Tubes of discontinuous solutions of dynamical systems and their stability

The article is devoted to investigation of nonlinear dynamical systems which applies the generalized effect. The generalized effect (or impulses) is the result of the presence on the right part of the system a generalized derivative of the function of bounded variation. Such system contains incorrect operation of multiplication of discontinuous function on the generalized function from the point of view of the theory of distributions. This incorrectness is overcome by the approximation of the generalized functions in the right part of system by the sequence of smooth approximations of the generalized influences by analogy with sequential approach of the theory of the generalized functions. This sequence generates a sequence of smooth solutions. Then limit of a sequence of smooth solutions is considered. If such limit exists it is offered to be used as a solution. The solution is understood as partial pointwise limit of such sequence if a sequence of smooth solutions does not converge. Such partial limits constitute a tube of solutions. The sufficient conditions are received for stability of tubes of discontinuous solutions. © 2017 Author(s).Russian Science Foundation, RSFThe research was supported by Russian Science Foundation (RSF)(project No.16-11-10146)

The stability of linear system with impulse action in the systems matrix and delay

В работе рассматриваются свойства устойчивости и асимптотической устойчивости решений линейной системы дифференциальных уравнений с обобщенным воздействием в матрице системы и запаздыванием. Получены достаточные условия, обеспечивающие устойчивость и асимптотическую решений системы уравнений.The work is devoted to the study of the properties of stability and asymptotic stability of solutions of linear system of differential equations with the generalized effect in the system matrix and delay. Sufficient conditions for stability and asymptotic stability for the systems equations solver were obtained.

On pulse optimal control of linear systems with aftereffect

The paper deals with the problem of pulse optimal control of a linear dynamic system with aftereffect. As a functional, the degenerate quadratic functional of the most common kind is considered. The absence of control in the functional leads to the fact that the optimal control contains a pulse component. Sufficient conditions of existence of the pulse optimal control are obtained and the equations describing coefficients in the optimal control are worked out. Sufficient conditions that make it possible to integrate equations and to find the coefficients in an explicit form for the optimal control are established. A model example is considered. © 2013 Pleiades Publishing, Ltd

IMPULSE–SLIDING REGIMES IN SYSTEMS WITH DELAY

The paper is devoted to the formalization of a concept of impulse-sliding regimes generated by positional impulse controls for systems with delay. We define the notion of impulse-sliding trajectory as a limit of a sequence of Euler polygonal lines generated by a discrete approximation of the impulse position control. The equations describing the trajectory of impulse-sliding regime are received

On the stability of tubes of discontinuous solutions of bilinear systems with delay

The paper considers the stability property of tubes of discontinuous solutions of a bilinear system with a generalized action on the right-hand side and delay. A feature of the system under consideration is that a generalized (impulsive) effect is possible non-unique reaction of the system. As a result, the unique generalized action gives rise to a certain set of discontinuous solutions, which in the work will be called the tube of discontinuous solutions.The concept of stability of discontinuous solutions tubes is formalized. Two versions of sufficient conditions for asymptotic stability are obtained. In the first case, the stability of the system is ensured by the stability property of a homogeneous system without delay; in the second case, the stability property is ensured by the stability property of a homogeneous system with delay. These results generalized the similar results for systems without delay. © 2020 Irkutsk State University. All rights reserved

Impulse–Sliding Regimes in Systems with Delay

The paper is devoted to the formalization of a concept of impulse-sliding regimes generated by positional impulse controls for systems with delay. We define the notion of impulse-sliding trajectory as a limit of a sequence of Euler polygonal lines generated by a discrete approximation of the impulse position control. The equations describing the trajectory of impulse-sliding regime are received.The research was supported by Russian Science Foundation (RSF) (project No. 16-11-10146)

