Search results for: infinite system

Authors: Hamid Abchir, Mohammed Sabak2

Abstract:

We construct an infinite family of links which are both almost alternating and quasi-alternating from a given either almost alternating diagram representing a quasi-alternating link, or connected and reduced alternating tangle diagram. To do that we use what we call a dealternator extension which consists in replacing the dealternator by a rational tangle extending it. We note that all non-alternating and quasi-alternating Montesinos links can be obtained in that way. We check that all the obtained quasi-alternating links satisfy Conjecture 3.1 of Qazaqzeh et al. (JKTR 22 (6), 2013), that is the crossing number of a quasi-alternating link is less than or equal to its determinant. We also prove that the converse of Theorem 3.3 of Qazaqzeh et al. (JKTR 24 (1), 2015) is false.

Keywords: quasi-alternating links, almost alternating links, tangles, determinants

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Authors: David Alejandro Lazo-Vasquez, Jorge Luis Balino

Abstract:

In the petroleum industry, multiphase flow occurs when oil, gas, and water are transported in the same pipe through large pipeline systems. The flow can take different patterns depending on parameters like fluid velocities, pipe diameter, pipe inclination, and fluid properties. Mainly, intermittent flow is produced by the natural propagation of short and long waves, according to the Kelvin-Helmholtz Stability Theory. To model stratified flow and the onset of intermittent flow, it is crucial to have knowledge of short and long waves behavior. The two-fluid model, frequently employed for characterizing multiphase systems, becomes ill-posed for high liquid and gas velocities and large inclination angles, for short waves can develop infinite growth rates. We are interested in focusing attention on long-wave instability, which leads to the production of roll waves that may grow and result in the transition from stratified flow to intermittent flow. In this study, global and local linear stability analyses for dynamic and kinematic stability criteria predict the regions of stability of the flow for different pipe inclinations and fluid velocities in regularized and non-regularized systems, concurrently. It was possible to distinguish when: wave growth rates are absolutely bounded (stable stratified smooth flow), waves have finite growth rates (unstable stratified wavy flow), and when the equation system becomes elliptic and hyperbolization is needed. In order to bound short wave growth rates and regularize the equation system, we incorporated some lower and higher-order terms like interfacial drag and surface tension, respectively.

Keywords: linear stability analysis, multiphase flow, onset of slugging, two-fluid model regularization

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Authors: Tribhuvan N. Soorya

Abstract:

Charging and discharging of a capacitor through a resistor can be shown as exponential curve. Theoretically, it takes infinite time to fully charge or discharge a capacitor. The flow of charge is due to electrons having finite and fixed value of charge. If we carefully examine the charging and discharging process after several time constants, the points on q vs t graph become discrete and curve become discontinuous. Moreover for all practical purposes capacitor with charge (q0-e) can be taken as fully charged, as it introduces an error less than one part per million. Similar is the case for discharge of a capacitor, where the capacitor with the last electron (charge e) can be taken as fully discharged. With this, we can estimate the finite value of time for fully charging and discharging a capacitor.

Keywords: charging, discharging, RC Circuit, capacitor

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Authors: Ivan Baravy

Abstract:

Interpolation problem, as it was initially posed in terms of polynomials, is well researched. However, further mathematical developments extended it significantly. Trigonometric interpolation is widely used in Fourier analysis, while its generalized representation as exponential interpolation is applicable to such problem of mathematical physics as modelling of Ziegler-Biersack-Littmark repulsive interatomic potentials. Formulated for finite fields, this problem arises in decoding Reed--Solomon codes. This paper shows the relation between different interpretations of the problem through the class of matrices of special structure - Hankel matrices.

Keywords: Berlekamp-Massey algorithm, exponential interpolation, finite fields, Hankel matrices, Hankel polynomials

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Authors: Filipa Cruz, Grecia P. Matos

Abstract:

