Search results for: Mathematical structure

Authors: Vahidreza Mahmoudabadi, Omid Bahar, Mohammad Kazem Jafari

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In many applied engineering problems, structural analysis is usually conducted by assuming a rigid bed, while imposing the effect of structure bed flexibility can affect significantly on the structure response. This article focuses on investigation and evaluation of the effects arising from considering a soil-structure system in evaluation of dynamic characteristics of a steel structure with respect to elastic and inelastic behaviors. The recorded structure acceleration during Taiwan’s strong Chi-Chi earthquake on different floors of the structure was our evaluation criteria. The respective structure is an eight-story steel bending frame structure designed using a displacement-based direct method assuring weak beam - strong column function. The results indicated that different identification methods i.e. reverse Fourier transform or transfer functions, is capable to determine some of the dynamic parameters of the structure precisely, rather than evaluating all of them at once (mode frequencies, mode shapes, structure damping, structure rigidity, etc.). Response evaluation based on the input and output data elucidated that the structure first mode is not significantly affected, even considering the soil-structure interaction effect, but the upper modes have been changed. Also, it was found that the response transfer function of the different stories, in which plastic hinges have occurred in the structure components, provides similar results.

Keywords: System identification, dynamic characteristics, soil-structure system, bending steel frame structure, displacement-based design.

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Authors: I. Benning

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Using technology to expand the learning space is critical for a productive mathematical discourse. This is a case study of two teachers who developed and enacted GeoGebra-based mathematics lessons following their engagement in a two-year professional development. The didactical and semiotic affordance of GeoGebra in widening the learning space for a productive mathematical discourse was explored. The approach of thematic analysis was used for lesson artefact, lesson observation, and interview data. The results indicated that constructing tools in GeoGebra provided a didactical milieu where students used them to explore mathematical concepts with little or no support from their teacher. The prompt feedback from the GeoGebra motivated students to practice mathematical concepts repeatedly in which they privately rethink their solutions before comparing their answers with that of their colleagues. The constructing tools enhanced self-discovery, team spirit, and dialogue among students. With regards to the semiotic construct, the tools widened the physical and psychological atmosphere of the classroom by providing animations that served as virtual concrete to enhance the recording, manipulation, testing of a mathematical idea, construction, and interpretation of geometric objects. These findings advance the discussion of widening the classroom for a productive mathematical discourse within the context of the mathematics curriculum of Ghana and similar sub-Saharan African countries.

Keywords: GeoGebra, theory of didactical situation, semiotic mediation, mathematics laboratory, mathematical discussion.

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Authors: Mikhail Semenov , Svetlana Kolupaeva, Tatiana Kovalevskaya, Olga Daneyko

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An investigation of the process of deformation hardening and evolution of deformation defect medium in dispersion-hardened materials with face centered cubic matrices and nanoparticles was done. Mathematical model including balance equation for the deformation defects was used.

Keywords: deformation defects, dispersion-hardened materials, mathematical modeling, plastic deformation

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Authors: Ghada Badr, Arwa Alturki

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The biological function of an RNA molecule depends on its structure. The objective of the alignment is finding the homology between two or more RNA secondary structures. Knowing the common functionalities between two RNA structures allows a better understanding and a discovery of other relationships between them. Besides, identifying non-coding RNAs -that is not translated into a protein- is a popular application in which RNA structural alignment is the first step A few methods for RNA structure-to-structure alignment have been developed. Most of these methods are partial structure-to-structure, sequence-to-structure, or structure-to-sequence alignment. Less attention is given in the literature to the use of efficient RNA structure representation and the structure-to-structure alignment methods are lacking. In this paper, we introduce an O(N2) Component-based Pairwise RNA Structure Alignment (CompPSA) algorithm, where structures are given as a component-based representation and where N is the maximum number of components in the two structures. The proposed algorithm compares the two RNA secondary structures based on their weighted component features rather than on their base-pair details. Extensive experiments are conducted illustrating the efficiency of the CompPSA algorithm when compared to other approaches and on different real and simulated datasets. The CompPSA algorithm shows an accurate similarity measure between components. The algorithm gives the flexibility for the user to align the two RNA structures based on their weighted features (position, full length, and/or stem length). Moreover, the algorithm proves scalability and efficiency in time and memory performance.

