284 results match your criteria Algebras And Representation Theory[Journal]


Amenability of coarse spaces and -algebras.

Bull Math Sci 2018 9;8(2):257-306. Epub 2017 Nov 9.

5Department of Mathematics, Penn State University, 109 McAllister Building, University Park, PA 16802 USA.

In this article we analyze the notions of amenability and paradoxical decomposition from an algebraic perspective. We consider this dichotomy for locally finite extended metric spaces and for general algebras over fields. In the context of algebras we also study the relation of amenability with proper infiniteness. Read More

View Article

Download full-text PDF

Source
http://link.springer.com/10.1007/s13373-017-0109-6
Publisher Site
http://dx.doi.org/10.1007/s13373-017-0109-6DOI Listing
http://www.ncbi.nlm.nih.gov/pmc/articles/PMC6434994PMC
November 2017
1 Read

as a symmetry of division algebraic ladder operators.

Authors:
C Furey

Eur Phys J C Part Fields 2018 12;78(5):375. Epub 2018 May 12.

1Department of Applied Mathematics and Theoretical Physics, University of Cambridge, Wilberforce Road, Cambridge, CB3 0WA UK.

We demonstrate a model which captures certain attractive features of (5) theory, while providing a possible escape from proton decay. In this paper we show how ladder operators arise from the division algebras , , , and . From the () symmetry of these ladder operators, we then demonstrate a model which has much structural similarity to Georgi and Glashow's (5) grand unified theory. Read More

View Article

Download full-text PDF

Source
http://link.springer.com/10.1140/epjc/s10052-018-5844-7
Publisher Site
http://dx.doi.org/10.1140/epjc/s10052-018-5844-7DOI Listing
http://www.ncbi.nlm.nih.gov/pmc/articles/PMC6435233PMC
May 2018
1 Read

On Construction of Projection Operators.

Authors:
Artur F Izmaylov

J Phys Chem A 2019 Apr 8;123(15):3429-3433. Epub 2019 Apr 8.

Department of Physical and Environmental Sciences , University of Toronto Scarborough , Toronto , Ontario M1C 1A4 , Canada.

The problem of construction of projection operators on eigensubspaces of symmetry operators is considered. This problem arises in many approximate methods for solving time-independent and time-dependent quantum problems, and its solution ensures proper physical symmetries in development of approximate methods. The projector form is sought as a function of symmetry operators and their eigenvalues characterizing the eigensubspace of interest. Read More

View Article

Download full-text PDF

Source
http://dx.doi.org/10.1021/acs.jpca.9b01103DOI Listing

Clifford Algebras Meet Tree Decompositions.

Algorithmica 2019 30;81(2):497-518. Epub 2018 Jul 30.

Faculty of Mathematics, Informatics, and Mechanics, University of Warsaw, Warsaw, Poland.

We introduce the non-commutative subset convolution-a convolution of functions useful when working with determinant-based algorithms. In order to compute it efficiently, we take advantage of Clifford algebras, a generalization of quaternions used mainly in the quantum field theory. We apply this tool to speed up algorithms counting subgraphs parameterized by the treewidth of a graph. Read More

View Article

Download full-text PDF

Source
http://dx.doi.org/10.1007/s00453-018-0489-3DOI Listing
http://www.ncbi.nlm.nih.gov/pmc/articles/PMC6386049PMC

Orthogonal Stochastic Duality Functions from Lie Algebra Representations.

J Stat Phys 2019 19;174(1):97-119. Epub 2018 Oct 19.

Technische Universiteit Delft, DIAM, PO Box 5031, 2600 GA Delft, The Netherlands.

We obtain stochastic duality functions for specific Markov processes using representation theory of Lie algebras. The duality functions come from the kernel of a unitary intertwiner between -representations, which provides (generalized) orthogonality relations for the duality functions. In particular, we consider representations of the Heisenberg algebra and . Read More

View Article

Download full-text PDF

Source
http://dx.doi.org/10.1007/s10955-018-2178-7DOI Listing
http://www.ncbi.nlm.nih.gov/pmc/articles/PMC6383627PMC
October 2018

Colombeau algebras without asymptotics.

Authors:
Eduard A Nigsch

J Pseudodiffer Oper Appl 2019 23;10(1):133-154. Epub 2017 Nov 23.

Wolfgang Pauli Institute, Oskar-Morgenstern-Platz 1, 1090 Vienna, Austria.

We present a construction of algebras of generalized functions of Colombeau-type which, instead of asymptotic estimates with respect to a regularization parameter, employs only topological estimates on certain spaces of kernels for its definition. Read More

View Article

Download full-text PDF

Source
http://dx.doi.org/10.1007/s11868-017-0230-zDOI Listing
http://www.ncbi.nlm.nih.gov/pmc/articles/PMC6373394PMC
November 2017
5 Reads

Quantum Groups as Hidden Symmetries of Quantum Impurities.

Phys Rev Lett 2018 Dec;121(25):255302

IST Austria (Institute of Science and Technology Austria), Am Campus 1, 3400 Klosterneuburg, Austria.

