IA Scholar Query: A Characterization of Fuzzy Subgroups of Some Abelian Groups.
https://scholar.archive.org/
Internet Archive Scholar query results feedeninfo@archive.orgMon, 03 Oct 2022 00:00:00 GMTfatcat-scholarhttps://scholar.archive.org/help1440On EMV-algebras with square roots
https://scholar.archive.org/work/vwvwbg3xnffjflpdd7wtao4fn4
A square root is a unary operation with some special properties. In the paper, we introduce and study square roots on EMV-algebras. First, the known properties of square roots defined on MV-algebras will be generalized for EMV-algebras, and we also find some new ones for MV-algebras. We use square roots to characterize EMV-algebras. Then, we find a relation between the square root of an EMV-algebra and the square root on its representing EMV-algebra with top element. We show that each strict EMV-algebra has a top element and we investigate the relation between divisible EMV-algebras and EMV-algebras with a special square root. Finally, we present square roots on tribes, EMV-tribes, and we present a complete characterization of any square root on an MV-algebra and on an EMV-algebra by group addition in the corresponding unital ℓ-group.Anatolij Dvurečenskij, Omid Zahiriwork_vwvwbg3xnffjflpdd7wtao4fn4Mon, 03 Oct 2022 00:00:00 GMTSome Aspects of Quantum Mechanics and Quantum Field Theory on Quantum Space- Time
https://scholar.archive.org/work/3vkj2kuonjhwhmayrlvmoxaq7e
This thesis is devoted to studying various aspects of quantum mechanics on non-commutative space-time and to capture some of the surviving aspects of symmetries of quantum field theory on such space-time, illustrated through toy models in (0 + 1) dimension. This allows one to gain some insights into this and other related issues in a more transparent manner.Partha Nandiwork_3vkj2kuonjhwhmayrlvmoxaq7eSat, 10 Sep 2022 00:00:00 GMTNoncommutative gauge and gravity theories and geometric Seiberg-Witten map
https://scholar.archive.org/work/jtftv7gw6red3pf6xi5afufthm
We give a pedagogical account of noncommutative gauge and gravity theories, where the exterior product between forms is deformed into a ⋆-product via an abelian twist (e.g. the Groenewold-Moyal twist). The Seiberg-Witten map between commutative and noncommutative gauge theories is introduced. It allows to express the action of noncommutative Einstein gravity coupled to spinor fields in terms of the usual commutative action with commutative fields plus extra interaction terms dependent on the noncommutativity parameter.Paolo Aschieri, Leonardo Castellaniwork_jtftv7gw6red3pf6xi5afufthmThu, 08 Sep 2022 00:00:00 GMTTameness in generalized metric structures
https://scholar.archive.org/work/264r2ab6hbhehnbbcrafludviu
We broaden the framework of metric abstract elementary classes (mAECs) in several essential ways, chiefly by allowing the metric to take values in a well-behaved quantale. As a proof of concept we show that the result of Boney and Zambrano on (metric) tameness under a large cardinal assumption holds in this more general context. We briefly consider a further generalization to partial metric spaces, and hint at connections to classes of fuzzy structures, and structures on sheaves.Michael Lieberman, Jiri Rosicky, Pedro Zambranowork_264r2ab6hbhehnbbcrafludviuThu, 08 Sep 2022 00:00:00 GMTSome Characterizations of Certain Complex Fuzzy Subgroups
https://scholar.archive.org/work/zqpw4kze4vfvva42hshkwykm3e
The complex fuzzy environment is an innovative tool to handle ambiguous situations in different mathematical problems. In this article, we commence the abstraction of (ρ,η)-complex fuzzy sets, (ρ,η)-complex fuzzy subgroupoid, (ρ,η)-complex fuzzy subgroups and describe important examples of the symmetric group under (ρ,η)-complex fuzzy sets. Additionally, we discuss the conjugacy class of the group with respect to (ρ,η)-complex fuzzy normal subgroups. We define (ρ,η)-complex fuzzy cosets and elaborate upon the certain operation of this analog to group theoretic operation. We prove that factors regarding the (ρ,η)-complex fuzzy normal subgroup form a group and establish an ordinary homomorphism. Moreover, we create the (ρ,η)-complex fuzzy subgroup of the factor group.Abeer Ali Alharbi, Dilshad Alghazzawiwork_zqpw4kze4vfvva42hshkwykm3eThu, 01 Sep 2022 00:00:00 GMTSome Developments in the Field of Homological Algebra by Defining New Class of Modules over Nonassociative Rings
