Efficient Decomposition Shooting Method for Solving Third-Order Boundary Value Problems

The present paper proposes a mathematical method to numerically treat a class of third-order linear Boundary Value Problems (BVPs). This method is based on the combination of the Adomian Decomposition Method (ADM) and, the modified shooting method. A complete derivation of the proposed method has been provided, in addition to its numerical implementation and, validation via the utilization of the Runge-Kutta method and, other existing methods. The method has been applied to diverse test problems and turned out to perform remarkably. Lastly, the simulated numerical results have been graphically illustrated and, also supported by some absolute error comparison tables.

THE LOWER ORDER AND LINEAR ORDER OF MULTIPLE DIRICHLET SERIES

The article investigates the growth of multiple Dirichlet series.The lower order and the linear order of n-tuple Dirichlet series in Cn are defined and some relations between them and the coefficients and exponents of n-tuple Dirichlet series are obtained.

Eigenstructure Assignment in a Class of Second-order Descriptor Linear Systems: A Complete Parametric Approach

In this paper eigenstructure assignment via proportional-plus-derivative feedback is investigated for a class of second-order descriptor linear systems. Under certain conditions, simple, general and complete parametric solutions of both finite closed-loop eigenvector matrices and feedback gain matrices are derived. The parametric approach utilizes directly original system data, involves manipulations only on n-dimensional matrices, and reveals all the design degrees of freedom which can be further utilized to achieve certain additional system specifications. A numerical example shows the effect of the proposed approach.

EXISTENCE OF MEROMORPHIC SOLUTIONS OF SOME HIGHER ORDER LINEAR DIFFERENTIAL EQUATIONS

This article discusses the problems on the existence of meromorphic solutions of some higher order linear differential equations with meromorphic coefficients. Some nice results are obtained. And these results perfect the complex oscillation theory of meromorphic solutions of linear differential equations.

UNIFORM DIFFERENCE SCHEME FOR A SINGULARLY PERTURBED LINEAR 2ND ORDER HYPERBOLIC PROBLEM WITH ZEROTH ORDER REDUCED EQUATION

In this paper a singularly perturbed linear second order hyperbolic problem with zeroth order reduced equation is discussed. Firstly, an energy inequality of the solution and an estimate of the remainder term of the asymptotic solution are given. Then an exponentially fitted difference scheme is developed in an equidistant mesh. Finally, uniform convergence in small parameter is proved in the sense of discrete energy norm.

A NEW METHOD FOR FINDING THE NATURAL FREQUENCY SET OF A LINEAR TIME-INVARIANT NETWORK

This paper presents a new method for finding the natural frequency set of a linear time invariant network. In the paper deriving and proving of a common equation are described. It is for the first time that in the common equation the natural frequencies of an n th order network are correlated with the n port parameters. The equation is simple and dual in form and clear in its physical meaning. The procedure of finding the solution is simplified and standardized, and it will not cause the loss of roots. The common equation would find wide use and be systematized.

Existence of positive solutions for integral boundary value problem of fractional differential equations

In this paper,we concern ourselves with the existence of positive solutions for a type of integral boundary value problem of fractional differential equations with the fractional order linear derivative operator. By using the fixed point theorem in cone,the existence of positive solutions for the boundary value problem is obtained. Some examples are also presented to illustrate the application of our main results.

Road traffic congestion measurement considering impacts on travelers

The article intends to find a method to quantify traffic congestion＇s impacts on travelers to help transportation planners and policy decision makers well understand congestion situations. Three new congestion indicators, including transportation environment satisfaction （TES）, travel time satisfaction （TTS）, and traffic congestion frequency and feeling （TCFF）, are defined to estimate urban traffic congestion based on travelers＇ feelings. Data of travelers＇ attitude about congestion and trip information were collected from a survey in Shanghai, China. Based on the survey data, we estimated the value of the three indi- cators. Then, the principal components analysis was used to derive a small number of linear combinations of a set of variables to estimate the whole congestion status. A linear regression model was used to find out the significant variables which impact respondents＇ feelings. Two ordered logit models were used to select significant variables of TES and TTS. Attitudinal factor variables were also used in these models. The results show that attitudinal factor variables and cluster category variables are as important as sociodemographic variables in the models. Using the three congestion indicators, the government can collect travelers＇ feeling about traffic congestion and estimate the transportation policy that might be applied to cope with traffic congestion.

HOSVD-based LPV modeling and mixed robust H_2/H_∞ control design for air-breathing hypersonic vehicle

This paper focuses on synthesizing a mixed robust H_2/H_∞ linear parameter varying（LPV） controller for the longitudinal motion of an air-breathing hypersonic vehicle via a high order singular value decomposition（HOSVD） approach.The design of hypersonic flight control systems is highly challenging due to the enormous complexity of the vehicle dynamics and the presence of significant uncertainties.Motivated by recent results on both LPV control and tensor-product（TP） model transformation approach,the velocity and altitude tracking control problems for the air-breathing hypersonic vehicle is reduced to that of a state feedback stabilizing controller design for a polytopic LPV system with guaranteed performances.The controller implementation is converted into a convex optimization problem with parameterdependent linear matrix inequalities（LMIs） constraints,which is intuitively tractable using LMI control toolbox.Finally,numerical simulation results demonstrate the effectiveness of the proposed approach.

Exact Boundary Controllability of Weak Solutions for a Kind of First Order Hyperbolic System——The Constructive Method

In this paper the authors first present the definition and some properties of weak solutions to 1-D first order linear hyperbolic systems. Then they show that the constructive method with modular structure originally given in the framework of classical solutions is still very powerful and effective in the framework of weak solutions to prove the exact boundary(null) controllability and the exact boundary observability for first order hyperbolic systems.

