Research and Application of a Multi-Field Co-Simulation Data Extraction Method Based on Adaptive Infinitesimal Element

Regarding the spatial profile extraction method of a multi-field co-simulation dataset,different extraction directions,locations,and numbers of profileswill greatly affect the representativeness and integrity of data.In this study,a multi-field co-simulation data extractionmethod based on adaptive infinitesimal elements is proposed.Themultifield co-simulation dataset based on related infinitesimal elements is constructed,and the candidate directions of data profile extraction undergo dimension reduction by principal component analysis to determine the direction of data extraction.Based on the fireworks algorithm,the data profile with optimal representativeness is searched adaptively in different data extraction intervals to realize the adaptive calculation of data extraction micro-step length.The multi-field co-simulation data extraction process based on adaptive microelement is established and applied to the data extraction process of the multi-field co-simulation dataset of the sintering furnace.Compared with traditional data extraction methods for multi-field co-simulation,the approximate model constructed by the data extracted from the proposed method has higher construction efficiency.Meanwhile,the relative maximum absolute error,root mean square error,and coefficient of determination of the approximationmodel are better than those of the approximation model constructed by the data extracted from traditional methods,indicating higher accuracy,it is verified that the proposed method demonstrates sound adaptability and extraction efficiency.

Infinitesimal dividing modeling method for dual suppliers inventory model with random lead times

As one of the basic inventory cost models, the （Q, τ）inventory cost model of dual suppliers with random procurement lead time is mostly formulated by using the concepts of ＂effective lead time＂ and ＂lead time demand＂, which may lead to an imprecise inventory cost. Through the real-time statistic of the inventory quantities, this paper considers the precise （Q, τ） inventory cost model of dual supplier procurement by using an infinitesimal dividing method. The traditional modeling method of the inventory cost for dual supplier procurement includes complex procedures. To reduce the complexity effectively, the presented method investigates the statistics properties in real-time of the inventory quantities with the application of the infinitesimal dividing method. It is proved that the optimal holding and shortage costs of dual supplier procurement are less than those of single supplier procurement respectively. With the assumption that both suppliers have the same distribution of lead times, the convexity of the cost function per unit time is proved. So the optimal solution can be easily obtained by applying the classical convex optimization methods. The numerical examples are given to verify the main conclusions.

ON THE INFINITESIMAL ISOMETRIC DEFORMATIONS OF SUBMANIFOLDS

In this paper, we consider the infinitesimal I- and Il-isometry deformations of submanifolds immersed in a space form N of constant curvature. We obtain some results which are new even in the case of N being the Euclidean space. At the same time, we generalize some classical results in E-3 Go the submanifolds immersed in a space form of constant curvature.

Characteristic Functional Structure of Infinitesimal Symmetry Transformations for Nonholonomic System

It was proved that velocity-dependent infinitesima l symmetry transformations of nonholonomic systems have a characteristic functio nal structure, which could be formulated by means of an auxiliary symmetry tra nsformation function and is manifestly dependent upon constants of motion of th e system. An example was given to illustrate the applicability of the results.

From Braided Infinitesimal Bialgebras to Braided Lie Bialgebras

The present paper is a continuation of [1], where we considered braided infinitesimal Hopf algebras (i.e., infinitesimal Hopf algebras in the Yetter-Drin feld category for any Hopf algebra H), and constructed their Drinfeld double as a generalization of Aguiar’s result. In this paper we mainly investigate the necessary and sufficient condition for a braided infinitesimal bialgebra to be a braided Lie bialgebra (i.e., a Lie bialgebra in the category ).

Influence of Infinitesimal Neglected Effects by Current Theory of Gravitation and Experiments on the Stability of the Universe

From the hypotheses compatible with microphysics theory, this paper establishes a new theoretical model of static universal gravitation and deduces new formula of the theory of universal gravitation. In a first order approximation, the new formula shows the inverse-square law consistent with Newton formula, which would indicate that the new theory is consistent with the experimental results that can be reasonably explained by the current theory of gravitation. The parameters and higher order terms among the coefficients of this paper reveal the numerous infinitesimal neglected effects by current theory and experiments. In the first order approximation, the meanings of the physical parameters included in coefficients are analyzed and the infinitesimal neglected effects are applied in the study of the stability of the universe, which overcomes the difficulty of singularity in the cosmology of Newton, Einstein, etc., and concludes that the boundary of universe is unlimited, without any need of the hypothesis that the universe starts off with the big bang. Therefore, this paper establishes a harmonious and ingenious relationship between microphysics and macrophysics theories. In addition, through the analysis of the formula derived from the theory of this paper, it is found that: in general, the gravitational constant is not always a constant in the gravitation formula requiring high precision;from the perspective of the interaction of field quantum, the acting force may not be equal to counter-acting force under the interaction of indirect contact;the gravity process is an exothermic process;in the gravitational process, annihilation effects may exist amongst gravitons;reciprocal translation may exist amongst fundamental forces.

