transition, i.e. mitochondrial swelling. Based on seminal papers [1], [2], [3], [5] and the book [4], in which ODE-PDE and PDE-PDE local models for the swelling of mitochondria have been considered, we suggest here new nonlocal models for this process. This new nonlocal deterministic continuous model for mitochondrial swelling scenario contains nonlocal diffusion, nonlocal chemotaxis, as well as nonlocal source term. We would like to especially emphasize that some of the new nonlocal models that we consider in this paper do not have local counterparts in the literature

On Korovkin type theorem in the space of locally integrable functions

summary:It is shown that a Korovkin type theorem for a sequence of linear positive operators acting in weighted space $L_{p,w}({\mathrm loc})$ does not hold in all this space and is satisfied only on some subspace