Search results for: mathematical structure
9054 Structure Function and Violation of Scale Invariance in NCSM: Theory and Numerical Analysis
Authors: M. R. Bekli, N. Mebarki, I. Chadou
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In this study, we focus on the structure functions and violation of scale invariance in the context of non-commutative standard model (NCSM). We find that this violation appears in the first order of perturbation theory and a non-commutative version of the DGLAP evolution equation is deduced. Numerical analysis and comparison with experimental data imposes a new bound on the non-commutative parameter.Keywords: NCSM, structure function, DGLAP equation, standard model
Procedia PDF Downloads 6119053 Comparative Study of Seismic Isolation as Retrofit Method for Historical Constructions
Authors: Carlos H. Cuadra
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Seismic isolation can be used as a retrofit method for historical buildings with the advantage that minimum intervention on super-structure is required. However, selection of isolation devices depends on weight and stiffness of upper structure. In this study, two buildings are considered for analyses to evaluate the applicability of this retrofitting methodology. Both buildings are located at Akita prefecture in the north part of Japan. One building is a wooden structure that corresponds to the old council meeting hall of Noshiro city. The second building is a brick masonry structure that was used as house of a foreign mining engineer and it is located at Ani town. Ambient vibration measurements were performed on both buildings to estimate their dynamic characteristics. Then, target period of vibration of isolated systems is selected as 3 seconds is selected to estimate required stiffness of isolation devices. For wooden structure, which is a light construction, it was found that natural rubber isolators in combination with friction bearings are suitable for seismic isolation. In case of masonry building elastomeric isolator can be used for its seismic isolation. Lumped mass systems are used for seismic response analysis and it is verified in both cases that seismic isolation can be used as retrofitting method of historical construction. However, in the case of the light building, most of the weight corresponds to the reinforced concrete slab that is required to install isolation devices.Keywords: historical building, finite element method, masonry structure, seismic isolation, wooden structure
Procedia PDF Downloads 1559052 Single Carrier Frequency Domain Equalization Design to Cope with Narrow Band Jammer
Authors: So-Young Ju, Sung-Mi Jo, Eui-Rim Jeong
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In this paper, based on the conventional single carrier frequency domain equalization (SC-FDE) structure, we propose a new SC-FDE structure to cope with narrowband jammer. In the conventional SC-FDE structure, channel estimation is performed in the time domain. When a narrowband jammer exists, time-domain channel estimation is very difficult due to high power jamming interference, which degrades receiver performance. To relieve from this problem, a new SC-FDE frame is proposed to enable channel estimation under narrow band jamming environments. In this paper, we proposed a modified SC-FDE structure that can perform channel estimation in the frequency domain and verified the performance via computer simulation.Keywords: channel estimation, jammer, pilot, SC-FDE
Procedia PDF Downloads 4759051 Synthesis of Filtering in Stochastic Systems on Continuous-Time Memory Observations in the Presence of Anomalous Noises
Authors: S. Rozhkova, O. Rozhkova, A. Harlova, V. Lasukov
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We have conducted the optimal synthesis of root-mean-squared objective filter to estimate the state vector in the case if within the observation channel with memory the anomalous noises with unknown mathematical expectation are complement in the function of the regular noises. The synthesis has been carried out for linear stochastic systems of continuous-time.Keywords: mathematical expectation, filtration, anomalous noise, memory
Procedia PDF Downloads 2479050 Crystal Structure, Vibration Study, and Calculated Frequencies by Density Functional Theory Method of Copper Phosphate Dihydrate
Authors: Soufiane Zerraf, Malika Tridane, Said Belaaouad
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CuHPO₃.2H₂O was synthesized by the direct method. CuHPO₃.2H₂O crystallizes in the orthorhombic system, space group P2₁2₁2₁, a = 6.7036 (2) Å, b = 7.3671 (4) Å, c = 8.9749 (4) Å, Z = 4, V = 443.24 (4) ų. The crystal structure was refined to R₁= 0.0154, R₂= 0.0380 for 19018 reflections satisfying criterion I ≥ 2σ (I). The structural resolution shows the existence of chains of ions HPO₃- linked together by hydrogen bonds. The crystalline structure is formed by chains consisting of Cu[O₃(H₂O)₃] deformed octahedral, which are connected to the vertices. The chains extend parallel to b and are mutually linked by PO₃ groups. The structure is closely related to that of CuSeO₃.2H₂O and CuTeO₃.2H₂O. The experimental studies of the infrared and Raman spectra were used to confirm the presence of the phosphate ion and were compared in the (0-4000) cm-1 region with the theoretical results calculated by the density functional theory (DFT) method to provide reliable assignments of all observed bands in the experimental spectra.Keywords: crystal structure, X-ray diffraction, vibration study, thermal behavior, density functional theory
Procedia PDF Downloads 1179049 Why Do We Need Hierachical Linear Models?