RELATIONS BETWEEN PERFORMANCE POTENTIALS AND INFINITESIMAL REALIZATION FACTORS IN CLOSED QUEUEING NETWORKS

In this paper,the concept of the infinitesimal realization factor is extended to the parameter dependent performance functions in closed queueing networks.Then the concepts of realization matrix (its elements are called realization factors) and performance potential are introduced,and the relations between infinitesimal realization factors and these two quantities are discussed.This provides a united framework for both IPA and non IPA approaches.Finally,another physical meaning of the service rate is given.

Infinitesimal nonrigidity of convex surfaces with planar boundary

In the present paper infinitesimal nonrigidity of a class of convex surfaces with planar boundary is given. This result shows that if the image of the Gauss map of an evolution convex surface with planar boundary covers some hemisphere, this surface may be of infinitesimal nonrigidity for the isometric deformation of planar boundary.

ON THE TRICOMI PROBLEM OF INFINITESIMAL DEFORMATION EQUATION FOR SURFACES WITH MIXED CURVATURE(Ⅱ)——EXISTENCE OF SOLUTION

In this paper, the L, weak solution and H^1 strong solution to the Tricomi problem of in-finitesimal deformation equation for surfaces witb a mixed curvatute are proved under veryweak conditions.

Equivalent construction of the infinitesimal time translation operator in algebraic dynamics algorithm for partial differential evolution equation

We give an equivalent construction of the infinitesimal time translation operator for partial differential evolution equation in the algebraic dynamics algorithm proposed by Shun-Jin Wang and his students. Our construction involves only simple partial differentials and avoids the derivative terms of δ function which appear in the course of computation by means of Wang-Zhang operator. We prove Wang’s equivalent theorem which says that our construction and Wang-Zhang’s are equivalent. We use our construction to deal with several typical equations such as nonlinear advection equation, Burgers equation, nonlinear Schrodinger equation, KdV equation and sine-Gordon equation, and obtain at least second order approximate solutions to them. These equations include the cases of real and complex field variables and the cases of the first and the second order time derivatives.

High-order field theory and a weak Euler–Lagrange–Barut equation for classical relativistic particle-field systems

In both quantum and classical field systems,conservation laws such as the conservation of energy and momentum are widely regarded as fundamental properties.A broadly accepted approach to deriving conservation laws is built using Noether's method.However,this procedure is still unclear for relativistic particle-field systems where particles are regarded as classical world lines.In the present study,we establish a general manifestly covariant or geometric field theory for classical relativistic particle-field systems.In contrast to quantum systems,where particles are viewed as quantum fields,classical relativistic particle-field systems present specific challenges.These challenges arise from two sides.The first comes from the mass-shell constraint.To deal with the mass-shell constraint,the Euler–Lagrange–Barut(ELB)equation is used to determine the particle's world lines in the four-dimensional(4D)Minkowski space.Besides,the infinitesimal criterion,which is a differential equation in formal field theory,is reconstructed by an integro-differential form.The other difficulty is that fields and particles depend on heterogeneous manifolds.To overcome this challenge,we propose using a weak version of the ELB equation that allows us to connect local conservation laws and continuous symmetries in classical relativistic particle-field systems.By applying a weak ELB equation to classical relativistic particle-field systems,we can systematically derive local conservation laws by examining the underlying symmetries of the system.Our proposed approach provides a new perspective on understanding conservation laws in classical relativistic particle-field systems.

Why Is an Integral an Accurate Value?

The derivative and integral in calculus are both exact values. To explain this reason, the integration interval can be infinitely subdivided. The difference in area between curved trapezoids and rectangles can be explained by the theory of higher-order infinitesimal, leading to the conclusion that the difference between the two is an infinitesimal value. From this, it can be inferred that the result obtained by integration is indeed an accurate value.

Could Long-Term Stability Last Forever?

