Resolvent Estimates for High-Contrast Elliptic Problems with Periodic Coefficients

We study the asymptotic behaviour of the resolvents (Aε+I)−1 of elliptic second-order differential operators Aε in Rd with periodic rapidly oscillating coefficients, as the period ε goes to zero. The class of operators covered by our analysis includes both the “classical” case of uniformly elliptic families (where the ellipticity constant does not depend on ε ) and the “double-porosity” case of coefficients that take contrasting values of order one and of order ε2 in different parts of the period cell. We provide a construction for the leading order term of the “operator asymptotics” of (Aε+I)−1 in the sense of operator-norm convergence and prove order O(ε) remainder estimates

Resolvent estimates for high-contrast elliptic problems with periodic coefficients.

We study the asymptotic behaviour of the resolvents (Aε+I)−1 of elliptic second-order differential operators Aε in Rd with periodic rapidly oscillating coefficients, as the period ε goes to zero. The class of operators covered by our analysis includes both the “classical” case of uniformly elliptic families (where the ellipticity constant does not depend on ε ) and the “double-porosity” case of coefficients that take contrasting values of order one and of order ε2 in different parts of the period cell. We provide a construction for the leading order term of the “operator asymptotics” of (Aε+I)−1 in the sense of operator-norm convergence and prove order O(ε) remainder estimates

Spectral Analysis of One-Dimensional High-Contrast Elliptic Problems with Periodic Coefficients

We study the behavior of the spectrum of a family of one-dimensional operators with periodic high-contrast coefficients as the period goes to zero, which may represent, e.g., the elastic or electromagnetic response of a two-component composite medium. Compared to the standard operators with moderate contrast, they exhibit a number of new effects due to the underlying nonuniform ellipticity of the family. The effective behavior of such media in the vanishing period limit also differs notably from that of multidimensional models investigated thus far by other authors, due to the fact that neither component of the composite forms a connected set. We then discuss a modified problem, where the equation coefficient is set to a positive constant on an interval that is independent of the period. Formal asymptotic analysis and numerical tests with finite elements suggest the existence of localized eigenfunctions (``defect modes''), whose eigenvalues are situated in the gaps of the limit spectrum for the unperturbed problem

N-силілімін трифторопірувату в асиметричному синтезі похідних трифтороаланіну

Aim. To develop a preparative method for the synthesis of N-trimethylsilylimine of trifluoropyruvate, and study its interaction with acetone under organocatalytic conditions.Results and discussion. A simple preparative approach to the first representative of N-silylimines of trifluoropyruvate was developed based on the interaction of triphenylphosphinimide and trifluoropyruvic acid methyl ester by the aza-Wittig reaction. It was found that the addition of acetone to N-silylimine occurred in the presence of L- or D-proline and led to the formation of enantiomerically enriched α-amino-γ-oxocarboxylates. The hydrolysis of the ester function resulted in (R)-α-trifluoromethyl aminocarboxylic acid, and the cyclocondensation with isocyanates or 2,5-dimethoxytetrahydrofuran yielded nitrogen-containing heterocycles containing pyrimidine or pyrrolizine nuclei.Experimental part. The synthetic procedures for the N-silylimine of trifluoropyruvate and its reaction with acetone are provided, along with the transformations of obtained α-amino-γ-oxocarboxylates (hydrolysis, cyclocondensations with isocyanates and 2,5-dimethoxytetrahydrofuran). The structures of the compounds synthesized were proven by 1H, 13C, 19F NMR spectroscopy methods, as well as by the elemental analysis.Conclusions. A convenient method for the synthesis of N-silylimine of trifluoropyruvate has been developed. Using the example of the Mannich reaction with acetone, it has been demonstrated that N-silylimine of trifluoropyruvate is a convenient substrate for the synthesis of optically active 3,3,3-trifluoroalanine derivatives.Мета. Розробити препаративний метод синтезу N-триметилсиліліміну трифторопірувату та дослідити закономірності його взаємодії з ацетоном в органокаталітичних умовах.Результати та їх обговорення. Розроблено простий препаративний підхід до першого представника N-силілімінів трифторопірувату, який полягає у взаємодії трифенілфосфініміду і метилового естеру трифторопіровиноградної кис-лоти за схемою реакції аза-Віттіга. Виявлено, що приєднання ацетону до N-силіліміну відбувається в присутності L- або D-проліну і призводить до утворення енантіомерно збагачених α-аміно-γ-оксокарбоксилатів. Гідролізом естерної функції останніх одержано (R)-α-трифторометиламінокарбонову кислоту, а циклоконденсацією з ізоціанатами та2,5-диметокситетрагідрофураном синтезовано нітрогеновмісні гетероцикли, що містять піримідинове або піролізинове ядро.Експериментальна частина. Наведено експериментальні методики синтезу N-силіліміну трифторопірувату, продуктів його реакції з ацетоном, а також перетворення отриманих α-аміно-γ-оксокарбоксилатів (гідроліз, циклоконденсації з ізоціанатами та 2,5-диметокситетрагідрофураном). Структури усіх отриманих сполук доведено методами ЯМР наядрах 1H, 13C і 19F, а також елементним аналізом.Висновки. Розроблено зручний метод синтезу N-силіліміну трифторопірувату. На прикладі реакції Манніха з ацетоном продемонстровано, що N-силілімін трифторопірувату є зручним субстратом для синтезу оптично активних похідних3,3,3-трифтороаланіну

