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collocation method for elliptic problems N. MaiDuy ∗ and T. TranCong
"... Abstract This paper is concerned with the use of integrated radialbasisfunction networks (IRBFNs) and nonoverlapping domain decompositions (DDs) for numerically solving one and twodimensional elliptic problems. A substructuring technique is adopted, where subproblems are discretized by means ..."
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Abstract This paper is concerned with the use of integrated radialbasisfunction networks (IRBFNs) and nonoverlapping domain decompositions (DDs) for numerically solving one and twodimensional elliptic problems. A substructuring technique is adopted, where subproblems are discretized by means of onedimensional IRBFNs. A distinguishing feature of the present DD technique is that the continuity of the RBF solution across the interfaces is enforced with one order higher than with conventional DD techniques. Several test problems governed by second and fourthorder differential equations are considered to investigate the accuracy of the proposed technique. KEY WORDS: nonoverlapping domain decomposition; radial basis function; collocation technique; highorder differential equations 1
From Coloa to the Trung Sisters ' Revolt: VIETNAM AS THE CHINESE FOUND IT
, 1978
"... HISTORIANS AND archaeologists ignore each other at their peril, but the peril is greater for the historian since concrete evidence which is at odds with a particular theory of historical development will simply not go away and eventually must be taken into consideration. In some areas of inquiry mo ..."
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the middle of the third century B.C. and the revolt of the Trung Sisters in A.D. 40. It is a period which poses a number of highly interesting theoretical problems for the historian and philologist, and recent developments in archaeology have contradicted older bibliocentric and sinocentric notions (the two
Trung tâm đào tạo, bồi dưỡng giảng viên lý luận chính trị
"... đối với việc giáo dục đạo đức cho học sinh ..."
Trung. On minimal logarithmic signatures of finite groups
 Experimental Math
, 2005
"... Logarithmic signatures (LS) are a kind of factorizations of nite groups which are used as a main component of cryptographic keys for secret key cryptosystems such as PGM and public key cryptosystems like MST1. As such, logarithmic signatures of short length are of special interest. In the present p ..."
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Logarithmic signatures (LS) are a kind of factorizations of nite groups which are used as a main component of cryptographic keys for secret key cryptosystems such as PGM and public key cryptosystems like MST1. As such, logarithmic signatures of short length are of special interest. In the present paper we deal with the fundamental question of the existence of logarithmic signatures of shortest length, called minimal logarithmic signatures (MLS), for nite groups. First studies of the problem can be found in [7], [3] and specially in [4], where Gonzalez Vasco, Rotteler and Steinwandt show that minimal logarithmic signatures exist for all groups of order < 175; 560 by direct computation using the method of factorization of a group into \disjoint " subgroups. We introduce new approaches to deal with the question. The rst method uses the double coset decomposition to construct minimal logarithmic signatures. This method allows to prove for instance that if gcd(n; q 1) 2 f1; 4; p j p primeg, then the projective special linear groups Ln(q) have an MLS. Another main goal is to construct MLS for all nite groups of order 1010. Surprisingly, the method of double coset decomposition turns out to be very eective, as we can construct MLS for all groups in the range except a small number of 8 groups. We are also able to prove that if an MLS for any these 8 groups exists, then it cannot be constructed by the method of double coset decomposition. We further discuss a method of construction of MLS for groups of the form G = A:B with subgroups A, B and A \ B 6 = 1, by building suitable MLS for A and B and \glueing " them together. Key words. Logarithmic signatures, group factorizations, double cosets, nite simple groups, cryptosystems. AMS Classication: 20D99, 94A60 1
Trung. On optimal bounds for separating hash families
, 2009
"... This paper concerns optimal bounds and constructions for separating hash families of type {1, w} and {2, 2}. We first prove optimal bounds for separating hash families of type {1, w} and show constructions of families achieving the bounds. As a byproduct of the results we obtain a positive answer t ..."
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This paper concerns optimal bounds and constructions for separating hash families of type {1, w} and {2, 2}. We first prove optimal bounds for separating hash families of type {1, w} and show constructions of families achieving the bounds. As a byproduct of the results we obtain a positive answer to a question put by Blackburn, Etzion, Stinson and Zaverucha recently. Next we study optimal bounds for separating hash families of type {2, 2} having a small number of symbols. We then prove new strong bounds for the general case of type {2, 2}. The paper exhibits a generic construction of separating hash families of type {2, 2} which shows the strength of the new bounds. Key words. Separating hash family, perfect hash family, frameproof code, 2IPP code. 1
Combinatorial Commutative Algebra
, 2004
"... The last decade has seen a number of exciting developments at the intersection of commutative algebra with combinatorics. New methods have evolved out of an influx of ideas from such diverse areas as polyhedral geometry, theoretical physics, representation theory, homological algebra, symplectic geo ..."
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Cited by 125 (5 self)
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The last decade has seen a number of exciting developments at the intersection of commutative algebra with combinatorics. New methods have evolved out of an influx of ideas from such diverse areas as polyhedral geometry, theoretical physics, representation theory, homological algebra, symplectic geometry, graph theory, integer programming, symbolic computation, and statistics. The purpose of this volume is to provide a selfcontained introduction to some of the resulting combinatorial techniques for dealing with polynomial rings, semigroup rings, and determinantal rings. Our exposition mainly concerns combinatorially defined ideals and their quotients, with a focus on numerical invariants and resolutions, especially under gradings more refined than the standard integer grading. This project started at the COCOA summer school in Torino, Italy, in June 1999. The eight lectures on monomial ideals given there by Bernd Sturmfels were later written up by Ezra Miller and David Perkinson and published in [MP01]. We felt it would be nice to add more material and
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