On the discrete logarithm problem on algebraic tori

... pre-cisely the algebraic torus Tn(Fq). On the Discrete Logarithm Problem on Algebraic Tori 692.2 The Algebraic TorusIn their CRYPTO 2003 paper [22], Rubin and Silverberg introduced the notionof ... r1r2)x2. On the Discrete Logarithm Problem on Algebraic Tori 79After expanding the product of the numerators and denominators, the left handside becomes the fairly general expressionb0+ ... q.Classically, one would ﬁrst reduce the problem to considering only monicpolynomials, i.e., one considers the quotient F×qm/F×q, and deﬁnes a factor baseF = {t + a : a ∈ Fq}. On the Discrete Logarithm...

UNCITRAL Digest of Case Law on the United Nations Convention on Contracts for the International Sale of Goods pptx

... Convention on Contracts for the International Sale of Goods NOTE BY THE SECRETARIAT1. 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 United Nations Convention on the ... to consult the full texts of the listed court and arbitral decisions rather than relying solely on the CLOUT abstracts.OVERVIEW OF THE CONVENTION1. The United Nations Convention on Contracts...

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FEEDBACK REPORT ON THE EUROPEAN OUTREACH EVENT ON EFRAG PROACTIVE DISCUSSION PAPERS pptx

... 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 methodology the working ... agreed with the analysis carried out in the discussion paper on the potential need to bifurcate transactions and splitting out the elements that are actually distributions/contributions. They believed...

Báo cáo khoa học: Diversity of human U2AF splicing factors Based on the EMBO Lecture delivered on 7 July 2005 at the 30th FEBS Congress in Budapest pptx

... arelocated in the same positions as in the humanCAPERa gene and the introns are found to be smallerin the CAPERb gene. Given the similarities between the evolutionary histories of the U2AF26and CAPERbgenes, ... unknown whether the dual function of PUF60 on transcription and spli-cing is coupled as in the case of the CAPER proteinsor whether PUF60 affects independently the transcrip-tion and splicing ... region. Making allowance only for GT_AG,GC_AG or AT_AC splice site consensus and excludingisoforms with extensive intron retentions, the non-redundant set of longest isoforms and correspondingaccessions...

Tài liệu Đề tài " Calder´on’s inverse conductivity problem in the plane " doc

... Proposition 3.1.(i) shows thatCALDER´ ON S INVERSE CONDUCTIVITY PROBLEM IN THE PLANE291 the family {ψ(·,k):k ∈ C,λ∈ ∂D} is equicontinuous. Combination of allthese observations shows that the convergence ... shown only for conductivities that aresuﬃciently smooth. In higher dimensions the problem remains open.Contents1. Introduction and outline of the method2. The Beltrami equation and the Hilbert ... this is consistent with (1.9).One way to identify ∂kF+is by readily observing that the unique solutionto (5.20) also has other realizations. Namely, if one subtracts the equation(5.9)...

Tài liệu Đề tài " On the complexity of algebraic numbers I. Expansions in integer bases " ppt

... Theorem 5. Keep the notation and the assumptions of this theorem. Assume that the parameter w>1 is fixed,as well as the sequences (Un)n≥1and (Vn)n≥1occurring in the definition ofCondition ... thanks to the greedy algorithm: we then get the β-expansion of ξ, introduced by Rényi[32]. Using Theorem 5, we easily see that the conclusions of Theorems 1 to 4remain true with the expansion in ... p−rn−wsn. We then follow the same lines as in the proof of Theo-rem 5, and we end up in a contradiction. This proves that αis transcendental. ON THE COMPLEXITY OF ALGEBRAIC NUMBERS I5637. Concluding...

Tài liệu Đề tài " On the classification problem for nuclear C -algebras " pdf

... 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; inSection 4 we prove Theorem 1.2; Section 5 demonstrates the complexity of the Cuntz semigroup, and discusses the ... classes of the algebras themselves. The consequences for the program to classify nuclear C∗-algebras are far-reaching: one has, among otherthings, that existing results on the classiﬁcation of...

Lectures On The Algebraic Theory Of Fields ppt

... ∞which proves the contention.If follows that if K/k is any extension, then the set L of elements αof 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 of16elements algebraically independent ... of K on K′. This provesTheorem 11. Two purely transcendental extensions of the same dimen-sion n over k k-isomorphic.This theorem is true even if the dimension is infinite.Chapter 2Algebraic...

Báo cáo " Some problem on the shadow of segments infinite boolean rings " doc

... order. The main result is concerned to the notion of shadowof a segment. We shall prove some necessary and sufficient conditions for the shadow of asegment to be a segment.1. IntroductionConsider ... the shadow of A contain all the elementsx ∈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 efficiently by many mathematicians ... that the segment [d;b] satisfysconditions of corollary 2.2, we now imitate the above proof to finish the corollary. Certaintly, the lastcorollary is a solution for our key questions, in the...

Đề tài "The Erd˝os-Szemer´edi problem on sum set and product set" ppt

... the primefactorization of a. Then the map ν : A →by sending a to (j1, ,j)isone-to-one. The multiplicative dimension of A is the dimension of the smallest(affine) linear space incontaining ... line-incidencesin the plane (see [S-T]). THE ERD˝OS-SZEMERÉDI PROBLEM 941 On the other hand, Nathanson and Tenenbaum [N-T] concluded some-thing stronger by assuming the sum set is small. They showedTheorem ... ERD˝OS-SZEMERÉDI PROBLEM 943 The paper is organized as follows:In Section 1, we prove Theorem 1 and introduce the concept of multi-plicative dimension. In Section 2, we show the lower bound of Theorem...

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