{"title":"Exact and Approximate Solutions of the Abel–Volterra Equations","authors":"J. Abdalkhani","doi":"10.3888/tmj.18-2","DOIUrl":"https://doi.org/10.3888/tmj.18-2","url":null,"abstract":"","PeriodicalId":91418,"journal":{"name":"The Mathematica journal","volume":"18 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2016-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"69962556","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}
{"title":"Developing an Understanding of the Steps Involved in Solving Navier–Stokes Equations","authors":"D. Adair, M. Jaeger","doi":"10.3888/TMJ.17-8","DOIUrl":"https://doi.org/10.3888/TMJ.17-8","url":null,"abstract":"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.","PeriodicalId":91418,"journal":{"name":"The Mathematica journal","volume":"17 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2015-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"69961993","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}
{"title":"Graphical Representation of Proximity Measures for Multidimensional Data: Classical and Metric Multidimensional Scaling.","authors":"Martin S Zand, Jiong Wang, Shannon Hilchey","doi":"10.3888/tmj.17-7","DOIUrl":"10.3888/tmj.17-7","url":null,"abstract":"<p><p>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 <i>Mathematica</i> programs are provided.</p>","PeriodicalId":91418,"journal":{"name":"The Mathematica journal","volume":"17 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2015-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://www.ncbi.nlm.nih.gov/pmc/articles/PMC4675631/pdf/","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"69961943","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
{"title":"RIFA: A Differential Gene Connectivity Algorithm","authors":"Todd Allen","doi":"10.3888/tmj.17-2","DOIUrl":"https://doi.org/10.3888/tmj.17-2","url":null,"abstract":"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.","PeriodicalId":91418,"journal":{"name":"The Mathematica journal","volume":"17 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2015-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"69962092","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}
{"title":"On the Maximal Orbit Transfer Problem","authors":"M. Muresan","doi":"10.3888/TMJ.17-4","DOIUrl":"https://doi.org/10.3888/TMJ.17-4","url":null,"abstract":"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.","PeriodicalId":91418,"journal":{"name":"The Mathematica journal","volume":"17 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2015-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"69962264","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}
{"title":"Domain Coloring on the Riemann Sphere","authors":"Á. Sandoval-Romero, Antonio Hernández-Garduño","doi":"10.3888/TMJ.17-9","DOIUrl":"https://doi.org/10.3888/TMJ.17-9","url":null,"abstract":"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.","PeriodicalId":91418,"journal":{"name":"The Mathematica journal","volume":"17 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2015-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"69962010","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}
{"title":"New Symbolic Solutions of Biot’s 2D Pore Elasticity Problem","authors":"A. Papusha, D. Gontarev","doi":"10.3888/TMJ.17-5","DOIUrl":"https://doi.org/10.3888/TMJ.17-5","url":null,"abstract":"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.","PeriodicalId":91418,"journal":{"name":"The Mathematica journal","volume":"15 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2015-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"69961818","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}