Hasil untuk "Folklore"

John D. Gibbon, Dario Vincenzi

Contrary to accepted turbulence folklore, which holds that no mathematical relation exists between the Navier-Stokes equations (NSEs) and the multifractal model (MFM) of Parisi and Frisch, we develop a theory that reconciles the MFM with Leray's weak solutions of Navier-Stokes analysis. From a combination of Euler invariant scaling and the NSEs we also derive the Paladin-Vulpiani inverse scale $Lη_{h,pav}^{-1} = Re^{1/(1+h)}$ which acts as a mediator between the two theories. This is achieved by considering $L^{2m}$-norms of the velocity gradient to find a correspondence between $m$ and the local scaling exponent $h$ in the multifractal model. The parameter $m$ acts as if it were the sliding focus control on a telescope which allows us to zoom in and out on different structures. The range $1 \leqslant m \leqslant \infty$ is equivalent to $-2/3 \leqslant h_{min} \leqslant 1/3$, which lies precisely in the region where Bandak et al. (2022, 2024) have suggested that thermal noise makes the NSEs inadequate and generates spontaneous stochasticity. The implications of this are discussed.

Julian Frank Rouw, Daniel Ronda, Robi Panggarra et al.

This study explores the resurgence of the Manarmakeri myth among the Biak people in Papua, Indonesia, as a socio-religious phenomenon centered on Messianic hope. Using mixed methods—survey questionnaires (n=38) and ethnographic interviews—this research identifies 14 core indicators, with Messianic Expectation emerging as the dominant factor, accounting for over 25% of the variance. The findings demonstrate that the myth of Manarmakeri is not merely folklore but functions as a theological framework, cultural narrative, and coping mechanism for socio political marginalization. This belief system aligns local eschatological expectations with biblical motifs, constructing what can be described as “indigenous Christology.” The figure of Manarmakeri is perceived as both a liberator and a returning Messiah, with strong parallels to Jesus Christ in Christian theology. The study argues that the myth fosters communal identity, symbolic resistance, and social cohesion. It also highlights the limitations of formal theological rejection by mainstream churches, suggesting the need for inclusive and dialogical pastoral models. Practically, the study urges culturally sensitive development strategies that consider spiritual aspirations, involve local leaders, and integrate material and non-material needs. The research contributes to postcolonial theological discourse and invites further interdisciplinary inquiry into how indigenous narratives interface with global religious traditions.

Pamela Fleischmann, Annika Huch, Melf Kammholz et al.

In this work, we combine the research on (absent) scattered factors with the one of jumbled words. For instance, $\mathtt{wolf}$ is an absent scattered factor of $\mathtt{cauliflower}$ but since $\mathtt{lfow}$, a jumbled (or abelian) version of $\mathtt{wolf}$, is a scattered factor, $\mathtt{wolf}$ occurs as a jumbled scattered factor in $\mathtt{cauliflower}$. A \emph{jumbled scattered factor} $u$ of a word $w$ is constructed by letters of $w$ with the only rule that the number of occurrences per letter in $u$ is smaller than or equal to the one in $w$. We proceed to partition and characterise the set of jumbled scattered factors by the number of jumbled letters and use the latter as a measure. For this new class of words, we relate the folklore longest common subsequence (scattered factor) to the number of required jumbles. Further, we investigate the smallest possible number of jumbles alongside the jumbled scattered factor relation as well as Simon's congruence from the point of view of jumbled scattered factors and jumbled universality.

Dougal Davis, Ruijie Yang

In this paper, we prove a Beilinson-type formula for the V-filtration of Kashiwara and Malgrange on a complex mixed Hodge module, using Hodge filtrations on the localization. Our formula expresses the V-filtration as the filtered D-module underlying a pro-mixed Hodge module. We apply this to the theory of higher multiplier and Hodge ideals. Our first result shows that higher multiplier ideals can be obtained directly from Hodge ideals by taking a suitable limit. As a corollary, we deduce that Hodge ideals are left semi-continuous if and only if they coincide with higher multiplier ideals, thereby improving results of Saito and Mustaţă--Popa and resolving a folklore question. We further prove a birational transformation formula for higher multiplier ideals, generalising the classical formula for multiplier ideals and answering a question of Schnell and the second author. Finally, we provide very quick proofs of the main vanishing theorems for Hodge ideals, and strengthen a result of B. Chen.

