小麦发育后期茎秆抗倒性的数学模型探析

围绕小麦发育后期茎秆抗倒性的数学模型建立的问题,首先,运用回归分析方法,得到了基于统计的倒伏指数的估计.然后,运用相关分析方法,并引入斐波那契数列及Euclidean距离,分析了小麦抗倒伏性与其茎秆形态参数之间的关系,得到了理想的小麦株型结构.最后,运用平衡理论、挠曲线近似方程、最小势能原理及弯矩平衡原理,考虑小麦自重和风载的共同作用,从平衡理论与弹性理论的角度建立了小麦茎秆抗倒伏性的精确模型.利用该模型结合估计的倒伏指数,对临界倒伏风速进行计算,结果验证了模型的有效性.     

典型群的增广商群

设G 为有限域K 上的一般线性群(特殊线性群、酉群、辛群及正交群), 记整群环ZG 的n 次增广理想为△ⁿ(G). 本文着重研究有限域上的典型群的增广商群Q_n(G) = △ⁿ(G)/△ⁿ⁺¹(G), 并刻画了这些连续商群的结构.     

Essentially normal Hilbert modules and K-homology IV: Quasi-homogenous quotient modules of Hardy module on the polydisks

In this paper,we give a complete characterization for the essential normality of quasi-homogenous quotient modules of the Hardy modules H2 (D2).Also,we show that if d 3,then all the principle homogenous quotient modules of H 2 (Dd) are not essentially normal.     

A derivative-free three-term projection algorithm involving spectral quotient for solving nonlinear monotone equations

ABSTRACT

In this paper, we develop a three-term conjugate gradient method involving spectral quotient, which always satisfies the famous Dai-Liao conjugacy condition and quasi-Newton secant equation, independently of any line search. This new three-term conjugate gradient method can be regarded as a variant of the memoryless Broyden-Fletcher-Goldfarb-Shanno quasi-Newton method with regard to spectral quotient. By combining this method with the projection technique proposed by Solodov and Svaiter in 1998, we establish a derivative-free three-term projection algorithm for dealing with large-scale nonlinear monotone system of equations. We prove the global convergence of the algorithm and obtain the R-linear convergence rate under some mild conditions. Numerical results show that our projection algorithm is effective and robust, and is more competitive with the TTDFP algorithm proposed Liu and Li [A three-term derivative-free projection method for nonlinear monotone system of equations. Calcolo. 2016;53:427–450].     

How happy is your web browsing? A model to quantify satisfaction of an Internet user searching for desired information

We feel happy when web browsing operations provide us with necessary information; otherwise, we feel bitter. How to measure this happiness (or bitterness)? How does the profile of happiness grow and decay during the course of web browsing? We propose a probabilistic framework that models the evolution of user satisfaction, on top of his/her continuous frustration at not finding the required information. It is found that the cumulative satisfaction profile of a web-searching individual can be modeled effectively as the sum of a random number of random terms, where each term is a mutually independent random variable, originating from ‘memoryless’ Poisson flow. Evolution of satisfaction over the entire time interval of a user’s browsing was modeled using auto-correlation analysis. A utilitarian marker, a magnitude of greater than unity of which describes happy web-searching operations, and an empirical limit that connects user’s satisfaction with his frustration level—are proposed too. The presence of pertinent information in the very first page of a website and magnitude of the decay parameter of user satisfaction (frustration, irritation etc.) are found to be two key aspects that dominate the web user’s psychology. The proposed model employed different combinations of decay parameter, searching time and number of helpful websites. The obtained results are found to match the results from three real-life case studies.     

Enumerations of peaks and valleys on non-decreasing Dyck paths

A valley in a Dyck path is a local minimum, and a peak is a local maximum. A Dyck path is non-decreasing if the $y$-coordinates of the valleys of the path valley form anon-decreasing sequence. In this paper we provide some statistics about peaks and valleys in non-decreasing Dyck paths, such as their total number, the number of low and high valleys, low and high peaks, etc. Our methods include bijective proofs, recursive relations, and the symbolic method for generating functions.     

Efimov spaces and the separable quotient problem for spaces Cp(K)

The classic Rosenthal–Lacey theorem asserts that the Banach space $C(K)$ of continuous real-valued maps on an infinite compact space K has a quotient isomorphic to c or ${?}_2$. More recently, Ka?kol and Saxon [20] proved that the space $C_p(K)$ endowed with the pointwise topology has an infinite-dimensional separable quotient algebra iff K has an infinite countable closed subset. Hence $C_p(\beta \mathbb{N})$ lacks infinite-dimensional separable quotient algebras. This motivates the following question: (?) Does$C_p(K)$admit an infinite-dimensional separable quotient (shortly SQ) for any infinite compact space K? Particularly, does $C_p(\beta \mathbb{N})$ admit SQ? Our main theorem implies that $C_p(K)$ has SQ for any compact space K containing a copy of $\beta \mathbb{N}$. Consequently, this result reduces problem (?) to the case when K is an Efimov space (i.e. K is an infinite compact space that contains neither a non-trivial convergent sequence nor a copy of $\beta \mathbb{N}$). Although, it is unknown if Efimov spaces exist in ZFC, we show, making use of some result of R. de la Vega (2008) (under ?), that for some Efimov space K the space $C_p(K)$ has SQ. Some applications of the main result are provided.