We present an approach to interacting quantum many-body systems based on the notion of quantum groups, also known as q-deformed Lie algebras. In particular, we show that, if the symmetry of a free quantum particle corresponds to a Lie group G, in the presence of a many-body environment this particle can be described by a deformed group, G_{q}. Crucially, the single deformation parameter, q, contains all the information about the many-particle interactions in the system. Read More

View Article

Download full-text PDF

Source
http://dx.doi.org/10.1103/PhysRevLett.121.255302DOI Listing
December 2018
1 Read

Developing a new approach for (biological) optimal control problems: Application to optimization of laccase production with a comparison between response surface methodology and novel geometric procedure.

Math Biosci 2019 Mar 19;309:23-33. Epub 2018 Dec 19.

Fouman Faculty of Engineering, College of Engineering, University of Tehran, P. O. Box 43581-39115, Guilan, Iran. Electronic address:

Laccase production by indigenous fungus, Phanerochaete chrysosporium, requires solving optimal problems to determine the maximum production of the enzyme within a definite time period and conditions specified in the solid-state fermentation process. For this purpose, parallel to response surface methodology, an analytical approach has been proposed based on the advanced concepts of Poisson geometry and Lie groups, which lead to a system of the Hamiltonian equations. Despite the dating of the Hamiltonian approach to solving biological problems, the novelty of this paper is based on the expression of a Hamiltonian system in notions of Poisson geometry, Lie algebras and symmetry groups and first integrals. Read More

View Article

Download full-text PDF

Source
https://linkinghub.elsevier.com/retrieve/pii/S00255564183060
Publisher Site
http://dx.doi.org/10.1016/j.mbs.2018.12.013DOI Listing
March 2019
1 Read

Reduction of quantum systems and the local Gauss law.

Lett Math Phys 2018 3;108(11):2515-2522. Epub 2018 May 3.

Institute for Mathematics, Astrophysics and Particle Physics, Radboud University Nijmegen, Heyendaalseweg 135, 6525 AJ Nijmegen, The Netherlands.

We give an operator-algebraic interpretation of the notion of an ideal generated by the unbounded operators associated with the elements of the Lie algebra of a Lie group that implements the symmetries of a quantum system. We use this interpretation to establish a link between Rieffel induction and the implementation of a local Gauss law in lattice gauge theories similar to the method discussed by Kijowski and Rudolph (J Math Phys 43:1796-1808, 2002; J Math Phys 46:032303, 2004). Read More

View Article

Download full-text PDF

Source
http://dx.doi.org/10.1007/s11005-018-1092-xDOI Listing
http://www.ncbi.nlm.nih.gov/pmc/articles/PMC6182777PMC

A new generalization of -algebras.

Heliyon 2018 Oct 17;4(10):e00863. Epub 2018 Oct 17.

Faculty of Science and Technology, Pibulsongkram Rajabhat University, Phitsanulok 65000, Thailand.

In this paper we introduce the notion of -algebras as a generalization of -algebras, we investigate its elementary properties. The aim of this paper is to investigate the concept of filters, left ideals (right ideal, ideal) and fuzzy filters in -algebras. Moreover, we investigate relationships between left ideals and filters in -algebras. Read More

View Article

Download full-text PDF

Source
http://dx.doi.org/10.1016/j.heliyon.2018.e00863DOI Listing
http://www.ncbi.nlm.nih.gov/pmc/articles/PMC6197410PMC
October 2018

Graph-algebras-Faithful representations and mediating objects in mathematics.

Authors:
Jessica Carter

Endeavour 2018 Jun - Sep;42(2-3):180-188. Epub 2018 Aug 31.

Department of Mathematics and Computer Science, University of Southern Denmark, Campusvej 55, 5230 Odense, Denmark. Electronic address:

I consider the role of diagrams in contemporary mathematics. More specifically the role of certain diagrams-so-called directed graphs-will be investigated. I propose that these graphs act as mediating objects. Read More

View Article

Download full-text PDF

Source
http://dx.doi.org/10.1016/j.endeavour.2018.07.006DOI Listing
December 2018

Efficient and Robust Direct Image Registration Based on Joint Geometric and Photometric Lie Algebra.

IEEE Trans Image Process 2018 Dec 10;27(12):6010-6024. Epub 2018 Aug 10.

This paper considers the joint geometric and photometric image registration problem. The inverse compositional (IC) algorithm and the efficient second-order minimization (ESM) algorithm are two typical efficient methods applied to the geometric registration problem. Their efficiency stems from the utilization of the group structure of geometric transformations. Read More

View Article

Download full-text PDF

Source
http://dx.doi.org/10.1109/TIP.2018.2864895DOI Listing
December 2018

Lie-Markov Models Derived from Finite Semigroups.

Bull Math Biol 2019 Feb 2;81(2):361-383. Epub 2018 Aug 2.

School of Physical Sciences, University of Tasmania, Hobart, Australia.

