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Elementary calculus in Riesz MV-algebras

Barnabás Bede, Antonio Di Nola
<span title="">2004</span> <i title="Elsevier BV"> <a target="_blank" rel="noopener" href="https://fatcat.wiki/container/sy2zvsxl4vdejh3zsp3utmplry" style="color: black;">International Journal of Approximate Reasoning</a> </i> &nbsp;
Moreover we introduce the concept of derivative and integral of MV-valued functions; i.e. functions with values in a Riesz MV-algebra. Finally we present two applications.  ...  We introduce and study a topological structure over vectorial and Riesz MV-algebras, similar to metric spaces.  ...  in the Riesz MV-algebra of fuzzy subsets of a given set.  ... 
<span class="external-identifiers"> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.1016/j.ijar.2003.09.003">doi:10.1016/j.ijar.2003.09.003</a> <a target="_blank" rel="external noopener" href="https://fatcat.wiki/release/g5epgv6g6jc6zgnhdobs4br46m">fatcat:g5epgv6g6jc6zgnhdobs4br46m</a> </span>
<a target="_blank" rel="noopener" href="https://web.archive.org/web/20170929070603/http://publisher-connector.core.ac.uk/resourcesync/data/elsevier/pdf/75d/aHR0cDovL2FwaS5lbHNldmllci5jb20vY29udGVudC9hcnRpY2xlL3BpaS9zMDg4ODYxM3gwMzAwMTQxNQ%3D%3D.pdf" title="fulltext PDF download" data-goatcounter-click="serp-fulltext" data-goatcounter-title="serp-fulltext"> <button class="ui simple right pointing dropdown compact black labeled icon button serp-button"> <i class="icon ia-icon"></i> Web Archive [PDF] <div class="menu fulltext-thumbnail"> <img src="https://blobs.fatcat.wiki/thumbnail/pdf/8e/7b/8e7b67793b2ce08c208cec773f1519b4dddee7ae.180px.jpg" alt="fulltext thumbnail" loading="lazy"> </div> </button> </a> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.1016/j.ijar.2003.09.003"> <button class="ui left aligned compact blue labeled icon button serp-button"> <i class="external alternate icon"></i> elsevier.com </button> </a>

Mapping abelian l-groups with strong unit one-one into MV algebras

Daniele Mundici
<span title="">1986</span> <i title="Elsevier BV"> <a target="_blank" rel="noopener" href="https://fatcat.wiki/container/h7qx4qsc2zf7hiupv27dke5fk4" style="color: black;">Journal of Algebra</a> </i> &nbsp;
As shown, for instance, in [4, 5, 16 , 222241, Chang's MV algebras are to tukasiewicz &valued sentential calculus [25, 21, 20 , 171 as boolean algebras are to ordinary (two-valued) sentential calculus  ...  -algebra can be associated with a set of sentences in the X,-valued sentential calculus; conversely, every consistent set of sentences corresponds to exactly one (up to isomorphism) AF C*-algebra.  ... 
<span class="external-identifiers"> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.1016/0021-8693(86)90015-3">doi:10.1016/0021-8693(86)90015-3</a> <a target="_blank" rel="external noopener" href="https://fatcat.wiki/release/b2l53c25lnel5gtmpc2kksfmpy">fatcat:b2l53c25lnel5gtmpc2kksfmpy</a> </span>
<a target="_blank" rel="noopener" href="https://web.archive.org/web/20171004100030/http://publisher-connector.core.ac.uk/resourcesync/data/elsevier/pdf/dd6/aHR0cDovL2FwaS5lbHNldmllci5jb20vY29udGVudC9hcnRpY2xlL3BpaS8wMDIxODY5Mzg2OTAwMTUz.pdf" title="fulltext PDF download" data-goatcounter-click="serp-fulltext" data-goatcounter-title="serp-fulltext"> <button class="ui simple right pointing dropdown compact black labeled icon button serp-button"> <i class="icon ia-icon"></i> Web Archive [PDF] <div class="menu fulltext-thumbnail"> <img src="https://blobs.fatcat.wiki/thumbnail/pdf/3a/ec/3aecf224ee8b35d37418f3a0ab7758d78f1b305a.180px.jpg" alt="fulltext thumbnail" loading="lazy"> </div> </button> </a> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.1016/0021-8693(86)90015-3"> <button class="ui left aligned compact blue labeled icon button serp-button"> <i class="external alternate icon"></i> elsevier.com </button> </a>