An Inexhaustible Will of Infinite is ongoing practice-based research focused on a psychophysiological conception of body and on the creative will that seeks to examine the possibility of art being simultaneously a pacifier and an intensifier in a physiological artistic production. This is a study where philosophy and art converge in a commentary on the affection of the concept of will to power in the art world through Nietzsche’s commentaries, through the analysis of case studies and a reflection arising from artistic practice. Through Nietzsche, it is sought to compare concepts that communicate with the artistic practice since creation is an intensification and engenders perspectives. It is also a practice highly embedded in the body, in the non-verbal, in the physiology of art and in the coexistence between the sensorial and the thought. It is questioned if the physiology of art could be thought of as a thinking-feeling with no primacy of the thought over the sensorial. Art as a manifestation of the will to power participates in a comprehension of the world. In this article, art is taken as a privileged way of communication – implicating corporeal-sensorial-conceptual – and of connection between humans. Problematized is the dream and the drunkenness as intensifications and expressions of life’s comprehension. Therefore, art is perceived as suggestion and invention, where the artistic intoxication breaks limits in the experience of life, and the artist, dominated by creative forces, claims, orders, obeys, proclaims love for life. The intention is also to consider how one can start from pain to create and how one can generate new and endless artistic forms through nightmares, daydreams, impulses, intoxication, enhancement, intensification in a plurality of subjects and matters. It is taken into consideration the fact that artistic creation is something that is intensified corporeally, expanded, continuously generated and acting on bodies. It is inextinguishable and a constant movement intertwining Apollonian and Dionysian instincts of destruction and creation of new forms. The concept of love also appears associated with conquering, that, in a process of intensification and drunkenness, impels the artist to generate and to transform matter. Just like a love relationship, love in Nietzsche requires time, patience, effort, courage, conquest, seduction, obedience, and command, potentiating the amplification of knowledge of the other / the world. Interlacing Nietzsche's philosophy, not with Modern Art, but with Contemporary Art, it is argued that intoxication, will to power (strongly connected with the creative will) and love still have a place in the artistic production as creative agents.

Keywords: artistic creation, body, intensification, psychophysiology, will to power

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Authors: Shiyun Liu

Abstract:

Radiant heating systems work fundamentally differently from air systems by taking advantage of both radiant and convective heat transfer to remove space heating load. There are rare studies on differences of heating systems between all-air system and radiant floor system. This paper uses the method of simulation based on state-space to calculate the indoor temperature and wall temperature of each system and shows how the dynamic heat transfer in rooms conditioned by a radiant system is different from an air system. Then this paper analyses the changes of indoor temperature of these two systems, finding out the differences between all-air heating system and radiant floor heating system to help the designer choose a more suitable heating system.

Keywords: radiant floor, all-air system, thermal comfort, simulation, heating system

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Authors: Ahmad Abdul-Razzak Aboudi Al-Issa

Abstract:

Thermal and Hydrodynamic are basic aspects in any hydraulic system and therefore, they must be assessed with regard to this aspect before constructing the system. This assessment needs a good expertise in this aspect to obtain an efficient hydraulic system. Therefore, this study aims to build an expert system called Hydraulic System Calculations (HSC) to ensure a smooth operation for the hydraulic system. The expert system (HSC) had been designed and coded in an user-friendly interactive program called Microsoft Visual Basic 2010. The suggested code provides the designer with a number of choices to resolve the problem of hydraulic oil overheating which may arise during the continuous operation of the hydraulic unit. As a result, the HSC can minimize the human errors, effort, time and cost of hydraulic machine design.

Keywords: fluid power, hydraulic system, thermal and hydrodynamic, expert system

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Authors: S.I.Mukhin, S. Seidov, A. Mukherjee

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The Dicke model is a key tool for the description of correlated states of quantum atomic systems, excited by resonant photon absorption and subsequently emitting spontaneous coherent radiation in the superradiant state. The Dicke Hamiltonian (DH) is successfully used for the description of the dynamics of the Josephson Junction (JJ) array in a resonant cavity under applied current. In this work, we have investigated a generalized model, which is described by DH with a frustrating interaction term. This frustrating interaction term is explicitly the infinite coordinated interaction between all the spin half in the system. In this work, we consider an array of N superconducting islands, each divided into two sub-islands by a Josephson Junction, taken in a charged qubit / Cooper Pair Box (CPB) condition. The array is placed inside the resonant cavity. One important aspect of the problem lies in the dynamical nature of the physical observables involved in the system, such as condensed electric field and dipole moment. It is important to understand how these quantities behave with time to define the quantum phase of the system. The Dicke model without frustrating term is solved to find the dynamical solutions of the physical observables in analytic form. We have used Heisenberg’s dynamical equations for the operators and on applying newly developed Rotating Holstein Primakoff (HP) transformation and DH we have arrived at the four coupled nonlinear dynamical differential equations for the momentum and spin component operators. It is possible to solve the system analytically using two-time scales. The analytical solutions are expressed in terms of Jacobi's elliptic functions for the metastable ‘bound luminosity’ dynamic state with the periodic coherent beating of the dipoles that connect the two double degenerate dipolar ordered phases discovered previously. In this work, we have proceeded the analysis with the extended DH with a frustrating interaction term. Inclusion of the frustrating term involves complexity in the system of differential equations and it gets difficult to solve analytically. We have solved semi-classical dynamic equations using the perturbation technique for small values of Josephson energy EJ. Because the Hamiltonian contains parity symmetry, thus phase transition can be found if this symmetry is broken. Introducing spontaneous symmetry breaking term in the DH, we have derived the solutions which show the occurrence of finite condensate, showing quantum phase transition. Our obtained result matches with the existing results in this scientific field.

