ANALYSIS FOR THE BEZOUT IDENTITY OF GENERALIZED SYSTEMS

The state space representation of the Bezout identity for generalized systems proposed by (Wang and Balas, 1989) is discussed again. A more concise way of description and proof is presented and the physical significance of the result in is also analyzed. Thus, our work is of independent interest.

A Numerical Convex Lens for the State-Discretized Modeling and Simulation of Megawatt Power Electronics Systems as Generalized Hybrid Systems

Modeling and simulation have emerged as an indispensable approach to create numerical experiment platforms and study engineering systems.However,the increasingly complicated systems that engineers face today dramatically challenge state-of-the-art modeling and simulation approaches.Such complicated systems,which are composed of not only continuous states but also discrete events,and which contain complex dynamics across multiple timescales,are defined as generalized hybrid systems(GHSs)in this paper.As a representative GHS,megawatt power electronics(MPE)systems have been largely integrated into the modern power grid,but MPE simulation remains a bottleneck due to its unacceptable time cost and poor convergence.To address this challenge,this paper proposes the numerical convex lens approach to achieve state-discretized modeling and simulation of GHSs.This approach transforms conventional time-discretized passive simulations designed for pure-continuous systems into state-discretized selective simulations designed for GHSs.When this approach was applied to a largescale MPE-based renewable energy system,a 1000-fold increase in simulation speed was achieved,in comparison with existing software.Furthermore,the proposed approach uniquely enables the switching transient simulation of a largescale megawatt system with high accuracy,compared with experimental results,and with no convergence concerns.The numerical convex lens approach leads to the highly efficient simulation of intricate GHSs across multiple timescales,and thus significantly extends engineers’capability to study systems with numerical experiments.

Research on Generalized Computing Systems

This paper presents a kind of artificial intelligent system-generalized computing system (GCS for short), and introduces its mathematical description, implement problem and learning problem.

NEW SYSTEMS OF GENERALIZED QUASI-VARIATIONAL INCLUSIONS IN FC-SPACES AND APPLICATIONS

In this paper, we study some new systems of generalized quasi-variational inclusion problems in FC-spaces without convexity structure.By applying an existence theorem of maximal elements of set-valued mappings due to the author, some new existence theorems of solutions for the systems of generalized quasi-variational inclusion problems are proved in noncompact FC-spaces. As applications, some existence results of solutions for the system of quasi-optimization problems and mathematical programs with the systems of generalized quasi-variational inclusion constraints are obtained in FC-spaces.

Symplectic-like Difference Schemes for Generalized Hamiltonian Systems

The nature of infinite-dimensional Hamiltonian systems are studied for the purpose of further study on some generalized Hamiltonian systems equipped with a given Poisson bracket. From both theoretical and practical viewpoints, we summarize a general method of constructing symplectic-like difference schemes of these kinds of systems. This study provides a new algorithm for the application of the symplectic geometry method in numerical solutions of general evolution equations.

Global Asymptotically Stable of a Generalized Discrete Ricker Competition System

The purpose of this article is to investigate the sufficient conditions for the global asymptotic stability of one equilibrium point of a generalized Ricker competition system,……which appears as a model for dynamics with one extinct species, by applying the technique of average functions and the new principle of competitive exclusion.

Disproportionation Reactions of HIO and NaIO in Static and Dynamic Systems

The paper refers to disproportionation of HIO and NaIO in aqueous media, in static and dynamic systems. The results of calculations, realized according to GATES/GEB principles, with use of an iterative computer program, are presented graphically. An example of the computer program with all physicochemical knowledge involved in the related algorithm is attached herewith.

Formulation of Titration Curves for Some Redox Systems

The formalism realised according to the Generalised Approach to Electrolytic Systems (GATES) is presented and applied to typical redox systems known from the laboratory practice. In any redox system, the Generalized Electron Balance (GEB), perceived as the law of the matter conservation, is derivable from linear combination 2·f(O) – f(H) of elemental balances: f(O) for oxygen and f(H) for hydrogen. It is an equation linearly independent from other (charge and concentration) balances referred to an electrolytic redox system (aqueous media) of any degree of complexity, and named as the primary form of GEB and then denoted as pr-GEB. A compact equation for GEB is obtained from linear combination of 2·f(O) – f(H) with other (charge and concentration) balances. For a non-redox electrolytic system, of any degree of complexity, the balance 2·f(O) – f(H) is not an independent equation. In the derivation of GEB, all known components (species) of the system tested, taken in their real (i.e., hydrated) form, are involved in the balances, and none simplifying assumptions are needed. The redox systems are simulated with use of an iterative computer program.

