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    ΠŸΡ€ΠΎΠ±Π»Π΅ΠΌΡ‹ ΠΎΠΏΡ‚ΠΈΠΌΠΈΠ·Π°Ρ†ΠΈΠΈ энСргопотрСблСния домохозяйств Π² Π·Π°Π΄Π°Ρ‡Π°Ρ… ΠΏΠΎΠ²Ρ‹ΡˆΠ΅Π½ΠΈΡ энСргоэффСктивности ΠΆΠΈΠ»ΠΈΡ‰Π½ΠΎΠ³ΠΎ сСктора

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    The aim of the work is to study the problem of optimizing energyΒ consumption and practical application of methods forΒ  improvingΒ energy efficiency in the housing sector. Optimization ofΒ  energyΒ efficiency management allows to reduce the expenditure ofΒ  energyΒ resources in the performance of various works, heating ofΒ buildings, etc. The creation of optimization methods will makeΒ itΒ  possible to reduce payments for utilities in a short time, andΒ inΒ  general for the industry, will help reduce the consumption ofΒ variousΒ  resources and improve the ecological state of the region.Β UnlikeΒ  other approaches, the emphasis in this paper is on theΒ convenienceΒ  and simplicity necessary for using this technique byΒ the population in households.Β The proposed integrated approach uses methods ofΒ  probability theory,Β linear programming, heat exchange models. TheΒ  conducted researchΒ confirms the effectiveness of the solutionΒ  obtained and can serve asΒ a basis for the creation of training andΒ  research stands. The article consists of two parts: the first partΒ  analyzes the leading works in this field and identifies the reasonsΒ  that make it difficult to apply the solutions proposed in these papers. Further, the statement of the problem was proposed and justified,Β  and a number of basic requirements to the mathematical model ofΒ  energy consumption, necessary for the constructed technique to beΒ  used to optimize energy consumption in households, wereΒ  