Exposome factors in the acne pathogenesis

The concept of the exposome, formulated more than fifteen years ago, is increasingly discussed in the modern scientific literature. The term “exposome” is understood as a cumulative measure of the impact of environmental factors on an individual throughout his or her life (from the prenatal period to death) and the biological response associated with it. The sum of these factors has a significant impact on the occurrence, course, and treatment efficacy of multifactorial diseases. The skin is a border organ and is constantly exposed to environmental influences, i.e., it is a target for the exposome. The influence of the latter components has been described in skin aging, atopic dermatitis, and malignant skin neoplasms. Acne is one of the most common chronic inflammatory dermatoses. Over the past decade, the worldwide increase in the incidence of acne, its early onset and a prolonged course, affecting adult men and women, has been noted. The review presents an analysis of the data on the effects of the components of the exposome – diet, medications, stress, and pollutants - on the course of acne. Particular attention is paid to the few data on the nature of interaction between the components of the exposome and the skin microbiome, which, on the one hand, is involved in the pathogenesis of dermatoses, including acne, and, on the other hand, is changed under the influence of exposome factors, acting as an intermediary between the environment and the human body. The search for environmental factors has at least two objectives: the discovery of potential pathogenetic links, the strength of their relationship with the clinical manifestations of the disease to develop new therapies aimed at new targets; and the creation and recommendation of a protective regime for factors with a proven effect on the course of the disease, for patients suffering from acne

Parathyroid carcinoma. The experience of treatment of 15 patients and a review

Background. Parathyroid cancer (PC) is extremely rare, usually diagnosed after surgery, there are no clinical recommendations for the treatment of metastatic PC.The study objective is to present the results of a clinical examination and treatment of patients with PC.Materials and methods. Retrospective analysis of 15 PC patients treated from 2001 to 2019. The results of laboratory tests, the surgical approach, the results of treatment, the rate of metastasis and relapse within 19 months (3 months – 11.6 years) after surgery are presented.Results. Tumor size is 35 mm (20–45 mm). Lymph node metastases – 1 (6.7 %), distant metastases – 2 (13 %). The median initial parathyroid hormone (PTH) is 735 pg/mL, calcium 3.22 mmol/L. Severe hyperparathyroidism with osteitis fibrosa cystica – in 6 (40 %). The surgical approach was parathyroidectomy in 10 (67 %), en bloc resection in 5 (33 %). Normalization of PTH and calcium after surgery – 13 (87 %). In two patients with distant metastases, the PTH and calcium remained high. A patient with Th6 vertebral metastasis was successfully operated on, with normalization of PTH and calcium, and 1.5 years was without relapse. A patient with lung and liver metastases received sorafenib after surgery, with decrease in calcium level. She died of progression 12 months after operation. Among patients with normalization of postoperative PTH, one had local relapse after 4 years. The patient was re-operated and 1 year after the second operation without relapse. The remaining patients are without relapse/progression.Conclusion. At the time of diagnosis, lymph node metastases are in 6.7 %, distant metastases – 13 %. Normalization of PTH and calcium after surgery suggests a good prognosis, but does not exclude the recurrence in the future, which requires long-term follow-up. Repeated surgery for local recurrence or solitary distant metastases can provide stable remission. Sorafenib in metastatic PC has managed to control hypercalcemia in the short term, however, antitumor efficacy requires further study

BONE SEVERE FORM OF HYPERPARATHYROIDISM IN A PATIENT WITH ADENOMA OF PARATHYROID GLAND

Hyperparathyroidism is one of the most common endocrinopathies. This disease leads to a violation of phosphorus-calcium metabolism and the washing out of calcium from bone tissue. Breach of the skeleton’s structure in hyperparathyroidism is often mistaken for metastatic bone damage, which leads to incorrect treatment tactics. In this work we present the clinical observation of a patient with an adenoma of the parathyroid gland and a severe bone form of hyperparathyroidism. Multiple lesions of bones with destruction of the cortical layer and the presence of the softtissue component were initially regarded as metastases in the bone. However, the morphological pattern of bone foci, as well as an elevated level of calcium and parathyroid hormone, made it possible to diagnose the bony form of hyperparathyroidism. The search for the cause of hyperparathyroidism revealed a tumor in the projection of the right lower parathyroid gland. Surgical removal of parathyroid adenoma led to the normalization of the level of calcium and parathyroid hormone. The article presents data of laboratory-instrumental methods of research and the results of surgical treatment of a patient