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On Small Complete Sets of Functions
"... Abstract. Using Local Residues and the Duality Principle a multidimensional variation of the completeness theorems by T. Carleman and A. F. Leontiev is proven for the space of holomorphic functions defined on a suitable open strip Tα ⊂ C2. The completeness theorem is a direct consequence of the Cauc ..."
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Abstract. Using Local Residues and the Duality Principle a multidimensional variation of the completeness theorems by T. Carleman and A. F. Leontiev is proven for the space of holomorphic functions defined on a suitable open strip Tα ⊂ C2. The completeness theorem is a direct consequence
On Pimmunity of nondeterministic complete sets
 In Proceedings of the 10th Annual Conference on Structure in Complexity Theory '95
, 1995
"... We show that every mcomplete set for NEXP as well as ats complement have an infinite subset in P. Thw nnswers an open question first raised in [Ber76]. 1 ..."
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Cited by 6 (0 self)
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We show that every mcomplete set for NEXP as well as ats complement have an infinite subset in P. Thw nnswers an open question first raised in [Ber76]. 1
An Extended Set of Fortran Basic Linear Algebra Subprograms
 ACM TRANSACTIONS ON MATHEMATICAL SOFTWARE
, 1986
"... This paper describes an extension to the set of Basic Linear Algebra Subprograms. The extensions are targeted at matrixvector operations which should provide for efficient and portable implementations of algorithms for high performance computers. ..."
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Cited by 526 (72 self)
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This paper describes an extension to the set of Basic Linear Algebra Subprograms. The extensions are targeted at matrixvector operations which should provide for efficient and portable implementations of algorithms for high performance computers.
Complete set of CHC tetrahedrons
, 2014
"... In this article, using K. W. Roeder’s Theorem, some properties of CHC (compact hyperbolic coxeter) tetrahedrons have been developed which are facilitated by the link of graph theory and combinatorics, and it has been found that there are exactly 3 CHC tetrahedrons upto symmetry. ..."
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Cited by 1 (1 self)
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In this article, using K. W. Roeder’s Theorem, some properties of CHC (compact hyperbolic coxeter) tetrahedrons have been developed which are facilitated by the link of graph theory and combinatorics, and it has been found that there are exactly 3 CHC tetrahedrons upto symmetry.
The Complete Atomic Structure of the Large Ribosomal Subunit at 2.4 Å Resolution
 Science
, 2000
"... ation, and termination phases of protein synthesis. Because the structures of several DNA and RNA polymerases have been determined at atomic resolution, the mechanisms of DNA and RNA synthesis are both well understood. Determination of the structure of the ribosome, however, has proven a daunting t ..."
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Cited by 529 (13 self)
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ation, and termination phases of protein synthesis. Because the structures of several DNA and RNA polymerases have been determined at atomic resolution, the mechanisms of DNA and RNA synthesis are both well understood. Determination of the structure of the ribosome, however, has proven a daunting task. It is several times larger than the largest polymerase, and 100 times larger than lysozyme, the first enzyme to be understood at atomic resolution. Until now an atomic resolution structure for the ribosome has not been available, and as a result the mechanism of protein synthesis has remained a mystery. Electron microscopy has contributed to our understanding of ribosome structure ever since the ribosome was discovered. In the last few years, threedimensional (3D) electron microscopic images of the ribosome have been produced at resolutions sufficiently high to visualize many of the proteins and nucleic acids that assist in protein synthesis bound to the ribosome (3). Earlier this yea
A Threshold of ln n for Approximating Set Cover
 JOURNAL OF THE ACM
, 1998
"... Given a collection F of subsets of S = f1; : : : ; ng, set cover is the problem of selecting as few as possible subsets from F such that their union covers S, and max kcover is the problem of selecting k subsets from F such that their union has maximum cardinality. Both these problems are NPhar ..."
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Cited by 778 (5 self)
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Given a collection F of subsets of S = f1; : : : ; ng, set cover is the problem of selecting as few as possible subsets from F such that their union covers S, and max kcover is the problem of selecting k subsets from F such that their union has maximum cardinality. Both these problems are NP
Complete Sets of Invariants for Dynamical
 J. Math. Phys
"... Consider a classical Hamiltonian H in n dimensions consisting of a kinetic energy term plus a potential. If the associated HamiltonJacobi equation admits an orthogonal separation of variables, then it is possible to generate algorithmically a canonical basis Q;P where P 1 = H , P 2 ; ; P n ar ..."
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Consider a classical Hamiltonian H in n dimensions consisting of a kinetic energy term plus a potential. If the associated HamiltonJacobi equation admits an orthogonal separation of variables, then it is possible to generate algorithmically a canonical basis Q;P where P 1 = H , P 2 ; ; P n are the other 2ndorder constants of the motion associated with the separable coordinates, and fQ i ; Q j g = fP i ; P j g = 0, fQ i ; P j g = ij . The 2n 1 functions Q 2 ; ; Q n ; P 1 ; ; P n form a basis for the invariants. We show how to determine for exactly which spaces and potentials the invariant Q j is a polynomial in the original momenta. We shed light on the general question of exactly when the Hamiltonian admits a constant of the motion that is polynomial in the momenta. For n = 2 we go further and consider all cases where the HamiltonJacobi equation admits a 2ndorder constant of the motion, not necessarily associated with orthogonal separable coordinates, or even separable coordinates at all. In each of these cases we construct an additional constant of the motion.
Strong Reductions and Isomorphism of Complete Sets
"... We study the structure of the polynomialtime complete sets for NP and PSPACE under strong nondeterministic polynomialtime reductions (SNPreductions). We show the following results. • If NP contains a prandom language, then all polynomialtime complete sets for PSPACE are SNPisomorphic. • If NP ..."
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We study the structure of the polynomialtime complete sets for NP and PSPACE under strong nondeterministic polynomialtime reductions (SNPreductions). We show the following results. • If NP contains a prandom language, then all polynomialtime complete sets for PSPACE are SNPisomorphic. • If NP
The KEGG resource for deciphering the genome
 Nucleic Acids Res
, 2004
"... A grand challenge in the postgenomic era is a complete computer representation of the cell and the organism, which will enable computational prediction of higherlevel complexity of cellular processes and organism behavior from genomic information. Toward this end we have been developing a knowledg ..."
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Cited by 504 (24 self)
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knowledgebased approach for network prediction, which is to predict, given a complete set of genes in the genome, the protein interaction networks that are responsible for various cellular processes. KEGG at
UCPOP: A Sound, Complete, Partial Order Planner for ADL
, 1992
"... We describe the ucpop partial order planning algorithm which handles a subset of Pednault's ADL action representation. In particular, ucpop operates with actions that have conditional effects, universally quantified preconditions and effects, and with universally quantified goals. We prove ucpo ..."
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Cited by 491 (24 self)
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ucpop is both sound and complete for this representation and describe a practical implementation that succeeds on all of Pednault's and McDermott's examples, including the infamous "Yale Stacking Problem" [McDermott 1991].
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