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Abstract We study a semilinear fractional order differential inclusion in a separable Banach space E of the form DqCx(t)∈Ax(t)+F(t,x(t)),t∈[0,T], $$ {}^{C}D^{q}x(t)\in Ax(t)+ F\bigl(t,x(t)\bigr),\quad t\in [0,T], $$ where DqC ${}^{C}D^{q}$ is the Caputo fractional derivative of order 0

In this paper we study the existence of a mild solution of a periodic boundary value problem for fractional quasilinear differential equations in a Hilbert spaces. We assume that a linear part in equations is a self-adjoint positive operator with dense domain in Hilbert space and a nonlinear part is a map obeying Carathéodory type conditions. We find the mild solution of this problem in the form of a series in a Hilbert space. In the space of continuous functions, we construct the corresponding resolving operator, and for it, by using Schauder theorem, we prove the existence of a fixed point. At the end of the paper, we give an example for a boundary value problem for a diffusion type equation.

We prove necessary and sufficient stability conditions for perturbed semigroups of linear operators in Banach spaces with cones and consider examples using these conditions. In particular, we consider an example where the boundary-value problem is perturbed by a linear operator with a delayed independent variable and establish stability conditions for such a perturbed semigroup., CONTENTS 1. Introduction 2. Preliminary Data 3. Stability: Necessary Condition 4. Positiving Multivalued Maps 5. Stability Preservation Theorem 6. Example: Infinite Matrices 7. Example: Perturbations of Boundary-Value Problems by Operators [...]

Abstract We apply the topological degree theory for condensing maps to study approximation of solutions to a fractional-order semilinear differential equation in a Banach space. We assume that the linear part of the equation is a closed unbounded generator of a C 0 $C_{0}$ -semigroup. We also suppose that the nonlinearity satisfies a regularity condition expressed in terms of the Hausdorff measure of noncompactness. We justify the scheme of semidiscretization of the Cauchy problem for a differential equation of a given type and evaluate the topological index of the solution set. This makes it possible to obtain a result on the approximation of solutions to the problem.

Статья написана в рамках проекта по изучению феномена самоубийства в России XVIII в. В еe основе – следственное дело по факту гибели майора Василия Апухтина в 1731 г. Как явствует из материалов расследования, майор покончил жизнь самоубийством, утопившись в собственном колодце. По многочисленным свидетельствам прислуги, родственников и знакомых, В. Апухтин был умалишенным, а причиной его помешательства, или скорее обстоятельством, усугубившим душевный недуг самоубийцы, стал страх предстать перед судом в результате ведшейся им тяжбы. Вполне заурядный имущественный процесс, неадекватно воспринятый самоубийцей, породил в его сознании ужас перед возможностью признания неблагонадежным, а значит, достойным пытки в рамках уже уголовного производства. Это обстоятельство позволяет рассмотреть эпизод Апухтина в рамках понятия «государственного страха», впервые введенного в историографию Е. Анисимовым. Анализ причин душевных терзаний несчастного майора, приведших к самоубийству, через призму этого понятия оказывается продуктивным для оценки многих других случаев, обрекавших русских людей XVIII столетия на такой же финал. Что же следует понимать под «государственным страхом»? Широкий круг исследованных документов позволяет утверждать, что это страх перед неизбежными физическими мучениями, сопровождавшими уголовный процесс того времени, в сочетании со страхом столкновения с бездушной карательной государственной машиной, не дававшей никакой возможности оправдаться; ощущение полного бессилия и безысходности. Этот страх оказывался присущ абсолютно всем, вне зависимости от их сословной принадлежности или места проживания, хотя чаще его суицидальные последствия сказывались на наименее защищенных слоях населения. Примечательно, что для крепостных карательную силу государства, вызывавшую страх, олицетворяли их душевладельцы. Принципиально важным выглядит вывод о том, что «государственный страх» – это явление, сформировавшееся

ZnFe2O4 (ZFO) nanospheres with complex structures have been synthesized by a one-step simple solvothermal method using two different types of precursors—metal chlorides and nitrates —and were fully characterized by XRD, SEM, XPS, and EDS. The ZFO nanospheres synthesized from chloride salts (ZFO_C) were loose with a size range of 100–200 nm, while the ZFO nanospheres synthesized from nitrate salts (ZFO_N) were dense with a size range of 300–500 nm but consisted of smaller nanoplates. The different morphologies may be caused by the different hydrolysis rates and different stabilizing effects of chloride and nitrate ions interacting with the facets of forming nanoparticles. Electrochemical tests of nitrate-based ZFO nanospheres as anode materials for lithium-ion batteries demonstrated their higher cyclic stability. The ZFO_C and ZFO_N samples have initial specific discharge/charge capacities of 1354/1020 and 1357/954 mAh∙g−1, respectively, with coulombic efficiencies of 75% and 71%. By the 100th cycle, ZFO_N has a capacity of 276 mAh∙g−1, and for ZFO_C, only 210 mAh∙g−1 remains after 100 cycles. [ABSTRACT FROM AUTHOR]

We obtained results on the existence and uniqueness of a mild solution for a fractional-order semi-linear differential inclusion in a Hilbert space whose right-hand side contains an unbounded linear monotone operator and a Carathéodory-type multivalued nonlinearity satisfying some monotonicity condition in the phase variables. We used the Yosida approximations of the linear part of the inclusion, the method of a priori estimates of solutions, and the topological degree method for condensing vector fields. As an example, we considered the existence and uniqueness of a solution to the Cauchy problem for a system governed by a perturbed subdifferential inclusion of a fractional diffusion type.

The electrodes of lithium-ion batteries (LIBs) are multicomponent systems and their electrochemical properties are influenced by each component, therefore the composition of electrodes should be properly balanced. At the beginning of lithium-ion battery research, most attention was paid to the nature, size, and morphology peculiarities of inorganic active components as the main components which determine the functional properties of electrode materials. Over the past decade, considerable attention has been paid to development of new binders, as the binders have shown great effect on the electrochemical performance of electrodes in LIBs. The study of new conductive binders, in particular water-based binders with enhanced electronic and ionic conductivity, has become a trend in the development of new electrode materials, especially the conversion/alloying-type anodes. This mini-review provides a summary on the progress of current research of the effects of binders on the electrochemical properties of intercalation electrodes, with particular attention to the mechanisms of binder effects. The comparative analysis of effects of three different binders (PEDOT:PSS/CMC, CMC, and PVDF) for a number of oxide-based and phosphate-based positive and negative electrodes for lithium-ion batteries was performed based on literature and our own published research data. It reveals that the combined PEDOT:PSS/CMC binder can be considered as a versatile component of lithium-ion battery electrode materials (for both positive and negative electrodes), effective in the wide range of electrode potentials.