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Symbolic Evaluation of Boundary Problems for Offshore Design Technology 海洋设计技术边界问题的符号评价
The Mathematica journal Pub Date : 2009-01-12 DOI: 10.3888/TMJ.11.1-6
A. Papusha, Victor Shtrasser, I. Fedorov
{"title":"Symbolic Evaluation of Boundary Problems for Offshore Design Technology","authors":"A. Papusha, Victor Shtrasser, I. Fedorov","doi":"10.3888/TMJ.11.1-6","DOIUrl":"https://doi.org/10.3888/TMJ.11.1-6","url":null,"abstract":"This article proposes a new symbolic technique for offshore design technology. Several solutions deal with the design of longitudinally elastic offshore constructions. Details are discussed for a drillstem and a riser. Both symbolic and numerical solutions derived with Mathematica are applied to solve problems in offshore design technology. All symbolic approaches are based on solutions of the linear boundary problems that arise. Additionally, a new symbolic solution for the generic boundary problem is discussed in detail.","PeriodicalId":91418,"journal":{"name":"The Mathematica journal","volume":"11 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2009-01-12","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"69959473","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 3
Buckets and Jumping Pet 水桶和跳跃的宠物
The Mathematica journal Pub Date : 2009-01-12 DOI: 10.3888/TMJ.11.1-3
J. Rangel-Mondragon
{"title":"Buckets and Jumping Pet","authors":"J. Rangel-Mondragon","doi":"10.3888/TMJ.11.1-3","DOIUrl":"https://doi.org/10.3888/TMJ.11.1-3","url":null,"abstract":"Consider the following question. Given two unmarked buckets of capacities 3 and 5 liters, how can we obtain exactly 1 liter of water from an inexhaustible well? The answer is to fill the 3-liter bucket first and empty it into the other bucket. Then, refill the 3-liter bucket from the well and use it to completely fill the other one, leaving the 1 liter desired. This problem is one of a famous category of “decanting” problems that have always appealed to a wide audience, including recreational mathematicians and computer scientists. Similar problems have found valuable applications in the analysis and teaching of algorithmic techniques, typifying many of the difficulties involved in the design of goal-oriented strategies. In the problem of the buckets, it is easy to show that if we have buckets of capacities a and b liters, and we start with both empty, the problem is solvable if and only if a and b are coprime. If this is the case, we have several ways to proceed. Each of them can be described by a sequence of ordered pairs accounting for the states through which we pass at each step towards our goal. Consider for instance, one of the shortest sequences that solves the problem for capacities 2 and 5: {{0, 0}, {0, 5}, {2, 3}, {0, 3}, {2, 1}}.","PeriodicalId":91418,"journal":{"name":"The Mathematica journal","volume":"11 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2009-01-12","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"69959407","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Dynamic Integration of Interpolating Functions and Some Concrete Optimal Stopping Problems 插值函数的动态积分及一些具体的最优停止问题
The Mathematica journal Pub Date : 2008-11-14 DOI: 10.3888/TMJ.10.4-3
A. Lyasoff
{"title":"Dynamic Integration of Interpolating Functions and Some Concrete Optimal Stopping Problems","authors":"A. Lyasoff","doi":"10.3888/TMJ.10.4-3","DOIUrl":"https://doi.org/10.3888/TMJ.10.4-3","url":null,"abstract":"This article describes a streamlined method for simultaneous integration of an entire family of interpolating functions that uses one and the same interpolation grid in one or more dimensions. A method for creating customized quadrature/cubature rules that takes advantage of certain special features of Mathematica’s InterpolatingFunction objects is presented. The use of such rules leads to a new and more efficient implementation of the method for optimal stopping of stochastic systems that was developed in [1]. In particular, this new implementation allows one to extend the scope of the method to free boundary optimal stopping problems in higher dimensions. Concrete applications to finance~mainly to Americanstyle financial derivatives~are presented. In particular, the price of an American put option that can be exercised with any one of two uncorrelated underlying assets is calculated as a function of the observed prices. This method is similar in nature to the well-known Longstaff|Schwartz algorithm, but does not involve Monte|Carlo simulation of any kind.","PeriodicalId":91418,"journal":{"name":"The Mathematica journal","volume":"10 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2008-11-14","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"69959083","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 2
