The Experts below are selected from a list of 270 Experts worldwide ranked by ideXlab platform
Abul Kashem - One of the best experts on this subject based on the ideXlab platform.
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Algorithms for solving the Symmetry Number problem on trees
Information Processing Letters, 2004Co-Authors: Pradipta Mitra, Muhammad Arshad Ul Abedin, Abul KashemAbstract:The Symmetry Number of a tree is defined as the Number of nodes of the maximum subtree of the tree that exhibits axial Symmetry. Chin and Yen have presented an algorithm for solving the problem of finding the Symmetry Number of unrooted unordered trees in time O(n4). In this paper we present an improved algorithm for solving the Symmetry Number problem on trees that runs in time O(n3). We also show that our algorithm needs O(n2 log n) time for trees with bounded degrees.
Yijie Han - One of the best experts on this subject based on the ideXlab platform.
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Improved algorithm for the Symmetry Number problem on trees
Information Processing Letters, 2006Co-Authors: Yijie HanAbstract:The Symmetry Number of a tree is defined as the Number of nodes of the maximum subtree of the tree that exhibits axial Symmetry. The best previous algorithm for computing the Symmetry Number for an unrooted unordered tree is due to [P.P. Mitra, M.A.U. Abedin, M.A. Kashem, Algorithms for solving the Symmetry Number problem on trees, Inform. Process. Lett. 91 (2004) 163-169] and runs in O(n^3) time. In this paper we show an improvement on this time complexity by encoding small trees. Our algorithm runs in time O(n^3(loglogn/logn)^2).
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Computers and Their Applications - Improved Algorithm for the Symmetry Number Problem on Trees.
2006Co-Authors: Yijie HanAbstract:The Symmetry Number of a tree is defined as the Number of nodes of the maximum subtree of the tree that exhibits axial Symmetry. The best previous algorithm for computing the Symmetry Number for an unrooted unordered tree is due to [P.P. Mitra, M.A.U. Abedin, M.A. Kashem, Algorithms for solving the Symmetry Number problem on trees, Inform. Process. Lett. 91 (2004) 163-169] and runs in O(n^3) time. In this paper we show an improvement on this time complexity by encoding small trees. Our algorithm runs in time O(n^3(loglogn/logn)^2).
Michael A. Collins - One of the best experts on this subject based on the ideXlab platform.
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Rigorous derivation of reaction path degeneracy in transition state theory
Chemical Physics Letters, 1992Co-Authors: Andrew J. Karas, Robert G. Gilbert, Michael A. CollinsAbstract:Abstract Using the complete nuclear permutation and inversion group formalism, a rigorous derivation is given of the formula for incorporating reaction path degeneracy into transition state theory as the factor m†σ/mσ†, where m is the Number of optical isomers and σ the Symmetry Number, and the dagger refers to the transition state.
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Rigorous derivation of reaction path degeneracy in transition state theory
Chemical Physics Letters, 1992Co-Authors: Andrew J. Karas, Robert G. Gilbert, Michael A. CollinsAbstract:Using the complete nuclear permutation and inversion group formalism, a rigorous derivation is given of the formula for incorporating reaction path degeneracy into transition state theory as the factor m(dagger)sigma/m-sigma(dagger), where m is the Number of optical isomers and sigma the Symmetry Number, and the dagger refers to the transition state
Hsu-chun Yen - One of the best experts on this subject based on the ideXlab platform.
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The Symmetry Number problem for trees
Information Processing Letters, 2001Co-Authors: Kien-weh Chin, Hsu-chun YenAbstract:For trees, we define the notion of the so-called Symmetry Number to measure the size of the maximum subtree that exhibits an axial Symmetry in graph drawing. For unrooted unordered trees, we are able to demonstrate a polynomial time algorithm for computing the Symmetry Number.
Donald G. Truhlar - One of the best experts on this subject based on the ideXlab platform.
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explanation of the unusual temperature dependence of the atmospherically important oh h2s h2o hs reaction and prediction of the rate constant at combustion temperatures
Journal of the American Chemical Society, 2007Co-Authors: Benjamin A. Ellingson, Donald G. TruhlarAbstract:Rate constants for the OH + H2S → H2O + HS reaction, which is important for both atmospheric chemistry and combustion, are calculated by direct dynamics with the M06-2X density functional using the MG3S basis set. Energetics are compared to high-level MCG3/3//MC-QCISD/3 wave function theory and to results obtained by other density functionals. We employ canonical variational transition-state theory with multidimensional tunneling contributions and scaled generalized normal-mode frequencies evaluated in redundant curvilinear coordinates with anharmonicity included in the torsion. The transition state has a quantum mechanically distinguishable, nonsuperimposable mirror image that corresponds to a separate classical reaction path; the effect of the multiple paths is examined through use of a Symmetry Number and by torsional methods. Calculations with the reference-potential Pitzer−Gwinn treatment of the torsional mode agree with experiment, within experimental scatter, and predict a striking temperature depe...
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Symmetry Numbers and chemical reaction rates
Theoretical Chemistry Accounts, 2007Co-Authors: Antonio Fernández-ramos, Benjamin A. Ellingson, Rubén Meana-pañeda, Jorge M. C. Marques, Donald G. TruhlarAbstract:This article shows how to evaluate rotational Symmetry Numbers for different molecular configurations and how to apply them to transition state theory. In general, the Symmetry Number is given by the ratio of the reactant and transition state rotational Symmetry Numbers. However, special care is advised in the evaluation of Symmetry Numbers in the following situations: (i) if the reaction is symmetric, (ii) if reactants and/or transition states are chiral, (iii) if the reaction has multiple conformers for reactants and/or transition states and, (iv) if there is an internal rotation of part of the molecular system. All these four situations are treated systematically and analyzed in detail in the present article. We also include a large Number of examples to clarify some complicated situations, and in the last section we discuss an example involving an achiral diasteroisomer.
