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91.
Nicholas I. M. Gould Daniel P. Robinson H. Sue Thorne 《Mathematical Programming Computation》2010,2(1):21-57
The solution of trust-region and regularisation subproblems that arise in unconstrained optimization is considered. Building
on the pioneering work of Gay, Moré and Sorensen, methods that obtain the solution of a sequence of parametrized linear systems
by factorization are used. Enhancements using high-order polynomial approximation and inverse iteration ensure that the resulting
method is both globally and asymptotically at least superlinearly convergent in all cases, including the notorious hard case.
Numerical experiments validate the effectiveness of our approach. The resulting software is available as packages TRS{\tt TRS} and RQS{\tt RQS} as part of the GALAHAD optimization library, and is especially designed for large-scale problems. 相似文献
92.
An assignment of positive integer weights to the edges of a simple graph G is called irregular if the weighted degrees of the vertices are all different. The irregularity strength, s(G), is the maximal edge weight, minimized over all irregular assignments, and is set to infinity if no such assignment is possible. In this paper, we take an iterative approach to calculating the irregularity strength of a graph. In particular, we develop a new algorithm that determines the exact value s(T) for trees T in which every two vertices of degree not equal to two are at distance at least eight. 相似文献
93.
94.
G. Lallement [5] proved that every idem potent congruence class of a regular semigroup contains an idem potent. P. Edwards [4] generalized this property of congruences to eventually regular semigroups. Using the natural partial order of the semigroup (see [6]) a weakened version of this result will be proved for the more general class of E-inversive semigroups. But for particular congruences the original result of Lallement still holds for every E-inversive semigroup. Finally, conditions for a congruence on a general semigroup (with E(S) a subsemigroup, resp.) are given, which ensure that Lallement's result holds. 相似文献
95.
For s≥3 a graph is K1,s-free if it does not contain an induced subgraph isomorphic to K1,s. Cycles in K1,3-free graphs, called claw-free graphs, have been well studied. In this paper we extend results on disjoint cycles in claw-free graphs satisfying certain minimum degree conditions to K1,s-free graphs, normally called generalized claw-free graphs. In particular, we prove that if G is K1,s-free of sufficiently large order n=3k with δ(G)≥n/2+c for some constant c=c(s), then G contains k disjoint triangles. Analogous results with the complete graph K3 replaced by a complete graph Km for m≥3 will be proved. Also, the existence of 2-factors for K1,s-free graphs with minimum degree conditions will be shown. 相似文献
96.
Mark D. Gould Christopher Taylor Stephen K. Wolff Graham S. Chandler Dylan Jayatilaka 《Theoretical chemistry accounts》2008,119(1-3):275-290
Formulae for hermitian operators representing covalent, ionic, and total bond indices are derived. The eigenstates of these
operators come in pairs, and can be considered as bonding, anti-bonding and lone-pair orbitals. The form of these operators
is derived by generalising the rule that the bond order be defined as the net number of bonding electron pairs. The percentage
of covalency and ionicity of a chemical bond may be obtained, and bond indices can also be defined between groups of atoms.
The calculation of the bond indices depends only on the electron density operator, and certain projection operators used to
represent each atom in the molecule. Bond indices are presented for a series of first and second row hydrides and fluorides,
hydrocarbons, a metal complex, a Diels–Alder reaction and a dissociative reaction. In general the agreement between the bond
indices is in accord with chemical intuition. The bond indices are shown to be stable to basis set expansion. 相似文献
97.
Stephanie L. Gould 《Tetrahedron》2008,64(36):8336-8345
We report the design, synthesis, thermal properties, and dynamic NMR characterization of four new molecular dirotors, each containing two rotary 1,4-diethynyl phenylene units, a bridging 1,3-bis(diphenylmethyl) benzene stator, and two capping triphenylmethyl groups. These compounds are variations of the well-known wheel and axle structures. Ambient temperature quadrupolar echo 2H NMR spectra of phenylene-deuterated samples revealed line shapes consistent with dynamic processes having exchange rates >108 s−1, and more than the two minima typically observed for most phenylene rotators. Reasonable line-shape simulations were obtained with a model that involves four minima related by angular displacements of 0°, 30°, 180°, and 230°. Cooling the samples to 260 K revealed spectra consistent with samples that contain two or more components. These results indicate that novel wheel and axle structures do create a certain amount of free volume that allows for the desired mobility of the rotating units. 相似文献
98.
Paul M. Donaldson Rui Guo Frederic Fournier Elizabeth M. Gardner Ian R. Gould David R. Klug 《Chemical physics》2008,350(1-3):201
Methylene is found in the repeat units of many polymers including proteins. In some cases it appears to be a useful reporter of variation in local environment whilst in other contexts average behaviour seems to dominate. In this paper we apply a particular 2DIR technique to a range of systems containing methylene groups, showing that mode frequencies, linewidths and splittings can be easily extracted even when the infrared absorption bands are too congested to allow reliable analysis. 2DIR spectra of polyethylene and several liquid alkanes are compared and it is shown for the case of l-arginine that the methylene scissor modes are split and that this can be resolved by tracking the 2DIR spectrum as a function of time. Calculations from first principles reveal that for most of the methylene modes studied, electrical anharmonicity is the dominant contributor to the 2DIR cross-peak intensity, with the mechanical anharmonicity making only a small contribution. 相似文献
99.
100.
The aim of this paper is to study \(\lambda \)-semidirect and \(\lambda \)-Zappa-Szép products of restriction semigroups. The former concept was introduced for inverse semigroups by Billhardt, and has been extended to some classes of left restriction semigroups. The latter was introduced, again in the inverse case, by Gilbert and Wazzan. We unify these concepts by considering what we name the scaffold of a Zappa-Szép product \(S\bowtie T\) where S and T are restriction. Under certain conditions this scaffold becomes a category. If one action is trivial, or if S is a semilattice and T a monoid, the scaffold may be ordered so that it becomes an inductive category. A standard technique, developed by Lawson and based on the Ehresmann-Schein-Nambooripad result for inverse semigroups, allows us to define a product on our category. We thus obtain restriction semigroups that are \(\lambda \)-semidirect products and \(\lambda \)-Zappa-Szép products, extending the work of Billhardt and of Gilbert and Wazzan. Finally, we explicate the internal structure of \(\lambda \)-semidirect products. 相似文献