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Inversive Geometry: Part 2 逆几何:第2部分
The Mathematica journal
Pub Date : 2016-01-01 DOI: 10.3888/TMJ.18-5
J. Rangel-Mondragon
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引用次数: 0
A Computational Strategy for Effective Gene Silencing through siRNAs 通过sirna进行有效基因沉默的计算策略
The Mathematica journal
Pub Date : 2016-01-01 DOI: 10.3888/TMJ.18-1
Todd Allen
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引用次数: 0
The Poisson-Influenced K-Means Algorithm 泊松影响的k -均值算法
The Mathematica journal
Pub Date : 2016-01-01 DOI: 10.3888/TMJ.18-3
Brian P. Morris, Z. Levine
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引用次数: 0
Exact and Approximate Solutions of the Abel–Volterra Equations Abel-Volterra方程的精确解和近似解
The Mathematica journal
Pub Date : 2016-01-01 DOI: 10.3888/tmj.18-2
J. Abdalkhani
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引用次数: 1
Developing an Understanding of the Steps Involved in Solving Navier–Stokes Equations 发展对求解Navier-Stokes方程的步骤的理解
The Mathematica journal
Pub Date : 2015-01-01 DOI: 10.3888/TMJ.17-8
D. Adair, M. Jaeger
This article describes how Mathematica can be used to develop an understanding of the basic steps involved in solving Navier– Stokes equations using a finite-volume approach for incompressible steady-state flow. The main aim is to let students follow from a mathematical description of a given problem through to the method of solution in a transparent way. The wellknown “driven cavity” problem is used as the problem for testing the coding, and the Navier–Stokes equations are solved in vorticity-streamfunction form. Building on what the students were familiar with from a previous course, the solution algorithm for the vorticity-streamfunction equations chosen was a relaxation procedure. However, this approach converges very slowly, so another method using matrix and linear algebra concepts was also introduced to emphasize the need for efficient and optimized code.
本文描述了如何使用Mathematica来理解使用有限体积方法求解不可压缩稳态流的Navier - Stokes方程所涉及的基本步骤。主要目的是让学生以一种透明的方式从给定问题的数学描述一直到解决方法。采用著名的“驱动腔”问题作为测试编码的问题，并以涡流函数形式求解Navier-Stokes方程。基于学生在之前课程中熟悉的内容，所选择的涡流函数方程的求解算法是一个松弛过程。然而，这种方法收敛速度很慢，因此还引入了另一种使用矩阵和线性代数概念的方法，以强调对高效和优化代码的需求。
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引用次数: 4
Graphical Representation of Proximity Measures for Multidimensional Data: Classical and Metric Multidimensional Scaling. 多维数据近似度量的图形表示：经典和公制多维标度。
The Mathematica journal
Pub Date : 2015-01-01 Epub Date: 2015-09-30 DOI: 10.3888/tmj.17-7
Martin S Zand, Jiong Wang, Shannon Hilchey

We describe the use of classical and metric multidimensional scaling methods for graphical representation of the proximity between collections of data consisting of cases characterized by multidimensional attributes. These methods can preserve metric differences between cases, while allowing for dimensional reduction and projection to two or three dimensions ideal for data exploration. We demonstrate these methods with three datasets for: (i) the immunological similarity of influenza proteins measured by a multidimensional assay; (ii) influenza protein sequence similarity; and (iii) reconstruction of airport-relative locations from paired proximity measurements. These examples highlight the use of proximity matrices, eigenvalues, eigenvectors, and linear and nonlinear mappings using numerical minimization methods. Some considerations and caveats for each method are also discussed, and compact Mathematica programs are provided.

我们介绍了如何使用经典和度量多维缩放方法，以图形表示由多维属性表征的案例组成的数据集合之间的接近性。这些方法可以保留案例之间的度量差异，同时允许降维并投影到二维或三维，是数据探索的理想选择。我们用三个数据集演示了这些方法：(i) 通过多维检测测量流感蛋白质的免疫学相似性；(ii) 流感蛋白质序列相似性；(iii) 通过成对邻近测量重建机场相关位置。这些示例重点介绍了利用数值最小化方法使用邻近矩阵、特征值、特征向量以及线性和非线性映射的情况。此外，还讨论了每种方法的一些注意事项，并提供了简洁的 Mathematica 程序。
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引用次数: 0
RIFA: A Differential Gene Connectivity Algorithm 差分基因连接算法
The Mathematica journal
Pub Date : 2015-01-01 DOI: 10.3888/tmj.17-2
Todd Allen
With the invention of microarray technology, scientists finally had a means to measure global changes in gene expression between two biological states [1]. This has led to thousands of scientific publications describing long lists of differentially expressed genes in each scientist’s favorite experimental system. What has gradually become apparent to biologists is that having a list of differentially expressed genes, while an important first step in understanding the differences between two phenotypes (where phenotype represents the physical manifestation of one or more traits), is often not enough to identify the genes most directly responsible for driving changes in phenotype. While it is true that genes that are differentially expressed between two biological states may be important in explaining those differences, it is also possible that genes whose expression is not changed can also be pivotal in driving phenotypic differences.
