Special Basis Research Articles

Well-posedness and stability for Kirchhoff equation with non-porous acoustic boundary conditions

In this paper we prove the well-posedness to the wave equation of Kirchhoff type. Under a portion of the boundary, we consider the acoustic boundary conditions. We also prove the exponential stability of the energy associated to the problem. Our result generalize the previous literature where only the Carrier model was considered (when the nonlinearity involves the L2(Ω) norm) or the Kirchhoff model with porous acoustic boundary conditions. The main tool is the Faedo-Galerkin method. Due to the presence of acoustic boundary conditions, we can not use special basis and new estimates are necessary. To prove the stability we use integral estimates.

Smart Specializations from the Standpoint of Leading Schools of Economic Theory

Focus on smart specialization is a key element of regional development strategizing in Ukraine, which, for example, is reflected in the State Regional Development Strategy for 2021-2027. But a comparative analysis of individual indicators of the economic development of the EU, the USA and China shows that smart specialization itself is not a competitive advantage on a global scale. At the same time, the researchers note that there is a gap between the theory and the practice of strategizing on the basis of smart specialization. Although theoretical issues related to smart specialization are not overlooked by researchers, the direct understanding of smart specialization processes from the standpoint of specific schools of economic theory is extremely limited. Therefore, the goal of the study is to reduce the essence of the concept of smart specialization from the standpoint of leading schools of economic theory. For the analysis, a classification was chosen, according to which 9 schools of economic theory are distinguished: (1) Classical, (2) Neoclassical, (3) Marxist, (4) Developmentalist, (5) Austrian, (6) Schumpeterian, (7) Keynesian, (8) Institutionalist, (9) Behaviouralist. Of the nine considered leading schools of economic theory, almost half of the schools (Classical, Developmentalist, Schumpeterian, and Institutionalist) significantly influenced the formation of the essence of smart specialization. Smart specialization has been moderately influenced by Neoclassical, Marxist and Keynesian schools. Austrian and Behaviouralist schools are characterized by a slight influence on smart specialization. Thus, smart specialization to a significant or moderate degree corresponds to individual provisions of 7 out of the 9 leading schools of economic theory considered in this study. Smart specialization synthesizes the positions of different schools of economic theory. Two alternatives follow from this: either the concept of smart specialization is a “constructive” tool for combining the “best” practices of various schools of economic theory, or it is an eclectic combination of ideas that are fundamentally incompatible. An unambiguous solution to this dilemma is possible on a practical level in the long term. Keywords smart specialization, schools of economic theory, definition, reduction.

Portuguese Recovery and Resilience Plan:

This article analyses the legal framework implemented in Portugal for the execution of its Recovery and Resilience Plan (RRP). Starting from the analysis of the legal framework offered by the European Recovery and Resilience Mechanism (MRR), it critically analyses the main regulations created on a special or exceptional basis for the implementation of the Portuguese Recovery and Resilience Plan, with emphasis on the governance model, but also on the exceptional measures to facilitate budgetary procedures, expenditure authorisation and staff hiring and also special public procurement measures. As these special and exceptional measures are, as a rule, intended to relax or reduce the mechanisms of prior administrative control of certain procedures, the external control of special public procurement measures by the Portuguese Court of Auditors was strengthened. Lastly, and despite the Portuguese legislator not dedicating special legislation to it, the most appropriate means for resolving any legal disputes arising from the implementation of the Portuguese Recovery and Resilience Plan are addressed. The present article will be divided and published in two parts. The first part will be dedicated to the MRR, Portuguese RRP and special measures for its implementation already with reference to the special procurement measures approved in this context. The second part will be dedicated to the analysis of the special measures for public procurement and the appropriate means for the resolution of possible disputes arising from the execution of the national RRP. In each part we will present the respective conclusions. Keywords: EU Next Generation Funds; Recovery and Resilience Mechanism; Portuguese Recovery and Resilience Plan; special public procurement measures; administrative arbitration

