Search results for: Almost periodic solutions
Commenced in January 2007
Frequency: Monthly
Edition: International
Paper Count: 1636

Search results for: Almost periodic solutions

1066 Optimization of Samarium Extraction via Nanofluid-Based Emulsion Liquid Membrane Using Cyanex 272 as Mobile Carrier

Authors: Maliheh Raji, Hossein Abolghasemi, Jaber Safdari, Ali Kargari

Abstract:

Samarium as a rare-earth element is playing a growing important role in high technology. Traditional methods for extraction of rare earth metals such as ion exchange and solvent extraction have disadvantages of high investment and high energy consumption. Emulsion liquid membrane (ELM) as an improved solvent extraction technique is an effective transport method for separation of various compounds from aqueous solutions. In this work, the extraction of samarium from aqueous solutions by ELM was investigated using response surface methodology (RSM). The organic membrane phase of the ELM was a nanofluid consisted of multiwalled carbon nanotubes (MWCNT), Span80 as surfactant, Cyanex 272 as mobile carrier, and kerosene as base fluid. 1 M nitric acid solution was used as internal aqueous phase. The effects of the important process parameters on samarium extraction were investigated, and the values of these parameters were optimized using the Central Composition Design (CCD) of RSM. These parameters were the concentration of MWCNT in nanofluid, the carrier concentration, and the volume ratio of organic membrane phase to internal phase (Roi). The three-dimensional (3D) response surfaces of samarium extraction efficiency were obtained to visualize the individual and interactive effects of the process variables. A regression model for % extraction was developed, and its adequacy was evaluated. The result shows that % extraction improves by using MWCNT nanofluid in organic membrane phase and extraction efficiency of 98.92% can be achieved under the optimum conditions. In addition, demulsification was successfully performed and the recycled membrane phase was proved to be effective in the optimum condition.

Keywords: Cyanex 272, emulsion liquid membrane, multiwalled carbon nanotubes, nanofluid, response surface methodology, Samarium.

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1065 Architectural Approaches to a Sustainable Community with Floating Housing Units Adapting to Climate Change and Sea Level Rise in Vietnam

Authors: Nguyen Thi Thu Trang

Abstract:

Climate change and sea level rise is one of the greatest challenges facing human beings in the 21st century. Because of sea level rise, several low-lying coastal areas around the globe are at risk of being completely submerged, disappearing under water. Particularly in Viet Nam, the rise in sea level is predicted to result in more frequent and even permanently inundated coastal plains. As a result, land reserving fund of coastal cities is going to be narrowed in near future, while construction ground is becoming increasingly limited due to a rapid growth in population. Faced with this reality, the solutions are being discussed not only in tradition view such as accommodation is raised or moved to higher areas, or “living with the water”, but also forwards to “living on the water”. Therefore, the concept of a sustainable floating community with floating houses based on the precious value of long term historical tradition of water dwellings in Viet Nam would be a sustainable solution for adaptation of climate change and sea level rise in the coastal areas. The sustainable floating community is comprised of sustainability in four components: architecture, environment, socio-economic and living quality. This research paper is focused on sustainability in architectural component of floating community. Through detailed architectural analysis of current floating houses and floating communities in Viet Nam, this research not only accumulates precious values of traditional architecture that need to be preserved and developed in the proposed concept, but also illustrates its weaknesses that need to address for optimal design of the future sustainable floating communities. Based on these studies the research would provide guidelines with appropriate architectural solutions for the concept of sustainable floating community with floating housing units that are adapted to climate change and sea level rise in Viet Nam.

Keywords: Climate change, floating houses, floating community, Viet Nam.

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1064 The Tendencies of Development of the Management in the Education System of the Republic of Kazakhstan

Authors: Altynai Zhaitapova, Aizhan Satyvaldiyeva

Abstract:

In this article the authors investigate the main tendencies of development of the management in the education system of the Republic of Kazakhstan: problems, solutions and development of the education system of Kazakhstan in the realities of globalization.

Keywords: Change management, education, globalization, innovations management systems, quality of education.

