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91.
We investigate bounds for point energies, separation radius, and mesh norm of certain arrangements of N points on sets A from a class of d-dimensional compact sets embedded in Rd′, 1dd′. We assume that these points interact through a Riesz potential V=|·|-s, where s>0 and |·| is the Euclidean distance in . With and denoting, respectively, the separation radius and mesh norm of s-extremal configurations, which are defined to yield minimal discrete Riesz s-energy, we show, in particular, the following.(A) For the d-dimensional unit sphere and s<d-1, and, moreover, if sd-2. The latter result is sharp in the case s=d-2. In addition, point energies for s-extremal configurations are asymptotically equal. This observation relates to numerical experiments on observed scar defects in certain biological systems.(B) For and s>d, and the mesh ratio is uniformly bounded for a wide subclass of . We also conclude that point energies for s-extremal configurations have the same order, as N→∞. 相似文献
92.
本文以抛物弓形为边界的周期环域的三次系统的Poincaré分支为例,说明具有相同边界的周期环域的相同次数的多项式系统的Poincaré分支,由于周期环域内闭轨的不同,它们所对应的Abel积分也不同,所以它们的Poincaré分支所能分支出极限环的个数也是不同的. 相似文献
93.
94.
M. Reimer 《Constructive Approximation》2002,18(2):183-204
Hyperinterpolation on the sphere, as introduced by Sloan in 1995, is a constructive approximation method which is favorable
in comparison with interpolation, but still lacking in pointwise convergence in the uniform norm. For this reason we combine
the idea of hyperinterpolation and of summation in a concept of generalized hyperinterpolation. This is no longer projectory,
but convergent if a matrix method A is used which satisfies some assumptions. Especially we study A partial sums which are defined by some singular integral used by Newman and Shapiro in 1964 to derive a Jackson-type inequality
on the sphere. We could prove in 1999 that this inequality is realized even by the corresponding discrete operators, which
are generalized hyperinterpolation operators. In view of this result the Newman—Shapiro operators themselves gain new attention.
Actually, in their case, A furnishes second-order approximation, which is best possible for positive operators. As an application we discuss a method
for tomography, which reconstructs smooth and nonsmooth components at their adequate rate of convergence. However, it is an
open question how second-order results can be obtained in the discrete case, this means in generalized hyperinterpolation
itself, if results of this kind are possible at all.
March 9, 2000. Date revised: October 2, 2000. Date accepted: March 8, 2001. 相似文献
95.
设 n维 Euclid空间 En(n≥ 2 )中单形 Ω(A)的顶点集为 A={ A0 ,A1,… ,An} .,Ω(A)内任一点 P至侧面 { A0 ,A1,… ,An} \{ Ai}的距离为 di(i=0 ,1,… ,n) ,Ω(A)的外接超球半径和内切超球半径分别为 R、r,记C( n,α) =(2 (n+ 1 2 ) + (n+ 1) 2α- (n+ 1) α) / 4 (n+ 12 ) ) α(α≥ 1) ,本文建立了涉及Ω (A)内一点的不等式∑0≤ i相似文献
96.
Jia Meng Haonan Qin Dr. Haitao Lei Dr. Xialiang Li Juan Fan Prof. Dr. Wei Zhang Prof. Dr. Ulf-Peter Apfel Prof. Dr. Rui Cao 《Angewandte Chemie (International ed. in English)》2023,62(51):e202312255
In nature, cytochrome c oxidases catalyze the 4e− oxygen reduction reaction (ORR) at the heme/Cu site, in which CuI is used to assist O2 activation. Because of the thermodynamic barrier to generate CuI, synthetic Fe-porphyrin/Cu complexes usually show moderate electrocatalytic ORR activity. We herein report on a Co-corrole/Co complex 1-Co for energy-efficient electrocatalytic ORR. By hanging a CoII ion over Co corrole, 1-Co realizes electrocatalytic 4e− ORR with a half-wave potential of 0.89 V versus RHE, which is outstanding among corrole-based electrocatalysts. Notably, 1-Co outperforms Co corrole hanged with CuII or ZnII. We revealed that the hanging CoII ion can provide an electron to improve O2 binding thermodynamically and dynamically, a function represented by the biological CuI ion of the heme/Cu site. This work is significant to present a remarkable ORR electrocatalyst and to show the vital role of a second-sphere redox-active metal ion in promoting O2 binding and activation. 相似文献
97.
Let q1 be an integer, denote the unit sphere embedded in the Euclidean space , and μq be its Lebesgue surface measure. We establish upper and lower bounds forwhere is the unit ball of a suitable Besov space on the sphere. The upper bounds are obtained for choices of xk and wk that admit exact quadrature for spherical polynomials of a given degree, and satisfy a certain continuity condition; the lower bounds are obtained for the infimum of the above quantity over all choices of xk and wk. Since the upper and lower bounds agree with respect to order, the complexity of quadrature in Besov spaces on the sphere is thereby established. 相似文献
98.
George A. Anastassiou 《Applicable analysis》2013,92(12):1837-1854
Here we adopt, develop further and use the principle of duality in time scales Caputo, [Time scales: from nabla calculus to delta calculus and vice versa via duality, arxiv: 0910.0085v1 [math.OC] 1 Oct. 2009]. Using this principle and based on a variety of important delta inequalities we produce the corresponding nabla ones. We give several applications. 相似文献
99.
Jaume Llibre 《Journal of Difference Equations and Applications》2013,19(3-4):417-422
Let M be a n -dimensional manifold with the same homology than the n -dimensional sphere. A C 1 map f : M M M is called transversal if for all m ] N the graph of f m intersects transversally the diagonal of M 2 M at each point ( x , x ) such that x is a fixed point of f m . We study the minimal set of periods of f by using the Lefschetz numbers for periodic points. In the particular case that n is even, we also study the set of periods for the transversal holomorphic self-maps of M . 相似文献
100.
Reza Rashidi Meybodi Ardeshir Karami Mohammadi Firooz Bakhtiari-Nejad 《Communications in Nonlinear Science & Numerical Simulation》2012,17(1):454-471
This paper presents the effect of rotor mass on the nonlinear dynamic behavior of a rigid rotor-bearing system excited by mass unbalance. Aerodynamic four-lobe journal bearing is used to support a rigid rotor. A finite element method is employed to solve the Reynolds equation in static and dynamical states and the dynamical equations are solved using Runge-Kutta method. To analyze the behavior of the rotor center in the horizontal and vertical directions under different operating conditions, the dynamic trajectory, the power spectra, the Poincare maps and the bifurcation diagrams are used. From this study, results show how the complex dynamic behavior of this type of system comprising periodic, KT-periodic and quasi-periodic responses of the rotor center varies with changes in rotor mass values by considering two bearing aspect ratios. Results of this study contribute a better understanding of the nonlinear dynamics of an aerodynamic four-lobe journal bearing system. 相似文献