Direct estimate on pointwise simultaneous approximation by combinations of Baskakov operators

2007 ◽  
Vol 44 (1) ◽  
pp. 1-14
Author(s):  
Linsen Xie ◽  
Xiaoping Zhang

In this paper we obtain a direct estimate on the pointwise simultanous approximation by the combinations of Baskakov operators.

Complexity ◽  
2020 ◽  
Vol 2020 ◽  
pp. 1-9 ◽  
Author(s):  
Xiao-jun Tang ◽  
Xin-chang Wang ◽  
Hua Yi

In this paper, the approximation property of the linear combinations of Baskakov operators is investigated by using a Jacobi weight function. Moreover, both the positive and inverse theorems for the weighted simultaneous approximation of the linear combinations of Baskakov operators are proved.


Filomat ◽  
2017 ◽  
Vol 31 (9) ◽  
pp. 2625-2632 ◽  
Author(s):  
Nadeem Rao ◽  
Abdul Wafi

In the present paper, we introduce Stancu-variant of generalized Baskakov operators and study the rate of convergence using modulus of continuity, order of approximation for the derivative of function f . Direct estimate is proved using K-functional and Ditzian-Totik modulus of smoothness. In the last, we have proved Voronovskaya type theorem.


Genetics ◽  
2001 ◽  
Vol 159 (2) ◽  
pp. 441-452
Author(s):  
Dominika M Wloch ◽  
Krzysztof Szafraniec ◽  
Rhona H Borts ◽  
Ryszard Korona

Abstract Estimates of the rate and frequency distribution of deleterious effects were obtained for the first time by direct scoring and characterization of individual mutations. This was achieved by applying tetrad analysis to a large number of yeast clones. The genomic rate of spontaneous mutation deleterious to a basic fitness-related trait, that of growth rate, was U = 1.1 × 10−3 per diploid cell division. Extrapolated to the fruit fly and humans, the per generation rate would be 0.074 and 0.92, respectively. This is likely to be an underestimate because single mutations with selection coefficients s < 0.01 could not be detected. The distribution of s ≥ 0.01 was studied both for spontaneous and induced mutations. The latter were induced by ethyl methanesulfonate (EMS) or resulted from defective mismatch repair. Lethal changes accounted for ~30–40% of the scored mutations. The mean s of nonlethal mutations was fairly high, but most frequently its value was between 0.01 and 0.05. Although the rate and distribution of very small effects could not be determined, the joint share of such mutations in decreasing average fitness was probably no larger than ~1%.


2015 ◽  
Vol 11 ◽  
pp. 2727-2736 ◽  
Author(s):  
Diego M Andrada ◽  
Nicole Holzmann ◽  
Thomas Hamadi ◽  
Gernot Frenking

Fifteen cyclic and acylic carbenes have been calculated with density functional theory at the BP86/def2-TZVPP level. The strength of the internal X→p(π) π-donation of heteroatoms and carbon which are bonded to the C(II) atom is estimated with the help of NBO calculations and with an energy decomposition analysis. The investigated molecules include N-heterocyclic carbenes (NHCs), the cyclic alkyl(amino)carbene (cAAC), mesoionic carbenes and ylide-stabilized carbenes. The bonding analysis suggests that the carbene centre in cAAC and in diamidocarbene have the weakest X→p(π) π-donation while mesoionic carbenes possess the strongest π-donation.


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