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1063 Construction Innovation: Support for 3D Printing House

Authors: Andrea Palazzo, Daniel Macek, Veronika Malinova

Abstract:

Contour processing is the new technology challenge for architects and construction companies. The many advantages it promises make it one of the most interesting solutions for construction in terms of automation of building processes. The technology for 3D printing houses offers many application possibilities, from low-cost construction, to being considered by NASA for visionary projects as a good solution for building settlements on other planets. Another very important point is that clients, as architects, will no longer have many limits in design concerning ideas and creativity. The prices for real estate are constantly increasing and the lack of availability of construction materials as well as the speculation that has been created around it in 2021 is bringing prices to such a level that in the future it will be difficult for developers to find customers for these ultra-expensive homes. Hence, this paper starts with the introduction of 3D printing, which now has the potential to gain an important position in the market, becoming a valid alternative to the classic construction process. This technology is not only beneficial from an economic point of view but it is also a great opportunity to have an impact on the environment by reducing CO2 emissions. Further on in the article we will also understand if, after the COP 26 (2021 United Nations Climate Change Conference), world governments could also push towards building technologies that reduce the waste materials that are needed to be disposed of and at the same time reduce emissions with the contribution of governmental funds. This paper will give us insight on the multiple benefits of 3D printing and emphasize the importance of finding new solutions for materials that can be used by the printer. Therefore, based on the type of material, it will be possible to understand the compatibility with current regulations and how the authorities will be inclined to support this technology. This will help to enable the rise and development of this technology in Europe and in the rest of the world on actual housing projects and not only on prototypes.

Keywords: Additive manufacturing, building development building regulation, contour crafting, printing material.

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1062 Nonoscillation Criteria for Nonlinear Delay Dynamic Systems on Time Scales

Authors: Xinli Zhang

Abstract:

In this paper, we consider the nonlinear delay dynamic system xΔ(t) = p(t)f1(y(t)), yΔ(t) = −q(t)f2(x(t − τ )). We obtain some necessary and sufficient conditions for the existence of nonoscillatory solutions with special asymptotic properties of the system. We generalize the known results in the literature. One example is given to illustrate the results.

Keywords: Dynamic system, oscillation, time scales, two-dimensional.

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1061 Automatically Generated and Marked E-Learning Exercises for Logistics Cost Accounting

Authors: Markus Siepermann, Christoph Siepermann

Abstract:

This paper presents the concept and realisation of an e-learning tool that provides predefined or automatically generated exercises concerning logistics cost accounting. Students may practise where and whenever they like to via the Internet. Their solutions are marked automatically by the tool while considering consecutive faults and without any intervention of lecturers.

Keywords: Automatic marking, e-learning environment, onlinepracticing, randomly-generated exercises.

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1060 Assets Integrity Management in Oil and Gas Production Facilities Through Corrosion Mitigation and Inspection Strategy: A Case Study of Sarir Oilfield

Authors: Iftikhar Ahmad, Youssef Elkezza

Abstract:

Sarir oilfield is in North Africa. It has facilities of oil and gas production. The assets of the Sarir oilfield can be divided into five following categories, namely: (i) Well bore and wellheads; (ii) Vessels such as separators, desalters, and gas processing facilities; (iii) Pipelines including all flow lines, trunk lines, and shipping lines; (iv) storage tanks; (v) Other assets such as turbines and compressors, etc. The nature of the petroleum industry recognizes the potential human, environmental and financial consequences that can result from failing to maintain the integrity of wellheads, vessels, tanks, pipelines, and other assets. The importance of effective asset integrity management increases as the industry infrastructure continues to age. The primary objective of assets integrity management (AIM) is to maintain assets in a fit-for-service condition while extending their remaining life in the most reliable, safe, and cost-effective manner. Corrosion management is one of the important aspects of successful asset integrity management. It covers corrosion mitigation, monitoring, inspection, and risk evaluation. External corrosion on pipelines, well bores, buried assets, and bottoms of tanks is controlled with a combination of coatings by cathodic protection, while the external corrosion on surface equipment, wellheads, and storage tanks is controlled by coatings. The periodic cleaning of the pipeline by pigging helps in the prevention of internal corrosion. Further, internal corrosion of pipelines is prevented by chemical treatment and controlled operations. This paper describes the integrity management system used in the Sarir oil field for its oil and gas production facilities based on standard practices of corrosion mitigation and inspection.

Keywords: Assets integrity management, corrosion prevention in oilfield assets, corrosion management in oilfield, corrosion prevention and inspection activities.

