Fractional-Order Logistic Differential Equation with Mittag–Leffler-Type Kernel

In this paper, we consider the Prabhakar fractional logistic differential equation. By using appropriate limit relations, we recover some other logistic differential equations, giving representations of each solution in terms of a formal power series. Some numerical approximations are implemented by using truncated series.

Kewenangan Kejaksaan dalam Melakukan Penahanan Terhadap Pelaku Tindak Pidana Ujaran Kebencian di Sosial Media

Authority is what is called formal power, power comes from legislative power (given by law) or from executive administrative power. Authority, which usually consists of several powers, is power over a certain group of people or power over an area of ​​government. The purposes of this study are to analyze the arrangement of the prosecutor's authority in detaining the perpetrators of hate speech crimes on social media and the prosecutor's obstacles in detaining the perpetrators of hate speech crimes on social media. The research method applied in this research is normative legal research with a statutory and a conceptual approach. The technique of collecting legal materials is done by means of a literature study. The of used are primary, secondary, and tertiary sources of legal materials. After the legal material has been collected, it will then be processed and analyzed using the method of processing legal materials systematically and presented descriptively. The results of the study reveal that the prosecutor's authority is regulated in the criminal procedural law code, the prosecutor's authority law. Which includes several laws, among others, Law no. 16 of 2004 which regulates the prosecutor's office, so that from the law it can be ascertained about the rights and powers of the prosecutor so that law enforcers, especially the prosecutor's office, can make detentions in accordance with the rules that have been in force, so that there is no abuse of authority by law enforcers, especially prosecutors and as The prosecutor's office should be obliged to realize equality for all Indonesian citizens who are being entangled in criminal, civil and other cases.

Leading With Compassion: A Story of Women Grassroots Leadership Amidst COVID-19 and Coastal Flooding

This article elaborates on two important elements of women's leadership. First, it explores how leadership theory has abandoned its masculine perspective in favour of a "more feminine" one. The COVID-19 pandemic, a crisis that crippled the socio-political structure, has contributed to this shift. Second, the experiences of grassroots leaders who are active in the domestic sphere have begun to be considered, as has their increased activeness in the public sphere during the COVID-19 pandemic. However, studies of women's leadership are highly elitist; such a paradigm is problematic, as it prioritises formal power structures and ignores the grassroots leaders who play a central role in maintaining the social order. This research finds that the pandemic has provided a valuable impetus not only for studies of formal elites but also women at the grassroots. Women have become highly powerful agents in the domestic sphere during the pandemic, and even expanded their agency into the public sphere. Women leaders have facilitated the implementation of government and community crisis response measures at the grassroots level.

Between Horizontality and Centralisation: Organisational Form and Practice in the Finns Party

This article provides the first comprehensive analysis of the Finns Party’s (Perussuomalaiset [PS]) formal organisation and how it operates in practice. Following the framework of this thematic issue, to what extent does the PS’s organisation follow the mass-party model and how centralised is the party in its internal decision-making? Analysis of party documents, association registries, and in-depth interviews with 24 party elite representatives reveal that the PS has developed a complex organisational structure and internal democracy since 2008. However, the power of members in regard to the party’s internal decision-making remains limited, despite the party’s leadership having facilitated a more horizontal and inclusionary organisational culture after 2017. The study reveals how the party combines radically democratic elements of its leadership selection and programme development with a very high level of centralisation of formal power in the party executive, and how the party organisationally relies on a vast and autonomous but heterogeneous network of municipal associations. The article also discusses how PS elites perceive the advantages of having a wide and active organisation characterised by low entry and participation requirements, and how party-adjacent online activism both complements and complicates the functioning of the formal party organisation.

Bell Polynomials and Nonlinear Inverse Relations

By means of the Lagrange expansion formula, we establish a general pair of nonlinear inverse series relations, which are expressed via partial Bell polynomials with the connection coefficients involve an arbitrary formal power series. As applications, two examples are presented with one of them recovering the difficult theorems discovered recently by Birmajer, Gil and Weiner (2012 and 2019).

The Spectrum of Mapping Ideals of Type Variable Exponent Function Space of Complex Variables with Some Applications

The topological and geometric behaviors of the variable exponent formal power series space, as well as the prequasi-ideal construction by s -numbers and this function space of complex variables, are investigated in this article. Upper bounds for s -numbers of infinite series of the weighted n th power forward and backward shift operator on this function space are being investigated, with applications to some entire functions.

ON TRANSCENDENTAL CONTINUED FRACTIONS IN FIELDS OF FORMAL POWER SERIES OVER FINITE FIELDS

In the field of formal power series over a finite field, we prove a result which enables us to construct explicit examples of $U_{m}$ -numbers by using continued fraction expansions of algebraic formal power series of degree $m>1$ .

A Combinatorial Approach to the Stirling Numbers of the First Kind with Higher Level

In this paper, we investigate a generalization of the classical Stirling numbers of the first kind by considering permutations over tuples with an extra condition on the minimal elements of the cycles. The main focus of this work is the analysis of combinatorial properties of these new objects. We give general combinatorial identities and some recurrence relations. We also show some connections with other sequences such as poly-Cauchy numbers with higher level and central factorial numbers. To obtain our results, we use pure combinatorial arguments and classical manipulations of formal power series.