GR的协变量子化与维数正规化计算及发散分析

将时空流形微分同胚当作规范交换，证明其构成群，用Ｆｅｙｎｍａｎ路径积分将引力场ｈ＿μｕ量子化．求得了引力子和虚位子的树图传播子，并计算了虚粒子圈和引力子自能图．同时还得到了Ｓｌａｖｎｏｖ－ｗａｒｄ恒等式，用计算证明了圈图修正满足该恒等式，并将此理论进行了维数正规化．最后将ＧＲ的发散进行分析．     

具有导数项的非线性反应扩散方程指数吸引子的存在性

利用挤压性的方法,讨论了带导数项的反应扩散方程在L~2(Ω)中指数吸引子的存在性,得到了新的结果,推广了相关文献的主要结果.     

耦合标量场的Einstein引力的背景场量子化方法

该文在’ｔＨｏｏｆｔ背景场方案下，用维数正规化方法计算了含标量场的Ｅｉｎｓｔｉｅｎ引力的单圈发散，并给出了其单圈级抵消拉氏函数．结果表明，如果被加进的是标量物质场，引力理论是单圈可重整的，而单圈级的纯引力理论是不需要重整化的．     

图的k-单圈划分中的优化问题

图的划分问题曾引起图论界的广泛关注，在文献[4]中讨论了k-单圈划分，本文进一步研究基于k-单圈划分的优化问题，即在一个赋权图中求一个最小权可k-单圈划分的支撑子图，以及对一个不存在k-单圈划分支撑子图的图，如何添最少的边使得它有k-单圈划分的支撑子图。     

一类非线性Schr(o)dinger方程的守恒差分法与Fourier谱方法

考察了一类带导数项的非线性Schrodinger方程的周期边值问题，提出了一种守恒的差分格式，在空间方向上采用Fourier谱方法，证明了格式的稳定性和收敛性．数值试验得到了与理论分析一致的结果．     

带附加项KdV方程族的双Hamilton结构(英文)

通过将ｔ看作空间变量，将ｘ作为发展参数，本文给出了带附加项的ＫｄＶ和ＭＫｄＶ方程族的ｔ型Ｈａｍｉｌｔｏｎ结构。再利用ｔ型Ｍｉｕｒａ变换，得到了带附加项ＫｄＶ方程族的第二个Ｈａｍｉｌｔｏｎ结构，进而构造出遗传算子及一族新的无穷维可积Ｈａｍｉｌｔｏｎ系统，并给出了带附加项的孤立子方程及孤立子方程的约束系统间Ｈａｍｉｌｔｏｎ结构的约化关系．     

强阻尼半线性波动方程的全局吸引子

本文讨论一类带强阻尼项的半线性波动方程的全局吸引子的存在性．首先给出了方程解的存在唯一性定理，建立了解的C°-半群；然后运用Hale提出的a-收缩理论，证明了该类方程存在全局吸引子．     

几类图张量乘积的同构因子分解

对任意给定的正整数ｔ，当ｔ能整除图Ｇ的边数时．Ｇ就可分解成ｔ个同构的生成子图，则称Ｇ为可分图．本文证明了路、圈的张量乘积，以及可分图与路、圈的张量乘积仍然是可分图．此外，文中讨论了完全图张量积乘的同构因子分解．     

带附加项KdV方程放的双Hamilton结构

通过将ｔ看作空间变量，将ｘ作为发展参数，本文给出了带附加项的ｋｄｖ和ＭＫｄＶ方程族的ｔ型Ｈａｍｉｌｔｏｎ结构。再利用ｔ型Ｍｉｕｒａ变换，得到了带附加项ＫｄＶ方程族的第二个Ｈａｍｉｌｔｏｎ结构，进而构造出遗传算子及一族新的无穷维可积Ｈａｍｉｌｔｏｎ系统，并给出了带附加项的孤立子方程及孤立子方程的约束系统间Ｈａｍｉｌｔｏｎ结构的约化关系。     

带非线性源项的双侧空间分数阶扩散方程的隐式中点方法

本文用隐式中点方法离散一阶时间偏导数,并用拟紧差分算子逼近Riemann-Liouville空间分数阶偏导数,构造了求解带非线性源项的空间分数阶扩散方程的数值格式.给出了数值方法的稳定性和收敛性分析.数值试验表明数值方法是有效的.     

