Approximating the Inertia of the Adjacency Matrix of a Connected Planar Graph That Is the Dual of a Geographic Surface Partitioning

This article addresses the calculation of the inertia of an adjacency matrix (i.e., the number of positive, zero, and negative eigenvalues) associated with a connected, undirected planar graph. A formula is derived that is an upper bound for the number of negative eigenvalues of this matrix, based upon standard matrix trace results, coupled with the use of nonextreme eigenvalue averages, and requiring calculations of the pair of extreme eigenvalues and the number of zero eigenvalues. The number of positive eigenvalues can be calculated easily from this specific result. Assessment of this formula is in terms of selected regular two‐dimensional tessellations and in terms of a set of empirical surface partitioning, commonly employed in spatial analyses. Proposed correction factors allow a modification of this formula to estimate more precisely the associated inertia of an adjacency matrix. Este artículo aborda el cálculo de la inercia de una matriz de adyacencia, (es decir, el número de valores propios (eigenvalues) positivos, cero y negativos) asociados a un grafo conexo plano no orientado (connected undirected planar graph). Se deriva una fórmula que es el límite superior del número de valores propios negativos de esta matriz basándose en los resultados estándar de la traza de la matriz (matrix trace) junto con el uso de los promedios de valores propios no extremos y que requiere cálculos del par de valores propios extremos y del número de valores propios cero. El número de valores propios positivos se puede calcular fácilmente a partir de este resultado. Se evalúa esta fórmula en términos de mosaicos regulares bidimensionales y en términos de un conjunto de superficies de partición (surface partitioning) empíricas comúnmente empleados en análisis espaciales. Los factores de corrección propuestos permiten modificar esta fórmula para estimar con mayor precisión la inercia de una matriz de adyacencia. 本文讨论了联通非有向平面图邻接矩阵的惯性逼近（即正的,零以及负的特征值的个数）问题。基于标准矩阵迹的结果,综合利用非极值特征值的平均值,通过计算极值特征值对和零特征值个数,构建了邻接矩阵中负特征值上界计算公式。正特征值的个数可以简单地从上述结果中直接计算。采用空间分析中常用的规则二维格网化选取,以及一系列的经验曲面剖分对该公式的评估。所提出的修正指数允许对该公式进行修正,从而更精确地估计邻接矩阵惯性。     

蜀国人口蠡测

献所见蜀国户口数据共计三条,其中两条只是蜀国户口的一部分。它很可能是蜀国建立之初和亡国之际所控制的以成都为中心的蜀郡人口。另一条则由吴国推及蜀国,说明蜀国中期户数有望达到百万。本认为蜀国初年的人口总数,相当于东汉后期这一地区人口总数的60％左右。蜀汉立国四十余年,其间人口有可能以5‰的速度逐年递增。由此推出,蜀国人口的峰值可达529万。     

Observations on Some of the Principal Portraits of Devonshire Worthies

Area excavation of five Middle Bronze Age Round Houses at Black Patch, Alcisten, E. Sussex, has conclusively proved that the house terrace itself was a major structural element in the house construction. The position of storage pits and artifacts confirms that the house floor consisted of the whole house terrace. The precise recording of the position of every artifact was used to define activity areas which indicate the possible function of individual houses. From this evidence it is possible to suggest the likely social organisation of the excavated compound.     

略论《天禄琳琅书目》的文献学价值——以其藏书史料为例

《天禄琳琅书目》是我国首部规范的官方善本书目,在版本学、目录学、藏书史诸方面均具发韧之功。本文以其所收藏书史料为例,揭示了其编纂的五个特点,全面阐述了其在文献学上的价值。     

对女性生命价值的探寻--读白玉芳女士的《秋霄落雁女儿情》

白玉芳女干所的《秋霄落雁女儿情》,从少数民族女作家的视角描写了战争中的女性,本着重评论了女作家描写战争中女性所表现的特点,主要有三方面,一,女性生命生存状态的复现;承担与回避;二,历史场景中女性的理性与情感交错;三,神话事故与女性情绪的有机结合。     

The Nature of Value and the Value of Nature: a Philosophical Overview

In an article exploring the philosophical issues raised by environmentalism, Ben Rogers argues for an alternative both to the narrowly economic and to an extravagantly mystical concept of Nature. Species and ecosystems, mountain ranges and mineral reserves have an intrinsic value in the sense that Nature moves and disturbs us independently of our concern for our own welfare or happiness. This analysis enables us to see the inadequacy of cost-benefit analysis, which treats natural goods as commodities. At the same time, recognizing that the natural environment has an intrinsic value does not in itself release us from the necessity of making difficult choices or from hard decisions as to what is and what is not 'natural'. One way of clarifying the place that Nature occupies in our scheme of values is by way of analogies with heirlooms, works of art and historic towns and cities. These analogies shed light on what it means to insist that natural goods are not commodities, but are something we hold in trust.     

