Centralizer and normalizer
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Knot invariants and higher representation theory Open
We construct knot invariants categorifying the quantum knot variants for all\nrepresentations of quantum groups. We show that these invariants coincide with\nprevious invariants defined by Khovanov for sl_2 and sl_3 and by\nMazorchuk-Strop…
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EXISTENCE OF -ANALOGS OF STEINER SYSTEMS Open
Let $\mathbb{F}_{q}^{n}$ be a vector space of dimension $n$ over the finite field $\mathbb{F}_{q}$ . A $q$ -analog of a Steiner system (also known as a $q$ - Steiner system ), denoted ${\mathcal{S}}_{q}(t,\!k,\!n)$ , is a set ${\mathcal{S}…
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A Certain Class of <i>t</i>-Intuitionistic Fuzzy Subgroups Open
In this study, the -intuitionistic fuzzy normalizer and centralizer of intuitionistic fuzzy subgroup are proposed. The -intuitionistic fuzzy centralizer is normal subgroup of -intuitionistic fuzzy normalizer and investigate various algebr…
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LOCALLY NORMAL SUBGROUPS OF TOTALLY DISCONNECTED GROUPS. PART II: COMPACTLY GENERATED SIMPLE GROUPS Open
We use the structure lattice, introduced in Part I, to undertake a systematic study of the class $\mathscr{S}$ consisting of compactly generated, topologically simple, totally disconnected locally compact groups that are nondiscrete. Given…
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Characterizations for pseudo core inverses in a ring with involution Open
Let R be a unital -ring. In this paper, we give several characterizations for the pseudo core and dual pseudo core inverses of an element by units in R. Moreover, their relations with -DMP are obtained. As a special case, the existence cri…
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Permutation centralizer algebras and multimatrix invariants Open
We introduce a class of permutation centralizer algebras which underly the\ncombinatorics of multi-matrix gauge invariant observables. One family of such\nnon-commutative algebras is parametrised by two integers. Its Wedderburn-Artin\ndeco…
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Modelling and improvement of the design of hinged centralizer for casing Open
We have researched an important problem for the oil-and-gas field, which is the problem of centralizing of cases in wellbores with a complex profile. Usually this problem is solved by equipping the case in problematic areas with special ce…
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The generalized Racah algebra as a commutant Open
The Racah algebra $R(n)$ of rank $(n-2)$ is obtained as the commutant of the\n\\mbox{$\\mathfrak{o}(2)^{\\oplus n}$} subalgebra of $\\mathfrak{o}(2n)$ in\noscillator representations of the universal algebra of $\\mathfrak{o}(2n)$. This\nre…
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Normalization matters: tracking the best strategy for sperm miRNA quantification Open
This work was supported by the 2014/SGR00524 project (Agència de Gestió d'Ajuts Universitaris i de Recerca, Generalitat de Catalunya, Spain) and UAB CF-180034 grant (Universitat Autònoma de Barcelona). Celia Corral-Vazquez is a recipient o…
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Centralizer’s applications to the inverse along an element Open
In this paper, we firstly prove that the absorption law for one-sided inverses along an element holds, and derive the absorption law for the inverse along an element. We then obtain the absorption law for the inverse along different elemen…
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Online normalizer calculation for softmax Open
The Softmax function is ubiquitous in machine learning, multiple previous works suggested faster alternatives for it. In this paper we propose a way to compute classical Softmax with fewer memory accesses and hypothesize that this reductio…
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Load Balanced GANs for Multi-view Face Image Synthesis Open
Multi-view face synthesis from a single image is an ill-posed problem and often suffers from serious appearance distortion. Producing photo-realistic and identity preserving multi-view results is still a not well defined synthesis problem.…
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Exhaustive Characterization of Quantum Many-Body Scars Using Commutant Algebras Open
We study quantum many-body scars (QMBS) in the language of commutant algebras, which are defined as symmetry algebras of of local Hamiltonians. This framework explains the origin of dynamically disconnected subspaces seen in models with ex…
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Detection of Pancreatic Ductal Adenocarcinoma by A qPCR-based Normalizer-free Circulating Extracellular Vesicles RNA Signature Open
Background: Pancreatic ductal adenocarcinoma (PDAC) is difficult to diagnose and many efforts have been made to evaluate EVs-derived RNAs as biomarkers to predict PDAC. However, lack of robust internal references largely limited their clin…
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The properties of central types with respect to enrichment by Jonsson set Open
The main results of the article are for a new class of theories, namely existential prime strongly convex Jonsson theories. This class is quite broad in terms of algebra, for example it includes the class of all Abelian groups and groups. …
