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Dual scattering channel schemes extending the Johns algorithm

Steffen Hein
2007 Mathematics and Computers in Simulation  
For one point, transmission line links are replaced by abstract scattering channels in terms of paired distributions (characteristic impedances are thus neither needed, nor in general defined, e.g.).  ...  Dual scattering channel schemes extend the transmission line matrix numerical method (JOHNS' TLM algorithm) in two directions.  ...  Dual scattering channel schemes are characterized by a two-step updating cycle with certain duality relations between the two steps.  ... 
doi:10.1016/j.matcom.2006.08.004 fatcat:c4keh6cm5zc37jjlycq23fysca

Dual field structure-preserving discretization of port-Hamiltonian systems using finite element exterior calculus [article]

Andrea Brugnoli, Ramy Rashad, Stefano Stramigioli
2022 arXiv   pre-print
Our approach relies on a dual-field representation of the physical system that is redundant at the continuous level but eliminates the need of mimicking the Hodge star operator at the discrete level.  ...  By considering the Stokes-Dirac structure representing the system together with its adjoint, which embeds the metric information directly in the codifferential, the need for an explicit discrete Hodge  ...  In Sec. 3 we introduce the concept and representation of the classical and adjoint Stokes-Dirac structure and the associated pH systems which is instrumental in the presented solution.  ... 
arXiv:2202.04390v2 fatcat:pjp4skz7frb45ghb6gebbhjrti

Dynamics in the magnetic/dual magnetic monopole [article]

Luigi Martina
2011 arXiv   pre-print
Inspired by the geometrical methods allowing the introduction of mechanical systems confined in the plane and endowed with exotic galilean symmetry, we resort to the Lagrange-Souriau 2-form formalism,  ...  in order to look for a wide class of 3D systems, involving not commuting and/or not canonical variables, but possessing geometric as well gauge symmetries in position and momenta space too.  ...  The work has been partially supported by the INFN -Sezione of Lecce under the project LE41.  ... 
arXiv:1110.6906v2 fatcat:tqto6kxkuzg2jc2ylxr6vgjaq4

Minimal representations and reductive dual pairs in conformal field theory [article]

Ivan Todorov
2010 arXiv   pre-print
It provides context for Roger Howe's notion of a reductive dual pair encountered recently in the description of global gauge symmetry of a (4-dimensional) conformal observable algebra.  ...  A minimal representation of a simple non-compact Lie group is obtained by "quantizing" the minimal nilpotent coadjoint orbit of its Lie algebra.  ...  The infinite Lie algebras generated by such bilocal fields are characterized by the following result of [NRT] .  ... 
arXiv:1006.1981v1 fatcat:ybinzdpjorel7mrtnr2hjoua3u

Fourier's Method of Linear Programming and Its Dual

H. P. Williams
1986 The American mathematical monthly  
Proceedings, conferences, collections, etc. 93Axx General 93A05 Axiomatic system theory 93A10 General systems 93A13 Hierarchical systems 93A14 Decentralized systems 93A15 Large scale systems  ...  47L40 Limit algebras, subalgebras of C * -algebras 47L45 Dual algebras; weakly closed singly generated operator algebras 47L50 Dual spaces of operator algebras 47L55 Licence: This text is  ...  Observational and experimental questions 83B05 Observational and experimental questions 83B99 None of the above, but in this section 83Cxx General relativity 83C05 Einstein's equations (general structure  ... 
doi:10.2307/2322281 fatcat:yvhgyh2epbcwdoqdhuaopkcrue

The Patch Construction is Dual to Algebraic DCPO Representation

C. F. Townsend
2008 Applied Categorical Structures  
Using the parallel between the preframe and the suplattice approach to locale theory it is shown that the patch construction, as an action on topologies, is the same thing as the process of recovering  ...  The general notation is ∀ f : ΩX → ΩY for the right adjoint of any frame homomorphism Ωf : ΩY → ΩX.  ...  To define the concept of a sober stably locally compact space the definition of saturation is needed.  ... 
doi:10.1007/s10485-008-9177-9 fatcat:gnis333vkbggte3xmmkxfjvqia

What Is Category Theory? [chapter]

Jean-Pierre Marquis
2006 Zenodo  
After giving a short description of the evolution of category theory, the paper sketches a tentative answer to the question constituting the title of the paper.  ...  I will go even one step further: category theory is the architectonic of concepts or of conceptual systems in general.  ...  claims that the invariant content of a conceptual system can be characterized by categorical means.  ... 
doi:10.5281/zenodo.584073 fatcat:3leiwhpm2fa53ovncgnellcjpe

Characterizations ofN(2,2,0)Algebras

Fang-an Deng, Lu Chen, ShouHeng Tuo, ShengZhang Ren
2016 Algebra  
The so-called ideal and subalgebra and some additional concepts ofN(2,2,0)algebras are discussed.  ...  Conflict of Interests The authors declare that there is no conflict of interests regarding the publication of this paper. Acknowledgment This work is supported by NSF of China (11305097).  ...  A pair of dual operations ( * , Δ) form an adjoint pair ( → , * ); that is, ≤ → ⇔ * ≤ , for every , , ∈ . Theorem 10.  ... 
doi:10.1155/2016/2752681 fatcat:334unpihobhxhnpu42feztwm7y