https://scholar.archive.org/work/ejtw6gn74jbsrdpo7ld3z2vscu
The LA-module is a nonassociative structure that extends modules over a nonassociative ring known as left almost rings (LA-rings). Because of peculiar characteristics of LA-ring and its inception into noncommutative and nonassociative theory, drew the attention of many researchers over the last decade. In this study, the ideas of projective and injective LA-modules, LA-vector space, as well as examples and findings, are discussed. We construct a nontrivial example in which it is proved that if the LA-module is not free, then it cannot be a projective LA-module. We also construct free LA-modules, create a split sequence in LA-modules, and show several outcomes that are connected to them. We have proved the projective basis theorem for LA-modules. Also, split sequences in projective and injective LA-modules are discussed with the help of various propositions and theorems.Asima Razzaque, Inayatur Rehman, Gohar Aliwork_ejtw6gn74jbsrdpo7ld3z2vscuWed, 31 Aug 2022 00:00:00 GMTCosmology from Strong Interactions
https://scholar.archive.org/work/f6gllt4gwreungkefh42gmtcta
The wealth of theoretical and phenomenological information about Quantum Chromodynamics at short and long distances collected so far in major collider measurements has profound implications in cosmology. We provide a brief discussion on the major implications of the strongly coupled dynamics of quarks and gluons as well as on effects due to their collective motion on the physics of the early universe and in astrophysics.Andrea Addazi, Torbjörn Lundberg, Antonino Marcianò, Roman Pasechnik, Michal Šumberawork_f6gllt4gwreungkefh42gmtctaMon, 29 Aug 2022 00:00:00 GMTAll noncommutative spaces of κ-Poincaré geodesics
https://scholar.archive.org/work/sjkxcobg7rbftjx4ro4u6sdlqe
Noncommutative spaces of geodesics provide an alternative way of introducing noncommutative relativistic kinematics endowed with quantum group symmetry. In this paper we present explicitly the seven noncommutative spaces of time-, space- and light-like geodesics that can be constructed from the time-, space- and light- versions of the κ-Poincaré quantum symmetry in (3+1) dimensions. Remarkably enough, only for the light-like (or null-plane) κ-Poincaré deformation the three types of noncommutative spaces of geodesics can be constructed, while for the time-like and space-like deformations both the quantum time-like and space-like geodesics can be defined, but not the light-like one. This obstruction comes from the constraint imposed by the coisotropy condition for the corresponding deformation with respect to the isotropy subalgebra associated to the given space of geodesics, since all these quantum spaces are constructed as quantizations of the corresponding classical coisotropic Poisson homogeneous spaces. The known quantum space of geodesics on the light cone is given by a five-dimensional homogeneous quadratic algebra, and the six nocommutative spaces of time-like and space-like geodesics are explicitly obtained as six-dimensional nonlinear algebras. Five out of these six spaces are here presented for the first time, and Darboux generators for all of them are found, thus showing that the quantum deformation parameter κ^-1 plays exactly the same algebraic role on quantum geodesics as the Planck constant ħ plays in the usual phase space description of quantum mechanics.Angel Ballesteros, Ivan Gutierrez-Sagredo, Francisco J. Herranzwork_sjkxcobg7rbftjx4ro4u6sdlqeThu, 11 Aug 2022 00:00:00 GMTRandom Quantum Circuits
https://scholar.archive.org/work/57bh7e2hhbawvbw6cngsbn555e
Quantum circuits -- built from local unitary gates and local measurements -- are a new playground for quantum many-body physics and a tractable setting to explore universal collective phenomena far-from-equilibrium. These models have shed light on longstanding questions about thermalization and chaos, and on the underlying universal dynamics of quantum information and entanglement. In addition, such models generate new sets of questions and give rise to phenomena with no traditional analog, such as new dynamical phases in quantum systems that are monitored by an external observer. Quantum circuit dynamics is also topical in view of experimental progress in building digital quantum simulators that allow control of precisely these ingredients. Randomness in the circuit elements allows a high level of theoretical control, with a key theme being mappings between real-time quantum dynamics and effective classical lattice models or dynamical processes. Many of the universal phenomena that can be identified in this tractable setting apply to much wider classes of more structured many-body dynamics.Matthew P. A. Fisher, Vedika Khemani, Adam Nahum, Sagar Vijaywork_57bh7e2hhbawvbw6cngsbn555eThu, 28 Jul 2022 00:00:00 GMTAFFINE LOGIC FOR CONSTRUCTIVE MATHEMATICS
