**Commenced**in January 2007

**Frequency:**Monthly

**Edition:**International

**Paper Count:**2706

# Search results for: real algebraic geometry

##### 2706 Identification of Configuration Space Singularities with Local Real Algebraic Geometry

**Authors:**
Marc Diesse,
Hochschule Heilbronn

**Abstract:**

**Keywords:**
Linkages,
configuration space singularities,
real
algebraic geometry,
analytic geometry,
computer algebra.

##### 2705 Automatic Iterative Methods for the Multivariate Solution of Nonlinear Algebraic Equations

**Authors:**
Rafat Alshorman,
Safwan Al-Shara',
I. Obeidat

**Abstract:**

**Keywords:**
Nonlinear Algebraic Equations,
Iterative Methods,
Homotopy
Analysis Method.

##### 2704 Pressure Losses on Realistic Geometry of Tracheobronchial Tree

**Authors:**
Michaela Chovancova,
Jakub Elcner

**Abstract:**

Real bronchial tree is very complicated piping system. Analysis of flow and pressure losses in this system is very difficult. Due to the complex geometry and the very small size in the lower generations is examination by CFD possible only in the central part of bronchial tree. For specify the pressure losses of lower generations is necessary to provide a mathematical equation. Determination of mathematical formulas for calculation of pressure losses in the real lungs is time consuming and inefficient process due to its complexity and diversity. For these calculations is necessary to slightly simplify the geometry of lungs (same cross-section over the length of individual generation) or use one of the idealized models of lungs (Horsfield, Weibel). The article compares the values of pressure losses obtained from CFD simulation of air flow in the central part of the real bronchial tree with the values calculated in a slightly simplified real lungs by using a mathematical relationship derived from the Bernoulli and continuity equations. The aim of the article is to analyse the accuracy of the analytical method and its possibility of use for the calculation of pressure losses in lower generations, which is difficult to solve by numerical method due to the small geometry.

**Keywords:**
Pressure gradient,
airways resistance,
real geometry
of bronchial tree,
breathing.

##### 2703 On Algebraic Structure of Improved Gauss-Seidel Iteration

**Authors:**
O. M. Bamigbola,
A. A. Ibrahim

**Abstract:**

Analysis of real life problems often results in linear systems of equations for which solutions are sought. The method to employ depends, to some extent, on the properties of the coefficient matrix. It is not always feasible to solve linear systems of equations by direct methods, as such the need to use an iterative method becomes imperative. Before an iterative method can be employed to solve a linear system of equations there must be a guaranty that the process of solution will converge. This guaranty, which must be determined apriori, involve the use of some criterion expressible in terms of the entries of the coefficient matrix. It is, therefore, logical that the convergence criterion should depend implicitly on the algebraic structure of such a method. However, in deference to this view is the practice of conducting convergence analysis for Gauss- Seidel iteration on a criterion formulated based on the algebraic structure of Jacobi iteration. To remedy this anomaly, the Gauss- Seidel iteration was studied for its algebraic structure and contrary to the usual assumption, it was discovered that some property of the iteration matrix of Gauss-Seidel method is only diagonally dominant in its first row while the other rows do not satisfy diagonal dominance. With the aid of this structure we herein fashion out an improved version of Gauss-Seidel iteration with the prospect of enhancing convergence and robustness of the method. A numerical section is included to demonstrate the validity of the theoretical results obtained for the improved Gauss-Seidel method.

**Keywords:**
Linear system of equations,
Gauss-Seidel iteration,
algebraic structure,
convergence.

##### 2702 Algebraic Riccati Matrix Equation for Eigen- Decomposition of Special Structured Matrices; Applications in Structural Mechanics

**Authors:**
Mahdi Nouri

**Abstract:**

In this paper Algebraic Riccati matrix equation is used for Eigen-decomposition of special structured matrices. This is achieved by similarity transformation and then using algebraic riccati matrix equation to triangulation of matrices. The process is decomposition of matrices into small and specially structured submatrices with low dimensions for fast and easy finding of Eigenpairs. Numerical and structural examples included showing the efficiency of present method.

**Keywords:**
Riccati,
matrix equation,
eigenvalue problem,
symmetric,
bisymmetric,
persymmetric,
decomposition,
canonical
forms,
Graphs theory,
adjacency and Laplacian matrices.