炉液倾动重心近似计算的数学分析

为给转炉设计提供依据,需要计算炉液倾动的重心.利用数学方法将实际问题进行简化,通过分析炉液倾动过程中变量间的相互关系,来确定每个倾动角度对应情况下的液面位置.利用数学中三重积分的有关应用,进一步得出转炉在每个倾动角度为α∈(0,π2)时的重心计算方法及相关结论,在理论上为工程计算重心的方法提供参考.     

改进的云重心评判法在高技术企业信用评价中的应用

提出一种改进的云重心评判法,并应用于高技术企业信用评价.首先,借鉴TOPSIS法的基本思想,基于理想状态和负理想状态,对综合云重心向量进行归一化,并采用修正的加权偏离度来衡量云重心的变化,从而克服了传统云重心评判法的不足.其次,针对高技术企业信用评价中的不确定性,运用改进的云重心评判法对高技术企业信用状态进行实证测评,结果证明了该方法的合理性和适用性.     

Optimization methods for pipeline transportation of natural gas with variable specific gravity and compressibility

In this paper, the problem of flow maximization in pipeline systems for transmission of natural gas is addressed. We extend previously suggested models by incorporating the variation in pipeline flow capacities with gas specific gravity and compressibility. Flow capacities are modeled as functions of pressure, compressibility and specific gravity by the commonly-used Weymouth equation, and the California Natural Gas Association method is used to model compressibility as a function of specific gravity and pressure. The sources feeding the transmission network do not necessarily supply gas with equal specific gravity. In our model, it is assumed that when different flow streams enter a junction point, the specific gravity of the resulting flow is a weighted average of the specific gravities of entering flows. We also assume the temperature to be constant, and the system to be in steady state. Since the proposed model is non-convex, and global optimization hence can be time consuming, we also propose a heuristic method based on an iterative scheme in which a simpler NLP model is solved in each iteration. Computational experiments are conducted in order to assess the computability of the model by applying a global optimizer, and to evaluate the performance of the heuristic approach. When applied to a wide set of test instances, the heuristic method provides solutions with deviations less than 10% from optimality, and in many instances turns out to be exact. We also report several experiments demonstrating that letting the compressibility and the specific gravity be global constants can lead to significant errors in the estimates of the total network capacity.     

Progress in Clifford Space Gravity

Clifford-space Gravity is revisited and new results are found. The Clifford space (C-space) generalized gravitational field equations are obtained from a variational principle and which is based on an extension of the Einstein-Hilbert-Cartan action. One of the main results of this work is that the C-space connection requires torsion in order to have consistency between the Clifford algebraic structure and the zero nonmetricity condition ${\nabla{\kappa g}^{MN} = 0}$ . A discussion on the field equations, the cosmological constant, dark energy and multi-metric theories of gravity follows. We continue by pointing out the relations of Clifford space gravity to Lanczos-Lovelock-Cartan (LLC) higher curvature gravity with torsion. We finalize by describing the Clifford bundle approach to C-space gravity and by pointing out that C-space gravity involves higher-spins beyond spin 2 and argue why one could view the LLC higher curvature actions, and other extended gravitational theories based on f(R), f(R _μν ), . . . actions, for polynomial-valued functions, as effective actions after integrating the C-space gravitational action with respect to all the poly-coordinates, except the vectorial ones x ^μ .     

Gravity Currents Produced by Sudden Release of a Fixed Volume of Heavy Fluid

In this paper we study various aspects of gravity (or density) currents arising from instantaneous releases of heavy fluids in a rectangular channel with a horizontal bottom. It is shown, by means of a scaling argument, that these plane currents can be successfully modeled by a two-by-two system in conservation form together with a pair of algebraic relations. A number of numerical experiments are carried out using this “weak stratification” model to elicit information concerning the behavior of gravity currents. A weakly nonlinear analysis is employed to clarify some aspects that were uncovered by the numerical experimentation.     

