Discrete variational principle and first integrals for Lagrange-Maxwell mechanico-electrical systems

This paper presents a discrete vaxiational principle and a method to build first-integrals for finite dimensional Lagrange-Maxwell mechanico-electrical systems with nonconservative forces and a dissipation function. The discrete variational principle and the corresponding Euler-Lagrange equations are derived from a discrete action associated to these systems. The first-integrals are obtained by introducing the infinitesimal transformation with respect to the generalized coordinates and electric quantities of the systems. This work also extends discrete Noether symmetries to mechanico-electrical dynamical systems. A practical example is presented to illustrate the results.

Research and Review on the Development of Mechanical and Electrical Integration of System Function Principle and Related Technologies

In this paper, we conduct research on the development of mechanical and electrical integration of system function principle and related technologies. Along with the rapid and continuous development of modem science and technology, it ＇ s for the penetration and cross of different subjects great push, the more important is caused by technological revolution in the field of engineering and mechanical engineering field under the rapid development of computer technology and microelectronic technology and penetration to the mechanical and electrical integration, which is formed by the mechanical industry lead to trigger a particularly large changes in the mechanical industry management system and mode of production, product and technical structure, composition and function, thus result in industrial production from the previous mechanical electrification progressively electromechanical integration which lead the trend of the current technology.

Several Fundamental Theorems and Conservative Integrals in Quasicrystal Elasticity Theory

Aim To extend several fundamental theorems of conventional elasticity theory to quasicrystalelasticity theory. Methods The basic governing equations of quasicrystal elasticity theory and Gauss's theorem were applied in the derivation. Results and Conclusion The principle of virtual work, Betti's reciprocal theorem and the uniqueness theorem of quasicrystal elasticity theory are proud, and some conservative integrals in quasicrystal elasticty theory are obtained.

EXISTENCE AND UNIQUENESS OF SOLUTIONS FOR NONLINEAR FRACTIONAL DIFFERENTIAL EQUATIONS WITH NON-SEPARATED TYPE INTEGRAL BOUNDARY CONDITIONS

In this paper, we study a boundary value problem of nonlinear fractional dif- ferential equations of order q （1 〈 q 〈 2） with non-separated integral boundary conditions. Some new existence and uniqueness results are obtained by using some standard fixed point theorems and Leray-Schauder degree theory. Some illustrative examples are also presented. We extend previous results even in the integer case q = 2.

GENERALIZED VARIATIONAL PRINCIPLES OF THE VISCOELASTIC BODY WITH VOIDS AND THEIR APPLICATIONS

From the Boltzmann's constitutive law of viscoelastic materials and the linear theory of elastic materials with voids, a constitutive model of generalized force fields for viscoelastic solids with voids was given. By using the variational integral method, the convolution-type functional was given and the corresponding generalized variational principles and potential energy principle of viscoelastic solids with voids were presented. It can be shown that the variational principles correspond to the differential equations and the initial and boundary conditions of viscoelastic body with voids. As an application, a generalized variational principle of viscoelastic Timoshenko beams with damage was obtained which corresponds to the differential equations of generalized motion and the initial and boundary conditions of beams. The variational principles provide a way for solving problems of viscoelastic solids with voids.

An Efficient Grid Service Discovery Mechanism Based on the Locality Principle

With the explosion of services in grid environment, it＇s necessary to develop a mechanism which has the ability of discovering suitable grid services efficiently. This paper attempts to establish a layered resource management model based on the locality principle which classifies services into different domains and virtual organizations （VOs） according to their shared purposes. We propose an ontologybased search method applying the ontology theory for characterizing semantic information. In addition, we extend the UD- D1 in querying, storing, and so on. Simulation experiments have shown that our mechanism achieves higher performance in precision, recall and query response time.

High-Order Hamilton's Principle and the Hamilton's Principle of High-Order Lagrangian Function

In this paper, based on the theorem of the high-order velocity energy, integration and variation principle, the high-order Hamilton＇s principle of general holonomic systems is given. Then, three-order Lagrangian equations and four-order Lagrangian equations are obtained from the high-order Hamilton＇s principle. Finally, the Hamilton＇s principle of high-order Lagrangian function is given.

VARIATIONAL PRINCIPLES OF FLUID FULLFILLED ELASTIC SOLIDS

The generalized variational principles of isothermal quasi-static fluid full-filled elastic solids are established by using Variational Integral Method. Then by introducing constraints, several kinds of variational principles are worked out, including five-field variable, four-field variable, three-field variable and two-field variable formulations. Some new variational principles are presented besides the principles noted in the previous works. Based on variational principles, finite element models can be set up.