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1059 Ant System with Acoustic Communication

Authors: S. Bougrine, S. Ouchraa, B. Ahiod, A. A. El Imrani

Abstract:

Ant colony optimization is an ant algorithm framework that took inspiration from foraging behavior of ant colonies. Indeed, ACO algorithms use a chemical communication, represented by pheromone trails, to build good solutions. However, ants involve different communication channels to interact. Thus, this paper introduces the acoustic communication between ants while they are foraging. This process allows fine and local exploration of search space and permits optimal solution to be improved.

Keywords: Acoustic Communication, Ant Colony Optimization, Local Search, Traveling Salesman Problem.

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1058 Effective Class of Discreet Programing Problems

Authors: Kaziyev G. Z., Nabiyeva G. S., Kalizhanova A.U.

Abstract:

We consider herein a concise view of discreet programming models and methods. There has been conducted the models and methods analysis. On the basis of discreet programming models there has been elaborated and offered a new class of problems, i.e. block-symmetry models and methods of applied tasks statements and solutions.

Keywords: Discreet programming, block-symmetry, analysis methods, information systems development.

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1057 Approximation of Sturm-Liouville Problems by Exponentially Weighted Legendre-Gauss Tau Method

Authors: Mohamed K. El Daou

Abstract:

We construct an exponentially weighted Legendre- Gauss Tau method for solving differential equations with oscillatory solutions. The proposed method is applied to Sturm-Liouville problems. Numerical examples illustrating the efficiency and the high accuracy of our results are presented.

Keywords: Oscillatory functions, Sturm-Liouville problems, legendre polynomial, gauss points.

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1056 On the Fuzzy Difference Equation xn+1 = A +

Authors: Qianhong Zhang, Lihui Yang, Daixi Liao,

Abstract:

In this paper, we study the existence, the boundedness and the asymptotic behavior of the positive solutions of a fuzzy nonlinear difference equations xn+1 = A + k i=0 Bi xn-i , n= 0, 1, · · · . where (xn) is a sequence of positive fuzzy numbers, A,Bi and the initial values x-k, x-k+1, · · · , x0 are positive fuzzy numbers. k ∈ {0, 1, 2, · · ·}.

Keywords: Fuzzy difference equation, boundedness, persistence, equilibrium point, asymptotic behaviour.

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1055 Conjugate Gradient Algorithm for the Symmetric Arrowhead Solution of Matrix Equation AXB=C

Authors: Minghui Wang, Luping Xu, Juntao Zhang

Abstract:

Based on the conjugate gradient (CG) algorithm, the constrained matrix equation AXB=C and the associate optimal approximation problem are considered for the symmetric arrowhead matrix solutions in the premise of consistency. The convergence results of the method are presented. At last, a numerical example is given to illustrate the efficiency of this method.

Keywords: Iterative method, symmetric arrowhead matrix, conjugate gradient algorithm.

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1054 Sperm Whale Signal Analysis: Comparison using the Auto Regressive model and the Daubechies 15 Wavelets Transform

Authors: Olivier Adam, Maciej Lopatka, Christophe Laplanche, Jean-François Motsch

Abstract:

This article presents the results using a parametric approach and a Wavelet Transform in analysing signals emitting from the sperm whale. The extraction of intrinsic characteristics of these unique signals emitted by marine mammals is still at present a difficult exercise for various reasons: firstly, it concerns non-stationary signals, and secondly, these signals are obstructed by interfering background noise. In this article, we compare the advantages and disadvantages of both methods: Auto Regressive models and Wavelet Transform. These approaches serve as an alternative to the commonly used estimators which are based on the Fourier Transform for which the hypotheses necessary for its application are in certain cases, not sufficiently proven. These modern approaches provide effective results particularly for the periodic tracking of the signal's characteristics and notably when the signal-to-noise ratio negatively effects signal tracking. Our objectives are twofold. Our first goal is to identify the animal through its acoustic signature. This includes recognition of the marine mammal species and ultimately of the individual animal (within the species). The second is much more ambitious and directly involves the intervention of cetologists to study the sounds emitted by marine mammals in an effort to characterize their behaviour. We are working on an approach based on the recordings of marine mammal signals and the findings from this data result from the Wavelet Transform. This article will explore the reasons for using this approach. In addition, thanks to the use of new processors, these algorithms once heavy in calculation time can be integrated in a real-time system.

Keywords: Autoregressive model, Daubechies Wavelet, Fourier Transform, marine mammals, signal processing, spectrogram, sperm whale, Wavelet Transform.