Darij Grinberg

In this expository paper, various properties of matrix traces, determinants and adjugate matrices are proved, including the *trace Cayley-Hamilton theorem*, which says that \[ kc_k + \sum_{i=1}^k \operatorname{Tr} (A^i) c_{k-i} = 0 \qquad \text{for every } k\in\mathbb{N} \] whenever $A$ is an $n\times n$-matrix with characteristic polynomial $\det (tI_n - A) = \sum_{i=0}^n c_{n-i} t^i$ over a commutative ring $\mathbb{K}$. While the results are not new, some of the proofs are. The proofs illustrate some general techniques in linear algebra over commutative rings.

Ніна [Nina] Данилюк [Danyliuk]

The Linguistic Image of the Mother of God in the Texts of Religious Songs of Book and Folk Origin This article analyses the stylistic means of verbalising the linguistic image of the Mother of God in the texts of religious songs of book and folk origin. It has been established that the image in question combines pagan ideas about the Mother Goddess and Christian beliefs in the Mother of the Son of God. The study also points out a synonymous-variant series for the designation of the Mother of God with such dominants as Virgin, Mary, Mother, Queen and Holy Protectress. As discussed, the semantics of key units is revealed through linguistic means, primarily epithets, similes and metaphors. The following peculiarities of the representation of the linguistic image of the Mother of God have been identified: in the works of book origin, the authors emphasise her divine essence, depicting her in an iconographic style; in folklore, the folk interpretation as an earthly woman prevails. The linguistic image of the Mother of God is qualified as a component of the linguistic and conceptual worldview of Ukrainians.   Językowy obraz Matki Boskiej w tekstach pieśni religijnych pochodzenia książkowego i ludowego Niniejszy artykuł analizuje środki stylistyczne użyte do werbalizacji językowego obrazu Matki Boskiej w tekstach pieśni religijnych pochodzenia książkowego i ludowego. Jak ustalono, obraz ten łączy pogańskie wyobrażenia o Bogini Matce i chrześcijańskie wierzenia w Matkę Syna Bożego. W opracowaniu wskazano również szeregi synonimiczno-wariantywne określenia Matki Boskiej z takimi dominantami, jak Dziewica, Maryja, Matka, Królowa, Święta Opiekunka. Semantyka kluczowych jednostek ujawnia się poprzez środki językowe, przede wszystkim epitety, porównania i metafory. Ustalono następującą specyfikę przedstawiania językowego obrazu Matki Boskiej: w utworach pochodzenia książkowego autorzy podkreślają jej boską istotę, przedstawiając ją w stylu ikonograficznym; w folklorze przeważa jej ludowa interpretacja jako ziemskiej niewiasty. Językowy obraz Matki Boskiej uznano za element językowego i pojęciowego obrazu świata Ukraińców. 

M. G. Pavlovets

In 1984, «Podval» («Basement»), the home publishing house of the poet Konstantin K. Kuzminsky, published a book by Vagrich Bakhchanyan called Akh, matom! («Oh, Obscenities!»). This was a small compilation of parodic adaptations of some early verse by Anna Akhmatova, in the spirit of travesty alterations of popular songs or poetry from the school curriculum that can be found in teenage folklore. Without a broader context created by several of Konstantin Kuzminsky’s texts polemically aimed at Anna Akhmatova and her poetic circle, as well as without a wider context of the avant-garde tradition of discrediting literary opponents through vulgarizing mockery of their writings, often using obscene vocabulary, the book might not seem like a very successful joke of the two authors, known to be inclined towards shocking the public. Knowing this context, one would see all the hidden meanings of the book, which were consciously made offensive for adherents of traditional art, but were fairly acceptable in terms of epatage or avant-garde art, for which even the emphasized negligence and «ineptitude» of form is considered to be a technique: that is, the artistic sign of «spoiling» the primary source, and not a banal manifestation of envy of the two supposed «graphomaniacs» and «misogynists» towards their great predecessor. This was essentially a form of debate between two inheritors of the avant-garde line of Russian poetry and an author, whose work they perceived as a precedent for the alternative, neo-acmeist tradition.

