Existence, uniqueness, variation-of-constant formula and controllability for linear dynamic equations with Perron Δ-integrals

In this paper, we investigate the existence and uniqueness of a solution for a linear Volterra-Stieltjes integral equation of the second kind, as well as for a homogeneous and a nonhomogeneous linear dynamic equations on time scales, whose integral forms contain Perron [Formula: see text]-integrals defined in Banach spaces. We also provide a variation-of-constant formula for a nonhomogeneous linear dynamic equations on time scales and we establish results on controllability for linear dynamic equations. Since we work in the framework of Perron [Formula: see text]-integrals, we can handle functions not only having many discontinuities, but also being highly oscillating. Our results require weaker conditions than those in the literature. We include some examples to illustrate our main results.

Individual psychological characteristics of students of different ethnic groups in the process of adaptation to living conditions in student dormitories

В статье отражены результаты эмпирического исследования индивидуально-психологических особенностей студентов различных этнических групп процессе адаптации к условиям проживания в студенческих общежитиях. Данная работа обусловлена необходимостью расширения области исследования взаимодействия во внутривузовской среде за счет включения межэтнического компонента. При этом учитываются основные особенности астраханского региона, исконно объединяющего на своей территории представителей различных этнических групп. В исследовании были применены психодиагностические методики: 1) многоуровневый личностный опросник «Адаптивность» (А.Г. Маклаков, С.В. Чермянин); 2) методика «Определения интегральных форм коммуникативных агрессивности» (В.В. Бойко); 3) экспресс-опросник «Индекс толерантности» (Г.У. Солдатова, О.А. Кравцова, О.Е. Хухлаев, Л.А. Шайгерова). Анализ результатов исследования позволяет сделать вывод о том, что группы с различными уровнями адаптивности различаются по такому показателю как «агрессивность», то есть студенты младших курсов имеющих такую черту личности как агрессивность обладают меньшими способностями к адаптации в новой среде, в том числе, к условиям проживания в студенческих общежитиях. Во внутривузовской среде исследование межэтнического взаимодействия может стать ключом к пониманию причин и динамики возникающих конфликтных ситуаций. В связи с этим, мы видим возможность использования результатов проведенного эмпирического исследования в практике урегулирования межэтнических конфликтов во внутривузовской среде. The article reflects the results of an empirical study of individual psychological characteristics of students of various ethnic groups in the process of adaptation to living conditions in student dormitories. This work is due to the need to expand the field of research of interaction in the intra-university environment by including an interethnic component. This takes into account the main features of the Astrakhan region, which traditionally unites representatives of various ethnic groups on its territory. The study used psychodiagnostic techniques: 1) multilevel personality questionnaire "Adaptability" (A.G. Maklakov, S.V. Chermyanin); 2) the methodology "Determination of integral forms of communicative aggressiveness" (V.V. Boyko); 3) express questionnaire "Index of Tolerance". (G.U. Soldatova, O.A. Kravtsova, O.E. Khukhlaev, L.A. Shaigerova). Analysis of the research results allows us to conclude that groups with different levels of adaptability differ in terms of such an indicator as "aggressiveness", that is, junior students with such a personality trait as aggressiveness have less ability to adapt to a new environment, including to conditions living in student hostels. In the intra-university environment, the study of interethnic interaction can become the key to understanding the causes and dynamics of emerging conflict situations. In this regard, we see the possibility of using the results of the empirical research in the practice of resolving interethnic conflicts in the intra-university environment.

Tube Expansion by Single Point Incremental Forming: An Experimental and Numerical Investigation

In this paper, we revisit the formability of tube expansion by single point incremental forming to account for the material strain hardening and the non-proportional loading paths that were not taken into consideration in a previously published analytical model of the process built upon a rigid perfectly plastic material. The objective is to provide a new insight on the reason why the critical strains at failure of tube expansion by single point incremental forming are far superior to those of conventional tube expansion by rigid tapered conical punches. For this purpose, we replaced the stress triaxiality ratio that is responsible for the accumulation of damage and cracking by tension in monotonic, proportional loading paths, by integral forms of the stress triaxiality ratio that are more adequate for the non-proportional paths resulting from the loading and unloading cycles of incremental tube expansion. Experimental and numerical simulation results plotted in the effective strain vs. stress triaxiality space confirm the validity of the new damage accumulation approach for handling the non-proportional loading paths that oscillate cyclically from shearing to biaxial stretching, as the single point hemispherical tool approaches, contacts and moves away from a specific location of the incrementally expanded tube surface

