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AbstractLet F be a field. We study the structure of finite groups G for which the socle of the center of the group algebra FG is an ideal in FG. In previous work (Brenner-Külshammer, 2024), we studied which general implications this ring-theoretic property of FG has on the structure of G. In the present article, we now focus on a detailed structural analysis of the groups with this property. We showcase its strength by deriving a complete classification for a prototype class of groups. [ABSTRACT FROM AUTHOR]

The chain group Ch(G) of a locally compact group G has one generator g ρ for each irreducible unitary G-representation ρ, a relation g ρ = g ρ ′ g ρ ″ whenever ρ is weakly contained in ρ ′ ⊗ ρ ″ , and g ρ * = g ρ − 1 for the representation ρ * contragredient to ρ. G satisfies chain-center duality if assigning to each g ρ the central character of ρ is an isomorphism of Ch(G) onto the dual Z (G) ̂ of the center of G. We prove that G satisfies chain-center duality if it is (a) a compact-by-abelian extension, (b) connected nilpotent, (c) countable discrete icc or (d) connected semisimple; this generalizes M. Müger's result compact groups satisfy chain-center duality. [ABSTRACT FROM AUTHOR]

The goal of the research is to discover the required and sufficient conditions for R(I) to be a neutrosophic regular as well as the properties of the neutrosophic ideals in the neutrosophic regular ring. Despite differences in the form of the elements and ideals in neutrosophic and classical rings, we discovered that the necessary and sufficient requirements for the classical ring to be regular also apply to neutrosophic rings. [ABSTRACT FROM AUTHOR]

We give a classification of noncommutative algebraic monoid structures on normal affine varieties such that the group of invertible elements of the monoid is connected, solvable, and has a one-dimensional unipotent radical. We describe the set of idempotents and the center of such a monoid and give a criterion for existence of the zero element. [ABSTRACT FROM AUTHOR]

Objective: There are limited data examining the relationship between transplant center volume and their use of Status 2 exceptions for heart transplant (OHT). Methods: A retrospective review of the Organ Procurement and Transplantation Network (OPTN) database identified all patients undergoing OHT under Status 2 exception between late 2018 and early 2023. Demographics were collected and transplant centers were categorized based on the number of OHT performed annually (very low volume = < 5 OHT per year; low volume = 5–24 OHT per year; medium volume = 25–50 OHT per year, high volume = > 50 OHT per year). Results: Across all centers, 6348 OHT were included, with n = 68 performed at very low volume centers, n = 1001 performed at low volume centers, n = 1834 performed at medium volume centers, and n = 3445 performed at high volume centers. Medium and high volume centers applied for at least one Status 2 exception about 30%–35% of the time, compared to 50%–60% of the time observed at very low and low volume centers. Compared to very low volume centers, medium volume centers applied for half the amount of Status 2 exceptions (IRR = 0.52 [0.35–0.76]; p < 0.001) while high volume centers applied for less than half the amount (IRR = 0.42 [0.29–0.62]; p < 0.001). High‐volume centers were also 18% less likely to apply for exceptions than medium‐volume centers (IRR = 0.82 [0.74–0.91]; p < 0.001). Conclusions: Lower volume transplant centers apply for Status 2 exceptions at a significantly higher rate, with a stepwise decrease in exception use with increasing transplant center volume. [ABSTRACT FROM AUTHOR]

After fixing a commutative ring with unit R, we present the definition of adequate category and consider the category of R-linear functors from an adequate category to the category of R-modules. We endow this category of functors with a monoidal structure and study monoids (generalized Green functors) over it. For one of these generalized Green functors, we define two new monoids, its commutant and its center, and study some of their properties and relations between them. This work generalizes the article [3]. [ABSTRACT FROM AUTHOR]

