On the family of Wigner functions for N-level quantum system

The family of unitary non-equivalent Weyl-Stratonovich kernels determining the Wigner probability distribution function of an arbitrary N-level quantum system is constructed

Relação entre lacunaridade e largura de banda de uma antena de arame koch-type

A dipole wire antenna of the Koch type is considered. The antenna represents a wire dipole symmetrical with respect to the point of feeding. Arms of the dipole have a geometry similar to Koch's pre-fractal. The curves forming the arms differ from the classical Koch fractal only by the position of the central vertex. A family of antennas is singled out, in which the antennas differ from each other by coordinates of the central vertices. An algorithm for calculating lacunarity is described. A correlation analysis is provided with a correlation of bandwidth as well as relative bandwidth with lacunarity. Antennas having the geometry of the first three iterations of a Koch-type curve are chosen for the analysis. The calculated correlation coefficients are given in the tables. It is shown that increasing the iteration leads to a decrease in the correlation between the selected parameters. It is obtained that the correlation coefficients for the relative bandwidth are smaller than those for the bandwidth. Single-parameter regression models for the bandwidth and the relative bandwidth are constructed. The root-mean-square errors for the models are calculated. The proposed regression formulas can be used to design broadband wire antennas.Se considera una antena de cable dipolo del tipo Koch. La antena representa un dipolo de alambre simétrico con respecto al punto de alimentación. Los brazos del dipolo tienen una geometría similar al prefractal de Koch. Las curvas que forman los brazos difieren del fractal clásico de Koch solo por la posición del vértice central. Se selecciona una familia de antenas, en la que las antenas difieren entre sí por las coordenadas de los vértices centrales. Se describe un algoritmo para calcular la lagunaridad. Se proporciona un análisis de correlación para la correlación del ancho de banda, así como el ancho de banda relativo con lagunaridad. Las antenas que tienen la geometría de las tres primeras iteraciones de una curva de tipo Koch se eligen para el análisis. Los coeficientes de correlación calculados se dan en las tablas. Se muestra que aumentar la iteración conduce a una disminución en la correlación entre los parámetros seleccionados. Se obtiene que los coeficientes de correlación para el ancho de banda relativo son más pequeños que los del ancho de banda. Se construyen modelos de regresión de un solo parámetro para el ancho de banda y el ancho de banda relativo. Se calculan los errores de raíz cuadrada-media para los modelos. Las fórmulas de regresión propuestas pueden usarse para diseñar antenas de cable de banda ancha.É considerada uma antena de cabo dipolo do tipo Koch. A antena representa um dipolo de arame simétrico em relação ao ponto de alimentação. Os braços do dipolo têm uma geometria similar à prefractal de Koch. As curvas que formam os braços diferem do fractal clássico de Koch apenas devido à posição do vértice central. Uma família de antenas é selecionada, na qual as antenas diferem umas das outras pelas coordenadas dos vértices centrais. Um algoritmo é descrito para calcular a lacunaridade. Uma análise de correlação é fornecida para a correlação da largura de banda, bem como a largura de banda relativa com a lagunaridade. As antenas que possuem a geometria das três primeiras iterações de uma curva do tipo Koch são escolhidas para a análise. Os coeficientes de correlação calculados são fornecidos nas tabelas. É mostrado que o aumento da iteração leva a uma diminuição na correlação entre os parâmetros selecionados. Obtém-se que os coeficientes de correlação para a largura de banda relativa são menores que os da largura de banda. Modelos de regressão de um único parâmetro são construídos para a largura de banda e a largura de banda relativa. Os erros médios de raiz quadrada para os modelos são calculados. As fórmulas de regressão propostas podem ser usadas para projetar antenas de cabo de banda larga

Proof of Efficient Liquidity: A Staking Mechanism for Capital Efficient Liquidity

The Proof of Efficient Liquidity (PoEL) protocol, designed for specialised Proof of Stake (PoS) consensus-based blockchains that incorporate intrinsic DeFi applications, aims to support sustainable liquidity bootstrapping and network security. This concept seeks to efficiently utilise budgeted staking rewards to attract and sustain liquidity through a risk-structuring engine and incentive allocation strategy, both of which are designed to maximise capital efficiency. The proposed protocol serves the dual objective of: (i) capital creation by attracting risk capital efficiently and maximising its operational utility for intrinsic DeFi applications, thereby asserting sustainability; and (ii) enhancing the adopting blockchain network's economic security by augmenting their staking (PoS) mechanism with a harmonious layer seeking to attract a diversity of digital assets. Finally, the protocol's conceptual framework, as detailed in the appendix, is extended to encompass service fee credits. This extension capitalises on the network's auxiliary services to disperse incentives and attract liquidity, ensuring the network achieves and maintains the critical usage threshold essential for its sustained operational viability and progressive growth

Evidence of historical seismicity and volcanism in the Armenian Highland (from Armenian and other sources)

This work presents a summary on the development of studies of historical earthquakes in Armenia and adjacent parts of Turkey and Iran. Since ancient times, this region has been an arena where active geodynamic and seismic history intermingled with no less active and dynamic evolution of human cultures and societies. A long-term historical record in this region beginning as early as the 8th century B.C. provides abundant evidence that can make an inestimable contribution to studies of historical seismicity and volcanism in the area. We discuss the main research methodology and sources used, and dwell on the principal catalogues of historical earthquakes compiled to date

Задачи оптимизации наноразмерных полупроводниковых гетероструктур

In the paper a new approach to solve the optimization problem of nanoscale semiconductor heterostructures is presented. In this paper the authors formulated and solved The problem of the barrier layer optimal doping is formulated for the case of multilayer barrier. The problem is solved using the effective optimization algorithms based on gradient methods. As an example, is considered heterostructure Al0.25GaN/GaN with the total thickness of the barrier layer 30 nm. Obtained in the computational experiment results are consistent with the modern trend to move from homogeneous doping profile to a planar-doping in the technology of manufacturing fieldeffect transistors. The developed tools of mathematical modeling and optimization can be used in the engineering of field effect transistors. The proposed approach creates the conditions for computer-aided design of such structures.Представлен новый подход, позволяющий решать задачи оптимизации наноразмерных полупроводниковых гетероструктур. Поставлена и решена задача, связанная с определением оптимального легирования барьерного слоя, состоящего из ряда подслоев, который обеспечивает заданную концентрацию электронов в канале проводимости в полупроводниковых гетероструктурах. Для решения поставленной задачи построены эффективные алгоритмы оптимизации, основанные на градиентных методах. В качестве примера рассмотрена гетероструктура Al0,25GaN/GaN с суммарной толщиной барьерного слоя 30 нм. Полученные в ходе вычислительного эксперимента результаты согласуются с современной тенденцией к переходу от однородного профиля легирования к планарному d-легированию в технологиях изготовления полевых транзисторов. Разработанные средства математического моделирования и оптимизации могут применяться в технологиях изготовления полевых транзисторов. Представленные в работе подходы создают условия для автоматизированного проектирования таких структур