Non-Monotonic Lyapunov-Krasovskii Functional Approach to Stability Analysis and Stabilization of Discrete Time-Delay Systems

In this paper, a novel non-monotonic Lyapunov-Krasovskii functional approach is proposed to deal with the stability analysis and stabilization problem of linear discrete time-delay systems. This technique is utilized to relax the monotonic requirement of the Lyapunov-Krasovskii theorem. In this regard, the Lyapunov-Krasovskii functional is allowed to increase in a few steps, while being forced to be overall decreasing. As a result, it relays on a larger class of Lyapunov-Krasovskii functionals to provide stability of a state-delay system. To this end, using the non-monotonic Lyapunov-Krasovskii theorem, new sufficient conditions are derived regarding linear matrix inequalities(LMIs)to study the global asymptotic stability of state-delay systems.Moreover, new stabilization conditions are also proposed for time-delay systems in this article. Both simulation and experimental results on a p H neutralizing process are provided to demonstrate the efficacy of the proposed method.

A new approach to stability analysis of neural networks with time-varying delay via novel Lyapunov-Krasovskii functional

In this paper, new delay-dependent stability criteria for asymptotic stability of neural networks with time-varying delays are derived. The stability conditions are represented in terms of linear matrix inequalities （LMIs） by constructing new Lyapunov-Krasovskii functional. The proposed functional has an augmented quadratic form with states as well as the nonlinear function to consider the sector and the slope constraints. The less conservativeness of the proposed stability criteria can be guaranteed by using convex properties of the nonlinear function which satisfies the sector and slope bound. Numerical examples are presented to show the effectiveness of the proposed method.

Skopos:The Central Theory of Functional Approach

Skopos is the central theory of functional approach. In this article, firstly, it will discuss Katharina Reiss's Skopostheorie. Secondly, it will explain Has. J. Vermeer's Skopostheorie. Thirdly, it will analyze Justa Holz-Manttari and Chrisriane Nord's Skopostheorie. Finally, it will give some opinions the importance and practicality of Skopostheorie in the translating.

Functional Approach to the C-E Translation of Tourist Material

Tourist material has its own text features.To translate tourist material is to achieve its purpose by transferring its pragmatic force,which is determined by text features and functions of tourist material.Which strategies exactly should be used in a certain circumstance is not important provided the pragmatic force is transmitted successfully.

Tailoring MXene Thickness and Functionalization for Enhanced Room‑Temperature Trace NO_(2) Sensing

In this study,precise control over the thickness and termination of Ti3C2TX MXene flakes is achieved to enhance their electrical properties,environmental stability,and gas-sensing performance.Utilizing a hybrid method involving high-pressure processing,stirring,and immiscible solutions,sub-100 nm MXene flake thickness is achieved within the MXene film on the Si-wafer.Functionalization control is achieved by defunctionalizing MXene at 650℃ under vacuum and H2 gas in a CVD furnace,followed by refunctionalization with iodine and bromine vaporization from a bubbler attached to the CVD.Notably,the introduction of iodine,which has a larger atomic size,lower electronegativity,reduce shielding effect,and lower hydrophilicity(contact angle:99°),profoundly affecting MXene.It improves the surface area(36.2 cm^(2) g^(-1)),oxidation stability in aqueous/ambient environments(21 days/80 days),and film conductivity(749 S m^(-1)).Additionally,it significantly enhances the gas-sensing performance,including the sensitivity(0.1119Ωppm^(-1)),response(0.2% and 23%to 50 ppb and 200 ppm NO_(2)),and response/recovery times(90/100 s).The reduced shielding effect of the–I-terminals and the metallic characteristics of MXene enhance the selectivity of I-MXene toward NO2.This approach paves the way for the development of stable and high-performance gas-sensing two-dimensional materials with promising prospects for future studies.

The Development of Meta-functional Approaches in Translation Studies

Functional linguistics has exerted an increasing impact on modern linguistic studies.Functional approaches,especially metafunctions have undergone a process of development and improvement.The affirmation of the metafunctions of language has aroused more and more scholars'concern on the"functional"facet of language,especially in Translation studies.The formation and improvement of functional approaches are introduced separately.