A Representation Theorem for MV-algebras

Gejza Jenča
<span title="2006-06-10">2006</span> <i title="Springer Nature"> <a target="_blank" rel="noopener" href="https://fatcat.wiki/container/e5brmbb4nne2bb6o5whxervgii" style="color: black;">Soft Computing - A Fusion of Foundations, Methodologies and Applications</a> </i> &nbsp;
We prove that for every MV-pair (B,G), the effect algebra B/∼_G is an MV- effect algebra. Moreover, for every MV-effect algebra M there is an MV-pair (B,G) such that M is isomorphic to B/∼_G.  ...  An MV-pair is a pair (B,G) where B is a Boolean algebra and G is a subgroup of the automorphism group of B satisfying certain conditions.  ...  By elementary Boolean calculus, this implies that x 2i \ x 2i−1 = (x 2i ∨ d) ∧ c \ (x 2i−1 ∨ d) ∧ c .  ... 
<span class="external-identifiers"> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.1007/s00500-006-0100-8">doi:10.1007/s00500-006-0100-8</a> <a target="_blank" rel="external noopener" href="https://fatcat.wiki/release/offluthmcjgxtczwga7xbi2jum">fatcat:offluthmcjgxtczwga7xbi2jum</a> </span>
<a target="_blank" rel="noopener" href="https://archive.org/download/arxiv-math0602169/math0602169.pdf" title="fulltext PDF download [not primary version]" data-goatcounter-click="serp-fulltext" data-goatcounter-title="serp-fulltext"> <button class="ui simple right pointing dropdown compact black labeled icon button serp-button"> <i class="icon ia-icon"></i> File Archive [PDF] <span style="color: #f43e3e;">&#10033;</span> </button> </a> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.1007/s00500-006-0100-8"> <button class="ui left aligned compact blue labeled icon button serp-button"> <i class="external alternate icon"></i> springer.com </button> </a>

Probabilistic logics based on Riesz spaces

Robert Furber, Radu Mardare, Matteo Mio
<span title="2019-03-25">2019</span> <i title="episciences.org"> <a target="_blank" rel="noopener" href="https://fatcat.wiki/container/c67srop7pbe3nciquoxzy3d6pm" style="color: black;">Logical Methods in Computer Science</a> </i> &nbsp;
By using powerful results from this theory, we develop the duality theory of the Riesz modal logic in the form of an algebra-to-coalgebra correspondence.  ...  The design of the syntax and semantics of this logic is directly inspired by the theory of Riesz spaces, a mature field of mathematics at the intersection of universal algebra and functional analysis.  ...  In [NL11] the authors have introduced Riesz MV-algebras, which are MV-algebras endowed with the operation of scalar multiplication by reals in the unit interval [0, 1].  ... 
<span class="external-identifiers"> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.23638/lmcs-16(1:6)2020">doi:10.23638/lmcs-16(1:6)2020</a> <a target="_blank" rel="external noopener" href="https://fatcat.wiki/release/vqm3un3yqfbs3nckws4dnqqzpu">fatcat:vqm3un3yqfbs3nckws4dnqqzpu</a> </span>
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Probabilistic logics based on Riesz spaces [article]

Robert Furber and Radu Mardare and Matteo Mio
<span title="2020-01-24">2020</span> <i > arXiv </i> &nbsp; <span class="release-stage" >pre-print</span>
By using powerful results from this theory, we develop the duality theory of the Riesz modal logic in the form of an algebra-to-coalgebra correspondence.  ...  The design of the syntax and semantics of this logic is directly inspired by the theory of Riesz spaces, a mature field of mathematics at the intersection of universal algebra and functional analysis.  ...  In [NL11] the authors have introduced Riesz MV-algebras, which are MV-algebras endowed with the operation of scalar multiplication by reals in the unit interval [0, 1].  ... 
<span class="external-identifiers"> <a target="_blank" rel="external noopener" href="https://arxiv.org/abs/1903.09463v3">arXiv:1903.09463v3</a> <a target="_blank" rel="external noopener" href="https://fatcat.wiki/release/pqk4bz4hiffxbklkm33ovkrehe">fatcat:pqk4bz4hiffxbklkm33ovkrehe</a> </span>
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Upper-Expectation Bisimilarity and Real-valued Modal Logics [article]

