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Independence-friendly cylindric set algebras

2009
*
Logic Journal of the IGPL
*

We define

doi:10.1093/jigpal/jzp029
fatcat:plijbqwbfbbslll4zh54i46754
*independence*-*friendly**cylindric**set**algebras*and prove two main results. First, every*independence*-*friendly**cylindric**set**algebra*over a structure has an underlying Kleene*algebra*. ... Second, every one-dimensional*independence*-*friendly**cylindric**set**algebra*over a structure has an underlying monadic Kleene*algebra*. ... An*independence*-*friendly**cylindric**set**algebra*(or IFG-*algebra*, for short) is any subalgebra of an*independence*-*friendly**cylindric*power*set**algebra*. ...##
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Cylindric Set Algebras and IF Logic
[chapter]

2013
*
Bolyai Society Mathematical Studies
*

*friendly*

*cylindric*

*set*

*algebra*, see IF

*algebra*

*independence*-

*friendly*logic, see IF logic Kalman, J. ... A DF α

*cylindric*

*set*

*algebra*(or DF α

*algebra*) is a DF

*cylindric*

*set*

*algebra*of dimension α.

*Independence*-

*friendly*

*cylindric*

*set*

*algebras*(IF

*algebras*) were defined in [20, Definition 2.1]. ... , 11 K three-element Kleene

*algebra*, 11 M centered four-element De Morgan

*algebra*, 11 ϕ ∧ J ψ DF conjuction, 3 ϕ ∨ J ψ DF disjunction, 3 a ≈ J b a and b are indistinguishable on J, 4 a(n : b) assignment ...

##
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In Memoriam: Leon Albert Henkin 1921–2006

2009
*
Bulletin of Symbolic Logic
*

Concrete

doi:10.2178/bsl/1246453978
fatcat:qfwwyh3tb5dfdmhzdglsaq73au
*cylindric**algebras*, corresponding to fields of*sets*for Boolean*algebras*, are*algebras*of*sets*of sequences, corresponding to satisfaction*sets*for formulas. ... Hintikka's*independence**friendly*logic can be considered as an elaboration of this idea. A problem which Henkin formulated in JSL, vol. 17, has led to an important field of research in logic. ...##
###
Page 750 of Mathematical Reviews Vol. , Issue 99b
[page]

1991
*
Mathematical Reviews
*

The authors of this article advocate a system called “

*independence**friendly*(IF) first-order logic”, in which one can express*independence*among the quantifiers and connectives. ... Collins and Hoon Hong, Partial*cylindrical**algebraic*decomposition for quantifier elimination (174-200); Hoon Hong, Simple solution formula construction in*cylindrical**algebraic*de- composition based quantifier ...##
###
Perfect IFG-Formulas

2008
*
Logica Universalis
*

We use the answer to show that the ordinary

doi:10.1007/s11787-008-0037-z
fatcat:b45jdilicnbeblsjzeryncnkaq
*cylindric**set**algebra*over a structure can be embedded into a reduct of the IFG-*cylindric**set**algebra*over the structure. ... IFG logic is a variant of the*independence*-*friendly*logic of Hintikka and Sandu. We answer the question: "Which IFG-formulas are equivalent to ordinary first-order formulas?" ... An IFG-*cylindric**set**algebra*(or IFG-*algebra*, for short) is any subalgebra of an IFG-*cylindric*power*set**algebra*. ...##
###
"Iff" is not expressible in independence-friendly logic
[article]

2008
*
arXiv
*
pre-print

We prove that

arXiv:0806.4785v1
fatcat:cb4fxoakczgj7nflwiqamtwzyi
*independence*-*friendly*logic does not have this property. ... An IFG-*cylindric**set**algebra*(or IFG-*algebra*, for short) is any subalgebra of an IFG-*cylindric*power*set**algebra*. ... IFG-*cylindric**set**algebras*. We introduced IFG-*cylindric**set**algebras*in [11, 12] as a way to study the*algebra*of IFG logic. ...##
###
Cylindric Versions of Specialised Macdonald Functions and a Deformed Verlinde Algebra

2012
*
Communications in Mathematical Physics
*

We define

doi:10.1007/s00220-012-1630-9
fatcat:v7otgoq26rdohfuibkl2norqqa
*cylindric*generalisations of skew Macdonald functions when one of their parameters is*set*to zero. ... The resulting*cylindric*Macdonald functions appear in the coproduct of a commutative Frobenius*algebra*, which is a particular quotient of the spherical Hecke*algebra*. ... In particular the g r 's are all*algebraically**independent*and, thus, theg r also form an*algebraically**independent**set*(note that g n+r and g r have different degree). ...##
###
Loop quantum geometry: a primer

