The Generation of a Sort of Fractal Graphs

We present an approach for generating a sort of fractal graphs by a simple probabilistic logic neuron network and show that the graphs can be represented by a set of compressed codings.An algorithm for quickly finding the codings,i.e.,recognizing the corresponding graphs,is given.The codings are shown to be optimal.The results above possibly give us the clue for studying image compression and pattern recognition.     

Lipschitz continuity of theε-subdifferential and nonmonotonic methods with averaging ofε-subgradients for nonsmooth optimization

Inertial methods with averaging of-subgradient are developed for convex optimization problems. Convergence is proved using Lipschitz continuity of the-subdifferential.Translated from Kibernetika i Sistemnyi Analiz, No. 2, pp. 70–78, March–April, 1992.     

Fractal analysis of the structure and dynamics of a satellite‐detected urban heat island

In this Letter, three fractal models—surface, profile and pixel models are developed to analyse the structure and dynamics of an urban heat island (UHI). These three models were tested using data from Shanghai taken in 1990, 1995 and 1998. The surface model is capable of capturing the fractal dimension of the entire study area. The profile model can be used to analyse the structural characteristics of the UHI along certain directions and is capable of revealing changes in the texture characteristics of UHI. The pixel model can describe the changes in thermal characteristics surrounding each pixel in a particular locale and is suitable for analysing the micro‐structure of the UHI.     

SWGMM: a semi-wrapped Gaussian mixture model for clustering of circular–linear data

Finite mixture models are widely used to perform model-based clustering of multivariate data sets. Most of the existing mixture models work with linear data; whereas, real-life applications may involve multivariate data having both circular and linear characteristics. No existing mixture models can accommodate such correlated circular–linear data. In this paper, we consider designing a mixture model for multivariate data having one circular variable. In order to construct a circular–linear joint distribution with proper inclusion of correlation terms, we use the semi-wrapped Gaussian distribution. Further, we construct a mixture model (termed SWGMM) of such joint distributions. This mixture model is capable of approximating the distribution of multi-modal circular–linear data. An unsupervised learning of the mixture parameters is proposed based on expectation maximization method. Clustering is performed using maximum a posteriori criterion. To evaluate the performance of SWGMM, we choose the task of color image segmentation in LCH space. We present comprehensive results and compare SWGMM with existing methods. Our study reveals that the proposed mixture model outperforms the other methods in most cases.     

Two Methods ‘for Synthesis of State and Disturbance Observers for an Unmanned Aerial Vehicle

Automation and Remote Control - As part of the synthesis of a tracking system for an unmanned aerial vehicle (UAV) exposed to uncontrolled external disturbances under the conditions of incomplete...     

ε-Optimality and duality for multiobjective fractional programming

Using the scalar ε-parametric approach, we establish the Karush-Kuhn-Tucker (which we call KKT) necessary and sufficient conditions for an ε-Pareto optimum of nondifferentiable multiobjective fractional objective functions subject to nondifferentiable convex inequality constraints, linear equality constraints, and abstract constraints. These optimality criteria are utilized as a basis for constructing one duality model with appropriate duality theorems. Subsequently, we employ scalar exact penalty function to transform the multiobjective fractional programming problem to an unconstrained problem. Under this case, we derive the KKT necessary and sufficient conditions without a constraint qualification for ε-Pareto optimality of multiobjective fractional programming.     

State feedback H ∞ control for a class of nonlinear systems using partition of unity method

The system model is nonlinear with respect to all its variables while the output model is linear. The nonlinear system model is firstly converted into an equivalent linear model with error by using partition of unity method. The stability with decay rate and the disturbance attenuation for the nonlinear system are discussed based on the equivalent model. A state feedback H _∞ controller is then proposed in terms of linear matrix inequalities (LMIs). Recommended by Editorial Board member Bin Jiang under the direction of Editor Jae Weon Choi. The authors would like to thank the anonymous reviewers and the editor for their constructive comments based on which this paper has been improved. Dong-Fang Han received the Ph.D. degree in Pure Mathematics from Shantou University in 2008. His research interests include nonlinear control, robust control and time-delay system. Yin-He Wang received the Ph.D. degree in Control Theory and Engineering from Northeast University in 1999. From 2000 to 2002, he was a Post-doctor in the department of automatic control, Northwestern Polytechnic University, China. His research interests include nonlinear systems, adaptive and robust control.     

Ring Delay Chain for Exact Measure of Pulse Cycle Error

This paper introduces a new method named a ring delay chain for exact measure of pulse eycle error.This method can measure a few nanoseconds' error and does not need any high frequency device.Applicationof this method has obtained very good result in a pilot equipment having a servo surface for magnetic diskstorage.     

