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Nabla Algebras and Chu Spaces [chapter]

Alessandra Palmigiano, Yde Venema
Algebra and Coalgebra in Computer Science  
The key ingredient is an F-lifting construction, for an arbitrary set functor F, on the category Chu of two-valued Chu spaces and Chu transforms, based on relation lifting.  ...  We establish a categorical isomorphism between the category of modal ∇algebra and that of modal algebras, and similarly for positive modal ∇-algebras and positive modal algebras.  ...  We already mentioned in the introduction that our first motivation was to pave the way for a 'coalgebraic proof theory', by which we mean to try and give an algebraic and syntactic account of nabla operators  ... 
doi:10.1007/978-3-540-73859-6_27 dblp:conf/calco/PalmigianoV07 fatcat:dpjgsz5inva77npdcgr7xg5nwy

Modal Logic and the Vietoris Functor [chapter]

Yde Venema, Jacob Vosmaer
2014 Leo Esakia on Duality in Modal and Intuitionistic Logics  
Specifically, we look at Stone duality for the Vietoris hyperspace and the Vietoris powerlocale, and at recent work combining coalgebraic modal logic and the Vietoris functor.  ...  In [17] , Esakia uses the Vietoris topology to give a coalgebra-flavored definition of topological Kripke frames, thus relating the Vietoris topology, modal logic and coalgebra.  ...  Additionally, we would like to thank the anonymous referee, whose thorough criticism contributed significantly to the quality of this paper, and in particular to the presentation and choice of contents  ... 
doi:10.1007/978-94-017-8860-1_6 fatcat:awd6iv5xhbfjtk2hoh2h746kxm

A COMMON THEORETICAL BASIS FOR PRECONDITIONED FIELD INTEGRAL EQUATIONS AND THE SINGULARITY EXPANSION METHOD

Robert J. Fleming
2008 Progress In Electromagnetics Research M  
An operator relation termed the Calderon preconditioner links the MFIE and EFIE, based on the fundamental Stratton-Chu integral representations for the problem geometry.  ...  Coupling coefficients for the MFIE are known, however, explicit formulations for the EFIE, and the modified coupling coefficients for the MEFIE and MMFIE are new contributions.  ...  Through a series of algebraic manipulations, following Hsiao et al.  ... 
doi:10.2528/pierm08110501 fatcat:yb2fex65ubd2hgilj2fwcqelwe

09502 Abstracts Collection – Coalgebraic Logics

Ernst-Erich Doberkat, Alexander Kurz
2010
are firmer and better understood.  ...  Traditionally, modal logics find their use when reasoning about behavioural and temporal properties of computation and communication, whereas coalgebras give a uniform account for a large class of different  ...  features such as variable binding and substitution.  ... 
doi:10.4230/dagsemproc.09502.1 fatcat:2ino5isdizeqpktf4jxfqc5yqu

Application-Oriented Relativistic Electrodynamics (2)

D. Censor
2000 Electromagnetic Waves  
We therefore need to define a syllabus and explore the best methods for educating future generations of such users. Such an attempt is presented here, and is of course biased by personal preferences.  ...  This article is a revised and upgraded edition of a previous one published in this journal, hence the label (2), see the General Remarks section below.  ...  I am deeply grateful to Ismo Lindell, Ari Sihvola and Sergei Tretyakov for being my hosts and for many stimulating discussions.  ... 
doi:10.2528/pier99120201 fatcat:tkxn3ueccfgtzhz4zxtnetzahe

Characterization of Maximum Likelihood Solutions to Image Reconstruction in Photon Emission Tomography

François Chapeau-Blondeau, Christian Jeanguillaume
2013 Journal of Mathematical Imaging and Vision  
to characterize their performance with expressions for the mean-squared error, bias and Cramér-Rao bound.  ...  No explicit closed-form solution is known in general for such a nonlinear ML equation, and numerical resolution is usually implemented, with a very popular iterative method formed by the expectation-maximization  ...  null space Ker(P ).  ... 
doi:10.1007/s10851-013-0477-9 fatcat:727eccgubzcznoinbcx47tc5qi

Generalized powerlocales via relation lifting [article]

Yde Venema, Steve Vickers, Jacob Vosmaer
2012 arXiv   pre-print
Finally, we prove that the operation preserves some properties of frames, such as regularity, zero-dimensionality, and the combination of zero-dimensionality and compactness.  ...  Our construction of the -powerlocale out of a frame is based on ideas from coalgebraic logic and makes explicit the connection between the Vietoris construction and Moss's coalgebraic cover modality.  ...  Palmigiano & Venema (Palmigiano & Venema, 2007) introduce a lifting construction on Chu spaces to prove that for Stone spaces, the Vietoris construction can be generalized from the power set case to  ... 
arXiv:1202.3264v1 fatcat:vtb3ptmdbfg25hrownc2sgbg64

Post-Newtonian Description of Quantum Systems in Gravitational Fields [article]

Philip K. Schwartz
2020 arXiv   pre-print
Furthermore, for stationary spacetimes, we show that the Hamiltonians arising from expansions of the KG equation and from canonical quantisation agree up to linear order in particle momentum, independent  ...  uniqueness results characterising the Newton–Wigner position observable for Poincaré-invariant classical Hamiltonian systems: one is a direct classical analogue of the quantum Newton–Wigner theorem, and  ...  leading up to atom interferometers of the Kasevich-Chu type, accomplishing, e.g., highly precise measurements of the gravitational acceleration g on the earth [Far+14] .  ... 
arXiv:2009.11319v2 fatcat:iocajhyq3ngm3deubixd3v27ae