Consider the family of polynomial differential systems of degree 3, or simply cubic systems x ′ = y , y ′ = - x + a 1 x 2 + a 2 x y + a 3 y 2 + a 4 x 3 + a 5 x 2 y + a 6 x y 2 + a 7 y 3 , in the plane R 2 . An equilibrium point (x 0 , y 0) of a planar differential system is a center if there is a neighborhood U of (x 0 , y 0) such that U \ { (x 0 , y 0) } is filled with periodic orbits. When R 2 \ { (x 0 , y 0) } is filled with periodic orbits, then the center is a global center. For this family of cubic systems Lloyd and Pearson characterized in Lloyd and Pearson (Comput Math Appl 60:2797–2805, 2010) when the origin of coordinates is a center. We classify which of these centers are global centers. [ABSTRACT FROM AUTHOR]

Peja has a great history with cultural sights and natural beauty, and it is a place that always offers warm hospitality and attractive social tourism innovations. Peja has all the right potential for a tourist destination, such as natural beauties, cultural heritage, and hospitality. Tourism is a very profitable sector for our country because it is directly related to the well-being and economic growth of the local community. Tourism is a sector that can guarantee sustainable economic development, providing employment, promotion of businesses, more income and more well-being for the citizens of the country and the community. This study was carried out through the design and implementation of 195 (one hundred and fifty-five) questionnaires. The study uses ethnographic design based on case studies. The promotion of tourism for our country will serve as an orientation opportunity for all local and foreign tourists who intend to visit these natural beauties and beautiful scenery in Kosovo. Precisely because tourism plays an important role, and the role plays in the well-being of the local community, the government of our country should continuously pay attention to promoting sustainable tourism in Kosovo. [ABSTRACT FROM AUTHOR]

A global center for a vector field in the plane is a singular point p having R 2 filled of periodic orbits with the exception of the singular point p. Polynomial differential systems of degree 2 have no global centers. In this paper we classify the global nilpotent centers of planar cubic polynomial Hamiltonian systems symmetric with respect to the y-axis. [ABSTRACT FROM AUTHOR]

University-based centers and institutes can play an important role in facilitating community-based, inter- and transdisciplinary research, and providing the capacity and expertise to address pressing issues. However, many centers and institutes face challenges related to long-term stability and resilience. In this paper we share recommendations on how to support centers and institutes that focus on food systems transformation. We drew these recommendations from insights and stories shared by leaders of nine diverse centers and institutes that participate in the Inter-Institutional Network for Food, Agriculture, and Sustainability (INFAS). We discuss how they are structured, the work they have done, and the benefits of that work, as well as the challenges they have faced and what they recommend for addressing those challenges. Their primary challenges include cultivating the support of university administrators and faculty, hiring and retaining supportive faculty, and securing sustainable funding. We provide a diverse range of recommendations to address each of these challenges, with the hope that other centers and institutes can find some that will be relevant to their particular institutional, social, and political contexts. [ABSTRACT FROM AUTHOR]

In this paper we provide a review of the concept of center of an n-gon, generalizing the original idea given by C. Kimberling for triangles. We also generalize the concept of central line for n-gons for n ≥ 3 and establish its basic properties. [ABSTRACT FROM AUTHOR]

The aim of this work is to give conditions on the parameters of a family of analytic planar vector fields with a fixed Newton diagram and a monodromic singularity in order to guarantee that the coefficient (generalized first Lyapunov constant) of the linear part of the Poincaré map has an explicit formula that depends only on the Newton diagram. As far as we know, all the monodromic classes appearing in the literature satisfy that formula. [ABSTRACT FROM AUTHOR]

Let (G,+) be a finite group, written additively with identity 0, but not necessarily abelian. Let T = {Hi} be a nonempty collection of nonzero, proper subgroups of G. Then N = {f: G ! G | f(0) = 0 and f(Hi) = Hi for all i} is a nearring under pointwise addition and function composition. We determine when N is abelian and distributive, identify the center of N, and find necessary and sufficient conditions for the center to be a subnearring of N. [ABSTRACT FROM AUTHOR]

In this paper, we obtain a basis for the center of the infinitesimal q-Schur algebra s q (2 , r) 1 in terms of its certain basis. [ABSTRACT FROM AUTHOR]

