共查询到20条相似文献,搜索用时 171 毫秒
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三条侧棱两两相互垂直的四面体是一种特殊的四面体,我们称之为直角四面体,它具有以下性质:(1)任何一条侧棱垂直另两个侧棱构成的平面;(2)三个侧面两两垂直;(3)顶点在底面上的射影是底面三角形的垂心等,立体几何中很重要的概念和定理.都能从这个直角四正面体中衍生,因此深入研究直角四面体,对于把握空间图形中直线和平面的关系,尤为重要.下面利用直角四面体的性质简解两道商考题.…… 相似文献
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一、专题的背景与分析
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闵行区的沪闵路─春申路口是交通特别拥挤的交叉路口之一.家住莘庄地区的同学有一个共同的感受,在他们到校或回家路上必经的沪闵路─春申路口时常遇到塞车现象.…… 相似文献
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"牛吃草"问题又称为消长问题,是17世纪英国伟大的科学家牛顿提出来的.典型牛吃草问题的条件是假设草的生长速度固定不变,不同头数的牛吃光同一片草地所需的天数各不相同,求若干头牛吃这片草地可以吃多少天.由于吃的天数不同,草又是天天在生长的,所以草的存量随吃的天数不断地变化.…… 相似文献
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每年的高考,较多的问题都渗透着对对称内容的考察.在解答它们时,若能挖掘潜在的对称性,根据几何图形的对称及数据、位置、关系等所隐含着的对称性特点,则能在纷繁的困惑中求得简捷的突 相似文献
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高三数学复习时常有习题课的教学,传统的教学方式往往是讲解一些同学们易犯的错误即"纠错课",或解决大多数学生所不能解的问题即"提高课".其目的是要求学生能通过例题的讲解与练习达到知识的掌握和能力的提高,以这种方式的教学容易产生学生"学后弃之"、"解后忘之"的现象.…… 相似文献
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This paper proposes a mathematical model to compare a network organization with a hierarchical organization. In order to formulate the model, we define a three-dimensional framework of the coordination structure of a network and of other typical coordination structures. In the framework, we can define a network structure by contrasting it with a hierarchy, in terms of the distribution of decision making, which is one of the main features of information processing. Based on this definition, we have developed a mathematical model for evaluating coordination structures. Using this model, we can derive two boundary conditions among the coordination structures with respect to the optimal coordination structure. The boundary conditions help us to understand why an organization changes its coordination structure from a hierarchy to a network and what factors cause this change. They enable us, for example, to find points of structural change where the optimal coordination structure shifts from a hierarchy to a hierarchy with delegation or from a hierarchy with delegation to a network, when the nature of the task changes from routine to non-routine. In conclusion, our framework and model may provide a basis for discussing the processes that occur when coordination structures change between a hierarchy and a network. 相似文献
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Chul Moon Noah Giansiracusa Nicole A. Lazar 《Journal of computational and graphical statistics》2018,27(3):576-586
Topological data analysis (TDA) is a rapidly developing collection of methods for studying the shape of point cloud and other data types. One popular approach, designed to be robust to noise and outliers, is to first use a smoothing function to convert the point cloud into a manifold and then apply persistent homology to a Morse filtration. A significant challenge is that this smoothing process involves the choice of a parameter and persistent homology is highly sensitive to that choice; moreover, important scale information is lost. We propose a novel topological summary plot, called a persistence terrace, that incorporates a wide range of smoothing parameters and is robust, multi-scale, and parameter-free. This plot allows one to isolate distinct topological signals that may have merged for any fixed value of the smoothing parameter, and it also allows one to infer the size and point density of the topological features. We illustrate our method in some simple settings where noise is a serious issue for existing frameworks and then we apply it to a real dataset by counting muscle fibers in a cross-sectional image. Supplementary material for this article is available online. 相似文献
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NBU*t0寿命分布中新元件的寿命随机地大于旧的年龄不小于t0的元件的剩余寿命,这为更广泛地模拟元件的老化和劣化现象提供了丰富的内容。本文首先对那些t0年龄点之后剩余寿命随机等于新元件寿命的元件的结构加以刻画,然后建立了一个非参数检验方法以区分这种随机等价性和t0年龄点后的严格的NBU性,并给出了针对一个NBU*t0但非NBU的寿命分布的例子的数值模拟结果。 相似文献
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David R. Nowicki Wesley S. Randall Jose Emmanuel Ramirez-Marquez 《European Journal of Operational Research》2012
We propose a new heuristic algorithm to improve the computational efficiency of the general class of Multi-Echelon Technique for Recoverable Item Control (METRIC) problems. The objective of a METRIC-based decision problem is to systematically determine the location and quantity of spares that either maximizes the operational availability of a system subject to a budget constraint or minimizes its cost subject to an operational availability target. This type of sparing analysis has proven essential when analyzing the sustainment policies of large-scale, complex repairable systems such as those prevalent in the defense and aerospace industries. Additionally, the frequency of these sparing studies has recently increased as the adoption of performance-based logistics (PBL) has increased. PBL represents a class of business strategies that converts the recurring cost associated with maintenance, repair, and overhaul (MRO) into cost avoidance streams. Central to a PBL contract is a requirement to perform a business case analysis (BCA) and central to a BCA is the frequent need to use METRIC-based approaches to evaluate how a supplier and customer will engage in a performance based logistics arrangement where spares decisions are critical. Due to the size and frequency of the problem there exists a need to improve the efficiency of the computationally intensive METRIC-based solutions. We develop and validate a practical algorithm for improving the computational efficiency of a METRIC-based approach. The accuracy and effectiveness of the proposed algorithm are analyzed through a numerical study. The algorithm shows a 94% improvement in computational efficiency while maintaining 99.9% accuracy. 相似文献
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Robert R. Miner 《Journal of Geometric Analysis》1999,9(1):143-160
A chain is the intersection of a complex totally geodesic subspace in complex hyperbolic 2-space with the boundary. The boundary
admits a canonical contact structure, and chains are distiguished curves transverse to this structure. The space of chains
is analyzed both as a quotient of the contact bundle, and as a subset of ℂP2. The space of chains admits a canonical, indefinite Hermitian metric, and curves in the space of chains with null tangent
vectors are shown to correspond to a path of chains tangent to a curve in the boundary transverse to the contact structure.
