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Quantifier-Elimination for the First-Order Theory of Boolean Algebras with Linear Cardinality Constraints
[chapter]

2004
*
Lecture Notes in Computer Science
*

We present for the first-order theory

doi:10.1007/978-3-540-30204-9_1
fatcat:4jaji3a2pjcfbit3suhp3jq3jm
*of*atomic Boolean algebras*of**sets*with*linear**cardinality*constraints*a*quantifier elimination algorithm. ... We also explain the connection*of*this new logical result with the evaluation*of*relational calculus queries*on*constraint databases that contain Boolean*linear**cardinality*constraints. ... Acknowledgment: I thank the conference organizers, especially András Benczur, for encouraging submission*of*this paper. ...##
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Graph Structure and Monadic Second-Order Logic: Language Theoretical Aspects
[chapter]

2008
*
Lecture Notes in Computer Science
*

tools for the construction

doi:10.1007/978-3-540-70575-8_1
fatcat:ftpcqszcb5fs5nswbqnbnmy5ja
*of*Fixed-Parameter Tractable algorithms and also for the extension*of*methods and results*of*Formal Language Theory to the description*of**sets**of**finite*graphs. ... Graph structure is*a*flexible concept covering many different types*of*graph properties. ... I thank*A*. Blumensath, M. Fellows and I. Walukiewicz for many useful comments*on**a*first draft*of*this overview. The first 11 references are books and survey articles. ...##
###
Patterns of quadratic residues and nonresidues for infinitely many primes

2007
*
Journal of Number Theory
*

We solve problem (1) and we show that problem (2) is equivalent to

doi:10.1016/j.jnt.2006.06.003
fatcat:jrcfykf3una2ho2rhcdhwcmmoe
*a*purely combinatorial problem concerning families*of*subsets*of**a**finite**set*. ... For*sets*S*of*(essentially) small*cardinality*, we solve problem (2). Related results and some associated enumerative combinatorics are also discussed. ... I also thank the referee for several comments which lead to significant improvements in the exposition*of*this paper. ...##
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Model structure on differential graded commutative algebras over the ring of differential operators
[article]

2017
*
arXiv
*
pre-print

We construct

arXiv:1505.07720v2
fatcat:ww2be7qzabh6ljbnrxcc23mgem
*a*cofibrantly generated model structure*on*the category*of*differential non-negatively graded quasi-coherent commutative D_X-algebras, where D_X is the sheaf*of*differential*operators**of**a*... This article is the first*of**a*series*of*works -located at the interface*of*homotopical algebra, algebraic geometry, and mathematical physics -*on**a*derived D-geometric approach to the BV-formalism. ... Introduction The solution functor*of**a*system*of**linear*PDE-s D · m = 0 is*a*functor Sol : Mod(D) →*Set*defined*on*the category*of*modules*over*the ring D*of*(*linear*) differential*operators**of**a*suitable ...##
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Categorified Algebra and Quantum Mechanics
[article]

2006
*
arXiv
*
pre-print

Examples include the interpretation

arXiv:math/0601458v1
fatcat:pdl5xduorzdjlcwl7rnh2e7yau
*of*N as the Burnside rig*of*the category*of**finite**sets*with product and coproduct, and the interpretation*of*N[x] as the category*of*combinatorial species. ... out to be*closely*related. ... the*operation**of*taking the*free*monoid*on**a**set*. ...##
###
Page 3816 of Mathematical Reviews Vol. , Issue 80J
[page]

1980
*
Mathematical Reviews
*

Kato [Perturbation theory for

*linear**operators*, Springer, New York, 1966; MR 34 #3324] proved that if*A*is an m-accretive*linear**operator*in*a*Hilbert space, then*A*has*a*unique m-accretive*square*root ... Let R be the*free*associative k-algebra*on*n’ generators*a*,, and R<x) the*free*associative k-algebra in*one*further indeterminate x. ...##
###
Monotone normality in products

1999
*
Topology and its Applications
*

It is shown that if the

doi:10.1016/s0166-8641(97)00230-7
fatcat:qndykxog25fmxieke3pv57z5di
*square**of**a*space is monotonically normal, then all*finite*powers are monotonically normal and hereditarily paracompact. ... Nonetheless,*a*monotonically normal topological group is constructed, all*of*whose*finite*powers are monotonically normal, but which is not linearly stratifiable. ... Acknowledgements The author would like to warmly thank Robin Knight for his invaluable assistance in finding*a*tangle*free*, nonlinear, filter. ...##
###
The incidence comodule bialgebra of the Baez-Dolan construction
[article]

2019
*
arXiv
*
pre-print

Starting from any operad P,

arXiv:1912.11320v1
fatcat:bto3lanw3vcbvhvfguzdn3ogxe
*one*can consider*on**one*hand the*free*operad*on*P, and*on*the other hand the Baez–Dolan construction*on*P. ... If P is any monoid Ω (considered as*a**one*-coloured operad with only unary*operations*), the resulting comodule bialgebra is the dual*of*the near-semiring*of*Ω-moulds under product and composition, as employed ...*on*various parts*of*this work. ...##
###
Introduction to mathematical logic - A problem solving course
[article]