ОСОБЛИВОСТІ ЗВІЛЬНЕННЯ ВІД ФІНАНСОВО-ПРАВОВОЇ ВІДПОВІДАЛЬНОСТІ ЗА ПОРУШЕННЯ ПОДАТКОВОГО ЗАКОНОДАВСТВА ПІД ЧАС КАРАНТИНУ

The article is devoted to the analysis of the moratorium on the application of fines for violation of tax legislation committed during coronavirus lockdown. It is established that non-use of fines indicates the non-application of the financial liability itself. It is proved that exemption from the application of penalties for violation of tax legislation committed during coronavirus lockdown is a special basis for exemption from financial liability. It is emphasized that the provisions of paragraph 52-1 of Section 10 of Section XX of the Tax Code of Ukraine do not allow to draw a clear conclusion on the dismissal of taxpayers from the use of late-payment interest for violation of other Ukrainian legislation, which is controlled by the tax authorities (except Tax Code of Ukraine). The author considered contradictory jurisprudence on this issue on the example of currency legislation and proved that the exemption from the late-payment interest does not contradict the Law of Ukraine “On Currency and Currency Transactions”, but is a special rule that has been consolidated in the Tax Code of Ukraine, based on the universality of the concept of “late-payment interest”, used in tax legislation. The analysis of the concept of a continuous tax offense and the peculiarities of determining the moment of its commission has made it possible to conclude that the moratorium on the application of fines for violation of tax legislation actually extends for taxpayers the time limits to fulfill their tax obligation at any time before the end of coronavirus lockdown. It is established that the legal regime of coronavirus lockdown partially coincides in time with the legal regime of martial law, and therefore the issues related to the ratio of moratorium (stopping) of fines for the period of coronavirus lockdown and martial law must be considered in their systemic interconnection. In this case, the moratorium on the use of penalties for violations committed during coronavirus lockdown does not work in the case of inspections that are allowed at the time of martial law. The possible risks of practical use of force majeure as a circumstance for exemption from financial liability are indicated. Criteria for differentiation of mechanisms of exemption from financial liability for tax offenses committed during coronavirus lockdown and martial law are proposed.

О ПРЕКРАЩЕНИИ ПРОФЕССИОНАЛЬНОЙ ДЕЯТЕЛЬНОСТИ СПОРТСМЕНА

In this article, legal issues associated with the termination of the professional activity of an athlete are considered. The results obtained show that there are no specific procedures for terminating professional activities in sports, but it does not follow from this circumstance that there is no need to comply with the already established obligations at all. From a legal perspective, an athlete terminates their professional activity when they decide to stop taking part in sports competitions that are specific to professional sports activities. The article draws attention to the fact that an athlete’s refusal to be included in the number of participants, any temporary restrictions on their admission, and their disqualification do not directly confirm the termination of their professional activity. In addition, there is no reason to consider the closure of a sports club or league (federation) as a special basis for terminating an athlete’s activities. The central provision of the Olympic Charter proclaims the right of every person, not only sports organizations or states, to play sports, and the latter must contribute to the realization of this right. Civil law has sufficient tools for leveraging the rules in sports to achieve this important social and humanitarian goal.

Formation of interregional clusters on the basis of industry specialization of the area

Subject. This article explores the socioeconomic relations that arise in the process of formation of interregional clusters. Objectives. The article aims to explore industry specialization and clustering within the territory of the Central Black Earth macroregion. Methods. For the study, I used analysis and synthesis, induction and deduction, and the empirical method. Results. Based on the analysis of the industry specialization of the Central Black Earth macroregion’s economy, the article shows the economic and social effects of the implementation of interregional agreements. It proposes to create a chemical and pharmaceutical cluster of the medical industry in this economic region. Conclusions. The chemical and pharmaceutical cluster is of great importance under present-day conditions. It is a driver to boost employment and improve the quality of life of the population.

