Generalization of the Modified Bessel Function and Its Generating Function

2000 Mathematics Subject Classification: 33C10, 33-02, 60K25This paper presents new generalizations of the modified Bessel function and its generating function. This function has important application in the transient solution of a queueing system

Fractional queues with catastrophes and their transient behaviour

Starting from the definition of fractional M/M/1 queue given in the reference by Cahoy et al. in 2015 and M/M/1 queue with catastrophes given in the reference by Di Crescenzo et al. in 2003, we define and study a fractional M/M/1 queue with catastrophes. In particular, we focus our attention on the transient behaviour, in which the time-change plays a key role. We first specify the conditions for the global uniqueness of solutions of the corresponding linear fractional differential problem. Then, we provide an alternative expression for the transient distribution of the fractional M/M/1 model, the state probabilities for the fractional queue with catastrophes, the distributions of the busy period for fractional queues without and with catastrophes and, finally, the distribution of the time of the first occurrence of a catastrophe

Transient numerical approximation of hyperbolic diffusions and beyond

In this paper different types of hyperbolic diffusions and their corresponding transient Fokker–Planck equation are described and numerical solutions are presented. Diffusion models were developed that can fit both the marginal distribution and correlation structure and they have found a wide application in finance, turbulence and environmental time series. Hyperbolic diffusions have a complicated structure and variety of parameters and are extremely difficult to study and to model. We propose a numerical technique that solves one-dimensional hyperbolic Fokker–Planck equation in time dependent case. Note that this is a first study where transient hyperbolic diffusions are considered. The numerical technique is based on adaptive reduced basis method with spectral element discretization. It involves enrichment and projection stages where an optimal basis is found in a dynamic way using the singular value decomposition (SVD). The approach dramatically reduces the number of degrees of freedom required to solve the problem. The numerical evaluations of the Fokker–Planck equation are verified with available stationary solutions

Communication of characteristics with sense of humour and characteristics of hardiness at students

The article presents data of theoretical bases of hardiness and sense of humour. The results of empiric research are presented on Ural State Pedagogical University students (n = 60 students, 17–22 years). A diagnostic tool was used: test of sense of humor H. Eysenk and H. Wilson, test of styles of humor M.Rod, test of hardiness of S. R. Maddi in adaptation of D. A. Leont’eva. Shows the relationship between characteristics of hardiness and abilities of sense of humour. The applied aspect of the investigated problem can be realized in development of the program of development of hardiness on facilities of development of sense of humour in group and in individual work.Изложены теоретические основания жизнестойкости и чувства юмора. Представлены результаты эмпирического исследования, выполненного на выборке студентов. Установлены связи между характеристиками жизнестойкости и чувством юмора

On Nonlinear Functionals of Random Spherical Eigenfunctions

We prove Central Limit Theorems and Stein-like bounds for the asymptotic behaviour of nonlinear functionals of spherical Gaussian eigenfunctions. Our investigation combine asymptotic analysis of higher order moments for Legendre polynomials and, in addition, recent results on Malliavin calculus and Total Variation bounds for Gaussian subordinated fields. We discuss application to geometric functionals like the Defect and invariant statistics, e.g. polyspectra of isotropic spherical random fields. Both of these have relevance for applications, especially in an astrophysical environment.Comment: 24 page

The Study of Socio-Political Forecasting as a Factor in Improving the Quality of Training of Future Managers at the University

The paper studies the issues of improving the quality of training of future managers at the university. It is considered how the study of socio-political forecasting will contribute to the formation of their professional competencies. The features of forecasting, which are necessary for studying with students in the teaching of the humanities, are analyzed. The features of forecasts and models of socio-political development of Russia in various historical periods are studied.В работе изучаются вопросы повышения качества подготовки будущих управленцев в вузе. Рассматривается, как изучение вопросов социально-политического прогнозирования будет способствовать формированию их профессиональных компетенций. Анализируются особенности прогнозирования, которые необходимы для изучения со студентами в преподавании гуманитарных дисциплин. Изучаются особенности прогнозов и моделей социально-политического развития России в различные исторические периоды

