Revisiting the radio interferometer measurement equation. IV. A generalized tensor formalism

The radio interferometer measurement equation (RIME), especially in its 2x2 form, has provided a comprehensive matrix-based formalism for describing classical radio interferometry and polarimetry, as shown in the previous three papers of this series. However, recent practical and theoretical developments, such as phased array feeds (PAFs), aperture arrays (AAs) and wide-field polarimetry, are exposing limitations of the formalism. This paper aims to develop a more general formalism that can be used to both clearly define the limitations of the matrix RIME, and to describe observational scenarios that lie outside these limitations. Some assumptions underlying the matrix RIME are explicated and analysed in detail. To this purpose, an array correlation matrix (ACM) formalism is explored. This proves of limited use; it is shown that matrix algebra is simply not a sufficiently flexible tool for the job. To overcome these limitations, a more general formalism based on tensors and the Einstein notation is proposed and explored both theoretically, and with a view to practical implementations. The tensor formalism elegantly yields generalized RIMEs describing beamforming, mutual coupling, and wide-field polarimetry in one equation. It is shown that under the explicated assumptions, tensor equations reduce to the 2x2 RIME. From a practical point of view, some methods for implementing tensor equations in an optimal way are proposed and analysed. The tensor RIME is a powerful means of describing observational scenarios not amenable to the matrix RIME. Even in cases where the latter remains applicable, the tensor formalism can be a valuable tool for understanding the limits of such applicability.Comment: 16 pages, no figures, accepted by A&

Comparative Analysis of the Approaches to Living Standards: Ukraine and Poland

The aim of the article is to identify the main directions to improve the regulatory framework for ensuring the living standard of Ukraine’s population. The approaches to the assessment of the living standard in Ukraine and Poland are analyzed. The advantages and disadvantages of the methodology for determining the living standard of the population are revealed. It is established that the Polish consumer basket includes four minimum consumption categories, namely: subsistence minimum, social minimum, social protection floor, family income support. In Ukraine, there is one category of consumption norms – the subsistence minimum without actual costs. As a result, the legislatively established normative living standard lags behind the actual needs of various groups of the population. It is substantiated that the minimum consumption categories in Poland guarantee a person the satisfaction of basic needs both at the constitutional and legislative levels. In Ukraine, the normative living standard is at the level of the poverty line and thus results in excluding part of the population from the accepted standard of living in the society. The shortcomings of the Polish legislation include: term of approval of state social guarantees; threshold value of the indexation of monetary incomes of the population; methodology for measuring the differentiation of living standards. The article presents proposals for the realignment of the measurement of the living standards, target group, and coverage of the population in need of social assistance, with selecting determination criteria close to the EU standards

ACTIVITY TEST ETHANOL EXTRACT MATOA (POMETIA PINNATA) ANTINFLAMMATION AGAINST MALE RATS INDUCED CARAGENAN

Matoa merupakan salah satu tanaman dari famili Sapindaceae yang tersebar di daerah tropis, termasuk Indonesia. Tanaman matoa banyak digunakan masyarakat dalam pengobatan tradisional. Penelitian ini dilakukan dengan tujuan untuk mengetahui efek antiinflamasi ekstrak etanol daun matoa (Pometia pinnata) terhadap mencit putih jantan yang di induksi karagenan. Penelitian ini adalah penelitian eksperimental yang dibagi menjadi 5 kelompok yaitu kontrol positif (Natrium Diklofenak 6,5 mg/kgBB), kontrol negatif (Na-CMC 0,5%) dan tiga dosis yang diuji yaitu 100 mg/kgBB, 200 mg/kgBB dan 300 mg/kgBB. Metode dalam penelitian ini adalah dengan induksi karagenan 0,1 ml sebagai iritan pada telapak kaki mencit selama 360 menit dengan parameter yang diamati adalah penghambatan udem kaki mencit menggunakan pletismometer. Hasil penelitian ini menunjukkan adanya perbedaan yang signifikan (P>0,05) dengan kesimpulan tiga dosis yang diuji yaitu 100 mg/kgBB, 200 mg/kgBB dan 300 mg/kgBB memiliki efek antiinflamasi dimana dosis yang lebih efektif adalah 300 mg/kgBB

