关于r边形数补数序列的混合均值性质

利用初等方法和解析方法,研究Smarandache函数φ(n)、δ_k(n)分别与本文定义的数论函数a(n)和b(n)的混合均值,获得了4个较强的渐近进公式,从而拓展了经典的算术函数的相关研究工作。

边形数、棱锥体数及其三角形的循序逐增规律

该文遵循循序逐增原理,从对边形数、棱锥体数以及其点与点之间连线形成的三角形的量的循序逐增现象研究中,求得其循序逐增规律。应用拓扑原理,可将边形数置换为扇形图表达,将棱锥体数置换为圆形图表达,发现了棱锥体数与边形数之间的相近相同规律。

2个r角形数补数序列的混合均值研究

利用初等方法和解析方法,研究了两个Smarandache函数的性质,获得了混合均值性质及渐近公式,从而拓展了经典的算术函数的相关研究工作.

两个Smarandache复合函数的均值估计

设n是正整数,ur(n)表示不小于n的最小r边形数部分数列,vr(n)表示不超过n的最大r边形数部分数列.研究了Smarandache函数S(n)与ur(n),vr(n)的混合均值,并用解析方法得到了几个较强的渐近公式。

Forming defects in aluminum alloy hot stamping of side-door impact beam

The forming defects, including thinning, rupture, wrinkling and springback, usually arising in producing a side-door impact beam, were investigated by trial and numerical simulation. A temperature-related constitutive model specific to the temperature range from 350 °C to 500 °C was established and used for the numerical simulation. The trial and numerical simulation were conducted to clarify the quantitative characteristics of forming defects and to analyze the effects of process parameters on the forming defects. Results show that the rupture situation is ameliorated and the springback is eliminated in the aluminum alloy hot stamping. The wrinkling severity decreases with increasing blank holder force (BHF), but the BHF greater than 15 kN causes the rupture at the deepest drawing position of workpiece. The forming defects are avoided with lubricant in the feasible ranges of process parameters: the BHF of 3 to 5 kN and the stamping speed of 50 to 200 mm/s.

Study on the Spatial Pattern Changes of Land Use Based on Fractal Dimensions in Tianjin New Coastal Area

[Objective] The aim was to discuss the spatial pattern changes of land use in Tianjin new coastal area based on fractal dimensions.[Method] By dint of remote and geographic information system technology to obtain the data of urban land use in new coastal area from 1993 to 2008,the boundary dimension,radius dimension and information dimension of each land use type were calculated based on fractal dimension.In addition,the revealed land use spatial dimension changes characteristics were analyzed.[Result] The spatial distribution of each land use type in new costal area had distinct fractal characteristics.And,the amount and changes of three types of dimension values effectively revealed the changes of complicatedness,centeredness and evenness of spatial pattern of land use in the study area.The boundary dimension of unused land and salty earth increased incessantly,which suggested its increasing complicatedness.The boundary of the port and wharf and shoal land was getting simpler.The radius dimension of the cultivated land was larger than 2,which suggested that its area spread from center to the surroundings;the one in salty land and waters distributed evenly within different radius space to the center of the city;the one in other land use types reduced gradually from center to the surroundings.The information dimension value in the woodland and orchard land,unused land and shoal land was small,and was in obvious concentrated distribution;the spatial distribution of cultivated and salty land concentrated in the outside area;the construction area in the port and wharf spread gradually on the basis of original state;the spatial distribution of waters and residents and mines were even.[Conclusion] Applying fractal dimensions to the study of spatial pattern changes of urban land use can make up for some disadvantages in classical urban spatial pattern quantitative research,which has favorable practical value.

A generalized cover renewal strategy for multiple crack propagation in two-dimensional numerical manifold method

Partition of unity based numerical manifold method can solve continuous and discontinuous problems in a unified framework with a two-cover system,i.e.,the mathematical cover and physical cover.However,renewal of the topology of the two-cover system poses a challenge for multiple crack propagation problems and there are few references.In this study,a robust and efficient strategy is proposed to update the cover system of the numerical manifold method in simulation of multiple crack propagation problems.The proposed algorithm updates the cover system with a bottom-up process:1)identification of fractured manifold elements according to the previous and latest crack tip position;and 2)local topological update of the manifold elements,physical patches,block boundary loops,and non-persistent joint loops according to the scenario classification of the propagating crack.The proposed crack tracking strategy and classification of the renewal cases promote a robust and efficient cover renewal algorithm for multiple crack propagation analysis.Three crack propagation examples show that the proposed algorithm performs well in updating the cover system.This cover renewal methodology can be extended for numerical manifold method with polygonal mathematical covers.