Keywords: Alignment, RNA secondary structure, pairwise, component-based, data mining.

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Authors: Evgeniy Burlutskiy

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The paper presents a one-dimensional transient mathematical model of compressible non-isothermal multicomponent fluid mixture flow in a pipe. The set of the mass, momentum and enthalpy conservation equations for gas phase is solved in the model. Thermo-physical properties of multi-component gas mixture are calculated by solving the Equation of State (EOS) model. The Soave-Redlich-Kwong (SRK-EOS) model is chosen. Gas mixture viscosity is calculated on the basis of the Lee-Gonzales- Eakin (LGE) correlation. Numerical analysis of rapid gas decompression process in rich and base natural gases is made on the basis of the proposed mathematical model. The model is successfully validated on the experimental data [1]. The proposed mathematical model shows a very good agreement with the experimental data [1] in a wide range of pressure values and predicts the decompression in rich and base gas mixtures much better than analytical and mathematical models, which are available from the open source literature.

Keywords: Mathematical model, Multi-Component gas mixture flow, Rapid Gas Decompression

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Authors: Manpreet Singh, Parvinder Singh Sandhu, Reet Kamal Kaur

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Protein structure determination and prediction has been a focal research subject in the field of bioinformatics due to the importance of protein structure in understanding the biological and chemical activities of organisms. The experimental methods used by biotechnologists to determine the structures of proteins demand sophisticated equipment and time. A host of computational methods are developed to predict the location of secondary structure elements in proteins for complementing or creating insights into experimental results. However, prediction accuracies of these methods rarely exceed 70%.

Keywords: Protein, Secondary Structure, Prediction, DNA, RNA.

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Authors: Ketan Naik, P. H. Bhathawala

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The purpose of this work is to develop a mathematical model of Human Cardiovascular System using lumped parameter method. The model is divided in three parts: Systemic Circulation, Pulmonary Circulation and the Heart. The established mathematical model has been simulated by MATLAB software. The innovation of this study is in describing the system based on the vessel diameters and simulating mathematical equations with active electrical elements. Terminology of human physical body and required physical data like vessel’s radius, thickness etc., which are required to calculate circuit parameters like resistance, inductance and capacitance, are proceeds from well-known medical books. The developed model is useful to understand the anatomic of human cardiovascular system and related syndromes. The model is deal with vessel’s pressure and blood flow at certain time.

Keywords: Cardiovascular system, lumped parameter method, mathematical modeling, simulation.

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Authors: Jaroslav Krutil, František Pochylý, Simona Fialová, Vladimír Habán

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A mathematical model of the additional effects of the liquid in the hydrodynamic gap is presented in the paper. An incompressible viscous fluid is considered. Based on computational modeling are determined the matrices of mass, stiffness and damping. The mathematical model is experimentally verified.

Keywords: Computational modeling, mathematical model, hydrodynamic gap, matrices of mass, stiffness and damping.

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Authors: Rana Abdul Jabbar Khan, Muhammad Akmal

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Personal computers draw non-sinusoidal current with odd harmonics more significantly. Power Quality of distribution networks is severely affected due to the flow of these generated harmonics during the operation of electronic loads. In this paper, mathematical modeling of odd harmonics in current like 3rd, 5th, 7th and 9th influencing the power quality has been presented. Live signals have been captured with the help of power quality analyzer for analysis purpose. The interesting feature is that Total Harmonic Distortion (THD) in current decreases with the increase of nonlinear loads has been verified theoretically. The results obtained using mathematical expressions have been compared with the practical results and exciting results have been found.

Keywords: Harmonic Distortion, Mathematical Modeling, Power Quality.

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Authors: Z. Charvat

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This paper considers the Zlin region in terms of the demographic conditions of the region - in particular the residential structure and the educational background of the inhabitants. The paper also considers migration of the population within the Zlin region. Migration is of importance in terms of conservation of the working potential of the region.