formulated. In the second part, a mathematical model of theirΒ  functioning is proposed using examples of specific householdΒ  electrical appliances. When researching existing methods forΒ  optimizing energy consumption in households, problems wereΒ  identified that were difficult to apply these methods in practice andΒ  recommendations were obtained that allowed to formulate the basicΒ  principles of constructing an optimization technique that wasΒ  convenient for practical application. It was shown that whenΒ  constructing such a technique, the primary question is the data thatΒ  the user can provide. The minimum composition of input data wasΒ  determined, according to which the necessary algorithms forΒ  optimizing energy consumption were designed. A number ofΒ  algorithms for determining some input indicators that are easy to use in households have also been proposed. Thus, the general plan of research in this paper is as follows:β€’ carry out grouping of devices by the way of setting functionalrequirements;β€’ determine the acceptable composition and type of input data forthe user;β€’ define the minimum set of input data for formalizing the limitationof the total power consumption;β€’ design optimization algorithms that work with the input dataspecified above.Β The most important results of the work performed are the following:β€’ the methodology for forecasting the graph of the maximum totalpower consumption has been developed.β€’ methods for optimizing energy consumption for each of the selectedΒ subsets of household appliances have been developed.β€’ the optimization algorithms obtained have been simulated, whichΒ showed their operability, efficiency and the possibility of their practicalΒ application without any adaptation.Thus, the article proposes the solution of the problem of optimizationΒ of energy consumption in the housing sector, oriented to practicalΒ application.ЦСлью Ρ€Π°Π±ΠΎΡ‚Ρ‹ являСтся исслСдованиС ΠΏΡ€ΠΎΠ±Π»Π΅ΠΌΡ‹ оптимизации энСргопотрСблСния ΠΈΒ  практичСского примСнСния ΠΌΠ΅Ρ‚ΠΎΠ΄ΠΎΠ² ΠΏΠΎΠ²Ρ‹ΡˆΠ΅Π½ΠΈΡ энСргоэффСктивности Π² ΠΆΠΈΠ»ΠΈΡ‰Π½ΠΎΠΌ сСкторС.Β  ΠžΠΏΡ‚ΠΈΠΌΠΈΠ·Π°Ρ†ΠΈΡΒ ΡƒΠΏΡ€Π°Π²Π»Π΅Π½ΠΈΡ ΡΠ½Π΅Ρ€Π³ΠΎΡΡ„Ρ„Π΅ΠΊΡ‚ΠΈΠ²Π½ΠΎΡΡ‚ΡŒΡŽ позволяСт ΡƒΠΌΠ΅Π½ΡŒΡˆΠ°Ρ‚ΡŒ расходованиС  энСргорСсурсов ΠΏΡ€ΠΈ Π²Ρ‹ΠΏΠΎΠ»Π½Π΅Π½ΠΈΠΈ Ρ€Π°Π·Π»ΠΈΡ‡Π½Ρ‹Ρ… Ρ€Π°Π±ΠΎΡ‚, ΠΎΡ‚ΠΎΠΏΠ»Π΅Π½ΠΈΠ΅ Π·Π΄Π°Π½ΠΈΠΉ ΠΈ Ρ‚.Π΄. Π‘ΠΎΠ·Π΄Π°Π½ΠΈΠ΅Β  ΠΌΠ΅Ρ‚ΠΎΠ΄ΠΎΠ² ΠΎΠΏΡ‚ΠΈΠΌΠΈΠ·Π°Ρ†ΠΈΠΈ ΠΏΠΎΠ·Π²ΠΎΠ»ΠΈΡ‚Β Π² ΠΊΠΎΡ€ΠΎΡ‚ΠΊΠΈΠ΅ сроки ΡΠ½ΠΈΠ·ΠΈΡ‚ΡŒ ΠΏΠ»Π°Ρ‚Π΅ΠΆΠΈ Π·Π° ΠΊΠΎΠΌΠΌΡƒΠ½Π°Π»ΡŒΠ½Ρ‹Π΅ услуги,Β  Π°Β Π² Ρ†Π΅Π»ΠΎΠΌ для отрасли, Π±ΡƒΠ΄Π΅Ρ‚ ΡΠΏΠΎΡΠΎΠ±ΡΡ‚Π²ΠΎΠ²Π°Ρ‚ΡŒ ΡƒΠΌΠ΅Π½ΡŒΡˆΠ΅Π½ΠΈΡŽ потрСблСния Ρ€Π°Π·Π»ΠΈΡ‡Π½Ρ‹Ρ… рСсурсов  ΠΈ ΡƒΠ»ΡƒΡ‡ΡˆΠ΅Π½ΠΈΡŽ экологичСского состояния рСгиона. Π’ ΠΎΡ‚Π»ΠΈΡ‡ΠΈΠΈ ΠΎΡ‚ Π΄Ρ€ΡƒΠ³ΠΈΡ… ΠΏΠΎΠ΄Ρ…ΠΎΠ΄ΠΎΠ², Π°ΠΊΡ†Π΅Π½Ρ‚ Π²Β  Π΄Π°Π½Π½ΠΎΠΉ работС ставится Π½Π° удобство ΠΈ простоту, Π½Π΅ΠΎΠ±Ρ…ΠΎΠ΄ΠΈΠΌΡƒΡŽ для использования этой  ΠΌΠ΅Ρ‚ΠΎΠ΄ΠΈΠΊΠΈ насСлСниСм Π² Π΄ΠΎΠΌΠ°ΡˆΠ½ΠΈΡ… хозяйствах.Β Π’ ΠΏΡ€Π΅Π΄Π»ΠΎΠΆΠ΅Π½Π½ΠΎΠΌ комплСксном ΠΏΠΎΠ΄Ρ…ΠΎΠ΄Π΅Β  ΠΈΡΠΏΠΎΠ»ΡŒΠ·ΡƒΡŽΡ‚ΡΡ ΠΌΠ΅Ρ‚ΠΎΠ΄Ρ‹Β Ρ‚Π΅ΠΎΡ€ΠΈΠΈ вСроятностСй, Π»ΠΈΠ½Π΅ΠΉΠ½ΠΎΠ³ΠΎ программирования, ΠΌΠΎΠ΄Π΅Π»ΠΈΒ Ρ‚Π΅ΠΏΠ»ΠΎΠΎΠ±ΠΌΠ΅Π½Π°. ΠŸΡ€ΠΎΠ²Π΅Π΄Π΅Π½Π½ΠΎΠ΅ исслСдованиС ΠΏΠΎΠ΄Ρ‚Π²Π΅Ρ€ΠΆΠ΄Π°Π΅Ρ‚ ΡΡ„Ρ„Π΅ΠΊΡ‚ΠΈΠ²Π½ΠΎΡΡ‚ΡŒ ΠΏΠΎΠ»ΡƒΡ‡Π΅Π½Π½ΠΎΠ³ΠΎΒ  Ρ€Π΅ΡˆΠ΅Π½ΠΈΡ ΠΈ ΠΌΠΎΠΆΠ΅Ρ‚ ΡΠ»ΡƒΠΆΠΈΡ‚ΡŒ основой для создания ΡƒΡ‡Π΅Π±Π½ΠΎ-ΠΈΡΡΠ»Π΅Π΄ΠΎΠ²Π°Ρ‚Π΅Π»ΡŒΡΠΊΠΈΡ… стСндов.