THE REGULARITY OF QUASI-MINIMA AND ω-MINIMA OF INTEGRAL FUNCTIONALS

In this article, we have two parts. In the first part, we are concerned with the locally Hlder continuity of quasi-minima of the following integral functional ∫Ωf（x, u, Du）dx, （1） where Ω is an open subset of Euclidean N-space （N ≥ 3）, u：Ω → R,the Carath′eodory function f satisfies the critical Sobolev exponent growth condition ｜Du｜^p＊ ｜u｜^p＊-a（x） ≤ f（x,u,Du） ≤ L（｜Du｜^p＋｜u｜^p＊ ＋ a（x））, （2） where L≥1, 1pN,p^＊ = Np/N-p , and a（x） is a nonnegative function that lies in a suitable Lp space. In the second part, we study the locally Hlder continuity of ω-minima of （1）. Our method is to compare the ω-minima of （1） with the minima of corresponding function determined by its critical Sobolev exponent growth condition. Finally, we obtain the regularity by Ekeland’s variational principal.

Two-step Design of Critical Control Systems Using Disturbance Cancellation Integral Controllers

An efficient critical control system design is proposed in this paper. The key idea is to decompose the design problem into two simpler design steps by the technique used in the classical loop transfer recovery method （LTR）. The disturbance cancellation integral controller is used as a basic controller. Since the standard loop transfer recovery method cannot be applied to the disturbance cancellation controller, the nonstandard version recently found is used for the decomposition. Exogenous inputs with constraints both on the amplitude and rate of change are considered. The majorant approach is taken to obtain the analytical sufficient matching conditions. A numerical design example is presented to illustrate the effiectiveness of the proposed design.

EQUIVALENT BOUNDARY INTEGRAL EQUATIONS WITH INDIRECT VARIABLES FOR PLANE ELASTICITY PROBLEMS

The exact form of the exterior problem for plane elasticity problems was produced and fully proved by the variational principle.Based on this,the equivalent boundary integral equations(EBIE) with direct variables,which are equivalent to the original boundary value problem,were deduced rigorously.The conventionally prevailing boundary integral equation with direct variables was discussed thoroughly by some examples and it is shown that the previous results are not EBIE.

Connection between the Principles of Thermodynamics and the Conservation Laws: Physical Meaning of the Principles of Thermodynamics

It has been shown that the first principle of thermodynamics follows from the conservation laws for energy and linear momentum. And the second principle of thermodynamics follows from the first principle of thermodynamics under realization of the integrating factor (namely, temperature) and is a conservation law. The significance of the first principle of thermodynamics consists in the fact that it specifies the thermodynamic system state, which depends on interaction between conservation laws and is non-equilibrium due to a non-commutativity of conservation laws. The realization of the second principle of thermodynamics points to a transition of the thermodynamic system state into a locally-equilibrium state. Phase transitions are examples of such transitions.

SINGULAR CONTROL OF STOCHASTIC VOLTERRA INTEGRAL EQUATIONS

This paper deals with optimal combined singular and regular controls for stochastic Volterra integral equations,where the solution X^(u,ξ)(t)=X(t)is given X(t)=φ(t)+∫_(0)^(t) b(t,s,X(s),u(s))ds+∫_(0)^(t)σ(t,s,X(s),u(s))dB(s)+∫_(0)^(t)h(t,s)dξ(s).by Here d B(s)denotes the Brownian motion It?type differential,ξdenotes the singular control(singular in time t with respect to Lebesgue measure)and u denotes the regular control(absolutely continuous with respect to Lebesgue measure).Such systems may for example be used to model harvesting of populations with memory,where X(t)represents the population density at time t,and the singular control processξrepresents the harvesting effort rate.The total income from the harvesting is represented by J(u, ξ) = E[∫_(0)^(t) f_(0)(t,X(t), u(t))dt + ∫_(0)^(t)f_(1)(t,X(t))dξ(t) + g(X(T))] for the given functions f0,f1 and g,where T>0 is a constant denoting the terminal time of the harvesting.Note that it is important to allow the controls to be singular,because in some cases the optimal controls are of this type.Using Hida-Malliavin calculus,we prove sufficient conditions and necessary conditions of optimality of controls.As a consequence,we obtain a new type of backward stochastic Volterra integral equations with singular drift.Finally,to illustrate our results,we apply them to discuss optimal harvesting problems with possibly density dependent prices.

