离散系统X_(n+1)=(Ax_n+Bx_(n-1))/(Cx_n+Dx_(n-1))的周期环

利用射影几何中常用的齐次坐标记法,把(αyn-1)/(βyn+yn-1)线性化表出,从而得到了方程有最小正周期m周期解的一个充要条件,从而解决了xn+1=(Axn+Bxn-1)/(Cxn+Dxn-1)的周期解。作为应用和例子,本文给出了m=1,2,3时方程的一般表达式。

Stabilization of discrete nonholonomic chained system

Aimed at the stabilization of the nonholonomic chained system under fixed sample control, two control laws were proposed. The discrete model of the nonholonomic chained system under zero-hold was obtained through the integrate method to the continuous model. And the discrete model was transformed to the form with two linear subsystems through coordinate transformation. Two feedback control laws, time-invariant control law and time-varying control law, were proposed; and the local stabilization and global stabilization were realized respectively. The simulation results show the effectiveness of the proposed control laws. The discrete nonholonomic chained system can converge to zero from any initial state exponentially, and the convergence rate can be changed through changing the parameters of the control laws.

Working Condition Real-Time Monitoring Model of Lithium Ion Batteries Based on Distributed Parameter System and Single Particle Model

Lithium ion batteries are complicated distributed parameter systems that can be described preferably by partial differential equations and a field theory. To reduce the solution difficulty and the calculation amount, if a distributed parameter system is described by ordinary differential equations （ODE） during the analysis and the design of distributed parameter system, the reliability of the system description will be reduced, and the systemic errors will be introduced. Studies on working condition real-time monitoring can improve the security because the rechargeable LIBs are widely used in many electronic systems and electromechanical equipment. Single particle model （SPM） is the simplification of LIB under some approximations, and can estimate the working parameters of a LIB at the faster simulation speed. A LIB modelling algorithm based on PDEs and SPM is proposed to monitor the working condition of LIBs in real time. Although the lithium ion concentration is an unmeasurable distributed parameter in the anode of LIB, the working condition monitoring model can track the real time lithium ion concentration in the anode of LIB, and calculate the residual which is the difference between the ideal data and the measured data. A fault alarm can be triggered when the residual is beyond the preset threshold. A simulation example verifies that the effectiveness and the accuracy of the working condition real-time monitoring model of LIB based on PDEs and SPM.

Performance of the geometric approach to fault detection and isolation in SISO,MISO,SIMO and MIMO systems

In this paper, a geometric approach to fault detection and isolation （FDI） is applied to a Multiple-Input Multipie-Output （MIMO） model of a frame and the FDI results are compared to the ones obtained in the Single-Input Single-Output （SISO）, Multiple-Input Single-Output （MISO）, and Single-Input Multiple-Output （SIMO） cases. A proper distance function based on parameters obtained from parametric system identification method is used in the geometric approach. ARX （Auto Regressive with exogenous input） and VARX （Vector ARX） models with 12 parameters are used in all of the above-mentioned models. The obtained results reveal that by increasing the number of inputs, the classification errors reduce, even in the case of applying only one of the inputs in the computations. Furthermore, increasing the number of measured outputs in the FDI scheme results in decreasing classification errors. Also, it is shown that by using probabilistic space in the distance function, fault diagnosis scheme has better performance in comparison with the deterministic one.

Tuning sol size to optimize organosilica membranes for gas separation

A series of organosilica sols are prepared by the polymeric sol–gel method using 1,2-bis(triethoxysilyl)ethane(BTESE)as the precursor.Particle size distributions of the BTESE-derived sols are systematically investigated by carefully adjusting the synthesis parameters(i.e.,water ratios,acid ratios and solvent ratios)in the sol process.In certain conditions,increasing the water ratio or the acid ratio tends to cause larger sol sizes and bimodal particle size distributions.However,higher solvent ratios lead to smaller sol sizes and unimodal particle size distributions.The organosilica membranes prepared from the optimized sols show excellent H_2 permeances(up to 4.2×10^(-7)mol·m^(-2)·s^(-1)·Pa^(-1))and gas permselectitivies(H_2/CO_2 is 9.5,H_2/N_2 is 50 and H_2/CH_4 is 68).This study offers significant insights into the relationship between the sol synthesis parameters,sol sizes and membrane performance.