##### 2701 Generalized π-Armendariz Authentication Cryptosystem

**Authors:**
Areej M. Abduldaim,
Nadia M. G. Al-Saidi

**Abstract:**

Algebra is one of the important fields of mathematics. It concerns with the study and manipulation of mathematical symbols. It also concerns with the study of abstractions such as groups, rings, and fields. Due to the development of these abstractions, it is extended to consider other structures, such as vectors, matrices, and polynomials, which are non-numerical objects. Computer algebra is the implementation of algebraic methods as algorithms and computer programs. Recently, many algebraic cryptosystem protocols are based on non-commutative algebraic structures, such as authentication, key exchange, and encryption-decryption processes are adopted. Cryptography is the science that aimed at sending the information through public channels in such a way that only an authorized recipient can read it. Ring theory is the most attractive category of algebra in the area of cryptography. In this paper, we employ the algebraic structure called skew -Armendariz rings to design a neoteric algorithm for zero knowledge proof. The proposed protocol is established and illustrated through numerical example, and its soundness and completeness are proved.

**Keywords:**
Cryptosystem,
identification,
skew π-Armendariz rings,
skew polynomial rings,
zero knowledge protocol.

##### 2700 A Real-Time Tracking System Developed for an Interactive Stage Performance

**Authors:**
S. Hu,
J. Mortensen,
Bernard F. Buxton

**Abstract:**

A real-time tracking system was built to track performers on an interactive stage. Using an ordinary, up to date, desktop workstation, the performers- silhouette was segmented from the background and parameterized by calculating the normalized central image moments. In the stage system, the silhouette moments were then sent to a parallel workstation, which used them to generate corresponding 3D virtual geometry and projected the generated graphic back onto the stage.

**Keywords:**
Image moment,
interactive stage,
real-time,
silhouette.

##### 2699 Proposal of Design Method in the Semi-Acausal System Model

**Authors:**
Junji Kaneko,
Shigeyuki Haruyama,
Ken Kaminishi,
Tadayuki Kyoutani,
Siti Ruhana Omar,
Oke Oktavianty

**Abstract:**

This study is used as a definition method to the value and function in manufacturing sector. In concurrence of discussion about present condition of modeling method, until now definition of 1D-CAE is ambiguity and not conceptual. Across all the physic fields, those methods are defined with the formulation of differential algebraic equation which only applied time derivation and simulation. At the same time, we propose semi-acausal modeling concept and differential algebraic equation method as a newly modeling method which the efficiency has been verified through the comparison of numerical analysis result between the semi-acausal modeling calculation and FEM theory calculation.

**Keywords:**
System Model,
Physical Models,
Empirical Models,
Conservation Law,
Differential Algebraic Equation,
Object-Oriented.

##### 2698 Some Properties of IF Rough Relational Algebraic Operators in Medical Databases

**Authors:**
Chhaya Gangwal,
R. N. Bhaumik,
Shishir Kumar

**Abstract:**

Some properties of Intuitionistic Fuzzy (IF) rough relational algebraic operators under an IF rough relational data model are investigated and illustrated using diabetes and heart disease databases. These properties are important and desirable for processing queries in an effective and efficient manner.

**Keywords:**
IF Set,
Rough Set,
IF Rough Relational Database,
IF rough Relational Operators.

##### 2697 Algebraic Specification of Serializability for Partitioned Transactions

**Authors:**
Walter Hussak,
John Keane

**Abstract:**

**Keywords:**
Algebraic Specification,
Partitioned Transactions,
Serializability.

##### 2696 Model for Knowledge Representation using Sample Problems and Designing a Program for Automatically Solving Algebraic Problems

**Authors:**
Nhon Do,
Hien Nguyen

**Abstract:**

**Keywords:**
educational software,
artificial intelligence,
knowledge base system,
knowledge representation.

##### 2695 Complexity Reduction Approach with Jacobi Iterative Method for Solving Composite Trapezoidal Algebraic Equations

**Authors:**
Mohana Sundaram Muthuvalu,
Jumat Sulaiman

**Abstract:**

In this paper, application of the complexity reduction approach based on half- and quarter-sweep iteration concepts with Jacobi iterative method for solving composite trapezoidal (CT) algebraic equations is discussed. The performances of the methods for CT algebraic equations are comparatively studied by their application in solving linear Fredholm integral equations of the second kind. Furthermore, computational complexity analysis and numerical results for three test problems are also included in order to verify performance of the methods.

**Keywords:**
Complexity reduction approach,
Composite trapezoidal
scheme,
Jacobi method,
Linear Fredholm integral equations