2005
*
Journal of Physics, Conference Series
*

The purpose of the written contribution is to provide a Primer version, that is, a first entry into Loop Quantum Gravity and to present at the same time a

doi:10.1088/1742-6596/24/1/001
fatcat:u5frufwfkrcpbl7b5bekv7m7y4
*friendly*guide to the existing pedagogical literature ... The other characterization is more*algebraic*. It is based on the observation that the (Abelian)*algebra*of*cylindrical*functions Cyl can be extended to a C * -*algebra*Cyl with unit. ... This has to be so if we want to have a fully background*independent*classical*algebra*for the quantization. A remark is in order. ...##
###
On the superselection theory of the Weyl algebra for diffeomorphism invariant quantum gauge theories
[article]

2003
*
arXiv
*
pre-print

As an important tool which is also interesting in its own right, we introduce a C*-

arXiv:gr-qc/0302090v2
fatcat:xu66dscnibbx3glkj6cnkpdj24
*algebra*which is very similar to the Weyl*algebra*used in the canonical quantization of free quantum field theories. ... Most notably, a diffeomorphism invariant representation of the*algebra*of basic observables of the theory, the Ashtekar-Lewandowski representation, has been constructed. ... Acknowledgments We thank the Erwin -Schrödinger Institute for providing a*friendly*hospitality and a challenging research environment during the 'Quantum field theory on curved spacetimes' workshop, where ...##
###
Cylindric plane partitions, Lambda determinants, Commutants in semicircular systems
[article]

2021
*
arXiv
*
pre-print

Semicircular systems were first introduced by Voiculescu as a part of his study of von Neumann

arXiv:2110.12629v1
fatcat:2kxjc7bysrhtlh3c7t7rq5r6lm
*algebras*. ...*Cylindric*plane partitions may be thought of as a natural generalization of reverse plane partitions. ... The Borel σ-*algebra*of R is the smallest σ*algebra*on R which is generated by the open*sets*of R. ...##
###
Computer facilitated generalized coordinate transformations of partial differential equations with engineering applications

2011
*
Computer Applications in Engineering Education
*

In our opinion, the use of Maple or similar computer

doi:10.1002/cae.20318
fatcat:irlqnkmyabaxtm5qi2e2wwepbi
*algebraic*systems (e.g. ... We illustrate this by considering a number of engineering problems governed by PDEs in different coordinate systems such as the bipolar, elliptic*cylindrical*, and prolate spheroidal. ... ð10Þ This form of writing the relationship between the ''old''*set*of coordinates, that is, x, y and the ''new''*set*of coordinates u, v provides us a further insight since we can notice that Equations ...##
###
Exhaustive Synthesis and Realization of Extended-Box Topologies With Dispersive Couplings

2021
*
2021 IEEE MTT-S International Microwave Filter Workshop (IMFW)
*

Following [8] and preceding section, the

doi:10.1109/imfw49589.2021.9642326
fatcat:6ydocwbst5cenirtvccssfafwi
*algebraic**set*of equation characterising all congruent transformations passing from former circuital realisation to our target topology is the following: ... The input and output couplings B S,k and B k,L are supposed to be frequency-*independent*. ...##
###
Distributed UAV-enabled zero-forcing cooperative jamming scheme for safeguarding future wireless networks
[article]

2021
*
arXiv
*
pre-print

The position of A is

arXiv:2109.13929v1
fatcat:57otzjfshve67kv3urgelxapqu
*set*at coordinates (0, 0) and B is located at coordinates (d AB , 0), so the*cylindrical*coordinates of both jammers become (R J , θ J1 , z J1 ) and (R J , θ J2 , z J2 ), respectively ... Analysing the region where ∆ > 1, for which jamming improves secrecy, basic*algebraic*derivation leads to the condition g INT > 0, which is always true. ...##
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A Spatial Search Framework for Executing Perceptions and Actions in Diagrammatic Reasoning
[chapter]

2010
*
Lecture Notes in Computer Science
*

We prove the correctness of our approach and show that it is more efficient than

doi:10.1007/978-3-642-14600-8_15
fatcat:evmdw7lbuzeljmfm7eft5e3wym
*cylindrical**algebraic*decomposition, a well-known*algebraic*approach, by executing perceptions/actions in two army applications ... We observe that the domain/task-specific perceptions/actions can be transformed into domain/task-*independent*spatial problems. ... The enhanced algorithm is shown to be more efficient than*cylindrical**algebraic*decomposition (CAD), a well-known*algebraic*approach, in executing perceptions/actions for two army applications. ...##
###
High-Speed GPU-Based Fully Three-Dimensional Diffuse Optical Tomographic System

2014
*
International Journal of Biomedical Imaging
*

They evaluated the performance of CULA (CULA is a

doi:10.1155/2014/376456
pmid:24891848
pmcid:PMC4003791
fatcat:3oegtrwva5gndoaj73eyqg4hg4
*set*of GPU-accelerated linear*algebra*libraries utilizing the CUDA parallel computing architecture) [32] based algorithms for DOT. ... The domain over which the function ( , ) is defined is divided into a finite*set*of disjoint elements. ...
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