We present and explore a general method for deriving a Lie-Markov model from a finite semigroup. If the degree of the semigroup is k, the resulting model is a continuous-time Markov chain on k-states and, as a consequence of the product rule in the semigroup, satisfies the property of multiplicative closure. This means that the product of any two probability substitution matrices taken from the model produces another substitution matrix also in the model. Read More

View Article

Download full-text PDF

Source
http://dx.doi.org/10.1007/s11538-018-0455-xDOI Listing
February 2019

Quantum heat engines: Limit cycles and exceptional points.

Phys Rev E 2018 Jun;97(6-1):062153

Institute of Chemistry, The Hebrew University, Jerusalem 91904, Israel.

We show that the inability of a quantum Otto cycle to reach a limit cycle is connected with the propagator of the cycle being noncompact. For a working fluid consisting of quantum harmonic oscillators, the transition point in parameter space where this instability occurs is associated with a non-Hermitian degeneracy (exceptional point) of the eigenvalues of the propagator. In particular, a third-order exceptional point is observed at the transition from the region where the eigenvalues are complex numbers to the region where all the eigenvalues are real. Read More

View Article

Download full-text PDF

Source
http://dx.doi.org/10.1103/PhysRevE.97.062153DOI Listing

Global exponential stability of octonion-valued neural networks with leakage delay and mixed delays.

Neural Netw 2018 Sep 14;105:277-293. Epub 2018 Jun 14.

Department of Computer and Software Engineering, Polytechnic University Timişoara, Blvd. V. Pârvan, No. 2, 300223 Timişoara, Romania. Electronic address:

This paper discusses octonion-valued neural networks (OVNNs) with leakage delay, time-varying delays, and distributed delays, for which the states, weights, and activation functions belong to the normed division algebra of octonions. The octonion algebra is a nonassociative and noncommutative generalization of the complex and quaternion algebras, but does not belong to the category of Clifford algebras, which are associative. In order to avoid the nonassociativity of the octonion algebra and also the noncommutativity of the quaternion algebra, the Cayley-Dickson construction is used to decompose the OVNNs into 4 complex-valued systems. Read More

View Article

Download full-text PDF

Source
http://dx.doi.org/10.1016/j.neunet.2018.05.006DOI Listing
September 2018

Cluster Adjacency Properties of Scattering Amplitudes in N=4 Supersymmetric Yang-Mills Theory.

Phys Rev Lett 2018 Apr;120(16):161601

School of Physics & Astronomy, University of Southampton, Highfield, Southampton SO17 1BJ, United Kingdom.

We conjecture a new set of analytic relations for scattering amplitudes in planar N=4 super Yang-Mills theory. They generalize the Steinmann relations and are expressed in terms of the cluster algebras associated to Gr(4,n). In terms of the symbol, they dictate which letters can appear consecutively. Read More

View Article

Download full-text PDF

Source
http://dx.doi.org/10.1103/PhysRevLett.120.161601DOI Listing
April 2018
1 Read

Toward a Definition of Complexity for Quantum Field Theory States.

Phys Rev Lett 2018 Mar;120(12):121602

Max Planck Institute for Gravitational Physics, Potsdam-Golm D-14476, Germany.

We investigate notions of complexity of states in continuous many-body quantum systems. We focus on Gaussian states which include ground states of free quantum field theories and their approximations encountered in the context of the continuous version of the multiscale entanglement renormalization ansatz. Our proposal for quantifying state complexity is based on the Fubini-Study metric. Read More

View Article

Download full-text PDF

Source
http://dx.doi.org/10.1103/PhysRevLett.120.121602DOI Listing
March 2018
1 Read

Nonunitary Lagrangians and Unitary Non-Lagrangian Conformal Field Theories.

Phys Rev Lett 2018 Feb;120(8):081601

CRST and School of Physics and Astronomy Queen Mary University of London, London E1 4NS, United Kingdom.

In various dimensions, we can sometimes compute observables of interacting conformal field theories (CFTs) that are connected to free theories via the renormalization group (RG) flow by computing protected quantities in the free theories. On the other hand, in two dimensions, it is often possible to algebraically construct observables of interacting CFTs using free fields without the need to explicitly construct an underlying RG flow. In this Letter, we begin to extend this idea to higher dimensions by showing that one can compute certain observables of an infinite set of unitary strongly interacting four-dimensional N=2 superconformal field theories (SCFTs) by performing simple calculations involving sets of nonunitary free four-dimensional hypermultiplets. Read More

View Article

Download full-text PDF

Source
http://dx.doi.org/10.1103/PhysRevLett.120.081601DOI Listing
February 2018
1 Read

Normal forms for Poisson maps and symplectic groupoids around Poisson transversals.

Lett Math Phys 2018 4;108(3):711-735. Epub 2017 Oct 4.

2IMAPP, Radboud University Nijmegen, 6500 GL Nijmegen, The Netherlands.

Poisson transversals are submanifolds in a Poisson manifold which intersect all symplectic leaves transversally and symplectically. In this communication, we prove a normal form theorem for Poisson maps around Poisson transversals. A Poisson map pulls a Poisson transversal back to a Poisson transversal, and our first main result states that simultaneous normal forms exist around such transversals, for which the Poisson map becomes transversally linear, and intertwines the normal form data of the transversals. Read More

View Article

Download full-text PDF

Source
http://dx.doi.org/10.1007/s11005-017-1007-2DOI Listing
http://www.ncbi.nlm.nih.gov/pmc/articles/PMC5818580PMC
October 2017

Filtrations on Springer fiber cohomology and Kostka polynomials.