Suppose G is a finite non-abelian group and (G) is a graph with non-central conjugacy classes of G as its vertex set. Two vertices L and K in such that ab = ba. This graph is called the commuting conjugacy class graph of G. The purpose of this paper is to compute the commuting conjugacy class graph of the finite 2 such that ab = ba. This graph is called the commuting conjugacy class graph of G. The purpose of this paper is to compute the commuting conjugacy class graph of the finite 2-group Gm(n) and G(n). [ABSTRACT FROM AUTHOR]

In this paper, we study the bifurcation of limit cycles, centers, and isochronous centers for a class of three-dimensional Kukles systems of degree 3. Through calculating the singular point quantities, we obtain a necessary condition for the origin to be a center, then the Darboux integrability theory is used to prove that the necessary condition is also sufficient. Then, we demonstrate that the origin is an isochronous center under the obtained center condition. Finally, we determine that the highest order of the origin to be a weak focus is ten, while the maximum number of small-amplitude limit cycles bifurcating from this weak focus is nine. Moreover, we show that this maximum number of 9 can be realized. It is worthwhile to say that this number is also a new lower bound on the number of limit cycles bifurcating from the single weak focus for three-dimensional cubic polynomial systems. [ABSTRACT FROM AUTHOR]

An element in a ring R is called CJ if it is of the form c+j, where c belongs to the center and j is an element from the Jacobson radical. A ring R is called CJ if each element of R is CJ. We establish the basic properties of CJ rings, give several characterizations of these rings, and connect this notion with many standard elementwise properties such as clean, uniquely clean, nil clean, CN, and CU. We study the behavior of this notion under various ring extensions. In particular, we show that the subring C + J is always a CJ ring and that if R[x] is a CJ ring then R satisfies the Köthe conjecture. [ABSTRACT FROM AUTHOR]

In this paper, we obtain a basis for the center of the infinitesimal q-Schur algebra s q (2 , r) 1 in terms of its certain basis. [ABSTRACT FROM AUTHOR]

The presence of war refugee camps around the world and their development into places of political resistance for identity formation, alternate governance systems and lives has been part of academic studies for quite some time now. Less attention has been paid to frame refugee camp spaces for studying the complexity of the concepts of resistance and indifference for reclamation of human identity. Despite attention to the mass movement of refugeesasylum seekers, there is a huge gap in scholarship to understand the center-controlled and marginalized refugee existence in camps because refugees are often silenced, insignificant obscure figures in the grand war discourse of reports and case studies—lives not worth saving. Furthermore, refugees’ resistance against the center’s anti-humanity beliefs, ideologies and practices calls for a reengagement with the camp space because it has become a source of material and knowledge production for the center to profile and subject all types of refugees to any physical, mental and psychological testing-experimentation whenever it develops a new weapon, therapy, theory or technology. This paper intends to cover these gaps and build its analysis of a refugee camp, through the text Red Birds (2018).

The article presents an analytical review of the development of the core-periphery and peripherality concepts in economic theory. The stages of formation of the core-periphery approach are marked by the contributions of the school of Latin American structuralism, theories of polarized development, dependency theory and world-system theory associated with the names of R. Prebisch, J. Friedmann, F. Perroux, S. Furtado, I. Wallerstein. The core-periphery concept has proved to be a useful analytical tool in studies of international trade and economic growth in the world economy. At the same time, uneven structures of distribution of economic activity in space, similar to the core-periphery structure, appear in many models of regional economy, starting with the model of agricultural production location by I. Thunen and ending with the core-periphery model by P. Krugman. These structures emerge without the help of the core-periphery concept, but as a result of the interaction of two fundamental factors – transport costs and economies of scale – and represent various combinations of dispersion and agglomeration. With regional inequality growing worldwide, the combination of the core-periphery approach and basic concepts of regional economics allows us to analyze the complex mechanisms of spatial polarization of economic space. Over time, the periphery has gone beyond the core-periphery dichotomy and developed into an independent category defined, defined by a combination of low accessibility of large markets, low population density and remoteness from decision-making centers. The concept of peripherality allows us to understand the processes of peripheralisation of previously prosperous territories through the interaction of power asymmetry and agglomeration effects