Matteo Mio
<span title="2013-10-02">2013</span> <i > arXiv </i> &nbsp; <span class="release-stage" >pre-print</span>
Several notions of bisimulation relations for probabilistic non-deterministic transition systems have been considered in the literature.  ...  We develop logical characterizations in terms of expressive probabilistic modal mu-calculi and a novel real-valued modal logic.  ...  In other words, the notion of closedness is norm-invariant in R n . Actually, the operation of scalar multiplication by q ∈ [0, 1], gives L a so-called Riesz MV-algebra structure.  ... 
<span class="external-identifiers"> <a target="_blank" rel="external noopener" href="https://arxiv.org/abs/1310.0768v1">arXiv:1310.0768v1</a> <a target="_blank" rel="external noopener" href="https://fatcat.wiki/release/7gvzvew36nd6neh6p6hlp6w3pe">fatcat:7gvzvew36nd6neh6p6hlp6w3pe</a> </span>
<a target="_blank" rel="noopener" href="https://web.archive.org/web/20200828105334/https://arxiv.org/pdf/1310.0768v1.pdf" title="fulltext PDF download" data-goatcounter-click="serp-fulltext" data-goatcounter-title="serp-fulltext"> <button class="ui simple right pointing dropdown compact black labeled icon button serp-button"> <i class="icon ia-icon"></i> Web Archive [PDF] <div class="menu fulltext-thumbnail"> <img src="https://blobs.fatcat.wiki/thumbnail/pdf/11/6c/116c1f7551a463773e6685a9658b7dc755c8a0cb.180px.jpg" alt="fulltext thumbnail" loading="lazy"> </div> </button> </a> <a target="_blank" rel="external noopener" href="https://arxiv.org/abs/1310.0768v1" title="arxiv.org access"> <button class="ui compact blue labeled icon button serp-button"> <i class="file alternate outline icon"></i> arxiv.org </button> </a>

The principal axis theorem for holomorphic functions

Joachim Gräter, Markus Klein
<span title="1999-09-27">1999</span> <i title="American Mathematical Society (AMS)"> <a target="_blank" rel="noopener" href="https://fatcat.wiki/container/a64sw4kcsveajhudnssdwrwvze" style="color: black;">Proceedings of the American Mathematical Society</a> </i> &nbsp;
We show that this result is a special version of a purely algebraic theorem on the diagonalization of matrices over fields with henselian valuations.  ...  An algebraic approach to Rellich's theorem is given which states that any analytic family of matrices which is normal on the real axis can be diagonalized by an analytic family of matrices which is unitary  ...  Furthermore, even the use of the Weierstrass preparation theorem may be avoided by use of the Riesz projection and the standard calculus of residues.  ... 
<span class="external-identifiers"> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.1090/s0002-9939-99-05451-9">doi:10.1090/s0002-9939-99-05451-9</a> <a target="_blank" rel="external noopener" href="https://fatcat.wiki/release/v344pabkenhc5hzvwumr44kvyq">fatcat:v344pabkenhc5hzvwumr44kvyq</a> </span>
<a target="_blank" rel="noopener" href="https://web.archive.org/web/20070303172341/http://www.ams.org:80/proc/2000-128-02/S0002-9939-99-05451-9/S0002-9939-99-05451-9.pdf" title="fulltext PDF download" data-goatcounter-click="serp-fulltext" data-goatcounter-title="serp-fulltext"> <button class="ui simple right pointing dropdown compact black labeled icon button serp-button"> <i class="icon ia-icon"></i> Web Archive [PDF] <div class="menu fulltext-thumbnail"> <img src="https://blobs.fatcat.wiki/thumbnail/pdf/3e/c9/3ec9f63326e2607f1ff02957fece554dd06e31c0.180px.jpg" alt="fulltext thumbnail" loading="lazy"> </div> </button> </a> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.1090/s0002-9939-99-05451-9"> <button class="ui left aligned compact blue labeled icon button serp-button"> <i class="unlock alternate icon" style="background-color: #fb971f;"></i> Publisher / doi.org </button> </a>

Upper-Expectation Bisimilarity and Łukasiewicz μ-Calculus [chapter]