https://scholar.archive.org/work/obtchz625bczjhvvjja4xo644u
We show that numerous distinctive concepts of constructive mathematics arise automatically from an "antithesis" translation of affine logic into intuitionistic logic via a Chu/Dialectica construction. This includes apartness relations, complemented subsets, anti-subgroups and anti-ideals, strict and nonstrict order pairs, cut-valued metrics, and apartness spaces. We also explain the constructive bifurcation of some classical concepts using the choice between multiplicative and additive affine connectives. Affine logic and the antithesis construction thus systematically "constructivize" classical definitions, handling the resulting bookkeeping automatically. This is a "preproof" accepted article for The Bulletin of Symbolic Logic. This version may be subject to change during the production process.MICHAEL SHULMANwork_obtchz625bczjhvvjja4xo644uWed, 20 Jul 2022 00:00:00 GMTThe Characterization of Substructures of γ -Anti Fuzzy Subgroups with Application in Genetics
https://scholar.archive.org/work/qxufguy3rndzje5dmedyws5tlm
Fuzzy and anti fuzzy normal subgroups are the current instrument for dealing with ambiguity in various decision-making challenges. This article discusses γ -anti fuzzy normal subgroups and γ -fuzzy normal subgroups. Set-theoretic properties of union and intersection are examined and it is observed that union and intersection of γ -anti fuzzy normal subgroups are γ -anti fuzzy normal subgroups. Employee selection impacts the input quality of employees and hence plays an important part in human resource management. The cost of a group is established in proportion to the fuzzy multisets of a fuzzy multigroup. It was a good idea to introduce anti-intuitionistic fuzzy sets and anti-intuitionistic fuzzy subgroups, as well as to demonstrate some of their algebraic features. Product of γ -anti fuzzy normal subgroups and γ -fuzzy normal subgroups is defined, the product's algebraic nature is analyzed, and the findings are supported by presenting γ -anti typical sections with blurring and γ -ordinary parts with the weirdness of well-defined and well-established groups of genetic codes.Kalaichelvan Kalaiarasi, P. Sudha, Nasreen Kausar, Sajida Kousar, Dragan Pamucar, Nasr Al Din Ide, Lele Qinwork_qxufguy3rndzje5dmedyws5tlmSat, 16 Jul 2022 00:00:00 GMTThe pure spectrum of a residuated lattice
https://scholar.archive.org/work/nzhrgnb4ibd43leesk77abbkee
This paper studies a fascinating type of filter in residuated lattices, the so-called pure filters. A combination of algebraic and topological methods on the pure filters of a residuated lattice is applied to obtain some new structural results. The notion of purely-prime filters of a residuated lattice has been investigated, and a Cohen-type theorem has been obtained. It is shown that the pure spectrum of a residuated lattice is a compact sober space, and a Grothendieck-type theorem has been demonstrated. It is proved that the pure spectrum of a Gelfand residuated lattice is a Hausdorff space, and deduced that the pure spectrum of a Gelfand residuated lattice is homeomorphic to its usual maximal spectrum. Finally, the pure spectrum of an mp-residuated lattice is investigated and verified that a given residuated lattice is mp iff its minimal prime spectrum is equipped with the induced dual hull-kernel topology, and its pure spectrum is the same.Saeed Rasouli, Amin Dehghaniwork_nzhrgnb4ibd43leesk77abbkeeSat, 16 Jul 2022 00:00:00 GMTAffine logic for constructive mathematics
https://scholar.archive.org/work/joxeqzqy7vg47inmoxcpafeksq
