Thermo-kinetic connectivity by integrating thermo-kinetic correlation and generalized stability

Designing structured materials with optimized mechanical properties generally focuses on engineering microstructures,which are closely determined by the processing routes,such as phase transformations(PTs)and plastic deformations(PDs).Both PTs and PDs follow inherent trade-off relation between thermodynamic driving force ΔG and kinetic energy barrier Q,i.e.,so-called thermo-kinetic correlation.By analyzing nucleation and growth and proposing a conception of negative driving force integrating strain energy,interface energy and any kind of energy that equivalently inhibits the PT itself,ΔG^(S),unified expressions for the thermo-kinetic correlation and generalized stability(GS)were derived for three kinds of PTs,i.e.,diffusive PTs with simultaneously decreasedΔG and increased Q,diffusive PTs with simultaneously increasedΔG and decreased Q,and displacive PTs with simultaneously increased ΔG and decreased Q.This leads to so-called thermo-kinetic connectivity by integrating the thermo-kinetic correlation and the GS,where,by application in typical PTs,it was clearly shown,a criterion of high ΔG-high GS can be predicted by modulating chemical driving force,negative driving force and kinetic energy barrier for diffusion or nucleation.Following thermo-kinetic connectivity,analogous procedure for dislocation evolution upon PDs was performed,and materials design in terms of the highΔG-high GS criterion was discussed and prospected.

Generalized stability criterion for controlling solidification segregation upon twin-roll casting

Macro-and micro-segregation formed upon twin-roll casting(TRC)can be inherited from sub-rapid solid-ification to solid-state transformation,even to plastic deformation,thus deteriorating drastically mechan-ical properties of as-produced thin sheets.Although many works focusing mainly on controlling fields of thermal,concentration and convection have been reported,how to control artificially and quantitatively the segregation using a theoretical connection between processing parameters and solidification models,has not been realized,yet.Regarding it,a systematical framework integrating non-equilibrium dendritic growth and overall solidification kinetics with the TRC parameters,was constructed applying a general-ized stability(GS)conception deduced from transient thermodynamic driving force△G^(t)and transient ki-netic energy barrier Q_(eff)^(t)evolving upon solidification.Departing from this framework considering synergy of thermodynamics and kinetics(i.e.,thermo-kinetic synergy),a criterion of high△G^(t)-high GS guaranteed that the macro(i.e.,the centerline)and the micro(i.e.,the edge)segregation can be suppressed by in-creasing△G^(t)and GS at the beginning and the ending stage of sub-rapid solidification,respectively.This typical thermo-kinetic combination producing the microstructure can be inherited into the plastic de-formation,as reflected by corresponding strength-ductility combinations.This work realized quantitative controlling of TRC by a theoretical connection between processing parameters and solidification models,where,an optimization for sub-rapid solidification segregation using the GS conception including△G^(t)and Q_(eff)^(t)has been performed.

Orbital Stability of Solitary Waves for Generalized Zakharov System

In the interaction of laser-plasma the system of Zakharov equation plays an important role.This system attracted many scientists' wide interest and attention.And the formation, evolution and interaction of the Langmuir solutions differ from solutions of the KDV equation. Here we consider the following generalized Zakharov

Stability analysis of approximately multidimensional additive mappings on fuzzy spaces

The intention of this paper is to study new additive kind multi-dimensional functional equations inspired by several applications of difference equations in biology,control theory,economics,and computer science,as well as notable implementation of fuzzy ideas in certain situations involving ambiguity or vagueness.In the context of different fuzzy spaces,we demonstrate their various fundamental stabilities related to Ulam stability theory.An appropriate example is given to show how stability result fails when the singular case occurs.The findings of this study suggest that stability results are valid in situations with uncertain or imprecise data.The stability results obtained under these fuzzy spaces are compared with previous stability results.

FIXED POINTS AND STABILITY FOR QUARTIC MAPPINGS IN β-NORMED LEFT BANACH MODULES ON BANACH ALGEBRAS

The goal of the present paper is to investigate some new HUR-stability results by applying the alternative fixed point of generalized quartic functional equationin β-Banach modules on Banach algebras. The concept of Ulam-Hyers-Rassias stability （briefly, HUR-stability） originated from Th. M. Rassias stability theorem that appeared in his paper： On the stability of the linear mapping in Banach spaces, Proc. Amer. Math. Soc. 72 （1978）, 297-300.

ON THE HYERS-ULAM STABILITY OF AN EQUATION CHARACTERIZING MULTI-QUADRATIC MAPPINGS

In this article, we prove, both in complete non-Archimedean normed spaces and in 2-Banach spaces, the generalized Hyers-Ulam stability of an equation characterizing multi- quadratic mappings. Our results generalize some known outcomes.

Solution and stability of mixed type functional equation in non-Archimedean random normed spaces

The generalized stability of the Euler-Lagrange quadratic mappings in the framework of non-Archimedean random normed spaces is proved. The interdisciplinary relation among the theory of random spaces, the theory of non-Archimedean spaces, and the theory of functional equations is presented.

ON AN EQUATION CHARACTERIZING MULTI-CAUCHY-JENSEN MAPPINGS AND ITS HYERS-ULAM STABILITY

In this paper, we give two characterizations of multi-Cauchy-Jensen mappings. One of them reduces the system of n equations defining these mappings to a single functional equation. We also prove, using the fixed point method, the generalized Hyers-Ulam stability of this equation. Our results generalize some known outcomes.