Keywords: Dicke Model, nonlinear dynamics, perturbation theory, superconductivity

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Authors: Syukri Himran, Erwin Eka Putra, Nanang Roni

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This study explains the natural convection of viscous fluid flowing on semi-infinite vertical plate. A set of the governing equations describing the continuity, momentum and energy, have been reduced to dimensionless forms by introducing the references variables. To solve the problems, the equations are formulated by explicit finite-difference in time dependent form and computations are performed by Fortran program. The results describe velocity, temperature profiles both in transient and steady state conditions. An approximate value of heat transfer coefficient and the effects of Pr on convection flow are also presented.

Keywords: natural convection, vertical plate, velocity and temperature profiles, steady and unsteady

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Authors: Thien X. Dinh, Peter Witt

Abstract:

A one-dimensional model for the simulation of condensation and solidification of a metallurgical vapor in the mixture of gas during supersonic expansion is presented. In the model, condensation is based on critical nucleation and drop-growth theory. When the temperature falls below the supercooling point, all the formed liquid droplets in the condensation phase are assumed to solidify at an infinite rate. The model was verified with a Computational Fluid Dynamics simulation of magnesium vapor condensation and solidification. The obtained results are in reasonable agreement with CFD data. Therefore, the model is a promising, efficient tool for use in the design process for supersonic nozzles applied in mineral processes since it is faster than the CFD counterpart by an order of magnitude.

Keywords: condensation, metallurgical flow, solidification, supersonic expansion

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Authors: Jaemyoung Lee

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We present a method to set up system functions through a near filed communication (NFC) of a smartphone. The short communication distance of the NFC which is usually less than 4 cm could prevent any interferences from other devices and establish a secure communication channel between a system and the smartphone. The proposed set-up method for system function values is demonstrated for a blacbox system in a car. In demonstration, system functions of a blackbox which is manipulated through NFC of a smartphone are controls of image quality, sound level, shock sensing level to store images, etc. The proposed set-up method for system function values can be used for any devices with NFC.

Keywords: system set-up, near field communication, smartphone, android

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Authors: Zakir Husain, Neem Sagar, Neeraj Gupta

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Due to the increased penetration of renewable energy resources in the distribution system, the system is no longer passive in nature. In this paper, a steady state analysis of the distribution system has been done with the inclusion of wind generation. The modeling of wind turbine generator system and wind generator has been made to obtain the average active and the reactive power injection into the system. The study has been conducted on a IEEE-33 bus system with two wind generators. The present research work is useful not only to utilities but also to customers.

Keywords: distributed generation, distribution network, radial network, wind turbine generating system

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Authors: Suraj Kumar Mukti

Abstract:

Enterprise Resource Planning (ERP) system is a management tool to integrate all departments in an organization. It integrates business processes, manages resources efficiently and provides an appropriate decision support system to management. ERP system implementation is a typical and time taking process as well as money consuming process. Articles related to key success factors of ERP system implementation are available in the literature, but rare authors have focused on roadmap of successful ERP system implementation. Postponement is better if the organization is not ready to implement ERP system in better way; hence checking of organization’s preparation to adopt new system is an important prerequisite to ensure the success of ERP system implementation in an organization. Then comes what will be called as success of ERP system implementation. Benefits achieved by ERP system may be categorized into two categories; viz. tangible and intangible benefits. This research article presents a roadmap to ensure the success of ERP system implementation and benefits achieved through the new system as in success indicator. A case study is presented to evaluate the success and benefit achieved through the new system. The article gives a comprehensive approach to academicians and a roadmap to the organizations seeking to implement the ERP system.