We show that numerous distinctive concepts of constructive mathematics arise automatically from an "antithesis" translation of affine logic into intuitionistic logic via a Chu/Dialectica construction. This includes apartness relations, complemented subsets, anti-subgroups and anti-ideals, strict and non-strict order pairs, cut-valued metrics, and apartness spaces. We also explain the constructive bifurcation of some classical concepts using the choice between multiplicative and additive affine connectives. Affine logic and the antithesis construction thus systematically "constructivize" classical definitions, handling the resulting bookkeeping automatically.Michael Shulmanwork_joxeqzqy7vg47inmoxcpafeksqFri, 15 Jul 2022 00:00:00 GMTWhy Gauge? Conceptual Aspects of Gauge Theory
https://scholar.archive.org/work/a2jxturmpbeh7iygcnvnzpwaqa
This thesis is about conceptual aspects of gauge theories. Gauge theories lie at the heart of modern physics: in particular, they constitute the standard model of particle physics. At its simplest, the idea of gauge is that nature is best described using a descriptively redundant language; the different descriptions are said to be related by a gauge symmetry. The over-arching question the thesis aims to answer is: how can descriptive redundancy be fruitful for physics? This question embraces many important topics in the philosophical literature on gauge theory, which I will address. This thesis has two main Parts. Part \ref{part:I} provides technical and conceptual background. It relates the redundancies of gauge theories with the redundancies in the foundations of spacetime physics. In particular, to those of Einstein's theory of general relativity, that are more familar to the average philosopher. This Part provides a perspicuous, geometrical understanding of the physics of gauge theory, on a par with the chronogeometric understanding of general relativity. In Part II I will assess two surprising uses of and one contentious question about gauge symmetry. First, I will provide one answer to the question: "Why gauge theory?", that is: why introduce redundancies in our models of nature in the first place? This type of answer is pragmatic: because such redundancies are useful for model-building, in a particular way; and they allow us to focus our mathematical apparatus on different aspects of the same phenomena. Second, I present a choice of gauge that is related to a physically natural, and general, splitting of the electric field; which undermines the way one usually thinks of a choice of gauge as motivated by calculational convenience, or as completely arbitrary. Last, I will assess arguments and counter-arguments for the direct physical significance of gauge symmetries. The conclusion provides a second type of answer to the question of "Why gauge?". Namely: because we need it to couple subsystems.Henrique Gomes, Apollo-University Of Cambridge Repository, Jeremy Butterfieldwork_a2jxturmpbeh7iygcnvnzpwaqaFri, 15 Jul 2022 00:00:00 GMTSemiring systems arising from hyperrings
https://scholar.archive.org/work/plg57cxwvzhi5dl7heb7kfie2m
Hyperfields and systems are two algebraic frameworks which have been developed to provide a unified approach to classical and tropical structures. All hyperfields, and more generally hyperrings, can be represented by systems. We show that, conversely, we show that the systems arising in this way, called hypersystems, are characterized by certain elimination axioms. Systems are preserved under standard algebraic constructions; for instance matrices and polynomials over hypersystems are systems, but not hypersystems. We illustrate these results by discussing several examples of systems and hyperfields, and constructions like matroids over systems.Marianne Akian, Stephane Gaubert, Louis Rowenwork_plg57cxwvzhi5dl7heb7kfie2mThu, 14 Jul 2022 00:00:00 GMTFoundations for the Analysis of Surreal-Valued Genetic Functions
https://scholar.archive.org/work/zs2fyujmbbfozkhzlw4p6jlasa