Authors: Mustafa Aydın, Ali Murat Sunbul
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Hierarchical or nested data structures usually are seen in many research areas. Especially, in the field of education, if we examine most of the studies, we can see the nested structures. Students in classes, classes in schools, schools in cities and cities in regions are similar nested structures. In a hierarchical structure, students being in the same class, sharing the same physical conditions and similar experiences and learning from the same teachers, they demonstrate similar behaviors between them rather than the students in other classes.Keywords: hierarchical linear modeling, nested data, hierarchical structure, data structure
Procedia PDF Downloads 6529048 Hybrid Structure Learning Approach for Assessing the Phosphate Laundries Impact
Authors: Emna Benmohamed, Hela Ltifi, Mounir Ben Ayed
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Bayesian Network (BN) is one of the most efficient classification methods. It is widely used in several fields (i.e., medical diagnostics, risk analysis, bioinformatics research). The BN is defined as a probabilistic graphical model that represents a formalism for reasoning under uncertainty. This classification method has a high-performance rate in the extraction of new knowledge from data. The construction of this model consists of two phases for structure learning and parameter learning. For solving this problem, the K2 algorithm is one of the representative data-driven algorithms, which is based on score and search approach. In addition, the integration of the expert's knowledge in the structure learning process allows the obtainment of the highest accuracy. In this paper, we propose a hybrid approach combining the improvement of the K2 algorithm called K2 algorithm for Parents and Children search (K2PC) and the expert-driven method for learning the structure of BN. The evaluation of the experimental results, using the well-known benchmarks, proves that our K2PC algorithm has better performance in terms of correct structure detection. The real application of our model shows its efficiency in the analysis of the phosphate laundry effluents' impact on the watershed in the Gafsa area (southwestern Tunisia).Keywords: Bayesian network, classification, expert knowledge, structure learning, surface water analysis
Procedia PDF Downloads 1289047 Process Integration: Mathematical Model for Contaminant Removal in Refinery Process Stream
Authors: Wasif Mughees, Malik Al-Ahmad
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This research presents the graphical design analysis and mathematical programming technique to dig out the possible water allocation distribution to minimize water usage in process units. The study involves the mass and property integration in its core methodology. Tehran Oil Refinery is studied to implement the focused water pinch technology for regeneration, reuse and recycling of water streams. Process data is manipulated in terms of sources and sinks, which are given in terms of properties. Sources are the streams to be allocated. Sinks are the units which can accept the sources. Suspended Solids (SS) is taken as a single contaminant. The model minimizes the mount of freshwater from 340 to 275m3/h (19.1%). Redesigning and allocation of water streams was built. The graphical technique and mathematical programming shows the consistency of results which confirms mass transfer dependency of water streams.Keywords: minimization, water pinch, process integration, pollution prevention
Procedia PDF Downloads 3199046 Synthesis, Structure and Properties of NZP/NASICON Structured Materials
Authors: E. A. Asabina, V. I. Pet'kov, P. A. Mayorov, A. V. Markin, N. N. Smirnova, A. M. Kovalskii, A. A. Usenko
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The purpose of this work was to synthesize and investigate phase formation, structure and thermophysical properties of the phosphates M0.5+xM'xZr2–x(PO4)3 (M – Cd, Sr, Pb; M' – Mg, Co, Mn). The compounds were synthesized by sol-gel method. The results showed formation of limited solid solutions of NZP/NASICON type. The crystal structures of triple phosphates of the compositions MMg0.5Zr1.5(PO4)3 were refined by the Rietveld method using XRD data. Heat capacity (8–660 K) of the phosphates Pb0.5+xMgxZr2-x(PO4)3 (x = 0, 0.5) was measured, and reversible polymorphic transitions were found at temperatures, close to the room temperature. The results of Rietveld structure refinement showed the polymorphism caused by disordering of lead cations in the cavities of NZP/NASICON structure. Thermal expansion (298−1073 K) of the phosphates MMg0.5Zr1.5(PO4)3 was studied by XRD method, and the compounds were found to belong to middle and low-expanding materials. Thermal diffusivity (298–573 K) of the ceramic samples of phosphates slightly decreased with temperature increasing. As was demonstrated, the studied phosphates are characterized by the better thermophysical characteristics than widespread fire-resistant materials, such as zirconia and etc.Keywords: NASICON, NZP, phosphate, structure, synthesis, thermophysical properties
