New Compacton Solutions of Nonlinearly Dispersive R(m, n) Equations

In this paper, we establish exact solutions for the R(m,n) equations by using an sn-cn method. As a result, abundant new compactons, i.e. solitons with the absence of infinite wings, new type of Jacobi elliptic function, solitary wave and periodic wave solutions, of this equation are obtained with minimal calculations. The properties of the R(m,n) equations are shown in figures.     

An alternative f(R, T) gravity theory and the dark energy problem

Recently, a generalized gravity theory was proposed by Harko et al. where the Lagrangian density is an arbitrary function of the Ricci scalar R and the trace of the stress-energy tensor T, known as F(R,T) gravity. In their derivation of the field equations, they have not considered conservation of the stress-energy tensor. In the present work, we have shown that a part of the arbitrary function f(R,T) can be determined if we take into account of the conservation of stress-energy tensor, although the form of the field equations remain similar. For homogeneous and isotropic model of the universe the field equations are solved and corresponding cosmological aspects has been discussed. Finally, we have studied the energy conditions in this modified gravity theory both generally and a particular case of perfect fluid with constant equation of state.     

振动盘式粘度计及R403B和R413A气相粘度的实验测量

建立了国内第一台振动盘式粘度计测量气体的粘度，扭丝采用钛镍合金丝．得到了测量的工作方程．在利用测量的ＨＣＦＣ２２的气相粘度进行校核的基础上测量了Ｒ４０３Ｂ在温度３０３－３６３Ｋ，压力０．１～２．１４ＭＰａ 内的气相粘度，及Ｒ４１３Ａ在温度３０５～３６３Ｋ，压力０．１～１．８２ ＭＰａ 内的气相粘度，并回归了其粘度计算方程．     

SL(2,R) PRINCIPAL PROLONGATION STRUCTURES OF SOLITON EQUATIONS AND THEIR CONSERVATION LAWS

We present the concept of principal prolongation structure (PPS) and a covariant criterion of the completeness of conserva-tion currents for the PPS of class of nonlinear evolution equations (NEES).The SL(2,R) × R'(l) PPS for AKNS systems is constructed, a new set of infinite number of polynomial conservation currents (PCCs) corresponding to the nonlinearity of SL (2,R) group manifold is given. These currents together with the usual PCCS of AKNS systems satisfy a covariant equation for the SL(2,R) × R'(l) PPS. This equation gives rise to a criterion of completeness of these currents. As an example,the sine-Gordon system is analysed.     

新的适用于整个热力面的1,1,1,2-四氟乙烷(R134a)跨接状态方程

1前言作者建立了一个新型的符合临界重整化群理论的跨接状态方程，能够描述物质的整个区域热力性质山。鉴于R134a是R12的新的主要替代制冷剂，为了计算其整个区域的热力性质，本文将新跨接状态方程应用于R134a，以便提供一个能在整个区域计算R134a热力性质的状态方程。2新跨接状态方程作者建立了以下型式的新跨接状态方程l‘］：上式中，西方一r一IDZ户一p巾c；，一DI—TD；T—To／T；产为密度；pc为临界密度；T为温度；To为临界温度；矿对比过余Helmholtz自由能；A是Helmholtz自由能。新函数中，a。一30，a，一10；0—0．325和西一…     

Solitons and SL(2, R)

The known relationship between non-linear partial differential equations which have soliton solutions, and SL (2, R), is developed to the point where it provides a framework for discussing Bäcklund transformations, and equations for the inverse scattering method.     

Spherical Gravitational Collapse in f(R) Gravity with Linear Equation of State

In a paper[Gen. Relativ. Gravit. 48 (2016) 57] Chakrabarti and Banerjee investigated perfect fluid collapse in f(R) gravity model and claimed that such a collapse is possible. In this paper we show that without the assumption of dark energy it is not possible that perfect fluid spherical gravitational collapse will occur. We have solved the field equations by assuming linear equation of state (p=ωμ) in metric f(R) gravity with ω=-1. It is shown that Chakrabarti and Banerjee reached to false conclusion as they derived wrong field equations. We have also discussed formation of apparent horizon and singularity.     

f(R,L m ) gravity

We generalize the f(R) type gravity models by assuming that the gravitational Lagrangian is given by an arbitrary function of the Ricci scalar R and of the matter Lagrangian L _m . We obtain the gravitational field equations in the metric formalism, as well as the equations of motion for test particles, which follow from the covariant divergence of the energy-momentum tensor. The equations of motion for test particles can also be derived from a variational principle in the particular case in which the Lagrangian density of the matter is an arbitrary function of the energy density of the matter only. Generally, the motion is non-geodesic, and it takes place in the presence of an extra force orthogonal to the four-velocity. The Newtonian limit of the equation of motion is also considered, and a procedure for obtaining the energy-momentum tensor of the matter is presented. The gravitational field equations and the equations of motion for a particular model in which the action of the gravitational field has an exponential dependence on the standard general relativistic Hilbert–Einstein Lagrange density are also derived.     

New Soliton Solutions with Compact Support for a Family of Two-Parameter Regularized Long-Wave Boussinesq Equations

Searching for special solitary wave solutions with compact support is of important significance in soliton theory. In this paper, to understand the role of nonlinear dispersion in pattern formation, a family of the regularized longwave Boussincsq equations with fully nonlinear dispersion (simply called R(m, n) equations), utt + a( un )xx + b(um )xxtt = 0(a, b const.), is studied. New solitary wave solutions with compact support of R(m, n) equations are found. In addition we find another compacton solutions of the two special cases, R(2, 2) equation and R(3, 3) equation. It is found that the nonlinear dispersion term in a nonlinear evolution equation is not a necessary condition of that it possesses compacton solutions.     