Matteo Mio
<span title="">2014</span> <i title="Springer Berlin Heidelberg"> <a target="_blank" rel="noopener" href="https://fatcat.wiki/container/2w3awgokqne6te4nvlofavy5a4" style="color: black;">Lecture Notes in Computer Science</a> </i> &nbsp;
a logical characterization in terms of an expressive probabilistic modal μ-calculus.  ...  We study a novel testing-based behavioral equivalence called upper expectation bisimilarity and, using standard results from functional analysis, we develop its coalgebraic and algebraic theory and provide  ...  Upper-Expectation Bisimilarity and Lukasiewicz μ-Calculus  ... 
<span class="external-identifiers"> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.1007/978-3-642-54830-7_22">doi:10.1007/978-3-642-54830-7_22</a> <a target="_blank" rel="external noopener" href="https://fatcat.wiki/release/zqn7qfnehrerflmrlivlestnra">fatcat:zqn7qfnehrerflmrlivlestnra</a> </span>
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Effective quantum observables

N. Brunner, K. Svozil, M. Baaz
<span title="">1995</span> <i title="Springer Nature"> Il Nuovo Cimento B </i> &nbsp;
In general, this is no longer true. 2.2. Functional calculus.  ...  In V we let be an atomic Boolean algebra with X the set of its atoms. Then is isomorphic with a set algebra X P ( A ) o f V ( X ),Athe set of atoms in the sense of sets.  ...  Since all parameters in this denition are in P Mand have the same meaning in P Mas in V (X),w e conclude, that K = K 1 2 P Mis the closure of e 00 H in P M.  ... 
<span class="external-identifiers"> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.1007/bf02849839">doi:10.1007/bf02849839</a> <a target="_blank" rel="external noopener" href="https://fatcat.wiki/release/4lq3jvi6dzdtjmwdvfyo7uts4u">fatcat:4lq3jvi6dzdtjmwdvfyo7uts4u</a> </span>
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On Henri Cartan's vectorial mean-value theorem and its applications to Lipschitzian operators and generalized Lebesgue-Bochner-Stieltjes integration theory [article]

Victor M. Bogdan
<span title="2009-10-13">2009</span> <i > arXiv </i> &nbsp; <span class="release-stage" >pre-print</span>
Cartan in his book on differential calculus proved a theorem generalizing a Cauchy's mean-value theorem to the case of functions taking values in a Banach space.  ...  Cartan used this theorem in a masterful way to develop the entire theory of differential calculus and theory of differential equations in finite and infinite dimensional Banach spaces.  ...  A theorem of Riesz The following theorem can be found in the monograph of F. Riesz and B. Sz.-Nagy [22] . Theorem 5.1 (Riesz) .  ... 
<span class="external-identifiers"> <a target="_blank" rel="external noopener" href="https://arxiv.org/abs/0910.2277v1">arXiv:0910.2277v1</a> <a target="_blank" rel="external noopener" href="https://fatcat.wiki/release/aaojvz4aafhjflkjxrzmfb6p3u">fatcat:aaojvz4aafhjflkjxrzmfb6p3u</a> </span>
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Measures, states and de Finetti maps on pseudo-BCK algebras [article]

Lavinia Corina Ciungu, Anatolij Dvurečenskij
<span title="2009-08-31">2009</span> <i > arXiv </i> &nbsp; <span class="release-stage" >pre-print</span>
In this paper, we extend the notions of states and measures presented in DvPu to the case of pseudo-BCK algebras and study similar properties.  ...  We prove that, under some conditions, the notion of a state in the sense of DvPu coincides with the Bosbach state, and we extend to the case of pseudo-BCK algebras some results proved by J.  ...  Mundici in [28] who showed that de Finetti's coherence principle that has an origin in Dutch book making, has a strong relationship with MV-states on MV-algebras.  ... 
<span class="external-identifiers"> <a target="_blank" rel="external noopener" href="https://arxiv.org/abs/0905.4789v2">arXiv:0905.4789v2</a> <a target="_blank" rel="external noopener" href="https://fatcat.wiki/release/6n3onq433zbqznvxkveggp6esm">fatcat:6n3onq433zbqznvxkveggp6esm</a> </span>
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Callias-type operators associated to spectral triples [article]

