Notion Of Singularity Research Articles

Remarks on q-difference opers arising from quantum toroidal algebras

Abstract We propose a conjectural correspondence between 
the spectra of the Bethe algebra for the quantum toroidal $\mathfrak{gl}_2$
algebra on relaxed Verma modules, 
and $q$-hypergeometric opers with apparent singularities.
We introduce alongside 
the notion of apparent singularities for linear $q$-difference 
operators and discuss some of their properties.
We also touch on a generalization to $\mathfrak{gl}_n$.

Home and psychological well‐being in global consumer mobility

AbstractHome is typically understood as a singular place that provides a sense of groundedness, belonging, and well‐being. Yet, this singular notion of home is challenged in global mobility, where consumers live and travel across borders and relocate internationally frequently. We expect globally mobile consumers to experience multiple and multilayered notions of home with significant psychological consequences for their sense of well‐being, ownership, and identity. In a qualitative study of 40 globally mobile consumers, we examine what it means to have multiple homes and how consumers cope with it. We identified four types of home that coexist in global mobility: emotional home, home away from home, base of operation, and home on the road. These types are characterized by different degrees of permanence and serve different psychological benefits that are at times in opposition or complementary (respectively, belonging and ontological security, functioning and psychological ownership, productivity, and flexibility). We also explored how this home portfolio provokes emotional, social, and cognitive consequences with which globally mobile consumers cope through strategic use of marketplace resources.

Rational singularities and q-birational morphisms

In this paper, we generalize the notion of rational singularities for any reflexive sheaf of rank [Formula: see text], link our notion of rational singularities with the notion of rational singularities in, [S. Kovacs, Irrational centers, Pure Appl. Math. Q. 7(4) (2011) 1495–1515], and prove generalizations of standard facts about rational singularities. Moreover, by using a definition of non-rational locus, we introduce the notion of [Formula: see text] as a dual notion of well-known Serre’s notion of [Formula: see text], and prove a theorem about [Formula: see text]-birational morphisms.

Intrinsic Disorder and Other Malleable Arsenals of Evolved Protein Multifunctionality.

Microscopic evolution at the functional biomolecular level is an ongoing process. Leveraging functional and high-throughput assays, along with computational data mining, has led to a remarkable expansion of our understanding of multifunctional protein (and gene) families over the past few decades. Various molecular and intermolecular mechanisms are now known that collectively meet the cumulative multifunctional demands in higher organisms along an evolutionary path. This multitasking ability is attributed to a certain degree of intrinsic or adapted flexibility at the structure-function level. Evolutionary diversification of structure-function relationships in proteins highlights the functional importance of intrinsically disordered proteins/regions (IDPs/IDRs) which are highly dynamic biological soft matter. Multifunctionality is favorably supported by the fluid-like shapes of IDPs/IDRs, enabling them to undergo disorder-to-order transitions upon binding to different molecular partners. Other new malleable members of the protein superfamily, such as those involved in fold-switching, also undergo structural transitions. This new insight diverges from all traditional notions of functional singularity in enzyme classes and emphasizes a far more complex, multi-layered diversification of protein functionality. However, a thorough review in this line, focusing on flexibility and function-driven structural transitions related to evolved multifunctionality in proteins, is currently missing. This review attempts to address this gap while broadening the scope of multifunctionality beyond single protein sequences. It argues that protein intrinsic disorder is likely the most striking mechanism for expressing multifunctionality in proteins. A phenomenological analogy has also been drawn to illustrate the increasingly complex nature of modern digital life, driven by the need for multitasking, particularly involving media.

