最小图

After analyzing the basic information of the ecological engineering construction, the spatial and temporal scale, and monitoring index, the 1m IKONOS image and 2.5m SPOT5 image were introdueced as data sources, the methodology of RPC modeling and GCP optimitiaztion as modification to the interpretation, the AHP used in determining combination of multi-light specrum and the whole band wave, the virtue reality technique monitoring the classification and recognation, variable cluster allocation coeffiecents and its adaptation in spatial and imaged attributs in the research on water and siol conservation subtracting the least pathches of the area. The final stage is to subtract the information via human and computer interactive to interpret and monitor the classification in the study assisted with GPS, field identification and construction supervision.

在对研究样区水土保持生态建设情况和监测尺度及监测指标分析的基础上，选择1m分辨率的IKONOS影像和2.5m分辨率的SPOT5影像为监测遥感数据源；采用"RPC模型+GCP优化"方法进行高分辨率遥感影像正射纠正；用主成分分析法进行遥感影像全色波段与多光谱图像融合；用虚拟现实技术进行高分辨率遥感影像监督分类模板定义研究，用不同大不的聚类处理参数并在研究水土保持生态建设措施的空间特征和影像特征的基础上，确定提取水土保持生态建设信息的最小图斑参数值；最后用全数字人机交互解译和监督分类提取研究样区水土保持生态建设信息，并结合GPS现场验证和工程监理成果对监测结果进行分析评价。

Meanwhile, the experiments show that the multi-level swarm intelligence refinement algorithm is better than the multi-level tabu search refinement algorithm, especially in view of the probability that the approximate global minimum partition of the coarser graph may be the local minimum partition of the finer graph. Furthermore, the experiments show that the multi-level ant colony optimization refinement algorithm achieves more performance improvement than the multi-level particle swarm optimization refinement algorithm, using the gain of vertex more effectively.

实验数据反映出，针对最小图上的全局最优剖分可能是初始图的局部最优剖分、粗化图上的全局最优剖分可能是细化图的局部最优剖分的情况，基于群智能的多水平迁移优化算法相比基于禁忌搜索的多水平迁移优化算具备更强的逃离局部最优的能力；基于蚁群的多水平迁移优化算法相比基于微粒群的多水平迁移优化算法，对收益值的启发信息更为有效地利用，取得最佳的性能改进。

First scanning the known handwriting materials then number them ,In pretreatment, we convert the valid part of the image into a standard size, as images carries out duotone and go throw off chirp handling in order to achieve better effect.draw features from the known handwriting materials with the Co-occurence,especially,we divided a copy of handwriting into 25 little pieces with the size of 128*128 ,drawing features from every little piecese with four directions(0 degree, 45 degrees, 90 degrees as well as 135 degrees) and calculate the four major feature values( veins and the statistical quantity of veins contrast and the statistical quantity of veins consistency Shang the statistical quantity of statistical quantity as well as the veins correlation of gray scale ), preservation all the feature value that drawn from all known ma terials to the handwriting characteristic database,then input the unknown handwriting materials, also using the method of the Co-occurence to draw those features, recycling the minimum European Distance law match the unknown writing material feature value with the handwriting characteristic feature database, export the label of the known hand writing materials which is most similar to the unknown material with minimum European Distance, and then we can confirm who is the author of the unknown material.

首先将笔迹材料作为图象扫描输入，并对其进行编号。预处理部分可将笔迹图象的有效部分规范化到一个统一尺寸，接着对其进行二值化和去除噪声的处理，以便于更好的提取图像的特征。在此我们采用了灰度共生矩阵法提取手写笔迹材料的纹理特征，与以往有所不同的是，我们将一份手写材料分割成64块大小为80*80象素的子图象，每个小块都从四个方向（0度、45度、90度以及135度）来更全面的提取特征，并计算出四个最主要的特征值（纹理一致性的统计量、纹理反差的统计量、纹理熵的统计量以及纹理灰度相关性的统计量），将从所有已知材料提取的特征值保存到纹理特征库中，对于待检手写材料，同样采用灰度共生矩阵的方法提取其纹理特征，再利用最小欧氏距离分类法将从待检手写材料中提取的特征值与纹理特征库中的特征值进行比对，与欧氏距离比对值最小的相匹配，输出匹配成功的原材料的标号，进而识别出待检材料书写者的身份。

