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1.
When solving large complex optimization problems, the user is faced with three major problems. These are (i) the cost in human time in obtaining accurate expressions for the derivatives involved; (ii) the need to store second derivative information; and (iii), of lessening importance, the time taken to solve the problem on the computer. For many problems, a significant part of the latter can be attributed to solving Newton-like equations. In the algorithm described, the equations are solved using a conjugate direction method that only needs the Hessian at the current point when it is multiplied by a trial vector. In this paper, we present a method that finds this product using automatic differentiation while only requiring vector storage. The method takes advantage of any sparsity in the Hessian matrix and computes exact derivatives. It avoids the complexity of symbolic differentiation, the inaccuracy of numerical differentiation, the labor of finding analytic derivatives, and the need for matrix store. When far from a minimum, an accurate solution to the Newton equations is not justified, so an approximate solution is obtained by using a version of Dembo and Steihaug's truncated Newton algorithm (Ref. 1).This paper was presented at the SIAM National Meeting, Boston, Massachusetts, 1986. 相似文献
2.
Sally Dixon 《Tetrahedron》2004,60(6):1401-1416
A wide range of carbenoids (1-lithio-1-halo species), including those with α-SiR3, OEt, SPh, SO2Ph, P(O)(OEt)2, and CN substituents, insert into 5-member zirconacycles (saturated and unsaturated, mono- and bi-cyclic) to afford functionalized 6-member zirconacycles. 1-Lithio-1-haloalkenes insert to afford 6-member zirconacycles with an alkylidene substituent next to the metal. Unexpected double insertion of some carbenoids, and evidence for endocylic β-hydride transfer processes provide additional mechanistic interest. 相似文献
3.
本文对广义风险过程中的渐近方差作了非参数估计,得出并证明了两个定理,为广义风险过程中破产概率的区间估计作了理论准备. 相似文献
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5.
Ammar R Ball RC Banerjee S Bhat PC Bosetti P Bromberg C Canough GE Coffin T Dershem TO Dixon RL Fenker HC Ganguli SN Gensch U Girtler P Goshaw AT Grard F Gurtu A Hamilton C Henri VP Hernandez JJ Hrubec J Iori M Jones LW Kuhn D Knauss D Leedom ID Legros P Lemonne J Leutz H Liu X Malhotra PK Marraffino JM Mendez GE Miller R Naumann T Nguyen A Nowak H Pilette P Poirier J Poppleton A Raghavan R Rasner K Reucroft S Robertson WJ Roe BP Roth A Senko M Struczinski W Subramanian A Touboul MC Vonck B 《Physical review letters》1988,61(19):2185-2188
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B. Brocklehurst R.S. Dixon E.M. Gardy V.J. Lopata M.J. Quinn A. Singh F.P. Sargent 《Chemical physics letters》1974,28(3):361-363
Excited state formation by ion recombination in solutions of fluorene in squalene has been studied by pulse radiolysis at the center of a large electromagnet. The products of the slower part of the ion recombination are affected by an applied magnetic field. The fluorescence yield increases by a factor of about 1.5 whereas the triplet yield decreases. 相似文献
8.
8,8"-Biflavonoidsareantw0rtantclass0fbiflavonoids.Asasystematicresearchofthe8,8"-biflav0noids,wehavepreviouslyreportedthestudyonthereactionof2'-hydroxychaloneswithl2-H2SO4-DMSOsystem.'InthispaPer,thesynthesisof5,5",7,7',-tetTameth0xy-8,8"-biflavonela2,4,4",7,7"-tetramethoxy-8,8"-biflavone1b',4',4",,5,5,',7,7"-hexamethoxy-8,8"-biflav0ne1c4and4,4"-dibenZyl0xy-5,5",7,7"-tetramothoxy-8,8"-biflavoneldisreported.ThesyntheticmethodisshownintheSchemebelow.2-Hydroxyacet0phenonescondensedwithsubsti… 相似文献
9.
Modifications to the distance geometry algorithm as embodied in the program DGEOM have been made to improve sampling capabilities. Specifically, torsion angle sampling replaces distance sampling for 1,4 atomic relationships and correlated distance sampling is disabled. The effects of these modifications are illustrated by comparing the different sets of conformations produced for butane. In addition, these changes are shown to increase the conformational sampling of two medium-sized rings, cycloheptadecane and caprylolactam. The current results for these molecules are compared to those of other conformational searching methods. 相似文献
10.
The Stark splittings and rotational asymmetry splittings of a number of levels of the Ã1A″ excited state of HNO have been measured using the sub-Doppler technique of optical—optical double resonance, μa is found to be 1.08 ± 0.01 D for the 100 vibronic state, and 1.05 ± 0.01 D for the 020 vibronic state. These values are to be compared with a recently determined ground state value of μa = 0.996 D. The asymmetry splittings of some of the levels studied are considerably larger than predicted from the known rotational constants, indicating minor rotational perturbations. 相似文献