Procedia PDF Downloads 1419045 Response of Buildings with Soil-Structure Interaction with Varying Soil Types
Authors: Shreya Thusoo, Karan Modi, Rajesh Kumar, Hitesh Madahar
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Over the years, it has been extensively established that the practice of assuming a structure being fixed at base, leads to gross errors in evaluation of its overall response due to dynamic loadings and overestimations in design. The extent of these errors depends on a number of variables; soil type being one of the major factor. This paper studies the effect of Soil Structure Interaction (SSI) on multi-storey buildings with varying under-laying soil types after proper validation of the effect of SSI. Analysis for soft, stiff and very stiff base soils has been carried out, using a powerful Finite Element Method (FEM) software package ANSYS v14.5. Results lead to some very important conclusions regarding time period, deflection and acceleration responses.Keywords: dynamic response, multi-storey building, soil-structure interaction, varying soil types
Procedia PDF Downloads 4859044 Complementary Mathematical Model for Underwater Vehicles under Load Variation Test Conditions
Authors: Erim Koyun
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This paper aim to construct a mathematical model for Underwater vehicles under load variation test conditions. Propeller effects on underwater vehicle are investigated. Body with counter rotating propeller model is analyzed by CFD methods, thus forces and moment are obtained. Propeller effects of vehicle’s hydrodynamic performance under load variation conditions will be investigated. Additionally, pressure contour is examined for differences between different load conditions. Axial force equation is established using hydrodynamic coefficients, which contains resistance, thrust, and additional coefficients occurs due to load variations. Additional coefficients helps to express completely axial force on underwater vehicle. When the vehicle accelerates, additional force occurs besides thrust force increment. This is propeller effect on the body. Hence, mathematical model cover this effect. For CFD analysis, the incompressible, three-dimensional, and unsteady Reynolds Averaged Navier-Stokes equations will be used Numerical results is verified with experimental results for verification. The overall goal of this study is to present complementary mathematical model for body with counter rotating propeller.Keywords: counter rotating propeller, CFD, hydrodynamic mathematic model, hydrodynamics analysis, thrust deduction
Procedia PDF Downloads 1369043 Schedule a New Production Plan by Heuristic Methods
Authors: Hanife Merve Öztürk, Sıdıka Dalgan
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In this project, a capacity analysis study is done at TAT A. Ş. Maret Plant. Production capacity of products which generate 80% of sales amount are determined. Obtained data entered the LEKIN Scheduling Program and we get production schedules by using heuristic methods. Besides heuristic methods, as mathematical model, disjunctive programming formulation is adapted to flexible job shop problems by adding a new constraint to find optimal schedule solution.Keywords: scheduling, flexible job shop problem, shifting bottleneck heuristic, mathematical modelling
Procedia PDF Downloads 4019042 Identifying Unknown Dynamic Forces Applied on Two Dimensional Frames
Authors: H. Katkhuda
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A time domain approach is used in this paper to identify unknown dynamic forces applied on two dimensional frames using the measured dynamic structural responses for a sub-structure in the two dimensional frame. In this paper a sub-structure finite element model with short length of measurement from only three or four accelerometers is required, and an iterative least-square algorithm is used to identify the unknown dynamic force applied on the structure. Validity of the method is demonstrated with numerical examples using noise-free and noise-contaminated structural responses. Both harmonic and impulsive forces are studied. The results show that the proposed approach can identify unknown dynamic forces within very limited iterations with high accuracy and shows its robustness even noise- polluted dynamic response measurements are utilized.Keywords: dynamic force identification, dynamic responses, sub-structure, time domain
Procedia PDF Downloads 3609041 Structure Design of Vacuum Vessel with Large Openings for Spacecraft Thermal Vacuum Test
Authors: Han Xiao, Ruan Qi, Zhang Lei, Qi Yan