Generating Function Methods for Coefficient-Varying Generalized Hamiltonian Systems

The generating function methods have been applied successfully to generalized Hamiltonian systems with constant or invertible Poisson-structure matrices.In this paper,we extend these results and present the generating function methods preserving the Poisson structures for generalized Hamiltonian systems with general variable Poisson-structure matrices.In particular,some obtained Poisson schemes are applied efficiently to some dynamical systems which can be written into generalized Hamiltonian systems(such as generalized Lotka-Volterra systems,Robbins equations and so on).

New paradigms of water-enabled electrical energy generation

Nanotechnology-inspired small-sized water-enabled electricity generation(WEG)has sparked widespread research interest,especially when applied as an electricity source for off-grid low-power electronic equipment and systems.Currently,WEG encompasses a wide range of physical phenomena,generator structures,and power generation environments.However,a systematic framework to clearly describe the connections and differences between these technologies is unavailable.In this review,a comprehensive overview of generator technologies and the typical mechanisms for harvesting water energy is provided.Considering the different roles of water inWEG processes,the related technologies are presented as two different scenarios.Moreover,a detailed analysis of the electrical potential formation in each WEG process is presented,and their similarities and differences are elucidated.Furthermore,a comprehensive compilation of advanced generator architectures and system designs based on hydrological cycle processes is presented,along with their respective energy efficiencies.These nanotechnology-inspired small-sized WEG devices show considerable potential for applications in the Internet of Things ecosystem(i.e.,microelectronic devices,integrated circuits,and smart clothing).Finally,the prospects and future challenges of WEG devices are also summarized.

FEEDBACK REALIZATION OF HAMILTONIAN SYSTEMS

This paper investigates the relationship between state feedback and Hamiltonian realization. First, it is proved that a completely controllable linear system always has a state feedback state equation Hamiltonian realization. Necessary and sufficient conditions are obtained for it to have a Hamiltonian realization with natural output. Then some conditions for an affine nonlinear system to have a Hamiltonian realization are given. For generalized outputs, the conditions of the feedback, keeping Hamiltonian, are discussed. Finally, the admissible feedback controls for generalized Hamiltonian systems are considered.

An Approximate Approach for Systems of Singular Volterra Integral Equations Based on Taylor Expansion

In this article, an extended Taylor expansion method is proposed to estimate the solution of linear singular Volterra integral equations systems. The method is based on combining the m-th order Taylor polynomial of unknown functions at an arbitrary point and integration method, such that the given system of singular integral equations is converted into a system of linear equations with respect to unknown functions and their derivatives. The required solutions are obtained by solving the resulting linear system. The proposed method gives a very satisfactory solution,which can be performed by any symbolic mathematical packages such as Maple, Mathematica, etc. Our proposed approach provides a significant advantage that the m-th order approximate solutions are equal to exact solutions if the exact solutions are polynomial functions of degree less than or equal to m. We present an error analysis for the proposed method to emphasize its reliability. Six numerical examples are provided to show the accuracy and the efficiency of the suggested scheme for which the exact solutions are known in advance.

Some new optimal quaternary constant weight codes

Constant weight codes (CWCs) are an important class of codes in coding theory. Generalized Steiner systems GS(2, k, v, g) were first introduced by Etzion and used to construct optimal nonlinear CWCs over an alphabet of size g+1 with minimum Hamming distance 2k - 3, in which each codeword has length v and weight k. In this paper, Weil's theorem on character sum estimates is used to show that there exists a GS(2,4, v, 3) for any prime v≡1 (mod 4) and v > 13. From the coding theory point of view, an optimal nonlinear quaternary (v, 5,4) CWC exists for such a prime v.