Are We Playing a Moral Lottery? Moral Disagreement from a Metasemantic Perspective

If someone disagrees with my moral views, or more generally if I’m in a group of n people who all disagree with each other, but I don’t have any special evidence or basis for my epistemic superiority, then it’s at best a 1-in-n chance that my views are correct. The skeptical threat from disagreement is thus a kind of moral lottery, to adapt a similar metaphor from Sharon Street. Her own genealogical debunking argument, as I discuss, relies on a premise of such disagreement among evolutionary counterparts.In this paper, I resist the threat from disagreement by showing that, on some of the most influential and most attractive theories of content determination, the premise of moral disagreement cannot serve any skeptical or revisionary purposes. I examine and criticize attempts, made by Gilbert Harman and Sharon Street, to argue from disagreement to relativism by relying on a theory of content determination that involves a principle that, within certain constraints, maximizes the attribution to us of true beliefs. And I examine and criticize Robert Williams’s attempt to show there is moral disagreement by relying on a theory of content determination that involves a principle that instead maximizes the attribution to us of rationality. My overall aim is to defend commonsense moral realism via a careful look at the theory of content and concepts.

HISTORICAL DEVELOPMENT OF PALLIATIVE ESTABLISHMENTS IN THE WORLD AND IN UKRAINE

The object of the research is centers of palliative help.
 The article of research is historical development of establishments of palliative medicine.
 Global environmental problems of today lead to increase in the incidence of population and increase in incurable cases. The problems of terminally ill patients are been dealt with by palliative medicine, which takes care of the situation of such patients and their families. The article deals with the history of development of palliative care facilities in the world - hospices. The situation of creation of such establishments in Ukraine is analyzed, which indicates the need to revise the state regulatory framework for design. The analysis conducted in the article indicates the inconsistency of the current norms and the absence of special normative bases for the design of hospices. Current situation does not allow for proper development of the construction of palliative care facilities. In addition, the main criteria and needs are discussed in the article:
 
 Physical comfort (achieved by creating a home atmosphere in the hospital)
 Psychological comfort (achieved using the principle of an individual approach to each patient, taking into account all their needs)
 Social comfort (achieved by designing places for communication with other patients, as well as with relatives and friends. It is important that such places possess and create a positive attitude and distract from negative thoughts)
 
 Visual comfort (achieved with the help of thoughtful landscaping and designing places for walks, squares, intimate areas for rest and relaxation, as well as for the hobbies of patients)

Structure of the plane waves for a spin 3/2 particle, massive and massless cases, gauge symmetry

The structure of the plane waves solutions for a relativistic spin 3/2 particle described by 16-component vector-bispinor is studied. In massless case, two representations are used: Rarita – Schwinger basis, and a special second basis in which the wave equation contains the Levi-Civita tensor. In the second representation it becomes evident the existence of gauge solutions in the form of 4-gradient of an arbitrary bispinor. General solution of the massless equation consists of six independent components, it is proved in an explicit form that four of them may be identified with the gauge solutions, and therefore may be removed. This procedure is performed in the Rarita – Schwinger basis as well. For the massive case, in Rarita – Schwinger basis four independent solutions are constructed explicitly.

Functional diversification gave rise to allelic specialization in a rice NLR immune receptor pair.

Cooperation between receptors from the nucleotide-binding, leucine-rich repeats (NLR) superfamily is important for intracellular activation of immune responses. NLRs can function in pairs that, upon pathogen recognition, trigger hypersensitive cell death and stop pathogen invasion. Natural selection drives specialization of host immune receptors towards an optimal response, whilst keeping a tight regulation of immunity in the absence of pathogens. However, the molecular basis of co-adaptation and specialization between paired NLRs remains largely unknown. Here, we describe functional specialization in alleles of the rice NLR pair Pik that confers resistance to strains of the blast fungus Magnaporthe oryzae harbouring AVR-Pik effectors. We revealed that matching pairs of allelic Pik NLRs mount effective immune responses, whereas mismatched pairs lead to autoimmune phenotypes, a hallmark of hybrid necrosis in both natural and domesticated plant populations. We further showed that allelic specialization is largely underpinned by a single amino acid polymorphism that determines preferential association between matching pairs of Pik NLRs. These results provide a framework for how functionally linked immune receptors undergo co-adaptation to provide an effective and regulated immune response against pathogens. Understanding the molecular constraints that shape paired NLR evolution has implications beyond plant immunity given that hybrid necrosis can drive reproductive isolation.