Β Π‘Ρ‚Π°Ρ‚ΡŒΡΒ  состоит ΠΈΠ· Π΄Π²ΡƒΡ… частСй: Π² ΠΏΠ΅Ρ€Π²ΠΎΠΉ части Π²Ρ‹ΠΏΠΎΠ»Π½Π΅Π½Β Π°Π½Π°Π»ΠΈΠ· Π²Π΅Π΄ΡƒΡ‰ΠΈΡ… Ρ€Π°Π±ΠΎΡ‚ Π² этой Ρ‚Π΅ΠΌΠ°Ρ‚ΠΈΠΊΠ΅ ΠΈΒ  ΠΎΠΏΡ€Π΅Π΄Π΅Π»Π΅Π½Ρ‹ ΠΏΡ€ΠΈΡ‡ΠΈΠ½Ρ‹, Π·Π°Ρ‚Ρ€ΡƒΠ΄Π½ΡΡŽΡ‰ΠΈΠ΅ массовоС ΠΏΡ€ΠΈΠΌΠ΅Π½Π΅Π½ΠΈΠ΅ ΠΏΡ€Π΅Π΄Π»Π°Π³Π°Π΅ΠΌΡ‹Ρ… Π² этих работах  Ρ€Π΅ΡˆΠ΅Π½ΠΈΠΉ. Π”Π°Π»Π΅Π΅ ΠΏΡ€Π΅Π΄Π»ΠΎΠΆΠ΅Π½Π° ΠΈ обоснована постановка задачи ΠΈ сформулирован ряд  основных Ρ‚Ρ€Π΅Π±ΠΎΠ²Π°Π½ΠΈΠΉ ΠΊ матСматичСской ΠΌΠΎΠ΄Π΅Π»ΠΈ энСргопотрСблСния, Π½Π΅ΠΎΠ±Ρ…ΠΎΠ΄ΠΈΠΌΡ‹Ρ… для Ρ‚ΠΎΠ³ΠΎ,Β Ρ‡Ρ‚ΠΎΠ±Ρ‹ ΡΠΊΠΎΠ½ΡΡ‚Ρ€ΡƒΠΈΡ€ΠΎΠ²Π°Π½Π½ΡƒΡŽ ΠΌΠ΅Ρ‚ΠΎΠ΄ΠΈΠΊΡƒ ΠΌΠΎΠΆΠ½ΠΎ Π±Ρ‹Π»ΠΎ ΠΏΡ€ΠΈΠΌΠ΅Π½ΡΡ‚ΡŒΒ Π΄Π»Ρ ΠΎΠΏΡ‚ΠΈΠΌΠΈΠ·Π°Ρ†ΠΈΠΈΒ  энСргопотрСблСния Π² Π΄ΠΎΠΌΠ°ΡˆΠ½ΠΈΡ… хозяйствах. Π’ΠΎΒ Π²Ρ‚ΠΎΡ€ΠΎΠΉ части Π½Π° ΠΏΡ€ΠΈΠΌΠ΅Ρ€Π°Ρ… ΠΊΠΎΠ½ΠΊΡ€Π΅Ρ‚Π½Ρ‹Ρ…Β  Π±Ρ‹Ρ‚ΠΎΠ²Ρ‹Ρ… элСктроприборов прСдлагаСтся матСматичСская модСль ΠΈΡ… функционирования.Β ΠŸΡ€ΠΈΒ  исслСдовании ΡΡƒΡ‰Π΅ΡΡ‚Π²ΡƒΡŽΡ‰ΠΈΡ… ΠΌΠ΅Ρ‚ΠΎΠ΄ΠΎΠ² ΠΎΠΏΡ‚ΠΈΠΌΠΈΠ·Π°Ρ†ΠΈΠΈ энСргопотрСблСния Π² домохозяйствах  Π±Ρ‹Π»ΠΈ выявлСны ΠΏΡ€ΠΎΠ±Π»Π΅ΠΌΡ‹,Β Π·Π°ΠΊΠ»ΡŽΡ‡Π°ΡŽΡ‰ΠΈΠ΅ΡΡ Π² слоТности примСнСния этих ΠΌΠ΅Ρ‚ΠΎΠ΄ΠΎΠ² Π½Π°Β ΠΏΡ€Π°ΠΊΡ‚ΠΈΠΊΠ΅ ΠΈ ΠΏΠΎΠ»ΡƒΡ‡Π΅Π½Ρ‹ Ρ€Π΅ΠΊΠΎΠΌΠ΅Π½Π΄Π°Ρ†ΠΈΠΈ, ΠΏΠΎΠ·Π²ΠΎΠ»ΡΡŽΡ‰ΠΈΠ΅ ΡΡ„ΠΎΡ€ΠΌΡƒΠ»ΠΈΡ€ΠΎΠ²Π°Ρ‚ΡŒ основныС ΠΏΡ€ΠΈΠ½Ρ†ΠΈΠΏΡ‹Β  построСния ΠΌΠ΅Ρ‚ΠΎΠ΄ΠΈΠΊΠΈ ΠΎΠΏΡ‚ΠΈΠΌΠΈΠ·Π°Ρ†ΠΈΠΈ,Β ΡƒΠ΄ΠΎΠ±Π½ΠΎΠΉ для практичСского примСнСния. Π‘Ρ‹Π»ΠΎ ΠΏΠΎΠΊΠ°Π·Π°Π½ΠΎ, Ρ‡Ρ‚ΠΎΒ ΠΏΡ€ΠΈ построСнии Ρ‚Π°ΠΊΠΎΠΉ ΠΌΠ΅Ρ‚ΠΎΠ΄ΠΈΠΊΠΈ ΠΏΠ΅Ρ€Π²ΠΈΡ‡Π½Ρ‹ΠΌ являСтся вопрос о Π΄Π°Π½Π½Ρ‹Ρ…, ΠΊΠΎΡ‚ΠΎΡ€Ρ‹Π΅ ΠΌΠΎΠΆΠ΅Ρ‚Β  ΠΏΡ€Π΅Π΄ΠΎΡΡ‚Π°Π²ΠΈΡ‚ΡŒ ΠΏΠΎΠ»ΡŒΠ·ΠΎΠ²Π°Ρ‚Π΅Π»ΡŒ. Π‘Ρ‹Π»Β ΠΎΠΏΡ€Π΅Π΄Π΅Π»Π΅Π½ ΠΌΠΈΠ½ΠΈΠΌΠ°Π»ΡŒΠ½Ρ‹ΠΉ состав Π²Ρ…ΠΎΠ΄Π½Ρ‹Ρ… Π΄Π°Π½Π½Ρ‹Ρ…, ΠΏΠΎ ΠΊΠΎΡ‚ΠΎΡ€Ρ‹ΠΌ сконструированы Π½Π΅ΠΎΠ±Ρ…ΠΎΠ΄ΠΈΠΌΡ‹Π΅ Π°Π»Π³ΠΎΡ€ΠΈΡ‚ΠΌΡ‹ оптимизации энСргопотрСблСния. Π’Π°ΠΊ ΠΆΠ΅ Π±Ρ‹Π» ΠΏΡ€Π΅Π΄Π»ΠΎΠΆΠ΅Π½ ряд алгоритмов опрСдСлСния Π½Π΅ΠΊΠΎΡ‚ΠΎΡ€Ρ‹Ρ… Π²Ρ…ΠΎΠ΄Π½Ρ‹Ρ… ΠΏΠΎΠΊΠ°Π·Π°Ρ‚Π΅Π»Π΅ΠΉ, ΠΊΠΎΡ‚ΠΎΡ€Ρ‹Π΅Β  Π»Π΅Π³ΠΊΠΎΒ ΠΈΡΠΏΠΎΠ»ΡŒΠ·ΠΎΠ²Π°Ρ‚ΡŒ Π² Π΄ΠΎΠΌΠ°ΡˆΠ½ΠΈΡ… хозяйствах.