Making Holes and Windows in Surfaces 在表面上打洞和窗户
The Mathematica journal Pub Date : 2008-11-14 DOI: 10.3888/tmj.10.4-4
A. Horwitz
{"title":"Making Holes and Windows in Surfaces","authors":"A. Horwitz","doi":"10.3888/tmj.10.4-4","DOIUrl":"https://doi.org/10.3888/tmj.10.4-4","url":null,"abstract":"In this article, we demonstrate makehole, a program which removes points from any Graphics or Graphics3D picture whose coordinates satisfy a stated condition. We also demonstrate transparent and makewindow, programs which make an entire or a specific portion of an opaque surface into a transparent mesh. We use these programs to view the region of integration for a triple integral. This article uses Mathematica 5.2, but with minor modifications all three programs work in Mathematica 6, as well as earlier versions. The makehole program duplicates some of the functionality of the RegionPlot3D command and RegionFunction option of the ParametricPlot3D command in Version 6, while the transparent program behaves like the PlotStyle O None option of the Plot3D command (see Editor’s Note for a demonstration of the Mathematica 6 code).","PeriodicalId":91418,"journal":{"name":"The Mathematica journal","volume":"10 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2008-11-14","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"69959088","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
MathCode : A System for C++ or Fortran Code Generation from Mathematica MathCode:从Mathematica生成c++或Fortran代码的系统
The Mathematica journal Pub Date : 2008-11-14 DOI: 10.3888/TMJ.10.4-7
P. Fritzson, V. Engelson, K. Sheshadri
{"title":"MathCode : A System for C++ or Fortran Code Generation from Mathematica","authors":"P. Fritzson, V. Engelson, K. Sheshadri","doi":"10.3888/TMJ.10.4-7","DOIUrl":"https://doi.org/10.3888/TMJ.10.4-7","url":null,"abstract":"MathCode is a package that translates a subset of Mathematica into a compiled language like Fortran or C++. The chief goal of the design of MathCode is to add extra performance and portability to the symbolic prototyping capabilities offered by Mathematica. This article discusses several important features of MathCode, such as adding type declarations, examples of functions that can be translated, ways to extend the compilable subset, and generating a stand-alone executable, and presents a few application examples.","PeriodicalId":91418,"journal":{"name":"The Mathematica journal","volume":"10 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2008-11-14","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"69959165","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 6
The Return of the Riemann Surface 黎曼曲面的回归
The Mathematica journal Pub Date : 2008-11-14 DOI: 10.3888/TMJ.10.4-1
M. Trott
{"title":"The Return of the Riemann Surface","authors":"M. Trott","doi":"10.3888/TMJ.10.4-1","DOIUrl":"https://doi.org/10.3888/TMJ.10.4-1","url":null,"abstract":"This is my first column since Version 6 came out a few months ago. Version 6, after being in the works for many years, provides a wealth of new features that are useful in many numeric and symbolic calculations, advanced programs, visualizations, and elsewhere. With so many exciting new possibilities, it was not easy to decide what to discuss in this column. So instead of delving into a new subject, I think the best way to see some of the new features and resulting capabilities of Version 6 is to compare with some corresponding Version 5 results. That is why today I will come back to a subject discussed in earlier columns and demonstrate how to go quite a bit further with Version 6.","PeriodicalId":91418,"journal":{"name":"The Mathematica journal","volume":"10 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2008-11-14","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"69959011","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 4
Graphing on the Riemann Sphere 在黎曼球上绘图
The Mathematica journal Pub Date : 2008-11-14 DOI: 10.3888/TMJ.10.4-5
Djilali Benayat