In chapter four, we study the second isoperimetric connectivity of line graphs and line digraphs. For line digraphs, we show that the second isoperimetric connectivity of strongly connected line digraphs with δ≥ 2 equals its connectivity. For line graphs, we give a sufficient and necessary condition for the existence of the second isoperimetric connectivity, and we show that under the condition that the second isoperimetric connectivity exists, the second isoperimetric con

第四章研究线图和有向线图的第二等周点连通度，得到了如下结果：(1)最小度大于等于2的强连通有向线图的第二等周点连通度等于它的点连通度；(2)对于无向线图，我们给出了第二等周点连通度存在的充要条件；(3)对于第二等周点连通度存在的无向线图，它的第二等周点连通度或者等于限制点连通度或者等于最小度和次最小度的和。

In this paper, the maximum graph packing and the minimum graph covering of two graphsD_1, D_2 with six vertices and eight edges and the 8-cycle C_8 are researched.

在统一的构作方法下，对于两个六点八边图所有可能的v和λ给出了相应的最大图填充和最小图覆盖的构造。

Factors with prescribed properties such as factors including or excluding some given edge, maximum or minimum factors, factor covering and connected factors; 3. Factorizations of graphs; 4. k-extendable graph and its generalizations. Fractional graph theory is a relatively younger research branch.

例如，因子与图的最小度，韧度，联结数：邻域并等参数之间的关系；2·研究图的有限制条件的因子，例如，有约束条件的因子，图的连通因子，图的最大最小因子；3·图的因子分解；4·k-可扩图及其推广等。

Chapter 7,discusses some unresolved problems about minimum genus and genus distribution of orientable embeddings for a graph,such as based on the joint tree model,calculation of minimum genus of complete graphs,determination of minimum genera for further types of graphs or even arbitrary graphs,etc.

第七章介绍了图的最小亏格及亏格分布领域中一些需要更进一步研究的问题，如如何利用联树模型计算完全图的最小亏格，以及如何通过刻画最小亏格关联曲面的特性来确定更广泛图类，乃至任意图类的最小亏格问题等等。

We determine the bounds on the upperand lower orientable strong radius and strong diameter of graphs satisfyingthe Ore condition. Let G_1, G_2 be any connected graph, we present the exactvalue of srad(G_1×G_2), consider the relationship between sdiam(G_1×G_2) andr(G_1×G_2), d (G_1×G_2). Moreover, we determine the values of the lower orientablestrong diameters of some special graphs. Furthermore, we give the exact value ofSDIAM, a lower bound for SDIAM, an upper and lowerbound for SRAD and SRAD, respectively.

对满足Ore条件的图，给出了最小强半径、最大强半径的上、下界；对笛卡尔乘积图G_1×G_2，确定了G_1×G_2的最小强半径与G_1×G_2的半径以及G_1和G_2的最小强直径之间的关系，并进而确定了一些特殊笛卡尔乘积图的最小强直径的值，确定了SDIAM的值，SDIAM的下界，SRAD和SRAD相应的上、下界。

Meanwhile, the experiments show that the approximate global minimum partition of the coarsest graph may be the local minimum partition of the finest graph and we need to strengthen the global search ability of refinement algorithm in the refinement phase.

同时实验数据也反映了在最小图上的全局近似最优剖分可能是初始图的局部最优剖分，需要加强多水平优化阶段的迁移优化算法逃离局部最优的能力。

According to the distances, the SPWUG algorithm computed the initial partition of the coarsest graph by extending the Laplacian spectral graph theory from the unweighted undirected graph into the weighted undirected graph.

SPWUG算法借助Laplacian矩阵次小特征值对应的特征向量，刻画了节点间相对距离，将基于非赋权无向图的Laplacian谱理论在图的剖分应用方面扩展到无向赋权图上，实现了对最小图的初始剖分。

On the other hand, the more important thing is because the urban housing is a kind of heterogeneity products.

另一方面，更重要的是由于城市住房是一种异质性产品。

Climate histogram is the fall that collects place measure calm value, cent serves as cross axle for a few equal interval, the area that the frequency that the value appears according to place is accumulated and becomes will be determined inside each interval, discharge the graph that rise with post, also be called histogram.

气候直方图是将所收集的降水量测定值，分为几个相等的区间作为横轴，并将各区间内所测定值依所出现的次数累积而成的面积，用柱子排起来的图形，也叫做柱状图。