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Space environment simulator is a facility used to conduct thermal test for spacecraft, and vacuum vessel is the main body of it. According to the requirements for thermal tests of the spacecraft and its solar array panels, the primary vessel and the side vessels are designed to be a combinative structure connected with aperture, which ratio reaches 0.7. Since the vacuum vessel suffers 0.1MPa external pressure during the process of thermal test, in order to ensure the simulator’s reliability and safety, it’s necessary to calculate the vacuum vessel’s intensity and stability. Based on the impact of large openings to vacuum vessel structure, this paper explored the reinforce design and analytical way of vacuum vessel with large openings, using a large space environment simulator’s vacuum vessel design as an example. Tests showed that the reinforce structure is effective to fulfill the requirements of external pressure and the gravity. This ensured the reliability of the space environment simulator, providing a guarantee for developing the spacecraft.Keywords: vacuum vessel, large opening, space environment simulator, structure design
Procedia PDF Downloads 5359040 Future Trends of Mechatronics Engineering in Pakistan
Authors: Aqeela Mir, Akhtar Nawaz Malik, Javaid Iqbal
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The paper presents a survey based approach in order to observe the level of awareness regarding Mechatronics in society of Pakistan and the factors affecting the future development trend of Mechatronics in Pakistan. With the help of these surveys a new direction for making a Mathematical model for the future development trend of Mechatronics in Pakistan is also suggested.Keywords: mechatronics society survey, future development trend of mechatronics in pakistan, probability estimation, mathematical model
Procedia PDF Downloads 5219039 Classification Based on Deep Neural Cellular Automata Model
Authors: Yasser F. Hassan
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Deep learning structure is a branch of machine learning science and greet achievement in research and applications. Cellular neural networks are regarded as array of nonlinear analog processors called cells connected in a way allowing parallel computations. The paper discusses how to use deep learning structure for representing neural cellular automata model. The proposed learning technique in cellular automata model will be examined from structure of deep learning. A deep automata neural cellular system modifies each neuron based on the behavior of the individual and its decision as a result of multi-level deep structure learning. The paper will present the architecture of the model and the results of simulation of approach are given. Results from the implementation enrich deep neural cellular automata system and shed a light on concept formulation of the model and the learning in it.Keywords: cellular automata, neural cellular automata, deep learning, classification
Procedia PDF Downloads 1989038 The Eye Tracking Technique and the Study of Some Abstract Mathematical Concepts at the University
Authors: Tamara Díaz-Chang, Elizabeth-H Arredondo
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This article presents the results of mixed approach research, where the ocular movements of students are examined while they solve questionnaires related to some abstract mathematical concepts. The objective of this research is to determine possible correlations between the parameters of ocular activity and the level of difficulty of the tasks. The difficulty level categories were established based on two types of criteria: a subjective one, through an evaluation, carried out by the subjects, and a behavioral one, related to obtaining the correct solution. Correlations of these criteria with ocular activity parameters, which were considered indicators of mental effort, were identified. The analysis of the data obtained allowed us to observe discrepancies in the categorization of difficulty levels based on subjective and behavioral criteria. There was a negative correlation of the eye movement parameters with the students' opinions on the level of difficulty of the questions, while a strong positive and significant correlation was noted between most of the parameters of ocular activity and the level of difficulty, determined by the percentage of correct answers. The results obtained by the analysis of the data suggest that eye movement parameters can be taken as indicators of the difficulty level of the tasks related to the study of some abstract mathematical concepts at the university.Keywords: abstract mathematical concepts, cognitive neuroscience, eye-tracking, university education
Procedia PDF Downloads 1209037 Explanation Conceptual Model of the Architectural Form Effect on Structures in Building Aesthetics
Authors: Fatemeh Nejati, Farah Habib, Sayeh Goudarzi