Public Key Cryptosystem Based on Two Sided Action of Different Exotic Semirings

The idempotent semirings Rmax and Rmin play a crucial role in several areas of mathematics and their applications such as discrete mathematics, algebraic geometry, computer science, computer languages, linguistic problems, optimization theory, discrete event systems, fuzzy logics. In this paper we consider the expansion of the semirings Rmax and Rmin with residuals and describe how to use these expended semirings in public key cryptography.

The Trinity Triangle and the Homonymy of the Word ＂Is＂ in Natural Language

There are philosophers and logicians who do think that the Trinity-triangle makes up an evident formal-logic inconsistency demonstrating convincingly that Christian faith is illogical and hence irrational one. The present paper submits a systematic counter-argumentation against such thinking. According to the submitted counter-arguments, there is no formal-logic inconsistency in the Holy-Trinity-triangle： There is only a logic-linguistic illusion of such inconsistency which illusion is naturally produced by the ambiguity of the word ＂is＂ in natural language. The author has invented an effective remedy for that illusion, namely, a precise formulation of the generalized and thus modernized Guillotine of Hume by means of an artificial language of two-valued algebraic system of formal ethics of moral rigor. Systematical using the mathematized formulation of the generalized Hume＇s Guillotine cuts down the mentioned linguistic illusion of logical inconsistency. Thus, the paper essentially interconnects discrete mathematical representations of formal iogic of thinking and formal ethics of acting. In relation to contemporary symbolic logic, the author submits not a technical result solving some important particular problem concerning some specific system of symbolic logic but a significantly new result of conceptual work concerning logic in general and its interconnection with mathematical ethics. The old idea of logic as a moral science is transformed into a novel idea of symbolic logic as a brunch of mathematical ethics. In particular, two-valued algebra of classical formal logic is considered as a particular case of two-valued algebra of formal ethics of moral rigor. The submitted conception of logic is instantiated by applying it to the knotty logic-problem of Holy-Trinity-triangle.

Matlab/Simulink Based Dynamic Simulation System for Distance Protection

To observe the inner operating process of distance protection,a Matlab/Simulink based dynamic simulation system for microprocessor-based distance protection is designed in this paper.As a modularized design,the simulation system is composed of several modules such as fault transient calculation,startup,Fourier algorithm,phase selection,impedance computing and impedance comparison etc.Some typical simulation cases,which focus on the main factors affecting distance relay's operation,have been simulated with the system.Simulation results show that the system is able to demonstrate the dynamic behaviors of distance protection under different operating conditions.

Molecular phylogeny and species separation of five morphologically similar Holosticha-complex ciliates(Protozoa, Ciliophora) using ARDRA riboprinting and multigene sequence data

To separate and redefine the ambiguous Holosticha-complex, a confusing group of hypotrichous ciliates, six strains belonging to five morphospecies of three genera, Holosticha heterofoissneri, Anteholosticha sp. popl, Anteholosticha sp. pop2, A. manca, A. gracilis and Nothoholostichafasciola, were analyzed using 12 restriction enzymes on the basis of amplified ribosomal DNA restriction analysis. Nine of the 12 enzymes could digest the DNA products, four （HinfⅠ, Hind Ⅲ, Msp Ⅰ, Taq Ⅰ） yielded species-specific restriction patterns, and Hind Ⅲ and Taq Ⅰ produced different pattems for two Anteholosticha sp. populations. Distinctly different restriction digestion haplotypes and similarity indices can be used to separate the species. The secondary structures of the five species were predicted based on the ITS2 transcripts and there were several minor differences among species, while two Anteholosticha sp. populations were identical. In addition, phylogenies based on the SSrRNA gene sequences were reconstructed using multiple algorithms, which grouped them generally into four clades, and exhibited that the genus Anteholosticha should be a convergent assemblage. The fact that Holosticha species clustered with the oligotrichs and choreotrichs, though with very low support values, indicated that the topology may be very divergent and unreliable when the number of sequence data used in the analyses is too low.