随着微阵列技术的发明，科学家们终于有了一种方法来测量两种生物状态之间基因表达的全局变化。这导致成千上万的科学出版物描述了每个科学家最喜欢的实验系统中差异表达基因的长列表。对于生物学家来说，逐渐变得明显的是，虽然拥有差异表达基因的列表是理解两种表型之间差异的重要第一步(表型代表一种或多种特征的物理表现)，但通常不足以确定最直接负责驱动表型变化的基因。虽然在两种生物状态之间表达差异的基因可能在解释这些差异方面很重要，但也有可能表达未改变的基因也可能是驱动表型差异的关键。
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引用次数: 0
On the Maximal Orbit Transfer Problem 关于最大轨道转移问题
The Mathematica journal
Pub Date : 2015-01-01 DOI: 10.3888/TMJ.17-4
M. Muresan
Assume that a spacecraft is in a circular orbit and consider the problem of finding the largest possible circular orbit to which the spacecraft can be transferred with constant thrust during a set time, so that the variable parameter is the thrust-direction angle β. Also assume that there is only one center of attraction at the common center of the two circular orbits. Finally, assume normalized values for all constants and variables.
假设航天器在一个圆形轨道上运行，考虑在给定时间内以恒定推力使航天器能够转移到的最大可能圆形轨道的问题，变量参数为推力方向角β。同时假设在两个圆形轨道的共同中心只有一个引力中心。最后，假设所有常量和变量的归一化值。
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引用次数: 5
Domain Coloring on the Riemann Sphere 黎曼球上的域着色
The Mathematica journal
Pub Date : 2015-01-01 DOI: 10.3888/TMJ.17-9
Á. Sandoval-Romero, Antonio Hernández-Garduño
Domain coloring is a technique for constructing a tractable visual object of the graph of a complex function. The package complexVisualize.m improves on existing domain coloring techniques by rendering a global picture on the Riemann sphere (the compactification of the complex plane). Additionally, the package allows dynamic visualization of families of Möbius transformations. In this article we discuss the implementation of the package and illustrate its usage with some examples.
域着色是一种构造复杂函数图的可处理的可视化对象的技术。这个包很复杂。m通过在黎曼球(复平面的紧化)上绘制全局图像，改进了现有的域着色技术。此外，该包还允许对Möbius转换族进行动态可视化。在本文中，我们将讨论该包的实现，并通过一些示例说明其用法。
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引用次数: 1
New Symbolic Solutions of Biot’s 2D Pore Elasticity Problem Biot二维孔隙弹性问题的新符号解
The Mathematica journal
Pub Date : 2015-01-01 DOI: 10.3888/TMJ.17-5
A. Papusha, D. Gontarev
This article presents new symbolic solutions for the problem of pore elasticity and pore pressure. These techniques are based on the classic theoretical approach proposed by M. A. Biot [1]. The new symbolic solutions differ from the well-known approximations of the functions proposed for the 2D pore elasticity problem. Both new symbolic and numerical solutions are then applied to solve problems arising in offshore design technology, specifically dealing with the penetration of a gravitybased rig installed in the Arctic region of the North Sea of Russia. All symbolic approaches are based on solutions of the linear problem of the pore elasticity for homogeneous soil. The new symbolic solutions are compared with Biot’s solutions.
本文对孔隙弹性和孔隙压力问题提出了新的符号解法。这些技术是基于m.a. Biot b[1]提出的经典理论方法。新的符号解不同于众所周知的为二维孔隙弹性问题提出的函数近似。然后将新的符号和数值解决方案应用于解决海上设计技术中出现的问题，特别是处理安装在俄罗斯北海北极地区的重力钻井平台的穿透问题。所有的符号方法都是基于均匀土的孔隙弹性线性问题的解。将新的符号解与Biot的解进行了比较。
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引用次数: 0
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