Search results for: Discrete boundary value problems
Commenced in January 2007
Frequency: Monthly
Edition: International
Paper Count: 3517

Search results for: Discrete boundary value problems

2587 CFD Simulations of a Co-current Spray Dryer

Authors: Saad Nahi Saleh

Abstract:

This paper presents the prediction of air flow, humidity and temperature patterns in a co-current pilot plant spray dryer fitted with a pressure nozzle using a three dimensional model. The modelling was done with a Computational Fluid Dynamic package (Fluent 6.3), in which the gas phase is modelled as continuum using the Euler approach and the droplet/ particle phase is modelled by the Discrete Phase model (Lagrange approach).Good agreement was obtained with published experimental data where the CFD simulation correctly predicts a fast downward central flowing core and slow recirculation zones near the walls. In this work, the effects of the air flow pattern on droplets trajectories, residence time distribution of droplets and deposition of the droplets on the wall also were investigated where atomizing of maltodextrin solution was used.

Keywords: Spray, CFD, multiphase, drying, droplet, particle.

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2586 Application of Agile Project Methodology in Computational Fluid Dynamics Engineering Project

Authors: Mohammed Bilal, Noor Hyder

Abstract:

Agile methodology is a popular project management methodology and is widely used in many engineering projects. In the recent years agile methodology is successful in countering the inherent problems seen in traditional methodology. The application of the Agile methodology in the computational fluid dynamic project had improved the project delivery performance. Computational Fluid Dynamics (CFD) is the method to solve and analyze the fluid flow problems by the application of the numerical analysis. In this paper, study is conducted using agile methodology and results are compared with waterfall methodology. The result shows that the agile methodology is improves the final delivery of the project.

Keywords: Agile methodology, traditional methodology, engineering management, engineering technology, Computational Fluid Dynamics, project management.

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2585 A Case Study of Bee Algorithm for Ready Mixed Concrete Problem

Authors: W. Wongthatsanekorn, N. Matheekrieangkrai

Abstract:

This research proposes Bee Algorithm (BA) to optimize Ready Mixed Concrete (RMC) truck scheduling problem from single batch plant to multiple construction sites. This problem is considered as an NP-hard constrained combinatorial optimization problem. This paper provides the details of the RMC dispatching process and its related constraints. BA was then developed to minimize total waiting time of RMC trucks while satisfying all constraints. The performance of BA is then evaluated on two benchmark problems (3 and 5construction sites) according to previous researchers. The simulation results of BA are compared in term of efficiency and accuracy with Genetic Algorithm (GA) and all problems show that BA approach outperforms GA in term of efficiency and accuracy to obtain optimal solution. Hence, BA approach could be practically implemented to obtain the best schedule.

Keywords: Bee Colony Optimization, Ready Mixed Concrete Problem.

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2584 Arduino Pressure Sensor Cushion for Tracking and Improving Sitting Posture

Authors: Andrew Hwang

Abstract:

The average American worker sits for thirteen hours a day, often with poor posture and infrequent breaks, which can lead to health issues and back problems. The Smart Cushion was created to alert individuals of their poor postures, and may potentially alleviate back problems and correct poor posture. The Smart Cushion is a portable, rectangular, foam cushion, with five strategically placed pressure sensors, that utilizes an Arduino Uno circuit board and specifically designed software, allowing it to collect data from the five pressure sensors and store the data on an SD card. The data is then compiled into graphs and compared to controlled postures. Before volunteers sat on the cushion, their levels of back pain were recorded on a scale from 1-10. Data was recorded for an hour during sitting, and then a new, corrected posture was suggested. After using the suggested posture for an hour, the volunteers described their level of discomfort on a scale from 1-10. Different patterns of sitting postures were generated that were able to serve as early warnings of potential back problems. By using the Smart Cushion, the areas where different volunteers were applying the most pressure while sitting could be identified, and the sitting postures could be corrected. Further studies regarding the relationships between posture and specific regions of the body are necessary to better understand the origins of back pain; however, the Smart Cushion is sufficient for correcting sitting posture and preventing the development of additional back pain.