Marco Fasolio

Review of Tommaso Braccini's book Trebisonda. L’impero incantato tra storia e leggenda, with comments regarding the content and the bibliography.

Eyal Z. Goren, Jonathan R. Love

This paper contains a survey of supersingular isogeny graphs associated to supersingular elliptic curves and their various applications to cryptography. Within limitation of space, we attempt to address a broad audience and make this part widely accessible. For those graphs we also present three recent results and sketch their proofs. We then discuss a generalization to superspecial isogeny graphs associated to superspecial abelian varieties with real multiplication. These graphs were introduced by Charles, Goren and Lauter and so our discussion is brief. Motivated by their cryptographic applications, we prove a general theorem concerning generation of lattices over totally real fields by elements of specified norm. Throughout the paper we have attempted to clarify certain considerations that are either vaguely stated in the literature, or are folklore. We hope this paper will be useful both to a novice wishing to familiarize themselves with this very active area, and to the expert who may enjoy some vignettes and an overview of some new results.

Makoto Natsuume

The holographic superconductor is the holographic dual of superconductors. We recently identified the dual Ginzburg-Landau (GL) theory for a class of bulk 5-dimensional holographic superconductors (arXiv:2207.07182 [hep-th]). However, the result is the strong coupling limit or the large-$N_c$ limit. A natural question is how the dual GL theory changes at finite coupling. We identify the dual GL theory for a minimal holographic superconductor at finite coupling (Gauss-Bonnet holographic superconductor), where numerical coefficients are obtained exactly. The GL parameter $κ$ increases at finite coupling, namely the system approaches a more Type-II superconductor like material. We also point out two potential problems in previous works: (1) the "naive" AdS/CFT dictionary, and (2) the condensate determined only from the GL potential terms. As a result, the condensate increases at finite coupling unlike common folklore.

Rishi Banerjee, Ruiyuan Chen

We show that the category of countable Borel equivalence relations (CBERs) is dually equivalent to the category of countable $\mathcal{L}_{ω_1ω}$ theories which admit a one-sorted interpretation of a particular theory we call $\mathcal{T}_\mathsf{LN} \sqcup \mathcal{T}_\mathsf{sep}$ that witnesses embeddability into $2^\mathbb{N}$ and the Lusin--Novikov uniformization theorem. This allows problems about Borel combinatorial structures on CBERs to be translated into syntactic definability problems in $\mathcal{L}_{ω_1ω}$, modulo the extra structure provided by $\mathcal{T}_\mathsf{LN} \sqcup \mathcal{T}_\mathsf{sep}$, thereby formalizing a folklore intuition in locally countable Borel combinatorics. We illustrate this with a catalogue of the precise interpretability relations between several standard classes of structures commonly used in Borel combinatorics, such as Feldman--Moore $ω$-colorings and the Slaman--Steel marker lemma. We also generalize this correspondence to locally countable Borel groupoids and theories interpreting $\mathcal{T}_\mathsf{LN}$, which admit a characterization analogous to that of Hjorth--Kechris for essentially countable isomorphism relations.

Ben Elias, Matthew Hogancamp

The Drinfeld centralizer of a monoidal category $\mathcal{A}$ in a bimodule category $\mathcal{M}$ is the category $\mathcal{Z}(\mathcal{A},\mathcal{M})$ of objects in $\mathcal{M}$ for which the left and right actions by objects of $\mathcal{A}$ coincide, naturally. In this paper we study the interplay between Drinfeld centralizers of $\mathcal{A}$ and its homotopy category $\mathcal{K}^b(\mathcal{A})$, culminating with our ``lifting lemma,'' which provides a sufficient condition for an object of $\mathcal{Z}(\mathcal{A}, \mathcal{K}^b(\mathcal{M}))$ to lift to an object of $\mathcal{Z}(\mathcal{K}^b(\mathcal{A}), \mathcal{K}^b(\mathcal{M}))$. The central application of this lifting lemma is a proof of some folklore facts about conjugation by Rouquier complexes in the Hecke category: the centrality of the full twist, and related properties of half twists and Coxeter braids. We also prove stronger, homotopy coherent versions of these statements, stated using the notion of the $A_{\infty}$-Drinfeld centralizer, which we believe is new.

