TRANSCENDENCE BASES AND N
... PROPOSITION 2: Suppose k[x1, …, xn] is a finitely generated integral domain over a field k, of transcendence degree r over k. Then there exist transcendence bases {y1, …, yr} k[x1, …, xn] so that k[y1, …, yr] k[x1, …, xn] is an integral extension. If k is an infinite field, the y’s can be chose ...
... PROPOSITION 2: Suppose k[x1, …, xn] is a finitely generated integral domain over a field k, of transcendence degree r over k. Then there exist transcendence bases {y1, …, yr} k[x1, …, xn] so that k[y1, …, yr] k[x1, …, xn] is an integral extension. If k is an infinite field, the y’s can be chose ...
Algorithms ・ 6.5 R
... of an integral variable or a real or computable variable, computable predicates, and so forth. The fundamental problems involved are, however, the same in each case, and I have chosen the computable numbers for explicit treatment as involving the least cumbrous technique. I hope shortly to give an a ...
... of an integral variable or a real or computable variable, computable predicates, and so forth. The fundamental problems involved are, however, the same in each case, and I have chosen the computable numbers for explicit treatment as involving the least cumbrous technique. I hope shortly to give an a ...
Automatic Continuity - Selected Examples Krzysztof Jarosz
... question remained open for many years until finally in 1977 H. G. Dales [3] and J. Esterle [6] announced two independent proofs. They showed that under the continuum hypothesis there is a non-complete submultiplicative norm on C(K). In this context one may ask if there can be a submultiplicative norm ...
... question remained open for many years until finally in 1977 H. G. Dales [3] and J. Esterle [6] announced two independent proofs. They showed that under the continuum hypothesis there is a non-complete submultiplicative norm on C(K). In this context one may ask if there can be a submultiplicative norm ...
Algorithms ・ 6.5 R
... of an integral variable or a real or computable variable, computable predicates, and so forth. The fundamental problems involved are, however, the same in each case, and I have chosen the computable numbers for explicit treatment as involving the least cumbrous technique. I hope shortly to give an a ...
... of an integral variable or a real or computable variable, computable predicates, and so forth. The fundamental problems involved are, however, the same in each case, and I have chosen the computable numbers for explicit treatment as involving the least cumbrous technique. I hope shortly to give an a ...
Algorithms 6.5 R
... in Opn2 plog log nq5{3 {plog nq2{3 q time. These results refute the strongest version of the 3SUM conjecture, namely that its decision tree (and algorithmic) complexity is Ωpn2 q. Our results lead directly to improved algorithms for k-variate linear degeneracy testing for all ...
... in Opn2 plog log nq5{3 {plog nq2{3 q time. These results refute the strongest version of the 3SUM conjecture, namely that its decision tree (and algorithmic) complexity is Ωpn2 q. Our results lead directly to improved algorithms for k-variate linear degeneracy testing for all ...
notes 1
... eigenvalues. Instead of the three unique principal axes you got in (8), you have infinitely many ones. One is a line along v3, the eigenvector for the non-repeated eigenvalue 3 . Here there is no choice. But any two lines through the origin that are orthogonal to each other and to v3 will do as ...
... eigenvalues. Instead of the three unique principal axes you got in (8), you have infinitely many ones. One is a line along v3, the eigenvector for the non-repeated eigenvalue 3 . Here there is no choice. But any two lines through the origin that are orthogonal to each other and to v3 will do as ...