Keywords: Arduino Sketch Algorithm, biomedical technology, pressure sensors, Smart Cushion.

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2583 Searching the Efficient Frontier for the Coherent Covering Location Problem

Authors: Felipe Azocar Simonet, Luis Acosta Espejo

Abstract:

In this article, we will try to find an efficient boundary approximation for the bi-objective location problem with coherent coverage for two levels of hierarchy (CCLP). We present the mathematical formulation of the model used. Supported efficient solutions and unsupported efficient solutions are obtained by solving the bi-objective combinatorial problem through the weights method using a Lagrangean heuristic. Subsequently, the results are validated through the DEA analysis with the GEM index (Global efficiency measurement).

Keywords: Coherent covering location problem, efficient frontier, Lagrangian relaxation, data envelopment analysis.

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2582 Gaussian Density and HOG with Content Based Image Retrieval System – A New Approach

Authors: N. Shanmugapriya, R. Nallusamy

Abstract:

Content-based image retrieval (CBIR) uses the contents of images to characterize and contact the images. This paper focus on retrieving the image by separating images into its three color mechanism R, G and B and for that Discrete Wavelet Transformation is applied. Then Wavelet based Generalized Gaussian Density (GGD) is practical which is used for modeling the coefficients from the wavelet transforms. After that it is agreed to Histogram of Oriented Gradient (HOG) for extracting its characteristic vectors with Relevant Feedback technique is used. The performance of this approach is calculated by exactness and it confirms that this method is wellorganized for image retrieval.

Keywords: Content-Based Image Retrieval (CBIR), Relevant Feedback, Histogram of Oriented Gradient (HOG), Generalized Gaussian Density (GGD).

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2581 A C1-Conforming Finite Element Method for Nonlinear Fourth-Order Hyperbolic Equation

Authors: Yang Liu, Hong Li, Siriguleng He, Wei Gao, Zhichao Fang

Abstract:

In this paper, the C1-conforming finite element method is analyzed for a class of nonlinear fourth-order hyperbolic partial differential equation. Some a priori bounds are derived using Lyapunov functional, and existence, uniqueness and regularity for the weak solutions are proved. Optimal error estimates are derived for both semidiscrete and fully discrete schemes.

Keywords: Nonlinear fourth-order hyperbolic equation, Lyapunov functional, existence, uniqueness and regularity, conforming finite element method, optimal error estimates.

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2580 Artificial Neural Network based Parameter Estimation and Design Optimization of Loop Antenna

Authors: Kumaresh Sarmah, Kandarpa Kumar Sarma

Abstract:

Artificial Neural Network (ANN)s are best suited for prediction and optimization problems. Trained ANNs have found wide spread acceptance in several antenna design systems. Four parameters namely antenna radiation resistance, loss resistance, efficiency, and inductance can be used to design an antenna layout though there are several other parameters available. An ANN can be trained to provide the best and worst case precisions of an antenna design problem defined by these four parameters. This work describes the use of an ANN to generate the four mentioned parameters for a loop antenna for the specified frequency range. It also provides insights to the prediction of best and worst-case design problems observed in applications and thereby formulate a model for physical layout design of a loop antenna.

Keywords: MLP, ANN, parameter, prediction, optimization.

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2579 Flow and Heat Transfer over a Shrinking Sheet: A Stability Analysis

Authors: Anuar Ishak

Abstract:

The characteristics of fluid flow and heat transfer over a permeable shrinking sheet is studied. The governing partial differential equations are transformed into a set of ordinary differential equations, which are then solved numerically using MATLAB routine boundary value problem solver bvp4c. Numerical results show that dual solutions are possible for a certain range of the suction parameter. A stability analysis is performed to determine which solution is linearly stable and physically realizable.

Keywords: Dual solutions, heat transfer, shrinking sheet, stability analysis.