Keywords: Demographic structure, migration, inhabitants, residential structure, age structure, learning structure, Zlin region.

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Authors: N. Azhikhanov, T. Turimbetov, Zh. Masanov, N. Zhunisov

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It can be determined in preference between representative mechanical and mathematical model of elasticcreeping deformation of transversally isotropic array with doubly periodic system of tilted slots, and offer of the finite elements calculation scheme, and inspection of the states of two diagonal arbitrary profile cavities of deep inception, and in setting up the tense and dislocation fields distribution nature in computing processes.

Keywords: Mathematical model, tunnel, transversally isotropic, finite elements.

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Authors: H. Nikzad, S. Yoshitomi

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This study investigates and develops the structural optimization method. The effect of size constraints on practical solution of reinforced concrete (RC) building structure with shear wall is proposed. Cross-sections of beam and column, and thickness of shear wall are considered as design variables. The objective function to be minimized is total cost of the structure by using a simple and efficient automated MATLAB platform structural optimization methodology. With modification of mathematical formulations, the result is compared with optimal solution without size constraints. The most suitable combination of section sizes is selected as for the final design application based on linear static analysis. The findings of this study show that defining higher value of upper bound of sectional sizes significantly affects optimal solution, and defining of size constraints play a vital role in finding of global and practical solution during optimization procedures. The result and effectiveness of proposed method confirm the ability and efficiency of optimal solutions for 3D RC shear wall-frame structure.

Keywords: Structural optimization, linear static analysis, ETABS, MATLAB, RC shear wall-frame structures.

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Authors: Paula Verdugo-Hernández, Patricio Cumsille

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We analyze a first-class on the convergence of real number sequences, named hereafter sequences, to foster exploration and discovery of concepts through graphical representations before engaging students in proving. The main goal was to differentiate between sequences and continuous functions-of-a-real-variable and better understand concepts at an initial stage. We applied the analytic frame of Mathematical Working Spaces, which we expect to contribute to extending to sequences since, as far as we know, it has only developed for other objects, and which is relevant to analyze how mathematical work is built systematically by connecting the epistemological and cognitive perspectives, and involving the semiotic, instrumental, and discursive dimensions.

Keywords: Convergence, graphical representations, Mathematical Working Spaces, paradigms of real analysis, real number sequences.

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Authors: Masrour Dowlatabadi, Jalil Shirazi

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In this paper, an improved edge detection algorithm based on fuzzy combination of mathematical morphology and wavelet transform is proposed. The combined method is proposed to overcome the limitation of wavelet based edge detection and mathematical morphology based edge detection in noisy images. Experimental results show superiority of the proposed method, as compared to the traditional Prewitt, wavelet based and morphology based edge detection methods. The proposed method is an effective edge detection method for noisy image and keeps clear and continuous edges.

Keywords: Edge detection, Wavelet transform, Mathematical morphology, Fuzzy logic.

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Authors: Xu Zhang, Qi Jiang, Liwei Li, Weiwei Cui, Jijun Cui, Yang Cao, Hairong Zhao

Abstract:

A kind of crash energy absorption structure adopted by vehicle simulator crash testing equipment based on mechanical energy storage was studied. Dynamic explicit finite element simulation was achieved for thin-walled tube structure under different conditions of section shape, thickness and inducement groove style. Crash energy absorption property of the structure was obtained. After optimization, a reasonable structure was given which can meet current vehicle crash regulation. And the optimized structure can be adopted in vehicle simulator, which can increase the practicability of the testing equipment.

Keywords: thin-walled tube structure, crash energy absorption, deceleration, finite element simulation

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Authors: R. Kongnuy, E. Naowanich

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In this paper we develop and analyze the model for the spread of Leptospirosis by age group in Thailand, between 1997 and 2010 by using mathematical modeling and computer simulation. Leptospirosis is caused by pathogenic spirochetes of the genus Leptospira. It is a zoonotic disease of global importance and an emerging health problem in Thailand. In Thailand, leptospirosis is a reportable disease, the top three age groups are 23.31% in 35-44 years olds group, 22.76% in 25-34 year olds group, 17.60% in 45-54 year olds group from reported leptospirosis between 1997 and 2010, with a peak in 35-44 year olds group. Our paper, the Leptosipirosis transmission by age group in Thailand is studied on the mathematical model. Some analytical and simulation results are presented.