Β Π’Π°ΠΊΠΈΠΌ ΠΎΠ±Ρ€Π°Π·ΠΎΠΌ, ΠΎΠ±Ρ‰ΠΈΠΉ ΠΏΠ»Π°Π½ исслСдований Π²Β  Π΄Π°Π½Π½ΠΎΠΉ Ρ€Π°Π±ΠΎΡ‚Π΅Β Π·Π°ΠΊΠ»ΡŽΡ‡Π°Π΅Ρ‚ΡΡ Π² ΡΠ»Π΅Π΄ΡƒΡŽΡ‰Π΅ΠΌ:β€’ провСсти Π³Ρ€ΡƒΠΏΠΏΠΈΡ€ΠΎΠ²ΠΊΡƒ ΠΏΡ€ΠΈΠ±ΠΎΡ€ΠΎΠ² ΠΏΠΎ способу задания Ρ„ΡƒΠ½ΠΊΡ†ΠΈΠΎΠ½Π°Π»ΡŒΠ½Ρ‹Ρ… Ρ‚Ρ€Π΅Π±ΠΎΠ²Π°Π½ΠΈΠΉ;β€’ Π²Ρ‹ΡΡΠ½ΠΈΡ‚ΡŒ ΠΏΡ€ΠΈΠ΅ΠΌΠ»Π΅ΠΌΡ‹ΠΉ для ΠΏΠΎΠ»ΡŒΠ·ΠΎΠ²Π°Ρ‚Π΅Π»Ρ состав ΠΈ Π²ΠΈΠ΄ Π²Ρ…ΠΎΠ΄Π½Ρ‹Ρ…Β Π΄Π°Π½Π½Ρ‹Ρ…;β€’ ΠΎΠΏΡ€Π΅Π΄Π΅Π»ΠΈΡ‚ΡŒ ΠΌΠΈΠ½ΠΈΠΌΠ°Π»ΡŒΠ½Ρ‹ΠΉ Π½Π°Π±ΠΎΡ€ Π²Ρ…ΠΎΠ΄Π½Ρ‹Ρ… Π΄Π°Π½Π½Ρ‹Ρ… для Ρ„ΠΎΡ€ΠΌΠ°Π»ΠΈΠ·Π°Ρ†ΠΈΠΈ ограничСния суммарной потрСбляСмой мощности;β€’ ΡΠΊΠΎΠ½ΡΡ‚Ρ€ΡƒΠΈΡ€ΠΎΠ²Π°Ρ‚ΡŒ Π°Π»Π³ΠΎΡ€ΠΈΡ‚ΠΌΡ‹ ΠΎΠΏΡ‚ΠΈΠΌΠΈΠ·Π°Ρ†ΠΈΠΈ, Ρ€Π°Π±ΠΎΡ‚Π°ΡŽΡ‰ΠΈΠ΅ с указанными Π²Ρ‹ΡˆΠ΅ Π²Ρ…ΠΎΠ΄Π½Ρ‹ΠΌΠΈ Π΄Π°Π½Π½Ρ‹ΠΌΠΈ.Π’Π°ΠΆΠ½Π΅ΠΉΡˆΠΈΠΌΠΈ Ρ€Π΅Π·ΡƒΠ»ΡŒΡ‚Π°Ρ‚Π°ΠΌΠΈ Π²Ρ‹ΠΏΠΎΠ»Π½Π΅Π½Π½ΠΎΠΉ Ρ€Π°Π±ΠΎΡ‚Ρ‹ ΡΠ²Π»ΡΡŽΡ‚ΡΡΒ ΡΠ»Π΅Π΄ΡƒΡŽΡ‰ΠΈΠ΅:β€’ Ρ€Π°Π·Ρ€Π°Π±ΠΎΡ‚Π°Π½Π° ΠΌΠ΅Ρ‚ΠΎΠ΄ΠΈΠΊΠ° прогнозирования Π³Ρ€Π°Ρ„ΠΈΠΊΠ° максимальной суммарной мощности потрСблСния.β€’ Ρ€Π°Π·Ρ€Π°Π±ΠΎΡ‚Π°Π½Ρ‹ ΠΌΠ΅Ρ‚ΠΎΠ΄ΠΈΠΊΠΈ ΠΎΠΏΡ‚ΠΈΠΌΠΈΠ·Π°Ρ†ΠΈΠΈ энСргопотрСблСния для каТдого ΠΈΠ· Π²Ρ‹Π΄Π΅Π»Π΅Π½Π½Ρ‹Ρ… подмноТСств Π±Ρ‹Ρ‚ΠΎΠ²Ρ‹Ρ… ΠΏΡ€ΠΈΠ±ΠΎΡ€ΠΎΠ².β€’ Π²Ρ‹ΠΏΠΎΠ»Π½Π΅Π½ΠΎ ΠΌΠΎΠ΄Π΅Π»ΠΈΡ€ΠΎΠ²Π°Π½ΠΈΠ΅ ΠΏΠΎΠ»ΡƒΡ‡Π΅Π½Π½Ρ‹Ρ… Π°Π»Π³ΠΎΡ€ΠΈΡ‚ΠΌΠΎΠ² ΠΎΠΏΡ‚ΠΈΠΌΠΈΠ·Π°Ρ†ΠΈΠΈ, ΠΊΠΎΡ‚ΠΎΡ€ΠΎΠ΅ ΠΏΠΎΠΊΠ°Π·Π°Π»ΠΎ ΠΈΡ…Β  Ρ€Π°Π±ΠΎΡ‚ΠΎΡΠΏΠΎΡΠΎΠ±Π½ΠΎΡΡ‚ΡŒ, ΡΡ„Ρ„Π΅ΠΊΡ‚ΠΈΠ²Π½ΠΎΡΡ‚ΡŒΒ ΠΈ Π²ΠΎΠ·ΠΌΠΎΠΆΠ½ΠΎΡΡ‚ΡŒ ΠΈΡ… практичСского примСнСния Π±Π΅Π· ΠΊΠ°ΠΊΠΎΠΉ- Π»ΠΈΠ±ΠΎΒ Π°Π΄Π°ΠΏΡ‚Π°Ρ†ΠΈΠΈ.Π’Π°ΠΊΠΈΠΌ ΠΎΠ±Ρ€Π°Π·ΠΎΠΌ, Π² ΡΡ‚Π°Ρ‚ΡŒΠ΅ ΠΏΡ€Π΅Π΄Π»ΠΎΠΆΠ΅Π½ΠΎ Ρ€Π΅ΡˆΠ΅Π½ΠΈΠ΅ Π·Π°Π΄Π°Ρ‡ΠΈ ΠΎΠΏΡ‚ΠΈΠΌΠΈΠ·Π°Ρ†ΠΈΠΈ энСргопотрСблСния Π²Β  ΠΆΠΈΠ»ΠΈΡ‰Π½ΠΎΠΌ сСкторС, ΠΎΡ€ΠΈΠ΅Π½Ρ‚ΠΈΡ€ΠΎΠ²Π°Π½Π½ΠΎΠ΅Β Π½Π° практичСскоС ΠΏΡ€ΠΈΠΌΠ΅Π½Π΅Π½ΠΈΠ΅

    The formation of human populations in South and Central Asia