The maximum number of centers is an open problem proposed by Gasull for planar polynomial differential systems of degree n with n ≥ 4. In this paper we study the problem for planar polynomial Kolmogorov differential systems of degree n , prove that the maximum number of centers is exactly seven for planar quartic polynomial Kolmogorov differential systems, and give the upper and lower bound for the maximum number of centers that the Kolmogorov differential systems of degree n can have. [ABSTRACT FROM AUTHOR]

Objectives The aim of the article is analysis the causes of differences in the regional development of Greater Poland and Warmia and Mazury. Material and methods The study used the methodology used in the science of politics and administration, using the comparative method, the systemic method and the historical method. Results The disproportions between dynamically developing areas and territories that cannot keep up with development are noticeable. The progressive polarization in this area requires analysis to explain the etiology of this phenomenon. The example of Wielkopolska and Warmia and Mazury clearly shows the differences in the development of the region which is the center and the peripheral region. Conclusions Wielkopolska and Warmia and Mazury are characterized by significant differences in the level of regional development. This is due to many factors. Historical conditions and geographical location of both regions play an important role. Another group of factors is the specificity of regions, which is determined by the topography, demography, degree of urbanization and the condition of economic and road infrastructure. The analysis of etiological factors may be the starting point for considerations about the possibilities of eliminating regional differences.

Examining the development of port cities has been highlighted in the process of “sea-based development.” Given their opportunities and capacities for facilitating development objectives, the ports are among the strategic and desirable projects that have been incorporated into land development plans. As a result, they contribute to the prosperity of sea-based industry and trade in a specific geographical area thanks to the increase in sea utilization. The outcome is the production of a tool and machine model that monopolizes the model of city development and its iconography. The concern of this study is the elements of the spatial organization of a port city, including contemporary life within the city, the contextual and physical transformation brought up by the sea-based development within the city, or the context where there is a connection between the city and the ports. This research employed a qualitative method with a descriptive and analytical approach, and data were collected through field observations and library and document studies. The research attempts to investigate the regulatory structural components, including the center, structure, territory, and small groups in the city of Bandar Abbas. As a result of this interaction, the relationships among the elements of the space organization are under threat. The construction of new neighborhoods just to accommodate immigrants has distorted the face of the city and made the urban structure useless. The structure of the city of Bandar Abbas is no longer dependent on the system of estuaries and coastal terraces but on the system of ports and the settlement of the immigrant population. Among these pillars, the core has lost its subjective and conceptual meaning as defined by the sea and has emerged only in the form of a physical thing in the market of the city. The transformation of the city of Bandar Abbas into the hinterland of Shahr-Bandar Shahid Rajaei has turned the communication corridors between the two into service corridors and has faded the concept of the road landscape and weakened the connection with the sea.

After the Ministry of Education proposed the initiative to develop the future learning center, Shandong University Library conducted in-depth practical explorations from four dimensions: new spatial view, new literature and information resource view, new service view, and new team view, based on the investigation and analysis of the practical experience of peer libraries nationwide. The aim was to promote the transformation and development of university libraries, better serve the reform of higher education and talent cultivation work. Progress has been made in several fields so as to enrich the theoretical cognition and practical experience of future learning center development. [ABSTRACT FROM AUTHOR]

We characterize the structure of a seven-dimensional Lie algebra with non-trivial center endowed with a closed G2-structure. Using this result, we classify all unimodular Lie algebras with non-trivial center admitting closed G2-structures, up to isomorphism, and we show that six of them arise as the contactization of a symplectic Lie algebra. Finally, we prove that every semi-algebraic soliton on the contactization of a symplectic Lie algebra must be expanding, and we determine all unimodular Lie algebras with center of dimension at least two that admit semi-algebraic solitons, up to isomorphism. [ABSTRACT FROM AUTHOR]

Let G be a finite p-group. Then G is said to be a CZ-group if HG ≤ Z(G) for every nonnormal subgroup H of G. In this paper, we study the CZ-group G and get c(G) ≤ 3. It is proved that exp(G′) = p if c(G) = 2 and |G|≤ p5 if c(G) = 3. [ABSTRACT FROM AUTHOR]

