Fundamental Identity Research Articles

Bi-Periodic (p,q)-Fibonacci and Bi-Periodic (p,q)-Lucas Sequences

In this paper, we define bi-periodic (p,q)-Fibonacci and bi-periodic (p,q)-Lucas sequences, which generalize Fibonacci type, Lucas type, bi-periodic Fibonacci type and bi-periodic Lucas type sequences, using recurrence relations of (p,q)-Fibonacci and (p,q)-Lucas sequences. Generating functions and Binet formulas that allow us to calculate the nth terms of these sequences are given and the convergence properties of their consecutive terms are examined. Also, we prove some fundamental identities of bi-periodic (p,q)-Fibonacci and bi-periodic (p,q)-Lucas sequences conform to the well-known properties of Fibonacci and Lucas sequences.

Christ's Love and Borders

AbstractThis article is a keynote address given at the Global Ecumenical Theological Institute (GETI) held in Karlsruhe, Germany, August‐September 2022, on the theme “Christ's love (re)moves borders” and organized in conjunction with the 11th Assembly of the World Council of Churches. The article argues that around the world, political borders are being cemented by populist nationalisms even as pandemics, capital flows, and climate change ignore them. If Christians are to resist such ideologies, they must recover a robust incarnational theology and their fundamental identity as members of the worldwide body of Christ. Simultaneously, even as borders between people are being reinforced, the border between people and machines is blurred by transhumanist and posthumanist agendas. Such paradoxes will continue to abound in an intellectual landscape where what is distinctively human is obscured by technological hubris and philosophical naïveté.

Russia’s civilizational identity: War and world

The article deals with the problem of identity of modern Russia. Since the end of the twentieth century, Russia has been in the process of an identity crisis. The Russian Federation, which abandoned the communist ideology and the regime of Soviet power, made attempts to build a European identity in a single civilizational space with the West. Russia’s acquisition of its identity implied an ongoing process of abandoning its integrity and more fundamental identities than ideology and regime. According to the Western model, Russia should dissolve nations “in a single cauldron”, or divide into many states according to their national identity. In this project, Russia is assigned the role of a regional state that performs the function of a raw material appendage of the West in the international system of division of labor, dominated by foreign capital. The history of Russia over the past three hundred years shows that national, civil identity is limited to the potential for its development. Eurasian civilizational identity explains the peculiarities of the unity and integrity of Russia. The political and civilizational Eurasian identity of Russia allows it to develop successfully, through the inevitable intertwining and unity of contradictions that make up its content.

A new approach to Jacobsthal, Jacobsthal-Lucas numbers and dual vectors

<abstract><p>This paper gives a detailed study of a new generation of dual Jacobsthal and dual Jacobsthal-Lucas numbers using dual numbers. Also some formulas, facts and properties about these numbers are presented. In addition, a new dual vector called the dual Jacobsthal vector is presented. Some properties of this vector apply to various properties of geometry which are not generally known in the geometry of dual space. Finally, this study introduces the dual Jacobsthal and the dual Jacobsthal-Lucas numbers with coefficients of dual numbers. Some fundamental identities are demonstrated, such as the generating function, the Binet formulas, the Cassini's, Catalan's and d'Ocagne identities for these numbers.</p></abstract>

Naipaul’s Divided Self in An Area of Darkness

This paper seeks to analyze V.S. Naipaul’s futile attempt of seeking his lost identity in particular reference to his travelogue An Area of Darkness. This study shows how he fails in grabbing the self identity as an Indian and how he diverts himself from his quest when he has time and again suffered by the memory of past. The study adopts qualitative methodology and takes memory studies as a theoretical tool to interpret and analyze the primary text. Moreover, the study focuses on analysis of the text in concern with seeking the fundamental identity that once was lost being a migrant to a distance land. The writer falls in the prey of his own memory time and again and finds himself distorted and distanced from his identity as he is seeking his Indianness there. The study argues that Naipaul remains neither Indian nor Trinidanian due to his own divided cultural and individual self that he possesses in his undying memory.

Zasada pierwszeństwa prawa Unii Europejskiej wczoraj i dziś

The principle of the primacy of European Union law is one of the most important and, at the same time, the most controversial principles of this law. The jurisprudence of the Court of Justice pointing to the absolute primacy of EU law, even over national norms of constitutional character, is not unconditionally accepted by the Member States. They are challenged in particular by constitutional courts, which want to retain the status of a last word court, reserving the right to assess the constitutionality of EU law at least in terms of fundamental rights, acting within the limits of competences conferred in the Treaties and the protection of fundamental constitutional identity. Recently, there are more and more judgments of constitutional courts that refuse to apply EU law, and the allegations against the priority principle are often financial or political. Denying the principle of priority, which is an exception, as in the case of the Czech, German or Danish, in some cases, especially Poland, becomes a rule that allows, under the misuse of constitutional identity, to lower the standard of legal protection resulting from EU regulations.

