Search results for: Two dimensional boundary value problems

Authors: A. Das, L. Hitihamillage, S. Moridpour

Abstract:

Natural disasters are inevitable to the biodiversity. Disasters such as flood, tsunami and tornadoes could be brutal, harsh and devastating. In Australia, flooding is a major issue experienced by different parts of the country. In such crisis, delays in evacuation could decide the life and death of the people living in those regions. Congestion management could become a mammoth task if there are no steps taken before such situations. In the past to manage congestion in such circumstances, many strategies were utilised such as converting the road shoulders to extra lanes or changing the road geometry by adding more lanes. However, expansion of road to resolving congestion problems is not considered a viable option nowadays. The authorities avoid this option due to many reasons, such as lack of financial support and land space. They tend to focus their attention on optimising the current resources they possess and use traffic signals to overcome congestion problems. Traffic Signal Management strategy was considered a viable option, to alleviate congestion problems in the City of Geelong, Victoria. Arterial road with signalised intersections considered in this paper and the traffic data required for modelling collected from VicRoads. Traffic signalling software SIDRA used to model the roads, and the information gathered from VicRoads. In this paper, various signal parameters utilised to assess and improve the corridor performance to achieve the best possible Level of Services (LOS) for the arterial road.

Keywords: Congestion, constraints, management, LOS.

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Authors: Sun Ailu, Zhao Wanmin

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In the process of rapid urbanization, old urban renewal is an important task in China's urban construction. This study, using status survey and Analytic Hierarchy Process (AHP) method, taking Chongqing of China as an example, puts forward the problems faced by the old urban area from the aspects of function, facilities and environment. Further, this study summarizes the types of the old urban area and proposes space renewal strategies for three typical old urban areas, such as old residential area, old factory and old market. These old urban areas are confronted with the problems of functional layout confounding, lack of infrastructure and poor living environment. At last, this paper proposes spatial strategies for urban renewal, which are hoped to be useful for urban renewal management in China.

Keywords: Old urban renewal, renewal mode, renewal strategy, Chongqing, China.

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Authors: Samira Laidaoui, Mohammed Djermane, Nazihe Terfaya

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The fluid-structure coupling is a natural phenomenon which reflects the effects of two continuums: fluid and structure of different types in the reciprocal action on each other, involving knowledge of elasticity and fluid mechanics. The solution for such problems is based on the relations of continuum mechanics and is mostly solved with numerical methods. It is a computational challenge to solve such problems because of the complex geometries, intricate physics of fluids, and complicated fluid-structure interactions. The way in which the interaction between fluid and solid is described gives the largest opportunity for reducing the computational effort. In this paper, a problem of fluid structure interaction is investigated with two-way coupling method. The formulation Arbitrary Lagrangian-Eulerian (ALE) was used, by considering a dynamic grid, where the solid is described by a Lagrangian formulation and the fluid by a Eulerian formulation. The simulation was made on the ANSYS software.

Keywords: ALE, coupling, FEM, fluid-structure interaction, one-way method, two-way method.

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Authors: Mhand Hifi, Hedi Mhalla

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In this paper, we study the knapsack sharing problem, a variant of the well-known NP-Hard single knapsack problem. We investigate the use of a tree search for optimally solving the problem. The used method combines two complementary phases: a reduction interval search phase and a branch and bound procedure one. First, the reduction phase applies a polynomial reduction strategy; that is used for decomposing the problem into a series of knapsack problems. Second, the tree search procedure is applied in order to attain a set of optimal capacities characterizing the knapsack problems. Finally, the performance of the proposed optimal algorithm is evaluated on a set of instances of the literature and its runtime is compared to the best exact algorithm of the literature.

Keywords: Branch and bound, combinatorial optimization, knap¬sack, knapsack sharing, heuristics, interval reduction.

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Authors: P. Bergl

Abstract:

Numerous divergence measures (spectral distance, cepstral distance, difference of the cepstral coefficients, Kullback-Leibler divergence, distance given by the General Likelihood Ratio, distance defined by the Recursive Bayesian Changepoint Detector and the Mahalanobis measure) are compared in this study. The measures are used for detection of abrupt spectral changes in synthetic AR signals via the sliding window algorithm. Two experiments are performed; the first is focused on detection of single boundary while the second concentrates on detection of a couple of boundaries. Accuracy of detection is judged for each method; the measures are compared according to results of both experiments.

