scholarly journals Representación gráfica de las funciones complejas con el Mathematica

2018 ◽  
pp. 52-56
Keyword(s):  
Complex Variable ◽  
Dimensional Space ◽  
Complex Function ◽  
Three Dimensional ◽  
Graphical Display ◽  
Model Based ◽  
Complex Functions ◽  
Complex Valued ◽  
Three Dimensional Space

Representación gráfica de las funciones complejas con el Mathematica Graphical display of complex functions with Mathematica Ricardo Velezmoro y Robert Ipanaqué Universidad Nacional de Piura, Urb. Miraflores s/n, Castilla, Piura, Perú. DOI: https://doi.org/10.33017/RevECIPeru2015.0008/ Resumen La representación gráfica de las funciones de valor complejo, de una variable compleja, es un tema de mucho interés dado que la gráfica de una función de este tipo tendría que ser dibujada en un espacio tetra dimensional. Este artículo presenta una propuesta para representar tales gráficas mediante el uso de un modelo basado en una submersión, del espacio tetra dimensional en el espacio tridimensional; para luego, con ayuda del Mathematica llegar a obtener una representación de las mencionadas gráficas en una pantalla 2D. Adicionalmente, se implementarán algunos comandos en el Mathematica, los mismos que permitirán realizar las representaciones de variados e interesantes ejemplos. Descriptores: función compleja, visualización, submersión Abstract The graphical display of complex-valued functions of a complex variable is a subject of much interest since the graph of such a function would have to be drawn in a four-dimensional space. This article presents a proposal to display such graphs using a model based on a submersion, from four-dimensional space to three-dimensional space; then, with the help of Mathematica arrive at a representation of the graphs mentioned in a 2D screen. Additionally, some commands are implemented in Mathematica, the same that will make representations varied and interesting examples. Keywords: complex function, visualization, submersion

Research on Combinational Reasoning of Directional Relations Based on Double Projections Model in Three-Dimensional Space

2011 ◽  
Vol 186 ◽  
pp. 61-65
Author(s):  
Yong Shan Liu ◽  
Wei Jie Gu
Keyword(s):  
Matrix Model ◽  
Dimensional Space ◽  
Three Dimensional ◽  
Model Based ◽  
Computational Performance ◽  
Minimum Bounding Rectangle ◽  
Directional Relations ◽  
Three Dimensional Space

The xoy and xoz planes are divided into nine areas in three-dimensional space respectively by the MBR (Minimum Bounding Rectangle), which are produced by the reference objects’ projection to their planes. The intersecting situations between the projection of target objects and the two of reference objects are expressed by two 3×3 matrices. Then, a directional relations matrix model based on double projections is put forward. A combinational reasoning method is proposed by using the computational performance of matrices based on this model. Moreover, a combinational reasoning experiment is given and the result matches the reality.

The Global Attractor of the 3D Complex GL Equation and the Estimate of its Dimensionality

2012 ◽  
Vol 588-589 ◽  
pp. 2051-2054
Author(s):  
Ben Tu Li ◽  
Zhi Chao Yuan
Keyword(s):  
Global Attractor ◽  
Nonlinear Term ◽  
Dimensional Space ◽  
A Priori ◽  
Three Dimensional ◽  
A Priori Estimation ◽  
Complex Valued ◽  
Three Dimensional Space

In three-dimensional space, by using the method of a priori estimation, we have studied the complex-valued GL equation, which has the 2 -th power of the nonlinear term. We have proved that the existence of the global attractor of this equation with the problem of period and border value, and we have studied the dimensionality of Hausdorff and fractal of the global attractor.

Visual-Graphic Design of a Unitary Constructive Model to Solve Analogues For Apollonius Problem Taking into Account Imaginary Geometric Images

2018 ◽  
Vol 6 (2) ◽  
pp. 23-46 ◽  
Author(s):  
Д. Волошинов ◽  
Denis Voloshinov
Keyword(s):  
Geometric Modeling ◽  
Dimensional Space ◽  
Three Dimensional ◽  
Constructive Model ◽  
Geometric Transformations ◽  
Automation Systems ◽  
Mathematical Problems ◽  
Visual Graphic ◽  
Complex Valued ◽  
Three Dimensional Space

