THE EFFECT OF THE STABILITY OF THE FREE ANKLE JOINT ON THE GAIT BALANCE OF CHRONIC STROKE PATIENTS BY THE ANKLE FOOT ORTHOSIS

Stroke patients have high foot instability and a high risk of falling down in walking and standing positions due to muscle and sensory disorders. There are many patients who complain of inconvenience in their daily lives, but independent walking is very difficult. In this work, we explore the effect on walking and dynamic balance by securing internal and external stability of the foot. Fifteen participants participated in the experiment, with 10m walk tests, timed and go tests, and functional reach tests. The walk 10m test was not statistically significant, with 0.59 ± 0.23 m/s before the device was worn and 0.66 ± 0.29 m/s after the device was worn. Timed up and Go tests were statistically significant 26.57 ± 6.12 seconds before wearing the device, 22.31 ± 4.32 seconds after wearing the device, 222.59 ± 10.31 cm before wearing the device, and 230.93 ± 11.33 cm after wearing the device. Securing internal and external stability of the foot can have a positive impact on securing a dynamic balance in which weight movement is performed.

Analysis of the Strong and Weak Monotonic External Stability of the Resonance in a Perturbed Dynamical System

A perturbed dynamical system involving two ordinary differential equations is under review. Whereupon, the differential equation for determining the fast phase contains the ratio of the two frequencies. When these frequencies coincide for a long time, a resonance is implemented in this system. The aim of this paper is to obtain the conditions of monotonic external stability and instability of this resonance. The sufficient conditions for the external stability and instability of the resonance defined in this paper assume that the signs of the analyzed derivatives remain unchanged in the non-resonant section of the change in the independent variable. This paper gives a new classification of the phenomenon of external stability of resonance, which includes weak, linear, and strong stability. It should be noted that the conditions of monotonic external stability and instability of the resonance presented in this paper can be used in various scientific and technological problems, in which resonances are observed. Particularly, the concluding part of the paper considers the application of the results obtained within the framework of the problem of the perturbed motion of a rigid body relative to a fixed point.

RELIGIOUS EXTREMISM IN KAZAKHSTAN: THREATS OF SPREADING AND MEANS OF OPPOSITION

Today, regional integration and globalization have added new dimensions to the problems of violence, religious extremism and terrorism that attract a lot of attention in the academic community of many counties. A polyconfessional and polyethnic state, Kazakhstan, where various trends of world religions are inevitably present, is especially aware of the problem of religious extremism. In these conditions, interconfessional relations as a guarantor of internal and external stability in our republic is one of its most important problems. This article presents the aspects related to the religious environment and threats of religious extremism in Kazakhstan and outlines feasible solutions.

External stability and $H_{\infty }$ control of switching systems with delay and impulse

In this paper, we investigate the external stability and $H_{\infty }$ H ∞ control of switching systems with time-varying delay and impulse. First of all, a modified two-direction inequality (relation) between the switching numbers and the maximum, minimum dwell time is proposed. This new inequality is applied to proving the external stability of switching systems with delay and impulse consisting of subsystems with Hurwitz stable matrices of internal dynamics. By using this new inequality, a normal $L_{2}$ L 2 norm constraint is derived rather than weighted $L_{2}$ L 2 norm constraint. In addition, by a realizable switching law, the obtained result is extended to the switching systems comprised of subsystems with both Hurwitz stable and unstable matrices of internal dynamics. The results are finally applied to $H_{\infty }$ H ∞ control and illustrated by a numerical example.