平均比赛局数的估计

讨论体育比赛中一个常见问题:甲乙两队进行比赛,规定先胜n局的队获胜,问平均而言比赛要进行几局?相对于平均数的波动程度有多大?实际比赛中所采用的三局两胜制,五局三胜制及七局四胜制都是这个问题的特例。

网球比赛局数与比赛胜负失衡现象研究

网球比赛规则的要求,使其计分规则与其他项目有着较大的区别,一场比赛是由分构成局,然后由局构成盘。比赛盘数是比赛胜负的关键,所以人们会把重点放在比赛盘数上,而忽略了每盘比赛局数情况或是整场比赛局数情况。因此,在一场比赛中即使是失败方也有可能在获胜局数上与胜利方的获胜局数相同或是比胜利方还要多。运用文献资料法、数理统计法、逻辑分析法等方法从多方面对比赛局数进行分析,找出其出现的规律,并对其出现的原因进行分析。

对赛制公平性的数学探讨

近年来，为满足体育运动不断深入发展的需要，有的运动项目在赛制上做了适当的调整。如国际乒联将“五局三胜”制(每局21分)改为“七局四胜”制(每局11分)，国际羽联也将“三局二胜”制(每局单打11分，双打15分)改为“五局三胜”制(每局7分)。

Global stability coefficient of large underground caverns under static loading and earthquake wave condition

Underground energy and resource development,deep underground energy storage and other projects involve the global stability of multiple interconnected cavern groups under internal and external dynamic disturbances.An evaluation method of the global stability coefficient of underground caverns based on static overload and dynamic overload was proposed.Firstly,the global failure criterion for caverns was defined based on its band connection of plastic-strain between multi-caverns.Then,overloading calculation of the boundary geostress and seismic intensity on the caverns model was carried out,and the critical unstable state of multi-caverns can be identified,if the plastic-strain band appeared between caverns during these overloading processes.Thus,the global stability coefficient for the multi-caverns under static loading and earthquake was obtained based on the corresponding overloading coefficient.Practical analysis for the Yingliangbao(YLB)hydraulic caverns indicated that this method can not only effectively obtain the global stability coefficient of caverns under static and dynamic earthquake conditions,but also identify the caverns’high-risk zone of local instability through localized plastic strain of surrounding rock.This study can provide some reference for the layout design and seismic optimization of underground cavern group.

Stability of second order Hopfield neural networks with time delays

Dynamical behaviors of a class of second order Hopfield neural networks with time delays is investigated.The existence of a unique equilibrium point is proved by using Brouwer's fixed point theorem and the counter proof method,and some sufficient conditions for the global asymptotic stability of the equilibrium point are obtained through the combination of a suitable Lyapunov function and an algebraic inequality technique.

Feature Extraction of Acoustic/Seismic Signal of Target

A microphone and a seismic sensor always become a basic unit of UGS(unattended ground sensors) system. The mechanism of acoustic and seismic property of target and its propagation are described. The acoustic and seismic signals of targets are analyzed with time frequency distribution according to its non stationary property. Narrow band energy function (NEF) and local power spectral density (LPSD) are proposed to extract features for target identification. Experiment results show that local power spectral density indicates corresponding target clearly.

Multiobjective particle swarm inversion algorithm for two-dimensional magnetic data

Regularization inversion uses constraints and a regularization factor to solve ill- posed inversion problems in geophysics. The choice of the regularization factor and of the initial model is critical in regularization inversion. To deal with these problems, we propose a multiobjective particle swarm inversion （MOPSOI） algorithm to simultaneously minimize the data misfit and model constraints, and obtain a multiobjective inversion solution set without the gradient information of the objective function and the regularization factor. We then choose the optimum solution from the solution set based on the trade-off between data misfit and constraints that substitute for the regularization factor. The inversion of synthetic two-dimensional magnetic data suggests that the MOPSOI algorithm can obtain as many feasible solutions as possible; thus, deeper insights of the inversion process can be gained and more reasonable solutions can be obtained by balancing the data misfit and constraints. The proposed MOPSOI algorithm can deal with the problems of choosing the right regularization factor and the initial model.

