Cient Conditions Research Articles

On the existence of time-periodic solutions of nonlinear parabolic differential equations with nonlocal boundary conditions of the Bitsadze-Samarskii type

We study a nonlinear parabolic differential equation in a bounded multidimensional domain with nonlocal boundary conditions of the Bitsadze-Samarskii type. We prove existence theorems for a periodic in time generalized solution. Su cient conditions for the existence of generalized solutions contain either an algebraic ellipticity condition or an algebraic strong ellipticity condition for the auxiliary differential-difference operator.

Methods for the graph realization problem

Abstract The graph realization problem seeks an answer to how and under what conditions a graph can be constructed if we know the degrees of its vertices. The problem was widely studied by many authors and in many ways, but there are still new ideas and solutions. In this sense, the paper presents the known necessary and su cient conditions for realization with the description in pseudocode of the corresponding algorithms. Two cases to solve the realization problem are treated: finding one solution, and finding all solutions. In this latter case a parallel approach is presented too, and how to exclude isomorphic graphs from solutions. We are also discussing algorithms using binary integer programming and flow networks. In the case of a bigraphical list with equal out- and in-degree sequences a modified Edmonds–Karp algorithm is presented such that the resulting graph will be always symmetric without containing loops. This algorithm solves the problem of graph realization in the case of undirected graphs using flow networks.

Western carrot and whip Diplomacy for Serbia

The multi-vector policy of the Serbian leadership makes it possible to maintain a delicate balance of relations with the West and the East — the European Union and Russia. Serbia, as a key country in the Balkan region, is experiencing tremendous pressure from Euro-American "well-wishers" to join the anti-Russian sanctions and sign the peace plan proposed by France and Germany to normalize the situation in Kosovo and Metohija. Serbia is successfully diversifying its relations with Russia and with other countries outside the Western bloc. At the same time, Belgrade in certain areas is forced to follow the policy of the collective West. This is done largely in connection with pragmatic goals — obtaining economic benefi ts from ties with EU countries and the West in general, adhering to such values and actively promoting them. At the same time, in order to speed up the process of subordinating Belgrade to the demands of Washington and Brussels, a hybrid war is already being waged against Serbia today with the threat of unleashing a proxy war and a color revolution. The eff orts of external and internal opponents of the current leadership of Serbia and its political line to preserve the independence, sovereignty and territorial integrity of the country form the necessary and suffi cient conditions for the use of modern strategies and technologies of interstate confrontation. The proxy war strategy provides for the possibility of using the self-proclaimed “Republic of Kosovo” as a proxy agent for the US and NATO for a military attack on Belgrade. At the same time, preparations are underway for a coup d'état in the course of a color revolution in order to bring to power a government manipulated by the West. Practical recommendations are given for organizing a rebuff to hybrid aggression.

Extensions of Orderings

Summary In this article we extend the algebraic theory of ordered fields [6], [8] in Mizar. We introduce extensions of orderings: if E is a field extension of F, then an ordering P of F extends to E, if there exists an ordering O of E containing P. We first prove some necessary and su cient conditions for P being extendable to E, in particular that P extends to E if and only if the set Q S E : = { ∑ a * b 2 | a ∈ P , b ∈ E } QS\,\,E: = \left\{ {\sum {a*{b^2}|a \in P,\,\,b \in E} } \right\} is a preordering of E – or equivalently if and only if −1 / ∉ QS E. Then we show for non-square a ∈ F that P extends to F ( a ) F\left( {\sqrt a } \right) if and only if P and finally that every ordering P of F extends to E if the degree of E over F is odd.

On domination in signed graphs

Abstract In this article the concept of domination in signed graphs is examined from an alternate perspective and a new definition of the same is introduced. A vertex subset D of a signed graph S is a dominating set, if for each vertex v not in D there exists a vertex u ∈ D such that the sign of the edge uv is positive. The domination number γ (S) of S is the minimum cardinality among all the dominating sets of S. We obtain certain bounds of γ (S) and present a necessary and su cient condition for a dominating set to be a minimal dominating set. Further, we characterise the signed graphs having small and large values for domination number.