Numerical analysis of the stability of nonequilibrium 3D evolutionary transfer processes in the network

Analytical methods for solving various problems of an applied nature (for example, non-stationary transfer problems over network hydro, gas and heat carriers), whose mathematical models use the formalisms of evolutionary differential systems, are possible with rare exceptions. That is why the construction of numerical and simulation models for the use of quantitative analysis methods becomes a universal research tool, if at the same time the implementation of these models on a computer is carried out – in other words, a complex of software engineering of the process under study is formed. The study uses the method of semidiscretization by a time variable of the mathematical model of the evolutionary non-equilibrium process of continuous medium transfer, which remains one of the most effective methods for analyzing applied problems. In this case, the elliptic operator of the mathematical model has a special basis (a system of eigenfunctions), which is why the analysis is reduced to the study of a boundary value problem for elliptic-type equations with a spatial variable changing on a network-like domain. The paper presents the conditions for unambiguous weak solvability of a differential-difference system, which is a difference analogue in the time variable of the original system, and the way of constructing an algorithm for finding an approximate solution is indicated. The study contains an analysis of the stability and convergence of difference schemes of evolutionary network-like nonequilibrium processes of continuous media transfer over network carriers and includes an analysis of the correctness of the mathematical model of this process. The results of the work are applicable in the framework of oil and gas engineering to the study of issues of stabilization and parametric optimization of the processes of transportation of liquid media through spatial networks.

The conformational cycle of prestin underlies outer-hair cell electromotility.

The voltage-dependent motor protein prestin (also known as SLC26A5) is responsible for the electromotive behaviour of outer-hair cells and underlies the cochlear amplifier1. Knockout or impairment of prestin causes severe hearing loss2-5. Despite the key role of prestin in hearing, the mechanism by which mammalian prestin senses voltage and transduces it into cellular-scale movements (electromotility) is poorly understood. Here we determined the structure of dolphin prestin in six distinct states using single-particle cryo-electron microscopy. Our structural and functional data suggest that prestin adopts a unique and complex set of states, tunable by the identity of bound anions (Cl- or SO42-). Salicylate, a drug that can cause reversible hearing loss, competes for the anion-binding site of prestin, and inhibits its function by immobilizing prestin in a new conformation. Our data suggest that the bound anion together with its coordinating charged residues and helical dipole act as a dynamic voltage sensor. An analysis of all of the anion-dependent conformations reveals how structural rearrangements in the voltage sensor are coupled to conformational transitions at the protein-membrane interface, suggesting a previously undescribed mechanism of area expansion. Visualization of the electromotility cycle of prestin distinguishes the protein from the closely related SLC26 anion transporters, highlighting the basis for evolutionary specialization of the mammalian cochlear amplifier at a high resolution.

Chern-Simons perturbative series revisited

A group-theoretical structure in a perturbative expansion of the Wilson loops in the 3d Chern-Simons theory with SU(N) gauge group is studied in symmetric approach. A special basis in the center of the universal enveloping algebra ZU(slN) is introduced. This basis allows one to present group factors in an arbitrary irreducible finite-dimensional representation. Developed methods have wide applications, the most straightforward and evident ones are mentioned. Namely, Vassiliev invariants of higher orders are computed, a conjecture about existence of new symmetries of the colored HOMFLY polynomials is stated, and the recently discovered tug-the-hook symmetry of the colored HOMFLY polynomial is proved.

Positive selection in noncoding genomic regions of vocal learning birds is associated with genes implicated in vocal learning and speech functions in humans.