Adam Caulton

The claim that a particle is an irreducible representation of the Poincaré group -- what I call \emph{Wigner's identification} -- is now, decades on from Wigner's (1939) original paper, so much a part of particle physics folklore that it is often taken as, or claimed to be, a definition. My aims in this paper are to: (i) clarify, and partially defend, the guiding ideas behind this identification; (ii) raise objections to its being an adequate definition; and (iii) offer a rival characterisation of particles. My main objections to Wigner's identification appeal to the problem of interacting particles, and to alternative spacetimes. I argue that the link implied in Wigner's identification, between a spacetime's symmetries and the generator of a particle's space of states, is at best misleading, and that there is no good reason to link the generator of a particle's space of states to symmetries of any kind. I propose an alternative characterisation of particles, which captures both the relativistic and non-relativistic setting. I further defend this proposal by appeal to a theorem which links the decomposition of Poincaré generators into purely orbital and spin components with canonical algebraic relations between position, momentum and spin.

Magda Górska

In the article, the author presents some of the works of the Polish artist Karolina Jarzębak, who uses cyber folklore in her work to narrate the problems of “millennials”, human loneliness and anxieties related to the current socio-political situation both in Poland and around the world. The analysis of artistic activity was based on the concepts of post-production and semionaut proposed by Nicolas Bourriaud and the theory of cultural remix, primarily in relation to its typology described in the theoretical texts of Eduardo Navas, where the so-called reflexive remix – the most important in these considerations – questions Benjamin’s aura and becoming an autonomous entity. Jarzębak’s multi-threaded works, created on the basis of Internet iconography centered around the so-called family of Oomer Wojaks, intertwine with forms characteristic of classical art history, but also of the 20th century neo-avant-garde. It opens the way to an extended interpretation of the works. The element that unites all the art installations is the reflection on the difficulties observed in social sciences in establishing lasting interpersonal relationships, faced by generations Y (and Z).

Kateryna Hodik

The article problematizes the formation of the topic of COVID-19 as part of the Ukrainian cultural discourse. Within the scope of this study, a repository of representative samples of literature was formed, texts of modern folklore devoted to this topic, as well as selections of poetic works were analyzed. The features of communication during the pandemic and its influence on literary creativity have been established. The conducted research made it possible to come to conclusions about the presence in Ukrainian culture of a scheme for dealing with crisis phenomena such as the COVID-19 pandemic, which involves the formation of a layer of folklore works at the first stages of working on the topic, then – working on it in the form of poetry, performances, etc., creating prose texts and new layer of folklore at the final stage of assimilation of the phenomena by the cultural discourse.

Nesibe Akıntuğ

In this study, intraterminal and non-intraterminal aspect representations in the oral language of native Cypriot Turkish and native Turkish speakers were investigated. In this study, the data obtained from the oral language usage of natural speakers of Cyprus Turkish and Turkey Turkish who study at university in the Turkish Republic of Northern Cyprus were used. Two experiments were conducted to determine how intraterminal and non-intraterminal aspect had been marked in the spoken language use of Turkish Cypriot and Turkish university students. In the data, the ways in which speakers in both clusters mark the intraterminal and non-intraterminal action aspect were examined. Two pictures were used to investigate intraterminal and non-intraterminal aspect representations in language usage of native Cypriot Turkish speaking young adults and native Turkey Turkish speaking young adults. Participants were asked to verbally express the actions in the pictures by showing two pictures reflecting intraterminal and non-intraterminal action appearances. The result obtained from this study suggests that intraterminal and non-intraterminal aspect oral expressions in native Cypriot Turkish and native Turkish speakers from Turkey differ from each other by using different morphemes. Cypriot Turkish speakers used –Ir (INTRANF) for intraterminality and –DI (FACT) for non-intraterminal aspect. Turkish speakers from Turkey used –Iyor (INTRALF) for intraterminality and –mIş (EVID) alongside, –DI (FACT) for non-intraterminal aspect.

