On Solvability of Some Chemotaxis Equations

Ｒｅｃｅｎｔｌｙ ,ｔｈｅｒｅｓｅａｒｃｈｅｓｏｎｃｈｅｍｏｔａｘｉｓｅｑｕａｔｉｏｎｓｈａｖｅｂｅｅｎｉｎｔｅｒｅｓｔｅｄｂｙａｌｏｔｏｆｐｅｏｐｌｅ(ｓｅｅ [1— 8]) .Ｉｎｆａｃｔ,ｗｅｃａｎｕｓｅｔｈｅｃｈｅｍｏｔａｘｉｓｅｑｕａｔｉｏｎｓｔｏｄｅｓｃｒｉｂｅｔｈｅｐｒｏｃｅｓｓｅｓｏｆａｇ ｇｒｅｇａｔｉｏｎａｎｄｄｉｓｐｅｒｓａｌｏｆｃｅｌｌｓｏｒｏｔｈｅｒｏｒｇａｎｉｓｍｓｉｎｍａｎｙｂｉｏｌｏｇｉｃａｌｓｙｓｔｅｍｓ .Ａｓｉｔｉｓｗｅｌｌｋｎｏｗｎ ,ｔｈｅｓｏｌｖａｂｉｌｉｔｙｉｓｖｅｒ…     

Some Properties of Fuzzy Filter and Its Category

Ｉｎｏｒｄｅｒｔｏｓｔｕｄｙｍａｎｙｖａｌｕｅｄｌｏｇｉｃｓｙｓｔｅｍａｎｄｅｖｅｎｔｈｅｌｏｇｉｃｓｙｓｔｅｍｂａｓｅｄｏｎｌａｔｔｉｃｅ，ａｎａｌｇｅｂｒａｉｃｓｔｒｕｃｔｕｒｅ－ｌａｔｔｉｃｅｉｍｐｌｉｃａｔｉｏｎａｌｇｅｂｒａｗａｓｉｎｔｒｏｄｕｃｅｄｉｎｒｅｆｅｒｅｎｃｅ［１］．Ｔｈｅｓｔｕｄｙｏｆｌａｔｔｉｃｅｉｍｐｌｉｃａｔｉｏｎａｌｇｅｂｒａａｓａｌｇｅｂｒａｉｃｓｙｓｔｅｍｉｓｏｆｉｎｄｅｐｅｎｄｅｎｔｉｎｔｅｒｅｓｔ．Ｉｎｒｅｆｅｒｅｎｃｅ［２，３］ｓｏｍｅｐｒｏｐｅｒｔｉｅ…     

Two Dimensional Submanifolds in Four Manifolds with Boundary

§０．　ＩｎｔｒｏｄｕｃｔｉｏｎＦｏｒａｃｌｏｓｅｄ４－ｍａｎｉｆｏｌｄ,ｉｔｉｓｗｅｌｌｋｎｏｗｎｔｈａｔａｎｙｔｗｏｄｉｍｅｎｓｉｏｎａｌｈｏｍｏｌｏｇｙｃｌａｓｓｃａｎｂｅｒｅｐｒｅｓｅｎｔｅｄｂｙａｎｅｍｂｅｄｄｅｄｓｕｒｆａｃｅ．Ａｆｕｎｄａｍｅｎｔａｌｐｒｏｂｌｅｍｉｎ４－ｄｉｍｅｎｓｉｏｎａｌｔｏｐｏｌｏｇｙｉｓｔｏｆｉｎｄａｓｕｒｆａｃｅｗｉｔｈｍｉｎｉｍａｌｇｅｎｕｓｗｈｉｃｈｒｅｐｒｅｓｅｎｔｓｔｈｅｇｉｖｅｎｈｏｍｏｌｏｇｙｃｌａｓｓ．Ａｓｐｅｃｉａｌｃａｓｅｏｆｔｈｉｓｑ…     

THE VARIATION OF INVARIANT LINES AND LIMIT CYCLES FOR A QUADRATIC DIFFERENTIAL SYSTEM

１ＩｎｔｒｏｄｕｃｔｉｏｎＣｏｎｓｉｄｅｒｔｈｅｒｅａｌｑｕａｄｒａｔｉｃｄｉｆｅｒｅｎｔｉａｌｓｙｓｔｅｍｘ＝－ｙ＋δｘ－４ｘ２＋３ｘｙ＋１３ｙ２ｙ＝ｘ（１－１３ｘ－ｙ）．（１）Ｆｉｒｓｔ，ｆｏｒｃｏｎｖｅｎｉｅｎｃｅ，ｗｅｄｅｎｏｔｅｔｈｅｔｗｏ...     