Vocal learning, the ability to imitate sounds from conspecifics and the environment, is a key component of human spoken language and learned song in three independently evolved avian groups—oscine songbirds, parrots, and hummingbirds. Humans and each of these three bird clades exhibit specialized behavioral, neuroanatomical, and brain gene expression convergence related to vocal learning, speech, and song. To understand the evolutionary basis of vocal learning gene specializations and convergence, we searched for and identified accelerated genomic regions (ARs), a marker of positive selection, specific to vocal learning birds. We found avian vocal learner-specific ARs, and they were enriched in noncoding regions near genes with known speech functions or brain gene expression specializations in humans and vocal learning birds, including FOXP2, NEUROD6, ZEB2, and MEF2C, and near genes with major neurodevelopmental functions, including NR2F1, NRP2, and BCL11B. We also found enrichment near the SFARI class S genes associated with syndromic vocal communication forms of autism spectrum disorders. These findings reveal strong candidate noncoding regions near genes for the evolutionary adaptations that distinguish vocal learning species from their close vocal nonlearning relatives and provide further evidence of molecular convergence between birdsong and human spoken language.

Competitiveness as the Basis of EU Regional Policy: Smart Specialization and Sustainability

Nowadays in the globalization era countries are forced to pay considerable attention to the integration aspects of development, regionalization processes ensuring their own competitiveness in order to enhance the competitive position in the market, which increases the scientific interest in the study of these issues. The purpose of the article is to consider competitiveness as the basis of EU regional policy and to determine the possibilities of applying such experience in Ukraine. A number of scientific research methods have been used: the method of deduction and induction, analysis, synthesis and comparison, a graphic method. Globalization contributes to the creation of new conditions of the world economic development, which forces economic actors to reconsider their role in the economy. Competitiveness provides them with a reliable competitive positions today and in the future. The high competitiveness of the region testifies to the effective organization and optimization of economic processes. EU regional policy takes into account that the competitiveness of the region is formed in the conditions of competitive relations at the national and international levels. The EU regional policy experience can be implemented in the Ukrainian regional policy. The competitiveness of the region allows to respond in time to market changes. EU regional policy takes this into account, so the category of regional competitiveness is paid much attention on as confirmed by the RCI calculation. The possibilities of increasing the competitiveness and sustainability of regions through the development of smart specialization and implementation of smart projects are outlined. The advantages of implementing European experience in the development of competitiveness of regions on the basis of smart specialization in Ukraine are proved.

ПРАВОВИЙ МЕХАНІЗМ ПОВЕРНЕННЯ СУДОВОГО ЗБОРУ У РАЗІ ЗАВЕРШЕННЯ РОЗГЛЯДУ БЕЗ УХВАЛЕННЯ РІШЕННЯ СУДУ В ЦИВІЛЬНОМУ СУДОЧИНСТВІ

The peculiarities of the legal mechanism of returning the court fee in case of completion of civil cases without a court decision are analyzed, issues of these applications practical resolving are considered, as well as suggestions for improving the legal regulation in case of the closure of the proceedings or leaving the application without consideration are proposed. While analyzing examples of case law, it was established that the lack of legislative regulation of the procedure for confirming or denying the existence of grounds for the amount of court fees refund causes a lot of confusion and contradictory solutions to the judiciary in this regard. The position on the impossibility of equalization due to the different procedural nature of leaving without consideration of statements on procedural issues, such as: on providing evidence, on securing a claim, on dismissal of a judge, and leaving without considering a statement of claim as a civil procedural institute, regulated by Art. 257 of CPC of Ukraine are justified. It has been concluded that in case the court finds circumstances that are grounds for the application of the institute of leaving the application without consideration and provided for in Art. 257 of CPS of Ukraine, when considering applications on procedural issues, should apply such a special legal consequence as a return of the application without consideration. It has been established that returning an application on procedural issues without consideration and leaving an application without consideration are completely different legal categories. Return of applications on procedural issues without consideration due to its legal nature is a special basis for the application of the return of the application institute, and therefore the legal consequence of such an application would be considered not filed at all. In this connection, it has been proposed to enshrine in the legislation the provisions on the refund of the court fee in case of return without consideration of the application on procedural issues, for the submission of which such payment was paid.

