BORDER RANK AND SCHEME RANK FOR LINEAR PROJECTIONS OF CURVES
نویسندگان
چکیده
منابع مشابه
On the rank of certain parametrized elliptic curves
In this paper the family of elliptic curves over Q given by the equation Ep :Y2 = (X - p)3 + X3 + (X + p)3 where p is a prime number, is studied. Itis shown that the maximal rank of the elliptic curves is at most 3 and someconditions under which we have rank(Ep(Q)) = 0 or rank(Ep(Q)) = 1 orrank(Ep(Q))≥2 are given.
متن کاملA note on the gap between rank and border rank
We study the tensor rank of the tensor corresponding to the algebra of n-variate complex polynomials modulo the dth power of each variable. As a result we find a sequence of tensors with a large gap between rank and border rank, and thus a counterexample to a conjecture of Rhodes. At the same time we obtain a new lower bound on the tensor rank of tensor powers of the generalised W-state tensor....
متن کاملEquations for Lower Bounds on Border Rank
We present new methods for determining polynomials in the ideal of the variety of bilinear maps of border rank at most r. We apply these methods to several cases including the case r = 6 in the space of bilinear maps C × C → C. This space of bilinear maps includes the matrix multiplication operator M2 for two by two matrices. We show these newly obtained polynomials do not vanish on the matrix ...
متن کاملFreud, Rank and, the problem of anxiety
Anxiety has always been a phenomenon of great importance among psychoanalysts. Freud, as the founder of psychoanalysis, took much notice of this phenomenon from the beginning of his career, and he was always trying to give a comprehensive explanation for this problem. Therefore, throughout his career, he modified his theories about anxiety frequently, and even one time, he changed his whole the...
متن کاملRandom Projections for Low Multilinear Rank Tensors
We proposed two randomized tensor algorithms for reducing multilinear ranks in the Tucker format. The basis of these randomized algorithms is from the randomized SVD of Halko, Martinsson and Tropp [9]. Here we provide randomized versions of the higher order SVD and higher order orthogonal iteration. Moreover, we provide a sharper probabilistic error bounds for the matrix low rank approximation....
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: International Journal of Pure and Apllied Mathematics
سال: 2013
ISSN: 1311-8080,1314-3395
DOI: 10.12732/ijpam.v85i5.6