1996
*
arXiv
*
pre-print

This is

arXiv:math/9601203v1
fatcat:aw7ratpzxncljorpdbe4kwnnrq
*a**set**of*288 questions written for*a*Moore-style course in Mathematical Logic. I have used these (or some variation) four times in*a*beginning graduate course. ... Topics covered are: propositional logic axioms*of*ZFC wellorderings and equivalents*of*AC ordinal and*cardinal*arithmetic first order logic, and the compactness theorem Lowenheim-Skolem theorems Turing ...*one*-to-*one*correspondence with an element*of*ω*A**set*is countable iff it is either*finite*or*of*the same*cardinality*as ω. ...##
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Decomposition Spaces, Incidence Algebras and Möbius Inversion
[article]

2015
*
arXiv
*
pre-print

We work

arXiv:1404.3202v5
fatcat:andjk5vfi5ag7nk4dl6zraqahi
*on*the objective level*of*homotopy*linear*algebra with coefficients in infinity-groupoids, developed along the way. ... Imposing certain homotopy*finiteness*conditions yields the notion*of*M\"obius decomposition space, an extension*of*the notion*of*M\"obius category*of*Leroux. ... Then*one*can take homotopy*cardinality*, and recover*linear*algebra*over*Q. The*finiteness*conditions are needed to be able to take homotopy*cardinality*. ...##
###
Page 1781 of Mathematical Reviews Vol. 51, Issue 6
[page]

1976
*
Mathematical Reviews
*

*A*continuous map /

*of*

*a*

*closed*cone Cc R™ into R* is said to be piecewise homogeneous

*linear*if there is

*a*

*finite*

*set*fis» Sn

*Of*homogeneous

*linear*functions R"—> R* such that, for each x € C, f(x)=f,( ... Also the authors give

*a*

*set*

*of*conditions

*on*an /-ring

*A*under each

*of*which L(

*A*) coincides with the

*set*N

*of*all nilpotents

*of*

*A*. S. P. ...

##
###
Page 1720 of Mathematical Reviews Vol. 50, Issue 6
[page]

1975
*
Mathematical Reviews
*

Table

*of*Contents:*A*. V. Buhvalov, The integral representation*of**linear**operators*(pp. 5-14); S.*A*. Vinogradov and V. P. Havin,*Free*interpolation in H® and in certain other classes*of*functions. ... Erdés,*A*. Hajnal, L. Pésa, Strong embeddings*of*graphs into colored graphs (pp. 585-595); P. Erdés and S. H. Hechler,*On*maximal almost-disjoint families*over*singular*cardinals*(pp. 597-604). Vol. ...##
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Plethysms and operads
[article]

2020
*
arXiv
*
pre-print

We introduce the 𝒯-construction, an endofunctor

arXiv:2008.09798v2
fatcat:nfixhhk3wze2jk2m365mzkdiym
*on*the category*of*generalized operads as*a*general mechanism by which various notions*of*plethystic substitution arise from more ordinary notions*of*substitution ... In the special case*of**one*-object unary operads, i.e. monoids, we recover the T-construction*of*Giraudo. ... Lemma 6 .1. 2 . 62 Consider the category*of**finite*ordinals and*set*maps. (i) The class*of*monotone pullback*squares*is*closed*under composition*of**squares*. ...##
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Algorithms for determining the smallest number of nonterminals (states) sufficient for generating (accepting) a regular language
[chapter]

1991
*
Lecture Notes in Computer Science
*

Important note: this is not

doi:10.1007/3-540-54233-7_170
fatcat:phnjlcnxdbbsnkq73acbvvezqa
*a*"due homework", but rather*a*"pool*of*problems" meant to calibrate the scope and depth*of*the knowledge & skills in CS theory that you (eventually) need to have for exams, ... Recall that most (and perhaps even all)*of*the midterm and final exam questions in this course will come from these problem*sets*, so your best strategy*of*studying for the exams in this course is to solve ... What is the*cardinality**of*the*set**of*all*finite*-sized matrices with rational entries? 5. What is the*cardinality**of*the*set**of*all infinite matrices with Boolean entries? 6. ...##
###
Quadratic Modules, C*-Algebras, and Free Convexity
[article]

2016
*
arXiv
*
pre-print

We show that the usual notion

arXiv:1602.01618v1
fatcat:hnwbgqx2ujggbhy5pfdugbtg2y
*of**a**free*convex hull is not able to detect residual*finite*-dimensionality. We thus propose*a*new notion*of**free*convexity, which is coordinate-*free*. ... We characterize semialgebraicity*of**free*convex hulls*of*semialgebraic*sets*, and show that they are not always semialgebraic, even at scalar level. ... semialgebraic*set*(*finite*intersections*of*such*sets*are also called basic*closed*). ...
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