The subject of the present paper is to prove that the recently introduced conjecture of boundedness puts a ban over the view of stability as asymptotic property. This result comes in sharp contrast with the prescription of the traditional thermodynamics and statistical physics which consider the existence of equilibrium as asymptotic property of all systems. The difference commences from the use of infinitesimal calculus as the basic implement for modelling by the latter while the primary premise of the conjecture of boundedness is sustaining the energy/matter/information permanently bounded and finite. The latter property overrules the infinitesimal calculus as the major implement of modelling because, among all, it is proven that the traditional one suffers unsoluble difficulties.

Conformal invariance and Hojman conserved quantities of first order Lagrange systems

In this paper the conformal invariance by infinitesimal transformations of first order Lagrange systems is discussed in detail. The necessary and sufficient conditions of conformal invariance and Lie symmetry simultaneously by the action of infinitesimal transformations are given. Then it gets the Hojman conserved quantities of conformal invariance by the infinitesimal transformations. Finally an example is given to illustrate the application of the results.

Conformal invariance and conserved quantities of dynamical system of relative motion

This paper discusses in detail the conformal invariance by infinitesimal transformations of a dynamical system of relative motion. The necessary and sufficient conditions of conformal invariance and Lie symmetry are given simultaneously by the action of infinitesimal transformations. Then it obtains the conserved quantities of conformal invariance by the infinitesimal transformations. Finally an example is given to illustrate the application of the results.

Experimental study on ceramic balls impact composite armor

Ceramic balls represent a new type of damaging element,and studies on their damaging power of composite armor are required for a comprehensive evaluation of the effectiveness of various types of weapons.The goal of this study was to determine the impact ofφ7 mm toughened Al2 O3 ceramic balls on a composite ceramic/metal armor.The influences of the ceramic panel and the thickness of the metal backing material on the destroying power of the ceramic balls were first determined.Based on the agreement between numerical simulation,experimental results,and calculation models of the target plate resistance,the response mechanism of the ceramic balls was further analyzed.The results indicate that for a back plate of Q235 steel,with an increasing thickness of the ceramic panel,the piercing speed limit of the ceramic balls gradually increases and the diameter of the out-going hole on the metal back decreases.Different conditions were tested to assess the effects on the piercing speed,the diameter of the out-going hole,the micro-element stress,and the integrity of the recovered ceramic bowl.

Perturbation to Noether Symmetries and Adiabatic Invariants for Generalized Birkhoff Systems Based on El-Nabulsi Dynamical Model

With the action of small perturbation on generalized El-Nabulsi-Birkhoff fractional equations,the perturbation to Noether symmetries and adiabatic invariants are studied under the framework of El-Nabulsi′s fractional model.Firstly,based on the invariance of El-Nabulsi-Pfaff action under the infinitesimal transformations of group,the exact invariants are given.Secondly,on the basis of the definition of higher order adiabatic invariants of a dynamical system,the adiabatic invariants of the Noether symmetric perturbation for disturbed generalized El-Nabulsi′s fractional Birkhoff system are presented under some conditions,and some special cases are discussed.Finally,an example known as Hojman-Urrutia problem is given to illustrate the application of the results.

Automatic Generation of Optimally Rigid Formations Using Decentralized Methods

In this paper, decentralized methods of optimally rigid graphs generation for formation control are researched. The notion of optimally rigid graph is first defined in this paper to describe a special kind of rigid graphs. The optimally rigid graphs can be used to decrease the topology complexity of graphs while maintaining their shapes. To minimize the communication complexity of formations, we study the theory of optimally rigid formation generation. First, four important propositions are presented to demonstrate the feasibility of using a decentralized method to generate optimally rigid graphs. Then, a formation algorithm for multi-agent systems based on these propositions is proposed. At last, some simulation examples are given to show the efficiency of the proposed algorithm.

Lie symmetry algebra of one-dimensional nonconservative dynamical systems

Lie symmetry algebra of linear nonconservative dynamical systems is studied in this paper. By using 1-1 mapping, the Lie point and Lie contact symmetry algebras are obtained from two independent solutions of the one-dimensional linear equations of motion.

(r, s)-STABILITY OF UNFOLDING OF г-EQUIVARIANT BIFURCATION PROBLEM

In this paper,the (?)-equivariant (s, t)-equivalence relation and (?)-equivariant infinitesimally (r, s)-stability of (?)-equivariant bifurcation problem are defined. The criterion for (?)-equivariant infinitesimally (r, s)-stability is proven when (?) is a compact finite Lie group .Transversality condition is used to characterize the stability.