In this thesis we systematize earlier results from the literature of functions on surreal num- bers and consider the generalization of results of Ehrlich and van den Dries regarding models of real-closed fields with exponentiation to the wider class of genetic functions, which includes many examples of interest such as the class of restricted analytic functions, exp, and log, as well as the ω map and other recursively definable functions. We do so by first amending the construction of arbitrary genetic functions found in the literature, so that we may properly compose functions, and so that one can easily recover the definition of exp. We then analyze our newly proposed inductive construction with two natural notions of complexity - that of generation, which tracks the dependence on earlier genetic functions, and that of Veblen rank, which describes the complexity of subtrees closed under a genetic function - in order to characterize the ordinals α such that the surreal numbers below height α will correspond to models satisfying the cofinality conditions and the axioms of real closed fields. After recovering fundamental analytic results for general surreal-valued functions, we further prove that every genetic function has a Veblen rank corresponding to an ordinal, and that our notion of Veblen rank behaves well under addition, multiplication, and composition, and in turn can be extended to arbitrary sets closed under said operations. In particular, the Veblen rank of a genetic function g identifies the largest subclass of epsilon numbers α such that sets of surreal numbers of height below α form a real closed field closed under g. From this, we establish many important functions, such as exp and log will have minimal Veblen rank, while the lambda and kappa maps used to define the Berarducci-Mantova derivative have non-trivial Veblen rank. As a further consequence of our Veblen rank bound, we establish that every entire genetic function is strictly tame in the sense of Fornasiero [4]. Afterwards, with G denoting a [...]Alexander Michael Berenbeimwork_zs2fyujmbbfozkhzlw4p6jlasaThu, 07 Jul 2022 00:00:00 GMTThe Gaussian conditional independence inference problem
https://scholar.archive.org/work/hzmnfg7kmbe77ijyxwv7efiryu
Die vorliegende Dissertation beschäftigt sich mit Strukturen Gaußscher bedingter Unabhängigkeit und ihrem Inferenzproblem. Bedingte Unabhängigkeit (engl. conditional independence, CI) ist ein Begriff aus der Wahrscheinlichkeits- und Informationstheorie und "Gaußsch" bezieht sich auf die bekannte multivariate Normalverteilung. Die CI-Relation einer multivariaten Zufallsvariable , deren Komponenten durch eine endliche Menge N indiziert sind, enthält Informationen darüber, welche Komponenten I die Verteilung anderer Komponenten J beeinflussen, wenn der Wert wieder anderer Komponenten K bekannt ist. Diese Relation wird als [ I ?? J j K] oder kurz (I; JjK) geschrieben. Bedingte Unabhängigkeit ist also eine dreiwertige Relation auf Teilvektoren von , die komplexe Abhängigkeiten zwischen den Variablen in kodiert. CI-Relationen werden formal in einem Zweig der künstlichen Intelligenz über logische Inferenzregeln studiert. Solche Inferenzregeln nehmen die folgende Form an: "wenn bestimmte bedingte Unabhängigkeiten gelten, welche (Disjunktionen von) anderen Unabhängigkeiten müssen ebenfalls gelten?" Kenntnis dieser Regeln erlaubt die automatische Deduktion von Informationen über die Abhängigkeitsstruktur von beobachteten Zufallsvariablen. Die Regeln, welche für CI-Relationen gelten, hängen von der Art der Wahrscheinlichkeitsverteilung ab. Binäre Verteilungen erfüllen beispielsweise andere Inferenzregeln als die kontinuierlichen Gaußschen Verteilungen. Eine multivariat Gauß-verteilte Zufallsvariable ist vollständig durch ihre Parameter, den Mittelwert 2 RN und die Kovarianzmatrix Σ 2 PDN, bestimmt. Unter dieser speziellen Annahme ist die bedingte Unabhängigkeitsaussage [ I ?? J j K] äquivalent zu einer Rangbedingung an die Teilmatrix von Σ mit Zeilen I [ K und Spalten J [ K, nämlich dass diese Matrix Rang jKj hat. Dieses Kriterium erlaubt die Behandlung von Gaußscher CI mit Mitteln der kommutativen Algebra, da die Rangbedingung als das Verschwinden einer Reihe von Polynomen in den Einträgen von Σ formuliert werden kann. Das [...]Tobias Boege, Universitäts- Und Landesbibliothek Sachsen-Anhalt, Martin-Luther Universität, Thomas Kahle, Volker Kaibelwork_hzmnfg7kmbe77ijyxwv7efiryuMon, 27 Jun 2022 00:00:00 GMTTopos and Stacks of Deep Neural Networks
https://scholar.archive.org/work/xw4jwxtjbbfetawfm7jayjlwgi