LOCAL NONLINEAR CHARACTERISTICS OF GAS LIQUID SOLID THREE PHASE SELF ASPIRATED REVERSED FLOW JET LOOP REACTOR

Hursts rescaled range (R/S) analysis and Wolfs attractor reconstruction technique have been adopted to estimate the local fractal dimensions and the local largest Lyapunov exponents in terms of the time series pressure fluctuations obtained from a gas liquid solid three phase self aspirated reversed flow jet loop reactor,respectively.The results indicate that the local fractal dimensions and the local largest Lyapunov exponents in both the jet region and the tubular region inside the draft tube increase with the increase in the jet liquid flowrates and the solid loadings,the local fractal dimension profiles are similar to those of the largest Lyapunov exponent,the local largest lyapunov exponents are positive for all cases,and the flow behavior of such a reactor is chaotic.The local nonlinear characteristic parameters such as the local fractal dimension and the local largest Lyapunov exponent could be applied to further study the flow properties such as the flow regime transitions and flow structures of this three phase jet loop reactor.

Aerodynamic Interpolation for Flight Vehicles with Aerodynamic Axial Asymmetry

Aim To study wind tunnel test data interpolation methods for flight vehicle with aerodynamic axial asymmetry. Methods For different body aerodynamic roll angles, proper wind tunnel test schemes were selected and trigonometric series were used for aerodynamic interpolation. Results and Conclusion A simple and effective scheme for wind tunnel test and an accurate aerodynamic interpolation method are developed with satisfactory results.

Spaces with σ-locally Countable Weak Bases

In this paper, by msss_mappings, the relations between metric spaces and spaces with σ _locally countable cs_networks or spaces with σ _locally countable weak bases are established. These are some answers to Alexandroff’s problems.

SELF-DEPENDENT LOCALITY PRESERVING PROJECTION WITH TRANSFORMED SPACE-ORIENTED NEIGHBORHOOD GRAPH

Locality preserving projection （LPP） is a typical and popular dimensionality reduction （DR） method,and it can potentially find discriminative projection directions by preserving the local geometric structure in data. However,LPP is based on the neighborhood graph artificially constructed from the original data,and the performance of LPP relies on how well the nearest neighbor criterion work in the original space. To address this issue,a novel DR algorithm,called the self-dependent LPP （sdLPP） is proposed. And it is based on the fact that the nearest neighbor criterion usually achieves better performance in LPP transformed space than that in the original space. Firstly,LPP is performed based on the typical neighborhood graph; then,a new neighborhood graph is constructed in LPP transformed space and repeats LPP. Furthermore,a new criterion,called the improved Laplacian score,is developed as an empirical reference for the discriminative power and the iterative termination. Finally,the feasibility and the effectiveness of the method are verified by several publicly available UCI and face data sets with promising results.

有关信函分拣机几个技术问题的思考

文章以解决提高信函分拣机性能的几个技术问题为目的，通过对我国部分省市引进信函分拣机后的技术经济分析，提出了引进设备时应考虑引进一体机、配备条码打印设备、实现消耗品国产化、确立格口与直封局数分拣机配套、选用全码输入、堵塞不规范编码书写和非标准信封入局等一系列措施，以期得到较好的经济效益。

Local Bifurcation of a Thin Rectangle Plate with the Friction Support Boundary

The dynamical equations of a thin rectangle plate subjected to the friction support boundary and its plane force are established in this paper. The local bifurcation of this system is investigated by using L S method and the singularity theory. The Z 2 bifurcation in non degenerate case is discussed. The local bifurcation diagrams of the unfolding parameters and the bifurcation response characters referred to the physical parameters of the system are obtained by numerical simulation. The results of the computer simulation are coincident with the theoretical analysis and experimental results.

Analysis of granular assembly deformation using discrete element method

The discrete element method is used to simulate specimens under three different loading conditions（conventional triaxial compression,plane strain,and direct shear）with different initial conditions to explore the underlying mechanics of the specimen deformation from a microscale perspective.Deformations of specimens with different initial void ratios at different confining stresses under different loading conditions are studied.Results show that the discrete element models successfully capture the specimen deformation and the strain localization.Particle behaviors including particle rotation and displacement and the mesoscale void ratio distributions are used to explain the strain localization and specimen deformation.It is found that the loading condition is one of the most important factors controlling the specimen deformation mode.Microscale behavior of the granular soil is the driving mechanics of the macroscale deformation of the granular assembly.

