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APPROXIMATION ALGORITHMS FOR SCHEDULING UNRELATED PARALLEL MACHINES
, 1990
"... We consider the following scheduling problem. There are m parallel machines and n independent.jobs. Each job is to be assigned to one of the machines. The processing of.job j on machine i requires time Pip The objective is to lind a schedule that minimizes the makespan. Our main result is a polynomi ..."
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Cited by 265 (7 self)
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We consider the following scheduling problem. There are m parallel machines and n independent.jobs. Each job is to be assigned to one of the machines. The processing of.job j on machine i requires time Pip The objective is to lind a schedule that minimizes the makespan. Our main result is a
A A COROLLARY to Dr. Caputto’s presenta
"... tion, I would like to discuss briefly the crucial points of some work carried out in the Section on Experimental Liver Diseases with the aim to identify the active site of tocopherol in enzyme systems. This work has been in progress since 1952 in conjunction with our systematic attempts to elucidat ..."
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somes is evident from electron microscope 3 Respiratory decline is indicative of a specific function of tocopherol in the maintenance of normal energy metabolism. The inipairment is prevented by feeding vitamin E; it disappears within ten minutes after injection of physiologic amounts of a
The honeycomb model of GLn(C) tensor products I: proof of the saturation conjecture
 J. AMER. MATH. SOC
, 1999
"... Recently Klyachko [Kl] has given linear inequalities on triples (λ, µ, ν) of dominant weights of GLn(C) necessary for the the corresponding LittlewoodRichardson coefficient dim(Vλ⊗Vµ⊗Vν) GLn(C) to be positive. We show that these conditions are also sufficient, which was known as the saturation con ..."
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Cited by 200 (5 self)
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conjecture. In particular this proves Horn’s conjecture from 1962, giving a recursive system of inequalities [H]. Our principal tool is a new model of the BerensteinZelevinsky cone for computing LittlewoodRichardson coefficients [BZ, Ze], the honeycomb model. The saturation conjecture is a corollary of our
Quantum invariants of Seifert 3–manifolds and their asymptotic expansions
 in Invariants of knots and 3–manifolds (Kyoto 2001 ), Geometry and Topology Monographs 4 (2002), 69–87
"... We derive explicit formulas for the Reshetikhin–Turaev invariants of all oriented Seifert manifolds associated to an arbitrary complex finite dimensional simple Lie algebra g in terms of the Seifert invariants and standard data for g. A main corollary is a determination of the full asymptotic expans ..."
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Cited by 28 (3 self)
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We derive explicit formulas for the Reshetikhin–Turaev invariants of all oriented Seifert manifolds associated to an arbitrary complex finite dimensional simple Lie algebra g in terms of the Seifert invariants and standard data for g. A main corollary is a determination of the full asymptotic
On the variety of special linear systems on a general algebraic curve
 Duke Mathematical Journal
, 1980
"... (a) Statement of the problem and of the main theorem; some references 233 (b) Corollaries of the main theorem 236 ..."
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Cited by 50 (1 self)
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(a) Statement of the problem and of the main theorem; some references 233 (b) Corollaries of the main theorem 236
Asymptotic Expansions for Martingales
 Annals of Probability
, 1993
"... Summary. The paper develops a way of embedding general martingales in continuous ones in such a way that the quadratic variation of the continuous martingale has conditional cumulants (given the original martingale) that are explicitly given in terms of optional and predictable variations of the ori ..."
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Cited by 22 (9 self)
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of the original process. Bartlett identities for the conditional cumulants are also found. A main corollary to these results is the establishment of second (and in some cases higher) order asymptotic expansions for martingales.
The second main theorem for small functions and related problems
 Acta Math
"... Abstract. We shall establish the following three results in more general forms. (1) The second main theorem for small functions. Let f be a meromorphic function on the complex plane C. Let a1,..., aq be distinct meromorphic functions on C. Assume that ai are small with respect to f; i.e., T (r, a) & ..."
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Cited by 13 (1 self)
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Abstract. We shall establish the following three results in more general forms. (1) The second main theorem for small functions. Let f be a meromorphic function on the complex plane C. Let a1,..., aq be distinct meromorphic functions on C. Assume that ai are small with respect to f; i.e., T (r, a
On the Hardness of Approximating the Chromatic Number
, 1993
"... We study the hardness of approximating the chromatic number when the input graph is kcolorable for some fixed k 3. Our main result is that it is NPhard to find a 4coloring of a 3chromatic graph. As an immediate corollary we obtain that it is NPhard to color a kchromatic graph with at most ..."
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Cited by 78 (6 self)
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We study the hardness of approximating the chromatic number when the input graph is kcolorable for some fixed k 3. Our main result is that it is NPhard to find a 4coloring of a 3chromatic graph. As an immediate corollary we obtain that it is NPhard to color a kchromatic graph with at most
The Kervaire invariant of framed manifolds as the obstruction to embeddability
, 2008
"... We construct a quadratic form which gives an obstruction to embedding N 4k+2 ⊂ R 6k+4 with sufficiently many nondegenerate sections of the normal bundle. As the main corollary we prove that 14connected (resp. 30connected) stablyparallelisable 30dimensional (resp. 62dimensional) manifold N 30 ( ..."
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We construct a quadratic form which gives an obstruction to embedding N 4k+2 ⊂ R 6k+4 with sufficiently many nondegenerate sections of the normal bundle. As the main corollary we prove that 14connected (resp. 30connected) stablyparallelisable 30dimensional (resp. 62dimensional) manifold N 30
The ArfKervaire invariant of framed manifolds as an obstruction to embeddability
, 2009
"... We define a quadratic form which gives an obstruction to embedding N 4k+2 ⊂ R 6k+4 of a smooth highly connected manifold into Euclidean space, with sufficiently many nondegenerate sections of the normal bundle. As the main corollary we prove that no 14connected (resp. 30connected) stably paralleli ..."
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We define a quadratic form which gives an obstruction to embedding N 4k+2 ⊂ R 6k+4 of a smooth highly connected manifold into Euclidean space, with sufficiently many nondegenerate sections of the normal bundle. As the main corollary we prove that no 14connected (resp. 30connected) stably
Results 1  10
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