A coupled system of fractional difference equations with anti-periodic boundary conditions

"In this article, we give su cient conditions for the existence, uniqueness and Ulam{Hyers stability of solutions for a coupled system of two-point nabla fractional di erence boundary value problems subject to anti-periodic boundary conditions, using the vector approach of Precup [4, 14, 19, 21]. Some examples are included to illustrate the theory."

Smoothness of solutions to the damping problem for nonstationary control system with delay of neutral type on the whole interval

We consider the damping problem for a nonstationary control system described by a system of differential-difference equations of neutral type with smooth matrix coe cients and several delays. This problem is equivalent to the boundary-value problem for a system of second-order differentialdifference equations, which has a unique generalized solution. It is proved that the smoothness of this solution can be violated on the considered interval and is preserved only on some subintervals. Su cient conditions for the initial function are obtained to ensure the smoothness of the generalized solution over the entire interval.

Por que Seguimos Regras? Analisando o Exemplo da Prevenção a COVID-19

The COVID-19 pandemic required the world’s population to quickly learn new behaviors that would help prevent the spread and contamination of the coronavirus. The presentation of rules that described these behaviors and their eff ectiveness was one of the strategies used by governments, scientifi c communities, and the media to produce the required behavioral changes. However, there was resistance on the part of the population to follow these rules. This study sought to describe and analyze the possible eff ects of some variables on the occurrence and maintenance of rule-following that prevented contamination by COVID-19, in the light of scientifi c evidence from the behavioral-analytic literature. The variables were: rule understanding, rule complexity, biological conditions and behavioral repertoire of the listener, environmental conditions, who is the speaker, consequences produced by following the rule, formal properties of rules, confl icting rules, and individual history of the listener. The results indicated that understanding the rule is not a suffi cient condition for following it. The interaction between favorable and unfavorable variables to which a listener is exposed changes the probability of following rules. This study exemplifi es how identifying appropriate ways of presenting rules and making them more probable increases the chance of preserving the lives of the world’s population.Keywords: Rules, rule-following, COVID-19, pandemic, prevention

Ukrainian National Revolution as a factor in the development of the law of Ukraine-Rus in the XVII century

The paper examines the impact of signifi cant historical events associated with the Ukrainian National Revolution of the 17th century to changes in the legal sphere, which were the origins of legal norms that have a long-term eff ect. In Ukraine, the jump in interest in the history of socio-cultural and state-legal institutions in our country and on the European continent is largely due to the events of the late XX –early XXI century, formation of Ukraine as an independent state. The problem became even more relevant in connection with the events in Ukraine in 2013-2014, as well as the temporary loss of Crimea and the occupation of some eastern territories, the desire to rewrite the history of development and achievements of our country. In the history of Ukraine and many other European countries highlights the events of the midseventeenth century in terms of their then signifi cance and long-term impact on the development of social and legal institutions in the future: the Peace of Westphalia in 1648, which was the source of modern international law; The English Revolution led by O. Cromwell; Ukrainian National Revolution led by B. Khmelnytsky. The aim of the paper is to study the impact of signifi cant historical events related to the B. Khmelnytsky Revolution on changes in the legal sphere, which were a source of legal norms that had long-term eff ect, as well as to compare the consequences of large-scale historical events in Ukraine and Europe to the development of the legal doctrine of the New Time. At the beginning of the XVII century in the Ukrainian-Russian lands there was a situation that can be called “revolutionary”. Legal sources related to the rule of Polish magnates, the Polish nobility and the Catholic Church in the Polish-Lithuanian Commonwealth ceased to exist. “Cossack law” became widespread, which meant the system of customary law, which was formed in the Zaporozhian Sich and was integrated into public relations during the Ukrainian National Revolution. Zaporozhian customary law was perceived not only as local, but also as purely national. Deep religiosity was one of the hallmarks of the Cossacks, and the protection of the Orthodox faith of ancestors and the church was the basis of their lives. The National Revolution in Ukraine in 1648–1676 was related to large-scale sociopolitica movements in a number of Central and Western European countries. Its signifi cance lay in the restoration of state life, the formation of the Ukrainian state idea, and the development of national consciousness. As a result of the turbulent events of the Ukrainian National Revolution, the development of legal institutions took a diff erent path than the development of legal institutions in European countries associated with the end of the Thirty Years’ War and the adoption of the Peace of Westphalia in 1648. Unlike the transformations in European countries, the events in Ukraine have not become a direct source in the legal sphere; in this regard there are not yet suffi cient conditions for signifi cant changes. Considering the further historical development of Ukraine, these events were only a necessary impetus for such changes in the future. Key words: Ukrainian National Revolution, necessary and suffi cient conditions for changes in the legal sphere, the origins of law.