Lett Math Phys 2018 26;108(3):679-698. Epub 2017 Sep 26.

2Department of Mathematics, Imperial College London, South Kensington Campus, London, SW7 2AZ UK.

We prove a conjecture which expresses the bigraded Poisson-de Rham homology of the nilpotent cone of a semisimple Lie algebra in terms of the generalized (one-variable) Kostka polynomials, via a formula suggested by Lusztig. This allows us to construct a canonical family of filtrations on the flag variety cohomology, and hence on irreducible representations of the Weyl group, whose Hilbert series are given by the generalized Kostka polynomials. We deduce consequences for the cohomology of all Springer fibers. Read More

View Article

Download full-text PDF

Source
http://dx.doi.org/10.1007/s11005-017-1002-7DOI Listing
http://www.ncbi.nlm.nih.gov/pmc/articles/PMC5818583PMC
September 2017

Poisson traces, D-modules, and symplectic resolutions.

Lett Math Phys 2018 5;108(3):633-678. Epub 2017 Dec 5.

2Imperial College London, London, UK.

We survey the theory of Poisson traces (or zeroth Poisson homology) developed by the authors in a series of recent papers. The goal is to understand this subtle invariant of (singular) Poisson varieties, conditions for it to be finite-dimensional, its relationship to the geometry and topology of symplectic resolutions, and its applications to quantizations. The main technique is the study of a canonical D-module on the variety. Read More

View Article

Download full-text PDF

Source
http://dx.doi.org/10.1007/s11005-017-1024-1DOI Listing
http://www.ncbi.nlm.nih.gov/pmc/articles/PMC5818674PMC
December 2017

Approximation of the generalized Cauchy-Jensen functional equation in -algebras.

J Inequal Appl 2018 12;2018(1):236. Epub 2018 Sep 12.

1Department of Mathematics, Faculty of Science, Naresuan University, Phitsanulok, Thailand.

In this paper, we prove Hyers-Ulam-Rassias stability of -algebra homomorphisms for the following generalized Cauchy-Jensen equation: for all and for any fixed positive integer , which was introduced by Gao et al. [ 3:63-77, 2009], on -algebras by using fixed poind alternative theorem. Moreover, we introduce and investigate Hyers-Ulam-Rassias stability of generalized -derivation for such functional equations on -algebras by the same method. Read More

View Article

Download full-text PDF

Source
http://dx.doi.org/10.1186/s13660-018-1824-6DOI Listing
http://www.ncbi.nlm.nih.gov/pmc/articles/PMC6154084PMC
September 2018

What Chern-Simons theory assigns to a point.

Proc Natl Acad Sci U S A 2017 12 5;114(51):13418-13423. Epub 2017 Dec 5.

Mathematical Institute, Oxford University, Oxford OX2 6GG, United Kingdom

We answer the questions, "What does Chern-Simons theory assign to a point?" and "What kind of mathematical object does Chern-Simons theory assign to a point?" Our answer to the first question is representations of the based loop group. More precisely, we identify a certain class of projective unitary representations of the based loop group [Formula: see text] We define the fusion product of such representations, and we prove that, modulo certain conjectures, the Drinfel'd center of that representation category of [Formula: see text] is equivalent to the category of positive energy representations of the free loop group [Formula: see text] The abovementioned conjectures are known to hold when the gauge group is abelian or of type [Formula: see text] Our answer to the second question is bicommutant categories. The latter are higher categorical analogs of von Neumann algebras: They are tensor categories that are equivalent to their bicommutant inside [Formula: see text], the category of bimodules over a hyperfinite [Formula: see text] factor. Read More

View Article

Download full-text PDF

Source
http://dx.doi.org/10.1073/pnas.1711591114DOI Listing
http://www.ncbi.nlm.nih.gov/pmc/articles/PMC5754777PMC
December 2017

Convex congruences.

Soft comput 2017 9;21(19):5641-5645. Epub 2016 Aug 9.

Faculty of Mathematics and Geoinformation, Institute of Discrete Mathematics and Geometry, TU Wien, Wiedner Hauptstraße 8-10, 1040 Vienna, Austria.

For an algebra [Formula: see text] belonging to a quasivariety [Formula: see text], the quotient [Formula: see text] need not belong to [Formula: see text] for every [Formula: see text]. The natural question arises for which [Formula: see text]. We consider algebras [Formula: see text] of type (2, 0) where a partial order relation is determined by the operations [Formula: see text] and 1. Read More

View Article

Download full-text PDF

Source
http://dx.doi.org/10.1007/s00500-016-2306-8DOI Listing
http://www.ncbi.nlm.nih.gov/pmc/articles/PMC5613104PMC

Knowledge-driven computational modeling in Alzheimer's disease research: Current state and future trends.

Alzheimers Dement 2017 Nov 14;13(11):1292-1302. Epub 2017 Sep 14.