Keywords: ERP system, decision support system, tangible, intangible

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Authors: Kushakov Kholmurodjon, Muhammadjonov Akbarshox

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This present paper is devoted to a system of second-order nonlinear differential equations with a special right-hand side, exactly, the linear part and a third-order polynomial of a special form. It is shown that for some relations between the parameters, there is a second-order curve in which trajectories leaving the points of this curve remain in the same place. Thus, the curve is invariant with respect to the given system. Moreover, this system is invariant under a non-degenerate linear transformation of variables. The form of this curve, depending on the relations between the parameters and the eigenvalues of the matrix, is proved. All solutions of this system of differential equations are shown analytically.

Keywords: dynamic system, ellipse, hyperbola, Hess system, polar coordinate system

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Authors: Farhad Ghasemi

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Along with transforming the international system into a complex and chaotic system, the fundamental question arises: how can deterrence be reconstructed conceptually and theoretically in this system model? The deterrence system is much more complex today than it was seven decades ago. This article suggests that the perception of deterrence as a linear system is a fundamental mistake because it does not consider the new dynamics of the international system, including network power dynamics. The author aims to improve this point by focusing on complexity and chaos theories, especially their nonlinearity and cascading failure principles. This article proposes that the perception of deterrence as a linear system is a fundamental mistake, as the new dynamics of the surrounding international system do not take into account. The author recognizes deterrence as a nonlinear system and introduces it as a concept in strategic studies.

Keywords: complexity, international system, deterrence, linear deterrence, nonlinear deterrence

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Authors: Boumediene Hamzi, Turky N. AlOtaiby, Saleh AlShebeili, Arwa AlAnqary

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We introduce a data-driven method for seizure detection drawing on recent progress in Machine Learning. The method is based on embedding probability measures in a high (or infinite) dimensional reproducing kernel Hilbert space (RKHS) where the Maximum Mean Discrepancy (MMD) is computed. The MMD is metric between probability measures that are computed as the difference between the means of probability measures after being embedded in an RKHS. Working in RKHS provides a convenient, general functional-analytical framework for theoretical understanding of data. We apply this approach to the problem of seizure detection.

Keywords: kernel methods, maximum mean discrepancy, seizure detection, machine learning

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Authors: Nora Arbaoui, Rachid Tadili

Abstract:

This study focuses on a solar system designed to heat an agricultural greenhouse. This solar system is based on the heating of a transfer fluid that circulates inside the greenhouse through a solar copper coil integrated into the roof of the greenhouse. The thermal energy stored during the day will be released during the night to improve the microclimate of the greenhouse. This system was tested in a small agricultural greenhouse in order to ameliorate the different operational parameters. The climatic and agronomic results obtained with this system are significant in comparison with a greenhouse with no heating system.

Keywords: solar system, agricultural greenhouse, heating, storage, drying

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Authors: Patricia Agboro

Abstract:

The definition of a concept is quite important in any philosophical discourse as it serves as a guide in the analysis of that concept. In the sciences, arriving at a consensus regarding concepts is quite easily achievable due to the nature of the discipline. Problem arises when one delves into the realm of the humanities. Discourses in the humanities are largely perspectival because the question of values come into play. Defining the concept of Art is no different as it has yielded unresolved and problematic issues arising from attempts at definition. A major problem arising from such attempt is that of exclusion of other art forms. In this paper therefore, we call for the rejection of an attempt at providing a comprehensive definition for Art since it is clear that the collection of definitions provided so far, has failed in capturing the nuances and intricacies of the infinite varieties of the art forms that there are. Rather, a more fruitful approach to philosophical discourses on Art is not to construe the theories of Art per-se but to reconstruct them as a collection of criteria for determining artistic excellence.

Keywords: art, creativity, definition, reconstruction

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Authors: Amal M. Alrayes

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Data and system quality play a central role in organizational success, and the quality of any existing information system has a major influence on the effectiveness of overall system performance.Given the importance of system and data quality to an organization, it is relevant to highlight their importance on organizational performance in the Kingdom of Bahrain. This research aims to discover whether system quality and data quality are related, and to study the impact of system and data quality on organizational success. A theoretical model based on previous research is used to show the relationship between data and system quality, and organizational impact. We hypothesize, first, that system quality is positively associated with organizational impact, secondly that system quality is positively associated with data quality, and finally that data quality is positively associated with organizational impact. A questionnaire was conducted among public and private organizations in the Kingdom of Bahrain. The results show that there is a strong association between data and system quality, that affects organizational success.