Well-posedness for set-valued equilibrium problems

"In this paper we extend a concept of well-posedness for vector equilibrium problems to the more general framework of set-valued equilibrium problems in topological vector spaces using an appropriate reformulation of the concept of minimality for sets. Su cient conditions for well-posedness are given in the generalized convex settings and we are able to single out classes of well-posed set-valued equilibrium problems. On the other hand, in order to relax some conditions, we introduce a concept of minimizing sequences for a set-valued problem, in the set criterion sense, and further we will have a concept of well-posedness for the set-valued equilibrium problem we are interested in. Suficient results are also given for this well-posedness concept."

Ricci soliton on the tangent bundle with semi-symmetric metric connection

In this paper, we studied the tangent bundle endowed with semi-symmetric metric connection obtained by vertical and complete lifts of a semi-symmetric metric P-connection on the base manifold. Firstly, we give a relationships between (TM; gc) and (M; g) to be an Einstein manifolds. Secondly, we investigate necessary and su cient conditions for (TM; gc) with complete and vertical lift of torqued potential elds to be Ricci soliton.

ЦИФРОВАЯ ТРАНСФОРМАЦИЯ ВЫСШЕГО ОБРАЗОВАНИЯ, ОСНОВНЫЕ ХАРАКТЕРИСТИКИ И ФУНКЦИИ SMART УНИВЕРСИТЕТА 4.0

The concept of a SMART university currently being developed in the popular understanding should meet the requirements of accelerated learning, use the achievements of digitalization and be based on the principles of self-development, adaptability, measurability, digital tools and distance education.However, this concept, supported in most modern methodological and scienti c works, seems to be insuf ciently complete and systematized.The article presents an extended joint contextual economic-technological and historical analysis of the evolution of informatics, the sphere of knowledge and technology, which made it possible to clarify the basic requirements for the new educational system and its elements, digitalization tools, its main characteristics and functions, as well as to raise a number of questions that require additional scienti c consideration and veri cation in practice.The existing international education system is a product and simultaneously an element of the rst industrial revolution, functioning on the basis of the principles of ow-type production established more than a hundred years ago, and solves the problem of maximum penetration of a typical set of knowledge into the masses of the population, rather than maximizing the quality of the obtained knowledge and its individualization.New industrial revolution based on wide digitalization and networking, which we are witnessing, requires modernization of most economic institutions, including education system, and offers for this modernization not only a new set of technologies, but also new principles of exibility, individualization, maximization of ef ciency. The subject of electronic education has been developing in different countries for quite a long period. By now the necessary set of technologies and organizational elements has been created. However, it is during the 2019-2021 pandemic that suf cient conditions have emerged for the non-alternative widespread implementation of a new holistic education system based on remote mode and adaptive digital content. The article considers the modernization of the education system, the creation of the Digital SMART University or University 4.0. The modernization of the educational system has many parallels with the digital transformation of other sectors of the economy. This makes it possible and necessary to use the experience and knowledge accumulated in other areas of economic activity, their systematization and analysis of applicability.