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Qudit hypergraph states Open
We generalize the class of hypergraph states to multipartite systems of qudits, by means of constructions based on the d-dimensional Pauli group and its normalizer. For simple hypergraphs, the different equivalence classes under local oper…
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Expanding Cone and Applications to Homogeneous Dynamics Open
Let $U$ be a horospherical subgroup of a noncompact simple Lie group $H$ and let $A$ be a maximal split torus in the normalizer of $U$. We define the expanding cone $A_U^+$ in $A$ with respect to $U$ and show that it can be explicitly calc…
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Morita equivalence classes of blocks with elementary abelian defect groups of order 16 Open
We classify the Morita equivalence classes of blocks with elementary abelian defect groups of order $16$ with respect to a complete discrete valuation ring with algebraically closed residue field of characteristic two. As a consequence, bl…
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Twisted orbital integrals and irreducible components of affine Deligne–Lusztig varieties Open
We analyze the asymptotic behavior of certain twisted orbital integrals arising from the study of affine Deligne-Lusztig varieties. The main tools include the Base Change Fundamental Lemma and $q$-analogues of the Kostant partition functio…
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Exhaustive Characterization of Quantum Many-Body Scars using Commutant Algebras Open
We study Quantum Many-Body Scars (QMBS) in the language of commutant algebras, which are defined as symmetry algebras of families of local Hamiltonians. This framework explains the origin of dynamically disconnected subspaces seen in model…
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Strong Solidity of free Araki-Woods factors Open
We show that Shlyakhtenko's free Araki-Woods factors are strongly solid,\nmeaning that for any diffuse amenable von Neumann subalgebra that is the range\nof a normal conditional expectation, the normalizer remains amenable. This\nprovides …
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Evaluating normalization approaches for the better identification of aberrant microRNAs associated with hepatocellular carcinoma Open
An optimal normalization strategy to identify biologically important miRNAs in HCC tissue studies of miRNA may be the combination of global mean and 2 stable miRNAs. Selection of appropriate normalization strategies to adjust miRNAs levels…
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Yang-Baxter relation planar algebras Open
We give a new type of Schur-Weyl duality for the representations of a family of quantum subgroups and their centralizer algebra. We define and classify singly-generated, Yang-Baxter relation planar algebras. We present the skein theoretic …
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Lusztig Correspondence and Howe Correspondence for Finite Reductive Dual Pairs Open
Let $(G,G')$ be a reductive dual pair of a symplectic group and an orthogonal group over a finite field of odd characteristic. The Howe correspondence establishes a correspondence between a subset of irreducible characters of $G$ and a sub…
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Haar expectations of ratios of random characteristic polynomials Open
We compute Haar ensemble averages of ratios of random characteristic\npolynomials for the classical Lie groups K = O(N), SO(N), and USp(N). To that\nend, we start from the Clifford-Weyl algebera in its canonical realization on\nthe complex…
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Quantum scrambling of observable algebras Open
In this paper we describe an algebraic/geometrical approach to quantum scrambling. Generalized quantum subsystems are described by an hermitian-closed unital subalgebra of operators evolving through a unitary channel. Qualitatively, quant…
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Hochschild cohomology and dominant dimension Open
A new approach is established to compare Hochschild cohomologies of an algebra and of its centralizer subalgebras. This approach is based on dominant dimension, a homological dimension that is shown to control the comparison in a precise s…
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On the algebra of parallel endomorphisms of a pseudo-Riemannian metric Open
On a (pseudo-)Riemannian manifold (M,g), some fields of endomorphisms i.e.\nsections of End(TM) may be parallel for g. They form an associative algebra A,\nwhich is also the commutant of the holonomy group of g. As any associative\nalgebra…
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The Racah algebra as a commutant and Howe duality Open
The Racah algebra encodes the bispectrality of the eponym polynomials. It is known to be the symmetry algebra of the generic superintegrable model on the $2$-sphere. It is further identified as the commutant of the $\mathfrak{o}(2) \oplus …
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Bipolar Complex Fuzzy Subgroups Open
In this study, firstly, we interpret the level set, support, kernel for bipolar complex fuzzy (BCF) set, bipolar complex characteristic function, and BCF point. Then, we interpret the BCF subgroup, BCF normal subgroup, BCF conjugate, norma…