Bézier curves with shape parameter

In this paper, Bézier basis with shape parameter is constructed by an integral approach. Based on this basis, we define the Bézier curves with shape parameter. The Bézier basis curves with shape parameter have most properties of Bernstein basis and the Bézier curves. Moreover the shape parameter can adjust the curves’ shape with the same control polygon. As the increase of the shape parameter, the Bézier curves with shape parameter approximate to the control polygon. In the last, the Bézier surface with shape parameter is also constructed and it has most properties of Bézier surface.

SOME RESULTSON R_2-EDGE-CONNECTIVITY OF EVEN REGULAR GRAPHS

Let Gbe a connected k(≥3)-regulargraph w ith girth g. A setSofthe edgesin G is called an R2-edge-cutifG- Sis disconnected and contains neither an isolated vertex nor a one- degree vertex. The R2-edge-connectivity of G, denoted by λ″(G), is the m inim um cardinality over allR2-edge-cuts, w hich is an im portantm easure for fault-tolerance of com puter intercon- nection netw orks. In this paper, λ″(G)= g(2k- 2) for any 2k-regular connected graph G(≠ K5) that is either edge-transitive or vertex-transitive and g≥5 is given.

Integrated Method of Recognizing Huge Target

An integrated novel method of recognizing huge target is described that combines some relatively mature image processing techniques such as edge detection, thresholding, morphology, image segmentation and so forth. After thresholding the edge image obtained by using Sobel operator, erosion is firstly used to reduce noise and extrusive pixels; then dilation is used to expand some separated pixels into various regions, after that the image segmentation technique is utilized to distinguish the target region with a criterion. The location of the target is also offered. Each technique adopted herein seems not complicated at all, the experimental results demonstrate the efficiency of the combination of these techniques. It is its high computational speed and remarkable robustness resulting from its simplicity that make the method promise to be applied in practical problems requiring real time processing.

Numerical Simulation of Sloshing in Rectangular Storage Tank Using Coupled FEM-BEM

Sloshing of liquid can increase the dynamic pressure on the storage sidewalls and bottom in tanker ships and LNG careers. Different geometric shapes were suggested for storage tank to minimize the sloshing pressure on tank perimeter. In this research, a numerical code was developed to model liquid sloshing in a rectangular partially filled tank. Assuming the fluid to be inviscid, Laplace equation and nonlinear free surface boundary conditions are solved using coupled FEM-BEM. The code performance for sloshing modeling is validated against available data. To minimize the sloshing pressure on tank perimeter, rectangular tanks with specific volumes and different aspect ratios were investigated and the best aspect ratios were suggested. The results showed that the rectangular tank with suggested aspect ratios, not only has a maximum surrounded tank volume to the constant available volume, but also reduces the sloshing pressure efficiently.

Topographic Characteristics for the Geomorphologic Zones in the Northwestern Edge of the Qinghai-Tibet Plateau

Based on geomorphologic and digital elevation model(DEM) data, the topographic characteristics of the northwestern edge of the Qinghai-Tibet Plateau are analyzed. Five representative peaks are first determined according to the topographic profile maps for the ridge and piedmont lines, and then the topographic gradient characteristics are analyzed according to the representative topographic profile acquisition method.Based on the geomorphologic database data, the regions between the ridge and the piedmont lines are divided into four geomorphologic zones; and the topographic characteristics are finally analyzed for the different geomorphologic zones regions using the DEM data. The research results show that from the piedmont to the ridge, there exist four geomorphologic zones: arid, fluvial, periglacial and glacial. The arid has the lowest elevation, topographic gradient, relief and slope characteristics. The fluvial has lower elevation and the highest topographic gradient, but with lower relief and slope characteristics. With higher elevation, the periglcial has lower topographic gradient, but the highest relief and slope characteristics. The glacial has the highest elevation with higher topographic gradient, relief and slope characteristics.