Delay-Dependent Stability Analysis of Haptic Systems via an Auxiliary Function-Based Integral Inequality

In this paper, the delay-dependent stability of haptic systems is studied by developing a new stability criterion. Firstly, the haptic system inevitably introduces time delays by using communication networks to transmit information between the controller and the haptic device. When discussing the stability of the haptic system near its operating point, the original nonlinear system is modeled as a linear system with the time delay mentioned above. In addition, a suitable augmented Lyapunov–Krasovskii functional (LKF) with more integral forms is constructed and an auxiliary function-based integral inequality is applied to estimate the derivative of the proposed LKF. Then, a less conservative delay-dependent criterion in terms of the linear matrix inequality (LMI) is derived to calculate the delay margin for the haptic system. Finally, case studies are carried out based on a one degree of freedom haptic system. The results show that, compared with criteria in existing works, the proposed criterion can obtain more accurate results and require less calculation complexity, and, with the increase in virtual damping in a certain range, the stable upper bound of the haptic system increases at first and then decreases.

A New Formulation of Maxwell’s Equations

In this paper, new forms of Maxwell’s equations in vector and scalar variants are presented. The new forms are based on the use of Gauss’s theorem for magnetic induction and electrical induction. The equations are formulated in both differential and integral forms. In particular, the new forms of the equations relate to the non-stationary expressions and their integral identities. The indicated methodology enables a thorough analysis of non-stationary boundary conditions on the behavior of electromagnetic fields in multiple continuous regions. It can be used both for qualitative analysis and in numerical methods (control volume method) and optimization. The last Section introduces an application to equations of magnetic fluid in both differential and integral forms.

PSYCHOLOGICAL PROTECTION OF PERSONS WITH DIFFERENT LEVELS OF AGGRESSIVENESS

Purpose. The purpose of this article is to present the results of theoretical and empirical research aimed at studying the features of psychological protection in people with different levels of aggression.Methods. The method “Life Style Index” by R. Plutchyk, G. Kellermann, H. Comte, adapted by L. Wasserman was used to diagnose the mechanisms of psychological protection. The method “Determination of integral forms of communicative aggression” by V. Boyko was used to study of communicative aggression.Results. The results of the correlation analysis between the indicators of the mechanisms of psychological protection and communicative aggression are presented. It was identified the positive and negative significant correlations between most indicators of psychological protection and communicative aggression. The profiles of features of psychological protection of “aggressive” and “non-aggressive” persons are considered. It is established that there are some differences in the manifestations of mechanisms of psychological protection in members of a group of people with different levels of aggression.Conclusions. Psychological protection is seen as a system of regulatory mechanisms of the psyche, which are aimed at eliminating or minimizing negative, traumatic personal experiences associated with internal or external conflicts, states of anxiety and discomfort. The function of psychological protection is to overcome feelings of insecurity, inferiority, protection of value consciousness and maintaining a stable self-esteem. Aggression is understood as a person’s behavior towards other people, which is characterized by a desire to cause them trouble, harm. Correlation analysis has shown that communicative aggression is most associated with psychological defense mechanisms such as displacement, regression, compensation, and substitution. The qualitative analysis was established that persons with a high level of communicative aggression are characterized by such mechanisms of psychological protection as regression, compensation and substitution. In the group of people with a low level of aggression is dominated such mechanisms of psychological protection as denial, compensation and reactive education.Key words: mechanisms of psychological protection, aggression, communicative aggression, personality trait, quantitative analysis, qualitative analysis. Метою статті є виклад результатів теоретико-емпіричного дослідження, спрямованого на вивчення особливостей психологічного захисту осіб з різним рівнем агресивності.Методи. Для діагностики механізмів психологічного захисту використовувалась методика «Індекс життєвого стилю» (Life Style Index) Р. Плутчика, Г. Келлерманна, Х. Конта, в адаптації Л.І. Васермана. Вивчення комунікативної агресивності здійснено за допомогою методики «Визначення інтегральних форм комунікативної агресивності» В.В. Бойко.Результати. Наведено результати кореляційного аналізу між показниками механізмів психологічного захисту і комунікативної агресивності. Виявлено наявність додатних і від’ємних значимих кореляційних зв’язків між більшістю показників психологічного захисту і комунікативної агресивності. Розглянуто профілі особливостей психологічного захисту «агресивних» і «неагресивних» осіб. Встановлено, що існують певні розбіжності у проявах механізмів психологічного захисту у представників групи осіб з різним рівнем агресивності.Висновки. Психологічний захист розглядається як система регуляторних механізмів психіки, які спрямовані на усунення або зведення до мінімуму негативних переживань, що травмують особистість, пов’язаних із внутрішніми або зовнішніми конфліктами, станами тривоги та дискомфорту. Функцією психологічному захисту є подолання відчуття невпевненості в собі, власної неповноцін-ності, захисту ціннісної свідомості та підтримки стабільної самооцінки. Агресивність розуміється як поведінка людини щодо інших людей, яка відрізняється прагненням заподіяти їм неприємності, завдати шкоди. За результатами кореляційного аналізу встановлено, що комунікативна агресивність найбільш пов’язана з такими механізмами психологічного захисту, як витіснення, регресія, компенсація і заміщення. За допомогою якісного аналізу встановлено, що особам із високим рівнем комунікативної агресивності притаманні такі механізми психологічного захисту, як регресія, компенсація і заміщення. В групі осіб із низьким рівнем агресивності переважають такі механізми психологічного захисту, як заперечення, компенсація і реактивне утворення.Ключові слова: механізми психологічного захисту, агресивність, комунікативна агресивність, властивість особистості, кількісний аналіз, якісний аналіз

