On the Equivalence of Certain Consequences of the Proper Forcing
... We will denote by TOP(col) a statement of TOP, with the additional assumption that A = B = co,; that is, the following axiom: 2.4. TOP(col). Suppose (T, : a C co,) is such that T, C a for all a. Suppose also that for any uncountable X C co, there exists P3< col, such that {X} U {T, : a > fl} has the ...
... We will denote by TOP(col) a statement of TOP, with the additional assumption that A = B = co,; that is, the following axiom: 2.4. TOP(col). Suppose (T, : a C co,) is such that T, C a for all a. Suppose also that for any uncountable X C co, there exists P3< col, such that {X} U {T, : a > fl} has the ...
Advanced NUMBERTHEORY
... The present text constitutes slightly more than enough for a secondsemester course, carrying the student on to the twentieth Century by motivating some heroic nineteenth-Century developments in algebra and analysis. The relation of this textbook to the great treatises Will necessarily be like that o ...
... The present text constitutes slightly more than enough for a secondsemester course, carrying the student on to the twentieth Century by motivating some heroic nineteenth-Century developments in algebra and analysis. The relation of this textbook to the great treatises Will necessarily be like that o ...
On the existence of equiangular tight frames
... There are two families of ETFs that arise for every dimension d and one family in dimension one with arbitrary number of vectors. (1) (Orthonormal Bases). When N = d, the sole examples of ETFs are unitary (and orthogonal) matrices. Evidently, the absolute inner product α between distinct vectors is ...
... There are two families of ETFs that arise for every dimension d and one family in dimension one with arbitrary number of vectors. (1) (Orthonormal Bases). When N = d, the sole examples of ETFs are unitary (and orthogonal) matrices. Evidently, the absolute inner product α between distinct vectors is ...
Higher regulators and values of L
... 1.6. ~ -Cohomologies of Algebraic Manifolds. We denote by H c H the complete subcategory consisting of those pairs (V, V) for which ~ is a (smooth) projective algebraic variety. Let ~ R or simply ~7~be the category of smooth quasiprojective schemes over R. According to GAGA, we have the functor g:~- ...
... 1.6. ~ -Cohomologies of Algebraic Manifolds. We denote by H c H the complete subcategory consisting of those pairs (V, V) for which ~ is a (smooth) projective algebraic variety. Let ~ R or simply ~7~be the category of smooth quasiprojective schemes over R. According to GAGA, we have the functor g:~- ...
Elliptic Curves - Department of Mathematics
... that the discrete logarithm problem in E1 (Fq ) is equivalent to the discrete logarithm problem in E2 (Fq ). In other words, the discrete logarithm problem on Fq -isomorphic curves has exactly the same security. To reduce storage in some applications it might be desirable to choose a model for ellip ...
... that the discrete logarithm problem in E1 (Fq ) is equivalent to the discrete logarithm problem in E2 (Fq ). In other words, the discrete logarithm problem on Fq -isomorphic curves has exactly the same security. To reduce storage in some applications it might be desirable to choose a model for ellip ...