Generalised powerlocales via relation lifting

YDE VENEMA, STEVE VICKERS, JACOB VOSMAER
2012 Mathematical Structures in Computer Science  
Our construction of the T -powerlocale V T L out of a frame L is based on ideas from coalgebraic logic and makes explicit the connection between the Vietoris construction and Moss's coalgebraic cover modality  ...  Finally, we prove that the operation V T preserves some properties of frames, such as regularity, zero-dimensionality and the combination of zero-dimensionality and compactness. ‡ Steve Vickers is grateful  ...  Spatiality and compact Hausdorff spaces Palmigiano and Venema (2007) introduced a lifting construction on Chu spaces to prove that for Stone spaces, the Vietoris construction can be generalised from  ... 
doi:10.1017/s0960129512000229 fatcat:2rgxxvlr2ncejhetf2ihmrnrou

New identities for Theta operators [article]

Michele D'Adderio, Marino Romero
2020 arXiv   pre-print
From this result, we can easily deduce several new identities that have combinatorial consequences in the study of Macdonald polynomials and diagonal coinvariants.  ...  In this article, we prove a new general identity involving the Theta operators introduced by the first author and his collaborators in [D'Adderio, Iraci, Vanden Wyngaerd 2020].  ...  Acknowledgments The authors are grateful to Alessandro Iraci and Anna Vanden Wyngaerd for interesting discussions, in particular for suggesting the identity in Corollary 9.2, and to Anton Mellit for encouraging  ... 
arXiv:2012.06402v1 fatcat:qnhe3uimbvebxiowsr4rrpu5ey

On Kottler's path: Origin and evolution of the premetric program in gravity and in electrodynamics

Friedrich W. Hehl, Yakov Itin, Yuri N. Obukhov
2016 International Journal of Modern Physics D  
He successfully applied this idea to Newton's gravitostatics and to Maxwell's electrodynamics, where Kottler recast the field equations in premetric form and specified a metric-dependent constitutive law  ...  We will discuss the basics of the premetric approach and some of its beautiful consequences, like the division of universal constants into two classes.  ...  Acknowledgments We would like to extend our sincere thanks to Wei-Tou Ni (Hsin-chu) for his encouragement to write up this article.  ... 
doi:10.1142/s0218271816400162 fatcat:7yk5hlophndbjav32fyrag224u

2021 Index IEEE Transactions on Circuits and Systems II: Express Briefs Vol. 68

2021 IEEE Transactions on Circuits and Systems - II - Express Briefs  
The primary entry includes the coauthors' names, the title of the paper or other item, and its location, specified by the publication abbreviation, year, month, and inclusive pagination.  ...  The Subject Index contains entries describing the item under all appropriate subject headings, plus the first author's name, the publication abbreviation, month, and year, and inclusive pages.  ...  Wu, C., +, TCSII Oct. 2021 3321-3325 Algebra Coefficient-Based Classes of Algebraic Conditions to Construct Positive Real Rational Functions.  ... 
doi:10.1109/tcsii.2022.3144928 fatcat:bm53w7gva5bthholfhhiq4yg3a

Derivation of New Staggered Compact Schemes with Application to Navier-Stokes Equations

Enrico De Angelis, Gennaro Coppola, Francesco Capuano, Luigi de Luca
2018 Applied Sciences  
of nodal values and collocated compact derivatives.  ...  The algorithm has its roots in an implicit interpolation theory consistent with compact schemes and reduces to the computation of the required staggered derivatives and interpolated quantities as a combination  ...  space and ∇ is the discrete nabla operator, assuming the meaning of discrete divergence or gradient operator, depending on the context.  ... 
doi:10.3390/app8071066 fatcat:wstlon3k6zhhtkzdkfxuqycpiu

Coupling of continuum mechanics and electrodynamics [article]

Felix Alexander Reich, Technische Universität Berlin, Technische Universität Berlin, Wolfgang H. Müller
2017
To show the implications of local effects, two similar problems are considered: an elastic and homogeneously magnetized sphere, and an elastic and linear [...]  ...  The debate as to which model of the electromagnetic force is "correct" for arbitrary materials and processes is ongoing.  ...  Later, another famous force model was given by Chu et al. [Chu, Haus, and Penfield (1966) ].  ... 
doi:10.14279/depositonce-6518 fatcat:jxzukgslj5fhpol5jssjzqqsqm

[Back cover]

1962 IRE Transactions on Antennas and Propagation  
In both Heaviside's and Gibbs' vector algebras the "Row of operations" is interrupted by the vector product xvhich can be defined as the detern~inant of a matrix com-* 0.  ...  Aeronautics and Space Adminlstratlon. partly by Goddard Space Fl!ght Center. Sational ferometers and satellite radio transmissions are summarized and interpreted.  ...  Chu and S. S. 1953 -1961 , Associate Professor 1951 -1953 , Assistant Professor 1949 -1951 , and Instructor 1947 -1949) .  ... 
doi:10.1109/tap.1962.1137902 fatcat:c7f6kvxiszhtnbf2tfyd3xhj6i
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