基于三角白化权函数的高校家庭经济困难学生动态认定研究

从对现行认定方法的对比分析出发,提出了建立以身份判定、定量评级、定性评估为一体的资格认定体系;考虑到学生家庭经济信息灰性,构建了基于三角白化权函数的灰色聚类模型;并着眼资格认定的动态性和资助育人目标,构建了三级综合动态定性评估体系,以期能为我国高校家庭经济困难学生资格认定研究和工作实践提供参考.     

Pointwise convergence of wavelets of generalized Shannon type

In this paper, a new result on pointwise convergence of wavelets of generalized Shannon type is proved, which improves a theorem established by Zayed.     

On the dispersion of data in non-symmetric distributions

In this paper a more accurate index of asymmetry is studied. Specifically, the use of the left and right variance is proposed and an index of asymmetry based on them is introduced. Several examples demonstrate its usefulness.     

The Hamilton‐Waterloo problem for Hamilton cycles and triangle‐factors

In this article, we consider the Hamilton‐Waterloo problem for the case of Hamilton cycles and triangle‐factors when the order of the complete graph K_n is even. We completely solved the problem for the case n≡24 (mod 36). For the cases n≡0 (mod 18) and n≡6 (mod 36), we gave an almost complete solution. © 2012 Wiley Periodicals, Inc. J. Combin. Designs 20: 305–316, 2012     

A triangular spectral method for the Stokes eigenvalue problem by the stream function formulation

An efficient spectral method is developed in this paper for the two‐dimensional Stokes eigenvalues on arbitrary triangle. By using the spectral theory of compact operator and approximate property of orthogonal polynomial, we give the error estimate of the approximate eigenvalues and eigenfunctions. In addition, we also present some numerical results to show the validity of our algorithm and the correctness of the theoretical results.     

Spirals in Hilbert space: With an application in information theory

A (logarithmic) spiral of order is defined as a continuous path tx(t) in a real Hilbert space such that

For α=0 the spiral becomes a helix. The elegant proof by P. Masani of the spectral characterization of helices, due to Kolmogorov and to von Neumann and Schoenberg, is adapted here to spirals. As an application a conjecture by F. Topsøe that certain kernels on considered in information theory are negative definite, and hence are squares of metrics on , is confirmed.     

黄酮类化合物^13C核磁共振谱的模式识别分类研究

黄酮类化合物广泛存在于植物的各个部位,根据其结构,主要分为黄酮、黄酮醇、双氢黄酮、异黄酮等。对于大多数植物化学工作者来说,解析一个未知化合物都必须经历先确定骨架类型,后确定基团位置这一过程。而前者则需要对该类型的数据规律有充分的认识,否则,就可能导致错误结果。     

关于一类修正的三角插值多项式

本文构造出一个以｛θ_ｋ＝ｋ/(ｎ＋１)π｝^ｎ_ｋ＝１为插值节点的ｆ（θ）∈Ｃ_２π且为奇函数的修正的三角插值多项式Ｗ_n（ｆ;ｒ,θ）（ｒ为自然数）．Ｗ_n（ｆ;ｒ,θ）对每个以２π为周期的奇连续函数都能在全实轴上一致地收敛到ｆ（θ）;若ｆ（θ）∈Ｃ^ｊ_２π（０≤ｊ≤ｒ－１）且是奇的,Ｗ_n（ｆ;ｒ,θ）对其收敛阶均达到最     

First Digits’ Shannon Entropy

Related to the letters of an alphabet, entropy means the average number of binary digits required for the transmission of one character. Checking tables of statistical data, one finds that, in the first position of the numbers, the digits 1 to 9 occur with different frequencies. Correspondingly, from these probabilities, a value for the Shannon entropy H can be determined as well. Although in many cases, the Newcomb–Benford Law applies, distributions have been found where the 1 in the first position occurs up to more than 40 times as frequently as the 9. In this case, the probability of the occurrence of a particular first digit can be derived from a power function with a negative exponent p > 1. While the entropy of the first digits following an NB distribution amounts to H = 2.88, for other data distributions (diameters of craters on Venus or the weight of fragments of crushed minerals), entropy values of 2.76 and 2.04 bits per digit have been found.     

Signal Fluctuations and the Information Transmission Rates in Binary Communication Channels

In the nervous system, information is conveyed by sequence of action potentials, called spikes-trains. As MacKay and McCulloch suggested, spike-trains can be represented as bits sequences coming from Information Sources (IS). Previously, we studied relations between spikes’ Information Transmission Rates (ITR) and their correlations, and frequencies. Now, I concentrate on the problem of how spikes fluctuations affect ITR. The IS are typically modeled as stationary stochastic processes, which I consider here as two-state Markov processes. As a spike-trains’ fluctuation measure, I assume the standard deviation σ, which measures the average fluctuation of spikes around the average spike frequency. I found that the character of ITR and signal fluctuations relation strongly depends on the parameter s being a sum of transitions probabilities from a no spike state to spike state. The estimate of the Information Transmission Rate was found by expressions depending on the values of signal fluctuations and parameter s. It turned out that for smaller s<1, the quotient ITRσ has a maximum and can tend to zero depending on transition probabilities, while for 1<s, the ITRσ is separated from 0. Additionally, it was also shown that ITR quotient by variance behaves in a completely different way. Similar behavior was observed when classical Shannon entropy terms in the Markov entropy formula are replaced by their approximation with polynomials. My results suggest that in a noisier environment (1<s), to get appropriate reliability and efficiency of transmission, IS with higher tendency of transition from the no spike to spike state should be applied. Such selection of appropriate parameters plays an important role in designing learning mechanisms to obtain networks with higher performance.