Classification of three-dimensional anti-dendriform algebras

This article is devoted to the classification of anti-dendriform algebras that are associated with associativity. They are characterized as algebras with two operations whose sum is associative. In particular, the paper is devoted to classifying anti-dendriform algebras associated with null-filiform associative algebras and three-dimensional algebras. It is known that any finite-dimensional associative algebra without a non-zero idempotent element is nilpotent. If an associative algebra has a non-zero idempotent element, then there does not exist a compatible anti-dendriform algebra structure associated with associative algebras.Comment: 14 pages. arXiv admin note: text overlap with arXiv:2209.08962 by other author

Mathematical model describing erythrocyte sedimentation rate. Implications for blood viscosity changes in traumatic shock and crush syndrome

BACKGROUND: The erythrocyte sedimentation rate (ESR) is a simple and inexpensive laboratory test, which is widespread in clinical practice, for assessing the inflammatory or acute response. This work addresses the theoretical and experimental investigation of sedimentation a single and multiple particles in homogeneous and heterogeneous (multiphase) medium, as it relates to their internal structure (aggregation of solid or deformed particles). METHODS: The equation system has been solved numerically. To choose finite analogs of derivatives we used the schemes of directional differences. RESULTS: (1) Our model takes into account the influence of the vessel wall on group aggregation of particles in tubes as well as the effects of rotation of particles, the constraint coefficient, and viscosity of a mixture as a function of the volume fraction. (2) This model can describe ESR as a function of the velocity of adhesion of erythrocytes; (3) Determination of the ESR is best conducted at certain time intervals, i.e. in a series of periods not exceeding 5 minutes each; (4) Differential diagnosis of various diseases by means of ESR should be performed using the aforementioned timed measurement of ESR; (5) An increase in blood viscosity during trauma results from an increase in rouleaux formation and the time-course method of ESR will be useful in patients with trauma, in particular, with traumatic shock and crush syndrome. CONCLUSION: The mathematical model created in this study used the most fundamental differential equations that have ever been derived to estimate ESR. It may further our understanding of its complex mechanism

WHY SHOULD UZBEKISTAN JOIN THE WTO?

The article analyzes the issues of potential accession of Uzbekistan to the World Trade Organization, as well as the possible benefits and risks of this. The author emphasizes the importance of Uzbekistan\u27s participation in reputable international financial and trade-economic institutions, including the WTO, for further deepening structural economic reforms, as well as ensuring the competitiveness of the national economy

TYPES OF FUNGAL DISEASES OF MULBERRY

Resolution of the President of the Republic of Uzbekistan dated March 29, 2017 No PP-2856 "On the organization and activities of the Association" Uzbekpaksanoat " and Resolution of the Cabinet of Ministers of the Republic of Uzbekistan dated August 11, 2017 No 616 "On the program of measures for further development of the silk industry in 2017-2021", as well as Resolution of the President of the Republic of Uzbekistan dated January 12, 2018 No PQ-3472 "On measures to further develop the silk industry in the country" will be the basis for increasing the efficiency of the industry, strengthening integration processes in the silk production complex and improving economic performance of farms and enterprises

Infinite transitivity on the Calogero-Moser space C₂

We prove a particular case of the conjecture of Berest–Eshmatov–Eshmatov by showing that the group of unimodular automorphisms of C[x, y] acts in an infinitely-transitive way on the Calogero-Moser space C₂

Molecular Mimicry between SARS-CoV-2 and Human Endocrinocytes: A Prerequisite of Post-COVID-19 Endocrine Autoimmunity?

Molecular mimicry between human and microbial/viral/parasite peptides is common and has long been associated with the etiology of autoimmune disorders provoked by exogenous pathogens. A growing body of evidence accumulated in recent years suggests a strong correlation between SARS-CoV-2 infection and autoimmunity. The article analyzes the immunogenic potential of the peptides shared between the SARS-CoV-2 spike glycoprotein (S-protein) and antigens of human endocrinocytes involved in most common autoimmune endocrinopathies. A total of 14 pentapeptides shared by the SARS-CoV-2 S-protein, thyroid, pituitary, adrenal cortex autoantigens and beta-cells of the islets of Langerhans were identified, all of them belong to the immunoreactive epitopes of SARS-CoV-2. The discussion of the findings relates the results to the clinical correlates of COVID-19-associated autoimmune endocrinopathies. The most common of these illnesses is an autoimmune thyroid disease, so the majority of shared pentapeptides belong to the marker autoantigens of this disease. The most important in pathogenesis of severe COVID-19, according to the authors, may be autoimmunity against adrenals because their adequate response prevents excessive systemic action of the inflammatory mediators causing cytokine storm and hemodynamic shock. A critique of the antigenic mimicry concept is given with an assertion that peptide sharing is not a guarantee but only a prerequisite for provoking autoimmunity based on the molecular mimicry. The latter event occurs in carriers of certain HLA haplotypes and when a shared peptide is only used in antigen processin

Infinite transitivity on the Calogero-Moser space C2

We prove a particular case of the conjecture of Berest--Eshmatov--Eshmatov by showing that the group of unimodular automorphisms of C[x,y] acts in an infinitely-transitive way on the Calogero-Moser space C2.</jats:p