##### 2694 Numerical Analysis of Laminar Mixed Convection within a Complex Geometry

**Authors:**
Y. Lasbet,
A. L. Boukhalkhal,
K. Loubar

**Abstract:**

**Keywords:**
Complex geometry,
heat transfer,
laminar flow,
mixed convection,
Nusselt number.

##### 2693 Function of Fractals: Application of Non-linear Geometry in Continental Architecture

**Authors:**
Mohammadsadegh Zanganehfar

**Abstract:**

Since the introduction of fractal geometry in 1970, numerous efforts have been made by architects and researchers to transfer this area of mathematical knowledge in the discipline of architecture and postmodernist discourse. The discourse of complexity and architecture is one of the most significant ongoing discourses in the discipline of architecture from the 70's until today and has generated significant styles such as deconstructivism and parametricism in architecture. During these years, several projects were designed and presented by designers and architects using fractal geometry, but due to the lack of sufficient knowledge and appropriate comprehension of the features and characteristics of this nonlinear geometry, none of the fractal-based designs have been successful and satisfying. Fractal geometry as a geometric technology has a long presence in the history of architecture. The current research attempts to identify and discover the characteristics, features, potentials and functionality of fractals despite their aesthetic aspect by examining case studies of pre-modern architecture in Asia and investigating the function of fractals.

**Keywords:**
Asian architecture,
fractal geometry,
fractal technique,
geometric properties

##### 2692 Condensation of Moist Air in Heat Exchanger Using CFD

**Authors:**
Jan Barák,
Karel Fraňa,
Jörg Stiller

**Abstract:**

This work presents results of moist air condensation in heat exchanger. It describes theoretical knowledge and definition of moist air. Model with geometry of square canal was created for better understanding and postprocessing of condensation phenomena. Different approaches were examined on this model to find suitable software and model. Obtained knowledge was applied to geometry of real heat exchanger and results from experiment were compared with numerical results. One of the goals is to solve this issue without creating any user defined function in the applied code. It also contains summary of knowledge and outlook for future work.

**Keywords:**
Condensation,
exchanger,
experiment,
validation.

##### 2691 Accurate Visualization of Graphs of Functions of Two Real Variables

**Authors:**
Zeitoun D. G.,
Thierry Dana-Picard

**Abstract:**

The study of a real function of two real variables can be supported by visualization using a Computer Algebra System (CAS). One type of constraints of the system is due to the algorithms implemented, yielding continuous approximations of the given function by interpolation. This often masks discontinuities of the function and can provide strange plots, not compatible with the mathematics. In recent years, point based geometry has gained increasing attention as an alternative surface representation, both for efficient rendering and for flexible geometry processing of complex surfaces. In this paper we present different artifacts created by mesh surfaces near discontinuities and propose a point based method that controls and reduces these artifacts. A least squares penalty method for an automatic generation of the mesh that controls the behavior of the chosen function is presented. The special feature of this method is the ability to improve the accuracy of the surface visualization near a set of interior points where the function may be discontinuous. The present method is formulated as a minimax problem and the non uniform mesh is generated using an iterative algorithm. Results show that for large poorly conditioned matrices, the new algorithm gives more accurate results than the classical preconditioned conjugate algorithm.

**Keywords:**
Function singularities,
mesh generation,
point allocation,
visualization,
collocation least squares method,
Augmented Lagrangian method,
Uzawa's Algorithm,
Preconditioned Conjugate Gradien

##### 2690 Comparing the Performance of the Particle Swarm Optimization and the Genetic Algorithm on the Geometry Design of Longitudinal Fin

**Authors:**
Hassan Azarkish,
Said Farahat,
S.Masoud H. Sarvari

**Abstract:**

**Keywords:**
Genetic Algorithm,
Geometry Optimization,
longitudinal Fin,
Particle Swarm Optimization

##### 2689 A Geometrical Perspective on the Insulin Evolution

**Authors:**
Yuhei Kunihiro,
Sorin V. Sabau,
Kazuhiro Shibuya

**Abstract:**

We study the molecular evolution of insulin from metric geometry point of view. In mathematics, and in particular in geometry, distances and metrics between objects are of fundamental importance. Using a weaker notion than the classical distance, namely the weighted quasi-metrics, one can study the geometry of biological sequences (DNA, mRNA, or proteins) space. We analyze from geometrical point of view a family of 60 insulin homologous sequences ranging on a large variety of living organisms from human to the nematode C. elegans. We show that the distances between sequences provide important information about the evolution and function of insulin.

