Matrix models of RNA folding with external interactions: A review

The matrix model of (simplified) RNA folding with an external linear interaction in the action of the partition function is reviewed. The important results for structure combinatorics of the model are discussed and analysed in terms of the already existing models.     

A note on improved estimations for integrated Szász-Mirakyan operators

In the present paper, we propose a modification of the integrated Szász-Mirakyan operators having the weight function of general Beta basis function. We study some direct results on the modified operators. It is also observed that our modified operators have better estimates over the original operators.     

Szász-Mirakian-Baskakov型算子的同时逼近

研究了Baskakov和Szász-Mirakian型算子的线性组合的同时逼近问题,得到了Voronovskaja型的渐进展开公式以及误差估计.     

A Note on Equivalent Theorem for Beta Operators

In this paper, we give an equivalent theorem concerning on the whole interval [0, +∞). Both the direct and converse theorems are derived. These results bridge the gap between the point-wise conclusions and global conclusions.     

Szász-Mirakian-Baskakov型算子的同时逼近

研究了Baskakov和Szász-Mirakian型算子的线性组合的同时逼近问题，得到了Voronovskaja型的渐进展开公式以及误差估计．     

Simultaneous Approximation for Szsz-Mirakian-Stancu-Durrmeyer Operators

The aim of this work is to generalize Szsz-Mirakian operator in the sense of Stancu-Durrmeyer operators. We obtain approximation properties of these operators. Here we study asymptotic as well as rate of convergence results in simultaneous approximation for these modified operators.     

A short note on sign changes

In this paper, we present a quantitative result for the number of sign changes for the sequences $\{a(n^j)\}_{n\ge 1}, j=2,3,4$ of the Fourier coefficients of normalized Hecke eigencusp forms for the full modular group SL ₂(?). We also prove a similar kind of quantitative result for the number of sign changes of the q-exponents $c(p)~(p \mbox{~vary ~over ~primes})$ of certain generalized modular functions for the congruence subgroup Γ₀(N), where N is square-free.     

Some approximation results for Durrmeyer operators

In the present paper, we obtain a sequence of positive linear operators which has a better rate of convergence than the Szász-Mirakian Durrmeyer and Baskakov Durrmeyer operators and their Voronovskaya type results.