Counting master integrals: Integration by parts vs. functional equations

We illustrate the usefulness of functional equations in establishing relationships between master integrals under the integration-by-parts reduction procedure by considering a certain two-loop propagator-type diagram as an example.Comment: 8 pages, 1 figur

Functional equations for one-loop master integrals for heavy-quark production and Bhabha scattering

The method for obtaining functional equations, recently proposed by one of the authors, is applied to one-loop box integrals needed in calculations of radiative corrections to heavy-quark production and Bhabha scattering. We present relationships between these integrals with different arguments and box integrals with all propagators being massless. It turns out that functional equations are rather useful for finding imaginary parts and performing analytic continuations of Feynman integrals. For the box master integral needed in Bhabha scattering, a new representation in terms of hypergeometric functions admitting one-fold integral representation is derived. The hypergeometric representation of a master integral for heavy-quark production follows from the functional equation.Comment: 14 pages, 3 figure

How Divine Images Became Art: Essays on the Rediscovery, Study and Collecting of Medieval Icons in the <i>Belle Époque</i>

How Divine Images Became Art tells the story of the parallel ‘discovery’ of Russian medieval art and of the Italian ‘primitives’ at the beginning of the twentieth century. While these two developments are well-known, they are usually studied in isolation. Tarasov’s study has the great merit of showing the connection between the art world in Russia and the West, and its impact in the cultural history of the continent in the pre-war period

Right to Health Care: The Practice of the ECTHR and the Case of Ukraine

The relevance of the research topic is due to the importance of human rights in a democratic society. Despite the fact that all natural human rights are important, the right to health care is practically in the forefront, because without its observance all other rights are leveled. Moreover, the relevance of the topic is even greater given the fact that for a long time the relevant law was not given due attention in law or in legal science. The right to health care is comprehensive and includes other human rights that derive from it. The existing case law of the European Court of Human Rights (ECtHR) confirms the importance of the human right to health care. In its judgments, the Court emphasizes the importance of this right and reaffirms the need for States to monitor its observance. The aim of the study – analysis of international legal norms and standards, as well as the practice of the ECtHR in the context of the human right to health. The leading research method used in the article is the formal-legal method, the application of which provided an effective analysis of the legal framework of international law, national legislation of Ukraine, and the case law of the ECtHR. Which, in turn, allowed to determine the importance of human rights to health and places of relevant law in the practice of the ECtHR. The article analyzes the theoretical and legal approaches to understanding the right to health care and on this basis identifies the place of relevant law in the human rights system and its main determinants. The case law of the European Court of Human Rights is analyzed and the main articles of the European Convention on Human Rights (ECHR), which the applicants applied for in violation of the right to health care, are identified. The analysis of the case law of the ECtHR provided an opportunity to identify existing shortcomings in the legislation of the member states. Based on this, it is possible to understand and distinguish ways to solve problems and methods for eliminating such violations in the future. The practical significance of the article lies in the analysis of the case law of the European Court of Human Rights, the separation of rights related to the right to protection of life, as well as the identification of the main determinants of the studied law

ABOUT POSSIBILITY TO CLASSIFY COAL LAYERS HAZARDOUS CHARACTERISTICS BY GENETIC AND PROCESS PARAMETERS OF COALS

The analysis of Ukrainian legal environment has been performed for solid fossil fuels production, which has shown existing of contradictories between parameters describing the accuracy of forecast to manifest the coal layers hazardous characteristics during independent of mining and does not exclude any possibility for emergency situation to occur, independent of the preventive measures full implementation. The base to determine the coal layers hazardous characteristics are: average reflectance of vitrinite, presence of some components in organic matter (С0, О0, Н0, N0), alteration of moisture and mineral impurities content. For these classificatory parameters, their quantitative assessment is available in the whole multiplicity of coals metamorphic transformation. The specific electrical resistivity logarithm and other proxy parameters may serve as additional classificatory parameters to reveal any hazardous characteristics of anthracites after grounding their using in some ranges of metamorphism series. It has been established that the existing wide range of vitrinite reflectance alteration for anthracites specifies significant alterations in the fossil fuel structure and properties. In their process of metamorphism, these peculiarities of anthracite alterations have almost not been classificatory established by their genetic and process parameters.The analysis of Ukrainian legal environment has been performed for solid fossil fuels production, which has shown existing of contradictories between parameters describing the accuracy of forecast to manifest the coal layers hazardous characteristics during independent of mining and does not exclude any possibility for emergency situation to occur, independent of the preventive measures full implementation. The base to determine the coal layers hazardous characteristics are: average reflectance of vitrinite, presence of some components in organic matter (С0, О0, Н0, N0), alteration of moisture and mineral impurities content. For these classificatory parameters, their quantitative assessment is available in the whole multiplicity of coals metamorphic transformation. The specific electrical resistivity logarithm and other proxy parameters may serve as additional classificatory parameters to reveal any hazardous characteristics of anthracites after grounding their using in some ranges of metamorphism series. It has been established that the existing wide range of vitrinite reflectance alteration for anthracites specifies significant alterations in the fossil fuel structure and properties. In their process of metamorphism, these peculiarities of anthracite alterations have almost not been classificatory established by their genetic and process parameters

Beyond the proton drip line: Bayesian analysis of proton-emitting nuclei

The limits of the nuclear landscape are determined by nuclear binding energies. Beyond the proton drip lines, where the separation energy becomes negative, there is not enough binding energy to prevent protons from escaping the nucleus. Predicting properties of unstable nuclear states in the vast territory of proton emitters poses an appreciable challenge for nuclear theory as it often involves far extrapolations. In addition, significant discrepancies between nuclear models in the proton-rich territory call for quantified predictions. With the help of Bayesian methodology, we mix a family of nuclear mass models corrected with statistical emulators trained on the experimental mass measurements, in the proton-rich region of the nuclear chart. Separation energies were computed within nuclear density functional theory using several Skyrme and Gogny energy density functionals. We also considered mass predictions based on two models used in astrophysical studies. Quantified predictions were obtained for each model using Bayesian Gaussian processes trained on separation-energy residuals and combined via Bayesian model averaging. We obtained a good agreement between averaged predictions of statistically corrected models and experiment. In particular, we quantified model results for one- and two-proton separation energies and derived probabilities of proton emission. This information enabled us to produce a quantified landscape of proton-rich nuclei. The most promising candidates for two-proton decay studies have been identified. The methodology used in this work has broad applications to model-based extrapolations of various nuclear observables. It also provides a reliable uncertainty quantification of theoretical predictions