A/the Common Good

Abstract The emerging school of “common good constitutionalism” takes a classical natural law approach of identifying the central case of law and constitutionalism, recognizing that a state may make positive law in part based on circumstance, convenience, or a need for social coordination. While law under the classical approach is rooted in realizing the common good of the complete community, this ideal does not dictate all of law’s specifics. Nevertheless, there is a difficulty within the emerging school of common good constitutionalism in the way it seeks to respect the diversity of constitutional orders while retaining a single reference point of the common good. Adrian Vermeule and others appeal to positive law as the determinatio through which public authorities make concrete the state’s pursuit of the common good. But there is often a gulf between common good principles and the determinatio of law. The move from principles to the legitimacy or justness of positive law lies, for Vermeule, in joining-up the central case method of natural law with a singular notion of the common good. The article criticizes this reliance, arguing that the central case method cannot be used to determine law in the sense of the determinatio of positive law. In his articulation of central case methodology, John Finnis is, by contrast, careful to leave space for varieties of coordination and forms of justice, such that the central case method plays a limited role in establishing what counts as common goods. Rather, the central case method identifies what law is. The same delicacy is present in Aquinas, who does not in fact define law as an ordinance of reason for the common good in the way that common good constitutionalists so far would like it to mean, because there are no articles in Latin grammar. In this regard, common good constitutionalism’s mistake is unfortunately in keeping with the majority of jurisprudence, which commits the logical fallacy that an internally consistent account of law is externally authoritative—in other words, that harmony in the way in which laws and legal principles relate to themselves can act as a basis to the body politic’s prioritization of some goods over others.

The making of the “transitional generation”: language politics, writing diaspora and strategic integration of Chinese students in post-war Australia

PurposeThis article explores the overlooked experiences of Chinese students in Australia from the White Australia Policy era to the post-war period. It argues that the emerging post-war transitional generation faced racial discrimination and geopolitical challenges, leading to the establishment of student societies and collaborations with religious groups and NGOs. Through writing and publishing in the 1950s and 1960s, they challenged rigid ethnic identities, shaping their ethnic identities, national belonging, language practices, and community involvement amidst historical contexts. Their narratives vividly depict a generational awakening, highlighting complex processes of integration and acculturation into a new societal landscape.Design/methodology/approachThis paper employs historical discourse analysis using Chinese student magazines and bilingual archives to explore language and identity evolution among Chinese students in 1950s’ and 1960s’ Australia. It contextualizes ethnic, cultural, and linguistic identity transformations and examines how language politics and diaspora writings shaped integration strategies. The study highlights education and language politics' transformative roles in redefining cultural belonging and fostering community cohesion within the diaspora amid shifting socio-political contexts.FindingsThe findings of this study reveal that the concept of the “transitional generation” highlights integration as a dynamic process involving ongoing dialogue, identity negotiation through language, and the redefinition of cultural boundaries. Through analysis of three student-centered magazines – Murhun, Asiana and East Wind – it becomes evident how Chinese students in Australia navigated ethnic, cultural and linguistic identities. Murhun used bilingual content to strengthen solidarity and political engagement among Chinese readers, while Asiana employed English to connect Asian students with Australian society and globally. East Wind facilitated a diverse expression of identity, challenging singular notions of “Chineseness” and promoting cultural integration. These insights reflect a transformative period where Chinese students reshaped their historical position, fostering autonomy and challenging stereotypes like “Yellow Perils”.Originality/valueThis paper examines the often-overlooked experiences of post-war Chinese students in Australia, emphasizing their profound influence on immigration history and shifting public perceptions of Asian immigrants. It introduces the concept of the “transitional generation” to address research gaps and highlight the nuanced complexities of integration, respecting the diverse experiences and identities within this dynamic student community. Emphasizing dynamic negotiation and shared experiences, the study underscores how Australia’s diverse Asian communities have transformative potential. Integration extends beyond adaptation, fostering inclusive spaces for identity negotiation, thriving NGOs and enriching Australia’s social fabric with resilience, diversity and cultural vibrancy.

Volume singularities in general relativity

We propose a new notion of singularity in general relativity which complements the usual notions of geodesic incompleteness and curvature singularities. Concretely, we say that a spacetime has a volume singularity if there exist points whose future or past has arbitrarily small spacetime volume: in particular, smaller than a Planck volume. From a cosmological perspective, we show that the (geodesic) singularities predicted by Hawking’s theorem are also volume singularities. In the black hole setting, we show that volume singularities are always hidden by an event horizon, prompting a discussion of Penrose’s cosmic censorship conjecture.