The Apollonius problem on construction of circles, tangent to three arbitrary given circles of a plane, is one of classical geometry’s well-studied problems. The presented paper’s materials are directed at development a unified theory for Apollonius problem solving, taking into account it’s not only real, but also invisible complex-valued images. In the paper it has been demonstrated, that fundamental geometric structures, on which Apollonius problem is based on, are applicable not only to real, but also to complex-valued data, that makes possible to eliminate many exceptions, currently existing in it. In this paper Apollonius problem’s fundamental nature and its strong correlation with projective and quadratic geometric transformations has been disclosed. It has been proved that Apollonius problem and its analogues have a single solution method, in contrast to the prevailing idea that these problems can be solved only by separate particular methods. A concept of geometric experiment proposed by the author has allowed find out many previously unknown and discussed in this paper common factors, due to the set of many computational tests in the system Simplex for visual design of geometric models. In this paper is considered an example for solving an analogue of Apollonian problem for three-dimensional space, but proposed algorithm’s operation is universal, and it can be equally applied to solving similar problems in spaces of arbitrary dimensions. Obtained results demonstrate capabilities of methods for constructive modeling and multidimensional descriptive geometry in application to solving of complex mathematical problems, and determine the trends in development for automation systems of constructive geometric modeling.

Extension of the Spatial PDI Model to Three Dimensions

1997 ◽  
Vol 84 (1) ◽  
pp. 176-178
Author(s):  
Frank O'Brien
Keyword(s):  
Population Density ◽  
Dimensional Space ◽  
Finite Lattice ◽  
Three Dimensional ◽  
Upper Bounds ◽  
Three Dimensions ◽  
Lower And Upper Bounds ◽  
Density Index ◽  
Three Dimensional Space

The author's population density index ( PDI) model is extended to three-dimensional distributions. A derived formula is presented that allows for the calculation of the lower and upper bounds of density in three-dimensional space for any finite lattice.

A Peptoid with Extended Shape in Water

2019 ◽  
Author(s):  
Jumpei Morimoto ◽  
Yasuhiro Fukuda ◽  
Takumu Watanabe ◽  
Daisuke Kuroda ◽  
Kouhei Tsumoto ◽  
...  
Keyword(s):  
Spectroscopic Analysis ◽  
Dimensional Space ◽  
Three Dimensional ◽  
Biomolecular Recognition ◽  
Biological Application ◽  
New Class ◽  
Proteolytic Resistance ◽  
Pharmacokinetic Properties ◽  
Optically Pure ◽  
Three Dimensional Space

<div> <div> <div> <p>“Peptoids” was proposed, over decades ago, as a term describing analogs of peptides that exhibit better physicochemical and pharmacokinetic properties than peptides. Oligo-(N-substituted glycines) (oligo-NSG) was previously proposed as a peptoid due to its high proteolytic resistance and membrane permeability. However, oligo-NSG is conformationally flexible and is difficult to achieve a defined shape in water. This conformational flexibility is severely limiting biological application of oligo-NSG. Here, we propose oligo-(N-substituted alanines) (oligo-NSA) as a new peptoid that forms a defined shape in water. A synthetic method established in this study enabled the first isolation and conformational study of optically pure oligo-NSA. Computational simulations, crystallographic studies and spectroscopic analysis demonstrated the well-defined extended shape of oligo-NSA realized by backbone steric effects. The new class of peptoid achieves the constrained conformation without any assistance of N-substituents and serves as an ideal scaffold for displaying functional groups in well-defined three-dimensional space, which leads to effective biomolecular recognition. </p> </div> </div> </div>

scholarly journals Quantitative image analysis of microbial communities with BiofilmQ

2021 ◽  
Author(s):  
Raimo Hartmann ◽  
Hannah Jeckel ◽  
Eric Jelli ◽  
Praveen K. Singh ◽  
Sanika Vaidya ◽  
...  
Keyword(s):  
Image Analysis ◽  
Microbial Communities ◽  
Dimensional Space ◽  
Three Dimensional ◽  
Software Tool ◽  
Image Cytometry ◽  
Quantitative Image Analysis ◽  
Space And Time ◽  
Quantitative Image ◽  
Three Dimensional Space

AbstractBiofilms are microbial communities that represent a highly abundant form of microbial life on Earth. Inside biofilms, phenotypic and genotypic variations occur in three-dimensional space and time; microscopy and quantitative image analysis are therefore crucial for elucidating their functions. Here, we present BiofilmQ—a comprehensive image cytometry software tool for the automated and high-throughput quantification, analysis and visualization of numerous biofilm-internal and whole-biofilm properties in three-dimensional space and time.

Sign in / Sign up

Export Citation Format

Share Document