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Local congruence of chain complexes [article]

Gianmaria DelMonte, Elia Onofri, Giorgio Scorzelli, Alberto Paoluzzi
2020 arXiv   pre-print
The object of this paper is to transform a set of local chain complexes to a single global complex using an equivalence relation of congruence of cells, solving topologically the numerical inaccuracies  ...  The target of this paper is to merge the local chains by using the equivalence relations of ϵ-congruence between 0-, 1-, and 2-cells (elementary chains).  ...  Chain Complex Congruence Algorithm In Section 4.1 we have discussed the block diagonal marshaling [∆ 0 ] and [∆ 1 ] of local coboundary matrices.  ... 
arXiv:2004.00046v1 fatcat:ie57rku3jrfpnacjkkfistfdxa

Page 820 of Mathematical Reviews Vol. 26, Issue 4 [page]

1963 Mathematical Reviews  
a 6 congruences non holonomes W ; dans un complexe avec un centre d’inflexion double, il y a seule- ment une congruence non holonome W; les complexes restants ne contiennent pas de congruence non holonome  ...  The possibility of such a trans- formation with conservation of generators depends (locally) on the nature of the envelope of the tangent hyperplanes through a ruling.  ... 

Policy transformation in software defined networks

Nanxi Kang, Joshua Reich, Jennifer Rexford, David Walker
2012 Computer communication review  
into a single list of rules.  ...  This would simplify programming by allowing programs written on one abstract switch to run over a more complex network topology, and simplify analysis by consolidating a policy spread over multiple switches  ...  may be applied correctly in a large context using the Congruence axiom as follows. l2 ↔ l 2 l1, l2, l3 ↔ l1, l 2 , l3 (Congruence) The Congruence axiom states that if a local rewrite applies then that  ... 
doi:10.1145/2377677.2377745 fatcat:o6ihcuj4lbgffa3ddaqe4bttga

Policy transformation in software defined networks

Nanxi Kang, Joshua Reich, Jennifer Rexford, David Walker
2012 Proceedings of the ACM SIGCOMM 2012 conference on Applications, technologies, architectures, and protocols for computer communication - SIGCOMM '12  
into a single list of rules.  ...  This would simplify programming by allowing programs written on one abstract switch to run over a more complex network topology, and simplify analysis by consolidating a policy spread over multiple switches  ...  may be applied correctly in a large context using the Congruence axiom as follows. l2 ↔ l 2 l1, l2, l3 ↔ l1, l 2 , l3 (Congruence) The Congruence axiom states that if a local rewrite applies then that  ... 
doi:10.1145/2342356.2342424 dblp:conf/sigcomm/KangRRW12 fatcat:pne643yt4vaitcgc5atbdv5atu

Page 497 of Mathematical Reviews Vol. 27, Issue 3 [page]

1964 Mathematical Reviews  
Let Il be a non-empty set of primes and let ZL, be the full linear group of degree n over the field of complex numbers.  ...  The author outlines a proof of the following theorem, which depends on a result of Dickson: If ¢> 2, every normal congruence subgroup of I’ of odd level is a principal congruence subgroup. J.  ... 

Page 2580 of Mathematical Reviews Vol. , Issue 95e [page]

1995 Mathematical Reviews  
Mamedov that a variety of algebras is congruence-regular if and only if it has n-transferable congruences for some natural number n.  ...  Chessboard complexes arise in combinatorics as coset complexes, deleted joins, matching complexes, complexes of injective func- tions, etc.  ... 

Page 3986 of Mathematical Reviews Vol. , Issue 99f [page]

1999 Mathematical Reviews  
They then show that a nonzero T with the S.V.E.P. is chain-finite if and only if it is locally chain-finite at x for each x.  ...  As for A = #(H), congruence is closely related to (arbi- trarily high) order of contact at each w € Q, and the main point is to prove that order of contact <k implies congruence and thus unitary equivalence  ... 

Page 970 of Mathematical Reviews Vol. 33, Issue 5 [page]

1967 Mathematical Reviews  
The group G is said to satisfy the minimal condition with respect to a given subset M of @ if and only if every descending chain of subgroups G,>G,> --- intersects M in a chain of finite length.  ...  The norm |x| = 4/tr(zz’) makes the algebra of all nxn matrices over the complex numbers into a metric algebra, and thus GL(n, C) into a metric group.  ... 

Page 4575 of Mathematical Reviews Vol. , Issue 96h [page]

1996 Mathematical Reviews  
complexes.  ...  This and a few more results follow by applications of two theo- rems about the localization of zeros of polynomials.  ... 

Finite algebras of finite complexity

Keith A. Kearnes, Emil W. Kiss
1999 Discrete Mathematics  
In particular, we describe all ÿnite algebras of ÿnite complexity and all ÿnite strongly abelian algebras which generate residually small varieties. (K.A. Kearnes), ewkiss@cs.elte.hu (E.W.  ...  The fact that is rectangularly nilpotent implies that there is a chain of congruences connecting 0 A to such that each quotient is rectangulated by . Add 1 A to the end of this chain.  ...  Now suppose that is a strongly nilpotent congruence of A in the weakest possible sense described above, that is, for a suitable chain of congruences we have either S( ; i+1 ; i ) or S( i+1 ; ; i ) for  ... 
doi:10.1016/s0012-365x(99)00042-4 fatcat:yucmgnhlyjfmfgzxr73epcdozm

Page 508 of Mathematical Reviews Vol. 22, Issue 4A [page]

1961 Mathematical Reviews  
In Ann. of Math. (2) 69 (1959), 223-246 [MR 21 #4423], the reviewer has shown that the chains on a fibre space are chain equivalent to a chain complex which is the tensor product of the chains of the base  ...  of semi-simplicial complexes and twisted cartesian products.  ... 

Page 2562 of Mathematical Reviews Vol. , Issue 84g [page]

1984 Mathematical Reviews  
investigations on a preliminary analysis of the structure of these congruences.  ...  such that each of its segments is a lattice, ie. that P be a local lattice.  ... 

Page 939 of Mathematical Reviews Vol. , Issue 2000b [page]

2000 Mathematical Reviews  
Wen (PRC-WUHAN,; Wuhan) Properties of the congruence lattice of a De Morgan algebra.  ...  The dimension of the cube hull of a cut-complex is shown to be the same as the maximum degree of the vertices in the complex.  ... 

Page 60 of Mathematical Reviews Vol. 48, Issue 1 [page]

1974 Mathematical Reviews  
Here she gives the following results. (1) Let (0C F,C-:: C F,,-1C G@,) be a chain of finite sub-group schemes of @, such that the local component of F,/F,_, is non-zero for 1<i<n-—1; then there is a u.c.c.r.n.k  ...  There are canonical maps A(V)->A(0,/m,"), where A(V) is the group of sections of A over V and m, is the maximal ideal of the local ring 0, of V at v.  ... 

Page 2534 of Mathematical Reviews Vol. 58, Issue 4 [page]

1979 Mathematical Reviews  
Lesohin, The local finite- ness of semigroups of bilinear complex functionals (pp. 132-135); S. G. Mamikonjan, Varieties of finitely approximable semigroups. II (pp. 136-140); V. N.  ...  Under the assumption that the congruence lattice A(S) of a band of groups S has no infinite chains it is shown that A(S) is upper semimodular if and only if S is 0-modular [C. Spitznagel, Trans.  ... 
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