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Article
The Effects of the Hydrogen Sulfide Donor GYY4137 on the Proteasome Pool of Colorectal Cancer Cells
Abstract—Cancer cells are characterized by an increased level of metabolism and are highly dependent on the correct functioning of the processes that ensure homeostasis. Reactive sulfur species (RSS) are importan...
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Article
Lotka–Volterra Competition Model with a Nonmonotone Therapy Function for Finding Optimal Strategies in the Treatment of Blood Cancers
The interaction of healthy and cancerous cell concentrations in diseases associated with blood cancer is described by a two-dimensional Lotka–Volterra competition model. A differential equation specifying the ...
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Article
Connecting a Third-Order Singular Arc with Nonsingular Arcs of Optimal Control in a Minimization Problem for a Psoriasis Treatment Model
We study a mathematical model of psoriasis treatment defined by a system of three differential equations on a fixed time interval. These equations describe the interaction between the populations of T-lymphoc...
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Article
Optimal Strategies in the Treatment of Cancers in the Lotka–Volterra Mathematical Model of Competition
The Lotka–Volterra competition model is applied to describe the interaction between the concentrations of healthy and cancerous cells in diseases associated with blood cancer. The model is supplemented with a ...
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Article
Open AccessThe comparison of the process of manual and robotic positioning of the electrode performing radiofrequency ablation under the control of a surgical navigation system
This study is aimed at the comparison of the process of manual and robotic positioning of the electrode performing radiofrequency ablation under the control of a surgical navigation system. The main hypothesis...
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Article
Correction to: Optimal Control Problems for a Mathematical Model of the Treatment of Psoriasis
To the article “Optimal Control Problems for a Mathematical Model of the Treatment of Psoriasis,” by N. L. Grigorenko, É. V. Grigorieva, P. K. Roi, and E. N. Khailov, Vol. 30, No. 4, pp. 352–363, October, 2019.
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Article
Optimal Control Problems for a Mathematical Model of the Treatment of Psoriasis
We consider a mathematical model of the treatment of psoriasis on a finite time interval. The model consists of three nonlinear differential equations describing the interrelationships between the concentratio...
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Article
Multistability of Spiking Regimes in a Model of a Laser with Delayed-Feedback
We use the methods of asymptotic analysis to obtain finite-dimensional maps, whose dynamics determines the dynamics of relaxation oscillations in a laser model with optoelectronic feedback. The coexistence of ...
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Article
Slow and Fast Oscillations in a Model of an Optoelectronic Oscillator with Delay
The local dynamics of a well-known model of an optoelectronic oscillator with delayed feedback is studied. In a neighborhood of zero equilibrium, normalized equations are constructed which are boundary value p...
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Article
On a Third-Order Singular Arc of Optimal Control in a Minimization Problem for a Mathematical Model of Psoriasis Treatment
We consider a mathematical model of psoriasis treatment on a given time interval. The model consists of three nonlinear differential equations that describe the relationship between the concentrations of T-lym...
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Article
Local Dynamics of a Model of an Opto-Electronic Oscillator with Delay
We consider the dynamics of an electro-optic oscillator described by a system of differential equations with delay. An essential feature of this model is that one of the derivatives is multiplied by a small pa...
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Article
Reachable Set of a Control Model for Two-Step Wastewater Biotreatment
We consider a mathematical model describing a two-step process of wastewater biotreatment. This is a four-dimensional nonlinear system of differential equations with a scalar constraint on the control. The Pon...
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Article
Quasi-periodic and chaotic relaxation oscillations in a laser model with variable delayed optoelectronic feedback
We derive asymptotically discrete map**s which determine the dynamics of relaxation spikes in a model of laser with optoelectronic feedback in the pump circuit. The time delay in the feedback path varies per...
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Article
Averaging principles applied to logistic equations with rapidly oscillating delays
The problem about local dynamics of the logistic equation with a rapidly oscillating timeperiodic piecewise constant coefficient of delay has been considered. It has been shown that the averaged equation is a ...
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Article
Time Optimal Control Problem for the Waste Water Biotreatment Model
This work is devoted to solving the time optimal control problem of a mathematical model describing the process of biological waste water treatment and is given as a three-dimensional nonlinear control system ...
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Article
Multistability in a laser model with large delay
Dynamics of laser generation is considered on the base of single-mode rate equations with retarded argument. In the framework of local analysis, we determine continual sets of families of quasi-normal forms in...
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Article
Solving the controllability problem for a nonlinear three-dimensional system
The controllability problem is solved for a nonlinear system of three differential equations that simulates aerated biological wastewater treatment using the thermal metabolism of thermophilic aerobic bacteria...
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Article
M31R and R335C polymorphic variants of the IL8RA gene in Russian and Buryat patients with atopic bronchial asthma
To test the M31R and R335C polymorphisms of the Il8RA gene for association with atopic bronchial asthma (BA), the allele and genotype frequency distributions of the polymorphisms were studied in Russian patients ...
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Article
Open AccessD -Glucuronyl C5-epimerase suppresses small-cell lung cancer cell proliferation in vitro and tumour growth in vivo
D -Glucuronyl C5-epimerase (GLCE) is a key enzyme involved in the biosynthesis of heparan sulphate proteoglycans, which has an important role in cell–cell and cell–matrix interactions and signalling. Decreased GL...
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Article
Hierarchical differential game between manufacturer, retailer, and bank
In this work, a microeconomic model describing interactions between a manufacturer, retailer and bank is created and investigated. The manufacturer produces a single product, the retailer buys the good in orde...
