类似“分量形式”的动能定理与动能守恒定律

本文将牛顿第二定律在某个任意方向的分量式进行恒等数学变形，证明合力、位移、速度在该方向的三个投影之间存在类似于“分量形式”的动能定理，并对如何正确应用这种形式的动能定理进行了详细的讨论。

High-Resolution Hindcast of Record-Breaking Rainfall in Beijing and Impact of Topography

In this paper,a hindcast study of the record-breaking rainfall event occurring in Beijing on 21July 2012,is conducted by using the Weather Research and Forecasting(WRF)model forced by National Centers for Environmental Prediction(NCEP)Global Forecasting System(GFS)outputs,paired with an investigation of the impact of topography in this region.The results indicate that WRF can reasonably predict the salient features of orographic precipitation;the 24-h rainfall amount and spatial distribution compare reasonably well with the observations.The hindcast simulation also indicates that rainfall events can be predicted approximately 36 h ahead.When the topography is removed,the spatial distribution of rainfall changes remarkably,suggesting the importance of the topography in determining rainfall structure.These results also indicate that prediction of such city-scale heavy rainfall events would benefit from a high-resolution prediction system.

Mechanism and kinetics of coal utilization by thermal analysis

Coals are carbon-rich materials with excellent aromatic nature and macro- molecular structure. They pose great potential as the source of organic chemical feed- stock and high value-added carbonaceous materials in the 21st century. As some of the most important analytical methods, thermal analysis (TA) techniques with strong com- petence in materials characterization and reaction mechanism research, have been ex- tensively employed to accumulate the knowledge about coal conversion and utilization in a most effective, efficient and responsible way. Unfortunately, some efforts did not promote the sound growth of a systematic discipline, which might arise from the intrinsic drawback of conventional TA. Proposals on acquiring much more reliable understanding of the mechanism and kinetics of reactions were made in this review.

The Discrete Horizontal Complex on Lattice Space

We define discrete total differential forms on lattice space by. changing coefficients of discrete differential forms from functions only of n to functions also of dependent variables un and their partial differences. And the discrete exterior derivative extends to be discrete total differential map which is also nilpotent. Then a discrete horizontal complex can be derived and be proved to be exact by constructing homotopy operators.

Mathieu Progressive Waves

A new family of exact solutions to the wave equation representing relatively undistorted progressive waves is constructed using separation of variables in the elliptic cylindrical coordinates and one of the Bateman transforms. The general form of this Bateman transform in an orthogonal eurvilinear cylindrical coordinate system is discussed and a specific problem of physical feasibility of the obtained solutions, connected with their dependence on the cyclic coordinate, is addressed. The limiting case of zero eccentricity, in which the elliptic cylindrical coordinates turn into their circular cylindrical counterparts, is shown to correspond to the focused wave modes of the Bessel-Gauss type.

A new capacitive borehole tiltmeter for crustal deformation measurement and its performance analysis

Borehole inclinometers are important observation instruments used to measure ground tilt movement and monitor crustal deformation of solid tides and geological landslide disasters.They are widely used in oil exploration,mineral resource drilling,well logging,exploration and other fields.There is potential for development of rock stress strain monitoring tools.Many types of tiltmeters have been installed,such as SQ-7,FSQ,VS and JB.However,these tiltmeters are generally installed in a deep cave to avoid the interference of temperature,humidity,and human activities.With the urbanization of human society,suitable installation locations are difficult to find.To solve the problem,a two-component borehole tiltmeter,named the CBT-type tiltmeter,is proposed in this paper.It can be installed in a borehole less than500 m deep to eliminate environmental influences.The tiltmeter is composed of two sophisticated gravitational swing and two capacitive transducers.From preliminary theory and experiment analysis,its linear correlation coefficient is higher than 0.99,its co-seismic response is rapid and its noise level is up to 10 4arc seconds in practice.

Conformal vector fields on some Finsler manifolds

We study conformal vector fields on a Finsler manifold whose metric is defined by a Riemannian metric, a 1-form and its norm. We find PDEs characterizing conformal vector fields. Then we obtain the explicit expressions of conformal vector fields for certain spherically symmetric metrics on R^n.

RECOGNITION AND CLASSIFICATION FOR O(n)-EQUIVARIANT BIFURCATIONS WITH O(n)-CODIMENSION LESS THAN 5

Bifurcation problems equivariant under the standard action of the orthogonal group O(n) up to O(n)-codimension 4 are classified into 19 classes. For each class the normal form and one universal unfolding are calculated and the recognition problem is solved.

Convergence analysis of the formal energies of symplectic methods for Hamiltonian systems

Based on Feng's theory of formal vector fields and formal flows, we study the convergence problem of the formal energies of symplectic methods for Hamiltonian systems and give the clear growth of the coefficients in the formal energies. With the help of B-series and Bernoulli functions, we prove that in the formal energy of the mid-point rule, the coefficient sequence of the merging products of an arbitrarily given rooted tree and the bushy trees of height 1(whose subtrees are vertices), approaches 0 as the number of branches goes to ∞; in the opposite direction, the coefficient sequence of the bushy trees of height m(m ≥ 2), whose subtrees are all tall trees, approaches ∞ at large speed as the number of branches goes to +∞. The conclusion extends successfully to the modified differential equations of other Runge-Kutta methods. This disproves a conjecture given by Tang et al.(2002), and implies:(1) in the inequality of estimate given by Benettin and Giorgilli(1994) for the terms of the modified formal vector fields, the high order of the upper bound is reached in numerous cases;(2) the formal energies/formal vector fields are nonconvergent in general case.

Positive energy theorem for(4+1)-dimensional asymptotically anti-de Sitter spacetimes

We define the total energy-momenta for(4+1)-dimensional asymptotically anti-de Sitter spacetimes,which comes from the boundary terms at infinity in the integral form of the Weitzenbck formula.Then we prove the positive energy theorem for such spacetimes,following Witten’s original argumentsfor the positive energy theorem in asymptotically flat spacetimes.

Charmed-Hadron Production in Υ(1S) Semi-inclusive Decay

In the framework of the NRQCD factorization formalism,we calculate the decay rate for the process Υ(1 S) → ccgg to the next-to-leading order(NLO) in the relative velocity v of the b quark in the bottomonium rest frame.We also study the momentum distributions of the charm quark and the charmed-hadron in the decay.The momentum distribution of the charmed-hadron is obtained by convolving the charm quark momentum distribution with a fragmentation function of the charm quark into the hadron.In addition,we fit the nonperturbative NRQCD matrix element v 2 Υ through comparing the theoretical prediction with the measurement from the BaBar collaboration for the decay rate of Υ(1 S) → D + X.In return,taking this matrix element as an input parameter,we predict the decay rates as well as the momentum distributions for a collection of charmed-hadrons in the process Υ(1S) → ccgg → hX.