Spatial pattern of dominant tree species of the secondary monsoon rain forest in Lianjiang, Guangdong Province

Based on the summed dominance ratios of species in sample plots, the first three dominant species (Litchi chinensis, Elaeocarpus sylvestris and Canarium album) of the secondary monsoon rain forest of Mt. Royal Shoe in Lianjiang City, western Guangdong, were chosen for analyzing their spatial distribution pattern with the analysis methods such as frequency models of Poisson Distribution, Two Negative Items Distribution, Neyman Distribution, aggregate indexes, Taylor exponential equation and Iwao’s equation modeling. The results showed that these three species distributed in the congregate spatial pattern. Litchi chinensis and Elaeocarpus sylvestris had the characteristic of basic congregate population and attractive characteristic between their plants. The patterns for Canarium album may change and become more evenly distributed with the increase of density. The overall species spatial pattern also depended on the conservation of the secondary monsoon rain forest besides it was affected by the species reproduction characteristics and its growing environment. The congregate spatial patterns of three dominant species showed that it is important to conserve forest urgent conservation of the forest.

A family of quasi-cubic blended splines and applications

A class of quasi-cubic B-spline base functions by trigonometric polynomials are established which inherit properties similar to those of cubic B-spline bases. The corresponding curves with a shape parameter a, defined by the introduced base functions, include the B-spline curves and can approximate the B-spline curves from both sides. The curves can be adjusted easily by using the shape parameter a, where dpi（a,t） is linear with respect to da for the fixed t. With the shape parameter chosen properly, the defined curves can be used to precisely represent straight line segments, parabola segments, circular arcs and some transcendental curves, and the corresponding tensor product surfaces can also represent spherical surfaces, cylindrical surfaces and some transcendental surfaces exactly. By abandoning positive property, this paper proposes a new C^2 continuous blended interpolation spline based on piecewise trigonometric polynomials associated with a sequence of local parameters. Illustration showed that the curves and surfaces constructed by the blended spline can be adjusted easily and freely. The blended interpolation spline curves can be shape-preserving with proper local parameters since these local parameters can be considered to be the magnification ratio to the length of tangent vectors at the interpolating points. The idea is extended to produce blended spline surfaces.

Geometric Parameters of a Bocs (Ⅰ)

In this paper, the group action of a local wild Bocs'rep. category is introduced. And, it computed the parametric numbers U(n) and P(n) of the rep. category mod n(A) and ind n(t) in case n=1,2 with geometric method.

Improvement of Fuzzy Inference Mechanism in FuzzyJ Toolkit

By applying the aggregation operator γ-operator and introducing a new method for global data contribution, the problems of information loss and the decrease of running efficiency in FuzzyJ Toolkit, an expert system shell, can be effectively solved. The example shows that the approach can overcome imprecision of max-operator and min-operator used during the process of fuzzy reasoning. Therefore, the information accuracy and the system performance can be effectively improved, which promotes the usability of FuzzyJ Toolkit.

Parameter optimization of gravity density inversion based on correlation searching and the golden section algorithm

For density inversion of gravity anomaly data, once the inversion method is determined, the main factors affecting the inversion result are the inversion parameters and subdivision scheme. A set of reasonable inversion parameters and subdivision scheme can, not only improve the inversion process efficiency, but also ensure inversion result accuracy. The gravity inversion method based on correlation searching and the golden section algorithm is an effective potential field inversion method. It can be used to invert 2D and 3D physical properties with potential data observed on flat or rough surfaces. In this paper, we introduce in detail the density inversion principles based on correlation searching and the golden section algorithm. Considering that the gold section algorithm is not globally optimized. we present a heuristic method to ensure the inversion result is globally optimized. With a series of model tests, we systematically compare and analyze the inversion result efficiency and accuracy with different parameters. Based on the model test results, we conclude the selection principles for each inversion parameter with which the inversion accuracy can be obviously improved.

Regional-scale Identification of Three-dimensional Pattern of Vegetation Landscapes

The altitudinal pattern of vegetation is usually identified by field surveys,however,these can only provide discrete data on a local mountain.Few studies identifying and analyzing the altitudinal vegetation pattern on a regional scale are available.This study selected central Inner Mongolia as the study area,presented a method for extracting vegetation patterns in altitudinal and horizontal directions.The data included a vegetation map at a 1∶1 000 000 scale and a digital elevation model at a 1∶250 000 scale.The three-dimensional vegetation pattern indicated the distribution probability for each vegetation type and the transition zones between different vegetation landscapes.From low to high elevations,there were five vegetation types in the southern mountain flanks,including the montane steppe,broad-leaved forest,coniferous mixed forest,montane dwarf-scrub and sub-alpine shrub-meadow.Correspondingly,only four vegetation types were found in the northern flanks,except for the montane steppe.This study could provide a general model for understanding the complexity and diversity of mountain environment and landscape.