The Application of Cognitive-Functional Approach in College English Teaching

The Cognitive-Functional Approach combines the linguistic views of two major linguistic theories,formalism linguistics and functional linguistics.This approach fully exerts the innate language competence of foreign language learners,help learners to set the language parameter of the target language and explore the rules of target language actively.On the other hand,this approach also advocates the ability of foreign language learners to choose the proper language form in a specific language environment and to train learners'communicative competence.

Relaxed Stability Criteria for Time-Delay Systems:A Novel Quadratic Function Convex Approximation Approach

This paper develops a quadratic function convex approximation approach to deal with the negative definite problem of the quadratic function induced by stability analysis of linear systems with time-varying delays.By introducing two adjustable parameters and two free variables,a novel convex function greater than or equal to the quadratic function is constructed,regardless of the sign of the coefficient in the quadratic term.The developed lemma can also be degenerated into the existing quadratic function negative-determination(QFND)lemma and relaxed QFND lemma respectively,by setting two adjustable parameters and two free variables as some particular values.Moreover,for a linear system with time-varying delays,a relaxed stability criterion is established via our developed lemma,together with the quivalent reciprocal combination technique and the Bessel-Legendre inequality.As a result,the conservatism can be reduced via the proposed approach in the context of constructing Lyapunov-Krasovskii functionals for the stability analysis of linear time-varying delay systems.Finally,the superiority of our results is illustrated through three numerical examples.

A functional approach to improving non-English majors＇ writing proficiency

Problems in generating and organizing ideas, in coherence and language competence are common in non-English majors＇ writings. To improve their writing proficiency, the writing course should have real-life purposes, balance between real and display writing, between product and process approaches, vary writing activities, train strategies in improving coherence, balance the content of feedback and use various forms of feedback.

Approaches to Pendent Groups' Functionalization of Polyimide

Pendent groups' functionalization of polyimide is an optimum approach to improve its processability and achieve functionalized polyimide materials. There are two types of modification routes for pendent groups' functionalization of polyimide: monomer route and macromolecular route. In this paper, various approaches for pendent groups' functionalization of polyimide are introduced. At the same time, a new method to achieve functional polyimide materials without decreasing its thermal stability and mechanical properties is mentioned.

FUZZY APPROACHING SET AND FUZZYAPPROACHING FUNCTIONAL MAPPING

By establishing the concepts of fuzzy approaching set and fuzzy approaching functional mapping and making research on them, a new method for time series prediction is introduced.

New Approach of Stability for Time-Delay Takagi-Sugeno Fuzzy System Based on Fuzzy Weighting-Dependent Lyapunov Functionals

This paper deals with the stability of Takagi-Sugeno fuzzy models with time delay. Using fuzzy weighting- dependent Lyapunov-Krasovskii functionals, new sufficient stability criteria are established in terms of Linear Matrix Inequality;hence the stability bound of upper bound delay time can be easily estimated. Finally, numeric simulations are given to validate the developed approach.

The Functional Approach： Material and Methods

From 1970 onwards, Halliday worked on the functional aspect of grammar. He mentioned the language as a form of ＂doing＂ rather than a form of ＂knowing＂. He believes that language is what it is because it has to serve certain function. In other words, social demands on language have helped to shape its structure. This theory distinguishes linguistic behavior potential from actual linguistic behavior. That means the speaker can do many things in certain language： making an invitation, expressing hope, inquiry, agreement, refuse and etc. Therefore EFL teaching is to develop the abilities to communicate with others, that is, listening, speaking, reading, writing and translating. This paper wants to discuss Halliday＇s theory about the functional approach and how to make good use of it to the language leaming and teaching.

A systemic functional approach to EFL writing assessment

The present study aims to describe theme choices in students＇ writing with a systemic functional approach. The analysis of a student＇s written work chosen at random shows the student writer can apply various theme types in writing after receiving instruction in reading class. The author hopes to propose the pedagogical implication of teaching functional linguistics knowledge to advanced learners, because it gives the view to the students to write cohesive and coherent texts.