A unified notion of regularity in one hypercomplex variable

We define a very general notion of regularity for functions taking values in an alternative real ⁎-algebra. Over Clifford numbers, this notion subsumes the well-established notions of monogenic function and slice-monogenic function. Over quaternions, in addition to subsuming the notions of Fueter-regular function and of slice-regular function, it gives rise to an entirely new theory, which we develop in some detail.

Joseph Reményi and socialist world literature

Hungarian American scholar, Joseph Reményi’s concepts of “minority literature,” “small nation literature,” and “world literatures” highlight the shift from the singular forms Deleuze and Guattari’s “minor literature,” Pascale Casanova’s “small literature,” and Marx and Engels and Karl Radek’s “world literature” to their plural counterparts. In the discourse on “minor literature” and “small literature,” Reményi offers a nuanced categorization of Hungarian literary production following the First World War. He delineates it into three distinct strands: “literature in Hungary,” “literature of Hungarian exiles,” and “Hungarian literature in the Successor States.” This tripartite classification not only encapsulates the varied loci of Hungarian literary expression but also underscores the emerging literary dichotomy between Hungarian and Slavic & Soviet literatures in the aftermath of the Second World War. As for “world literature”, Reményi’s conceptual framework, which pivots on the axes of “regionalism” and “internationalism,” segments world literature into four stratified layers: minority and marginal → local → national → world. This theoretical model facilitates a repositioning of the intrinsic diversities inherent within each stratum, mapping them onto a spectrum of diverse nations, cultural groups, and minority populations. Furthermore, Reményi’s concept of “world literatures” represents a shift from the singular notion of Geothe’s “eine allemeine Weltliteratur”, Marx and Engels’ “eine Weltliteratur”, and Radek’s “contemporary world literature” to a pluralized understanding. For “socialist literature”, Reményi’s categorization of Hungarian literature within the Western European tradition, as opposed to Eastern European literature, signifies the multifaceted nature of socialist literature. This concept, initially introduced by Marx and Engels in 1848, further elaborated by Radek in 1934, is eventually expanded by Reményi into a more pluralistic form as socialist literatures in 1956. The fusion of Reményi’s concept of “world literatures” and “socialist literatures” provided a gateway to construct Socialist World Literature.

An Eternal gravitational collapse in f(R) theory of gravity and their astrophysical implications

The present investigation explores a novel facet of gravitational collapse, surpassing conventional notions of black holes and naked singularities. In this work, we explore a new aspects on the final fate of Gravitational Collapse of a stellar system within the framework of f(R) gravity and find the continued homogeneous gravitational collapse: an eternal collapsing phenomenon. The exact solutions of field equations have been obtained in an independent way by the parametrization of the expansion scalar (Θ) governed by the interior spherically symmetric FLRW metric. We impose the Darmois junction condition required for the smooth matching of the interior region to the Schwarzschild exterior metric across the boundary hypersurface of the star. The junction conditions demand that the pressure is non-vanishing at the boundary and is proportional to the non-linear terms of f(R) gravity, and the mass function m(t,r) is equal to Schwarzschild mass M. The eight massive stars, namely Westerhout49−2,BAT99−98,R136a1,R136a2,WR24,Pismis24−1, λ−Cephei, and β−CanisMajoris with their known astrophysical data (masses and radii) are used to estimate the numerical values of the model parameters which allows us to study the solutions numerically and graphically. Here we have discussed two f(R) gravity models describing the collapse phenomenon. The singularity analysis of models is discussed via the apparent horizon and we have shown that stars tend to collapse for an infinite co-moving time in order to attain the singularity (an eternal collapsing phenomenon). We have also shown that our models satisfy the energy conditions and stability requirements for stellar systems.

The fundamental facts can be logically simple

AbstractI like the view that the fundamental facts are logically simple, not complex. However, some universal generalizations and negations may appear fundamental, because they cannot be explained by logically simple facts about particulars. I explore a natural reply: those universal generalizations and negations are true because certain logically simple facts—call them φφ—are the fundamental facts. I argue that this solution is only available given some metaphysical frameworks, some conceptions of metaphysical explanation and fundamentality. It requires a ‘fitting’ framework, according to which metaphysical theories explain the aptness of representations in terms of how things are fundamentally. Fitting frameworks conceive of the fundamental facts as those that are metaphysically ‘real’; call them the ‘facts‐in‐reality’. Moreover, we must take as primary a plural notion of the facts‐in‐reality, not the singular notion of a fact‐in‐reality. By contrast, a metaphysics that grounds facts is incompatible with my strategy for keeping the fundamental facts logically simple.