Delignification of Lignocellulosic Biomass Sugarcane Bagasse by Using Ozone as Initial Step to Produce Bioethanol

The choice of pretreatment is a very important in bioethanol production from lignocellulosic biomass. This helps to eliminate lignin partition between cellulose and hemicellulose. However, various methods generate diverse effects on the material structure and composition. The purpose of this study, therefore, was to delignify sugarcane bagasse by ozonolysis, followed by hydrolysis and fermentation. Also, the morphology of the samples was analyzed using SEM, while hemicellulose, cellulose, and lignin content were characterized by the Chesson process. The sample was hydrolyzed using 1% (v/v) sulfuric acid and the bioethanol fermented with Saccharomyces cerevisiae was detected by gas chromatography. Furthermore, ozone was applied for 90 minutes at pH 3.0 in the deligni cation process. This produces cellulose, hemicellulose, and lignin estimated at 59%, 22%, and 6%, respectively. However, ozonolysis was employed to reduce lignin for up to 217%. Meanwhile, the hydrolysed samples were known to rapidly decrease the reducing sugar from 19.342 to 2.86 mg/L after heating at 100oC. Subsequently, the fermentation stage recorded the highest ethanol production, estimated at 0.79% (v/v). The result showed lignin removal was conducted in an eco-friendly and ef cient condition. Therefore, the need for further study is possible in order to optimize certain parameters for maximum bioethanol production.

Bond Power Exchange Options

We study power exchange options written on zero-coupon bonds under a stochastic string frame- work. We obtain closed-form expressions for pricing and hedging bond power exchange options and, as particular cases, the corresponding expressions for call power options and constant underlying elasticity in strikes (CUES) options. Suffi cient conditions for the equivalence of the European and the American versions of bond power exchange options are provided and the put- call parity relation for this kind of option is also stated. Finally, we consider several applications of our results including duration and convexity measures for bond power exchange options, pric- ing extendable/accelerable maturity zero-coupon bonds, options to price a zero-coupon bond off of a shifted term-structure, and options on interest rates and rate spreads.

APPLICATIONS OF MATRIX TRANSFORMATIONS TO ABSOLUTE SUMMABILITY

Rhoades and Sava¸s [6],[11] established necessary for inclusions of the absolute matrix summabilities under additional conditions. In this paper we determine necessary or su¢ cient conditions for some classes of in…nite matrices, and using this get necessary or su¢ cient conditions for more general absolute summabilities applied to all matrices.

Basarab loop and the generators of its total multiplication group

A loop (Q; ·) is called a Basarab loop if the identities: (x · yxρ)(xz) = x · yz and (yx) · (xλz · x) = yz · x hold. It was shown that the left, right and middle nuclei of the Basarab loop coincide, and the nucleus of a Basarab loop is the set of elements x whose middle inner mapping Tx are automorphisms. The generators of the inner mapping group of a Basarab loop were refined in terms of one of the generators of the total inner mapping group of a Basarab loop. Necessary and su_cient condition(s) in terms of the inner mapping group (associators) for a loop to be a Basarab loop were established. It was discovered that in a Basarab loop: the mapping x ↦ Tx is an endomorphism if and only if the left (right) inner mapping is a left (right) regular mapping. It was established that a Basarab loop is a left and right automorphic loop and that the left and right inner mappings belong to its middle inner mapping group. A Basarab loop was shown to be an automorphic loop (A-loop) if and only if it is a middle automorphic loop (middle A-loop). Some interesting relations involving the generators of the total multiplication group and total inner mapping group of a Basarab loop were derived, and based on these, the generators of the total inner mapping group of a Basarab loop were finetuned. A Basarab loop was shown to be a totally automorphic loop (TA-loop) if and only if it is a commutative and exible loop. These aforementioned results were used to give a partial answer to a 2013 question and an ostensible solution to a 2015 problem in the case of Basarab loop