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Architecture and structure have always been closely interrelated so that they should be integrated into a unified, coherent and beautiful universe, while in the contemporary era, both structures and architecture proceed separately. The purpose of architecture is the art of creating form and space and order for human service, and the goal of the structural engineer is the transfer of loads to the structure, too. This research seeks to achieve the goal by looking at the relationship between the form of architecture and structure from its inception to the present day to the Global Identification and Management Plan. Finally, by identifying the main components of the design of the structure in interaction with the architectural form, an effective step is conducted in the Professional training direction and solutions to professionals. Therefore, after reviewing the evolution of structural and architectural coordination in various historical periods as well as how to reach the form of the structure in different times and places, components are required to test the components and present the final theory that one hundred to be tested in this regard. Finally, this research indicates the fact that the form of architecture and structure has an aesthetic link, which is influenced by a number of components that could be edited and has a regular order throughout history that could be regular. The research methodology is analytic, and it is comparative using analytical and matrix diagrams and diagrams and tools for conducting library research and interviewing.Keywords: architecture, structural form, structural and architectural coordination, effective components, aesthetics
Procedia PDF Downloads 2159036 Dynamic Soil Structure Interaction in Buildings
Authors: Shreya Thusoo, Karan Modi, Ankit Kumar Jha, Rajesh Kumar
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Since the evolution of computational tools and simulation software, there has been considerable increase in research on Soil Structure Interaction (SSI) to decrease the computational time and increase accuracy in the results. To aid the designer with a proper understanding of the response of structure in different soil types, the presented paper compares the deformation, shear stress, acceleration and other parameters of multi-storey building for a specific input ground motion using Response-spectrum Analysis (RSA) method. The response of all the models of different heights have been compared in different soil types. Finite Element Simulation software, ANSYS, has been used for all the computational purposes. Overall, higher response is observed with SSI, while it increases with decreasing stiffness of soil.Keywords: soil-structure interaction, response spectrum, analysis, finite element method, multi-storey buildings
Procedia PDF Downloads 4809035 Numerical Study of Sloshing in a Flexible Tank
Authors: Wissem Tighidet, Faïçal Naït Bouda, Moussa Allouche
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The numerical study of the Fluid-Structure Interaction (FSI) in a partially filled flexible tank submitted to a horizontal harmonic excitation motion. It is investigated by using two-way Fluid-Structure Interaction (FSI) in a flexible tank by Coupling between the Transient Structural (Mechanical) and Fluid Flow (Fluent) in ANSYS-Workbench Student version. The Arbitrary Lagrangian-Eulerian (ALE) formulation is adopted to solve with the finite volume method, the Navier-Stokes equations in two phases in a moving domain. The Volume of Fluid (VOF) method is applied to track the free surface. However, the equations of the dynamics of the structure are solved with the finite element method assuming a linear elastic behavior. To conclude, the Fluid-Structure Interaction (IFS) has a vital role in the analysis of the dynamic behavior of the rectangular tank. The results indicate that the flexibility of the tank walls has a significant impact on the amplitude of tank sloshing and the deformation of the free surface as well as the effect of liquid sloshing on wall deformation.Keywords: arbitrary lagrangian-eulerian, fluid-structure interaction, sloshing, volume of fluid
Procedia PDF Downloads 1049034 The Effect of the Cultural Constraint on the Reform of Corporate Governance: The Observation of Taiwan's Efforts to Transform Its Corporate Governance
Authors: Yuanyi (Richard) Fang