The Mayr-Pentegov Model of Electric Arc Involving the Use of the Exponential Function and Enabling the Approximation of Static Characteristics

The article presents the justified use of functions containing the exponential component for the approximation of the static current-voltage characteristics of electric arc. The Author proposed a new function approximating the above-named characteristics which were next used in the mathematical Mayr-Pentegov model, expressed in two, i.e. differential and integral, forms. The two forms constituted the basis enabling the development of macromodels using controlled voltage and current sources. The article also presents families of dynamic current-voltage characteristics obtained through the simulation of processes in a circuit containing macromodels of arc powered by the source of current characterised by sinusoidal and trapezoidal waveforms and various frequency. The article demonstrates the usability of the proposed variants of the Mayr-Pentegov model.

Spontaneous and Stimulated Undulator Radiation in Symmetric and Asymmetric Multi-Periodic Magnetic Fields

In this work, the radiation from electrons in multi-periodic undulator fields with symmetric and asymmetric harmonics was analyzed using generalized Bessel functions formalism. The asymmetric, symmetric, and anti-symmetric periodic magnetic fields with harmonics were studied in order to get the enhanced radiation of the high harmonics of undulator radiation (UR). The effect on the spontaneous and stimulated UR was explored. The exact integral forms for the Bessel coefficients were obtained for undulators with general symmetric and asymmetric field harmonics. Spectral properties of the radiation from several configurations of the undulator fields with harmonics were compared with each other. The resulting spontaneous UR spectrum and harmonic intensities were obtained analytically in the form of integrals and compared with the respective results that were obtained numerically with SPECTRA program. The dimensionless scaling parameter of a free electron laser (FEL)—the Pierce parameter (ρ)—was computed and compared for the different considered undulators. We studied the differences in the behavior of the high-gain single pass FEL harmonics and the spontaneous UR harmonics in the same undulators. The undulators with variable deflection parameter (k) were considered. The effect of the k parameter (deflection parameter for a common planar undulator) on the spontaneous UR and on the high-gain FEL radiation was explored. In this context, an experiment with variable strength undulators at FLASH 2 FEL was analyzed; the shorter saturated length in high harmonic self-seeding (HHSS) regime vs. self-amplified spontaneous emission (SASE) is explained.