Explicit solutions to hyper-Bessel integral equations of second kind

AbstractIn earlier papers, the authors have used the transmutation method to find solutions to Volterra integral or differ-integral equations of second kind, involving Erdélyi-Kober fractional integration operators (see [1,2]), as well as to dual integral equations and some Bessel-type differential equations (see [3,4]). Here we consider the so-called hyper-Bessel integral equations whose kernel-function is a rather general special function (a Meijer's G-function). Such an equation can be written also in a form involving a product of arbitrary number of Erdélyi-Kober integrals. By means of a Poisson-type transmutation, we reduce its solution to the well-known solution of a simpler Volterra equation involving Riemann-Liouville integration only. In the general case, the solution is found as a series of integrals of G-functions, easily reducible to series of G-functions. For particular nonhomogeneous (right-hand side) parts, this solution reduces to some known special functions. The main techniques are based on the generalized fractional calculus

General covariant Horava-Lifshitz gravity without projectability condition and its applications to cosmology

We consider an extended theory of Horava-Lifshitz gravity with the detailed balance condition softly breaking, but without the projectability condition. With the former, the number of independent coupling constants is significantly reduced. With the latter and by extending the original foliation-preserving diffeomorphism symmetry ${{Diff}}(M, {\cal{F}})$ to include a local U(1) symmetry, the spin-0 gravitons are eliminated. Thus, all the problems related to them disappear, including the instability, strong coupling, and different speeds in the gravitational sector. When the theory couples to a scalar field, we find that the scalar field is not only stable in both the ultraviolet (UV) and infrared (IR), but also free of the strong coupling problem, because of the presence of high-order spatial derivative terms of the scalar field. Furthermore, applying the theory to cosmology, we find that due to the additional U(1) symmetry, the Friedmann-Robertson-Walker (FRW) universe is necessarily flat. We also investigate the scalar, vector, and tensor perturbations of the flat FRW universe, and derive the general linearized field equations for each kind of the perturbations.Comment: 19 pages, comments are welcome!!

AXIOLOGICAL ASPECT OF STUDENT PROFESSIONAL TRAINING: MATCHING DEMAND AND OFFERS OF LABOR MARKET

The purpose of the article: The Relevance of the study is determined by modern trends in the development of the labor market, based on demand and supply of goods - a graduate of the University. At the same time, student’s professional training in the educational process of the University is traditionally carried out based on the basic values of the specialist's individual, due to the need for them, and the demand and supply of the labor market are determined by the demand for a specialist as an intellectual resource of production. Materials and methods: The methodology of this study is based on the innovative content of professional training of a University student, focused on the needs of a specialist in professional self-affirmation as a personal and social value corresponding to the demand and supply of the labor market, presented in the concept of cultural competency-based approach to training, in the theory of changes in the labor market, in projects of future changes in the labor market, where demand and supply for the training of a modern competent specialist are used as driving forces. Results of the research: the algorithm of designing cognitive, motivational, behavioral, emotional components of the values of the student’s professional training is justified and their compliance with the demand and supply of the labor market is proved. Knowledge about the value aspects of a University student’s professional training, about the features of their compliance with the labor market’s demand and supply, will help to avoid, localize or eliminate problems in the real educational process. Applications: This research can be used for universities, teachers, and students. Novelty/Originality: In this research, the model of an axiological aspect of student professional training: matching demand and offers of labor market is presented in a comprehensive and complete manner

Detailed balance in Horava-Lifshitz gravity

We study Horava-Lifshitz gravity in the presence of a scalar field. When the detailed balance condition is implemented, a new term in the gravitational sector is added in order to maintain ultraviolet stability. The four-dimensional theory is of a scalar-tensor type with a positive cosmological constant and gravity is nonminimally coupled with the scalar and its gradient terms. The scalar field has a double-well potential and, if required to play the role of the inflation, can produce a scale-invariant spectrum. The total action is rather complicated and there is no analog of the Einstein frame where Lorentz invariance is recovered in the infrared. For these reasons it may be necessary to abandon detailed balance. We comment on open problems and future directions in anisotropic critical models of gravity.Comment: 10 pages. v2: discussion expanded and improved, section on generalizations added, typos corrected, references added, conclusions unchange