Damping Behavior of the Free Liquid Interface Oscillation upon Step Reduction in Gravity

Experiments were carried out to investigate the damping behavior of the reorientation of a free liquid interface in a right circular cylinder, partly filled with a liquid and suddenly exposed to a step reduction in gravity. The damping behavior basically depends on the Ohnesorge number and the static contact angle. This study shows the strong influence of the contact point for low static contact angles.     

Experimental Investigation of the Free Liquid Interface Oscillation upon Step Reduction in Gravity

Experiments have been carried out to investigate the reorientation behavior of a free liquid surface in a partly filled right circular cylinder upon step reduction in gravity. In the initial situation the system is dominated by hydrostatic forces. In this case the equilibrium of the free liquid surface is generally characterized by a flat shape with a curvature at the cylinder wall given by the static contact angle. After transition to reduced gravity, capillary forces govern the flow and a capillary driven reorientation of the liquid to the new equilibrium position is established in a damped oscillation. The particular interest of this study is to determine the main characteristics of the surface oscillation as well as the behavior of the dynamic contact angle.     

Dynamic analysis of non-uniform taper bars in post-elastic regime under body force loading

This paper presents a simulation study of the free flexural vibration behavior of non-uniform taper bars of circular and rectangular cross-section under body force loading due to gravity. The loading is controlled statically to take the bar to its post-elastic state so as to predict its dynamic behavior in the presence of plastic deformation. Hence the analysis is carried out in two parts; first the static problem under axial gravity loading is solved, then the dynamic problem is solved in this loaded condition. Appropriate variational method is employed to derive the set of governing equations for both the problems. The formulation is based on unknown displacement field which is approximated by finite linear combinations of orthogonal admissible functions. The present method is validated successfully with a well-known finite element package. Results are presented to investigate the effect of shape and size on the dynamic behavior of non-uniform taper bars. The study can be extended to study the post-elastic dynamic behavior of other related problems such as rotating beams and rotating disks.     

Unified description of cosmological and static solutions in affine generalized theories of gravity: Vecton-scalaron duality and its applications

We briefly describe the simplest class of affine theories of gravity in multidimensional space-times with symmetric connections and their reductions to two-dimensional dilaton-vecton gravity field theories. The distinctive feature of these theories is the presence of an absolutely neutral massive (or tachyonic) vector field (vecton) with an essentially nonlinear coupling to the dilaton gravity. We emphasize that the vecton field in dilaton-vecton gravity can be consistently replaced by a new effectively massive scalar field (scalaron) with an unusual coupling to the dilaton gravity. With this vecton-scalaron duality, we can use the methods and results of the standard dilaton gravity coupled to usual scalars in more complex dilaton-scalaron gravity theories equivalent to dilaton-vecton gravity. We present the dilaton-vecton gravity models derived by reductions of multidimensional affine theories and obtain one-dimensional dynamical systems simultaneously describing cosmological and static states in any gauge. Our approach is fully applicable to studying static and cosmological solutions in multidimensional theories and also in general one-dimensional dilaton-scalaron gravity models. We focus on general and global properties of the models, seeking integrals and analyzing the structure of the solution space. In integrable cases, it can be usefully visualized by drawing a “topological portrait” resembling the phase portraits of dynamical systems and simply exposing the global properties of static and cosmological solutions, including horizons, singularities, etc. For analytic approximations, we also propose an integral equation well suited for iterations.     

重力输水管道优化设计方法研究

针对重力输水管道设计中存在的问题，文章以管道造价最小为目标，应用动态规划，提出了一种新的重力输水管道优化设计方法，对输水管的当量管径、流量分配、连接管设置与可靠性校核计算等问题作了探讨。该方法可用于沿线有节点流量流出的并联输水管道优化设计，能明显节省投资，有良好的实用性