Fuzzy Modeling, Tracking Control and Synchronization of the Rossler's Chaotic System

In this paper, a novel method to model, track control and synchronize the Rossler’s chaotic system is proposed. The fuzzy logical system is used so that the fuzzy inference rule is transferred into a type of variable coefficient nonlinear ordinary differential equation. Consequently the model of the chaotic system is obtained. Then a fuzzy tracking control and a fuzzy synchronization for chaotic systems is proposed as well. First, a known tracking control for the Rossler’s system is used in this paper. We represent the Rossler’s chaotic and control systems into fuzzy inference rules. Then the variable coefficient nonlinear ordinary differential equation is also got. Simulation results show that such an approach is effective and has a high precision.

Development of slope mass rating system using K-means and fuzzy c-means clustering algorithms

Classification systems such as Slope Mass Rating(SMR) are currently being used to undertake slope stability analysis. In SMR classification system, data is allocated to certain classes based on linguistic and experience-based criteria. In order to eliminate linguistic criteria resulted from experience-based judgments and account for uncertainties in determining class boundaries developed by SMR system,the system classification results were corrected using two clustering algorithms, namely K-means and fuzzy c-means(FCM), for the ratings obtained via continuous and discrete functions. By applying clustering algorithms in SMR classification system, no in-advance experience-based judgment was made on the number of extracted classes in this system, and it was only after all steps of the clustering algorithms were accomplished that new classification scheme was proposed for SMR system under different failure modes based on the ratings obtained via continuous and discrete functions. The results of this study showed that, engineers can achieve more reliable and objective evaluations over slope stability by using SMR system based on the ratings calculated via continuous and discrete functions.

Numerical Study of the Secondary Circulations in Rip Current Systems

To investigate the mechanism of secondary circulations in rip current systems, and to explore the relationship between wave conditions and secondary circulation intensity, a series of numerical experiments is performed using coupled nearshore wave model and circulation model. In these experiments, the rip currents and secondary circulations generated above barred beaches with rip channels are simulated. A comparison experiment is conducted to investigate the formation and hydrodynamics of the secondary circulations. Model results indicate that the secondary circulations consist of alongshore flows driven by wave set-up near the shoreline, part of the feeder currents driven by the wave set-up over the bars, and onshore flows at the end of the rip channel driven by wave breaking and convection. The existence of the secondary circulation barely affects the rip current, but narrows and intensifies the feeder currents. Three groups of experiments of varying incident wave conditions are performed to investigate the relationship between wave conditions and secondary circulation intensity. The velocity of the alongshore flow of the secondary circulation is sensitive to the variation of the incident wave height and water depth. It is also found that the alongshore flow intensity is in direct proportion to the alongshore variation of the wave height gradient between the bars and the shoreline.

Charge and Levitation of Grains in Plasma Sheath with Dust Thermic Emission

By taking into account thermic emission current from hot dust surface, the problem involved in dust charging and levitation of dust grains in plasma sheath has been researched. The results are compared to that without including thermal emission current while the system parameters are same. It is found that the thermal emission current has played a significant role on modifying the dust charging and balance levitations. Both of the charging numbers of dust and the dust radius in balance are dramatically reduced. The stability of dust levitation is also analyzed and discussed.

Multi-objective robust controller synthesis for discrete-time systems with convex polytopic uncertain domain

Multi-objective robust state-feedback controller synthesis problems for linear discrete-time uncertain systems are addressed. Based on parameter-dependent Lyapunov functions, the Gl2 and GH2 norm expressed in terms of LMI (Linear Matrix Inequality) characterizations are further generalized to cope with the robust analysis for convex polytopic uncertain system. Robust state-feedback controller synthesis conditions are also derived for this class of uncertain systems. Using the above results, multi-objective state-feedback controller synthesis procedures which involve the LMI optimization technique are developed and less conservative than the existing one. An illustrative example verified the validity of the approach.

Electrodynamic Tethered Deorbit System Dynamics and Performance Analysis

Electrodynamic tethered deorbit technology is a novel way to remove abandoned spacecrafts like upper stages or unusable satellites. This paper investigates and analyses the deorbit performance and mission applicability of the electrodynamic tethered system. To do so, the electrodynamic tethered deorbit dynamics with multi-perturbation is firstly formulated, where the Earth magnetic field, the atmospheric drag, and the Earth oblateness effect are considered. Then, the key system parameters, including payload mass, tether length and tether type, are analyzed by numerical simulations to investigate their influences on the deorbit performance and to give the setting principles for choosing system parameters. Based on this and given an appropriate group of system parameters, numerical simulations are undertaken to study the impact of the mission parameters, including orbit height and orbit inclination, and thus to investigate the mission applicability of the electrodynamic tethered deorbit technology.