{"title":"Graphing on the Riemann Sphere","authors":"Djilali Benayat","doi":"10.3888/TMJ.10.4-5","DOIUrl":"https://doi.org/10.3888/TMJ.10.4-5","url":null,"abstract":"Graphing a curve in the Cartesian plane can be done only in a restricted “window” @a, bDμ @c, dD. If the function to be plotted has a large domain or range, it is practically impossible to get a global view of the curve. This makes it difficult to understand the asymptotic behavior of complicated curves with various kinds of infinities. Furthermore, for most functions (e.g., polynomials of degree greater than four), graphing in a large window loses important details, while graphing in a small window loses the global features.","PeriodicalId":91418,"journal":{"name":"The Mathematica journal","volume":"10 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2008-11-14","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"69959097","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Airfoil Aerodynamics Using Panel Methods 使用面板方法的翼型空气动力学
The Mathematica journal Pub Date : 2008-11-14 DOI: 10.3888/TMJ.10.4-6
R. Fearn
{"title":"Airfoil Aerodynamics Using Panel Methods","authors":"R. Fearn","doi":"10.3888/TMJ.10.4-6","DOIUrl":"https://doi.org/10.3888/TMJ.10.4-6","url":null,"abstract":"Potential flow over an airfoil plays an important historical role in the theory of flight. The governing equation for potential flow is Laplaceʼs equation, a widely studied linear partial differential equation. One of Greenʼs identities can be used to write a solution to Laplaceʼs equation as a boundary integral. Numerical models based on this approach are known as panel methods in the aerodynamics community. This article introduces the availability of a collection of computational tools for constructing numerical models for potential flow over an airfoil based on panel methods. Use of the software is illustrated by implementing a specific model using vortex panels of linearly varying strength to compute the flow over a member of the NACA four-digit family of airfoils.","PeriodicalId":91418,"journal":{"name":"The Mathematica journal","volume":"10 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2008-11-14","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"69959156","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 20
Classic Puzzles in Wolfram Demonstrations Wolfram演示中的经典谜题
The Mathematica journal Pub Date : 2008-01-01 DOI: 10.3888/tmj.10.4-2
E. Pegg
{"title":"Classic Puzzles in Wolfram Demonstrations","authors":"E. Pegg","doi":"10.3888/tmj.10.4-2","DOIUrl":"https://doi.org/10.3888/tmj.10.4-2","url":null,"abstract":"","PeriodicalId":91418,"journal":{"name":"The Mathematica journal","volume":"10 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2008-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"69959081","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
A Mode-Matching Method for Multichannel Scattering Problems 多通道散射问题的模式匹配方法
The Mathematica journal Pub Date : 2007-08-07 DOI: 10.3888/tmj.10.3-6
P. Falloon
{"title":"A Mode-Matching Method for Multichannel Scattering Problems","authors":"P. Falloon","doi":"10.3888/tmj.10.3-6","DOIUrl":"https://doi.org/10.3888/tmj.10.3-6","url":null,"abstract":"The motivation for the work presented in this article is a problem from condensed matter physics concerning electron transport through ferromagnetic domain walls. Domain walls are spatially extended boundaries which separate magnetically homogeneous domains existing in ferromagnetic materials. They are regions in which the magnetization vector reverses by 180° over a length l typically on the order of 10 –100nm (Figure 1) [1]. Electrons travelling through such a structure experience a scattering due to the interaction of their intrinsic spin magnetic moment with the rotating magnetization. Recently, this scattering effect has been the subject of a large amount of experimental and theoretical research [2]. Much of this interest has been stimulated by the exciting potential for technological applications in solid state information storage devices that may be offered by storing domain walls in nanowire structures.","PeriodicalId":91418,"journal":{"name":"The Mathematica journal","volume":"10 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2007-08-07","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"69958875","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
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