Keywords: Age Group, Equilibrium State, Leptospirosis, Mathematical Modeling.

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Authors: Océane Grosset, Charles Pézerat, Jean-Hugh Thomas, Frédéric Ablitzer

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This paper presents a method to take into account the fluid-structure coupling into an inverse method, the Force Analysis Technique (FAT). The FAT method, also called RIFF method (Filtered Windowed Inverse Resolution), allows to identify the force distribution from local vibration field. In order to only identify the external force applied on a structure, it is necessary to quantify the fluid-structure coupling, especially in naval application, where the fluid is heavy. This method can be decomposed in two parts, the first one consists in identifying the fluid-structure coupling and the second one to introduced it in the FAT method to reconstruct the external force. Results of simulations on a plate coupled with a cavity filled with water are presented.

Keywords: Fluid-structure coupling, inverse methods, naval, vibrations.

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Authors: M.A. Kamely, S.M. Kamil, C.W. Chong

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A mathematical model of the surface roughness has been developed by using response surface methodology (RSM) in grinding of AISI D2 cold work tool steels. Analysis of variance (ANOVA) was used to check the validity of the model. Low and high value for work speed and feed rate are decided from design of experiment. The influences of all machining parameters on surface roughness have been analyzed based on the developed mathematical model. The developed prediction equation shows that both the feed rate and work speed are the most important factor that influences the surface roughness. The surface roughness was found to be the lowers with the used of low feed rate and low work speed. Accuracy of the best model was proved with the testing data.

Keywords: Mathematical Modeling, Response surfacemethodology, Surface roughness, Cylindrical Grinding.

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Authors: Moussa Hamdan, Abdulati Abdullah

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This paper presents an investigation of the fabrication of the optical devices in terms of their characteristics based on the use of the electromagnetic waves. Planar waveguides are used to examine the field modes (bound modes) and the parameters required for this structure. The modifications are conducted on surface plasmons based waveguides. Simple symmetric dielectric slab structure is used and analyzed in terms of transverse electric mode (TE-Mode) and transverse magnetic mode (TM-Mode. The paper presents mathematical and numerical solutions for solving simple symmetric plasmons and provides simulations of surface plasmons for field confinement. Asymmetric TM-mode calculations for dielectric surface plasmons are also provided.

Keywords: Surface plasmons, optical waveguides, semiconductor lasers, refractive index, slab dialectical.

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Authors: M. Mokhtar, A. Shuib, D. Mohamad

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Portfolio optimization problem has received a lot of attention from both researchers and practitioners over the last six decades. This paper provides an overview of the current state of research in portfolio optimization with the support of mathematical programming techniques. On top of that, this paper also surveys the solution algorithms for solving portfolio optimization models classifying them according to their nature in heuristic and exact methods. To serve these purposes, 40 related articles appearing in the international journal from 2003 to 2013 have been gathered and analyzed. Based on the literature review, it has been observed that stochastic programming and goal programming constitute the highest number of mathematical programming techniques employed to tackle the portfolio optimization problem. It is hoped that the paper can meet the needs of researchers and practitioners for easy references of portfolio optimization.

Keywords: Portfolio optimization, Mathematical programming, Multi-objective programming, Solution approaches.

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Authors: P. Tej, P. Kněž, M. Blank

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The paper presents design and production of thin-walled U-profile footbridge made of UHPFRC. The main structure of the bridge is one prefabricated shell structure made of UHPFRC with dispersed steel fibers without any conventional reinforcement. The span of the bridge structure is 10 m and the clear width of 1.5 m. The thickness of the UHPFRC shell structure oscillated in an interval of 30-45 mm. Several calculations were made during the bridge design and compared with the experiments. For the purpose of verifying the calculations, a segment of 1.5 m was first produced, followed by the whole footbridge for testing. After the load tests were done, the design was optimized to cast the final footbridge.