A novel group signature with one time secret key

A new group signature with one time secret key is proposed. The main merits are that it only needs the trusted center issuing the partial secret key one time for each group member; and that the group member can generate his different secret key each time when he wants to sign a message. The group public key is constant and the size of the signature is independent of the number of group members. The total computation cost of signature and verification requires only 8 modular exponentiations.

Distance-Stability of Nonlinear Discrete Systems

In this paper,the distance-sability of nonlinear discrete system is investigated by means of the Gauss-Seidel iteration method.Some algebric criteria of the distance-stability are ob-tained.Construction of Lyapunov function is avoided.

Model Order Reduction Methods for Discrete Systems via Discrete Pulse Orthogonal Functions

This paper explores model order reduction(MOR)methods for discrete linear and discrete bilinear systems via discrete pulse orthogonal functions(DPOFs).Firstly,the discrete linear systems and the discrete bilinear systems are expanded in the space spanned by DPOFs,and two recurrence formulas for the expansion coefficients of the system’s state variables are obtained.Then,a modified Arnoldi process is applied to both recurrence formulas to construct the orthogonal projection matrices,by which the reduced-order systems are obtained.Theoretical analysis shows that the output variables of the reducedorder systems can match a certain number of the expansion coefficients of the original system’s output variables.Finally,two numerical examples illustrate the feasibility and effectiveness of the proposed methods.

Algebraic encoding scheme for aperture 3 hexagonal discrete global grid system

Discrete Global Grid Systems(DGGSs) are spatial references that use a hierarchical tessellation of cells to partition and address the entire globe. They provide an organizational structure that permits fast integration between multiple sources of large and variable geospatial data sufficient for visualization and analysis. Despite a significant body of research supporting hexagonal DGGSs as the superior choice, the application thereof has been hindered owing in part to the lack of a rational hierarchy with an efficient addressing system. This paper presents an algebraic model of encoding scheme for the Aperture 3 Hexagonal(A3H) DGGS. Firstly, the definition of a grid cell, which is composed of vertices, edges, and a center, is introduced to describe fundamental elements of grids. Secondly, by identifying the grid cell with its center, this paper proves that cell centers at different levels can be represented exactly using a mixed positional number system in the complex plane through the recursive geometric relationship between two successive levels, which reveals that grid cells are essentially special complex radix numbers. Thirdly, it is shown that through the recursive geometric relationship of successive odd or even levels, the mixed positional number system can also be applied to uniquely represent cell centers at different levels under specific constraint conditions, according to which the encoding scheme is designed. Finally, it is shown that by extending the scheme to 20 triangular faces of the regular icosahedron,multi-resolution grids on closed surfaces of the icosahedron are addressed perfectly. Contrast experiments show that the proposed encoding scheme has the advantages of theoretical rigor and high programming efficiency and that the efficiency of cross-face adjacent cell searching is 242.9 times that of a similar scheme. Moreover, the proposed complex radix number representation is an ideal formalized description tool for grid systems. The research ideas introduced herein can be used to create a universal theoretical framework for DGGSs.

Numerical study on the response of the Earth's magnetosphere-ionosphere system to a super solar storm

With the approaching of the 24th solar cycle peak year （2012-2014）, the impacts of super solar storms on the geospace envi- ronment have drawn attentions. Based on the geomagnetic field observations during Carrington event in 1859, we estimate the interplanetary solar wind conditions at that time, and investigate the response of the magnetosphere-ionosphere system to this extreme solar wind conditions using global 3D MHD simulations. The main findings include： l） The day-side magnetopause and bow shock are compressed to 4.3 and 6.0 Re （Earth radius）, and their flanks are also strongly compressed. The magneto- pause shifts inside the geosynchronous orbit, exposing geosynchronous satellites in the solar wind in the magnetosheath. 2） During the storm, the region-1 current increases by about 60 times, and the cross polar potential drop increases by about 80 times; the reconnection voltage is about 5 to 6 times larger than the average storms, which means a larger amount of the solar wind energy enters the magnetosphere, resulting in strong space weather phenomena.