Keywords: data quality, performance, system quality, Kingdom of Bahrain

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Authors: H. Soltani, J. Hadfield, M. Redmond, D. S. Nobes

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The passage of oil droplets through a vertical mini-slot were investigated in this study. Oil-in-water emulsion can undergo coalescence of finer oil droplets forming droplets of a size that need to be considered individually. This occurs in a number of industrial processes and has important consequences at a scale where both body and surfaces forces are relevant. In the study, two droplet diameters of smaller than the slot width and a relatively larger diameter where the oil droplet can interact directly with the slot wall were generated. To monitor fluid motion, a particle shadow velocimetry (PSV) imaging technique was used to study fluid flow motion inside and around a single oil droplet rising in a net co-flow. The droplet was a transparent canola oil and the surrounding working fluid was glycerol, adjusted to allow a matching of refractive index between the two fluids. Particles seeded in both fluids were observed with the PSV system allowing the capture of the velocity field both within the droplet and in the surrounds. The effect of droplet size on the droplet internal circulation was observed. Part of the study was related the potential generation of flow structures, such as von Karman vortex shedding already observed in rising droplets in infinite reservoirs and their interaction with the mini-channel. Results show that two counter-rotating vortices exist inside the droplets as they pass through slot. The vorticity map analysis shows that the droplet of relatively larger size has a stronger internal circulation.

Keywords: rising droplet, rectangular orifice, particle shadow velocimetry, match refractive index

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Authors: Anuphan Suttimarn, Natcha Wattanaprapa, Suwaree Yordchim

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The aim of this study is to develop the online journal system using a web application to manage the journal service of Suan Sunandha Rajabhat University in order to improve the journal management of the university. The main structures of the system process consist of 1. journal content management system 2. membership system of the journal and 3. online submission or review process. The investigators developed the system based on a web application using open source OJS software and phpMyAdmin to manage a research database. The system test showed that this online system 'Online Journal System (OJS)' could shorten the time in the period of submission article to journal and helped in managing a journal procedure efficiently and accurately. The quality evaluation of Suan Sunandha Rajabhat online journal system (SSRUOJS) undertaken by experts and researchers in 5 aspects; design, usability, security, reducing time, and accuracy showed the highest average value (X=4.30) on the aspect of reducing time. Meanwhile, the system efficiency evaluation was on an excellent level (X=4.13).

Keywords: online journal system, Journal management, Information system development, OJS

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Authors: J. J. Peña, J. Morales, J. García-Ravelo, L. Arcos-Díaz

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The Point canonical transformation method is applied for solving the Schrödinger equation with position-dependent mass. This class of problem has been solved for continuous mass distributions. In this work, a staggered mass distribution for the case of a free particle in an infinite square well potential has been proposed. The continuity conditions as well as normalization for the wave function are also considered. The proposal can be used for dealing with other kind of staggered mass distributions in the Schrödinger equation with different quantum potentials.

Keywords: free particle, point canonical transformation method, position-dependent mass, staggered mass distribution

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Authors: Xuezhang Hou

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In the present paper, a hybrid hyperbolic dynamic system formulated by partial differential equations with initial and boundary conditions is considered. First, the system is transformed to an abstract evolution system in an appropriate Hilbert space, and spectral analysis and semigroup generation of the system operator is discussed. Subsequently, a sliding model control problem is proposed and investigated, and an equivalent control method is introduced and applied to the system. Finally, a significant result that the state of the system can be approximated by an ideal sliding mode under control in any accuracy is derived and examined.

Keywords: hyperbolic dynamic system, sliding model control, semigroup of linear operators, partial differential equations

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Authors: Stephen A. Akinlabi, Esther T. Akinlabi

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The drip irrigation system is one of the important areas that affect the livelihood of farmers directly. The use of drip irrigation system has been the most efficient system compared to the other types of irrigations systems because the drip irrigation helps to save water and increase the productivity of crops. But like any other system, it can be considered inefficient when the filters and the emitters get clogged while in operation. The efficiency of the entire system is reduced when the emitters are clogged and blocked. This consequently impact and affect the farm operations which may result in scarcity of farm products and increase the demand. This design work focuses on how to overcome some of the challenges affecting drip irrigation system through the design of an efficient filtration and flushing system.

