组合函数

We propose a new resynchronization attack based on the difference performances of combinational functions.

基于组合函数的差分特性，提出了一种新型的再同步攻击方法。

Under the concave transaction costs function, using the variance of profolio return rate to express profolio risk, and taking the risk-return combination difference as the objective function, we propose Mean-variance D.C- integer optimization model under concave transaction costs and minimal transaction unit constraints.

2考虑凹交易费用函数，用投资组合收益率的方差反映组合风险，以风险-收益的组合差作为目标函数，提出了考虑交易费用及最小交易量的均值—方差D.C-整数优化模型。

Properties of efficient portfolios and the efficient frontier to the model are systematically analyzed. Our main results concerning the properties are: every efficient portfolio can be solved by minimizing portfolio risk under a given level of portfolio return or by maximizing portfolio return under a given level of portfolio risk; on the efficient frontier, the risk is a convex and strictly increasing function of the return and the return is a concave and strictly increasing function of the risk; the utility function on the efficient frontier can be expressed as a quasi-concave function of the risk or the return if the investor's utility function is quasi-concave.

从理论上系统地对该模型下的有效投资组合和有效前沿的性质进行了分析，结果表明：每一个有效投资组合可通过在给定期望收益水平的条件下最小化投资组合风险来获得，或者在给定风险水平的条件下最大化期望投资组合收益来获得；在有效前沿上，风险是收益的严格单调递增凸函数，收益是风险的严格单调递增凹函数；当投资者的效用函数是拟凹函数时，则有效前沿上的效用可表达成风险或收益的拟凹函数。

Using finite field theory, number theory, combination mathematics, etc., we investigate deeply linear complexity on stream cipher and its stability theory, cryptographical characteristic of nonlinear combination function.

运用有限域理论、数论、组合数学等方法，对流密码的线性复杂度及其稳定性理论，非线性组合函数的密码学特性等进行了深入的研究和探索。

Counting is the combination of mathematics in one of the main content, and generating function is an important tool for counting, therefore, the mother of mathematical functions in the portfolio has an important position is to solve the problem of combination of powerful tools.

计数是组合数学中主要的内容之一，而母函数是计数的重要工具，因此，母函数在组合数学中有着重要的地位，是解决组合问题的强有力的工具。

Using the concept of Boolean functions and combinatorics theory comprehensively, we investigate the construction on annihilators of Boolean functions and the algebraic immunity of symmetric Boolean functions in cryptography:Firstly, we introduce two methods of constructing the annihilators of Boolean functions, Construction I makes annihilators based on the minor term expression of Boolean function, meanwhile we get a way to judge whether a Boolean function has low degree annihilators by feature matrix. In Construction II, we use the subfunctions to construct annihilators, we also apply Construction II to LILI-128 and Toyocrypt, and the attacking complexity is reduced greatly. We study the algebraic immunitiy of (5,1,3,12) rotation symmetric staturated best functions and a type of constructed functions, then we prove that a new class of functions are invariants of algebraic attacks, and this property is generalized in the end.Secondly, we present a construction on symmetric annihilators of symmetric Boolean functions.

本文主要利用布尔函数的相关概念并结合组合论的相关知识，对密码学中布尔函数的零化子构造问题以及对称布尔函数代数免疫性进行了研究，主要包括以下两方面的内容：首先，给出两种布尔函数零化子的构造方法，构造Ⅰ利用布尔函数的小项表示构造零化子，得到求布尔函数f代数次数≤d的零化子的算法，同时得到通过布尔函数的特征矩阵判断零化子的存在性：构造Ⅱ利用布尔函数退化后的子函数构造零化子，将此构造方法应用于LILI-128，Toyocrypt等流密码体制中，使得攻击的复杂度大大降低；通过研究(5，1，3，12)旋转对称饱和最优函数的代数免疫和一类构造函数的代数免疫，证明了一类函数为代数攻击不变量，并对此性质作了进一步推广。

The method improves performance of KPCA by reasonably combining a local conditionally positive definite kernel and a global kernel. The experiment results indicate the new kernel function certainly improves the performance of KPCA.

利用组合核函数提高核主分量分析的性能，该方法将一个全局核函数与一个新的局部核函数条件正定核函数进行合理组合，从而提高KPCA所提取特征的质量。

In Chapter 2 the foundamental principle of GAs is introduced and the mathematic background of GAs is discussed. Then, a genetic algorithm based on non-Abel group theory and a parallel genetic algorithm based on supercube computer system are proposed.

遗传算法广泛地应用于函数优化和组合函数优化问题，然而如何改善其性能，提高收敛效率，仍然是当今遗传算法研究界的重要课题。

In the paper, the BP Neural Network is introduced to pick up the first break. And aiming at the shortcomings of BP neural network, such as the low speed in training, the tendency to local minimum, the limitation of amplitude, the momentum factor method and the self-adjusting learning rate are used to improve the BP algorithm.

将BP神经网络引入到初至波拾取中，并针对经典BP神经网络收敛速度慢、易于陷入局部极小的缺点，利用组合函数法、限幅法、动量因子法及自适应学习率法等进行了改进。

This paper presents the portfolio selection problem of two-attribute money and creates a model of portfolio selection based on two-attribute money, which can both contain the existing portfolio models and overcome the above-mentioned deficiencies. A series of new concepts is put forward, such as, holding wealth, obtainable wealth, short-term utility function, short-term expectation-variance utility function, state-expectation-variance utility function, short-term expectation-variance utility curve, long-term expectation-variance utility curve, margin utility contribution force, additional contribution force, profit-risk exchange rate and optimal portfolio expansion curve; The state-expectation-variance analytical method is developed from the expectation-variance analytical method; A set of systematic theories concerning two-attribute portfolio selection is thus established.

本文提出了两属性货币的证券组合选择问题；创建了既能包含现有证券组合选择模型又能克服上述两点不足的两属性证券组合选择模型；提出了持有财富、可获财富，短期效用函数，短期期望—方差效用函数、状态—期望—方差效用函数，短期期望—方差效用曲线、长期期望—方差效用曲线，边际效用贡献力，附加贡献力，收益—风险替换率，最优证券组合扩展线等一系列新概念；把期望—方差分析方法发展成状态—期望—方差分析方法；建立了两属性证券组合选择模型的一套系统的理论。

The absorption and distribution of chromium were studied in ryeusing nutrient culture technique and pot experiment.

采用不同浓度K2CrO4(0，0.4，0.8和1.2 mmol/L)的Hoagland营养液处理黑麦幼苗，测定铬在黑麦体内的亚细胞分布、铬化学形态及不同部位的积累。

By analyzing theory foundation of mathematical morphology in the digital image processing, researching morphology arithmetic of the binary Image, discussing two basic forms for the least structure element: dilation and erosion.

通过分析数学形态学在图像中的理论基础，研究二值图像的形态分析算法，探讨最小结构元素的两种基本形态：膨胀和腐蚀；分析了数学形态学复杂算法的基本原理，把数学形态学的部分并行处理理念引入到家实际应用中。