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41.
Theorem 3 gives a condition when two -weights can be ``pasted' together to yield another -weight. It is subsequently used in Example 6 to give an example that shows that a necessary condition by Gohberg, Krupnik, and Spitkovsky is not sufficient.
42.
In this paper we study a particular class of primal-dual path-following methods which try to follow a trajectory of interior feasible solutions in primal-dual space toward an optimal solution to the primal and dual problem. The methods investigated are so-called first-order methods: each iteration consists of a long step along the tangent of the trajectory, followed by explicit recentering steps to get close to the trajectory again. It is shown that the complexity of these methods, which can be measured by the number of points close to the trajectory which have to be computed in order to achieve a desired gain in accuracy, is bounded by an integral along the trajectory. The integrand is a suitably weighted measure of the second derivative of the trajectory with respect to a distinguished path parameter, so the integral may be loosely called a curvature integral. 相似文献
43.
44.
J. E. Prez J. C. Cesco O. E. Taurian F. S. Ortiz A. E. Rosso C. C. Denner G. O. Giubergia 《International journal of quantum chemistry》2004,99(2):70-79
This article presents a variation of the integral transform method to evaluate multicenter bielectronic integrals (12|34), with 1s Slater‐type orbitals. It is proved that it is possible to define, out of the expression of (12|34) given by the integral transform method, a function F(q) that has the property of having a unique Q, such that F(Q) = (12|34). Therefore, F(q) may be used to calculate (12|34). It is shown that the evaluation of F(Q) turns out to be simpler than the three‐dimensional integral involved in the calculation of (12|34), and an algorithm is presented to calculate Q. The results show that relative errors on the order of 10?3 or lower are obtained very efficiently. In addition, it is shown that the proposed algorithm is very stable. © 2004 Wiley Periodicals, Inc. Int J Quantum Chem, 2004 相似文献
45.
We present formulas for the evaluation of molecular integrals over basis functions with an explicit Gaussian dependence on
interelectronic coordinates. These formulas use expansions in Hermite Gaussian functions and represent an extension to the
work of McMurchie and Davidson to two-electron basis functions. Integrals that depend on the coordinates of up to four electrons
are discussed explicitly. A key feature of this approach is that it allows full exploitation of the shell structure of the
orbital part of the basis.
Received: 24 February 1997 / Accepted: 4 March 1997 相似文献
46.
《Arabian Journal of Chemistry》2022,15(9):103970
Ethnopharmacological relevanceMetabolic syndrome is closely related to the intestinal microbiota and disturbances in the host metabolome. Hyperuricemia (HUA), a manifestation of metabolic syndrome, can induce various cardiovascular diseases and gout, seriously affecting a patient’s quality of life. Astragalus membranaceus has a long history as a commonly used traditional Chinese medicine to treat kidney disease in China and East Asia.Materials and methodsWe compared the therapeutic effect of benzbromarone and two different doses Astragalus membranaceus ultrafine powder (AMUP) in rats with HUA. Ultra-performance liquid chromatography-mass spectrometer was used to analyze the AMUP metabolism in the plasma, urine, and feces. Further, 16S ribosome RNA sequencing and feces metabolomic were performed to capture the variation of the gut microbiota and metabolites changes before and after drug administration.ResultsAMUP had a notable impact on reducing blood uric acid levels while protecting the liver and kidney. Drug metabolism analysis demonstrated that effective constituent flavonoids are distributed in the blood, whereas saponins remain in the intestine. Gut microbiota analysis showed that low-dose AMUP ameliorated HUA-induced gut dysbiosis by reducing the abundance of harmful bacteria and increasing that of some beneficial bacteria with anti-inflammatory properties, such as Clostridia, Lachnospiraceae, and Muribaculaceae. In addition, HUA-induced changes in metabolite contents in bile acid and adrenal hormone biosynthesis pathways were restored after treatment with AMUP.ConclusionLow-dose AMUP exerts remarkable therapeutic effects on HUA by regulating the gut microbiome and mediating gut metabolism pathways associated with uric acid excretion. 相似文献
47.
48.
D. Zorrilla Cuenca J. Sánchez Márquez M. Fernández Núñez R. Rodríguez Huertas 《International journal of quantum chemistry》2007,107(4):879-893
This project consists of two parts. In the first part, a series of test calculations is performed to verify that the integrals involved in the determination of atomic and molecular properties by standard self‐consistent field (SCF) methods can be obtained through Halton, Korobov, or Hammersley quasi‐random integration procedures. Through these calculations, we confirm that all three methods lead to results that meet the levels of precision required for their use in the calculation of properties of small atoms or molecules at least at a Hartree–Fock level. Moreover, we have ensured that the efficiency of quasi‐random integration methods that we have tested is Halton=Korobov>Hammersley?pseudo‐random. We also find that these results are comparable to those yielded by ordinary Monte Carlo (pseudo‐random) integration, with a calculation effort of two orders of smaller magnitude. The second part, which would not have been possible without the integration method previously analyzed, contains a first study of atoms constrained in spherical boxes through SCF calculations with basis functions adapted to the features of the problem: Slater‐type orbitals (STOs) trimmed by multiplying them by a function that yields 1 for 0 < r < (R‐δ), polynomial values for (R‐δ) < r < R and null for r > R, R being the radius of the box and δ a variationally determined interval. As a result, we obtain a equation of state for electrons of small systems, valid just in the limit of low temperatures, but fairly simple. © 2006 Wiley Periodicals, Inc. Int J Quantum Chem, 2007 相似文献
49.
By the use of complete orthonormal sets of -exponential-type orbitals, where ( = 1, 0, –1, –2,...) the multicenter electronic attraction (EA), electric field (EF) and electric field gradient (EFG) integrals of nonscreened and Yukawa-like screened Coulomb potentials are expressed through the two-center overlap integrals with the same screening constants and the auxiliary functions
introduced in our previous paper (I.I. Guseinov, J. Phys. B, 3 (1970) 1399). The recurrence relations for auxiliary functions are useful for the calculation of multicenter EA, EF and EFG integrals for arbitrary integer and noninteger values of principal quantum numbers, screening constants, and location of slater-type orbitals. The convergence of the series is tested by calculating concrete cases. 相似文献
50.
The auxiliary functions $Q_{nn'}^{q}(p,pt)$ and $G_{-nn'}^{q}(p_{a},p,pt)$ which are used in our previous paper [Guseinov, I. I.; Mamedov, B. A. Int J Quantum Chem 2001, 81, 117] for the computation of multicenter electron‐repulsion integrals over Slater‐type orbitals (STOs) are discussed in detail, and the method is given for their numerical computation. The present method is suitable for all values of the parameters pa, p, and pt. Three‐ and four‐center electron‐repulsion integrals are calculated for extremely large quantum numbers using relations for auxiliary functions obtained in this paper. © 2001 John Wiley & Sons, Inc. Int J Quantum Chem, 2001 相似文献