Keywords: drip irrigation system, filters, soil texture, mechanical engineering design, analysis

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Authors: Young-Kwan Choi, Han-Sang Jeong

Abstract:

Floating photovoltaic system is a technology that combines photovoltaic power generation with floating structure. However, since floating technology has not been utilized in photovoltaic generation, there are no standardized criteria. It is separately developed and used by different installation bodies. This paper aims to discuss the change of floating photovoltaic system technology based on examples of floating photovoltaic systems installed in Korea.

Keywords: floating photovoltaic system, floating PV installation, ocean floating photovoltaic system, tracking type floating photovoltaic system

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Authors: Issa Hussein Manita

Abstract:

This paper presents an example of industrial information system design and implementation (IIDC), the most common software engineering design steps that are applied to the different design stages. We are going through the life cycle of software system development. We start by a study of system requirement and end with testing and delivering system, going by system design and coding, program integration and system integration step. The most modern software design tools available used in the design this includes, but not limited to, Unified Modeling Language (UML), system modeling, SQL server side application, uses case analysis, design and testing as applied to information processing systems. The system is designed to perform tasks specified by the client with real data. By the end of the implementation of the system, default or user defined acceptance policy to provide an overall score as an indication of the system performance is used. To test the reliability of he designed system, it is tested in different environment and different work burden such as multi-user environment.

Keywords: software engineering, design, system requirement, integration, unified modeling language

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Authors: Satien Janpla, Kunyanuth Kularbphettong

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This paper aims to present the development of a web‑based system to serve the need of selling OTOP products in Samut Songkhram, Thailand. This system was designed to promote and sell OTOP products on website. We describe the design approaches and functional components of this system. The system was developed by PHP and JavaScript and MySQL database System. To evaluate the system performance, questionnaires were used to measure user satisfaction with system usability by specialists and users. The results were satisfactory as followed: Means for specialists and users were 4.05 and 3.97, and standard deviation for specialists and users were 0.563 and 0.644 respectively. Further analysis showed that the quality of One Tambon One Product (OTOP) Website was also at a good level as well.

Keywords: web-based system, OTOP, product, website

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Authors: Muna Alghabshi, Edmana Krishnan

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A nonlinear Schrodinger equation has been considered for solving by mapping methods in terms of Jacobi elliptic functions (JEFs). The equation under consideration has a linear evolution term, linear and nonlinear dispersion terms, the Kerr law nonlinearity term and three terms representing the contribution of meta materials. This equation which has applications in optical fibers is found to have soliton solutions, shock wave solutions, and singular wave solutions when the modulus of the JEFs approach 1 which is the infinite period limit. The equation with special values of the parameters has also been solved using the tanh method.

Keywords: Jacobi elliptic function, mapping methods, nonlinear Schrodinger Equation, tanh method

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Authors: E. Karami, M. Bohloul, P. Najmadi

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The superconducting system is a suitable system for quantum computers. Quantum entanglement is a fundamental phenomenon that is key to the power of quantum computers. Quantum entanglement has been studied in different superconducting systems. In this paper, we are investigating a superconducting two-qubit system as a macroscopic system. These systems include two coupled Quantronium circuits. We calculate quantum entanglement and thermalization for system evolution and compare them. We observe, thermalization and entanglement have different behavior, and equilibrium thermal state has maximum entanglement.

Keywords: macroscopic system, quantum entanglement, thermalization, superconducting system

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Authors: Nkongho Ayuketang Arreyndip, Ebobenow Joseph

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In this paper, to model a real life wind turbine, a probabilistic approach is proposed to model the dynamics of the blade elements of a small axial wind turbine under extreme stochastic wind speeds conditions. It was found that the power and the torque probability density functions even though decreases at these extreme wind speeds but are not infinite. Moreover, we also found that it is possible to stabilize the power coefficient (stabilizing the output power) above rated wind speeds by turning some control parameters. This method helps to explain the effect of turbulence on the quality and quantity of the harness power and aerodynamic torque.

Keywords: probability, probability density function, stochastic, turbulence

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