Keywords: Abrupt changes detection, autoregressive model, divergence measure.

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Authors: Monika Neda, Elena Nikonova

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We present a numerical study of the sensitivity of the so called time relaxation family of models of fluid motion with respect to the time relaxation parameter χ on the two dimensional cavity problem. The goal of the study is to compute and compare the sensitivity of the model using finite difference method (FFD) and sensitivity equation method (SEM).

Keywords: Sensitivity, time relaxation, deconvolution, Navier- Stokes equations.

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Authors: Alberto Hananel

Abstract:

The aim of this work is to modelize the occlusion of a person with temporomandibular disorders as an evolutionary equation and approach its solution by the construction and characterizing of discrete variational splines. To formulate the problem, certain boundary conditions have been considered. After showing the existence and the uniqueness of the solution of such a problem, a convergence result of a discrete variational evolutionary spline is shown. A stress analysis of the occlusion of a human jaw with temporomandibular disorders by finite elements is carried out in FreeFem++ in order to prove the validity of the presented method.

Keywords: Approximation, evolutionary PDE, finite element method, temporomandibular disorders, variational spline.

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Authors: Chein-Shung Hwang, Ruei-Siang Fong

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User-based Collaborative filtering (CF), one of the most prevailing and efficient recommendation techniques, provides personalized recommendations to users based on the opinions of other users. Although the CF technique has been successfully applied in various applications, it suffers from serious sparsity problems. The cloud-model approach addresses the sparsity problems by constructing the user-s global preference represented by a cloud eigenvector. The user-based CF approach works well with dense datasets while the cloud-model CF approach has a greater performance when the dataset is sparse. In this paper, we present a hybrid approach that integrates the predictions from both the user-based CF and the cloud-model CF approaches. The experimental results show that the proposed hybrid approach can ameliorate the sparsity problem and provide an improved prediction quality.

Keywords: Cloud model, Collaborative filtering, Hybridrecommender system

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Authors: Souleymane Oumtanaga, Kadjo Tanon Lambert, Koné Tiémoman, Tety Pierre, Kimou KouadioProsper

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Multicast transmissions allow an host (the source) to send only one flow bound for a group of hosts (the receivers). Any equipment eager to belong to the group may explicitly register itself to that group via its multicast router. This router will be given the responsibility to convey all information relating to the group to all registered hosts. However in an environment in which the final receiver or the source frequently moves, the multicast flows need particular treatment. This constitutes one of the multicast transmissions problems around which several proposals were made in the Mobile IPv6 case in general. In this article, we describe the problems involved in this IPv6 multicast mobility and the existing proposals for their resolution. Then architecture will be proposed aiming to satisfy and optimize these transmissions in the specific case of a mobile multicast receiver in NC-HMIPv6 environment.

Keywords: Mobile IP, NC-HMIPv6, Multicast, MLD, PIM, SSM, Rendezvous Point.

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Authors: Mohammad Modarres, Shirin Aslani

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The goal of this paper is to develop a model to integrate “pricing" and “advertisement" for short life cycle products, such as branded fashion clothing products. To achieve this goal, we apply the concept of “Dynamic Pricing". There are two classes of advertisements, for the brand (regardless of product) and for a particular product. Advertising the brand affects the demand and price of all the products. Thus, the model considers all these products in relation with each other. We develop two different methods to integrate both types of advertisement and pricing. The first model is developed within the framework of dynamic programming. However, due to the complexity of the model, this method cannot be applicable for large size problems. Therefore, we develop another method, called hieratical approach, which is capable of handling the real world problems. Finally, we show the accuracy of this method, both theoretically and also by simulation.

Keywords: Advertising, Dynamic programming, Dynamic pricing, Promotion.

