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In this study, the authors introduce a solvability of special type of Langevin differential equations (LDEs) in virtue of geometric function theory. The analytic solutions of the LDEs are considered by utilizing the Caratheodory functions joining the subordination concept. A class of Caratheodory functions involving special functions gives the upper bound solution.

The methodology is based on the geometric function theory.

The authors present a new analytic function for a class of complex LDEs.

The authors introduced a new class of complex differential equation, presented a new technique to indicate the analytic solution and used some special functions.

The authors discover a new identity concerning differentiable mappings defined on m-invex set via fractional integrals. By using the obtained identity as an auxiliary result, some fractional integral inequalities for generalized relative semi- m-(r;h1,h2)-preinvex mappings by involving generalized Mittag-Leffler function are presented. It is pointed out that some new special cases can be deduced from main results of the paper. Also these inequalities have some connections with known integral inequalities. At the end, some applications to special means for different positive real numbers are provided as well.

Marx’s monetary theory is an important part of Marxist economics and an irreplaceable milestone in the intellectual history of the monetary theory. The purpose of this paper is to summarize the main content of Marx’s monetary theory from three aspects: the source and nature of money, the function of money and the historical significance of money.

Moreover, this paper also gives an extended understanding of Marx’s monetary theory from four perspectives: the endogenous credit mechanism of money, the functions of money and demands for money, the financial function of money and the economic and social functions of money.

Lastly, the present paper discusses the practical significance of Marx’s monetary theory from three perspectives, namely, the inspection of “Bitcoin” from the nature and function of money, the definition of demands and the division of supplies at the monetary level, and the prevention of systemic financial risks and the focus of financial supervision.

Marx’s monetary theory is an important part of Marxist economics and an irreplaceable milestone in the intellectual history of the monetary theory. However, for a long time, the contribution of Marx has rarely been mentioned in the intellectual history of monetary theory. Even the book, Political Economy (On Capitalism), has been only summarily concerned with the source and function of money in Marx’s monetary theory, rather than revealing Marx’s outstanding contribution in the monetary theory and the financial connotation of Marx’s monetary theory, and expounding its practical significance.

Diversity management is seen as a decisive factor for ensuring the development of socially responsible innovations (Beacham and Shambaugh, 2011; Sonntag, 2014; López, 2015; Uebernickel et al., 2015). However, many diversity management approaches fail due to a one-sided consideration of diversity (Thomas and Ely, 2019) and a lacking linkage between the prevailing organizational culture and the perception of diversity in the respective organization. Reflecting the importance of diverse perspectives, research institutions have a special responsibility to actively deal with diversity, as they are publicly funded institutions that drive socially relevant development and educate future generations of developers, leaders and decision-makers. Nevertheless, only a few studies have so far dealt with the influence of the special framework conditions of the science system on diversity management. Focusing on the interdependency of the organizational culture and diversity management especially in a university research environment, this chapter aims in a first step to provide a theoretical perspective on the framework conditions of a complex research organization in Germany in order to understand the system-specific factors influencing diversity management. In a second step, an exploratory cluster analysis is presented, investigating the perception of diversity and possible influencing factors moderating this perception in a scientific organization. Combining both steps, the results show specific mechanisms and structures of the university research environment that have an impact on diversity management and rigidify structural barriers preventing an increase of diversity. The quantitative study also points out that the management level takes on a special role model function in the scientific system and thus has an influence on the perception of diversity. Consequently, when developing diversity management approaches in research organizations, it is necessary to consider the top-down direction of action, the special nature of organizational structures in the university research environment as well as the special role of the professorial level as role model for the scientific staff.