Keywords: Footbridge, UHPFRC, non-linear analysis, shell structure.

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Authors: Dibyendu Ghoshal, Pinaki Pratim Acharjya

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Image segmentation process based on mathematical morphology has been studied in the paper. It has been established from the first principles of the morphological process, the entire segmentation is although a nonlinear signal processing task, the constituent wise, the intermediate steps are linear, bilinear and conformal transformation and they give rise to a non linear affect in a cumulative manner.

Keywords: Image segmentation, linear transform, bilinear transform, conformal transform, mathematical morphology.

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Authors: Oh Hyeon Jeon, WooYoung Jung

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In this study, seepage analysis was performed by the level difference between upstream and downstream of weir structure for safety evaluation of weir structure against flooding. Monte Carlo Simulation method was employed by considering the probability distribution of the adjacent ground parameter, i.e., permeability coefficient of weir structure. Moreover, by using a commercially available finite element program (ABAQUS), modeling of the weir structure is carried out. Based on this model, the characteristic of water seepage during flooding was determined at each water level with consideration of the uncertainty of their corresponding permeability coefficient. Subsequently, fragility function could be constructed based on this response from numerical analysis; this fragility function results could be used to determine the weakness of weir structure subjected to flooding disaster. They can also be used as a reference data that can comprehensively predict the probability of failur,e and the degree of damage of a weir structure.

Keywords: Weir structure, seepage, flood disaster fragility, probabilistic risk assessment, Monte-Carlo Simulation, permeability coefficient.

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Authors: Alexei M. Mikhailov

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The paper attempts to elucidate the columnar structure of the cortex by answering the following questions. (1) Why the cortical neurons with similar interests tend to be vertically arrayed forming what is known as cortical columns? (2) How to describe the cortex as a whole in concise mathematical terms? (3) How to design efficient digital models of the cortex?

Keywords: Cortex, pattern recognition, artificial neural cortex, computational biology, brain and neural engineering.

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Authors: Lili Chen, Chao Yuan

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On path space kQ, there is a trivial kQ^a-module structure determined by the multiplication of path algebra kQ^a and a trivial kQ^c-comodule structure determined by the comultiplication of path coalgebra kQ^c. In this paper, on path space kQ, a nontrivial kQ^a-module structure is defined, and it is proved that this nontrivial left kQ^a-module structure is isomorphic to the dual module structure of trivial right kQ^c-comodule. Dually, on path space kQ, a nontrivial kQ^c-comodule structure is defined, and it is proved that this nontrivial right kQ^c-comodule structure is isomorphic to the dual comodule structure of trivial left kQ^a-module. Finally, the trivial and nontrivial module structures on path space are compared from the aspect of submodule, and the trivial and nontrivial comodule structures on path space are compared from the aspect of subcomodule.

Keywords: Quiver, path space, module, comodule, dual.

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Authors: Natalya G. Filimonova, Mariya G. Ozerova, Irina N. Ermakova

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The long-term strategy of the economic development of Russia up to 2030 is based on the concept of sustainable growth. The determining factor of such development is complex changes in the economic system which may be achieved by making progressive changes in its structure. The structural changes determine the character and the direction of economic development, as well as they include all elements of this system without exception, and their regulated character ensures the most rapid aim achievement. This article has discussed the industrial structure of the agriculture in Russia. With the use of the system of indexes, the article has determined the directions, intensity, and speed of structural shifts. The influence of structural changes on agricultural production development has been found out. It is noticed that the changes in the industrial structure are synchronized with the changes in the organisation and economic structure. Efficiency assessment of structural changes allowed to trace the efficiency of structural changes and elaborate the main directions for agricultural policy improvement.

Keywords: Russian agriculture system, sectoral structure, organizational and economic structure, structural changes.