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Under the theory of La Porta, Lopez-de-Silanes, Shleifer, and Vishny, if a country can increase its legal protections for minority shareholders, the country can develop an ideal securities market that only arises under the dispersed ownership corporate governance. However, the path-dependence scholarship, such as Lucian Arye Bebchuk and Mark J. Roe, presented a different view with LLS&V. They pointed out that the initial framework of the ownership structure and traditional culture will prevent the change of the corporate governance structure through legal reform. This paper contends that traditional culture factors as an important aspect when forming the corporate governance structure. However, it is not impossible for the government to change its traditional corporate governance structure and traditional culture because the culture does not remain intact. Culture evolves with time. The occurrence of the important events will affect the people’s psychological process. The psychological process affects the evolution of culture. The new cultural norms can help defeat the force of the traditional culture and the resistance from the initial corporate ownership structure. Using Taiwan as an example, through analyzing the historical background, related corporate rules and the reactions of adoption new rules from the media, this paper try to show that Taiwan’s culture norms do not remain intact and have changed with time. It further provides that the culture is not always the hurdle for the adoption of the dispersed ownership corporate governance structure as the culture can change. A new culture can provide strong support for the adoption of the new corporate governance structure.Keywords: LLS&V theory, corporate governance, culture, path–dependent theory
Procedia PDF Downloads 4769033 Effect of Natural Molecular Crowding on the Structure and Stability of DNA Duplex
Authors: Chaudhari S. G., Saxena, S.
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We systematically and quantitatively investigated the effect of glucose as a model of natural molecular crowding agent on the structure and thermodynamics of Watson-Crick base paired three duplexes (named as D1, D2 and D3) of different base compositions and lengths. Structural analyses demonstrated that duplexes (D1 and D2) folded into B-form with different cations in the absence and presence of glucose while duplex (D3) folded into mixed A and B-form. Moreover, we demonstrated that the duplex was more stable in the absence of glucose, and marginally destabilized in its presence because glucose act as a weak structure breaker on the tetrahedral network of water. In the absence of glucose, the values of ΔG°25 for duplex (D1) were -13.56, -13.76, -12.46, and -12.36 kcal/mol, for duplex (D2) were -13.64, -12.93, -12.86, and -12.30 kcal/mol, for duplex (D3) were -10.05, -11.76, -9.91, -9.70 kcal/mol in the presence of Na+, K+, Na+ + Mg++ and K+ + Mg++ respectively. At high concentration of glucose (1:10000), there was increase in ΔG°25 for duplex (D1) -12.47, -12.37, -11.96, -11.55 kcal/mol, for duplex (D2) -12.37, -11.47, -11.98, -11.01 kcal/mol and for duplex (D3) -8.47, -9.17, -9.16, -8.66 kcal/mol. Our results provide the information that structure and stability of DNA duplex depends on the structure of molecular crowding agent present in its close vicinity. In this study, I have taken the hydration of simple sugar as an essential model for understanding interactions between hydrophilic groups and interfacial water molecules and its effect on hydrogen bonded DNA duplexes. On the basis of these relatively simple building blocks I hope to gain some insights for understanding more generally the properties of sugar–water–salt systems with DNA duplexes.Keywords: natural molecular crowding, DNA Duplex, structure of DNA, bioengineering and life sciences
Procedia PDF Downloads 4669032 The Modelling of Real Time Series Data
Authors: Valeria Bondarenko
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We proposed algorithms for: estimation of parameters fBm (volatility and Hurst exponent) and for the approximation of random time series by functional of fBm. We proved the consistency of the estimators, which constitute the above algorithms, and proved the optimal forecast of approximated time series. The adequacy of estimation algorithms, approximation, and forecasting is proved by numerical experiment. During the process of creating software, the system has been created, which is displayed by the hierarchical structure. The comparative analysis of proposed algorithms with the other methods gives evidence of the advantage of approximation method. The results can be used to develop methods for the analysis and modeling of time series describing the economic, physical, biological and other processes.Keywords: mathematical model, random process, Wiener process, fractional Brownian motion
Procedia PDF Downloads 3579031 On Algebraic Structure of Improved Gauss-Seide Iteration
Authors: O. M. Bamigbola, A. A. Ibrahim
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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 a priori, 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 algebraic system, Gauss-Seidel iteration, algebraic structure, convergence
Procedia PDF Downloads 4649030 The Reason Why Al-Kashi’s Understanding of Islamic Arches Was Wrong
Authors: Amin Moradi, Maryam Moeini