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2578 Manifold Analysis by Topologically Constrained Isometric Embedding

Authors: Guy Rosman, Alexander M. Bronstein, Michael M. Bronstein, Ron Kimmel

Abstract:

We present a new algorithm for nonlinear dimensionality reduction that consistently uses global information, and that enables understanding the intrinsic geometry of non-convex manifolds. Compared to methods that consider only local information, our method appears to be more robust to noise. Unlike most methods that incorporate global information, the proposed approach automatically handles non-convexity of the data manifold. We demonstrate the performance of our algorithm and compare it to state-of-the-art methods on synthetic as well as real data.

Keywords: Dimensionality reduction, manifold learning, multidimensional scaling, geodesic distance, boundary detection.

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2577 Intelligent Transport System: Classification of Traffic Signs Using Deep Neural Networks in Real Time

Authors: Anukriti Kumar, Tanmay Singh, Dinesh Kumar Vishwakarma

Abstract:

Traffic control has been one of the most common and irritating problems since the time automobiles have hit the roads. Problems like traffic congestion have led to a significant time burden around the world and one significant solution to these problems can be the proper implementation of the Intelligent Transport System (ITS). It involves the integration of various tools like smart sensors, artificial intelligence, position technologies and mobile data services to manage traffic flow, reduce congestion and enhance driver's ability to avoid accidents during adverse weather. Road and traffic signs’ recognition is an emerging field of research in ITS. Classification problem of traffic signs needs to be solved as it is a major step in our journey towards building semi-autonomous/autonomous driving systems. The purpose of this work focuses on implementing an approach to solve the problem of traffic sign classification by developing a Convolutional Neural Network (CNN) classifier using the GTSRB (German Traffic Sign Recognition Benchmark) dataset. Rather than using hand-crafted features, our model addresses the concern of exploding huge parameters and data method augmentations. Our model achieved an accuracy of around 97.6% which is comparable to various state-of-the-art architectures.

Keywords: Multiclass classification, convolution neural network, OpenCV, Data Augmentation.

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2576 Image Enhancement of Medical Images using Gabor Filter Bank on Hexagonal Sampled Grids

Authors: Veni.S , K.A.Narayanankutty

Abstract:

For about two decades scientists have been developing techniques for enhancing the quality of medical images using Fourier transform, DWT (Discrete wavelet transform),PDE model etc., Gabor wavelet on hexagonal sampled grid of the images is proposed in this work. This method has optimal approximation theoretic performances, for a good quality image. The computational cost is considerably low when compared to similar processing in the rectangular domain. As X-ray images contain light scattered pixels, instead of unique sigma, the parameter sigma of 0.5 to 3 is found to satisfy most of the image interpolation requirements in terms of high Peak Signal-to-Noise Ratio (PSNR) , lower Mean Squared Error (MSE) and better image quality by adopting windowing technique.

Keywords: Hexagonal lattices, Gabor filter, Interpolation, imageprocessing.

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2575 Lodging Business Management in Nakhon Pathom with Sufficient Economy Approach

Authors: Krisada Sungkhamanee

Abstract:

The objectives of this research are to search the management pattern of Nakhon Pathom lodging entrepreneurs for sufficient economy ways, to know the threat that affects this sector and design fit arrangement model to sustain their business with Nakhon Pathom 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 12 managers and 400 questionnaires. A mixed method 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: Nakhon Pathom Province, Lodging Business, Sufficient Economy.

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2574 Locating Critical Failure Surface in Rock Slope Stability with Hybrid Model Based on Artificial Immune System and Cellular Learning Automata (CLA-AIS)

Authors: Ramin Javadzadeh, Emad Javadzadeh

Abstract:

Locating the critical slip surface with the minimum factor of safety for a rock slope is a difficult problem. In recent years, some modern global optimization methods have been developed with success in treating various types of problems, but very few of such methods have been applied to rock mechanical problems. In this paper, use of hybrid model based on artificial immune system and cellular learning automata is proposed. The results show that the algorithm is an effective and efficient optimization method with a high level of confidence rate.

Keywords: CLA-AIS, failure surface, optimization methods, rock slope.