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    By sequencing 523 ancient humans, we show that the primary source of ancestry in modern South Asians is a prehistoric genetic gradient between people related to early hunter-gatherers of Iran and Southeast Asia. After the Indus Valley Civilization’s decline, its people mixed with individuals in the southeast to form one of the two main ancestral populations of South Asia, whose direct descendants live in southern India. Simultaneously, they mixed with descendants of Steppe pastoralists who, starting around 4000 years ago, spread via Central Asia to form the other main ancestral population. The Steppe ancestry in South Asia has the same profile as that in Bronze Age Eastern Europe, tracking a movement of people that affected both regions and that likely spread the distinctive features shared between Indo-Iranian and Balto-Slavic languages

    EPR of Yb 3+ ions in a monoclinic KY(WO 4) 2 single crystal

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    The electron paramagnetic resonance (EPR) of Yb 3+ ions in a KY(WO 4) 2 single crystal was investigated at T=4.2Β K and fixed frequency of 9.38Β GHz. The resonance absorption observed on the lowest Kramers doublet represents the complex superposition of three spectra, corresponding to the ytterbium isotopes with different nuclear moments. The EPR spectrum is characterized by a strong anisotropy of the g-factors. The temperature dependence of the g-factors is shown to be caused by the strong spin-orbital and orbital-lattice coupling. The resonance lines broaden with increasing temperature due to the short spin-lattice relaxation times. Copyright EDP Sciences/SocietΓ  Italiana di Fisica/Springer-Verlag 200775.30.Gw Magnetic anisotropy, 76.30.-v Electron paramagnetic resonance and relaxation,

    Smooth cocycles for an irrational rotation

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    Benefits of Printed Graphene with Variable Resistance for Flexible and Ecological 5G Band Antennas

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    The possibility of creating antennas of the 5G standard (5.2–5.9 GHz) with specified electrodynamic characteristics by printing layers of variable thickness using a graphene suspension has been substantiated experimentally and by computer simulation. A graphene suspension for screen printing on photographic paper and other flexible substrates was prepared by means of exfoliation from graphite. The relation between the graphene layer thickness and its sheet resistance was studied with the aim of determining the required thickness of the antenna conductive layer. To create a two-sided dipole, a technology has been developed for the double-sided deposition of graphene layers on photographic paper. The electrodynamic characteristics of graphene and copper antennas of identical design are compared. The antenna design corresponds to the operating frequency of 2.4 GHz. It was found that the use of graphene as a conductive layer made it possible to suppress the fundamental (first) harmonic (2.45 GHz) and to observe radiation at the second harmonic (5.75 GHz). This effect is assumed to observe in the case when the thickness of graphene is lower than that of the skin depth. The result indicates the possibility of changing the antenna electrodynamic characteristics by adjusting the graphene layer thickness
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