Irina N. Polynskaya

The article is devoted to the problems of professional training of future teachers of fine arts. The purpose of the work is to consider the role and significance of the study by students of the Faculty of Arts and Design of traditional religious rites and holidays of the peoples of the Far North, the Khanty and Mansi. The material for the study was the traditional rites of the peoples of the Khanty and Mansi. Based on the method of theoretical analysis, the pedagogical potential of the traditional rites of the Khanty and Mansi peoples was revealed and the pedagogical conditions for the process of professional training of students – future teachers of fine arts were substantiated. The article describes in detail the traditions associated with hunting, fishing; the most common folk holidays associated with the bear, elk, crow day; national rites – wedding, funeral, rite of birth of a child. Comprehension and understanding of the world are reflected in oral folk art, legends, legends, myths, folklore. The future teacher of fine arts needs to know the traditional way of life of the indigenous people of Ugra, so that in his pedagogical work he can convey artistic and creative experience to schoolchildren. In conclusion, a description of the main pedagogical conditions for preparing students – future teachers of fine arts for professional activities, taking into account national traditions and the ethno-cultural specifics of the region, is given.

Danara V. Ubushieva

Goals. The article examines bear-related rudiments of Kalmyk folklore and draws semantic parallels with the bear cult of Tungus-Manchu and other Turko-Mongolian peoples to reconstruct Kalmyk mythoritual representations about this animal. Since quite a number of such mythoritual elements are represented in Kalmyk epic and folktales implicitly, it seems topical enough to reveal the former’s semantics. Materials and methods. The study focuses on The Song of Khan Zambal included in the Baga Tsokhor cycle of the Jangar epic. The employed research methods are structural/semantic, structural/typological, and comparative ones. Results. The attempted reconstruction attests to that mythological and ritual knowledge about the bear had been implicitly preserved in folklore foundations of Kalmyks, the ethnographic essentials proper to show extensive ties to those of Tungus-Manchu peoples. A set of ideas associated with the tradition of reciting the Jangar in long winter evenings and nights, epic motifs of brotherhood, hero’s sound sleep, and Savar’s moves along the moon road somewhat complete the Kalmyks’ knowledge of bear. These also indirectly confirm the assumption that Savar has a dual nature and is an anthropomorphic manifestation of a bear. In general, the image of Savar in epic space organically agrees with the ideas about bear articulated following the model — ‘ours among aliens’ and ‘alien to compatriots’.

C. Krattenthaler

Let $p_n(x)$, $n=0,1,\dots$, be the orthogonal polynomials with respect to a given density $dμ(x)$. Furthermore, let $dν(x)$ be a density which arises from $dμ(x)$ by multiplication by a rational function in $x$. We prove a formula that expresses the Hankel determinants of moments of $dν(x)$ in terms of a determinant involving the orthogonal polynomials $p_n(x)$ and associated functions $q_n(x)=\int p_n(u) \,dμ(u)/(x-u)$. Uvarov's formula for the orthogonal polynomials with respect to $dν(x)$ is a corollary of our theorem. Our result generalises a Hankel determinant formula for the case where the rational function is a polynomial that existed somehow hidden in the folklore of the theory of orthogonal polynomials but has been stated explicitly only relatively recently (see [arXiv:2101.04225]). Our theorem can be interpreted in a two-fold way: analytically or in the sense of formal series. We apply our theorem to derive several curious Hankel determinant evaluations.

Marijan Beg, Juliette Taka, Thomas Kluyver et al.

Literate computing has emerged as an important tool for computational studies and open science, with growing folklore of best practices. In this work, we report two case studies - one in computational magnetism and another in computational mathematics - where domain-specific software was exposed to the Jupyter environment. This enables high-level control of simulations and computation, interactive exploration of computational results, batch processing on HPC resources, and reproducible workflow documentation in Jupyter notebooks. In the first study, Ubermag drives existing computational micromagnetics software through a domain-specific language embedded in Python. In the second study, a dedicated Jupyter kernel interfaces with the GAP system for computational discrete algebra and its dedicated programming language. In light of these case studies, we discuss the benefits of this approach, including progress toward more reproducible and reusable research results and outputs, notably through the use of infrastructure such as JupyterHub and Binder.