Organizations are affected top-down by the overarching societies and bottom-up by foundational face-to-face encounters: societies provide norms, values, laws, institutions, beliefs, markets, political structures, and knowledge bases. What happens within organizations is done by people interacting with other people, arguing, discussing, convincing each other when preparing and making decisions. Organizations operate within social environments that leave their – however indirect – imprint on what is going on within organizations. This article argues that organizational sociology can benefit from an integrated theoretical framework that accounts for the embeddedness of organizations within the micro- and macro-levels of social order. The argument is developed in two main points: First, this article introduces the multilevel framework provided by Niklas Luhmann’s systems theory to demonstrate how organizations are shaped by the functionally differentiated macro-structure of society. Organizations follow and reproduce the operational logics of societal domains such as the political system, the economy, science, law, religion, etc. Second, this paper demonstrates how organizations are shaped by micro-level dynamics of face-to-face interactions. Face-to-face encounters form a social reality of its own kind that restricts and resists the formalization of organizational processes. Here, this article draws on Erving Goffman’s and Randall Collins’ work on interaction rituals, emotions, and solidarity, which is inspired by Durkheimian micro-sociology. At the end, this article brings together all the elements into one general account of organizations within the context of their macro- and micro-structural social environments. This account can yield a deeper and more sociological understanding of organizational behavior.

This study aims to use new formula derived based on the shifted Jacobi functions have been defined and some theorems of the left- and right-sided fractional derivative for them have been presented.

In this article, the authors apply the method of lines (MOL) together with the pseudospectral method for solving space-time partial differential equations with space left- and right-sided fractional derivative (SFPDEs). Then, using the collocation nodes to reduce the SFPDEs to the system of ordinary differential equations, which can be solved by the ode45 MATLAB toolbox.

Applying the MOL method together with the pseudospectral discretization method converts the space-dependent on fractional partial differential equations to the system of ordinary differential equations.

This paper contributes to gain choosing the shifted Jacobi functions basis with special parameters a, b and give the authors this opportunity to obtain the left- and right-sided fractional differentiation matrices for this basis exactly. The results of the examples are presented in this article. The authors found that the method is efficient and provides accurate results, and the authors found significant implications for success in the science, technology, engineering and mathematics domain.

The discrete Fourier transform (dft) of a fractional process is studied. An exact representation of the dft is given in terms of the component data, leading to the frequency domain form of the model for a fractional process. This representation is particularly useful in analyzing the asymptotic behavior of the dft and periodogram in the nonstationary case when the memory parameter d≥12. Various asymptotic approximations are established including some new hypergeometric function representations that are of independent interest. It is shown that smoothed periodogram spectral estimates remain consistent for frequencies away from the origin in the nonstationary case provided the memory parameter d < 1. When d = 1, the spectral estimates are inconsistent and converge weakly to random variates. Applications of the theory to log periodogram regression and local Whittle estimation of the memory parameter are discussed and some modified versions of these procedures are suggested for nonstationary cases.

Paley's and Hardy's inequality are proved on a Hardy-type space for the Fourier–Dunkl expansions based on a complete orthonormal system of Dunkl kernels generalizing the classical exponential system defining the classical Fourier series.

Although the difficulties related to the Dunkl settings, the techniques used by K. Sato were still efficient in this case to establish the inequalities which have expected similarities with the classical case, and Hardy and Paley theorems for the Fourier–Bessel expansions due to the fact that the Bessel transform is the even part of the Dunkl transform.

Paley's inequality and Hardy's inequality are proved on a Hardy-type space for the Fourier–Dunkl expansions.

This work is a participation in extending the harmonic analysis associated with the Dunkl operators and it shows the utility of BMO spaces to establish some analytical results.

Dunkl theory is a generalization of Fourier analysis and special function theory related to root systems. Establishing Paley and Hardy's inequalities in these settings is a participation in extending the Dunkl harmonic analysis as it has many applications in mathematical physics and in the framework of vector valued extensions of multipliers.

In this paper, the author introduces a degenerate exponential integral function and further studies some of its analytical properties. The new function is a generalization of the classical exponential integral function and the properties established are analogous to those satisfied by the classical function.

The methods adopted in establishing the results are theoretical in nature.

A degenerate exponential integral function which is a generalization of the classical exponential integral function has been introduced and its properties investigated. Upon taking some limits, the established results reduce to results involving the classical exponential integral function.

The results obtained in this paper are new and have the potential of inspiring further research on the subject.