On the discrete logarithm problem on algebraic tori

... pre- cisely the algebraic torus T n (F q ). On the Discrete Logarithm Problem on Algebraic Tori 69 2.2 The Algebraic Torus In their CRYPTO 2003 paper [22], Rubin and Silverberg introduced the notion of ... r 1 r 2 )x 2 . On the Discrete Logarithm Problem on Algebraic Tori 79 After expanding the product of the numerators and denominators, the lef...

Ngày tải lên: 13/05/2014, 22:10

... Convention on Contracts for the International Sale of Goods NOTE BY THE SECRETARIAT 1. The United Nations Convention on Contracts for the International Sale of Goods, 1980 (the Convention, or CISG) ... information on the interpretation of the Convention in a clear, concise and objective manner. 8 This request originated the UNCITRAL Digest of Case Law on the Uni...

Ngày tải lên: 07/03/2014, 08:20

... local regimes. One participant noted that the concept of contribution and distribution depended on the applicable legislation. In some jurisdictions the price of the combination may be set by ... entities belonging to the same group even if they are not included in the consolidation area of the listed entities. In addition, the EFRAG Research Director explained the m...

Ngày tải lên: 16/03/2014, 19:20

... are located in the same positions as in the human CAPERa gene and the introns are found to be smaller in the CAPERb gene. Given the similarities between the evolutionary histories of the U2AF 26 and CAPERb genes, ... unknown whether the dual function of PUF60 on transcription and spli- cing is coupled as in the case of the CAPER proteins or whether PUF60 affects independ...

Ngày tải lên: 23/03/2014, 10:20

... Proposition 3.1.(i) shows that CALDER ´ ON S INVERSE CONDUCTIVITY PROBLEM IN THE PLANE 291 the family {ψ(·,k):k ∈ C,λ∈ ∂D} is equicontinuous. Combination of all these observations shows that the convergence ... shown only for conductivities that are sufficiently smooth. In higher dimensions the problem remains open. Contents 1. Introduction and outline of the method 2. The Belt...

Ngày tải lên: 16/02/2014, 05:20

... Theorem 5. Keep the notation and the assumptions of this theorem. Assume that the parameter w>1 is fixed, as well as the sequences (U n ) n≥1 and (V n ) n≥1 occurring in the definition of Condition ... thanks to the greedy algorithm: we then get the β-expansion of ξ, introduced by R´enyi [32]. Using Theorem 5, we easily see that the conclusions of Theorems 1 to 4 remain true...

Ngày tải lên: 16/02/2014, 06:20

... that ON THE CLASSIFICATION PROBLEM FOR NUCLEAR C ∗ -ALGEBRAS 1043 the moment one relaxes the slow dimension growth condition for AH algebras (and therefore, a fortiori for ASH algebras), one obtains ... the definition of the Cuntz semigroup W (•); in Section 3 we prove Theorem 1.1; in Section 4 we prove Theorem 1.2; Section 5 demonstrates the complexity of the Cuntz semigroup...

Ngày tải lên: 16/02/2014, 06:20

... ∞ which proves the contention. If follows that if K/k is any extension, then the set L of elements α of K algebraic over k is a field L which is algebraic over k. L is called the algebraic closure ... algebraic. Since K/k(S ) is algebraic, it follows that B satisfies the conditions of the theorem. The importance of the theorem is two fold; firstly that every set of16 elemen...

Ngày tải lên: 16/03/2014, 15:20

... order. The main result is concerned to the notion of shadow of a segment. We shall prove some necessary and sufficient conditions for the shadow of a segment to be a segment. 1. Introduction Consider ... the shadow of A contain all the elements x ∈B(n,k-1) which can be obtained by removing an index from the element in A .The conception about the shadow of a set was used efficie...

Ngày tải lên: 22/03/2014, 11:20

... the prime factorization of a. Then the map ν : A →  by sending a to (j 1 , ,j  )is one-to-one. The multiplicative dimension of A is the dimension of the smallest (affine) linear space in  containing ... line-incidences in the plane (see [S-T]). THE ERD ˝ OS-SZEMER ´ EDI PROBLEM 941 On the other hand, Nathanson and Tenenbaum [N-T] concluded some- thing stronger by assuming...

Ngày tải lên: 22/03/2014, 15:21