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Authors: Michael G. Pantelyat

Abstract:

Fundamental basics of pure and applied research in the area of magneto-thermo-mechanical numerical analysis and design of innovative electromagnetic devices (modern induction heaters, novel thermoelastic actuators, rotating electrical machines, induction cookers, electrophysical devices) are elaborated. Thus, mathematical models of magneto-thermo-mechanical processes in electromagnetic devices taking into account main interactions of interrelated phenomena are developed. In addition, graphical representation of coupled (multiphysics) phenomena under consideration is proposed. Besides, numerical techniques for nonlinear problems solution are developed. On this base, effective numerical algorithms for solution of actual problems of practical interest are proposed, validated and implemented in applied 2D and 3D computer codes developed. Many applied problems of practical interest regarding modern electrical engineering devices are numerically solved. Investigations of the influences of various interrelated physical phenomena (temperature dependences of material properties, thermal radiation, conditions of convective heat transfer, contact phenomena, etc.) on the accuracy of the electromagnetic, thermal and structural analyses are conducted. Important practical recommendations on the choice of rational structures, materials and operation modes of electromagnetic devices under consideration are proposed and implemented in industry.

Keywords: Electromagnetic devices, multiphysics, numerical analysis, simulation and design.

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Authors: Sayyed R Mousavi

Abstract:

The Far From Most Strings Problem (FFMSP) is to obtain a string which is far from as many as possible of a given set of strings. All the input and the output strings are of the same length, and two strings are said to be far if their hamming distance is greater than or equal to a given positive integer. FFMSP belongs to the class of sequences consensus problems which have applications in molecular biology. The problem is NP-hard; it does not admit a constant-ratio approximation either, unless P = NP. Therefore, in addition to exact and approximate algorithms, (meta)heuristic algorithms have been proposed for the problem in recent years. On the other hand, in the recent years, hybrid algorithms have been proposed and successfully used for many hard problems in a variety of domains. In this paper, a new metaheuristic algorithm, called Constructive Beam and Local Search (CBLS), is investigated for the problem, which is a hybridization of constructive beam search and local search algorithms. More specifically, the proposed algorithm consists of two phases, the first phase is to obtain several candidate solutions via the constructive beam search and the second phase is to apply local search to the candidate solutions obtained by the first phase. The best solution found is returned as the final solution to the problem. The proposed algorithm is also similar to memetic algorithms in the sense that both use local search to further improve individual solutions. The CBLS algorithm is compared with the most recent published algorithm for the problem, GRASP, with significantly positive results; the improvement is by order of magnitudes in most cases.

Keywords: Bioinformatics, Far From Most Strings Problem, Hybrid metaheuristics, Matheuristics, Sequences consensus problems.

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Authors: Ivan Yatchev, Ewen Ritchie

Abstract:

Comparison of two approaches for the simulation of the dynamic behaviour of a permanent magnet linear actuator is presented. These are full coupled model, where the electromagnetic field, electric circuit and mechanical motion problems are solved simultaneously, and decoupled model, where first a set of static magnetic filed analysis is carried out and then the electric circuit and mechanical motion equations are solved employing bi-cubic spline approximations of the field analysis results. The results show that the proposed decoupled model is of satisfactory accuracy and gives more flexibility when the actuator response is required to be estimated for different external conditions, e.g. external circuit parameters or mechanical loads.

Keywords: Coupled problems, dynamic models, finite elementanalysis, linear actuators, permanent magnets.

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Authors: S. Mohan Kumar, Rajashekar Patil, Tanuja Ajit Desphande

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It is necessary to incorporate technological advances achieved in the field of engineering into dentistry in order to enhance the process of diagnosis, treatment planning and enable the doctors to render better treatment to their patients. To achieve this ultimate goal long distance collaborations are often necessary. This paper discusses the various collaborative tools and their applications to solve a few burning problems confronted by the dentists. Customization is often the solution to most of the problems. But rapid designing, development and cost effective manufacturing is a difficult task to achieve. This problem can be solved using the technique of digital manufacturing. Cases from 6 major branches of dentistry have been discussed and possible solutions with the help of state of art technology using rapid digital manufacturing have been proposed in the present paper. The paper also entails the usage of existing tools in collaborative and digital manufacturing area.

Keywords: Customisation, collaborative tools, dentistry, digital manufacturing.