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It is a widely held view that Ghiyath al-Din Jamshid-e-Kashani, also known as al-Kashi (1380-1429 CE), was the first who played a significant role in the interaction between mathematicians and architects by introducing theoretical knowledge in Islamic architecture. In academic discourses, geometric rules extracted from his splendid volume titled as Key of Arithmetic has uncritically believed by historians of architecture to contemplate the whole process of arch design all throughout the Islamic buildings. His theories tried to solve the fundamental problem of structural design and to understand what makes an Islamic structure safe or unsafe. As a result, al-Kashi arrived at the conclusion that a safe state of equilibrium is achieved through a specific geometry as a rule. This paper reassesses the stability of al-Kashi's systematized principal forms to evaluate the logic of his hypothesis with a special focus on large spans. Besides the empirical experiences of the author in masonry constructions, the finite element approach was proposed considering the current standards in order to get a better understanding of the validity of geometric rules proposed by al-Kashi for the equilibrium conditions of Islamic masonry arches and vaults. The state of damage of his reference arches under loading condition confirms beyond any doubt that his conclusion of the geometrical configuration measured through his treaties present some serious operational limits and do not go further than some individualized mathematical hypothesis. Therefore, the nature of his mathematical studies regarding Islamic arches is in complete contradiction with the practical knowledge of construction methodology.Keywords: Jamshid al-Kashani, Islamic architecture, Islamic geometry, construction equilibrium, collapse mechanism
Procedia PDF Downloads 1329029 Population Structure Analysis of Pakistani Indigenous Cattle Population by Using High Density SNP Array
Authors: Hamid Mustafa, Huson J. Heather, Kim Eiusoo, McClure Matt, Khalid Javed, Talat Nasser Pasha, Afzal Ali1, Adeela Ajmal, Tad Sonstegard
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Genetic differences associated with speciation, breed formation or local adaptation can help to preserve and effective utilization of animals in selection programs. Analyses of population structure and breed diversity have provided insight into the origin and evolution of cattle. In this study, we used a high-density panel of SNP markers to examine population structure and diversity among ten Pakistani indigenous cattle breeds. In total, 25 individuals from three cattle populations, including Achi (n=08), Bhagnari (n=04) and Cholistani (n=13) were genotyped for 777, 962 single nucleotide polymorphism (SNP) markers. Population structure was examined using the linkage model in the program STRUCTURE. After characterizing SNP polymorphism in the different populations, we performed a detailed analysis of genetic structure at both the individual and population levels. The whole-genome SNP panel identified several levels of population substructure in the set of examined cattle breeds. We further searched for spatial patterns of genetic diversity among these breeds under the recently developed spatial principal component analysis framework. Overall, such high throughput genotyping data confirmed a clear partitioning of the cattle genetic diversity into distinct breeds. The resulting complex historical origins associated with both natural and artificial selection have led to the differentiation of numerous different cattle breeds displaying a broad phenotypic variety over a short period of time.Keywords: Pakistan, cattle, genetic diversity, population structure
Procedia PDF Downloads 6209028 Qualitative Measurement of Literacy
Authors: Indrajit Ghosh, Jaydip Roy
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Literacy rate is an important indicator for measurement of human development. But this is not a good one to capture the qualitative dimension of educational attainment of an individual or a society. The overall educational level of an area is an important issue beyond the literacy rate. The overall educational level can be thought of as an outcome of the educational levels of individuals. But there is no well-defined algorithm and mathematical model available to measure the overall educational level of an area. A heuristic approach based on accumulated experience of experts is effective one. It is evident that fuzzy logic offers a natural and convenient framework in modeling various concepts in social science domain. This work suggests the implementation of fuzzy logic to develop a mathematical model for measurement of educational attainment of an area in terms of Education Index. The contribution of the study is two folds: conceptualization of “Education Profile” and proposing a new mathematical model to measure educational attainment in terms of “Education Index”.Keywords: education index, education profile, fuzzy logic, literacy