Belonging in the New South Africa: Justice Froneman’s Search for a Fundamental Constitutional Identity for the People of South Africa

Belonging in the New South Africa: Justice Froneman’s Search for a Fundamental Constitutional Identity for the People of South Africa

Imaginaries, directionalities, agency and new path creation

This study focuses on how imaginaries and directionalities, i.e. the interpretation of the urban economic history and the derived fundamental perceptions, conventions, mental representations and identities, influence stakeholder behaviour (agency) with regard to enabling or inhibiting new path creation. Applying concepts of evolutionary economic geography (EEG) and sociology, this paper aims to contribute to the literature on the impact of historical dependences on urban structural change processes. These theoretical reflections are applied to an empirical case study analysing the decline and renaissance of the textile industry in Mönchengladbach, Germany. The qualitative case study is based on a document-based analysis and seven guideline-based interviews with local experts from the textile and clothing industry. It concludes that imaginaries and directionalities can take effect via four mechanisms: communication and cooperation, motivation, training and employment, and research and innovation.

Toward Empowered Identities: An Exploration of Female ESL Learners’ Literacy Through Digital Storytelling

This research explores the learner identity of female students learning English as a second language (ESL) at a public university in Pakistan through digital texts of identity (DTIs) created by them and learners’ associations of educational experiences across time and locations which impact their emergent identities. Following the poststructuralist framework on identity negotiation and “thematic” and “dialogic/performative” analysis, and image analysis framework by Kress and van Leeuwen, 33 DTIs were gathered and analyzed from 10 female ESL learners. The function of gender as a fundamental identity marker in educational experiences was investigated in particular, in order to demonstrate how social identity is established through multiple discourses. The study highlights DTIs’ ability to strengthen learners’ identities and promote more empowered identities through diverse learning environments. The main argument of the research is that female learners use digital stories to create an interpersonal space that expresses strong ties between their family and everyday locations, such as university, and the target language population, all of which shape their social identities as women and learners. The participants felt empowered by associating themselves with competent users of English making authority claims, developing their authority in and via their digital texts.

Nizarî İsmâilîlerinde Takiyye, Meşruiyet ve Tasavvuf İlişkisi Üzerine Değerlendirme

Nizārī Ismāʿīlīs, who established an autonomous structure centered in Alamūt by organizing in the geographies of Rudbar, Quhistan, Daylam, and Syria between 1090 and 1257, have been one of the movements practicing the method of taqiyya most strictly. This method they practiced against all Sunni or non-Sunni authorities was utilized as a way of protecting their lives, property, doctrine, and traditions both within themselves and against the outside. It was also seen as a suitable way for their achievement of political legitimacy, association, and gaining power. Taqiyya in the history of Nizārī Ismāʿīlīs started first in the form of hiding the imam who would come from the lineage of Nizār, the son of the Fāṭimid Caliph al-Mustansir Billāh, with the separation that started through conflicts about the Imāmate following the death of the Caliph (1036-1096). Ḥasan-i Ṣabbāḥ, who took on the authority of the imam until the expected imam arrived, aimed to get his legitimacy recognized when he made invitations in the name of Nizār with the doctrine of Ta‘līm (teaching). When the hiding of the imam during the periods of Ḥasan-i Ṣabbāḥ and his first two successors put the Alamūt government in a bind in the political and theological sense, in the period of Hasan II in 1162, Qiyāmāt was proclaimed. In the context of custody-mentorship linked from Ḥujjat (proof) to the lineage of the Imāmate, the Nizārī Ismāʿīlī community continued their association. At the same time, with the arrival of the imam, legitimacy was reinforced, and defence was launched against Sunni authorities. The proclamation of Qiyāmāt that attracted objections and pressure from the world of Islam created a new source of oppression on the Nizārī community, while it also led them to shut themselves from the outer world politically and doctrinally. To change this practice that had not gained general acceptance, this time, an outward and reconciliatory policy was chosen, and the Satr period started, that is, a new taqiyya process started with a Sunnification policy. While the reconciliatory policy was being maintained, between 1221 and 1258, Sunni practices started to be gradually abandoned, and a return to the community’s fundamental identity took place.

Japanese Dedekind Domains Are Excellent

The well-known fundamental identity in number theory expresses the degree of an extension of global fields in terms of local information. In this article we show a generalized fundamental identity for arbitrary Dedekind domains. As an application, we show that any Japanese Dedekind domain is excellent.