Explicit Solution of the Time Evolution of the Wigner Function

Previously, an explicit solution for the time evolution of the Wigner function was presented in terms of auxiliary phase space coordinates which obey simple equations that are analogous with, but not identical to, the classical equations of motion. They can be solved easily and their solutions can be utilized to construct the time evolution of the Wigner function. In this paper, the usefulness of this explicit solution is demonstrated by solving a numerical example in which the Wigner function has strong spatial and temporal variations as well as regions with negative values. It is found that the explicit solution gives a correct description of the time evolution of the Wigner function. We examine next the pseudoparticle approximation which uses classical trajectories to evolve the Wigner function. We find that the pseudoparticle approximation reproduces the general features of the time evolution, but there are deviations. We show how these deviations can be systematically reduced by including higher-order correction terms in powers of $\hbar^2$.Comment: 16 pages, in LaTex, invited talk presented at the Wigner Centennial Conference, Pecs, Hungary, July 8-12, 2002, to be published in the Journal of Optics B: Quantum and Classical Optics, June 200

Nonlinear effects in tunnelling escape in N-body quantum systems

We consider the problem of tunneling escape of particles from a multiparticle system confined within a potential trap. The process is nonlinear due to the interparticle interaction. Using the hydrodynamic representation for the quantum equations of the multiparticle system we find the tunneling rate and time evolutions of the number of trapped particles for different nonlinearity values.Comment: 10 pages, 3 figure

Analyzing the Dynamics and Structure of the Foreign Trade Activity of Ukraine

The article is aimed at defining the problems in foreign trade activity of Ukraine, which may entail unsatisfactory status of foreign economic security of the country. Based on data from 2011 to 2017, the dynamics of the main quantitative characteristics of foreign trade, structural shifts in foreign trade (with the help of indices of L. Kazinets and V. Ryabtsev), and also structure of foreign trade in the context of regions of Ukraine are researched. The key problems determining high risks of foreign economic security of the country are defined: significant reduction of volumes of foreign trade; prevalence of negative trade balance; high value of the share of total exports and imports in GDP; weak development of trade with the EU countries; low level of diversification of export commodity positions and its raw material orientation; loss of traditional market of machine-building products; at the regional level, there is a deformed structure of foreign trade, while the main exporter and importer of goods and services is the city of Kiev

The Impact of the COVID-19 Pandemic on Regional Labor Markets in Ukraine

In March 2019, the World Health Organization (WHO) announced the global outbreak of COVID-19 to be a pandemic. The probable source of the virus was Wuhan (China), from where it quickly spread all over the world. Experts say that from the start of the pandemic in Ukraine and to the second quarter of 2022, 5.04 million cases of infection were recorded. The fraction of people who have received at least one dose of the COVID-19 vaccine is 36.4%, making Ukraine the least vaccinated country in Europe. High morbidity rate made it necessary to introduce quarantine measures that have negatively affected the socio-economic development of Ukraine as a whole, and regional labor markets, in particular. The article is aimed at assessing the impact of the coronavirus pandemic on regional labor markets in Ukraine. To achieve this aim, the following tasks were solved: a) to analyze the COVID-19 dynamics as for Ukraine’s regions, taking into account the aggravation of the humanitarian crisis; b) to identify the situation in regional labor markets by economic activity indicators; c) to analyze state regulation as for its compliance with the state social guarantees in labor relations. It has been determined that the most negative situation with the COVID-19 epidemic is present in the regions with the largest cities of the country (which are home to a population of 1,029,049 to 2,611,327 people). It proves that a particularly negative impact of the pandemic was made on the regional labor markets with high economic activity and strong economic potential. It is established that the pandemic has led to employment reduction in all the regions, which went hand in hand with the increase in informal employment of economically active population. Rising unemployment and wage arrears are also signs of the negative impact of the COVID-19 pandemic on Ukraine’s regional labor markets. It can be concluded that the key problems requiring managerial decisions are those connected with inclusive economic recovery after COVID-19 and the fulfillment of state social guarantees in the labor market in almost every region in Ukraine, given the impact of the ongoing military conflict and the need for economic recovery after it

Gauge Invariance and Hall Terms in the Quasiclassical Equations of Superconductivity

This paper presents a careful derivation of the quasiclassical equations of superconductivity so that a manifest gauge invariance is retained with respect to the space-time arguments of the quasiclassical Green's function $\hat{g}$. The terms responsible for the Hall effect naturally appear from the derivation. The equations are applicable to clean as well as dirty superconductors for an arbitrary external frequency much smaller than the Fermi energy. Thus, they will form a basis toward a complete microscopic understanding of the Hall effect in type-II superconductors.Comment: 9 pages, 1 figur

Generalized gradient expansions in quantum transport equations

Gradient expansions in quantum transport equations of a Kadanoff-Baym form have been reexamined. We have realized that in a consistent approach the expansion should be performed also inside of the self-energy in the scattering integrals of these equations. In the first perturbation order this internal expansion gives new correction terms to the generalized Boltzman equation. These correction terms are found here for several typical systems. Possible corrections to the theory of a linear response to weak electric fields are also discussed.Comment: 20 pages, latex, to appear in Journal of Statistical Physics, March (1997