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1053 Parametric Study of 3D Micro-Fin Tubes on Heat Transfer and Friction Factor

Authors: Shima Soleimani, Steven Eckels

Abstract:

One area of special importance for the surface-level study of heat exchangers is tubes with internal micro-fins (< 0.5 mm tall). Micro-finned surfaces are a kind of extended solid surface in which energy is exchanged with water that acts as the source or sink of energy. Significant performance gains are possible for either shell, tube, or double pipe heat exchangers if the best surfaces are identified. The parametric studies of micro-finned tubes that have appeared in the literature left some key parameters unexplored. Specifically, they ignored three-dimensional (3D) micro-fin configurations, conduction heat transfer in the fins, and conduction in the solid surface below the micro-fins. Thus, this study aimed at implementing a parametric study of 3D micro-finned tubes that considered micro-fine height and discontinuity features. A 3D conductive and convective heat-transfer simulation through coupled solid and periodic fluid domains is applied in a commercial package, ANSYS Fluent 19.1. The simulation is steady-state with turbulent water flow cooling the inner wall of a tube with micro-fins. The simulation utilizes a constant and uniform temperature on the tube outer wall. Performance is mapped for 18 different simulation cases, including a smooth tube using a realizable k-ε turbulence model at a Reynolds number of 48,928. Results compared the performance of 3D tubes with results for the similar two-dimensional (2D) one. Results showed that the micro-fine height has a greater impact on performance factors than discontinuity features in 3D micro-fin tubes. A transformed 3D micro-fin tube can enhance heat transfer, and pressure drops up to 21% and 56% compared to a 2D one, respectfully.

Keywords: Three-dimensional micro-fin tube, heat transfer, friction factor, heat exchanger.

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1052 On a Class of Inverse Problems for Degenerate Differential Equations

Authors: Fadi Awawdeh, H.M. Jaradat

Abstract:

In this paper, we establish existence and uniqueness of solutions for a class of inverse problems of degenerate differential equations. The main tool is the perturbation theory for linear operators.

Keywords: Inverse Problem, Degenerate Differential Equations, Perturbation Theory for Linear Operators

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1051 Approximate Solutions to Large Stein Matrix Equations

Authors: Khalide Jbilou

Abstract:

In the present paper, we propose numerical methods for solving the Stein equation AXC - X - D = 0 where the matrix A is large and sparse. Such problems appear in discrete-time control problems, filtering and image restoration. We consider the case where the matrix D is of full rank and the case where D is factored as a product of two matrices. The proposed methods are Krylov subspace methods based on the block Arnoldi algorithm. We give theoretical results and we report some numerical experiments.

Keywords: IEEEtran, journal, LATEX, paper, template.

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1050 Genetic Algorithm for In-Theatre Military Logistics Search-and-Delivery Path Planning

Authors: Jean Berger, Mohamed Barkaoui

Abstract:

Discrete search path planning in time-constrained uncertain environment relying upon imperfect sensors is known to be hard, and current problem-solving techniques proposed so far to compute near real-time efficient path plans are mainly bounded to provide a few move solutions. A new information-theoretic –based open-loop decision model explicitly incorporating false alarm sensor readings, to solve a single agent military logistics search-and-delivery path planning problem with anticipated feedback is presented. The decision model consists in minimizing expected entropy considering anticipated possible observation outcomes over a given time horizon. The model captures uncertainty associated with observation events for all possible scenarios. Entropy represents a measure of uncertainty about the searched target location. Feedback information resulting from possible sensor observations outcomes along the projected path plan is exploited to update anticipated unit target occupancy beliefs. For the first time, a compact belief update formulation is generalized to explicitly include false positive observation events that may occur during plan execution. A novel genetic algorithm is then proposed to efficiently solve search path planning, providing near-optimal solutions for practical realistic problem instances. Given the run-time performance of the algorithm, natural extension to a closed-loop environment to progressively integrate real visit outcomes on a rolling time horizon can be easily envisioned. Computational results show the value of the approach in comparison to alternate heuristics.

Keywords: Search path planning, false alarm, search-and-delivery, entropy, genetic algorithm.

