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51.
The maximized overlap population, defined as Σμ≠νPμνSμν, and a related quantity, Σμ,νPμνS2μν are computed for a series of configurations. The extremum of both approximate molecular geometries, the latter with an accuracy suitable for predictive value. The maximum overlap orbitals predict dipole and quadrupole moments that give reasonable agreement with experimental values. 相似文献
52.
Shlomo Carmi 《Zeitschrift für Angewandte Mathematik und Physik (ZAMP)》1969,20(4):487-500
Zusammenfassung Die Energiemethode wird zur Untersuchung der Stabilität einer beliebigen Kanalströmung angewandt. Es wird eine auf Eigenwertabschätzungen basierte qualitative Beschreibung der Fläche (, ) gegeben, welche die Schranke für den Instabilitätsbereich in Abhängigkeit von Längs- bzw. Querwellenzahl der Störungen darstellt. Eine allgemeine untere Grenze für die minimalisierende Querwellenzahl und den zugehörigen Eigenwert (0, ) wird angegeben. Das Problem der Energiestabilität wird dann für eine Klasse von Geschwindigkeitsprofilen mit Wendepunkt gelöst. Die durch numerische Integration erhaltenen Ergebnisse werden mit den Ergebnissen der linearen Stabilitätstheorie verglichen. 相似文献
53.
A procedure is presented which allows the application of linear response theory and the random phase approximation to an open shell. The procedure is applied to Ca isotopes. The general features of giant multipole resonances are found to vary smoothly with the mass. The resonances exhibit more structure in the open 1f shell nuclei. While the energy-weighted dipole sum is practically constant in all isotopes, the isoscalar quadrupole and octupole energy weighted sums increase continuously by ~ 30 % from 40Ca to 48Ca. 相似文献
54.
55.
Shlomo S. Razamat 《Letters in Mathematical Physics》2014,104(6):673-690
We define an infinite sequence of superconformal indices, ${{\mathcal{I}}_n}$ , generalizing the Schur index for ${{\mathcal{N}}=2}$ theories. For theories of class ${{\mathcal{S}}}$ we then suggest a recursive technique to completely determine ${{\mathcal{I}}_n}$ . The information encoded in the sequence of indices is equivalent to the ${{\mathcal{N}}=2}$ superconformal index depending on a maximal set of fugacities. Mathematically, the procedure suggested in this note provides a perturbative algorithm for computing a set of eigenfunctions of the elliptic Ruijsenaars–Schneider model. 相似文献
56.
Several features of the trapping of random walks on a one-dimensional lattice are analyzed. The results of this investigation are as follows: (1) The correction term to the known asymptotic form for the survival probability ton steps is O((
2n)–1/3), where =–ln(1–c), andc is the trap concentration. (2) The short time form for the survival probability is found to be exp[–a(c)n
1/2], wherea(c) is given in Eq. (21). (3) The mean-square displacement of a surviving random walker is found to go liken
2/3for largen. (4) When the distribution of trap-free regions is changed so that very large regions are much rarer than for ideally random trap placement the asymptotic survival probability changes its dependence onn. One such model is studied. 相似文献
57.
This work demonstrates the unique features of the never used before Py?BrF(3) complex in the field of aromatic organic fluorinations. The main disadvantage of the noncomplexed BrF(3) is the fact that usually, in addition to the desired fluorination, a parallel electrophilic aromatic bromination takes place as well. Use of the Py?BrF(3) complex reduces this electrophilic bromination, which is observed with most reagents based on fluorine and bromine [BrF]. 相似文献
58.
59.
Summary. In this paper we again consider the rate of convergence of the conjugate gradient method. We start with a general analysis
of the conjugate gradient method for uniformly bounded solutions vectors and matrices whose eigenvalues are uniformly bounded
and positive. We show that in such cases a fixed finite number of iterations of the method gives some fixed amount of improvement
as the the size of the matrix tends to infinity. Then we specialize to the finite element (or finite difference) scheme for
the problem . We show that for some classes of function we see this same effect. For other functions we show that the gain made by performing a fixed number of iterations of the
method tends to zero as the size of the matrix tends to infinity.
Received July 9, 1998 / Published online March 16, 2000 相似文献
60.