Department of Molecular and Integrative Physiology, and Beckman Institute for Advanced Science and Technology, University of Illinois at Urbana-Champaign, Urbana, IL, USA.

Neurodegenerative diseases such as Alzheimer's disease (AD) follow a slowly progressing dysfunctional trajectory, with a large presymptomatic component and many comorbidities. Using preclinical models and large-scale omics studies ranging from genetics to imaging, a large number of processes that might be involved in AD pathology at different stages and levels have been identified. The sheer number of putative hypotheses makes it almost impossible to estimate their contribution to the clinical outcome and to develop a comprehensive view on the pathological processes driving the clinical phenotype. Read More

View Article

Download full-text PDF

Source
http://dx.doi.org/10.1016/j.jalz.2017.08.011DOI Listing
November 2017
15 Reads

Parametric model measurement: reframing traditional measurement ideas in neuropsychological practice and research.

Clin Neuropsychol 2017 Aug - Oct;31(6-7):1047-1072. Epub 2017 Jun 15.

c San Diego State University/University of California San Diego Joint Doctoral Program in Clinical Psychology , San Diego , CA , USA.

Objective: Neuropsychology is an applied measurement field with its psychometric work primarily built upon classical test theory (CTT). We describe a series of psychometric models to supplement the use of CTT in neuropsychological research and test development.

Method: We introduce increasingly complex psychometric models as measurement algebras, which include model parameters that represent abilities and item properties. Read More

View Article

Download full-text PDF

Source
http://dx.doi.org/10.1080/13854046.2017.1334829DOI Listing
February 2018
6 Reads

Simple nuclear *-algebras not isomorphic to their opposites.

Proc Natl Acad Sci U S A 2017 06 30;114(24):6244-6249. Epub 2017 May 30.

Department of Mathematics, Ben-Gurion University of the Negev, Be'er Sheva 84105, Israel.

We show that it is consistent with Zermelo-Fraenkel set theory with the axiom of choice (ZFC) that there is a simple nuclear nonseparable [Formula: see text]-algebra, which is not isomorphic to its opposite algebra. We can furthermore guarantee that this example is an inductive limit of unital copies of the Cuntz algebra [Formula: see text] or of the canonical anticommutation relations (CAR) algebra. Read More

View Article

Download full-text PDF

Source
http://dx.doi.org/10.1073/pnas.1619936114DOI Listing
http://www.ncbi.nlm.nih.gov/pmc/articles/PMC5474777PMC

Modeling electron fractionalization with unconventional Fock spaces.

Authors:
Emilio Cobanera

J Phys Condens Matter 2017 Aug 8;29(30):305602. Epub 2017 May 8.

Present address: Department of Physics and Astronomy, Dartmouth College, 6127 Wilder Laboratory, Hanover, NH 03755, United States of America.

It is shown that certain fractionally-charged quasiparticles can be modeled on D-dimensional lattices in terms of unconventional yet simple Fock algebras of creation and annihilation operators. These unconventional Fock algebras are derived from the usual fermionic algebra by taking roots (the square root, cubic root, etc) of the usual fermionic creation and annihilation operators. If the fermions carry non-Abelian charges, then this approach fractionalizes the Abelian charges only. Read More

View Article

Download full-text PDF

Source
http://dx.doi.org/10.1088/1361-648X/aa718fDOI Listing
August 2017
1 Read

Quantum field theory and coalgebraic logic in theoretical computer science.

Prog Biophys Mol Biol 2017 11 4;130(Pt A):39-52. Epub 2017 May 4.

Dipartimento di Fisica "E.R.Caianiello", Università di Salerno, INFN Gruppo collegato di Salerno, Fisciano (SA) 84084, Italy. Electronic address:

We suggest that in the framework of the Category Theory it is possible to demonstrate the mathematical and logical dual equivalence between the category of the q-deformed Hopf Coalgebras and the category of the q-deformed Hopf Algebras in quantum field theory (QFT), interpreted as a thermal field theory. Each pair algebra-coalgebra characterizes a QFT system and its mirroring thermal bath, respectively, so to model dissipative quantum systems in far-from-equilibrium conditions, with an evident significance also for biological sciences. Our study is in fact inspired by applications to neuroscience where the brain memory capacity, for instance, has been modeled by using the QFT unitarily inequivalent representations. Read More

View Article

Download full-text PDF

Source
http://dx.doi.org/10.1016/j.pbiomolbio.2017.04.006DOI Listing
November 2017
1 Read

Integrability of systems of two second-order ordinary differential equations admitting four-dimensional Lie algebras.

Proc Math Phys Eng Sci 2017 Jan;473(2197):20160461

Laboratory 'Group analysis of mathematical models in natural and engineering sciences' , Ufa State Aviation Technical University , 450 008 Ufa, Russia.