**Keywords:**
Metric geometry,
evolution,
insulin.

##### 2688 Positive Solutions for Discrete Third-order Three-point Boundary Value Problem

**Authors:**
Benshi Zhu

**Abstract:**

**Keywords:**
Positive solutions,
Discrete boundary value problem,
Third-order,
Three-point,
Algebraic topology

##### 2687 Conceptual Design of Unmanned Aerial Targets

**Authors:**
M. Adamski,
J. Cwiklak

**Abstract:**

**Keywords:**
Aerial target,
aerodynamics,
imitator,
performance.

##### 2686 Geometry Design Supported by Minimizing and Visualizing Collision in Dynamic Packing

**Authors:**
Johan Segeborn,
Johan S. Carlson,
Robert Bohlin,
Rikard Söderberg

**Abstract:**

**Keywords:**
Dynamic packing,
path planning,
shrinking.

##### 2685 A New Vision of Fractal Geometry with Triangulati on Algorithm

**Authors:**
Yasser M. Abd El-Latif,
Fatma S.Abousaleh,
Daoud S. S.

**Abstract:**

L-system is a tool commonly used for modeling and simulating the growth of fractal plants. The aim of this paper is to join some problems of the computational geometry with the fractal geometry by using the L-system technique to generate fractal plant in 3D. L-system constructs the fractal structure by applying rewriting rules sequentially and this technique depends on recursion process with large number of iterations to get different shapes of 3D fractal plants. Instead, it was reiterated a specific number of iterations up to three iterations. The vertices generated from the last stage of the Lsystem rewriting process are used as input to the triangulation algorithm to construct the triangulation shape of these vertices. The resulting shapes can be used as covers for the architectural objects and in different computer graphics fields. The paper presents a gallery of triangulation forms which application in architecture creates an alternative for domes and other traditional types of roofs.

**Keywords:**
Computational geometry,
fractal geometry,
L-system,
triangulation.

##### 2684 A Survey on Positive Real and Strictly Positive Real Scalar Transfer Functions

**Authors:**
Mojtaba Hakimi-Moghaddam

**Abstract:**

**Keywords:**
Real rational transfer functions,
positive realness property,
strictly positive realness property,
equivalent conditions.

##### 2683 Algebraic Quantum Error Correction Codes

**Authors:**
Ming-Chung Tsai,
Kuan-Peng Chen,
Zheng-Yao

**Abstract:**

**Keywords:**
Quotient-Algebra Partition,
Codeword Spinors,
Basis
Codewords,
Syndrome Spinors

##### 2682 Applications of Trigonometic Measures of Fuzzy Entropy to Geometry

**Authors:**
Om Parkash,
C.P.Gandhi

**Abstract:**

**Keywords:**
Entropy,
Uncertainty,
Fuzzy Entropy,
Concavity,
Symmetry.

##### 2681 Some Algebraic Properties of Universal and Regular Covering Spaces

**Authors:**
Ahmet Tekcan

**Abstract:**

Let X be a connected space, X be a space, let p : X -→ X be a continuous map and let (X, p) be a covering space of X. In the first section we give some preliminaries from covering spaces and their automorphism groups. In the second section we derive some algebraic properties of both universal and regular covering spaces (X, p) of X and also their automorphism groups A(X, p).

**Keywords:**
covering space,
universal covering,
regular covering,
fundamental group,
automorphism group.

##### 2680 Efficient Filtering of Graph Based Data Using Graph Partitioning

**Authors:**
Nileshkumar Vaishnav,
Aditya Tatu

**Abstract:**

**Keywords:**
Graph signal processing,
graph partitioning,
inverse
filtering on graphs,
algebraic signal processing.

##### 2679 Effect of the Cross-Sectional Geometry on Heat Transfer and Particle Motion of Circulating Fluidized Bed Riser for CO2 Capture

**Authors:**
Seungyeong Choi,
Namkyu Lee,
Dong Il Shim,
Young Mun Lee,
Yong-Ki Park,
Hyung Hee Cho

**Abstract:**

Effect of the cross-sectional geometry on heat transfer and particle motion of circulating fluidized bed riser for CO_{2} capture was investigated. Numerical simulation using Eulerian-eulerian method with kinetic theory of granular flow was adopted to analyze gas-solid flow consisting in circulating fluidized bed riser. Circular, square, and rectangular cross-sectional geometry cases of the same area were carried out. Rectangular cross-sectional geometries were analyzed having aspect ratios of 1: 2, 1: 4, 1: 8, and 1:16. The cross-sectional geometry significantly influenced the particle motion and heat transfer. The downward flow pattern of solid particles near the wall was changed. The gas-solid mixing degree of the riser with the rectangular cross section of the high aspect ratio was the lowest. There were differences in bed-to-wall heat transfer coefficient according to rectangular geometry with different aspect ratios.

**Keywords:**
Bed geometry,
computational fluid dynamics,
circulating fluidized bed riser,
heat transfer.

##### 2678 Comparison of Three Versions of Conjugate Gradient Method in Predicting an Unknown Irregular Boundary Profile

**Authors:**
V. Ghadamyari,
F. Samadi,
F. Kowsary

**Abstract:**

**Keywords:**
Boundary elements,
Conjugate Gradient Method,
Inverse Geometry Problem,
Sensitivity equation.

##### 2677 Jointly Learning Python Programming and Analytic Geometry

**Authors:**
Cristina-Maria Păcurar

**Abstract:**

**Keywords:**
Analytic geometry,
conics,
Python programming language,
quadrics.