gravitation, gauge theories and differential geometry
... the same class of problems was being attacked simultaneously by mathematicians and physicists and that a new basis existed for mutual discourse. The attention of the mathematicians was now drawn to the problem of constructing Yang—Mills solutions with index k which exhausted the available free param ...
... the same class of problems was being attacked simultaneously by mathematicians and physicists and that a new basis existed for mutual discourse. The attention of the mathematicians was now drawn to the problem of constructing Yang—Mills solutions with index k which exhausted the available free param ...
Computational problems in lattice
... Full security analysis given by van Dijk, Gentry, Halevi and Vaikuntanathan. Variant where X0 = pq0 is also given in public key, and computations are modulo X0 . (ρ, η, γ)-Approximate GCD problem: Given X1 , . . . , Xk ∈ Z ∩ [0, 2γ ] find an integer 2η−1 < p < 2η such that [Xi ]p < 2ρ for all 1 ≤ i ...
... Full security analysis given by van Dijk, Gentry, Halevi and Vaikuntanathan. Variant where X0 = pq0 is also given in public key, and computations are modulo X0 . (ρ, η, γ)-Approximate GCD problem: Given X1 , . . . , Xk ∈ Z ∩ [0, 2γ ] find an integer 2η−1 < p < 2η such that [Xi ]p < 2ρ for all 1 ≤ i ...
Linear Algebra Math 308 S. Paul Smith
... Curvy things play no role in linear algebra or linear geometry. We ignore circles, spheres, ellipses, parabolas, etc. All is linear. 1.1. What is a line? You already “know” what a line is. More accurately, you know something about lines in the plane, R2 , or in 3-space, R3 . In this course, you need ...
... Curvy things play no role in linear algebra or linear geometry. We ignore circles, spheres, ellipses, parabolas, etc. All is linear. 1.1. What is a line? You already “know” what a line is. More accurately, you know something about lines in the plane, R2 , or in 3-space, R3 . In this course, you need ...
On Fitting ideals of logarithmic vector fields and Saito`s criterion
... on the ideals Ik (L), 1 ≤ k ≤ n, where Ik (L) is generated by the k × k minors of a matrix of a generating set of L; these are the Fitting ideals of DerCn ,p /L, but we shall abuse terminology and call them the Fitting ideals of L. An understanding of the geometric content of these ideals may also a ...
... on the ideals Ik (L), 1 ≤ k ≤ n, where Ik (L) is generated by the k × k minors of a matrix of a generating set of L; these are the Fitting ideals of DerCn ,p /L, but we shall abuse terminology and call them the Fitting ideals of L. An understanding of the geometric content of these ideals may also a ...
Introduction to Linear Transformation
... Question: Describe all vectors ~u so that T (~u ) = ~b. Answer: This is the same as finding all vectors ~u so that A~u = ~b. Could be no ~u , could be exactly one ~u , or could be a parametrized family of such ~u ’s. Recall the idea: row reduce the augmented matrix [A : ~b] to merely echelon form. A ...
... Question: Describe all vectors ~u so that T (~u ) = ~b. Answer: This is the same as finding all vectors ~u so that A~u = ~b. Could be no ~u , could be exactly one ~u , or could be a parametrized family of such ~u ’s. Recall the idea: row reduce the augmented matrix [A : ~b] to merely echelon form. A ...