A family of local differential chain curvature operators are introduced which exactly characterize when a transverse curve
is a chain. In particular, operators that are invariant under the stabilizer of a point in the interior of complex hyperbolic
space, or a point on the boundary, are developed in detail. Finally, these chain curvature operators are used to prove a generalization
of Louiville's theorem: a sufficiently smooth mapping from the boundary of complex hyperbolic 2-space to itself which preserves
chains must be the restriction of a global automorphism. 相似文献
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Vladimir S. Lerner 《Journal of Mathematical Analysis and Applications》2007,334(1):441-466
The paper introduces a new approach to dynamic modeling, using the variation principle, applied to a functional on trajectories of a controlled random process, and its connection to the process' information functional. In [V.S. Lerner, Dynamic approximation of a random information functional, J. Math. Anal. Appl. 327 (1) (2007) 494-514, available online 5-24-06], we presented the information path functional with the Lagrangian, determined by the parameters of a controlled stochastic equation. In this paper, the solution to the path functional's variation problem provides both a dynamic model of a random process and the model's optimal control, which allows us to build a two-level information model with a random process at the microlevel and a dynamic process at the macrolevel. A wide class of random objects, modeled by the Markov diffusion process and a common structure of the process' information functional, leads to a universal information structure of the dynamic model, which is specified and identified on a particular object with the applied optimal control functions. The developed mathematical formalism, based on classical methods, is aimed toward the solution of problems identification, combined with an optimal control synthesis, which is practically implemented and also demonstrated in the paper's example. 相似文献
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Method of successive projections for finding a common point of sets in metric spaces 总被引:4,自引:0,他引:4
Many problems in applied mathematics can be abstracted into finding a common point of a finite collection of sets. If all the sets are closed and convex in a Hilbert space, the method of successive projections (MOSP) has been shown to converge to a solution point, i.e., a point in the intersection of the sets. These assumptions are however not suitable for a broad class of problems. In this paper, we generalize the MOSP to collections of approximately compact sets in metric spaces. We first define a sequence of successive projections (SOSP) in such a context and then proceed to establish conditions for the convergence of a SOSP to a solution point. Finally, we demonstrate an application of the method to digital signal restoration. 相似文献
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Winter road maintenance operations involve a host of decision-making problems at the strategic, tactical, operational, and real-time levels. Those operations include spreading of chemicals and abrasives, snow plowing, loading snow into trucks, and hauling snow to disposal sites. In this paper, we present a model and two heuristic solution approaches based on mathematical optimization for the problem of partitioning a road network into sectors and allocating sectors to snow disposal sites for snow disposal operations. Given a road network and a set of planned disposal sites, the problem is to determine a set of non-overlapping subnetworks, called sectors, according to several criteria related to the operational effectiveness and the geographical layout, and to assign each sector to a single snow disposal site so as to respect the capacities of the disposal sites, while minimizing relevant variable and fixed costs. Our approach uses single street segments as the units of analysis and we consider sector contiguity, sector balance and sector shape constraints, hourly and annual disposal site capacities, as well as single assignment requirements. The resulting model is based on a multi-commodity network flow structure to impose the contiguity constraints in a linear form. The two solution approaches were tested on data from the city of Montreal in Canada. 相似文献
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The paper studies stochastic integration with respect to Gaussian processes and fields. It is more convenient to work with a field than a process: by definition, a field is a collection of stochastic integrals for a class of deterministic integrands. The problem is then to extend the definition to random integrands. An orthogonal decomposition of the chaos space of the random field, combined with the Wick product, leads to the Itô-Skorokhod integral, and provides an efficient tool to study the integral, both analytically and numerically. For a Gaussian process, a natural definition of the integral follows from a canonical correspondence between random processes and a special class of random fields. Also considered are the corresponding linear stochastic evolution equations. 相似文献
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The sampling theorem is one of the most powerful tools in signal analysis. It says that to recover a function in certain function spaces, it suffices to know the values of the function on a sequence of points. Most of known results, e.g., regular and irregular sampling theorems for band-limited functions, concern global sampling. That is, to recover a function at a point or on an interval, we have to know all the samples which are usually infinitely many. On the other hand, local sampling, which invokes only finite samples to reconstruct a function on a bounded interval, is practically useful since we need only to consider a function on a bounded interval in many cases and computers can process only finite samples. In this paper, we give a characterization of local sampling sequences for spline subspaces, which is equivalent to the celebrated Schönberg-Whitney Theorem and is easy to verify. As applications, we give several local sampling theorems on spline subspaces, which generalize and improve some known results. 相似文献