The Geography of the Mathematics Research Collaboration Graph

Social networks have become a hot topic for research in the last decade or so. I study one such network in considerable detail: the graph of research collaborations among mathematicians. This graph displays many of the characteristics that various authors have found common to social networks in general. My “geographical” analysis includes the size of this graph, the distribution of the degrees of its vertices, its connectivity, the distances between its vertices, and its clustering coefficient. I also discuss the playful concept of Erd?s numbers. Las redes sociales se han convertido en un tema de gran interés de investigación durante la última década más o menos. El autor analiza una de esas redes a detalle: el grafo de las colaboraciones de investigación entre matemáticos. Este grafo muestra muchas de las características comunes que varios autores han encontrado en redes sociales en general. El análisis “geográfico” incluye el tamaño de este grafo, la distribución de los grados de sus vértices, su conectividad, las distancias entre sus vértices, y su coeficiente de concentración o clustering. El estudio también trata el concepto lúdico de los números de Erdos. 社会网络已成为近十年来研究的热点。作者详尽地研究了数学家间研究合作图。该图显示了不同作者间常拥有一般社会网络共有的许多特性。本文的地理分析包括图的大小、顶点的分布度与连结性,不同边之间的距离以及聚类指数。同时还讨论了有趣的Erd?s 数的概念。     

John Toland's Conjecture on the First Invention of Typographic Printing as Inspired by Cicero: Text and Context

This is a translation of a short text in Latin by John Toland (1670–1722), with an introduction and annotations. Toland's text is a conjecture on the influence of a passage from Cicero on modern printing. The translator's introduction discusses the theories mentioned by Toland, and sketches the background of the text. It discusses Toland's interest in Cicero and the context of the text's publication in 1722 by Michel Maittaire, and Toland's and Maittaire's intertwined circles of literary patronage.     

胡适任中国公学校长史事述论

胡适在1928年春任中国公学校长实际上是一种过渡时期的权宜选择,并无久居的打算.得益于胡适的个人声望及其开明的治校风格,中国公学在其任内获得了长足发展.但作为一所私立大学,中国公学面临的基本困境并未因胡适掌校而消除.随着时势演变,国民党对上海教育界的控制日益加强,加上北平的政治环境日渐宽松,胡适最终选择北返.胡适辞职后,中国公学的问题集中爆发,在胡适任内未实现的党化渗透,并未因其离职而避免.胡适离职不到半年,学校即发生大的风潮,导致中国公学由兴盛急剧转向衰败.胡适任中国公学校长实际上是内外各种因素作用下的偶然结果,故而其在中国公学创造的成就只能是昙花一现.     

Results of a New Approach to Solving the p-Median Problem with Maximum Distance Constraints

Considerable interest has been directed in the past to developing approaches for solving the p-median problem with maximum distance constraints. All current solution techniques consider potential facilities to be located only at nodes of the network. This paper deals with the solution of this problem under the condition where facility placement is not restricted to nodes. The examples given show that improvement in weighted distance can be obtained by solving the unrestricted site problem. In addition, feasible solutions can be obtained for smaller numbers of facilities than possible by all nodal facility placement.     

Graph Theory Interpretation of Flow Matrices: A Note on Maximization Procedures for Identifying Significant Links

A maximization procedure for identifying significant links in a flow matrix is described and its use illustrated. The method appears to have advantages over primary-flow linkage methods and over methods based on flow-combination procedures.     

以诗窥画——试论唐代花鸟画的审美价值取向

唐代是中国花鸟画科的正式形成时期,据考证,当时擅长花鸟画的画家高手如云．但因年代久远,作品真迹早已遗失,今人已无从得知其庐山真面,通过唐代题画诗这扇窗口,对唐代花鸟画的审美价值取向作一探索。     

中西方文化遗产旅游者感知价值差异研究

通过多维度多指标体系构建了文化遗产旅游者感知价值的测量量表,对比分析了中西方游客的感知价值差异。研究发现文化遗产旅游者感知价值由效率价值、质量价值、成本价值、服务价值、社会价值与享乐价值六个维度构成,除成本价值与感知价值负相关外,其他均正向影响感知价值。中西方游客在质量价值、成本价值和享乐价值的感知上存在显著差异。