We suggest an algorithm for integrating systems of two second-order ordinary differential equations with four symmetries. In particular, if the admitted transformation group has two second-order differential invariants, the corresponding system can be integrated by quadratures using invariant representation and the operator of invariant differentiation. Otherwise, the systems reduce to partially uncoupled forms and can also be integrated by quadratures. Read More

View Article

Download full-text PDF

Source
http://dx.doi.org/10.1098/rspa.2016.0461DOI Listing
http://www.ncbi.nlm.nih.gov/pmc/articles/PMC5312120PMC
January 2017

Asymptotic aspect of derivations in Banach algebras.

J Inequal Appl 2017 6;2017(1):36. Epub 2017 Feb 6.

Department of Mathematics, Chungnam National University, 99 Daehangno, Yuseong-gu, Daejeon, 34134 Korea.

We prove that every approximate linear left derivation on a semisimple Banach algebra is continuous. Also, we consider linear derivations on Banach algebras and we first study the conditions for a linear derivation on a Banach algebra. Then we examine the functional inequalities related to a linear derivation and their stability. Read More

View Article

Download full-text PDF

Source
http://dx.doi.org/10.1186/s13660-017-1308-0DOI Listing
http://www.ncbi.nlm.nih.gov/pmc/articles/PMC5306381PMC
February 2017
1 Read

Infinite order decompositions of C*-algebras.

Springerplus 2016 21;5(1):1827. Epub 2016 Oct 21.

Faculty of Mathematics, Andizhan State University, Andizhan, Uzbekistan.

The present paper is devoted to infinite order decompositions of C*-algebras. It is proved that an infinite order decomposition (IOD) of a C*-algebra forms the complexification of an order unit space, and, if the C*-algebra is monotone complete (not necessarily weakly closed) then its IOD is also monotone complete ordered vector space. Also it is established that an IOD of a C*-algebra is a C*-algebra if and only if this C*-algebra is a von Neumann algebra. Read More

View Article

Download full-text PDF

Source
http://dx.doi.org/10.1186/s40064-016-3468-7DOI Listing
http://www.ncbi.nlm.nih.gov/pmc/articles/PMC5074999PMC
October 2016
3 Reads

Analytic real algebras.

Springerplus 2016 29;5(1):1684. Epub 2016 Sep 29.

Department of Mathematics, Chungbuk National University, Cheongju, 28644 Korea.

In this paper we construct some real algebras by using elementary functions, and discuss some relations between several axioms and its related conditions for such functions. We obtain some conditions for real-valued functions to be a (edge) -algebra. Read More

View Article

Download full-text PDF

Source
http://dx.doi.org/10.1186/s40064-016-3334-7DOI Listing
http://www.ncbi.nlm.nih.gov/pmc/articles/PMC5042926PMC
September 2016
4 Reads

On discrete evolutionary dynamics driven by quadratic interactions.

Theory Biosci 2016 Dec 21;135(4):187-200. Epub 2016 Jul 21.

Laboratoire de Physique Théorique et Modélisation, CNRS-UMR 8089 et Université de Cergy-Pontoise, 2 Avenue Adolphe Chauvin, 95302, Cergy-Pontoise, France.

After an introduction to the general topic of models for a given locus of a diploid population whose quadratic dynamics is determined by a fitness landscape, we consider more specifically the models that can be treated using genetic (or train) algebras. In this setup, any quadratic offspring interaction can produce any type of offspring and after the use of specific changes of basis, we study the evolution and possible stability of some examples. We also consider some examples that cannot be treated using the framework of genetic algebras. Read More

View Article

Download full-text PDF

Source
http://dx.doi.org/10.1007/s12064-016-0232-zDOI Listing
December 2016

Ideals and primitive elements of some relatively free Lie algebras.

Springerplus 2016 22;5(1):833. Epub 2016 Jun 22.

Department of Mathematics, Çukurova University, 01330 Adana, Turkey.

Let F be a free Lie algebra of finite rank over a field K. We prove that if an ideal [Formula: see text] of the algebra [Formula: see text] contains a primitive element [Formula: see text] then the element [Formula: see text] is primitive. We also show that, in the Lie algebra [Formula: see text] there exists an element [Formula: see text] such that the ideal [Formula: see text] contains a primitive element [Formula: see text] but, [Formula: see text] and [Formula: see text] are not conjugate by means of an inner automorphism. Read More

View Article

Download full-text PDF

Source
http://dx.doi.org/10.1186/s40064-016-2545-2DOI Listing
http://www.ncbi.nlm.nih.gov/pmc/articles/PMC4917519PMC

Neurons the decision makers, Part I: The firing function of a single neuron.

Authors:
Thomas Saaty

Neural Netw 2017 Feb 6;86:102-114. Epub 2016 May 6.

University of Pittsburgh, United States. Electronic address:

This paper is concerned with understanding synthesis of electric signals in the neural system based on making pairwise comparisons. Fundamentally, every person and every animal are born with the talent to compare stimuli from things that share properties in space or over time. Comparisons always need experience to distinguish among things. Read More

View Article

Download full-text PDF

Source
http://dx.doi.org/10.1016/j.neunet.2016.04.003DOI Listing
February 2017

Quantum walks, deformed relativity and Hopf algebra symmetries.