Hydrothermal Syntheses, Supramolecular Structures and the Third-order Non-linear Optical Properties of Three Copper(I) Halide Amine Complexes Connected via Secondary Bonding Interactions

The hydrothermal reactions of CuI, KI and bidentate amines [ 1,10 phenanthroline (phen) or ethylenediamine (en)] gave the three copper(I) halide compounds, Cu3I3(phen)2 (1), CuI(phen)2 (2) and 2 (3), which were structurally characterized via singlecrystal Xray diffraction studies. Hydrogen bonds and ππ interactions are the most remarkable structural features of the title compounds. All can be described as higherdimensional supramolecular compounds connected via these secondary bondings. Moreover, the title compounds were characterized by elemental analyses, IR spectra and TGA analyses. The thirdorder nonlinear optical properties of the title compounds were also investigated and all exhibit nicer nonlinear absorption and selffocusing performance.Keywords copper(I) halide, hydrothermal synthesis, the thirdorder nonlinear optical property, supramolecular structure

Exact Boundary Controllability of Weak Solutions for a Kind of First Order Hyperbolic System——the HUM Method

The exact boundary controllability and the exact boundary observability for the 1-D first order linear hyperbolic system were studied by the constructive method in the framework of weak solutions in the work[Lu,X.and Li,T.T.,Exact boundary con-trollability of weak solutions for a kind of first order hyperbolic system—the constructive method,Chin.Ann.Math.Ser.B,42(5),2021,643-676].In this paper,in order to study these problems from the viewpoint of duality,the authors establish a complete the-ory on the HUM method and give its applications to first order hyperbolic systems.Thus,a deeper relationship between the controllability and the observability can be revealed.Moreover,at the end of the paper,a comparison will be made between these two methods.

Direct fractional order MRAC adaptive control design for a class of fractional order commensurate linear systems

In this paper,we introduce a direct fractional order adaptive control design based on model reference adaptive control(MRAC)structure for a class of commensurate fractional order linear systems with an arbitrary relative degree,and whose parameters are unknown.By generalising the application of standard direct MRAC strategy to plants described by fractional order models,we develop a fractional adaptive control scheme(FOMRAC)based on the output feedback.We also define an adaptation control law ensuring the stability of the closed-loop system and the good tracking of the reference trajectory.The asymptotic stability of the fractional order control system is proven using an extension of the Lyapunov theorem.Simulation results show the effectiveness of the proposed control method even for plants with model parametric variations and additive noises.

Subspace Trajectory Piecewise-Linear Model Order Reduction for Nonlinear Circuits

Despite the efficiency of trajectory piecewise-linear(TPWL)model order re-duction(MOR)for nonlinear circuits,it needs large amount of expansion points forlarge-scale nonlinear circuits.This will inevitably increase the model size as well as the simulation time of the resulting reduced macromodels.In this paper,subspaceTPWL-MOR approach is developed for the model order reduction of nonlinear cir-cuits.By breaking the high-dimensional state space into several subspaces with much lower dimensions,the subspace TPWL-MOR has very promising advantages of re-ducing the number of expansion points as well as increasing the effective region of thereduced-order model in the state space.As a result,the model size and the accuracy of the TWPL model can be greatly improved.The numerical results have shown dra-matic reduction in the model size as well as the improvement in accuracy by using the subspace TPWL-MOR compared with the conventional TPWL-MOR approach.

THE ESTIMATION OF CHARACTERISTIC EXPONENTS FOR A CLASS OF SECOND ORDER LINEAR DIFFERENTIAL EQUATION WITH PERIODIC COEFFICIENTS

In this paper we shall give a simple and easy method to estimate the characteristic exponents for a class of second order linear different equation with periodic coefficient which frequently occurs in application.

On a Linear Partial Differential Equation of the Higher Order in Two Variables with Initial Condition Whose Coefficients are Real-valued Simple Step Functions

By using the method developed in the paper [Georg. Inter. J. Sci. Tech., Volume 3, Issue 1 （2011）, 107-129], it is obtained a representation in an explicit form of the weak solution of a linear partial differential equation of the higher order in two variables with initial condition whose coefficients are real-valued simple step functions.

Measures of Semi Noncompactness and Set Valued AM Mappings

In this paper we define measures of semi noncompactness in a locally convex topological linear space with respect to a given seminorm. Then we get a fixed point theorem for a class of condensing set valued mappings and apply it to differential inclusions.

Regional differences of urbanization in China and its driving factors

After more than 30 years of rapid urbanization, the overall urbanization rate of China reached 56.1% in 2015.However, despite China's rapid increase in its overall rate of urbanization, clear regional differences can be observed. Furthermore, inadequate research has been devoted to in-depth exploration of the regional differences in China's urbanization from a national perspective, as well as the internal factors that drive these differences. Using prefecture-level administrative units in China as the main research subject, this study illustrates the regional differences in urbanization by categorizing the divisions into four types based on their urbanization ratio and speed(high level: low speed; high level: high speed; low level: high speed; and low level: low speed). Next, we selected seven economic and geographic indicators and applied an ordered logit model to explore the driving factors of the regional differences in urbanization. A multiple linear regression model was then adopted to analyze the different impacts of these driving factors on regions with different urbanization types. The results showed that the regional differences in urbanization were significantly correlated to per capita GDP, industry location quotients, urban-rural income ratio,and time distance to major centers. In addition, with each type of urbanization, these factors were found to have a different driving effect. Specifically, the driving effect of per capita GDP and industry location quotients presented a marginally decreasing trend, while main road density appeared to have a more significant impact on cities with lower urbanization rates.