An Analysis of Lyrics Translation Based on Functional Approaches of Reiss——A case study of Qian Li Zhi Wai

As a bridge for cross-cultural communication, Chinese songs, which lay considerable emphasis on literary value of lyrics,play a critical role in promoting Chinese culture. High-qualitytWraanis lation of lyrics is of great importance in cross-cultural process.By conducting a case study of lyrics translation of Qian Li Zhibased on Functional approaches of Reiss—Functional charac-teristics of text types and its links to translation methods, this paper explores practical methods and principles in lyrics translation.

Analysis of radial basis function interpolation approach

The radial basis function （RBF） interpolation approach proposed by Freedman is used to solve inverse problems encountered in well-logging and other petrophysical issues. The approach is to predict petrophysical properties in the laboratory on the basis of physical rock datasets, which include the formation factor, viscosity, permeability, and molecular composition. However, this approach does not consider the effect of spatial distribution of the calibration data on the interpolation result. This study proposes a new RBF interpolation approach based on the Freedman＇s RBF interpolation approach, by which the unit basis functions are uniformly populated in the space domain. The inverse results of the two approaches are comparatively analyzed by using our datasets. We determine that although the interpolation effects of the two approaches are equivalent, the new approach is more flexible and beneficial for reducing the number of basis functions when the database is large, resulting in simplification of the interpolation function expression. However, the predicted results of the central data are not sufficiently satisfied when the data clusters are far apart.

A hyperbolic function approach to constructing exact solitary wave solutions of the Hybrid lattice and discrete mKdV lattice

Some new exact solitary wave solutions of the Hybrid lattice and discrete mKdV lattice are obtained by using a hyperbolic function approach. This approach can also be applied to other nonlinear differential-difference equations.

A DUAL-RELAX PENALTY FUNCTION APPROACH FOR SOLVING NONLINEAR BILEVEL PROGRAMMING WITH LINEAR LOWER LEVEL PROBLEM

The penalty function method, presented many years ago, is an important nu- merical method for the mathematical programming problems. In this article, we propose a dual-relax penalty function approach, which is significantly different from penalty func- tion approach existing for solving the bilevel programming, to solve the nonlinear bilevel programming with linear lower level problem. Our algorithm will redound to the error analysis for computing an approximate solution to the bilevel programming. The error estimate is obtained among the optimal objective function value of the dual-relax penalty problem and of the original bilevel programming problem. An example is illustrated to show the feasibility of the proposed approach.

Ideal Spin Hydrodynamics from the Wigner Function Approach

Based on the Wigner function in local equilibrium, we derive hydrodynamical quantities for a system of polarized spin-1/2 particles: the particle number current density, the energy-momentum tensor, the spin tensor, and the dipole moment tensor. Compared with ideal hydrodynamics without spin, additional terms at the first and second orders in the Knudsen number Κ_(n) and the average spin polarization Χ_(s) have been derived. The Wigner function can be expressed in terms of matrix-valued distributions, whose equilibrium forms are characterized by thermodynamical parameters in quantum statistics. The equations of motion for these parameters are derived by conservation laws at the leading and next-to-leading order Κ_(n) and Χ_(s).

Isogeometric nonlocal strain gradient quasi-three-dimensional plate model for thermal postbuckling of porous functionally graded microplates with central cutout with different shapes

This study presents the size-dependent nonlinear thermal postbuckling characteristics of a porous functionally graded material(PFGM) microplate with a central cutout with various shapes using isogeometric numerical technique incorporating nonuniform rational B-splines. To construct the proposed non-classical plate model, the nonlocal strain gradient continuum elasticity is adopted on the basis of a hybrid quasithree-dimensional(3D) plate theory under through-thickness deformation conditions by only four variables. By taking a refined power-law function into account in conjunction with the Touloukian scheme, the temperature-porosity-dependent material properties are extracted. With the aid of the assembled isogeometric-based finite element formulations,nonlocal strain gradient thermal postbuckling curves are acquired for various boundary conditions as well as geometrical and material parameters. It is portrayed that for both size dependency types, by going deeper in the thermal postbuckling domain, gaps among equilibrium curves associated with various small scale parameter values get lower, which indicates that the pronounce of size effects reduces by going deeper in the thermal postbuckling regime. Moreover, we observe that the central cutout effect on the temperature rise associated with the thermal postbuckling behavior in the presence of the effect of strain gradient size and absence of nonlocality is stronger compared with the case including nonlocality in absence of the strain gradient small scale effect.