Philos Trans A Math Phys Eng Sci 2016 May;374(2068)

QUIT group, Dipartimento di Fisica, Università degli Studi di Pavia, and INFN, Gruppo IV, via Bassi 6, 27100 Pavia, Italy.

We show how the Weyl quantum walk derived from principles in D'Ariano & Perinotti (D'Ariano & Perinotti 2014Phys. Rev. A90, 062106. Read More

View Article

Download full-text PDF

Source
http://dx.doi.org/10.1098/rsta.2015.0232DOI Listing
http://www.ncbi.nlm.nih.gov/pmc/articles/PMC4843635PMC
May 2016
1 Read

The birth of out of the spinors of the icosahedron.

Proc Math Phys Eng Sci 2016 Jan;472(2185):20150504

Departments of Mathematics and Biology , York Centre for Complex Systems Analysis, University of York , Heslington, York YO10 5GG, UK.

is prominent in mathematics and theoretical physics, and is generally viewed as an exceptional symmetry in an eight-dimensional (8D) space very different from the space we inhabit; for instance, the Lie group features heavily in 10D superstring theory. Contrary to that point of view, here we show that the root system can in fact be constructed from the icosahedron alone and can thus be viewed purely in terms of 3D geometry. The 240 roots of arise in the 8D Clifford algebra of 3D space as a double cover of the 120 elements of the icosahedral group, generated by the root system . Read More

View Article

Download full-text PDF

Source
http://dx.doi.org/10.1098/rspa.2015.0504DOI Listing
http://www.ncbi.nlm.nih.gov/pmc/articles/PMC4786034PMC
January 2016
2 Reads

Split Orthogonal Group: A Guiding Principle for Sign-Problem-Free Fermionic Simulations.

Phys Rev Lett 2015 Dec 17;115(25):250601. Epub 2015 Dec 17.

Alfréd Rényi Institute of Mathematics, Reáltanoda utca 13-15., Budapest H-1053, Hungary.

We present a guiding principle for designing fermionic Hamiltonians and quantum Monte Carlo (QMC) methods that are free from the infamous sign problem by exploiting the Lie groups and Lie algebras that appear naturally in the Monte Carlo weight of fermionic QMC simulations. Specifically, rigorous mathematical constraints on the determinants involving matrices that lie in the split orthogonal group provide a guideline for sign-free simulations of fermionic models on bipartite lattices. This guiding principle not only unifies the recent solutions of the sign problem based on the continuous-time quantum Monte Carlo methods and the Majorana representation, but also suggests new efficient algorithms to simulate physical systems that were previously prohibitive because of the sign problem. Read More

View Article

Download full-text PDF

Source
http://dx.doi.org/10.1103/PhysRevLett.115.250601DOI Listing
December 2015
3 Reads

Testing Nonassociative Quantum Mechanics.

Phys Rev Lett 2015 Nov 24;115(22):220402. Epub 2015 Nov 24.

Institute for Gravitation and the Cosmos, The Pennsylvania State University, 104 Davey Lab, University Park, Pennsylvania 16802, USA.

The familiar concepts of state vectors and operators in quantum mechanics rely on associative products of observables. However, these notions do not apply to some exotic systems such as magnetic monopoles, which have long been known to lead to nonassociative algebras. Their quantum physics has remained obscure. Read More

View Article

Download full-text PDF

Source
http://dx.doi.org/10.1103/PhysRevLett.115.220402DOI Listing
November 2015
22 Reads

The Umwelt of an embodied agent--a measure-theoretic definition.

Theory Biosci 2015 Dec;134(3-4):105-16

Universität Duisburg-Essen, Thea-Leymann-Strasse 9, 45117, Essen, Germany.

We consider a general model of the sensorimotor loop of an agent interacting with the world. This formalises Uexküll's notion of a function-circle. Here, we assume a particular causal structure, mechanistically described in terms of Markov kernels. Read More

View Article

Download full-text PDF

Source
http://link.springer.com/10.1007/s12064-015-0217-3
Publisher Site
http://dx.doi.org/10.1007/s12064-015-0217-3DOI Listing
December 2015
1 Read

Automation of Presentation Record Production Based on Rich-Media Technology Using SNT Petri Nets Theory.

Authors:
Ivo Martiník

ScientificWorldJournal 2015 14;2015:303705. Epub 2015 Jul 14.

Faculty of Economics, VŠB-Technical University of Ostrava, Sokolská třída 33, 701 21 Ostrava 1, Czech Republic.

Rich-media describes a broad range of digital interactive media that is increasingly used in the Internet and also in the support of education. Last year, a special pilot audiovisual lecture room was built as a part of the MERLINGO (MEdia-rich Repository of LearnING Objects) project solution. It contains all the elements of the modern lecture room determined for the implementation of presentation recordings based on the rich-media technologies and their publication online or on-demand featuring the access of all its elements in the automated mode including automatic editing. Read More

View Article

Download full-text PDF

Source
http://dx.doi.org/10.1155/2015/303705DOI Listing
http://www.ncbi.nlm.nih.gov/pmc/articles/PMC4516835PMC
January 2016

Finite-Dimensional Lie Algebras for Fast Diffeomorphic Image Registration.