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Authors: Herath MPC Jayaweera, Samer Hanoun

Abstract:

Path planning for on-time obstacle avoidance is an essential and challenging task that enables drones to achieve safe operation in any application domain. The level of challenge increases significantly on the obstacle avoidance technique when the drone is following a ground mobile entity (GME). This is mainly due to the change in direction and magnitude of the GMEs velocity in dynamic and unstructured environments. Force field techniques are the most widely used obstacle avoidance methods due to their simplicity, ease of use and potential to be adopted for three-dimensional dynamic environments. However, the existing force field obstacle avoidance techniques suffer many drawbacks including their tendency to generate longer routes when the obstacles are sideways of the drones route, poor ability to find the shortest flyable path, propensity to fall into local minima, producing a non-smooth path, and high failure rate in the presence of symmetrical obstacles. To overcome these shortcomings, this paper proposes an on-time three-dimensional obstacle avoidance method for drones to effectively and efficiently avoid dynamic and static obstacles in unknown environments while pursuing a GME. This on-time obstacle avoidance technique generates velocity waypoints for its obstacle-free and efficient path based on the shape of the encountered obstacles. This method can be utilize on most types of drones that have basic distance measurement sensors and autopilot supported flight controllers. The proposed obstacle avoidance technique is validated and evaluated against existing force field methods for different simulation scenarios in Gazebo and ROS supported PX4-SITL. The simulation results show that the proposed obstacle avoidance technique outperforms the existing force field techniques and is better suited for real-world applications.

Keywords: Drones, force field methods, obstacle avoidance, path planning.

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Authors: Attila Vámosi, Tamás Mankovits, Dávid Huri, Imre Kocsis, Tamás Szabó

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Non-linear FEM calculations are indispensable when important technical information like operating performance of a rubber component is desired. For example rubber bumpers built into air-spring structures may undergo large deformations under load, which in itself shows non-linear behavior. The changing contact range between the parts and the incompressibility of the rubber increases this non-linear behavior further. The material characterization of an elastomeric component is also a demanding engineering task. The shape optimization problem of rubber parts led to the study of FEM based calculation processes. This type of problems was posed and investigated by several authors. In this paper the time demand of certain calculation methods are studied and the possibilities of time reduction is presented.

Keywords: Rubber bumper, data acquisition, finite element analysis, support vector regression.

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Authors: Anil Kumar Tripathi, Ratneshwer

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All the software engineering researches and best industry practices aim at providing software products with high degree of quality and functionality at low cost and less time. These requirements are addressed by the Component Based Software Engineering (CBSE) as well. CBSE, which deals with the software construction by components’ assembly, is a revolutionary extension of Software Engineering. CBSE must define and describe processes to assure timely completion of high quality software systems that are composed of a variety of pre built software components. Though these features provide distinct and visible benefits in software design and programming, they also raise some challenging problems. The aim of this work is to summarize the pertinent issues and considerations in CBSE to make an understanding in forms of concepts and observations that may lead to development of newer ways of dealing with the problems and challenges in CBSE.

Keywords: Software Component, Component Based Software Engineering, Software Process, Testing, Maintenance.

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Authors: Krisada Sungkhamanee

Abstract:

The objectives of this research are to search the management pattern of Bang Khonthi lodging entrepreneurs for sufficient economy ways, to know the threat that affects this sector and design fit arrangement model to sustain their business with Samut Songkram style. What will happen if they do not use this approach? Will they have a financial crisis? The data and information are collected by informal discussions with 8 managers and 400 questionnaires. A mixed methods of both qualitative research and quantitative research are used. Bent Flyvbjerg-s phronesis is utilized for this analysis. Our research will prove that sufficient economy can help small business firms to solve their problems. We think that the results of our research will be a financial model to solve many problems of the entrepreneurs and this way will can be a model for other provinces of Thailand.

Keywords: Bang Khonthi, Lodging Business, Sufficient Economy.

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Authors: A. Moradi, S. Khodadadiyan

Abstract:

In this paper, one-dimensional analysis of flow in a single-stage gas gun is conducted. The compressible inviscid flow equations are numerically solved by the second-order Roe TVD method, by using moving boundaries. For investigation of real gas effect the Noble-Able equation is applied. The numerical results are compared with the experimental data to validate the numerical scheme. The results show that with using the Noble-Able equation, the muzzle velocity decreases.

Keywords: Gas gun, Roe, projectile, muzzle velocity

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Authors: Aaqif Afzaal Abbasi, Javaid Iqbal, Akhtar Nawaz Malik

Abstract:

4G Communication Networks provide heterogeneous wireless technologies to mobile subscribers through IP based networks and users can avail high speed access while roaming across multiple wireless channels; possible by an organized way to manage the Quality of Service (QoS) functionalities in these networks. This paper proposes the idea of developing a novel QoS optimization architecture that will judge the user requirements and knowing peak times of services utilization can save the bandwidth/cost factors. The proposed architecture can be customized according to the network usage priorities so as to considerably improve a network-s QoS performance.