A family of sets is called a star if there exists an element (a center) in each of its sets. Given a graph G and an integer r ⩾ 1 , let I r (G) be the family of independent sets of size r of G. A star S of I r (G) is maximum if no star of I r (G) is bigger than S. In 2011, Hurlbert and Kamat conjectured that in trees there exists a maximum star of I r (G) that is centered at a leaf for any r , and they also showed that this conjecture is true for r ⩽ 4. In 2021, Estrugo and Pastine proposed the following problem: Find which leaves are the centers of the maximum stars in caterpillars. In this contribution, we consider the problem on the maximum star of I r (G) for a connected graph G with at least one leaf. Firstly, we show that in unicyclic graphs with at least one leaf there exists a maximum star of I r (G) that is centered at a leaf for r ⩽ 4 , and there exists a counterexample in which the maximum star of I r (G) is not centered at a leaf for r ⩾ 5. Secondly, we show that in connected graphs having at least one leaf and at least two cycles, there exist two counterexamples in which the maximum stars of I r (G) are not centered at leaves for r ⩾ 3. Finally, we determine the centers of the maximum stars of I r (G) for three types of caterpillars, which partially solves the problem proposed by Estrugo and Pastine. [ABSTRACT FROM AUTHOR]

• Music may offer physiological and psychological impacts on humans. • Establishing centers of music for health in academia can help develop inter-disciplinary approaches to unravel the power of music. • Raising awareness about the potential health benefits of music can lead to further studies and the establishment of guidelines for employing music in health settings. A multitude of clinical trials measuring hemodynamic and psychological parameters have shown the beneficial effects of music on health. However, there are no clear instructions on how to utilize the potential benefits of music to improve health outcomes. Moreover, whether the effect of music is transient or enduring has yet to be determined. To address the effect of music on vital parameters and emotional well-being of patients we provide an overview of methods and findings of some studies that have evaluated the physiological or psychological impacts of music. This review puts forward a proposed model for fostering an individualized approach that can examine the therapeutic effects of music. [ABSTRACT FROM AUTHOR]

In this paper, we study the center-focus problem for a generalized cubic Kukles system with a nilpotent singular point, which consists of a cubic system with an extra 4th-order term. A complete classification is given on the center conditions which are explicitly expressed in term of the system parameters. A total of 15 cases are obtained, among them 4 for the generalized cubic Kukles system and 12 for the cubic Kukles system, with one common for both. One of the center conditions is analytic. Moreover, it is shown that 8 small-amplitude limit cycles can bifurcate in the neighborhood of the singular point for the generalized cubic Kukles system, while only 7 small-amplitude limit cycles can exist around the singular point for the cubic Kukles system. The center-focus problem for the generalized cubic Kukles system with a nilpotent origin is thoroughly solved. [ABSTRACT FROM AUTHOR]

This paper is an expository one on necessary and sufficient conditions for the real Jacobian conjecture, which states that if F = f 1 , … , f n : R n → R n is a polynomial map such that det D F ≠ 0 , then F is a global injective. In Euclidean space R n , the Hadamard’s theorem asserts that the polynomial map F with det D F ≠ 0 is a global injective if and only if ‖ F x ‖ approaches to infinite as ‖ x ‖ → ∞ . The first part of this paper is to study the two-dimensional real Jacobian conjecture via Bendixson compactification, by which we provide a new version of Sabatini’s result. This version characterizes the global injectivity of polynomial map F by the local analysis of a singular point (at infinity) of a suitable vector field coming from the polynomial map F. Moreover, applying the above results we present a dynamical proof of the two-dimensional Hadamard’s theorem. In the second part, we give an alternative proof of the Cima’s result on the n-dimensional real Jacobian conjecture by the n-dimensional Hadamard’s theorem. [ABSTRACT FROM AUTHOR]