Hermann Schulz-Baldes, Tom Stoiber
<span title="2022-03-28">2022</span> <i > arXiv </i> &nbsp; <span class="release-stage" >pre-print</span>
Callias-type (or Dirac-Schr\"odinger) operators associated to abstract semifinite spectral triples are introduced and their indices are computed in terms of an associated index pairing derived from the  ...  Consider the modified potential H m = H mṼ mṼ −F (H) , which we check to be a differentiable self-adjoint multiplier w.r.t. D ⊗ 1 2 .  ...  It is a * -algebra and an ideal in N .  ... 
<span class="external-identifiers"> <a target="_blank" rel="external noopener" href="https://arxiv.org/abs/2108.06368v2">arXiv:2108.06368v2</a> <a target="_blank" rel="external noopener" href="https://fatcat.wiki/release/zlvx7p4f3rafrlxd65oefck5nm">fatcat:zlvx7p4f3rafrlxd65oefck5nm</a> </span>
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Functional models in linear algebra

P.A. Fuhrmann
<span title="">1992</span> <i title="Elsevier BV"> <a target="_blank" rel="noopener" href="https://fatcat.wiki/container/wsx3rzhpingfvewcn5nwhfkq3e" style="color: black;">Linear Algebra and its Applications</a> </i> &nbsp;
This paper examines the role of functional models in linear algebra and some related areas of application, notably linear systems theory.  ...  It is a powerful method which simplifies many proofs, provides insights, and illuminates the less obvious connections between linear algebra and operator theory, approximation theory, moment problems,  ...  Less than analyticity in the whole complex plane was shown to be enough, and replacing it by analyticity on the spectrum led to the Riesz-Dunford functional calculus.  ... 
<span class="external-identifiers"> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.1016/0024-3795(92)90373-i">doi:10.1016/0024-3795(92)90373-i</a> <a target="_blank" rel="external noopener" href="https://fatcat.wiki/release/4myvvf3vbvdxngpoiov65reobm">fatcat:4myvvf3vbvdxngpoiov65reobm</a> </span>
<a target="_blank" rel="noopener" href="https://web.archive.org/web/20170808135832/https://www.cs.bgu.ac.il/~paf/functionalmodels.pdf" title="fulltext PDF download" data-goatcounter-click="serp-fulltext" data-goatcounter-title="serp-fulltext"> <button class="ui simple right pointing dropdown compact black labeled icon button serp-button"> <i class="icon ia-icon"></i> Web Archive [PDF] <div class="menu fulltext-thumbnail"> <img src="https://blobs.fatcat.wiki/thumbnail/pdf/cf/42/cf426bfff8a404e11b4436f1ee080b5886be8d1c.180px.jpg" alt="fulltext thumbnail" loading="lazy"> </div> </button> </a> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.1016/0024-3795(92)90373-i"> <button class="ui left aligned compact blue labeled icon button serp-button"> <i class="external alternate icon"></i> elsevier.com </button> </a>

Asymptotics of sums of subcoercive operators

Nick Dungey, A. ter Elst, Derek Robinson
<span title="">1999</span> <i title="Institute of Mathematics, Polish Academy of Sciences"> <a target="_blank" rel="noopener" href="https://fatcat.wiki/container/qja4hqeadzam7ph6bhaks7ersu" style="color: black;">Colloquium Mathematicum</a> </i> &nbsp;
But since H is maximal accretive it has a bounded Hoo-holomorphic functional calculus by [ADM], Theorem G. Consequently In.  ...  of the Riesz transforms without further assumptions.  ... 
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Fourier's Method of Linear Programming and Its Dual

H. P. Williams
<span title="">1986</span> <i title="JSTOR"> <a target="_blank" rel="noopener" href="https://fatcat.wiki/container/6jb2mei4hzg4vdohokley4c5om" style="color: black;">The American mathematical monthly</a> </i> &nbsp;
Frames, locales {For topological questions see 54-XX} 06D25 Post algebras [See also 03G20] 06D30 De Morgan algebras, Lukasiewicz algebras [See also 03G20] 06D35 MV-algebras 06D50 Lattices and  ...  Vector algebra 97G80 Descriptive geometry 97G99 None of the above, but in this section 97Hxx Algebra 97H10 Comprehensive works 97H20 Elementary algebra 97H30 Equations and inequalities 97H40  ...  equations 83C25 Approximation procedures, weak fields 83C27 Lattice gravity, Regge calculus and other discrete methods 83C30 Asymptotic procedures (radiation, news functions, H-spaces, etc.) 83C35 Gravitational  ... 
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