ASYMPTOTIC EXPANSION OF THE SOLUTION FOR SINGULARPERTURBED LINEAR IMPULSIVE SYSTEMS

In this study, a singularly perturbed linear impulsive system with singularly perturbed impulses is considered. Many books discuss different types of singular perturbation problems. In the present work, an impulse system is considered in which a small parameter is introduced into the impulse equation. This is the main novelty of our study, since other works [25] have only considered a small parameter in the differential equation. A necessary condition is also established to prevent the impulse function from bloating as the parameter approaches zero. As a result, the notion of singularity for discontinuous dynamics is greatly extended. An asymptotic expansion of the solution of a singularly perturbed initial problem with an arbitrary degree of accuracy for a small parameter is constructed. A theorem for estimating the residual term of the asymptotic expansion is formulated, which estimates the difference between the exact solution and its approximation. The results extend those of [32], which formulates an analogue of Tikhonov’s limit transition theorem. The theoretical results are confirmed by a modelling example.

Interaction, Satisfaction, and the PCC

The Person-Case Constraint (PCC) is a family of restrictions on the relative person of the two objects of a ditransitive. PCC effects offer a testing ground for theories of Agree and of syntactic features, both those on nominals and those found on agreement probes. This article offers a new theory of PCC effects in an interaction/satisfaction theory of Agree (Deal 2015a) and shows the advantages of this framework in capturing PCC typology. On this model, probes are specified for interaction, determining which features will be copied to them, and for satisfaction, determining which features will cause probing to stop. Applied to the PCC, this theory (a) captures all four types of PCC effect recognized by Nevins (2007) under a unified notion of Agree; (b) captures the restriction of PCC effects to contexts of “Double Weakness” in many prominent examples (e.g., in Italian, Greek, and Basque, where PCC effects hold only when both objects are expressed with clitics); (c) naturally extends to PCC effects in syntactic environments without visible clitics or agreement for one or both objects, as well as to the absence of PCC effects in some languages with clitics or agreement for both objects. Two refinements of the interaction/ satisfaction theory are offered: a new notation for probes’ interaction and satisfaction specifications, clarifying the absence of uninterpretable/unvalued features as drivers of Agree; and a proposal for the way that probes’ behavior may change over the course of a derivation, dubbed dynamic interaction.

Geodesics orbiting a singularity

We study the behaviour of geodesics on a Riemannian manifold near a generalized conical or cuspidal singularity. We show that geodesics entering a small neighbourhood of the singularity either hit the singularity or approach it to a smallest distance δ\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\delta $$\\end{document} and then move away from it, winding around the singularity a number of times. We study the limiting behaviour δ→0\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\delta \\rightarrow 0$$\\end{document} in the second case. In the cuspidal case the number of windings goes to infinity as δ→0\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\delta \\rightarrow 0$$\\end{document}, and we compute the precise asymptotic behaviour of this number. The asymptotics have explicitly given leading term determined by the warping factor that describes the type of cuspidal singularity. We also discuss in some detail the relation between differential and metric notions of conical and cuspidal singularities.

Neolithic as a Historical Period and its Eurasian Variants / Neolit jako historické období a jeho podoby v Eurasii

It has become evident that the term Neolithic needs to be expanded to encompass the historical period during which human societies began, in various ways, to break away from a dependence on the products of natural evolution. This change was without doubt due to climatic oscillations which, over several centuries, disrupted the steady life of Palaeolithic hunters. New findings have shattered the unified notion of what was previously termed the Neolithic into a series of regionally and chronologically specific complexes. The first step is to redefine the terms ‘western’ and ‘eastern’ Neolithic according to the different developments that led to the emergence of pottery.

