Results 211 to 220 of about 77,930 (235)
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Codimensions and trace codimensions of matrices are asymptotically equal
Israel Journal of Mathematics, 1984In a sequence of papers the author has obtained important results on codimensions and cocharacters of T-ideals over a field of characteristic zero. The main theorem in the paper under review claims that the codimensions of the \(k\times k\) matrix algebra \(F_ k\) are asymptotically equal to the trace codimensions: \(c_ n(F_ k)\cong t_ n(F_ k)\cong s(n)
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1985
The main purpose of this chapter is to classify all bifurcation problems (in one state variable) of codimension three or less. We find that there are eleven such singularities, which we call the elementary bifurcation problems. In the course of the chapter, we tabulate the following data for each of these eleven singularities: (i) Normal form ...
Martin Golubitsky, David G. Schaeffer
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The main purpose of this chapter is to classify all bifurcation problems (in one state variable) of codimension three or less. We find that there are eleven such singularities, which we call the elementary bifurcation problems. In the course of the chapter, we tabulate the following data for each of these eleven singularities: (i) Normal form ...
Martin Golubitsky, David G. Schaeffer
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2003
Typically, level set methods are used to model codimension-one objects such as points in ℜ1, curves in ℜ2, and surfaces in ℜ3. Burchard, Cheng, Merriman, and Osher [22] extended level set technology to treat codimension-two objects using the intersection of the zero level sets of two level set functions.
Stanley Osher, Ronald Fedkiw
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Typically, level set methods are used to model codimension-one objects such as points in ℜ1, curves in ℜ2, and surfaces in ℜ3. Burchard, Cheng, Merriman, and Osher [22] extended level set technology to treat codimension-two objects using the intersection of the zero level sets of two level set functions.
Stanley Osher, Ronald Fedkiw
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Asymptotic codimensions of M(E)
Advances in Mathematics, 2020If \(A\) is an associative PI-algebra with 1 in characteristic zero, then the codimension sequence \(c_n(A)\) is asymptotic to a function of the form \(\alpha n^t C^n\), where \(C\) is a positive integer [the first author, Adv. Appl. Math., 41, 52--75 (2008; Zbl 1145.05052)].
Berele, Allan, Regev, Amitai
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On Mappings of Finite Codimension
Proceedings of the London Mathematical Society, 1985The author studies abstract conditions on the pair (dim N,dim P) under which the set of \(C^{\infty}\)-stable maps \(N\to P\) is not dense in \(C^{\infty}(N,P)\), and also conditions under which there are no \(C^{\infty}\)-stable maps in a given homotopy class of maps \(N\to P\).
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Minimal Submanifolds of Higher Codimension
Vietnam Journal of Mathematics, 2021A concise survey of part of the major results concerning minimal submanifolds is presented by the author, who has strongly contributed to the recent development of the subject. Starting with the celebrated Bernstein theorem, see [\textit{S. Bernštein}, Charĭkov, Comm. Soc. Math.
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1988
Let F be a transversally oriented foliation of codimension one on (Mn+1, gM). Let Z ∈ ΓL⊥ be a unit vector field and ν ∈ Ω1(M) the dual form, defined by $$ \nu (Y) = {g_M}(Z,Y)\,{\text{for}}\,Y \in \Gamma TM $$ .
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Let F be a transversally oriented foliation of codimension one on (Mn+1, gM). Let Z ∈ ΓL⊥ be a unit vector field and ν ∈ Ω1(M) the dual form, defined by $$ \nu (Y) = {g_M}(Z,Y)\,{\text{for}}\,Y \in \Gamma TM $$ .
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1998
This chapter reviews codimension q surgery theory for q ≥ 1. Refer to Chap. 7 of Ranicki [237] for a previous account of the algebraic theory of codimension q surgery. For q ≥ 3 this is the same as the ordinary surgery obstruction theory on the submanifold, while for q = 1, 2 the situation is considerably more complicated. It may appear that case q = 2
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This chapter reviews codimension q surgery theory for q ≥ 1. Refer to Chap. 7 of Ranicki [237] for a previous account of the algebraic theory of codimension q surgery. For q ≥ 3 this is the same as the ordinary surgery obstruction theory on the submanifold, while for q = 1, 2 the situation is considerably more complicated. It may appear that case q = 2
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1998
Lopez de Medrano [170] formulated “the general philosophy for dealing with surgery problems in codimension 2: do not insist on obtaining homotopy equivalences when you are doing surgery on the complement of a submanifold, be happy if you can obtain the correct homology conditions.” Cappell and Shaneson [40], [46] developed the appropriate homology ...
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Lopez de Medrano [170] formulated “the general philosophy for dealing with surgery problems in codimension 2: do not insist on obtaining homotopy equivalences when you are doing surgery on the complement of a submanifold, be happy if you can obtain the correct homology conditions.” Cappell and Shaneson [40], [46] developed the appropriate homology ...
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Unknotting tori in codimension one and spheres in codimension two
Mathematical Proceedings of the Cambridge Philosophical Society, 1965We shall present this paper in the framework and terminology of differential topology though all our arguments are valid in the piecewise linear ease also, under local un-knottedness hypotheses. In particular we use Rp for Euclidean space of dimension p, Sp−1 for the standard unit sphere in it, and Dp for the disc which it bounds.
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