Energy Bounds for Static Spherically Symmetric Spacetime in f(R,G) Gravity

The main purpose of this paper is to investigate energy bounds in the context of f(R,G) gravity. To meet this aim, we choose static spherically symmetric spacetime in f(R,G) gravity to develop the field equations. We select three different models of f(R,G) gravity, which are thoroughly discussed in the literature. Firstly, the inequalities are formulated using energy bounds and then viability of the considered models are checked respectively. Graphical analysis show that specific f(R,G) gravity models are satisfied under suitable values of model parameters. It is shown that in a certain case energy bounds are satisfied expect SEC, which supports the late time acceleration expansion of unverse.     

Energy Bounds for Static Spherically Symmetric Spacetime in f(R,G) Gravity

The main purpose of this paper is to investigate energy bounds in the context of f(R, G) gravity. To meet this aim, we choose static spherically symmetric spacetime in f(R, G) gravity to develop the field equations. We select three different models of f(R, G) gravity, which are thoroughly discussed in the literature. Firstly, the inequalities are formulated using energy bounds and then viability of the considered models are checked respectively. Graphical analysis show that specific f(R, G) gravity models are satisfied under suitable values of model parameters. It is shown that in a certain case energy bounds are satisfied expect SEC, which supports the late time acceleration expansion of unverse.     

Higher-Dimensional Integrable Systems Arising from Motions of Curves on S2(R) and S3(R)

We show that higher-dimensional integrable systems including the (2+1)-dimensional generalized sine-Gordon equation and the (2+1)-dimensional complex mKdV equation are associated with motions of surfaces induced by endowing with an extra space variable to the motions of curves on S²(R) and S³(R).     

Covariant Prolongation Structure of Konno-Asai-Kakuhata Equation

Based upon the covariant prolongation structures theory, we construct the sl(2,R)×R(ρ) prolongation structure for Konno-Asai-Kakuhata equation. By taking two and one-dimensional prolongation spaces, we obtain the inverse scattering equations given by Konno et al. and the corresponding Riccati equation. The Bäcklund transformations are also presented.     

Kinematics and dynamics off(R) theories of gravity

We generalise the equations governing relativistic fluid dynamics given by Ehlers and Ellis for general relativity, and by Maartens and Taylor for quadratic theories, to generalisedf(R) theories of gravity. In view of the usefulness of this alternative framework to general relativity, its generalisation can be of potential importance for deriving analogous results to those obtained in general relativity. We generalise, as an example, the results of Maartens and Taylor to show that within the framework of generalf(R) theories, a perfect fluid spacetime with vanishing vorticity, shear and acceleration is Friedmann-Lemaître-Robertson-Walker only if the fluid has in addition a barotropic equation of state. It then follows that the Ehlers-Geren-Sachs theorem and its almost extension also hold forf(R) theories of gravity.     

First order formalism off(R) gravity

The first order formalism is applied to study the field equations of a general Lagrangian density for gravity of the form . These field equations correspond to theories which are a subclass of conformally metric theories in which the derivative of the metric is proportional to the metric by a Weyl vector field. The resulting geometrical structure is unique, except whenf(R)=aR ², in the sense that the Weyl field is identifiable in terms of the trace of the energy-momentum tensor and its derivatives. In the casef(R)=aR ² the metric is only defined up to a conformai factor. We discuss the matter conservation equations which are implied by the invariance of the theories under diffeomorphisms. We apply the results to the case of dust and obtain that in general the dust particles will not follow geodesic Unes. We consider the linearized field equations and apply them to obtain the weak field slow motion limit. It is found that the gravitational potential acquires a new term which depends linearly on the mass density. The importance of these new equations is briefly discussed.     

Rotating,Stationary, Axially Symmetric Spacetimes with Collisionless Matter

The existence of stationary solutions to the Einstein–Vlasov system which are axially symmetric and have non-zero total angular momentum is shown. This provides mathematical models for rotating, general relativistic and asymptotically flat non-vacuum spacetimes. If angular momentum is allowed to be non-zero, the system of equations to solve contains one semilinear elliptic equation which is singular on the axis of rotation. This can be handled very efficiently by recasting the equation as one for an axisymmetric unknown on ${\mathbb{R}^5}$ .     

Bianchi types I and V bulk viscous fluid cosmological models in f(R,T) gravity theory

In this paper we present non-singular Bianchi types I and V cosmological models, in the presence of bulk viscous fluid and within the framework of f(R,T) gravity theory. Exact solutions to the field equations are obtained by choosing a particular form of the function f(R,T) and a special value for the average scale factor of the model, which corresponds to a time- dependent deceleration parameter. The cosmological models initially accelerate for a certain period of time and thereafter decelerate. The physical and kinematical properties of the models of the universe are discussed.     

A bridge between hyperspherical and integro-differential approaches to the many-body bound states

The solution of the Schrödinger equation can be obtained from the one of a system of coupled differential equations generated from the potential harmonic expansion of the bound-state wave function of a system of identical particles governed by two-body central interactions. It is shown that the system of coupled equations can be transformed into an equivalent integro-differential equation. For three bosons inS states this equation is identical to the Faddeev equation as written by Noyes. The integro-differential equations describing the triton for non-central realisticN-N forces are explicitly given.Laboratoire associé au C.N.R.S.     

Numerical Simulation of Antennae by Discrete Exterior Calculus

Numerical simulation of antennae is a topic in computational lectromagnetism, which is concerned with the numerical study of Maxwell equations. By discrete exterior calculus and the lattice gauge theory with coefficient R, weobtain the Bianchi identity on prism lattice. By defining an inner product of discrete differential forms, we derive the source equation and continuity equation. Those equations compose the discrete Maxwell equations in vacuum case on discrete manifold, which are implemented on Java development platform to simulate the Gaussian pulse radiation on antennaes.