Stability of HEB receivers at THz frequencies

Stability of a hot-electron bolometer (HEB) heterodyne receiver was investigated at frequencies from 0.6THz to 1.9THz. The Allan variance was measured as a function of the integration time and the Allan time was obtained for HEB mixers of different size, as well as with different types of the local oscillator: FIR laser, multiplier chain, and BWO. We have found that due to stronger dependence of the mixer gain and noise vs mixer bias voltage and current the Allan time is shorter for smaller mixers. At 1.6THz the Allan time is 3 sec for 4x0.4μm^2 bolometer, and 0.15-0.2 sec for 1x0.15μm^2 bolometer. Obtained stability apears to be the same for the FIR laser and the mulitplier chain. The Allan time for smaller bolometers increases to 0.4-0.5sec at 0.6-0.7THz LO frequencies. The influence of the IF chain on the obtained results is also analyzed

Full characterization and analysis of a terahertz heterodyne receiver based on a NbN hot electron bolometer

We present a complete experimental characterization of a quasioptical twin-slot antenna coupled small area (1.0×0.15 µm^2) NbN hot electron bolometer (HEB) mixer compatible with currently available solid state tunable local oscillator (LO) sources. The required LO power absorbed in the HEB is analyzed in detail and equals only 25 nW. Due to the small HEB volume and wide antenna bandwidth, an unwanted direct detection effect is observed which decreases the apparent sensitivity. Correcting for this effect results in a receiver noise temperature of 700 K at 1.46 THz. The intermediate frequency (IF) gain bandwidth is 2.3 GHz and the IF noise bandwidth is 4 GHz. The single channel receiver stability is limited to 0.2–0.3 s in a 50 MHz bandwidth

Heterodyne performance and characteristics of terahertz MgB2hot electron bolometers

We have studied THz heterodyne detection in sub-micrometer MgB2 hot electron bolometer (HEB) mixers based on superconducting MgB2 films of ∼5nm (HEB-A), corresponding to a critical temperature (Tc) of 33.9 K, and ∼7nm (HEB-B), corresponding to a \u1d447\u1d450 of 38.4 K. We have measured a double sideband (DSB) receiver noise temperature of 2590 K for HEB-A and 2160 K for HEB-B at 1.6 THz and 5 K. By correcting for optical losses, both HEBs show receiver noise temperatures of ∼1600 K referenced to the front of anti-reflection (AR)-coated Si lenses. An intermediate frequency (IF) noise bandwidth of 11 GHz has been measured for both devices. The required local oscillator (LO) power is about 13 μW for both HEBs. We have also measured a DSB receiver noise temperature of 3290 K at 2.5 THz and 5 K but with an AR-coated lens optimized for 1.6 THz. Besides, we have observed a step-like structure in current voltage (IV) curves, which becomes weaker when the LO power increases and observable only in their differential resistance. Such a correlated structure appears also in the receiver output power as a function of voltage, which is likely due to electronic inhomogeneities intrinsic to the variations in the thickness of the MgB2 films. Different behavior in the IV curves around the low bias voltages, pumped with the same LO power at 1.6 and 5.3 THz, was observed for HEB-B, suggesting the presence of a high-energy σ-gap in the MgB2 film

Финансовая политика государственной поддержки отрасли микроэлектроники в России в условиях санкций