Fractional oscillator process with two indices

We introduce a new fractional oscillator process which can be obtained as solution of a stochastic differential equation with two fractional orders. Basic properties such as fractal dimension and short range dependence of the process are studied by considering the asymptotic properties of its covariance function. The fluctuation--dissipation relation of the process is investigated. The fractional oscillator process can be regarded as one-dimensional fractional Euclidean Klein-Gordon field, which can be obtained by applying the Parisi-Wu stochastic quantization method to a nonlocal Euclidean action. The Casimir energy associated with the fractional field at positive temperature is calculated by using the zeta function regularization technique.Comment: 32 page

Genetic risk for alzheimer disease is distinct from genetic risk for amyloid deposition

OBJECTIVE: Alzheimer disease (AD) is the most common form of dementia and is responsible for a huge and growing health care burden in the developed and developing world. The polygenic risk score (PRS) approach has shown 75 to 84% prediction accuracy of identifying individuals with AD risk. // METHODS: In this study, we tested the prediction accuracy of AD, mild cognitive impairment (MCI), and amyloid deposition risks with PRS, including and excluding APOE genotypes in a large publicly available dataset with extensive phenotypic data, the Alzheimer's Disease Neuroimaging Initiative cohort. Among MCI individuals with amyloid-positive status, we examined PRS prediction accuracy in those who converted to AD. In addition, we divided polygenic risk score by biological pathways and tested them independently for distinguishing between AD, MCI, and amyloid deposition. // RESULTS: We found that AD and MCI are predicted by both APOE genotype and PRS (area under the curve [AUC] = 0.82% and 68%, respectively). Amyloid deposition is predicted by APOE only (AUC = 79%). Further progression to AD of individuals with MCI and amyloid-positive status is predicted by PRS over and above APOE (AUC = 67%). In pathway-specific PRS analyses, the protein-lipid complex has the strongest association with AD and amyloid deposition even when genes in the APOE region were removed (p = 0.0055 and p = 0.0079, respectively). // INTERPRETATION: The results showed different pattern of APOE contribution in PRS risk predictions of AD/MCI and amyloid deposition. Our study suggests that APOE mostly contributes to amyloid accumulation and the PRS affects risk of further conversion to AD

Humanization of Education and Improving the Quality of Teaching Students of Management Specialties

В статье рассматриваются вопросы повышения качества обучения студентов управленческих направлений подготовки. Одним из важных факторов данного процесса выступает гуманизация образования, включающая в себя внедрение различных элементов индивидуальных образовательных траекторий обучения. В работе рассматриваются проблемные аспекты внедрения индивидуальных образовательных траекторий в подготовке студентов управленческих специальностей. Подчеркивается важность грамотной организации воспитательно-педагогической работы с будущими управленцами.The article discusses the issues of improving the quality of teaching students in management training areas. One of the important factors of this process is the humanization of education, which includes the introduction of various elements of individual educational trajectories of learning. The paper deals with the problematic aspects of the implementation of individual educational trajectories in the training of students of management specialties. The importance of competent organization of educational and pedagogical work with future managers is emphasized

CULTURAL AND HISTORICAL MEMORY OF SOCIETY AND ITS IMPACT ON SOCIAL SECURITY: QUESTIONS OF STUDYING WITH STUDENTS

Культурно-историческая память общества является сложным феноменом для изучения. Особенности ее трансляции на различных уровнях общественного сознания могут как способствовать сплочению общества, направлять энергию населения на реализацию крупных проектов, так и приводить к негативным результатам и дезинтеграции. Преподавательский опыт авторов показывает, что современным студенчеством часто слабо осознается данная проблематика, что затрудняет рефлексию социально-политических и культурно-исторических событий. Предлагаются методы более доступного объяснения студентам данной проблематики.The cultural and historical memory of a society is a complex phenomenon to study. The features of its transmission at various levels of public consciousness can both contribute to the cohesion of society, direct the energy of the population to the implementation of large projects, and lead to negative results and disintegration. The teaching experience of the authors shows that modern students are often poorly aware of this issue. This makes it diffi cult to refl ect on socio-political and cultural-historical events. Methods for a more accessible explanation of this problem for students are proposed