The Algebraic Criteria for the All-delay Stabilityof Two-dim ensional Degenerate Differential System swith Delay

§１．　ＩｎｔｒｏｄｕｃｔｉｏｎＡｓｔｈｅｄｅｅｐｌｙｄｅｖｅｌｏｐｍｅｎｔｏｆｔｈｅｓｔｕｄｙａｎｄａｐｐｌｉｃａｔｉｏｎｆｏｒｍａｎｙｐｒａｃｔｉｃａｌｓｙｓｔｅｍｓ，ｓｕｃｈａｓｅｃｏｎｏｍｉｃｍａｎａｇｅｍｅｎｔｓｙｓｔｅｍｓ，ｅｎｇｉｎｅｅｒｉｎｇｓｙｓｔｅｍｓ，ｐｏｗｅｒｓｙｓｔｅｍｓａｎｄｓｏｏｎ，ｐｅｏｐｌｅｄｅｖｏｔｅｍｕｃｈａｎｄｍｕｃｈａｔｔｅｎｔｉｏｎｔｏｔｈｅｐｈｅｎｏｍｅｎａｏｆｄｅｌａｙｓ［１］［２］．Ａｔｔｈｅｓａｍｅｔｉｍｅ，ｐｅｏｐｌｅｆｏｕｎｄｔｈａｔｔｈｅ…     

On the Method of Multiplier-enlargement and Approximation of Unbounded Continuous Functions

Ａｓｉｓｋｎｏｗｎ ,ｉｔｉｓｖｅｒｙｉｍｐｏｒｔａｎｔｔｏａｐｐｒｏｘｉｍａｔｅｕｎｂｏｕｎｄｅｄｃｏｎｔｉｎｕｏｕｓｆｕｎｃｔｉｏｎｓ,ｅｓｐｅｃｉａｌｌｙｔｈｏｓｅｄｅｆｉｎｅｄｏｎａｌａｒｇｅｒａｎｇｅ .Ａｎｅｆｆｅｃｔｉｖｅｍｅｔｈｏｄｃａｌｌｅｄｔｈｅｍｅｔｈｏｄｏｆｍｕｌｔｉｐｌｉｅｒ ｅｎｌａｒｇｅｍｅｎｔｈａｓｂｅｅｎｐｕｔｆｏｒｗａｒｄｂｙＬ .Ｃ .ＨｓｕａｎｄＲ .Ｈ .Ｗａｎｇ[1— 3].Ｔｈｉｓｍｅｔｈｏｄｗａｓｇｒｅａｔｌｙｄｅｖｅｌｏｐｅｄｉｎ [4,5] .Ｉｎｔｈｉｓｐａｐｅｒ,ｗｅ…     

On Maximal Distance Separable Codes

ＯｎＭａｘｉｍａｌＤｉｓｔａｎｃｅＳｅｐａｒａｂｌｅＣｏｄｅｓ￥（万哲先，谢邦杰）ＷａｎＺｈｅｉｘａｎ（ＩｎｓｔｉｔｕｔｅｏｆＳｙｓｔｅｍｓＳｃｉｅｎｃｅ，ＣｈｉｎｅｓｅＡｃａｄｅｍｙｏｆＳｃｉｅｎｃｅ，Ｂｅｉｊｉｎｇ，１０００８０，Ｃｈｉｎａ）ａｎ...     

On Rational Bases of Subspaces of F((D))~n

ＯｎＲａｔｉｏｎａｌＢａｓｅｓｏｆＳｕｂｓｐａｃｅｓｏｆＦ（（Ｄ））~ｎＷａｎＺｈｅｘｉａｎ（万哲先）（ＩｎｓｔｉｔｕｔｅｏｆＳｙｓｔｅｍｓＳｃｉｅｎｃｅ，ＣｈｉｎｅｓｅＡｃａｄｅｍｙｏｆＳｃｉｅｎｃｅｓ，Ｂｅｉｊｉｎｇ，１０００８０ａｎｄＤｅｐａｒ?..     

ON GENERALIZATION OF SONAR SEQUENCES AND INTERMODULATION－FREE FREQUENCIES ASSIGNMENT SEQUENCES

ＣＨＥＮＷＥＮＤＥ（陈文德）（ＩｎｓｔｉｔｕｔｅｏｆＳｙｓｔｅｍｓＳｃｉｅｎｃｅｓ，ｔｈｅＣｈｉｎｅｓｅＡｃａｄｅｍｙｏｆＳｃｉｅｎｃｅｓ，Ｂｅｉｊｉｎｇ１０００８０，ＣｈｉｎａａｎｄＳｔａｔｅＫｅｙＬａｂｒａｒｙｏｆＩｎｆｏｒｍａｔｉｏｎＳｅｃｕｒ...     