Communal recognition and human flourishing: a Kierkegaardian account

ABSTRACT Recent debates over the role of recognition by the community for one’s development and flourishing generally discuss community in a univocal sense: the way that recognition functions in particular communities is not fundamentally different from the way it functions in the larger community. They also tend to logically prioritize a fundamental human identity over particular religious, ethnic, or societal identities, which are understood to be secondary to, and derivative of, this basic identity. In his depiction of how communal recognition contributes to individual selfhood, Søren Kierkegaard challenges these accounts by (1) differentiating between how communal recognition occurs in society in general and in one particular community, the Christian church and (2) questioning the idea that the self created in the former is more fundamental than that created in the latter. For Kierkegaard, one’s identities as both a Christian and a fully-developed self depend essentially on recognition by the Other: initially and fundamentally on recognition by God alone, and secondarily and derivatively on recognition by the human Other.

Nearly Cosymplectic Manifolds of Constant Type

Fundamental identities characterizing a nearly cosymplectic structure and analytical expressions for the first and second structural tensors are obtained in this paper. An identity that is satisfied by the first structural tensor of a nearly cosymplectic structure is proved as well. A contact analog of nearly cosymplectic manifolds’ constancy of type is introduced in this paper. Pointwise constancy conditions of the type of nearly cosymplectic manifolds are obtained. It is proved that for nearly cosymplectic manifolds of dimension greater than three, pointwise constancy of type is equivalent to global constancy of type. A complete classification of nearly cosymplectic manifolds of constant type is obtained. It is also proved that a nearly cosymplectic manifold of dimension less than seven is a proper nearly cosymplectic manifold.

A combinatorial approach to geometric rough paths and their controlled paths

We develop the structure theory for transformations of weakly geometric rough paths of bounded 1 < p $1 < p$ -variation and their controlled paths. Our approach differs from existing approaches as it does not rely on smooth approximations. We derive an explicit combinatorial expression for the rough path lift of a controlled path, and use it to obtain fundamental identities such as the associativity of the rough integral, the adjunction between pushforwards and pullbacks and a change of variables formula for rough differential equations (RDEs). As applications we define rough paths, rough integration and RDEs on manifolds, extending the results of Cass, Driver, and Litterer (Proc. Lond. Math. Soc. (3) 111 (2015), no. 6, 1471–1518) to the case of arbitrary p $p$ .

An alternative linear flow model and boundary integral flow representation for ship motions in regular waves

The basic issue of formulating a linear flow model for the analysis of potential flow around a ship advancing at a constant speed in regular waves is considered. Specifically, the ‘rigid-waterplane flow model’, previously considered for diffraction–radiation of regular waves by offshore structures, is applied to analyze flows around ships advancing in regular waves. A straightforward application of Green’s fundamental identity to the rigid-waterplane flow model yields a remarkable new boundary integral flow representation. Indeed, this flow representation does not involve a line integral around the mean waterline of the ship hull surface, is weakly singular, does not involve a distribution of dipoles over the ship-hull surface, and is free from irregular frequencies. In the particular case of flow around a ship steadily advancing in calm water, the boundary integral flow representation obtained in the study via an analysis based on the rigid-waterplane flow model is identical to the flow representation associated with the Neumann–Michell theory, which is based on a different linear flow model that only considers the flow region strictly outside the ship but consistently accounts for the linear contribution of the thin band of water between the wave profile along the ship hull surface and the undisturbed free surface. This result strongly suggests that the classical application of Green’s basic identity to analyze linear potential flow around a ship advancing in regular waves or in calm water, which yields a notoriously troublesome line integral around the ship waterline, may be questionable due to possible incompatibilities between the Neumann boundary condition at the ship hull surface and the linear free surface boundary condition associated with flows around ships advancing in calm water or in regular waves. This fundamental difficulty may be alleviated in the rigid-waterplane flow model, which imposes a compatibility condition between the Neumann boundary condition at the rigid lid that artificially closes the open ship hull surface and the linear boundary condition at the free surface above the waterplane-lid. The boundary integral flow representation given in the study also holds for diffraction–radiation of regular waves by offshore structures. Thus, this new flow representation provides a common mathematical basis, which fundamentally differs from the basis steadfastly adopted over the past fifty years, for the analysis of three basic classes of flows in ship and offshore hydrodynamics, and indeed can be applied more generally to other boundary-value problems such as those associated with flexural-gravity waves for ice sheets or very large floating structures.