Inf Process Med Imaging 2015 ;24:249-59

This paper presents a fast geodesic shooting algorithm for diffeomorphic image registration. We first introduce a novel finite-dimensional Lie algebra structure on the space of bandlimited velocity fields. We then show that this space can effectively represent initial velocities for diffeomorphic image registration at much lower dimensions than typically used, with little to no loss in registration accuracy. Read More

View Article

Download full-text PDF

Source
September 2015
4 Reads

Bounding the Set of Finite Dimensional Quantum Correlations.

Phys Rev Lett 2015 Jul 7;115(2):020501. Epub 2015 Jul 7.

Institute for Nuclear Research, Hungarian Academy of Sciences, P.O. Box 51, H-4001 Debrecen, Hungary.

We describe a simple method to derive high performance semidefinite programing relaxations for optimizations over complex and real operator algebras in finite dimensional Hilbert spaces. The method is very flexible, easy to program, and allows the user to assess the behavior of finite dimensional quantum systems in a number of interesting setups. We use this method to bound the strength of quantum nonlocality in Bell scenarios where the dimension of the parties is bounded from above. Read More

View Article

Download full-text PDF

Source
http://dx.doi.org/10.1103/PhysRevLett.115.020501DOI Listing
July 2015
1 Read

Discrimination in a General Algebraic Setting.

ScientificWorldJournal 2015 1;2015:824268. Epub 2015 Jun 1.

Department of Mathematics, Temple University, Philadelphia, PA 19122, USA.

Discriminating groups were introduced by G. Baumslag, A. Myasnikov, and V. Read More

View Article

Download full-text PDF

Source
http://dx.doi.org/10.1155/2015/824268DOI Listing
http://www.ncbi.nlm.nih.gov/pmc/articles/PMC4485932PMC
January 2016

(Fuzzy) Ideals of BN-Algebras.

ScientificWorldJournal 2015 1;2015:925040. Epub 2015 Jun 1.

Institute of Mathematics and Physics, Siedlce University, 3 Maja 54, 08-110 Siedlce, Poland.

The notions of an ideal and a fuzzy ideal in BN-algebras are introduced. The properties and characterizations of them are investigated. The concepts of normal ideals and normal congruences of a BN-algebra are also studied, the properties of them are displayed, and a one-to-one correspondence between them is presented. Read More

View Article

Download full-text PDF

Source
http://dx.doi.org/10.1155/2015/925040DOI Listing
http://www.ncbi.nlm.nih.gov/pmc/articles/PMC4466498PMC
January 2016
3 Reads

The geometric semantics of algebraic quantum mechanics.

Philos Trans A Math Phys Eng Sci 2015 Aug;373(2047)

Mathematical Institute, University of Oxford, 24-29 St Giles, Oxford OX1 3LB, UK.

In this paper, we will present an ongoing project that aims to use model theory as a suitable mathematical setting for studying the formalism of quantum mechanics. We argue that this approach provides a geometric semantics for such a formalism by means of establishing a (non-commutative) duality between certain algebraic and geometric objects. Read More

View Article

Download full-text PDF

Source
http://dx.doi.org/10.1098/rsta.2014.0245DOI Listing

Faces of Platonic solids in all dimensions.

Acta Crystallogr A Found Adv 2014 Jul 11;70(Pt 4):358-63. Epub 2014 Jun 11.

Centre de Recherches Mathématiques, Université de Montréal, Montréal, Québec, Canada.

This paper considers Platonic solids/polytopes in the real Euclidean space R(n) of dimension 3 ≤ n < ∞. The Platonic solids/polytopes are described together with their faces of dimensions 0 ≤ d ≤ n - 1. Dual pairs of Platonic polytopes are considered in parallel. Read More

View Article

Download full-text PDF

Source
http://dx.doi.org/10.1107/S205327331400638XDOI Listing

Fuzzy logical algebras and their applications.

ScientificWorldJournal 2015 25;2015:682648. Epub 2015 Mar 25.

Department of Mathematics, Hanyang University, Seoul 133-791, Republic of Korea.

View Article

Download full-text PDF

Source
http://dx.doi.org/10.1155/2015/682648DOI Listing
http://www.ncbi.nlm.nih.gov/pmc/articles/PMC4390104PMC
December 2015
3 Reads

Quanta of geometry: noncommutative aspects.

Phys Rev Lett 2015 Mar 5;114(9):091302. Epub 2015 Mar 5.

Theoretical Physics, Ludwig Maxmillians University, Theresienstraße 37, 80333 Munich, Germany.

In the construction of spectral manifolds in noncommutative geometry, a higher degree Heisenberg commutation relation involving the Dirac operator and the Feynman slash of real scalar fields naturally appears and implies, by equality with the index formula, the quantization of the volume. We first show that this condition implies that the manifold decomposes into disconnected spheres, which will represent quanta of geometry. We then refine the condition by involving the real structure and two types of geometric quanta, and show that connected spin manifolds with large quantized volume are then obtained as solutions. Read More

View Article

Download full-text PDF

Source
http://dx.doi.org/10.1103/PhysRevLett.114.091302DOI Listing