Stability of Periodic Solutions of Ordinary Differential Equations in Banach Spaces

§１．ＤｅｆｉｎｉｔｉｏｎｓａｎｄＮｏｔａｔｉｏｎｓＬｅｔＥｂｅａｒｅａｌＢａｎａｃｈｓｐａｃｅ,ａｎｄｌｅｔｘ,ｙ∈Ｅ．Ｔｈｅｄｉｒｅｃｔｉｏｎａｌｄｅｒｉｖａｔｉｖｅ［ｘ,ｙ］－ｏｆｘａｎｄｙｉｓｄｅｆｉｎｅｄｂｙ（ｆｏｒｍｏｒｅｄｅｔａｉｌｓｓ...     

Identification of MIMO systems using radial basis function networks with hybrid learning algorithm

When a radial basis function network (RBFN) is used for identification of a nonlinear multi-input multi-output (MIMO) system, the number of hidden layer nodes, the initial parameters of the kernel, and the initial weights of the network must be determined first. For this purpose, a systematic way that integrates the support vector regression (SVR) and the least squares regression (LSR) is proposed to construct the initial structure of the RBFN. The first step of the proposed method is to determine the number of hidden layer nodes and the initial parameters of the kernel by the SVR method. Then the weights of the RBFN are determined by solving a simple minimization problem based on the concept of LSR. After initialization, an annealing robust learning algorithm (ARLA) is then applied to train the RBFN. With the proposed initialization approach, one can find that the designed RBFN has few hidden layer nodes while maintaining good performance. To show the feasibility and superiority of the annealing robust radial basis function networks (ARRBFNs) for identification of MIMO systems, several illustrative examples are included.     

New fuzzy wavelet network for modeling and control: The modeling approach

In this paper, a fuzzy wavelet network is proposed to approximate arbitrary nonlinear functions based on the theory of multiresolution analysis (MRA) of wavelet transform and fuzzy concepts. The presented network combines TSK fuzzy models with wavelet transform and ROLS learning algorithm while still preserve the property of linearity in parameters. In order to reduce the number of fuzzy rules, fuzzy clustering is invoked. In the clustering algorithm, those wavelets that are closer to each other in the sense of the Euclidean norm are placed in a group and are used in the consequent part of a fuzzy rule. Antecedent parts of the rules are Gaussian membership functions. Determination of the deviation parameter is performed with the help of gold partition method. Here, mean of each function is derived by averaging center of all wavelets that are related to that particular rule. The overall developed fuzzy wavelet network is called fuzzy wave-net and simulation results show superior performance over previous networks.The present work is complemented by a second part which focuses on the control aspects and to be published in this journal([17]). This paper proposes an observer based self-structuring robust adaptive fuzzy wave-net (FWN) controller for a class of nonlinear uncertain multi-input multi-output systems.     

Day‐ahead price forecasting based on hybrid prediction model

Short‐Term Price Forecast is a key issue for operation of both regulated power systems and electricity markets. Energy price forecast is the key information for generating companies to prepare their bids in the electricity markets. However, this forecasting problem is complex due to nonlinear, nonstationary, and time variant behavior of electricity price time series. So, in this article, the forecast model includes wavelet transform, autoregressive integrated moving average, and radial basis function neural networks (RBFN) is presented. Also, an intelligent algorithm is applied to optimize the RBFN structure, which adapts it to the specified training set, reduce computational complexity and avoids over fitting. Effectiveness of the proposed method is applied for price forecasting of electricity market of mainland Spain and its results are compared with the results of several other price forecast methods. These comparisons confirm the validity of the developed approach. © 2016 Wiley Periodicals, Inc. Complexity 21: 156–164, 2016     

Evaluation of fuzzy regression models by fuzzy neural network

In this paper, a novel hybrid method based on fuzzy neural network for approximate fuzzy coefficients (parameters) of fuzzy linear and nonlinear regression models with fuzzy output and crisp inputs, is presented. Here a neural network is considered as a part of a large field called neural computing or soft computing. Moreover, in order to find the approximate parameters, a simple algorithm from the cost function of the fuzzy neural network is proposed. Finally, we illustrate our approach by some numerical examples.     