Every known artificial deep neural network (DNN) corresponds to an object in a canonical Grothendieck's topos; its learning dynamic corresponds to a flow of morphisms in this topos. Invariance structures in the layers (like CNNs or LSTMs) correspond to Giraud's stacks. This invariance is supposed to be responsible of the generalization property, that is extrapolation from learning data under constraints. The fibers represent pre-semantic categories (Culioli, Thom), over which artificial languages are defined, with internal logics, intuitionist, classical or linear (Girard). Semantic functioning of a network is its ability to express theories in such a language for answering questions in output about input data. Quantities and spaces of semantic information are defined by analogy with the homological interpretation of Shannon's entropy of P.Baudot and D.Bennequin in 2015). They generalize the measures found by Carnap and Bar-Hillel (1952). Amazingly, the above semantical structures are classified by geometric fibrant objects in a closed model category of Quillen, then they give rise to homotopical invariants of DNNs and of their semantic functioning. Intentional type theories (Martin-Loef) organize these objects and fibrations between them. Information contents and exchanges are analyzed by Grothendieck's derivators.Jean-Claude Belfiore, Daniel Bennequinwork_xw4jwxtjbbfetawfm7jayjlwgiThu, 16 Jun 2022 00:00:00 GMTResearch Topic Flows in Co-Authorship Networks
https://scholar.archive.org/work/ri4uwd2j4jaullhd2qlseitiv4
In scientometrics, scientific collaboration is often analyzed by means of co-authorships. An aspect which is often overlooked and more difficult to quantify is the flow of expertise between authors from different research topics, which is an important part of scientific progress. With the Topic Flow Network (TFN) we propose a graph structure for the analysis of research topic flows between scientific authors and their respective research fields. Based on a multi-graph and a topic model, our proposed network structure accounts for intratopic as well as intertopic flows. Our method requires for the construction of a TFN solely a corpus of publications (i.e., author and abstract information). From this, research topics are discovered automatically through non-negative matrix factorization. The thereof derived TFN allows for the application of social network analysis techniques, such as common metrics and community detection. Most importantly, it allows for the analysis of intertopic flows on a large, macroscopic scale, i.e., between research topic, as well as on a microscopic scale, i.e., between certain sets of authors. We demonstrate the utility of TFNs by applying our method to two comprehensive corpora of altogether 20 Mio. publications spanning more than 60 years of research in the fields computer science and mathematics. Our results give evidence that TFNs are suitable, e.g., for the analysis of topical communities, the discovery of important authors in different fields, and, most notably, the analysis of intertopic flows, i.e., the transfer of topical expertise. Besides that, our method opens new directions for future research, such as the investigation of influence relationships between research fields.Bastian Schäfermeier and Johannes Hirth and Tom Hanikawork_ri4uwd2j4jaullhd2qlseitiv4Thu, 16 Jun 2022 00:00:00 GMTNon-Liquid Cellular States
https://scholar.archive.org/work/n5dfco2s7zdafm5cwc7dyymgga
The existence of quantum non-liquid states and fracton orders, both gapped and gapless states, challenges our understanding of phases of entangled matter. We generalize the cellular topological states to liquid or non-liquid cellular states. We propose a mechanism to construct more general non-abelian states by gluing gauge-symmetry-breaking vs gauge-symmetry-extension interfaces as extended defects in a cellular network, including defects of higher-symmetries, in any dimension. Our approach also naturally incorporates the anyonic particle/string condensations and composite string (related to particle-string or p-string)/membrane condensations. This approach shows gluing the familiar extended topological quantum field theory or conformal field theory data via topology, geometry, and renormalization consistency criteria (via certain modified group cohomology or cobordism theory data) in a tensor network can still guide us to analyze the non-liquid states. (Part of the abelian construction can be understood from the K-matrix Chern-Simons theory approach and the coupled-layer-by-junction constructions.) This approach may also lead us toward a unifying framework for quantum systems of both higher-symmetries and sub-system/sub-dimensional symmetries.Juven Wangwork_n5dfco2s7zdafm5cwc7dyymggaFri, 03 Jun 2022 00:00:00 GMT