The stability optimization of the international lithium trade

The international mineral resources trade is an important way to correct the unbalanced distribution of global mineral resources. This paper proposes a bi-objective model to improve the stability of the mineral resource trade by optimizing the trade structure. The improved nondominated sorting genetic algorithm (NSGA-II) was used to solve the bi-objective optimization model, and a more robust trade structure was obtained. We applied the model to the optimization of the global lithium carbonate trade. The optimized results enabled us to identify the key trade relationships that play the most critical role in improving the stability of lithium carbonate trade. The effectiveness of the optimization model was proved by analyzing the stability of major net importing countries and the influence of major net exporting countries. Furthermore, the strongest destructive model, which was opposite to the optimal model, was used to analyze the core trade relations and core countries in the actual lithium trade. These core trade relations provide a foundation for maintaining the stability of the international trade. Our work provides new ideas for improving the stability of the global mineral trade and provides a new perspective and special basis for trading countries to choose trade partners.

Almost exact diagonal reflection symmetries and three-zero texture

In this paper, we consider the three-zero texture with diagonal reflection symmetries in the SM. The three-zero texture has two less assumptions ((Mu)11,(Mν)11≠0) than the universal four-zero texture of mass matrices (Mf)11=(Mf)13,31=0 for f=u,d,ν,e. The texture allows diagonal reflection symmetries to be almost exact and d-e unification. They reproduce the CKM and MNS matrices with accuracies of O(10−4) and O(10−3). By using perturbative approximations of the diagonalization, two relations with good accuracy for quark mass and mixing are obtained. Although this calculation is done in a special basis, it is a general result in a sense, because other textures and generalized CP symmetries exist by some weak basis transformation.By assuming a d-e unified relation (Md∼Me), we obtain the lightest neutrino mass m1≃2.12−5.64[meV] and the effective mass of the double beta decay |mee|≃1.23−2.15[meV].

Damage assessment for structure subjected to earthquake using wavelet packet decomposition and time-varying frequency

The seismic damage assessment method based on frequency change rate is applied with the advantages such as clear mechanism and high precision, but the time resolution and the frequency resolution cannot be accurately meet at the same time when the traditional methods for signal analysis are used. Thus, the time-varying frequencies cannot be obtained directly from the response signals and the application of this damage assessment method is insufficient. The corresponding accuracy evaluation criterion for different signal analysis methods is presented based on the marginal condition in time-frequency domain, and wavelet packet decomposition method with special wavelet basis functions is verified as an efficient tool in establishing time-varying power spectrum on the basis of theoretical and computational analysis. The time-varying frequency extraction method based on wavelet packet ridge is proposed, and the time-varying seismic damage index can be calculated according to frequency changes, furthermore, the multi-dimensional seismic damage assessment can be realized. The numerical examples and experimental results show that the damage assessment method based on wavelet packet transform and time-varying frequency can accurately reveal the integral damage evolution process and the damage states. This method only requires structural response histories, and has superior adaptability on structural dynamic analysis, seismic design verification and seismic damage assessment for actual structures.

The Seventh International Olympiad in Cryptography: Problems and solutions

The International Olympiad in Cryptography NSUCRYPTO is the unique Olympiad containing scientific mathematical problems for professionals, school and university students from any country. Its aim is to involve young researchers in solving curious and tough scientific problems of modern cryptography. In 2020, it was held for the seventh time. Prizes and diplomas were awarded to 84 participants in the first round and 49 teams in the second round from 32 countries. In this paper, problems and their solutions of NSUCRYPTO'2020 are presented. We consider problems related to attacks on ciphers and hash functions, protocols, permutations, primality tests, etc. We discuss several open problems on JPEG encoding, Miller -- Rabin primality test, special bases in the vector space, AES-GCM. The problem of a modified Miller -- Rabin primality test was solved during the Olympiad. The problem for finding special bases was partially solved.