Optimizing mechanical properties of magnesium alloys by philosophy of thermo-kinetic synergy:Review and outlook

Although several strategies(including grain refinement,texture adjustment,precipitation hardening,etc.)have been verified to effectively improve the mechanical properties of lightweight magnesium(Mg)alloys,considerable efforts are still needed to be made to comprehensively understand the potential mechanisms controlling complex microstructures and deformation behaviors exhibited by the hexagonal close-packed host lattice of Mg,thus assisting the rational design of materials at a more physical level.As the cornerstone of this review,a universal rule,the so-called synergy of thermodynamics and kinetics(i.e.,thermo-kinetic diversity,correlation and connectivity),including a recently proposed theory of generalized stability(GS),is introduced to deepen our understanding on common behaviors in Mg alloys(i.e.,deformations(slip and twining modes),phase transformations(especially for precipitations)and interactions in between)at a new perspective.Guided by the GS theory,typical cases for Mg alloys design are qualitatively evaluated to reemphasize the traditional strengthening and toughening strategies mentioned above and to illuminate their exquisite coordination for breaking through the trade-off relationship between strength and ductility,corresponding to a typical thermo-kinetic pair(i.e.,high driving force(ΔG)-high GS).To produce the Mg alloys with superior strength-ductility balances,the potential capacity of this GS theory for guiding processing path design is discussed,finally。

Robust Input-Output Energy Decoupling for Uncertain Singular Systems

This paper addresses the robust input-output energy decoupling problem for uncertain singular systems in which all parameter matrices except E exist as time-varying uncertainties. By means of linear matrix inequalities (LMIs), sufficient conditions are derived for the existence of linear state feedback and input transformation control laws, such that the resulting closed-loop uncertain singular system is generalized quadratically stable and the energy of every input controls mainly the energy of a corresponding output, and influences the energy of other outputs as weakly as possible. Keywords Uncertain singular systems - generalized quadratical stability - input-output energy decoupling - linear matrix inequality (LMI) Xin-Zhuang Dong graduated from the Institute of Information Engineering of People’s Liberation Army, China, in 1994. She received the M. S. degree from the Institute of Electronic Technology of People’s Liberation Army, in 1998 and the Ph.D. degree from Northeastern University, China, in 2004. She is currently a post-doctoral fellow at the Key Laboratory of Systems and Control, CAS.Her research interests include singular and nonlinear systems, especially the control of singular systems such as H ∞ control, passive control and dissipative control. Qing-Ling Zhang received the Ph.D. degree from Northeastern University, China, in 1995. He is currently a professor with the Institute of Systems Science, Northeastern University. His research interests include singular systems, fuzzy systems, decentralized control, and H 2/H ∞ control.

Attitude control of a rigid spacecraft with one variable-speed control moment gyro

Nonlinear controllability and attitude stabilization are studied for the underactuated nonholonomic dynamics of a rigid spacecraft with one variable-speed control moment gyro （VSCMG）, which supplies only two internal torques. Nonlinear controllability theory is used to show that the dynamics are locally controllable from the equilibrium point and thus can be asymptotically stabilized to the equilibrium point via time-invariant piecewise continuous feedback laws or time-periodic continuous feedback laws. Specifically, when the total angular momentum of the spacecraft-VSCMG system is zero, any orientation can be a controllable equilib- rium attitude. In this case, the attitude stabilization problem is addressed by designing a kinematic stabilizing law, which is implemented through a nonlinear proportional and deriva- tive controller, using the generalized dynamic inverse （GDI） method. The steady-state instability inherent in the GDI con- troller is elegantly avoided by appropriately choosing control gains. In order to obtain the command gimbal rate and wheel acceleration from control torques, a simple steering logic is constructed to accommodate the requirements of attitude sta- bilization and singularity avoidance of the VSCMG. Illustrative numerical examples verify the efficacy of the proposed control strategy.

FOURIER PSEUDOSPECTRAL－FINITE DIFFERENCE METHOD FOR TWO－DIMENSIONAL VORICITY EQUATION

A Fourier pseudospectral-finite difference sheme is proposed for solving two-dimensionalvorticity equations. The generalized stability and the convergence are proved.The numericalresults are given.

Homomorphisms in Quasi-Banach Algebras Associated with a Pexiderized Cauchy-Jensen Functional Equation

In this paper, we prove the generalized Hyers-Ulam stability of homomorphisms in quasi- Banach algebras associated with the following Pexiderized Jensen functional equation f（x＋y/2＋z）-g（x-y/2＋z）=h（y）.This is applied to investigating homomorphisms between quasi-Banach algebras. The concept of the generalized Hyers-Ulam stability originated from Rassias＇ stability theorem that appeared in his paper： On the stability of the linear mapping in Banach spaces, Proc. Amer. Math. Soc., 72, 297-300 （1978）.

Refined Functional Equations Stemming from Cubic,Quadratic and Additive Mappings

Let n ≥ 2 be an integer. In this paper, we investigate the generalized Hyers-Ulam stability problem for the following functional equation f（n-1∑j=1 xj＋2xn）＋f（n-1∑j=1 xj-2xn）＋8 n-1∑j=1f（xj）=2f（n-1∑j=1 xj） ＋4 n-1∑j=1[f（xj＋xn）＋f（xj-xn）] which contains as solutions cubic, quadratic or additive mappings.

Approximate （m, n）-Cauchy-Jensen Additive Mappings in C^＊-algebras

Concerning the stability problem of functional equations, we introduce a general （m, n）- Cauchy-Jensen functional equation and establish new theorems about the Hyers-Ulam stability of general （m, n）-Cauchy Jensen additive mappings in C^＊-algebras, which generalize the result＇s obtained for Cauchy-Jensen type additive mappings.