Kolmogorov ε-Entropy in the Problems on Global Attractors for Evolution Equations of Mathematical Physics

We study the Kolmogorov -entropy and the fractal dimension of global attractors for autonomous and nonautonomous equations of mathematical physics. We prove upper estimates for the -entropy and fractal dimension of the global attractors of nonlinear dissipative wave equations.     

Sinc approximation of eigenvalues of Sturm–Liouville problems with a Gaussian multiplier

Eigenvalue problems with eigenparameter appearing in the boundary conditions usually have complicated characteristic determinant where zeros cannot be explicitly computed. Sampling theory is one of the most important mathematical tools used in communication engineering since it enables engineers to reconstruct signals from some of their sampled data. The sinc Gaussian sampling technique derived by Qian (Proc Am Math Soc 131:1169–1176, 2002) establishes a sampling technique which converges faster than the classical sampling technique. Schmeisser and Stenger (Sampl Theory Signal Image Process 6:199–221, 2007) studied the associated error analysis. In the present paper we apply a sinc Gaussian technique to compute approximate values of the eigenvalues of Sturm–Liouville problems with eigenvalue parameter in one or two boundary conditions. The error of this method decays exponentially in terms of the number of involved samples. Therefore the accuracy of the new technique is higher than the classical sinc method. Numerical worked examples with tables and illustrative figures are given at the end of the paper.     

Development and application of a model for analysis and design phases of Web-based system development

The major characteristics of Web systems that shall be taken into account can be summarized as follows: First, the implementation of Web systems shall have a beneficial effect. To meet the requirements of Internet business system, the Web systems shall enable businesses to provide customers with something valuable through the Internet and profit from this process in return[1]. Second, the way to express the contents on the Web matters. To express the contents, Web systems shall introduce mu…     

Research and Implementation of a Graphic System for Doppler Radar

Doppler radar have become one of the most important instruments for weather now casting, and for meso-scale weather research because of its higher spatial and temporal resolutions. A dealing system for Doppler radar graphic was researched and implemented so as to providing a convenient tool for users. We research and realized CINRAD/XD Doppler radar＇s graphic system. It contains three important parts： reading, standardization and pretreatment. It can be used very easily and conveniently. Besides, the system can be expanded and transplanted simply.     

Optimal Point-Wise Error Estimate of a Compact Difference Scheme for the Coupled Gross–Pitaevskii Equations in One Dimension

The coupled Gross–Pitaevskii (CGP) equation studied in this paper is an important mathematical model describing two-component Bose–Einstein condensate with an internal atomic Josephson junction. We here analyze a compact finite difference scheme which conserves the total mass and energy in the discrete level for the CGP equation. In general, due to the difficulty caused by compact difference on nonlinear terms, optimal point-wise error estimates without any restrictions on the grid ratios of compact difference schemes for nonlinear partial differential equations are very hard to be established. To overcome the difficulty caused by the compact difference operator, we introduce a new norm and an interesting transformation by which the difference scheme is transformed into a special equivalent vector form, we then use the energy method and some important lemmas on the equivalent system to obtain the optimal convergent rate, without any restrictions on the grid ratio, at the order of $O(h^{4}+\tau ^2)$ in the maximum norm with time step $\tau $ and mesh size $h$ . Finally, numerical results are reported to test the theoretical results and simulate the dynamics of the CGP equation.     

ε-Guarantee of a covering of 2D domains using random-looking curves

The problem of covering a given 2D convex domain D with a C¹ random-looking curve C is considered. C within D is said to cover D up to ϵ > 0 if all points of D are within ϵ distance of C. This problem has applications, for example, in manufacturing, 3D printing, automated spray-painting, polishing, and also in devising a (pseudo) random patrol-path that will visit (i.e. cover) all of D using a sensor of ϵ distance span. Our distance bound approach enumerates the complete set of local distance extrema, enumeration that is used to provide a tight bound on the covering distance. This involves computing bi/tri-normals, or circles tangent to C at two/three different points, etc. A constructive algorithm is then proposed to iteratively refine and modify C until C covers a given convex domain D and examples are given to illustrate the effectiveness of our algorithm.     

Hybrid Estimation of State and Input for Linear Continuous Time-varying Systems:A Game Theory Approach

1IntroductionWhen estimated signal includes both state and unknown input of the system,estimation problemis referred to as state and input hybrid estimation(in the following,only hybrid estimation will beused for brevity).Hybrid estimation is originated f…