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Authors: M. B. El_Mashade, I. I. Mahamoud, M. S. El_Tokhy

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Improving the performance of the QCL through block diagram as well as mathematical models is the main scope of this paper. In order to enhance the performance of the underlined device, the mathematical model parameters are used in a reliable manner in such a way that the optimum behavior was achieved. These parameters play the central role in specifying the optical characteristics of the considered laser source. Moreover, it is important to have a large amount of radiated power, where increasing the amount of radiated power represents the main hopping process that can be predicted from the behavior of quantum laser devices. It was found that there is a good agreement between the calculated values from our mathematical model and those obtained with VisSim and experimental results. These demonstrate the strength of mplementation of both mathematical and block diagram models.

Keywords: Quantum Cascaded Lasers (QCLs), Modeling, Block Diagram Programming, Intersubband transitions

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Authors: Gilbert Makanda, Roelf Sypkens

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A mathematical model for knowledge acquisition in teaching and learning is proposed. In this study we adopt the mathematical model that is normally used for disease modelling into teaching and learning. We derive mathematical conditions which facilitate knowledge acquisition. This study compares the effects of dropping out of the course at early stages with later stages of learning. The study also investigates effect of individual interaction and learning from other sources to facilitate learning. The study fits actual data to a general mathematical model using Matlab ODE45 and lsqnonlin to obtain a unique mathematical model that can be used to predict knowledge acquisition. The data used in this study was obtained from the tutorial test results for mathematics 2 students from the Central University of Technology, Free State, South Africa in the department of Mathematical and Physical Sciences. The study confirms already known results that increasing dropout rates and forgetting taught concepts reduce the population of knowledgeable students. Increasing teaching contacts and access to other learning materials facilitate knowledge acquisition. The effect of increasing dropout rates is more enhanced in the later stages of learning than earlier stages. The study opens up a new direction in further investigations in teaching and learning using differential equations.

Keywords: Differential equations, knowledge acquisition, least squares nonlinear, dynamical systems.

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Authors: Kamel Hashem, Ibrahim Arman

Abstract:

Information and Communication Technologies (ICT) in mathematical education is a very active field of research and innovation, where learning is understood to be meaningful and grasping multiple linked representation rather than rote memorization, a great amount of literature offering a wide range of theories, learning approaches, methodologies and interpretations, are generally stressing the potentialities for teaching and learning using ICT. Despite the utilization of new learning approaches with ICT, students experience difficulties in learning concepts relevant to understanding mathematics, much remains unclear about the relationship between the computer environment, the activities it might support, and the knowledge that might emerge from such activities. Many questions that might arise in this regard: to what extent does the use of ICT help students in the process of understanding and solving tasks or problems? Is it possible to identify what aspects or features of students' mathematical learning can be enhanced by the use of technology? This paper will highlight the interest of the integration of information and communication technologies (ICT) into the teaching and learning of mathematics (quadratic functions), it aims to investigate the effect of four instructional methods on students- mathematical understanding and problem solving. Quantitative and qualitative methods are used to report about 43 students in middle school. Results showed that mathematical thinking and problem solving evolves as students engage with ICT activities and learn cooperatively.

Keywords: Dynamic Geometry Software, Information and Communication Technologies, Visualization, Mathematical Education.

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Authors: Erhan Ata, Yusuf Yaylı

Abstract:

Let M be an almost split quaternionic manifold on which its almost split quaternionic structure is defined by a three dimensional subbundle V of ( T M) T (M) * Ôèù and {F,G,H} be a local basis for V . Suppose that the (global) (1, 2) tensor field defined[V ,V ]is defined by [V,V ] = [F,F]+[G,G] + [H,H], where [,] denotes the Nijenhuis bracket. In ref. [7], for the almost split-hypercomplex structureH = J α,α =1,2,3, and the Obata connection ÔêçH vanishes if and only if H is split-hypercomplex. In this study, we give a prof, in particular, prove that if either M is a split quaternionic Kaehler manifold, or if M is a splitcomplex manifold with almost split-complex structure F , then the vanishing [V ,V ] is equivalent to that of all the Nijenhuis brackets of {F,G,H}. It follows that the bundle V is trivial if and only if [V ,V ] = 0 .

Keywords: Almost split - hypercomplex structure, Almost split quaternionic structure, Almost split quaternion Kaehler manifold, Obata connection.

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