粒子群优化模糊神经网络在语音识别中的应用

针对模糊神经网络训练采用BP算法比较依赖于网络的初始条件,训练时间较长,容易陷入局部极值的缺点,利用粒子群优化算法(PSO)的全局搜索性能,将PSO用于模糊神经网络的训练过程.由于基本PSO算法存在一定的早熟收敛问题,引入一种自适应动态改变惯性因子的PSO算法,使算法具有较强的全局搜索能力.将此算法训练的模糊神经网络应用于语音识别中,结果表明,与BP算法相比,粒子群优化的模糊神经网络具有较高的收敛速度和识别率.     

A hybrid intelligent algorithm for portfolio selection problem with fuzzy returns

Portfolio selection theory with fuzzy returns has been well developed and widely applied. Within the framework of credibility theory, several fuzzy portfolio selection models have been proposed such as mean–variance model, entropy optimization model, chance constrained programming model and so on. In order to solve these nonlinear optimization models, a hybrid intelligent algorithm is designed by integrating simulated annealing algorithm, neural network and fuzzy simulation techniques, where the neural network is used to approximate the expected value and variance for fuzzy returns and the fuzzy simulation is used to generate the training data for neural network. Since these models are used to be solved by genetic algorithm, some comparisons between the hybrid intelligent algorithm and genetic algorithm are given in terms of numerical examples, which imply that the hybrid intelligent algorithm is robust and more effective. In particular, it reduces the running time significantly for large size problems.     

基于知识的模糊神经网络的旋转机械故障诊断

提出了一种基于知识的模糊神经网络并用于故障诊断．首先基于粗糙集对样本数据进行初步规则获取,并计算规则的依赖度和条件覆盖度,然后根据规则数目进行模糊神经网络结构部分设计,规则的依赖度和条件覆盖度用于设定网络初始权重,而用遗产算法对神经网络输出参数进行优化．这样的模糊神经网络称为基于知识的模糊神经网络．使用该网络对旋转机械常见故障进行诊断,结果表明,和一般模糊神经网络相比,该网络具有训练时间短而诊断率高的特点．     

An efficient indirect RBFN‐based method for numerical solution of PDEs

This article presents an efficient indirect radial basis function network (RBFN) method for numerical solution of partial differential equations (PDEs). Previous findings showed that the RBFN method based on an integration process (IRBFN) is superior to the one based on a differentiation process (DRBFN) in terms of solution accuracy and convergence rate (Mai‐Duy and Tran‐Cong, Neural Networks 14(2) 2001, 185). However, when the problem dimensionality N is greater than 1, the size of the system of equations obtained in the former is about N times as big as that in the latter. In this article, prior conversions of the multiple spaces of network weights into the single space of function values are introduced in the IRBFN approach, thereby keeping the system matrix size small and comparable to that associated with the DRBFN approach. Furthermore, the nonlinear systems of equations obtained are solved with the use of trust region methods. The present approach yields very good results using relatively low numbers of data points. For example, in the simulation of driven cavity viscous flows, a high Reynolds number of 3200 is achieved using only 51 × 51 data points. © 2005 Wiley Periodicals, Inc. Numer Methods Partial Differential Eq, 2005     

三级倒立摆的T-S型前馈补偿模糊神经网络控制

为解决T akag i-Sugeno型模糊神经网络在控制多变量系统时的规则组合爆炸问题,提出一种误差前馈补偿的模糊神经网络控制方案,有效实现了三级倒立摆的稳定控制。该控制方案适用对状态变量可按性质和重要程度划分的多变量系统的控制,大大减少了模糊神经网络控制器的规则数,有利于利用专家的控制经验,具有良好的鲁棒性和非线性适应能力。     

Analysis of interpretability-accuracy tradeoff of fuzzy systems by multiobjective fuzzy genetics-based machine learning

This paper examines the interpretability-accuracy tradeoff in fuzzy rule-based classifiers using a multiobjective fuzzy genetics-based machine learning (GBML) algorithm. Our GBML algorithm is a hybrid version of Michigan and Pittsburgh approaches, which is implemented in the framework of evolutionary multiobjective optimization (EMO). Each fuzzy rule is represented by its antecedent fuzzy sets as an integer string of fixed length. Each fuzzy rule-based classifier, which is a set of fuzzy rules, is represented as a concatenated integer string of variable length. Our GBML algorithm simultaneously maximizes the accuracy of rule sets and minimizes their complexity. The accuracy is measured by the number of correctly classified training patterns while the complexity is measured by the number of fuzzy rules and/or the total number of antecedent conditions of fuzzy rules. We examine the interpretability-accuracy tradeoff for training patterns through computational experiments on some benchmark data sets. A clear tradeoff structure is visualized for each data set. We also examine the interpretability-accuracy tradeoff for test patterns. Due to the overfitting to training patterns, a clear tradeoff structure is not always obtained in computational experiments for test patterns.