scholarly journals Maximal rank for schemes of small multiplicity by Évain’s differential Horace method

2013 ◽  
Vol 366 (2) ◽  
pp. 857-874 ◽  
Author(s):  
Joaquim Roé
Keyword(s):  
Maximal Rank ◽  
Small Multiplicity

Maximal rank divisors on M_g,n

2020 ◽  
Vol 20 (1) ◽  
pp. 349-371
Author(s):  
İrfan Kadiköylü
Keyword(s):  
Maximal Rank

On fixed subgroups of maximal rank

1997 ◽  
Vol 25 (10) ◽  
pp. 3361-3375 ◽  
Author(s):  
Enric Ventura
Keyword(s):  
Maximal Rank ◽  
Fixed Subgroups

Algebraization of Maximal Rank Webs

2015 ◽  
pp. 115-149
Author(s):  
Jorge Vitório Pereira ◽  
Luc Pirio
Keyword(s):  
Maximal Rank

scholarly journals On the maximal rank problem for the complex homogeneous Monge–Ampère equation

2019 ◽  
Vol 12 (2) ◽  
pp. 493-503
Author(s):  
Julius Ross ◽  
David Witt Nyström
Keyword(s):  
Maximal Rank ◽  
Monge Ampere

scholarly journals Generalization of real interval matrices to other fields

2019 ◽  
Vol 35 ◽  
pp. 285-296
Author(s):  
Elena Rubei
Keyword(s):  
Full Rank ◽  
Maximal Rank ◽  
Interval Matrix ◽  
Real Interval ◽  
Rational Matrix ◽  
Rank One ◽  
Rational Rank ◽  
Q Matrix ◽  
Rational Interval ◽  
Rank Of A Matrix

An interval matrix is a matrix whose entries are intervals in $\R$. This concept, which has been broadly studied, is generalized to other fields. Precisely, a rational interval matrix is defined to be a matrix whose entries are intervals in $\Q$. It is proved that a (real) interval $p \times q$ matrix with the endpoints of all its entries in $\Q$ contains a rank-one matrix if and only if it contains a rational rank-one matrix, and contains a matrix with rank smaller than $\min\{p,q\}$ if and only if it contains a rational matrix with rank smaller than $\min\{p,q\}$; from these results and from the analogous criterions for (real) inerval matrices, a criterion to see when a rational interval matrix contains a rank-one matrix and a criterion to see when it is full-rank, that is, all the matrices it contains are full-rank, are deduced immediately. Moreover, given a field $K$ and a matrix $\al$ whose entries are subsets of $K$, a criterion to find the maximal rank of a matrix contained in $\al$ is described.

A Geometric Characterization of Nonnegative Bands

2004 ◽  
Vol 47 (2) ◽  
pp. 257-263
Author(s):  
Alka Marwaha
Keyword(s):  
Invariant Subspace ◽  
Geometric Structure ◽  
Finite Rank ◽  
Special Kind ◽  
Maximal Rank ◽  
Geometric Characterization ◽  
Idempotent Operators ◽  
Rank One ◽  
Standard Subspace

AbstractA band is a semigroup of idempotent operators. A nonnegative band S in having at least one element of finite rank and with rank (S) > 1 for all S in S is known to have a special kind of common invariant subspace which is termed a standard subspace (defined below).Such bands are called decomposable. Decomposability has helped to understand the structure of nonnegative bands with constant finite rank. In this paper, a geometric characterization of maximal, rank-one, indecomposable nonnegative bands is obtained which facilitates the understanding of their geometric structure.

Some Applications of Artamonov-Quillen-Suslin Theorems to Metabelian Inner Rank and Primitivity

1994 ◽  
Vol 46 (2) ◽  
pp. 298-307 ◽  
Author(s):  
C. K. Gupta ◽  
N. D. Gupta ◽  
G. A. Noskov
Keyword(s):  
Metabelian Group ◽  
Sufficient Conditions ◽  
Surface Group ◽  
Maximal Rank ◽  
Orientable Surface ◽  
Surface Groups ◽  
Modular Element ◽  
Free Metabelian Group ◽  
One Relator Groups ◽  
Necessary And Sufficient

AbstractFor any variety of groups, the relative inner rank of a given groupG is defined to be the maximal rank of the -free homomorphic images of G. In this paper we explore metabelian inner ranks of certain one-relator groups. Using the well-known Quillen-Suslin Theorem, in conjunction with an elegant result of Artamonov, we prove that if r is any "Δ-modular" element of the free metabelian group Mn of rank n > 2 then the metabelian inner rank of the quotient group Mn/(r) is at most [n/2]. As a corollary we deduce that the metabelian inner rank of the (orientable) surface group of genus k is precisely k. This extends the corresponding result of Zieschang about the absolute inner ranks of these surface groups. In continuation of some further applications of the Quillen-Suslin Theorem we give necessary and sufficient conditions for a system g = (g1,..., gk) of k elements of a free metabelian group Mn, k ≤ n, to be a part of a basis of Mn. This extends results of Bachmuth and Timoshenko who considered the cases k = n and k < n — 3 respectively.

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