Gaudin model and Deligne's category

We show that the construction of the higher Gaudin Hamiltonians associated to the Lie algebra $\mathfrak{gl}_{n}$ admits an interpolation to any complex $n$. We do this using the Deligne's category $\mathcal{D}_{t}$, which is a formal way to define the category of finite-dimensional representations of the group $GL_{n}$, when $n$ is not necessarily a natural number. We also obtain interpolations to any complex $n$ of the no-monodromy conditions on a space of differential operators of order $n$, which are considered to be a modern form of the Bethe ansatz equations. We prove that the relations in the algebra of higher Gaudin Hamiltonians for complex $n$ are generated by our interpolations of the no-monodromy conditions. Our constructions allow us to define what it means for a pseudo-deifferential operator to have no monodromy. Motivated by the Bethe ansatz conjecture for the Gaudin model associated with the Lie superalgebra $\mathfrak{gl}_{n\vert n'}$, we show that a ratio of monodromy-free differential operators is a pseudo-differential operator without monodromy.Comment: 35 page

Mechanochemical synthesis of carbon-based nanocomposites for supercapacitors

New nanoporous carbon-SiO2 composite materials were synthesized from organic raw materials (rice shells) and their electrochemical properties were investigated by cyclic voltammetry in liquid electrolytes (6 M KOH or 1 M H2SO4). A correlation between specific capacitance and specific surface area was observed. Due to high specific capacitance of 90 F/g the carbon materials under study may be regarded as promising electrode materials for electrochemical supercapacitors

Fuse Selection for the Two-Stage Explosive Type Switches

In the two-level explosive switch destruction of a delay happens in the form of electric explosion. Criteria of similarity of electric explosion in transformer oil are defined. The challenge of protecting the power electrical equipment from short circuit currents is still urgent, especially with the growth of unit capacity. Is required to reduce the tripping time as much as possible, and limit the amplitude of the fault current, that is very important for saving of working capacity of life-support systems. This is particularly important when operating in remote stand-alone power supply systems with a high share of renewable energy, working through the inverter transducers, as well as inverter-type diesel generators. The explosive breakers copes well with these requirements. High-speed flow of transformer oil and high pressure provides formation rate of a contact gap of 20 - 100 m/s. In these conditions there is as a rapid increase in voltage on the discontinuity, and recovery of electric strength (Ures) after current interruption

Measuring the Dispersion Forces Near the van der Waals-Casimir Transition

Forces induced by quantum fluctuations of the electromagnetic field control adhesion phenomena between rough solids when the bodies are separated by distances of approximately 10 nm. However, this distance range remains largely unexplored experimentally in contrast with the shorter (van der Waals forces) or the longer (Casimir forces) separations. The reason for this is the pull-in instability of the systems with the elastic suspension that poses a formidable limitation. In this paper we propose a genuine experimental configuration that does not suffer from the short distance instability. The method is based on the adhered cantilever, whose shape is sensitive to the forces acting near the adhered end. The general principle of the method, its possible realization, and feasibility are extensively discussed. The dimensions of the cantilever are determined by the maximum sensitivity to the forces. If the adhesion is defined by strong capillary or chemical interactions, the method loses its sensitivity. Special discussion is presented for the determination of the minimum distance between the rough solids upon contact, and for the compensation of the residual electrostatic contribution. The proposed method can be applied to any kind of solids (metals, semiconductors, or dielectrics) and to any intervening medium (gas or liquid).</p

Стохастические функциональные характеристики радиоэлектронных аппаратов

Розглянутi моделі фізичних процесів у радіоелектронних апаратах (РЕА) у вигляді стохастичних диференціальних рівнянь. Показано, що всі фізичні процеси у РЕА є стохастичними, а функціональні характеристики апаратів повинні бути представлені функціями з імовірнісними показниками. Наведені стохастичні диференціальні рівняння для електромагнітних, електричних, механічних, теплових процесів та запропоновані методи одержання їх розв’язків на основі детермінованих моделей. Наведені приклади визначення функціональних характеристик за дії механічних та теплових впливівThe models of physical processes in radio electronic devices (RED) as the stochastic differential equations are considered. Is shown, that all physical processes in RED - stochastic, and functional characteristics of devices should be submitted by functions with stochastic by parameters. The stochastic differential equations for electromagnetic, electrical, mechanical, thermal processes are given and the methods of reception of their decisions are offered on the basis of the determined models. The examples of reception of the functional characteristics are given at mechanical and thermal influencesРассмотрены модели физических процессов в радиоэлектронных аппаратах (РЭА) в виде стохастических дифференциальных уравнений. Показано, что все физические процессы в РЭА – стохастические, а функциональные характеристики аппаратов должны быть представлены функциями с вероятностными показателями. Приведены стохастические дифференциальные уравнения для электромагнитных, электрических, механических, тепловых процессов и предложены методы получения их решений на основе детерминированных моделей. Приведены примеры получения функциональных характеристик при механических и тепловых воздействия

Transformer Oil Dielectric Strength in the Contact Gap of the Explosive Arc-Extinguishing Device

The article describes the experimental results on the breakdown of the high-speed flow of transformer oil. In real conditions, the flow moves in the contact gap of a high-voltage explosive switch with speeds from 67 to 152 m /s. The geometry of the contact gap is sharply inhomogeneous and forms turbulence in the flow zone. In the arc chute medium the air inclusions pass from the dissolved state to the gaseous and the emerging bubbles enter to the electric field. Breakdown occurs, mainly through gas inclusions. In the moment, the gradient of the breakdown voltage is reduced by 91.6% compared to the static state of the oil. The experiments were carried out on the model of a high-voltage explosive switch, connected to the power circuit of the surge generator. The probing of the gap was made by a standard pulse of 1.5 / 50 [mu]s. As a result, the dependences of the gradient of the breakdown voltage on the flow rate of the transformer oil for the usual geometry of the high-voltage explosive switch contact system are constructed

Гіпервипадкові характеристики теплових процесів у пристроях радіоелектронної апаратури

Thermal process in devices REА are submitted as hyperbolic-accidental of function. Are considered е of the characteristic of mathematical models and their decisions. The example of definition of the numerical characteristics hyperbolic-accidental of functional parame-ters of the radioelectronic equipments is given.Тепловые процессы в устройствах РЭА представлены как гиперслучайные функции. Рассмотрены вероятностные характеристики математических моделей и их решений. Приведен пример определения числовых характеристик гиперслучайных функциональных показателей РЭС.Теплові процеси у пристроях РЕА представлені як гіпервипадкові функції. Розглянути ймовірносні характеристики математичних моделей та їх рішень. Наведений приклад визначення числових характеристик гіпервипадкових функціональних показників РЕЗ

Методи оптимізації конструкцій радіоелектронних модулів

The methods of designing of radioelectronic modules as printedcircuit-boards are considered which should ensure identical reliability of a design on conditions vibration strength and thermal mode of radioelectronic componentsРассмотрены методы проектирования радиоэлектронных модулей в виде печатных плат, которые должны обеспечить одинаковую надежность конструкции по условиям вибропрочности и теплового режима электрорадиоэлементовРозглянуті методи проектування радіоелектронних модулів у вигляді друкованих плат, що повинні забезпечити однакові показники надійності конструкції з умов віброміцності та теплового режиму електрорадіоелементі