Keywords: QoS, Network Coverage Boundary, ServicesArchives Units (SAU), Cumulative Services Archives Units (CSAU).

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Authors: Wen-Pai Wang, Mei-Ching Tang

Abstract:

The service sector continues to grow and the percentage of GDP accounted for by service industries keeps increasing. The growth and importance of service to an economy is not just a phenomenon of advanced economies, service is now a majority of the world gross domestic products. However, the performance evaluation process of new service development problems generally involves uncertain and imprecise data. This paper presents a 2-tuple fuzzy linguistic computing approach to dealing with heterogeneous information and information loss problems while the processes of subjective evaluation integration. The proposed method based on group decision-making scenario to assist business managers in measuring performance of new service development manipulates the heterogeneity integration processes and avoids the information loss effectively.

Keywords: Heterogeneity, Multigranular linguistic computing, New service development, Performance evaluation.

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Authors: Morteza Mirhosseini, Amir B. Khoshnevis

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The boundary layer separation and new active flow control of a NACA 0025 airfoil were studied experimentally. This new flow control is sometimes known as a co-flow jet (cfj) airfoil. This paper presents the fluctuating velocity in a wall jet over the co-flow jet airfoil subjected to an adverse pressure gradient and a curved surface. In these results, the fluctuating velocity at the inner part increasing by increased the angle of attack up to 12^o and this has due to the jet energized, while the angle of attack 20^o has different. The airfoil cord based Reynolds number has 10⁵.

Keywords: Adverse pressure gradient, fluctuating velocity, wall jet, co-flow jet airfoil.

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Authors: Kazuki Kamada, Haruka Yamashita

Abstract:

In Japan, taxi is one of the popular transportations and taxi industry is one of the big businesses. However, in recent years, there has been a difficult problem of reducing the number of taxi drivers. In the taxi business, mainly three passenger catching methods are applied. One style is "cruising" that drivers catches passengers while driving on a road. Second is "waiting" that waits passengers near by the places with many requirements for taxies such as entrances of hospitals, train stations. The third one is "dispatching" that is allocated based on the contact from the taxi company. Above all, the cruising taxi drivers need the experience and intuition for finding passengers, and it is difficult to decide "the destination for cruising". The strong recommendation system for the cruising taxies supports the new drivers to find passengers, and it can be the solution for the decreasing the number of drivers in the taxi industry. In this research, we propose a method of recommending a destination for cruising taxi drivers. On the other hand, as a machine learning technique, the embedding models that embed the high dimensional data to a low dimensional space is widely used for the data analysis, in order to represent the relationship of the meaning between the data clearly. Taxi drivers have their favorite courses based on their experiences, and the courses are different for each driver. We assume that the course of cruising taxies has meaning such as the course for finding business man passengers (go around the business area of the city of go to main stations) and course for finding traveler passengers (go around the sightseeing places or big hotels), and extract the meaning of their destinations. We analyze the cruising history data of taxis based on the embedding model and propose the recommendation system for passengers. Finally, we demonstrate the recommendation of destinations for cruising taxi drivers based on the real-world data analysis using proposing method.

Keywords: Taxi industry, decision making, recommendation system, embedding model.

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Authors: M. Aslam, Farrukh, A. R. Gardezi, Nasir Hayat

Abstract:

Automated material handling is given prime importance in the semi automated and automated facilities since it provides solution to the gigantic problems related to inventory and also support the latest philosophies like just in time production JIT and lean production. Automated storage and retrieval system is an antidote (if designed properly) to the facility sufferings like getting the right material , materials getting perished, long cycle times or many other similar kind of problems. A working model of automated storage and retrieval system (AS/RS) is designed and developed under the design parameters specified by Material Handling Industry of America (MHIA). Later on analysis was carried out to calculate the throughput and size of the machine. The possible implementation of this technology in local scenario is also discussed in this paper.

Keywords: Automated storage and retrieval system (AS/RS), Material handling, Computer integrated manufacturing (CIM), Lightdependent resistor (LDR)

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Authors: C. Ardil

Abstract:

A mathematical model and an effective numerical method for calculating the temperature field of the profile part of convection cooled blades have been developed. The theoretical substantiation of the method is proved by corresponding theorems. To this end, convergent quadrature processes were developed and error estimates were obtained in terms of the Zygmund continuity moduli.The boundary conditions for heat exchange are determined from the solution of the corresponding integral equations and empirical relations.The reliability of the developed methods is confirmed by the calculation-experimental studies of the thermohydraulic characteristics of the nozzle apparatus of the first stage of a gas turbine.