Geometrical characteristic investigation of the Baihetan irregular columnar jointed basalt and corresponding numerical reconstruction method

Columnar jointed rock mass with unique geometric and geological properties is one spectacular example of geometrical order in nature.Columnar joints are generally accepted to be formed by spatially uniform volume contraction during cooling.In this paper,substantial field work was performed to study the geological characteristics of irregular columnar jointed basalt on the left bank dam foundation in the Baihetan Hydropower Station,where the columnar jointed rock mass is extensively exposed due to excavation.The quantitative measurements of the sizing of polygonal crack pattern of columnar joints and assessment of their degree of irregularity were summarized.Considering the irregularity of polygonal crack pattern,a modified Voronoi polygon(MVP)method was developed to model the special polygonal crack pattern of columnar joints.The new polygonal pattern obtained by the MVP method consists of a large number of irregular polygons,of which the degree of irregularity is consistent with the field measurement results.This method can reproduce the rapid evolution from an initial ideal regular hexagonal pattern to a final actual irregular polygonal pattern as the degree of irregularity increases.The compression tests of columnar jointed rock mass with different irregularity show that the geometric irregularity has a great influence on its mechanical properties.This numerical construction method provides a reliable way to reconstruct columnar joint structure with specific polygonal crack pattern,which is consistent with onsite columnar jointed basalt.

Relationship of Uncertainty Between Polygon Segment and Line Segment for Spatial Data in GIS

The mathematic theory for uncertainty model of line segment are summed up to achieve a general conception, and the line error hand model of εσ is a basic uncertainty model that can depict the line accuracy and quality efficiently while the model of εm and error entropy can be regarded as the supplement of it. The error band model will reflect and describe the influence of line uncertainty on polygon uncertainty. Therefore, the statistical characteristic of the line error is studied deeply by analyzing the probability that the line error falls into a certain range. Moreover, the theory accordance is achieved in the selecting the error buffer for line feature and the error indicator. The relationship of the accuracy of area for a polygon with the error loop for a polygon boundary is deduced and computed.

Bandwidth Numerical Analysis of Triangular Patch Antenna Fed by L-Shaped Probe

A single layer triangular patch antenna fed by an L-shaped probe was investigated numerically by using FDTD (Finite Difference Time Domain) method. It achieves >40% impedance bandwidth (VSWR<2) and stable radiation pattern across the passband. The triangular patch antenna with two orientations of L-shaped probe has almost the same characteristics, such as impedance bandwidth and radiation pattern. The bandwidth vs feeding position was also investigated, the broadband characteristic can be observed when the feeding position is only in a small segment along the centerline.

Back analysis for soil slope based on measuring inclination data

Based on the analysis of several objective functions,a new method was proposed.Firstly,the feature of the inclination curve was analyzed.On this basis,the soil could be divided into several blocks with different displacements and deformations.Then,the method of the soil division was presented,and the characteristic of single soil block was studied.The displacement of the block had two components:sliding and deformation.Moreover,a new objective function was constructed according to the deformation of the soil block.Finally,the sensitivities of the objective functions by traditional method and the new method were calculated,respectively.The result shows that the new objective function is more sensitive to mechanical parameters and the inversion result is close to that obtained by the large direct shear apparatus.So,this method can be used in slope back analysis and its effectiveness is proved.

A New Method to Extract Text from Natural Scenes

This paper presents a new method for text detection, location and binarization from natural scenes. Several morphological steps are used to detect the general position of the text, including English, Chinese and Japanese characters. Next bonnding boxes are processed by a new “Expand, Break and Merge” （EBM） method to get the precise text areas. Finally, text is binarized by a hybrid method based on Otsu and Niblack. This new approach can extract different kinds of text from complicated natural scenes. It is insensitive to noise, distortedness, and text orientation. It also has good performance on extracting texts in various sizes.

Analytical solutions for a uniformly loaded circular plate with clamped edges

A bi-harmonic potential function was constructed in this study. Love solution was employed to obtain analytical solutions of uniformly loaded plates with two different types of clamped edges. The treatment of clamped boundary conditions was the same as that adopted by Timoshenko and Goodier (1970). The analytical solution for the first type of clamped boundary condition is identical with that obtained by Luo et al.(2004), and the solutions for both types were compared with the FEM results and the calculations of thin plate theory.

Boundary States and Correlation Functions of Tricritical Ising Model from Coulomb-Gas Formalism

We consider the minimal conformaJ model describing the tricritical Ising model on the disk and on the upper half plane. Using the coulomb-gas formalism we determine its consistents boundary states as well as its one-point and two-point correlation functions.