计算的复杂性理论

I want to learn some complexity theory,mathematics theory such as Computational number theory,Algorithmic Algebra,Algebraic function fields over finite fields and the group thoery.

在这半年里，我将系统地加深学习一些必要的数学知识，比如计算复杂性理论，计算性数论算法，群论，算法的代数学等等。

Computability theory differs from the related discipline of computational complexity theory, which deals with the question of how efficiently a problem can be solved, rather than whether it is solvable at all.

可计算性理论的不同之处相关学科的计算复杂性理论，其中涉及的问题是，如何有效的问题可以得到解决，而不是它是否解决了。

Q. Aren't computability theory and computational complexity the keys to AI?

可计算性理论和计算复杂性理论是不是AI的关键？

In recognition of his fundamental contributions to the theory of computation, including the complexity-based theory of pseudorandom number generation, cryptography, and communication complexity.

授 予姚期智图灵奖以表彰其在计算理论领域的基础性的卓越贡献，其中包括产生伪随机数的复杂性理论，密码系统和通讯复杂性等。

Turing Award Citation): In recognition of his fundamental contributions to the theory of computation, including the complexity-based theory of pseudorandom number generation, cryptography, and communication complexity.

(授予姚期智图灵奖以表彰其在)计算理论领域的基础性的卓越贡献，其中包括产生伪随机数的复杂性理论，密码系统和通讯复杂性等。

The Luneburg lens antenna is composed of a series of concentric shells of constant permittivity. Considering the complexity of numerical calculation, this paper presents a closed-form approach, which combines the spherical vector wave method and the reciprocity theorem.

摘要伦伯透镜是一种球形分层介质天线，考虑到数值计算的复杂性，本文提出用矢量球面波理论和互易原理相结合，分析其性能。

On this basis, according to historical data, apply ANN and differential simulation method to get the quantitatively correlative relations between each production and its own influence factors, and introduce the new methods of prediction for dynamic indexes with gas-field development (The combinatorial prediction method based on fuzzy comprehensive evaluation, the method of ANN to select optimally combinatorial prediction models and the ANN prediction method based on genetic algorithm).(2) Base on mathematical programming, combine with quantitative economics and techno-economics, introduce economical indexes to establish production"s distribution optimal model, production"s constitution optimal model and measured production"s constitution optimal model, including multi-objective models and five-years models. Upon this, the optimal project for all gas field and each gas-collected factory can be got. Also, introduce the time value of capitals to improve on these models.(3) Base on the optimal solution theory and algorithm theory for the nonlinear programming problem, introduce the SUMT algorithm and genetic algorithm to study how to solve the models, and on the basis of normal genetic algorithm, make use of auto-adaptively modulating method to improve on normal genetic algorithm; Base on algorithm"s convergence theory and calculation"s complexity theory to analyze seriatim SUMT algorithm"s convergence and genetic algorithms convergence, and compare performance with each other.

在此基础上，利用神经网络方法和微分模拟方法根据历史数据得到各分项产量与其影响因素之间的定量关联关系，并引入气田开发动态指标新的预测方法(基于模糊综合评判的组合预测方法、神经网络优选组合预测模型预测方法以及基于遗传优化的神经网络预测方法)；(2)以数学规划为基础，结合数量经济学和技术经济学，引入经济指标建立产量分配优化模型、产量构成优化模型、措施产量构成优化模型、气田开发多目标规划模型以及五年规划模型，进而获得全气田及各采气厂的最优方案，并引入资金时间价值对五年规划模型进行改进；(3)以非线性规划问题的最优解及算法理论为基础，引入SUMT算法以及遗传算法对模型的求解进行研究，并在原有的遗传算法基础上，引入自适应调整方法对遗传算法进行改进；以算法的收敛性理论和计算复杂性理论为基础，逐一分析SUMT算法以及遗传算法的收敛性，并比较三种算法的优劣性。

On the basis of chaos theory, phase space reconstruction and embedding theory, time series of dissolved oxygen of the Lianshui River are analyzed and attractors dimension and Lyapunov exponent are calculated as well.

基于混沌理论、相空间重构思想和嵌入理论分析涟水流域溶解氧的时间序列，计算吸引子维数和最大的Lyapunov指数，研究河流水质系统的复杂性特征。

According to parameterized complexity theory, a decidable parameterized problem is fixed-parameter tractable if and only if it can be kernelized.

在参数计算与复杂性理论中，一个参数问题是固定参数可解的问题当且仅当该问题是可核心化的。

This is generally defined as being identical in the length to the width of the footing in the direction normal to the analytical plane. However, there is little knowledge about whether the results obtained from the historic method analysis are overestimated or underestimated, comparing with those obtained from the applicable values. So in this paper a new methodology considering the soil-pile dynamic interaction for sea warf has been imposed.

在总结理论的基础上，指出土-结构动力相互作用目前的发展水平与工程实用之间仍存在相当大的差距，理论与实际之间也还有距离，这是由于土-结构动力相互作用问题本身的复杂性，不同的计算方法都引进了一些假设和进行了不同程度的简化，以致不同方法给出的结构和地基反应存在有很大的差别，加之计算工作量大，试验验证也比较困难，所以在实际的抗震设计中考虑桩-土共同作用是有很大的研究意义的。

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。