The relevance of this study is determined by the need to develop the domestic semiconductors industry in Russia, taking into account the negative effects both internal and external.The purpose of this paper is to test the hypothesis of the positive impact of the methods used by the state of financial support of domestic companies to acquire advanced technologies in a specific area in the context of a lack of funding and the significant lag of the national semiconductor industry in the world’s leading countries.The target of this study is the analysis of possible tools of state support, including subsidies and grants, and methods of their application for the creation of competitive industry of domestic semiconductor production.The key methods used in this study include the collection and processing of statistical data, their comparative analysis, as well as the elaboration of the regulatory framework on tax regulation in this sector of the economy.The main methods applied in this study are data collection and processing, comparative analysis, and the development of a regulatory framework for tax regulation in this sector of the economy. The authors analyzed the semiconductors industry in the world, including the production of microprocessors and other semiconductor components. The situation in countries such as China, USA, Japan, Europe, Taiwan, India and Russia is discussed in more detail. The main problems with semiconductor industry development in Russia have been revealed. Additionally, researchers have evaluated and outlined fields of federal budget spendings in the industry in the period of years 2022 and 2025.The scientific novelty of this paper is to identify the relationship between the measures of state tax incentives provided to the radio-electronic industry and macroeconomic indicators. Based on that authors have developed evaluation criteria of the relevance and efficiency of fiscal preferences for the analyzed industry which is considered as the result of research.It concluded that the state’s initiatives to promote the radio-electronics industry might provide Russia a chance to catch up to the world’s leading countries in this industry.Актуальность исследования определяется необходимостью развития отечественной отрасли микроэлектроники в России с учетом сложившихся негативных как внутренних, так и внешних эффектов.Целью является проверка гипотезы о положительном влиянии используемых государством методов финансовой поддержки отечественных компаний для получения прорывных технологий в конкретной области в условиях недостатка финансирования и существенного отставания национальной отрасли микроэлектроники от ведущих стран мира.Задачей данного исследования является анализ возможных инструментов государственной поддержки, включая субсидии и гранты, а также методов их применения с целью создания конкурентной отрасли производства отечественной микроэлектроники.Основные методы, используемые в данном исследовании, включают в себя сбор и обработку статистических данных, их сравнительный анализ, а также проработку нормативной базы по налоговому регулированию в данном секторе экономики. Авторы проанализировали состояние отрасли микроэлектроники в мире, включая производство микропроцессоров и других полупроводниковых компонентов. Более детально рассмотрена ситуация в таких странах, как Китай, США, Япония, Европа, Тайвань, Индия и Россия. На основе проведенного анализа выявлены основные проблемы развития отрасли микроэлектроники в России. Дана оценка масштабов и выявлены направления расходования средств федерального бюджета на развитие радиоэлектронной промышленности в период 2022–2025 гг.Научная новизна проведенного исследования заключается в выявлении взаимосвязи между предоставляемыми мерами государственного налогового стимулирования радиоэлектронной промышленности и макроэкономическими показателями.Результаты позволили авторам выработать критерии оценки востребованности и эффективности фискальных преференций для исследуемого вида деятельности.Сделан вывод, что используемые государством меры поддержки радиоэлектронной промышленности могут дать России шанс преодолеть значительное отставание в этой отрасли от ведущих стран мира

Low noise MgB₂ hot electron bolometer mixer operated at 5.3 THz and at 20 K

We have demonstrated a low noise superconducting MgB2 hot electron bolometer (HEB) mixer working at the frequency of 5.3 terahertz (THz) with 20 K operation temperature. The bolometer consists of a 7 nm thick MgB2 submicrometer bridge contacted with a spiral antenna to couple THz radiation through a high resistive Si lens, and it has a superconducting critical temperature of 38 K. By using hot/cold blackbody loads and a Mylar beam splitter all in vacuum and applying a 5.25 THz far-infrared gas laser as a local oscillator, we measured a minimal double sideband receiver noise temperature of 3960 K at the LO power of 9.5 mu W. This can be further reduced to 2920 K if a Si lens with an antireflection coating optimized at this frequency and a 3 mu m beam splitter are used. The measured intermediate frequency (IF) noise bandwidth is 9.5 GHz. The low noise, wide IF bandwidth mixers, which can be operated in a compact, low dissipation Stirling cooler, are more suitable for space applications than the existing HEB mixers. Furthermore, we likely observed a signature of the double-gap in MgB2 by comparing current-voltage curves pumped at 5.3 and 1.6 THz