‘Disciplining Oneself’and‘Disciplining Others’in Social Life:On the Contemporary Significance of Confucius’s Principle of Loyalty and Reciprocity

In a moral sense,there is an essential di erence between“disciplining oneself”and“disciplining others”in that the former means one setting rules for and giving orders to oneself in regard to one’s own conduct,which are unconditionally compulsory,while the latter is exible in the sense that one’s rules and orders for oneself are not compulsory to others and cannot prohibit others from doing something.In principle,Confucius’s sayings,“do not impose upon others that which you would not wish for yourself”and“establish others in seeking to establish yourself and promote others in s eeking to promote yourself”have epitomized the line of demarcation between them.His doctrine of“not imposing upon others that which you would not wish for yourself,”though based on self-preservation and self-interest,represents a standard of conduct of highly universal value.If the overwhelming majority of a society follows it as their standard of conduct,refraining from harming others in order to protect oneself from harm,then the whole society will endure little,if not no,strife and struggle.

THE RECIPROCAL THEOREM AND LINEAR ELASTIC VARIATIONAL PRINCIPLES

In this paper classical linear elastic variational principles are systematically derivedfrom the reciprocal theorem and mixed variational principles of variations of boundaryconditions are given.

Scattering Relations for Two-Dimensional Electromagnetic Waves in Chiral Media

We consider the scattering of time-harmonic plane waves by an infinitely long penetrable chiral cylinder. The electromagnetic scattering problem is reduced to a transmission problem for a system of two-dimensional Helmholtz equations. We prove the classical reciprocity principle, a general scattering theorem and an optical theorem in R2. Using Herglotz wave functions we define the corresponding far field operator. Applying the general scattering theorem useful relations are proved for the reconstruction of the scatterer. We also prove that for real chirality measure of the penetrable scatterer the far field operator has a countable number of eigenvalues which lie on a circle.

On the Far Field Pattern for Acoustic Scattering by a Piecewise Homogeneous Obstacle in Two Dimensions

A time-harmonic plane acoustic wave is scattered by a piecewise homogeneous obstacle with a penetrable or impenetrable core. We construct in the close form an integral representation for the far field pattern in which we have incorporated the physical and geometrical characteristics of the scatterer. Through this representation, we obtain the far field pattern for this scatterer. We prove scattering relations between the far field patterns of two scattering problems due to two distinct incident waves on the same scatterer. In particular, we prove reciprocity and general scattering theorems. The optical theorem, connecting the total power that the scatterer extracts from the incident plane wave either by radiation or by absorption with the corresponding far field pattern of an incident plane wave, is recovered as a corollary of the general scattering theorem. Moreover, if we consider incident waves to be both a plane and a spherical, we derive a mixed reciprocity theorem. We define the corresponding far field operators and using these relations, we prove some properties that can be used for solving inverse scattering problems.

A Receiver Model for Ultrasonic Ray Tracing in an Inhomogeneous Anisotropic Weld

In this paper, a receiver model for ultrasonic ray tracing simulation is described. This is a complementary part of an existing simulation model and is the next step towards a numerical solution to the inverse problem and thus a NDT methodology for characterization of the dendrite orientation in a weld. The establishment of the receiver model is based on the electromechanical reciprocity principle. A concise retrospect of the weld model and the 2D model is made. The reciprocity principle is applied in an original way to handle the model problem including the back wall. Experimental qualitative validations for both P and SV waves on a specific weld are also made for C-scans included in this paper. Two different cases are studied. The first is a direct incidence of an ultrasonic ray towards the weld, and the second is a reflection from the back surface in the base material followed by an incidence to the weld. Even though mode-converted rays are excluded in the simulations, both the P and SV probe-models show the same behavior as the experimental results. The qualitative validation though reveals that it even if a thorough time-gating of received information would enable exclusion of mode-conversion in the model, inaccuracy of experimental results is affecting the evaluation of the weld model.

Motion Equation and Solution of Mushroom Cloud

Using model like hot air bloom with zero-weighted membrane wrapped hot air, surrounded by cold air, this paper sets up a partial differential equation (PDE) of motion of mushroom cloud by modifying Navier-Stokes (N-S) equations. The obtained equation is a vector PDE. It states that the derivative of velocity is with respect to time proportions to the gradient of temperature with respect to trace. Its solution is obtained by the method of separating variables for scalar function. These results have been compared with well agreement with literatures. Highlight: The Principle of Minimum Energy Release (PMER) is used to prove the pulse-mode of explosion of nuclear weapon, as great Earthquake, and optimum path problems.

Some Theorems in the Theory of Microstretch Thermomagnetoelectroelasticity

The linear dynamic theory of microstretch thermomagnetoelectroelasticity is studied in this paper.First,a reciprocity relation which involves two processes at different instants is established to form the basis of a uniqueness result and a reciprocal theorem.The proof of the reciprocal theorem avoids both using the Laplace transform and incorporating the initial conditions into the equations of motion.The uniqueness theorem is derived with no definiteness assumption on the elastic constitutive coefficients.Then the continuous dependence theorem is discussed upon two external data systems.Finally,the variational principle of Hamilton type which fully characterizes the solution of the mixed boundary-initial-value problem（mixed problem） is obtained.These theorems lay a solid foundation for further theoretical and numerical studies on microstretch thermomagnetoelectroelastic materials.