Ethical framework for artificial intelligence in healthcare research:A path to integrity

The integration of Artificial Intelligence(AI)into healthcare research promises unprecedented advancements in medical diagnostics,treatment personalization,and patient care management.However,these innovations also bring forth significant ethical challenges that must be addressed to maintain public trust,ensure patient safety,and uphold data integrity.This article sets out to introduce a detailed framework designed to steer governance and offer a systematic method for assuring that AI applications in healthcare research are developed and executed with integrity and adherence to medical research ethics.

Stochastic Maximum Principle for Square-Integrable Optimal Control of Linear Stochastic Systems

The authors give a stochastic maximum principle for square-integrable optimal control of linear stochastic systems.The control domain is not necessarily convex and the cost functional can have a quadratic growth.In particular,they give a stochastic maximum principle for the linear quadratic optimal control problem.

Geometric formulations and variational integrators of discrete autonomous Birkhoff systems

The variational integrators of autonomous Birkhoff systems are obtained by the discrete variational principle. The geometric structure of the discrete autonomous Birkhoff system is formulated. The discretization of mathematical pendulum shows that the discrete variational method is as effective as symplectic scheme for the autonomous Birkhoff systems.

Research and application of sidewall stability predic-tion method based on analytic hierarchy process and fuzzy integrative evaluation method

As a difficult problem, sidewall instability has been beset drilling workers all the time. Not only does it cause huge economic losses, but also it determines the success or failure of drilling engineering. Due to complex relationship between various factors which influence sidewall stability, it hasn’t been found a widely applied method to predicate sidewall stability so far. Therefore, in order to formulate corresponding measures to ensure successful drilling, searching for a kind of better method to forecast sidewall stability before drilling becomes an imperative and significant topic for drilling engineering. On the basis of traditional sidewall stability analytical method, we have put forward the Fuzzy Comprehensive Evaluation Method to forecast sidewall stability regulation using physico-chemical performance parameters of the clay mineral. This method has been improved by introducing the Analytic Hierarchy Process (AHP) and the Maximum Subjection Principle in the application process. After introducing Analytic Hierarchy Process to identify weight, and Maximum Subjection Principle to obtain evaluation results, it has reduced the influence of human factors and enhanced the accuracy of the fuzzy evaluation results. The application in Hailaer Area indicates that this method can predict sidewall stability of gas-oil well with high credibility and strong practicability.

Integrated device for multiscale series vibration reduction and energy harvesting

A multi-degree-of-freedom device is proposed,which can achieve efficient vibration reduction as the main objective and energy harvesting as the secondary purpose.The device comprises a multiscale nonlinear vibration absorber(NVA)and piezoelectric components.Energy conversion and energy measurement methods are used to evaluate the device performance from multiple perspectives.Research has shown that this device can efficiently transfer transient energy from the main structure and convert a portion of transient energy into electrical energy.Main resonance and higher-order resonance are the main reasons for efficient energy transfer.The device can maintain high vibration reduction performance even when the excitation amplitude changes over a large range.Compared with the single structures with and without precompression,the multiscale NVA-piezoelectric device offers significant vibration reduction advantages.In addition,there are significant differences in the parameter settings of the two substructures for vibration reduction and energy harvesting.

New way to construct high order Hamiltonian variational integrators

This paper develops a new approach to construct variational integrators. A simplified unconventional Hamilton＇s variational principle corresponding to initial value problems is proposed, which is convenient for applications. The displacement and mo- mentum are approximated with the same Lagrange interpolation. After the numerical integration and variational operation, the original problems are expressed as algebraic equations with the displacement and momentum at the interpolation points as unknown variables. Some particular variational integrators are derived. An optimal scheme of choosing initial values for the Newton-Raphson method is presented for the nonlinear dynamic system. In addition, specific examples show that the proposed integrators are symplectic when the interpolation point coincides with the numerical integration point, and both are Gaussian quadrature points. Meanwhile, compared with the same order symplectic Runge-Kutta methods, although the accuracy of the two methods is almost the same, the proposed integrators are much simpler and less computationally expensive.

Path-dependent backward stochastic Volterra integral equations with jumps,differentiability and duality principle

We study the existence and uniqueness of a solution to path-dependent backward stochastic Volterra integral equations(BSVIEs)with jumps,where path-dependence means the dependence of the free term and generator of a path of a c`adl`ag process.Furthermore,we prove path-differentiability of such a solution and establish the duality principle between a linear path-dependent forward stochastic Volterra integral equation(FSVIE)with jumps and a linear path-dependent BSVIE with jumps.As a result of the duality principle we get a comparison theorem and derive a class of dynamic coherent risk measures based on path-dependent BSVIEs with jumps.