It is known that rank‐two bimolecular mass‐action systems do not admit limit cycles. With a view to understanding which small mass‐action systems admit oscillation, in this paper we study rank‐two networks with bimolecular source complexes but allow target complexes with higher molecularities. As our goal is to find oscillatory networks of minimal size, we focus on networks with three reactions, the minimum number that is required for oscillation. However, some of our intermediate results are valid in greater generality. One key finding is that an isolated periodic orbit cannot occur in a three‐reaction, trimolecular, mass‐action system with bimolecular sources. In fact, we characterize all networks in this class that admit a periodic orbit; in every case, all nearby orbits are periodic too. Apart from the well‐known Lotka and Ivanova reactions, we identify another network in this class that admits a center. This new network exhibits a vertical Andronov–Hopf bifurcation. Furthermore, we characterize all two‐species, three‐reaction, bimolecular‐sourced networks that admit an Andronov–Hopf bifurcation with mass‐action kinetics. These include two families of networks that admit a supercritical Andronov–Hopf bifurcation and hence a stable limit cycle. These networks necessarily have a target complex with a molecularity of at least four, and it turns out that there are exactly four such networks that are tetramolecular. [ABSTRACT FROM AUTHOR]

The definitions of stored gravitational energy are given. The value of the limited gravitational energy of two massive mutually nonpenetrating balls is calculated. It is established that the stored gravitational energy is always positive. A formula is presented for the maximum possible gravitational energy of two massive balls, which can be used to estimate the energy of the merger of space objects, in particular, gaseous, dusty, and plasma, as well as for ballistic calculations of space flights. [ABSTRACT FROM AUTHOR]

A Lie algebra g is considered generalized reductive if it is a direct sum of a semisimple Lie algebra and a commutative radical. This paper extends the BGG category O over complex semisimple Lie algebras to the category O ′ over complex generalized reductive Lie algebras. Then, we preliminarily research the highest weight modules and the projective modules in this new category O ′ , and generalize some conclusions for the classical case. Also, we investigate the associated varieties with respect to the irreducible modules in O ′ and obtain a result that extends Joseph's result on the associated varieties for reductive Lie algebras. Finally, we study the center of the universal enveloping algebra U(g ) and independently provide a new proof of a theorem by Ou–Shu–Yao for the center in the case of enhanced reductive Lie algebras. [ABSTRACT FROM AUTHOR]

We study the center of two-parameter quantum supergroup U r , s (o s p (1 , 2)) using the Dickson polynomial. We show that the Scasimir operator is completely determined by the q -deformed Chebychev polynomial, generalizing an earlier work of Arnaudon and Bauer. [ABSTRACT FROM AUTHOR]

Copyright of Journal of Modern Science is the property of Alcide De Gasperi University of Euroregional Economy and its content may not be copied or emailed to multiple sites or posted to a listserv without the copyright holder's express written permission. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract. (Copyright applies to all Abstracts.)

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ABSTRACT: The concept of "the Other" is intensely present in the writings of Malika Mokeddem, manifesting as the foreigner, the close one, the lover, and the friend, whether as a central figure or a marginal one. This diverse representation contributes to varying perspectives and highlights the stance on the vital features of society, its human formations, hierarchical structures, and its political, social, and especially cultural systems in postmodern discourses. This research employs cultural criticism to observe the manifestations of the relationship with "the Other" in the novel "My Men" and the techniques that expose the implicit cultural patterns that direct this social hierarchy. The research findings reveal that the novel seeks to rearrange positions and distribute roles to place itself at a central point that moves the Other as a silent follower. In a further act of defiance, the work is not merely a fictional novel but an autobiographical one, expressing a strong desire to make this fiction a reality, thus challenging the political and religious authorities and the Arab social system. الملخص: يحضر الآخر في كتابات مليكة مقدم بشكل مكثّف فهو الأجنبي، وهو القريب والحبيب والصديق مركزا كان أو هامشا، واستثمار هذا الاستحضار المتنوّع يسهم في تنويع زاوية الرؤية، وإبراز الموقف من الملامح الحيوية للمجتمع وتشكيلاته البشرية، وبنياته التراتبية، ونظمه السياسية والاجتماعية وبخاصة الثقافية في الخطابات ما بعد الحداثية. وينطلق هذا البحث من مقولات النقد الثقافي هادفا إلى رصد تمظهرات علاقتها بالآخر في رواية "رجالي"، والفنيات التي عرّت بها الأنساق الثقافية المضمرة الموجِهة لهذه التراتبية الاجتماعية، وقد بيّنت نتائج البحث أنها كانت تعمد إلى إعادة ترتيب المواقع وتوزيع المهام، لتتموقع في مركز جوهري يحرّك الآخر كتابع مغيّب الصوت، وأنها إمعانا منها في التحدي لا تجعل العمل تخييلا روائيا بحتا بل عملا سيرذاتيا، معلنة رغبة قوية في جعل هذا التخييل بكل تفاصيله واقعا، تحقيقا لرغبة مناوشة السلطة السياسية والدينية، والمنظومة الاجتماعية العربية.

