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991.
《Discrete Mathematics》2023,346(1):113206
Two closed-form solutions of a general second order linear recurrence with variable coefficients are established. The first form is combinatorial in nature and is derived through the use of a set which counts the number of elements which are two units apart. The second form is closely related to continued fractions and is derived through the use of continued fraction-like relation. Several applications including a number of verifications of conjectures produced from the Ramanujan Machine are worked out, which illustrate its versatility in this respect. 相似文献
992.
993.
Mutsuo Igarashi 《Molecular Crystals and Liquid Crystals》2013,570(2):437-440
Abstract Spin-spin relaxation of 23Na-NMR is observed by the spin echo method at room temperature for Y-type zeolite loaded with Na metal without hydration. For saturated and no levels of loading, the echo decay is well fitted by single exponential function. T 2 decreases to be 0.25 times smaller by loading. This decrease of T 2 is explained semiquantitatively with assuming nuclear dipole-dipole interaction between neighboring Na. 相似文献
994.
考虑一类"中度偏离"单位根过程,y_t=q_ny_t-1+u_t,其中qn=1+c/(k_n),k_n=o(n),c为一非零常数,{u_t}为随机扰动项序列.在允许扰动项方差无穷的条件下,构造q_n的复合分位数估计,并得到了该估计的渐近分布.最后通过数值模拟,在扰动项服从t(2)分布下,说明了该估计的稳健和有效性. 相似文献
995.
Primal, dual and saddle-point characterizations of optimality are given for convex programming in the general case (nondifferentiable functions and no constraint qualification). 相似文献
996.
Juan I. Rodríguez 《Journal of computational chemistry》2013,34(8):681-686
An efficient method for computing the quantum theory of atoms in molecules (QTAIM) topology of the electron density (or other scalar field) is presented. A modified Newton–Raphson algorithm was implemented for finding the critical points (CP) of the electron density. Bond paths were constructed with the second‐order Runge–Kutta method. Vectorization of the present algorithm makes it to scale linearly with the system size. The parallel efficiency decreases with the number of processors (from 70% to 50%) with an average of 54%. The accuracy and performance of the method are demonstrated by computing the QTAIM topology of the electron density of a series of representative molecules. Our results show that our algorithm might allow to apply QTAIM analysis to large systems (carbon nanotubes, polymers, fullerenes) considered unreachable until now. © 2012 Wiley Periodicals, Inc. 相似文献
997.
The geometrical anisotropy in the shape of swallow-tailed ST liquid crystalline molecules results in an extremely strong tendency of an antiparallel order in the short range. Dielectric measurements on a binary system of a ST and a double ST compound show that even at a mole fraction of 0.5 this effect can be observed. The strong deviations from the statistical distribution of the directions of the molecular long axis is caused by the asymmetric repulsive forces and the dipole-dipole interaction. 相似文献
998.
Martina Hofmanová 《随机分析与应用》2013,31(4):663-670
In the first part of this article a new method of proving existence of weak solutions to stochastic differential equations with continuous coefficients having at most linear growth was developed. In this second part, we show that the same method may be used even if the linear growth hypothesis is replaced with a suitable Lyapunov condition. 相似文献
999.
A. G. Shannon† 《International Journal of Mathematical Education in Science & Technology》2013,44(4):497-507
The semantic differential—one approach to attitude measurement— basically records a combination of a person's associations with a particular concept with a scaling procedure. This paper considers the implications of such a device for teachers of mathematics. 相似文献
1000.
Andrew Fiore 《Numerical Functional Analysis & Optimization》2013,34(6):679-690
Our goal is to demonstrate the utility of the calculus of moving surfaces (CMS) in boundary variation problems. We discuss the relative advantages of the CMS compared to the alternative approach of interior variations. We illustrate the technique by calculating the two leading terms of a power series for the Laplace eigenvalues on an ellipse with semi-axes 1 + a and 1 + b, where a and b are small. We compare the CMS estimates with those obtained by the conventional finite element method with Richardson extrapolation. The comparison confirms the cubic rate of convergence for the CMS estimates. 相似文献