Internal transformations and internal symmetries in linear photonic systems

Lorentz reciprocity, energy conservation, and time-reversal symmetry are three important global constraints of Maxwell's equations. Unlike time-reversal symmetry, Lorentz reciprocity and energy conservation usually are not considered as symmetries, i.e., they are not associated with operators. In this paper, we provide a unified treatment of these three global constraints from a perspective of internal symmetry. We define operators of transformations associated with each of these constraints, referred to as internal transformations. When Maxwell's equations are written as a linear system of equations, these internal transformations correspond to the operations of transpose, conjugate transpose, and conjugate of the system matrix, respectively. We show the three global constraints naturally follow from three fundamental identities of linear systems under the three matrix operations. We discuss the properties of electromagnetic fields and scattering matrices associated with these internal transformations. These internal transformations form the Klein four-group ${V}_{4}={\mathbb{Z}}_{2}\ifmmode\times\else\texttimes\fi{}{\mathbb{Z}}_{2}$, and the internal symmetry group of any photonic structure corresponds to one of the five subgroups of ${V}_{4}$. Our paper provides a theoretical foundation for further exploration of symmetries in photonic systems.

Exploring smoking-gun signals of the Schwinger mechanism in QCD

In Quantum Chromodynamics, the Schwinger mechanism endows the gluons with an effective mass through the dynamical formation of massless bound-state poles that are longitudinally coupled. The presence of these poles affects profoundly the infrared properties of the interaction vertices, inducing crucial modifications to their fundamental Ward identities. Within this general framework, we present a detailed derivation of the non-Abelian Ward identity obeyed by the pole-free part of the three-gluon vertex in the soft-gluon limit, and determine the smoking-gun displacement that the onset of the Schwinger mechanism produces to the standard result. Quite importantly, the quantity that describes this distinctive feature coincides formally with the bound-state wave function that controls the massless pole formation. Consequently, this signal may be computed in two independent ways: by solving an approximate version of the pertinent Bethe-Salpeter integral equation, or by appropriately combining the elements that enter in the aforementioned Ward identity. For the implementation of both methods we employ two- and three-point correlation functions obtained from recent lattice simulations, and a partial derivative of the ghost-gluon kernel, which is computed from the corresponding Schwinger-Dyson equation. Our analysis reveals an excellent coincidence between the results obtained through either method, providing a highly nontrivial self-consistency check for the entire approach. When compared to the null hypothesis, where the Schwinger mechanism is assumed to be inactive, the statistical significance of the resulting signal is estimated to be 3 standard deviations.

Relevansi Nilai Lokasamgraha Terhadap Wacana Politk Identitas Dan Masa Depan Kebangsaan

This article is a study of national identity, identity politics, and the value of Lokasamgraha in Hinduism and their relevance to the escalation of identity politics and the discourse of the future of the nation. This is a library research with qualitative approach. Lokasamgraha is a material object in this research. This research used data collection techniques and using data analysis, namely: interpretative, holistic and descriptive. Results of this study are: 1) national identity is Bhinneka Tunggal Ika inspired by Pancasila and Undang-Undang Dasar 1945, and explored into three, fundamental identity, instrumental identity, and natural identity; 2) identity politics is irrelevant and has lost its meaning. The emergence of identity politics lately must be viewed as a threat and sabotage against the existence of Indonesia. And the last is 3) the value of Lokasamgraha is at odds with identity politics but found similar resonance with the discourse on the future of the nation. Lokasamgraha finds its urgency in two things, namely: identity politics and the future of nation.

Uniform stabilisation of a thermoelastic system with static Wentzell conditions

In this paper, we consider a thermoelastic system with static Wentzell boundary conditions. We show the well-posedness, using the semigroup theory, and establish an explicit decay rate result, using the multiplier method. More precisely, we prove an exponential decay result under the influence of competing both boundary damping b u ′ and localised interior damping l ( x ) u ′ . Our method consists in establishing a crucial fundamental identity and exploiting it to derive the decay rates.

Blood and Honey: Culinary Nationalism and Yugonostalgia in a Canadian City

ABSTRACT For decades, the very same markers one used to identify national and ethnic belonging in the “homeland,” such as history, language, and ritual, have been the same indicators deployed in diaspora communities to demarcate their level of group identity both within the assimilatory, hegemonic, and new national identity (eg., “Canadian”), as well as against other ethnic minorities. Members of the Balkan diaspora in North America very much perform their Serb, Croatian, or Bosniak identities through the way they talk about food. But there exists a split in Balkan food identity which overlaps with a fundamental political identity: those who see, for example, Serb cuisine as unique tend to be proudly, nationalistically Serb, while those who see a common Balkan cuisine are more likely to identify with a federalist, shared Yugoslav past.