Basarab loop and the generators of its total multiplication group

A loop (Q; ·) is called a Basarab loop if the identities: (x · yxρ)(xz) = x · yz and (yx) · (xλz · x) = yz · x hold. It was shown that the left, right and middle nuclei of the Basarab loop coincide, and the nucleus of a Basarab loop is the set of elements x whose middle inner mapping Tx are automorphisms. The generators of the inner mapping group of a Basarab loop were refined in terms of one of the generators of the total inner mapping group of a Basarab loop. Necessary and su_cient condition(s) in terms of the inner mapping group (associators) for a loop to be a Basarab loop were established. It was discovered that in a Basarab loop: the mapping x ↦ Tx is an endomorphism if and only if the left (right) inner mapping is a left (right) regular mapping. It was established that a Basarab loop is a left and right automorphic loop and that the left and right inner mappings belong to its middle inner mapping group. A Basarab loop was shown to be an automorphic loop (A-loop) if and only if it is a middle automorphic loop (middle A-loop). Some interesting relations involving the generators of the total multiplication group and total inner mapping group of a Basarab loop were derived, and based on these, the generators of the total inner mapping group of a Basarab loop were finetuned. A Basarab loop was shown to be a totally automorphic loop (TA-loop) if and only if it is a commutative and exible loop. These aforementioned results were used to give a partial answer to a 2013 question and an ostensible solution to a 2015 problem in the case of Basarab loop.

Mapping properties of certain linear operator associated with hypergeometric functions

The main object of the present paper is to nd some su¢ cient conditions in terms of hypergeometric inequalities so that the linear operator denoted by Ha;b;c : maps a certain subclass of close-to-convex function R (A;B) into subclasses of k-uniformly starlike and k-uniformly convex functions k 􀀀ST () and k 􀀀UCV() respectively. Further, we consider an integral operator and discuss its properties. Our results generalize some relevant results.

Цифровой SMART Университет - Университет 4.0

The existing international education system is a product and simultaneously an element of the rst industrial revolution, functioning on the basis of the principles of ow-type production established more than a hundred years ago, and solves the problem of maximum penetration of a typical set of knowledge into the masses of the population, rather than maximizing the quality of the obtained knowledge and its individualization.New industrial revolution based on wide digitalization and networking, which we are witnessing, requires modernization of most economic institutions, including education system, and offers for this modernization not only a new set of technologies, but also new principles of exibility, individualization, maximization of ef ciency. The subject of electronic education has been developing in different countries for quite a long period. By now the necessary set of technologies and organizational elements has been created. However, it is during the 2019-2021 pandemic that suf cient conditions have emerged for the non-alternative widespread implementation of a new holistic education system based on remote mode and adaptive digital content. The article considers the modernization of the education system, the creation of the Digital SMART University or University 4.0. The main problems of implementing the new educational system and approaches to their solutions are analyzed. The modernization of the educational system has many parallels with the digital transformation of other sectors of the economy. This makes it possible and necessary to use the experience and knowledge accumulated in other areas of economic activity, their systematization and analysis of applicability.The main tasks in creating a new e-university are the introduction of new processes of design, production, systematization, storage and delivery of educational content, as well as modernization of management and administration of the educational process. Implementation of e-learning is based on integrated organizational and functional structures, IT-architectures with their own rules, responsibilities, people, processes, system of interaction and relationship, i.e. the new business structure, which is built into the overall corporate information system and business architecture of the university system. The paper examines the business processes, services, IT infrastructure of the university, providing a new form of e-learning. The object of the study is the electronic educational environment of the university, which is an electronic educational platform of a new set of educational IT-services. The term «service» de nes a service for the educational business, which is quanti ed by a set of business metrics, the metrics of availability, continuity, security, reproducibility, repeatability and scalability. The result of the implementation of the new University 4.0 should be a progressively developing catalog of electronic educational services of the university, which can be used as a basis for designing specialized educational trajectories and use in various educational institutions.

Ruled Surfaces with Constant Slope Ruling According to Darboux Frame

The main scope of this paper is to examine ruled surfaces with constant slope ruling with respect to the given surface according to Darboux Frame. We give necessary and su¢ cient conditions for these types surfaces to be developable. Also, the investigations are observed under some special cases. Especially we obtained that the striction lines and Gaussian curvature of the surfaces. .