Categorical Quantum Mechanics [chapter]

Samson Abramsky, Bob Coecke
2009 Handbook of Quantum Logic and Quantum Structures  
, Dirac bra-ket notation, traces, scalars, the Born rule, Hilbert-Schmidt norm, etc. • Dictionary of interpretation of QM concepts in the abstract setting Some Results • Characterization of free strongly  ...  Also, while at this level of abstraction there is no underlying field of complex numbers, there is still an intrinsic notion of 'scalar', and we can still make sense of dual vs. adjoint [5, 6] , and global  ...  Appendix: Diagrammatic Proofs Definition of Duality Duality is Involutive  ... 
doi:10.1016/b978-0-444-52869-8.50010-4 fatcat:4rt4qyfu4fd2hprwiztwwx2pmm

Page 284 of Mathematical Reviews Vol. 39, Issue 2 [page]

1970 Mathematical Reviews  
A substantial part of the work is devoted to the characterization of objects, morphisms and other concepts by means of the inclusion (¢) and composition (c), from a viewpoint that recalls that of C.  ...  These types of full im- beddings are both generalizations of the concept ‘‘realiza- tion’’ [cf. the author, same Comment. 8 (1967), 53-83 ; MR 35 #1650).  ... 

An axiomatic approach of fuzzy rough sets based on residuated lattices

Yan-Hong She, Guo-Jun Wang
2009 Computers and Mathematics with Applications  
As a further generalization of the notion of rough sets, L-fuzzy rough sets were proposed by Radzikowska and Kerre.  ...  The methods of axiomatization of L-fuzzy upper and L-fuzzy lower set-theoretic operators guarantee the existence of corresponding L-fuzzy relations which produce the operators.  ...  (h1) and (h2) form the axiomatic system for the upper approximators of the generalized crisp rough set model, whereas (l1) and (l2) provide the axiomatic characterizations for the lower approximators in  ... 
doi:10.1016/j.camwa.2009.03.100 fatcat:g2wal5giy5dhfjnxhptr7u7k5q

Orientation in operator algebras

E. M. Alfsen, F. W. Shultz
1998 Proceedings of the National Academy of Sciences of the United States of America  
It was Connes (4) who first realized that a concept of orientation is relevant for this purpose (and his concept was later used in the axiomatic context of JBW-algebras by Bellissard and Iochum in refs  ...  A problem that dates back to the 1950s is to characterize the ordered linear spaces that are the self-adjoint parts of C*algebras or of von Neumann algebras.  ...  We call it the bundle of oriented local algebras. Then the concept of consistency for a crosssection of this bundle and the concept of a global orientation of ᏹ is defined as in the dual context.  ... 
doi:10.1073/pnas.95.12.6596 pmid:9618457 pmcid:PMC22571 fatcat:zfcx7rpxkzfipham4e6lnhrbjy

Axiomatic foundations of nonrelativistic quantum mechanics: A realistic approach

S. E. Perez Bergliaffa, H. Vucetich, G. E. Romero
1993 International Journal of Theoretical Physics  
A realistic axiomatic formulation of nonrelativistic quantum mechanics for a single microsystem with spin is presented, from which the most important theorems of the theory can be deduced.  ...  The standard formalism is naturally obtained from the latter, starting from a central primitive concept: the Galilei group.  ...  Bunge for valuable comments on the preparation of the manuscript.  ... 
doi:10.1007/bf00672852 fatcat:xjs5r6ah5zgo5cvtlewsd24loq

Complete Axiomatizations for Quantum Actions

A. Baltag, S. Smets
2005 International Journal of Theoretical Physics  
We present two equivalent axiomatizations for a logic of quantum actions: one in terms of quantum transition systems, and the other in terms of quantum dynamic algebras.  ...  Orthomodularity, Covering Law); 2) it reduces the complexity of the Solèr-Mayet axiomatization by replacing some of their key higherorder concepts (e.g.  ...  Also, the existing complete latticetheoretic characterizations of H (based on the work of [25, 2, 23, 30] ) are not given in first-order logical terms, but they make an essential use of higher-order concepts  ... 
doi:10.1007/s10773-005-8022-2 fatcat:zcyr5i7265dznoln5sul2g75ge

Quantum measurements without sums [article]

Bob Coecke, Dusko Pavlovic
2008 arXiv   pre-print
Surprisingly, a conceptual analysis of quantum measurement seems to suggest that quantum mechanics can be done without direct sums, expressed entirely in terms of the tensor product.  ...  The sums turn out to be an implicit implementation of this capabilities.  ...  In Section 1.5.1 we discuss a systemic way of defining these 'relative to X'-concepts.  ... 
arXiv:quant-ph/0608035v2 fatcat:h7v5ejg3qjgd7bvnatuynr2gim
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