Design and Evaluation of a Differential Accelerometer for Drop-Tower Equivalence Principle Test with Rotating Masses

A differential accelerometer comprising of two rotating masses made of the same material is proposed for drop tower-based free-fall testing of the spin-spin force between the rotating mass and the Earth. The measurement is performed by placing the two concentric masses of very different momenta in a vacuum drop capsule which is falling freely in the Earth＇s gravitational field. A nonzero output of the differential aeeelerometer is an indication of possible violation of new equivalence principle （NEP）. We present the conceptual design of a modified free-fall NEP experiment which can be performed at the Belting drop tower. Design and evaluation of the differential accelerometer with a hybrid electrostatic/magnetic suspension system are presented to accommodate for operation on ground and drop-tower tests. Details specific to the measurement uncertainty are discussed to yield an NEP test accuracy of 7.2×10^-9.

The Principle of Differentiation into Physical and Mathematical Theories

The article formulates the main principle of physics, which underlies this science. This principle has been called by the author of this article the Principle of differentiation into physical and mathematical theories. The article gives examples of the application of this principle in quantum mechanics and cosmology. A more detailed proof of the principle of equivalence of the electromagnetic field and the field of strong interaction to a free material particle is given. This principle, formulated in the article “Electrodynamics in Curvilinear Coordinates and the Equation of a Geodesic Line”, revealed the nature of the mass of elementary particles and became the basis for the formulation of the Principle of differentiation into physical and mathematical theories.

Conservation laws for Birkhoffian systems of Herglotz type

Conservation laws for the Birkhoffian system and the constrained Birkhoffian system of Herglotz type are studied. We propose a new differential variational principle, called the Pfaff-Birkhoff-d＇Alembert principle of Herglotz type. Birkhoff＇s equations for both the Birkhoffian system and the constrained Birkhoffian system of Herglotz type are obtained. According to the relationship between the isochronal variation and the nonisochronal variation, the conditions of the invariance for the Pfaff-Birkhoff-d＇Alembert principle of Herglotz type are given. Then, the conserved quantities for the Birkhoffian system and the constrained Birkhoffian system of Herglotz type are deduced. Furthermore, the inverse theorems of the conservation theorems are also established.

A new type of adiabatic invariants for disturbed non-conservative nonholonomic system

According to the Herglotz variational principle and differential variational principle of Herglotz type, we study the adiabatic invariants for a non-conservative nonholonomic system. Firstly, the differential equations of motion of the non-conservative nonholonomic system based upon the generalized variational principle of Herglotz type are given, and the exact invariant for the non-conservative nonholonomic system is introduced. Secondly, a new type of adiabatic invariant for the system under the action of a small perturbation is obtained. Thirdly, the inverse theorem of the adiabatic invariant is given. Finally, an example is given.

Stochastic maximum principle for mean-field forward-backward stochastic control system with terminal state constraints

In this paper,we consider an optimal control problem with state constraints,where the control system is described by a mean-field forward-backward stochastic differential equation(MFFBSDE,for short)and the admissible control is mean-field type.Making full use of the backward stochastic differential equation theory,we transform the original control system into an equivalent backward form,i.e.,the equations in the control system are all backward.In addition,Ekeland's variational principle helps us deal with the state constraints so that we get a stochastic maximum principle which characterizes the necessary condition of the optimal control.We also study a stochastic linear quadratic control problem with state constraints.

Stochastic Differential Games with Reflection and Related Obstacle Problems for Isaacs Equations

In this paper we first investigate zero-sum two-player stochastic differential games with reflection, with the help of theory of Reflected Backward Stochastic Differential Equations （RBSDEs）. We will establish the dynamic programming principle for the upper and the lower value functions of this kind of stochastic differential games with reflection in a straightforward way. Then the upper and the lower value functions are proved to be the unique viscosity solutions to the associated upper and the lower Hamilton-Jacobi-Bettman-Isaacs equations with obstacles, respectively. The method differs significantly from those used for control problems with reflection, with new techniques developed of interest on its own. Further, we also prove a new estimate for RBSDEs being sharper than that in the paper of E1 Karoui, Kapoudjian, Pardoux, Peng and Quenez （1997）, which turns out to be very useful because it allows us to estimate the LP-distance of the solutions of two different RBSDEs by the p-th power of the distance of the initial values of the driving forward equations. We also show that the unique viscosity solution to the approximating Isaacs equation constructed by the penalization method converges to the viscosity solution of the Isaacs equation with obstacle.

A Systematic Analysis of the Theory and Practice of Syndrome Differentiation

Syndrome differentiation is a methodology unique to Chinese medicine. It threads the diagnosis process with clinical treatment into a holistic web of links to determine and regulate the patterns of dysfunctions in the human body. It is seen as the essence of Chinese medicine because it takes into account the theoretical principles, diagnostic methodologies and the modality of treatment holistically. In this process the progressive development and changes of syndromes are also considered by the physician. This paper is a systematic study of the methodology of syndrome differentiation in relation to its clinical applications in the treatment of diseases. To illustrate the efficacy of syndrome differentiation, the relationship between pattern identification and diseases is analysed to provide a guiding principle for integration between Chinese medicine and Western medicine. nclude cancer, cardiovascular and metabolic syndromes. A study of renal and hepatic Diseases being selected include cancer, cardiovascular and metabolic syndromes. A study of renal and hepatic diseases related to lifestyle is also included to highlight the clinical efficacy of syndrome differentiation. The paper also includes an analytical summary of the theoretical advancements made in integrative differentiation methodology during the past five decades which links to the recent clinical thinking and practice.