This article is based on the results of a comprehensive research on the religiosity experiences of students in the public sphere of the Middle East Technical University (METU) in Türkiye. The research examines the multifaceted behavioral practices, categories and tactics of religious students in the context of an academic institution that has historically been shaped by a secular tradition. Through in-depth interviews with religious students at METU, this study examines how these students participate in public life on campus, where they find their place in the public space, and the areas they deliberately avoid. The study seeks to understand how these individuals maintain their religious identity, maintain their religious feelings and sense of belonging, and ultimately overcome the challenges posed by a predominantly secular environment. Phenomenological approach and purposive sampling technique from qualitative research approaches were used in the research. The data were obtained from in-depth interviews with 18 students studying at METU through a semistructured interview form. Based on the data obtained, the behavioral practices and tactics of religious students were categorized in three different areas: center, periphery and semiperiphery. It has been observed that each of these areas has different cultural characteristics, relations among themselves and various forms of being. The findings highlight that the METU public sphere resists the political and cultural inclusion of religious actors and practices, insisting on preserving its secular and culturally exclusionary character. As an institution with a secular tradition, METU has developed a secular public space where religious students, who are considered as the "other", are politically and culturally marginalized. The data show that the dominant culture and lifestyles in these public spaces are significantly far from religiosity and sometimes lead to overreaction, marginalization and exclusion, which can be characterized as secular. By presenting a detailed examination of the typologies and tactics adopted by religious individuals settled in these regions, the article further strengthens our understanding of their experience within the secular public sphere of METU. Students who choose to be in the center of METU's public space present a typology that adapts to current practices under the influence of secular actors and practices there. On the other hand, students who prefer to be in the environment try to stay away from METU's secular actors and practices as much as possible and resist adapting through very religious practices. Students who chose to be in the middle of these two areas developed a contextual and hybrid self. These students sometimes show harmony and sometimes resistance, and present a lifestyle that is compatible with both secular actors and practices and religious actors and practices. In this way, actors and practices that vary according to fields interact and are affected by each other from time to time. Therefore, the typology and practices developed may vary depending on the context. However, an emerging fact is that the representation of Islamic lifestyles at the center of these public spaces has turned out to be rather weak compared to secular orientations. It has been concluded that the areas where Islam is practiced freely and without tension are the environmental areas where places such as mosques are located. As a result, it has been revealed that rather different religious typologies and practices have been developed in secular public spaces instead of a uniform religiosity and practices. [ABSTRACT FROM AUTHOR]

Skew braces are algebraic structures related to the solutions of the set-theoretic quantum Yang–Baxter equation. We develop the central nilpotency theory for such algebraic structures in the sense of Freese–McKenzie [12] and we compare the universal algebraic notion of central nilpotency with the notion of right and left nilpotency developed in [7]. [ABSTRACT FROM AUTHOR]

Let \mathbb {G} be a Lie group with solvable connected component and finitely-generated component group and \alpha \in H^2(\mathbb {G},\mathbb {S}^1) a cohomology class. We prove that if (\mathbb {G},\alpha) is of type I then the same holds for the finite central extensions of \mathbb {G}. In particular, finite central extensions of type-I connected solvable Lie groups are again of type I. This is in contrast to the general case, whereby the type-I property does not survive under finite central extensions. We also show that ad-algebraic hulls of connected solvable Lie groups operate on these even when the latter are not simply connected, and give a group-theoretic characterization of the intersection of all Euclidean subgroups of a connected, simply-connected solvable group \mathbb {G} containing a given central subgroup of \mathbb {G}. [ABSTRACT FROM AUTHOR]

