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On Δ-Modular Integer Linear Problems In The Canonical Form And Equivalent Problems
[article]

2022
*
arXiv
*
pre-print

We show that any ILP problem

arXiv:2002.01307v6
fatcat:ps4zs63kxbbpheavasyutx5z5i
*in*the standard form can be*polynomially*reduced to some ILP problem*in*the canonical form, preserving m and Δ(*A*), but the reverse reduction is not always possible. ... Many papers*in*the field of integer linear programming (ILP,*for*short) are devoted to problems of the type max{c^⊤ x*A*x = b, x ∈ℤ^n_≥ 0}, where all the entries of*A*,b,c are integer, parameterized by ... Paat*for*useful discussions during preparation of this article. Additionally, the authors would like to thank anonymous reviewers*for*their useful comments and remarks. ...##
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Gromov's theorem on groups of polynomial growth and elementary logic

1984
*
Journal of Algebra
*

Define f E S' by f (i,) = uj, wherej is maximal such that aj E Ai,, if j exists,

doi:10.1016/0021-8693(84)90223-0
fatcat:7ke4eipwt5fjlofzehjhukohxa
*a*,,j otherwise, where j is*minimal*such that*a*, +j E*A**in*; since f (i) E Ai*for*all i E Z, we have f/D EA. ... (See [8, Chap. 71*for*the notion of Hausdorff*dimension*and its connections with topological*dimension*.) ...##
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Orientation Dynamics And Microscope Imaging Of Colloidal Suspensions

2016

Morexi xii xv 4.1 (

doi:10.7298/x4x63jvp
fatcat:uuwfageysbf7ndoc2kfts7gn54
*a*) ρ(φ)*for*particles with aspect ratio p = 5.0 under continuous shear is sharply peaked and constant*in*time. ... These particles are large enough to be easily imaged with*a*microscope, allowing*for*detailed, mechanistic testing of statistical theories, yet small enough to still feel the effects of Brownian motion ... Sethna*for*useful discussions. ...##
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Polyhedral and combinatorial aspects in optimization
[article]

2018

Note added

doi:10.25673/3869
fatcat:lnnb3uceujdufb7gghvybgazdy
*in*preparation: Following the results*in*this manuscript, an alternative proof of the fact that the tree routing property holds*for*csVPN has been given [GOS08a] . ... Cops & Robber The game of Cops and Robber is played on*a*connected graph by two players -the cops and the robber. ... latter is*a*full-*dimensional*unbounded polyhedron*in*R E [CFN85] , the former is*a*polytope of*dimension*n 2 − n [Nor55] , and the inequality e∈E x e ≥ n is valid*for*P and satisfied with equality only ...##
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Position Papers of the 2014 Federated Conference on Computer Science and Information Systems

2014
*
Polskie Towarzystwo Informatyczne Annals of Computer Science and Information Systems
*
unpublished

*A*significant advantage of the SMCVB

*algorithm*is that it is not restricted to

*fixed*-

*dimensional*space. ... Considering the

*discrete*and ordinal nature of the above parameters, there is

*a*possibility to create mathematical model of security S

*in*

*a*form of

*a*

*discrete*

*function*: S = f(

*A*, V, E, I, O) Evidently, ... /

*convic*) II. ...