UNIVERSITY INTELLECTUAL CAPITAL FORMATION AND DEVELOPMENT

Purpose of the study: One of the most important terms to solve the problems of the education system is the educational institution’s intellectual capital, which significantly transforms the role and functions of the modern educator. The purpose of the article is to identify the essence of the University's intellectual capital and to justify the trajectory of its development, due to the needs and capabilities of education stakeholders. Methodology: Based on the methodology of education quality management the article justifies the leading role of quality education as an imperative of the University development. Intellectual capital is considered from the standpoint of organizational resources that determine the cost of the final product – the quality of education and the competitive position of the University; its development is carried out based on the project-target approach. Results: Modern requirements for the intellectual capital of the educational organization are revealed, the role and essence of pedagogical activity of teachers of higher education institutions in its formation are shown. The importance of continuous improvement of hard and soft competencies of University teachers as a way of incrementing intellectual capital is shown. The adaptive model’s design of University teachers’ career strategies based on design-target mechanisms is presented that determines the organizational development of the University. Applications of this study: The results determined the possibility to consider organizational and human knowledge and competence as a special type of investment to improve the functioning of the University. The recommendations for the construction of models of the University intellectual capital management are presented. The article is intended for employees of the education system, educators, researchers, and heads of the University departments. Novelty/Originality of this study: The contribution is made to the theory of the University’s social and cognitive management based on expanding the powers of quality management in the field of intellectual capital management

Student Attitude to Internet Search Engines: Navigation and Optimization Problems

The article relevance. Currently, the world is rapidly undergoing the process of Informatization of all aspects of society, the development and introduction of new information technologies. This highlights the need for further reflection and research on the development of the Internet and its opening opportunities for people. The aim of the research is to study the peculiarities of the attitude of students to search and recommendation services on the Internet. Research methods: as a research method, we used a questionnaire survey as a method of collecting primary information, which allows us to identify various aspects related to the attitude of students to search and recommendation systems on the Internet. Research results: the article examines the specifics of Russian search and recommendation systems, students' attitude to these services, and their place in their lives. The novelty and originality of the research lies in the fact that for the first time the search and recommendation services of the Internet space were studied. It is shown that these services were initially developed in the sphere of culture and gradually began to spread to other spheres of people's life, which attracted e-Commerce figures. It is revealed that those students who discovered search and recommendation services a few years ago still use them to choose leisure activities. It is shown that students still identify some disadvantages of these systems: inaccurate recommendations, a large number of questions to determine preferences. There is some distrust to new Internet technologies among those who are used to relying on their intuition when choosing. It is determined that students often use search and recommendation services, since in most cases gadgets help them spend their free time, have fun: read a book, watch a movie, listen to music. It is revealed that the majority of students trust Internet services, although they are not always satisfied with the recommendations. It is shown that the level of student-user confidence in traditional advertising and marketing decreases simultaneously. It is determined that from the point of view of students, today not only printed versions of Newspapers, traditional radio, but even mass broadcast television are losing ground before the Internet as the most promising communication channel. Practical significance: the data Obtained in this work can be used in marketing research, economic Sciences, advertising psychology, as well as for further theoretical development of this issue

University as an Environment of Innovative Interactions

Orenburg State University is presented as an environment of multilevel multidimensional interaction of various subjects. The dynamics of value interaction between students and teachers is revealed. In the conditions of modern social and digital transformations, the nature of joint activity is changing from formal-reproductive to value-creative. It is pointed out that the dominant instrumental values of students are shifting due to the information and technological features of distance educational technologies. Youth interactions and socio-cultural practices are integrated into the comprehensive program for the development of the OSU socio-cultural environment on the basis of various project activities. The implementation of the program is characterized by receiving grant support for student initiatives. International aspects of university interaction are represented by the development of forms of scientific and educational export to universities of the Republic of Kazakhstan

Development of Youth Communities in the University Ecosystem: Resources, Projects, and Risks

The article explores the development of youth communities in the ecosystem of the Orenburg State University. The modern university is designed to create new conditions for the development of youth communities. The study of students’ creative challenges demonstrates a wide range of aspirations and needs, their uncertainty and spontaneity. The answer to creative challenges is timely competent navigation and organizational and pedagogical support of young people for integration into socially positive communities. A regional university can become a center, space and mobilizer for the development of youth communities. Youth communities are dynamically changing, their reality goes beyond educational and scientific activities. In this regard, the traditional scientist-oriented model of the university is being transformed into an ecosystem model, which equally reveals the areas of training, development and education. Modern education at the empirical level masters the ecosystem approach. The article aims at revealing resources, projects, and risks of youth communities development in the conditions of the formation of a regional university ecosystem. The subject of study is the structure, axiological, organizational and procedural foundations of the university ecosystem. The resources, methods and risks of developing modern youth communities also represent the perspective of the study of the humanities. Ecosystem resources of the Orenburg State University are presented in many aspects: axiology and pedagogical technologies, projects of the Priority 2030 program, integration with the Orenburg University (Educational) District Association, international educational cooperation with universities in Kazakhstan. The article identifies external and internal risks specific to the development of youth communities in the logic of “potential applicants – university ecosystem – potential employers” based on the study of accelerator programs, streams, online surveys