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1049 Laplace Adomian Decomposition Method Applied to a Two-Dimensional Viscous Flow with Shrinking Sheet

Authors: M. A. Koroma, S. Widatalla, A. F. Kamara, C. Zhang

Abstract:

Our aim in this piece of work is to demonstrate the power of the Laplace Adomian decomposition method (LADM) in approximating the solutions of nonlinear differential equations governing the two-dimensional viscous flow induced by a shrinking sheet.

Keywords: Adomian polynomials, Laplace Adomian decomposition method, Padé Approximant, Shrinking sheet.

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1048 Closed-Form Solutions for Nanobeams Based On the Nonlocal Euler-Bernoulli Theory

Authors: Francesco Marotti de Sciarra, Raffaele Barretta

Abstract:

Starting from nonlocal continuum mechanics, a thermodynamically new nonlocal model of Euler-Bernoulli nanobeams is provided. The nonlocal variational formulation is consistently provided and the governing differential equation for transverse displacement is presented. Higher-order boundary conditions are then consistently derived. An example is contributed in order to show the effectiveness of the proposed model.

Keywords: Bernoulli-Euler beams, Nanobeams, nonlocal elasticity.

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1047 Microwave Assisted Fast Synthesis of Flower-like ZnO Based Guanidinium Template for Photodegradation of Azo Dye Congo Red

Authors: N. F .Hamedani, A.R. Mahjoub, A. A. khodadadi, Y. Mortazavi, F.Farzaneh

Abstract:

ZnO nanostructure were synthesized via microwave method using zinc acetate as starting material, guanidinium as structure directing agents, and water as solvent.. This work investigates the photodegradation of azo dyes using the ZnO Flowerlike in aqueous solutions. As synthesized ZnO samples were characterized using X-Ray powder diffraction (XRD), scanning electron microscopy (SEM), and FTIR spectroscopy.In this work photodecolorization of congored azo dye under UV irradiation by nano ZnO was studied.

Keywords: Photo catalyst, Nano crystals, Zinc Oxide

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1046 Rarefactive and Compressive Solitons in Warm Dusty Plasma with Electrons and Nonthermal Ions

Authors: Hamid Reza Pakzad

Abstract:

Dust acoustic solitary waves are studied in warm dusty plasma containing negatively charged dusts, nonthermal ions and Boltzmann distributed electrons. Sagdeev pseudopotential method is used in order to investigate solitary wave solutions in the plasmas. The existence of compressive and rarefractive solitons is studied.

Keywords: Nonthermal, Soliton, Dust, Sagdeev potential

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1045 On the Positive Definite Solutions of Nonlinear Matrix Equation

Authors: Tian Baoguang, Liang Chunyan, Chen Nan

Abstract:

In this paper, the nonlinear matrix equation is investigated. Based on the fixed-point theory, the boundary and the existence of the solution with the case r>-δi are discussed. An algorithm that avoids matrix inversion with the case -1<-δi<0 is proposed.

Keywords: Nonlinear matrix equation, Positive definite solution, The maximal-minimal solution, Iterative method, Free-inversion

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1044 Automated Method Time Measurement System for Redesigning Dynamic Facility Layout

Authors: Salam Alzubaidi, G. Fantoni, F. Failli, M. Frosolini

Abstract:

The dynamic facility layout problem is a really critical issue in the competitive industrial market; thus, solving this problem requires robust design and effective simulation systems. The sustainable simulation requires inputting reliable and accurate data into the system. So this paper describes an automated system integrated into the real environment to measure the duration of the material handling operations, collect the data in real-time, and determine the variances between the actual and estimated time schedule of the operations in order to update the simulation software and redesign the facility layout periodically. The automated method- time measurement system collects the real data through using Radio Frequency-Identification (RFID) and Internet of Things (IoT) technologies. Hence, attaching RFID- antenna reader and RFID tags enables the system to identify the location of the objects and gathering the time data. The real duration gathered will be manipulated by calculating the moving average duration of the material handling operations, choosing the shortest material handling path, and then updating the simulation software to redesign the facility layout accommodating with the shortest/real operation schedule. The periodic simulation in real-time is more sustainable and reliable than the simulation system relying on an analysis of historical data. The case study of this methodology is in cooperation with a workshop team for producing mechanical parts. Although there are some technical limitations, this methodology is promising, and it can be significantly useful in the redesigning of the manufacturing layout.

Keywords: Dynamic facility layout problem, internet of things, method time measurement, radio frequency identification, simulation.