Keywords: Integral methods, determination of temperature fields, cooled blades, gas turbines.

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Authors: A. M. Pashaev, R. A. Sadihov, A. S. Samedov, C. Ardil

Abstract:

A mathematical model and a numerical method for computing the temperature field of the profile part of convectionally cooled blades are developed. The theoretical substantiation of the method is proved by corresponding theorems. To this end, convergent quadrature processes were developed and error estimates were obtained in terms of the Zygmund continuity moduli. The boundary conditions for heat exchange are determined from the solution of the corresponding integral equations and empirical relations. The reliability of the developed methods is confirmed by calculation and experimental studies of the thermohydraulic characteristics of the nozzle apparatus of the first stage of the gas turbine.

Keywords: Aviation gas turbine, temperature field, cooled blades, numerical modeling.

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Authors: I. Abuiziah, N. Shakarneh

Abstract:

Genetic Algorithm (GA) is a powerful technique for solving optimization problems. It follows the idea of survival of the fittest - Better and better solutions evolve from previous generations until a near optimal solution is obtained. GA uses the main three operations, the selection, crossover and mutation to produce new generations from the old ones. GA has been widely used to solve optimization problems in many applications such as traveling salesman problem, airport traffic control, information retrieval (IR), reactive power optimization, job shop scheduling, and hydraulics systems such as water pipeline systems. In water pipeline systems we need to achieve some goals optimally such as minimum cost of construction, minimum length of pipes and diameters, and the place of protection devices. GA shows high performance over the other optimization techniques, moreover, it is easy to implement and use. Also, it searches a limited number of solutions.

Keywords: Genetic Algorithm, optimization, pipeline systems, selection, cross over.

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Authors: Siriporn Meenanan

Abstract:

The objective of this study is to investigate the attitude of Thai students towards the Thai series "Hormones the Series Season 2". This study was conducted in the quantitative research, and the questionnaires were used to collect data from 400 people of the sample group. Descriptive statistics were used in data analysis. The findings reveal that most participants have positive comments regarding the series. They strongly agreed that the series reflects on the way of life and problems of teenagers in Thailand. Hence, the participants believe that if adults have a chance to watch the series, they will have the better understanding of the teenagers. In addition, the participants also agreed that the contents of the play are appropriate and satisfiable as the contents of “Hormones the Series Season 2” will raise awareness among the teens and use it as a guide to prevent problems that might happen during their teenage life.

Keywords: Content analysis, attitude, Thai series, Hormones the series.

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Authors: Shazalina Mat Zin, Ahmad Abd. Majid, Ahmad Izani Md. Ismail, Muhammad Abbas

Abstract:

The generalized wave equation models various problems in sciences and engineering. In this paper, a new three-time level implicit approach based on cubic trigonometric B-spline for the approximate solution of wave equation is developed. The usual finite difference approach is used to discretize the time derivative while cubic trigonometric B-spline is applied as an interpolating function in the space dimension. Von Neumann stability analysis is used to analyze the proposed method. Two problems are discussed to exhibit the feasibility and capability of the method. The absolute errors and maximum error are computed to assess the performance of the proposed method. The results were found to be in good agreement with known solutions and with existing schemes in literature.

Keywords: Collocation method, Cubic trigonometric B-spline, Finite difference, Wave equation.

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Authors: Thomas Shermer, Godfried T. Toussaint

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A chord of a simple polygon P is a line segment [xy] that intersects the boundary of P only at both endpoints x and y. A chord of P is called an interior chord provided the interior of [xy] lies in the interior of P. P is weakly visible from [xy] if for every point v in P there exists a point w in [xy] such that [vw] lies in P. In this paper star-shaped, L-convex, and convex polygons are characterized in terms of weak visibility properties from internal chords and starshaped subsets of P. A new Krasnoselskii-type characterization of isothetic star-shaped polygons is also presented.

Keywords: Convex polygons, L-convex polygons, star-shaped polygons, chords, weak visibility, discrete and computational geometry

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