For a three-dimensional chaotic system, little seems to be known about the perturbation of invariant algebraic surface and the center on this surface. This question is very interesting and worth investigating. This paper is devoted to analyzing the limit cycles from perturbed center (trivial and nontrivial equilibria) on the invariant algebraic surface of the unified Lorenz-type system (ULTS), which contains some common chaotic systems as its particular cases. First, based on the parameter-dependent center manifold, we obtain the approximate two-dimensional center manifold from the perturbation of invariant algebraic surface, as well as the two-dimensional system on this center manifold. Second, by applying the averaging method of third order to the above two-dimensional system, we show that under suitable perturbation of parameters of the ULTS, there is one limit cycle bifurcating from the perturbed center on the invariant algebraic surface of the ULTS, and the stability of this limit cycle is determined as well. By using the averaging method of fourth order, we show the same results with the averaging method of third order. Finally, numerical simulation is used to verify the theoretical analyses. [ABSTRACT FROM AUTHOR]

Let Y M | N (s) be the super Yangian associated with an arbitrary fixed 0 M 1 N -sequence s. In the present paper, we give a new formula for the quantum Berezinian by using the parabolic generators, which generalizes the usual expression in terms of RTT generators or Drinfeld generators. [ABSTRACT FROM AUTHOR]

Jacobson investigated the structure of rings with the property that some power of each element is central, in the procedure of the study of commutativity. In this paper, we consider a class of rings in which this property occurs only for central elements, and such rings are called ppnc. We first prove that a noncommutative ppnc ring is infinite, and that a ppnc ring is commutative when it is a K-ring or a locally finite ring. We next study the structure of ppnc rings, and the relation between ppnc rings and related concepts (for example, K-rings, commutative rings and NI rings), through matrix rings, polynomial rings, right quotient rings and direct products. [ABSTRACT FROM AUTHOR]

A center for a differential system x ˙ = f (x) in R 2 is a singular point p having a neighborhood U such that U \ { p } is filled with periodic orbits. A global center is a center p such that R 2 \ { p } is filled with periodic orbits. There are three kinds of centers, the centers p such that the Jacobian matrix Df(p) has purely imaginary eigenvalues, the nilpotent centers p such that Df(p) is a nilpotent matrix, and the degenerate centers p such that the matrix Df(p) is the zero matrix. For the first class of centers there are several works studying when such centers are global. As far as we know there are no works for studying the nilpotent global centers. One of the most studied classes of differential systems in R 2 are the polynomial Liénard differential systems. The objective of this paper is to study the nilpotent global centers of the polynomial Liénard differential systems. [ABSTRACT FROM AUTHOR]

The "center" is a key concept in early Chinese philosophy. While readings of the Laozi 老子 and Zhuangzi 莊子 often rely on concepts of "nature" and the "natural", this article proposes the "center" as an interpretive key that informs discussion of contemporary issues while remaining faithful to the core concerns of the texts. While both texts use the "center" to promote a philosophy of moderation, in the Laozi, "holding to the center" (shou zhong 守中) refers to a focus on one's inner center to counteract the dangers of the external, whereas the Zhuangzi speaks of a centeredness between inner cultivation and outward socialization. In the Laozi, we examine images of one-, two- and three-dimensional centers as well as the bodily practice of focusing on the inner stomach rather than the outward-looking eyes. Our discussion of the Zhuangzi focuses on occupying the "center" (zhongyang 中央) between extreme inward and outward modes of being. The result is a philosophy of moderation that fosters a sense of humility, balance, and impartiality, cautioning against a drive for overreaching solutions for all humanity, and tempering attempts to conform to extreme "naturalness" or reject all "artificiality". [ABSTRACT FROM AUTHOR]