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1043 On the Move to Semantic Web Services

Authors: Jorge Cardoso

Abstract:

Semantic Web services will enable the semiautomatic and automatic annotation, advertisement, discovery, selection, composition, and execution of inter-organization business logic, making the Internet become a common global platform where organizations and individuals communicate with each other to carry out various commercial activities and to provide value-added services. There is a growing consensus that Web services alone will not be sufficient to develop valuable solutions due the degree of heterogeneity, autonomy, and distribution of the Web. This paper deals with two of the hottest R&D and technology areas currently associated with the Web – Web services and the Semantic Web. It presents the synergies that can be created between Web Services and Semantic Web technologies to provide a new generation of eservices.

Keywords: Semantic Web, Web service, Web process, WWW.

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1042 Quartic Nonpolynomial Spline Solutions for Third Order Two-Point Boundary Value Problem

Authors: Talaat S. El-Danaf

Abstract:

In this paper, we develop quartic nonpolynomial spline method for the numerical solution of third order two point boundary value problems. It is shown that the new method gives approximations, which are better than those produced by other spline methods. Convergence analysis of the method is discussed through standard procedures. Two numerical examples are given to illustrate the applicability and efficiency of the novel method.

Keywords: Quartic nonpolynomial spline, Two-point boundary value problem.

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1041 Iterative Solutions to Some Linear Matrix Equations

Authors: Jiashang Jiang, Hao Liu, Yongxin Yuan

Abstract:

In this paper the gradient based iterative algorithms are presented to solve the following four types linear matrix equations: (a) AXB = F; (b) AXB = F, CXD = G; (c) AXB = F s. t. X = XT ; (d) AXB+CYD = F, where X and Y are unknown matrices, A,B,C,D, F,G are the given constant matrices. It is proved that if the equation considered has a solution, then the unique minimum norm solution can be obtained by choosing a special kind of initial matrices. The numerical results show that the proposed method is reliable and attractive.

Keywords: Matrix equation, iterative algorithm, parameter estimation, minimum norm solution.

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1040 Two Different Solutions for Gigabit Ethernet Transmission over POF

Authors: Stefano Straullu, Silvio Abrate, Antonino Nespola, Paolo Savio, Roberto Gaudino

Abstract:

Two completely different approaches for a Gigabit Ethernet compliant stream transmission over 50m of 1mm PMMA SI-POF have been experimentally demonstrated and are compared in this paper. The first solution is based on a commercial RC-LED transmission and a careful optimization of the physical layer architecture, realized during the POF-PLUS EU Project. The second solution exploits the performance of an edge-emitting laser at the transmitter side in order to avoid any sort of electrical equalization at the receiver side.

Keywords: Gigabit Ethernet, Home Networking, Step-Index Polymer Optical Fiber (SI-POF)

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1039 Localized Non-Stability of the Semi-Infinite Elastic Orthotropic Plate

Authors: Reza Sharifian, Vagharshak Belubekyan

Abstract:

This paper is concerned with an investigation into the localized non-stability of a thin elastic orthotropic semi-infinite plate. In this study, a semi-infinite plate, simply supported on two edges and different boundary conditions, clamped, hinged, sliding contact and free on the other edge, are considered. The mathematical model is used and a general solution is presented the conditions under which localized solutions exist are investigated.

Keywords: Localized, Non-stability, Orthotropic, Semi-infinite

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1038 Positive Solutions for Three-Point Boundary Value Problems of Third-Order Nonlinear Singular Differential Equations in Banach Space

Authors: Li Xiguang

Abstract:

In this paper, by constructing a special set and utilizing fixed point index theory, we study the existence of solution for singular differential equation in Banach space, which improved and generalize the result of related paper.

Keywords: Banach space, cone, fixed point index, singular differential equation.

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1037 Recursive Similarity Hashing of Fractal Geometry

Authors: Timothee G. Leleu

Abstract:

A new technique of topological multi-scale analysis is introduced. By performing a clustering recursively to build a hierarchy, and analyzing the co-scale and intra-scale similarities, an Iterated Function System can be extracted from any data set. The study of fractals shows that this method is efficient to extract self-similarities, and can find elegant solutions the inverse problem of building fractals. The theoretical aspects and practical implementations are discussed, together with examples of analyses of simple fractals.

Keywords: hierarchical clustering, multi-scale analysis, Similarity hashing.

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