On categorical structures arising from implicative algebras: From topology to assemblies

Implicative algebras have been recently introduced by Miquel in order to provide a unifying notion of model, encompassing the most relevant and used ones, such as realizability (both classical and intuitionistic), and forcing. In this work, we initially approach implicative algebras as a generalization of locales, and we extend several topological-like concepts to the realm of implicative algebras, accompanied by various concrete examples. Then, we shift our focus to viewing implicative algebras as a generalization of partial combinatory algebras. We abstract the notion of a category of assemblies, partition assemblies, and modest sets to arbitrary implicative algebras, and thoroughly investigate their categorical properties and interrelationships.

Serving the Dead as Serving the Living: Examining the Concept of Burial and Life Consciousness in Medieval China

In the minds of ancient people, tombs and burials were where the lives of this world ended and another type of life began. By incorporating the concepts of life found in Confucianism, Taoism, Buddhism, and the widespread belief in ghosts and immortals, burial ceremonies evolved during the Wei and Jin 魏晋 dynasties (220–420) into an integrated and unified notion of burial. The funeral ritual’s imaginative and fanciful depictions of the hereafter express sentimental devotion to life and contemplation of death. The burial ceremony and tomb architecture change in accordance with how the concepts of sacrifice and ghosts develop. The features of people’s belief in ghosts and immortality are reflected in particular burial practices. The popularity of necromancy burials and ghost marriages during the Middle Ages (third to sixth centuries) bring to light the binary antagonism between the soul and the body in burial, as well as the emphasis on spiritual freedom and physical immortality in the life philosophy.

Efficient Quantum Algorithms for Testing Symmetries of Open Quantum Systems

Symmetry is an important and unifying notion in many areas of physics. In quantum mechanics, it is possible to eliminate degrees of freedom from a system by leveraging symmetry to identify the possible physical transitions. This allows us to simplify calculations and characterize potentially complicated dynamics of the system with relative ease. Previous works have focused on devising quantum algorithms to ascertain symmetries by means of fidelity-based symmetry measures. In our present work, we develop alternative symmetry testing quantum algorithms that are efficiently implementable on quantum computers. Our approach estimates asymmetry measures based on the Hilbert–Schmidt distance, which is significantly easier, in a computational sense, than using fidelity as a metric. The method is derived to measure symmetries of states, channels, Lindbladians, and measurements. We apply this method to a number of scenarios involving open quantum systems, including the amplitude damping channel and a spin chain, and we test for symmetries within and outside the finite symmetry group of the Hamiltonian and Lindblad operators.

Realms unseen

AbstractSince 2006, albinism has emerged as both a subject and an object of contestation in Tanzania and beyond. An abiding global narrative purports that, as a recessively inherited condition, albinism is fetishized by Africans who falsely attribute otherworldly potentials to albino body parts and commodify them in a grisly market run by “traditional” healers and their patrons. In response, translocal albinism rights stakeholders have formed to cement a singular notion of albinism and, with “it,” a notion of unseen power that cancels the agency of particular nonhumans. Their work diverges from those who insist on multiple other instantiations of albinism and worlds unseen, some of which offer compelling explanations of recent violence rooted in entanglement and complicity, rather than an Indigenous cosmology. In this context, I argue for a conceptual and methodological approach to social movements and minority groups rooted in decolonizing unseen realms and embracing epistemic and ontological openness.

Openness of splinter loci in prime characteristic

A splinter is a notion of singularity that has seen numerous recent applications, especially in connection with the direct summand theorem, the mixed characteristic minimal model program, Cohen–Macaulayness of absolute integral closures and cohomology vanishing theorems. Nevertheless, many basic questions about these singularities remain elusive. One outstanding problem is whether the splinter property spreads from a point to an open neighborhood of a noetherian scheme. Our paper addresses this problem in prime characteristic, where we show that a locally noetherian scheme that has finite Frobenius or that is locally essentially of finite type over a quasi-excellent local ring has an open splinter locus. In particular, all varieties over fields of positive characteristic have open splinter loci. Intimate connections are established between the openness of splinter loci and F-compatible ideals, which are prime characteristic analogues of log canonical centers. We prove the surprising fact that for a large class of noetherian rings with pure (aka universally injective) Frobenius, the splinter condition is detected by the splitting of a single generically étale finite extension. We also show that for a noetherian N-graded ring over a field, the homogeneous maximal ideal detects the splinter property.