Procedia PDF Downloads 3169027 Quantifying Meaning in Biological Systems
Authors: Richard L. Summers
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The advanced computational analysis of biological systems is becoming increasingly dependent upon an understanding of the information-theoretic structure of the materials, energy and interactive processes that comprise those systems. The stability and survival of these living systems are fundamentally contingent upon their ability to acquire and process the meaning of information concerning the physical state of its biological continuum (biocontinuum). The drive for adaptive system reconciliation of a divergence from steady-state within this biocontinuum can be described by an information metric-based formulation of the process for actionable knowledge acquisition that incorporates the axiomatic inference of Kullback-Leibler information minimization driven by survival replicator dynamics. If the mathematical expression of this process is the Lagrangian integrand for any change within the biocontinuum then it can also be considered as an action functional for the living system. In the direct method of Lyapunov, such a summarizing mathematical formulation of global system behavior based on the driving forces of energy currents and constraints within the system can serve as a platform for the analysis of stability. As the system evolves in time in response to biocontinuum perturbations, the summarizing function then conveys information about its overall stability. This stability information portends survival and therefore has absolute existential meaning for the living system. The first derivative of the Lyapunov energy information function will have a negative trajectory toward a system's steady state if the driving force is dissipating. By contrast, system instability leading to system dissolution will have a positive trajectory. The direction and magnitude of the vector for the trajectory then serves as a quantifiable signature of the meaning associated with the living system’s stability information, homeostasis and survival potential.Keywords: meaning, information, Lyapunov, living systems
Procedia PDF Downloads 1319026 The Structure of Invariant Manifolds after a Supercritical Hamiltonian Hopf Bifurcation
Authors: Matthaios Katsanikas
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We study the structure of the invariant manifolds of complex unstable periodic orbits of a family of periodic orbits, in a 3D autonomous Hamiltonian system of galactic type, after a transition of this family from stability to complex instability (Hamiltonian Hopf bifurcation). We consider the case of a supercritical Hamiltonian Hopf bifurcation. The invariant manifolds of complex unstable periodic orbits have two kinds of structures. The first kind is represented by a disk confined structure on the 4D space of section. The second kind is represented by a complicated central tube structure that is associated with an extended network of tube structures, strips and flat structures of sheet type on the 4D space of section.Keywords: dynamical systems, galactic dynamics, chaos, phase space
Procedia PDF Downloads 1389025 Why and When to Teach Definitions: Necessary and Unnecessary Discontinuities Resulting from the Definition of Mathematical Concepts
Authors: Josephine Shamash, Stuart Smith
Abstract:
We examine reasons for introducing definitions in teaching mathematics in a number of different cases. We try to determine if, where, and when to provide a definition, and which definition to choose. We characterize different types of definitions and the different purposes we may have for formulating them, and detail examples of each type. Giving a definition at a certain stage can sometimes be detrimental to the development of the concept image. In such a case, it is advisable to delay the precise definition to a later stage. We describe two models, the 'successive approximation model', and the 'model of the extending definition' that fit such situations. Detailed examples that fit the different models are given based on material taken from a number of textbooks, and analysis of the way the concept is introduced, and where and how its definition is given. Our conclusions, based on this analysis, is that some of the definitions given may cause discontinuities in the learning sequence and constitute obstacles and unnecessary cognitive conflicts in the formation of the concept definition. However, in other cases, the discontinuity in passing from definition to definition actually serves a didactic purpose, is unavoidable for the mathematical evolution of the concept image, and is essential for students to deepen their understanding.Keywords: concept image, mathematical definitions, mathematics education, mathematics teaching
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