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2573 Linear-Operator Formalism in the Analysis of Omega Planar Layered Waveguides

Authors: António L. Topa

Abstract:

A complete spectral representation for the electromagnetic field of planar multilayered waveguides inhomogeneously filled with omega media is presented. The problem of guided electromagnetic propagation is reduced to an eigenvalue equation related to a 2 ´ 2 matrix differential operator. Using the concept of adjoint waveguide, general bi-orthogonality relations for the hybrid modes (either from the discrete or from the continuous spectrum) are derived. For the special case of homogeneous layers the linear operator formalism is reduced to a simple 2 ´ 2 coupling matrix eigenvalue problem. Finally, as an example of application, the surface and the radiation modes of a grounded omega slab waveguide are analyzed.

Keywords: Metamaterials, linear operators, omega media, layered waveguide, orthogonality relations

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2572 The Economic Lot Scheduling Problem in Flow Lines with Sequence-Dependent Setups

Authors: M. Heydari, S. A. Torabi

Abstract:

The problem of lot sizing, sequencing and scheduling multiple products in flow line production systems has been studied by several authors. Almost all of the researches in this area assumed that setup times and costs are sequence –independent even though sequence dependent setups are common in practice. In this paper we present a new mixed integer non linear program (MINLP) and a heuristic method to solve the problem in sequence dependent case. Furthermore, a genetic algorithm has been developed which applies this constructive heuristic to generate initial population. These two proposed solution methods are compared on randomly generated problems. Computational results show a clear superiority of our proposed GA for majority of the test problems.

Keywords: Economic lot scheduling problem, finite horizon, genetic algorithm, mixed zero-one nonlinear programming, sequence-dependent.

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2571 Determination of Required Ion Exchange Solution for Stabilizing Clayey Soils with Various PI

Authors: R. Ziaie Moayed, F. Allahyari

Abstract:

Soil stabilization has been widely used to improve soil strength and durability or to prevent erosion and dust generation. Generally to reduce problems of clayey soils in engineering work and to stabilize these soils additional materials are used. The most common materials are lime, fly ash and cement. Using this materials, although improve soil property , but in some cases due to financial problems and the need to use special equipment are limited .One of the best methods for stabilization clayey soils is neutralization the clay particles. For this purpose we can use ion exchange materials. Ion exchange solution like CBR plus can be used for soil stabilization. One of the most important things in using CBR plus is determination the amount of this solution for various soils with different properties. In this study a laboratory experiment is conduct to evaluate the ion exchange capacity of three soils with various plasticity index (PI) to determine amount or required CBR plus solution for soil stabilization.

Keywords: CBR plus, clayey soils, ion exchange, soil stabilization

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2570 Despeckling of Synthetic Aperture Radar Images Using Inner Product Spaces in Undecimated Wavelet Domain

Authors: Syed Musharaf Ali, Muhammad Younus Javed, Naveed Sarfraz Khattak, Athar Mohsin, UmarFarooq

Abstract:

This paper introduces the effective speckle reduction of synthetic aperture radar (SAR) images using inner product spaces in undecimated wavelet domain. There are two major areas in projection onto span algorithm where improvement can be made. First is the use of undecimated wavelet transformation instead of discrete wavelet transformation. And second area is the use of smoothing filter namely directional smoothing filter which is an additional step. Proposed method does not need any noise estimation and thresholding technique. More over proposed method gives good results on both single polarimetric and fully polarimetric SAR images.

Keywords: Directional Smoothing, Inner product, Length ofvector, Undecimated wavelet transformation.

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2569 Conduction Model Compatible for Multi-Physical Domain Dynamic Investigations: Bond Graph Approach

Authors: A. Zanj, F. He

Abstract:

In the current paper, a domain independent conduction model compatible for multi-physical system dynamic investigations is suggested. By means of a port-based approach, a classical nonlinear conduction model containing physical states is first represented. A compatible discrete configuration of the thermal domain in line with the elastic domain is then generated through the enhancement of the configuration of the conventional thermal element. The presented simulation results of a sample structure indicate that the suggested conductive model can cover a wide range of dynamic behavior of the thermal domain.

Keywords: Multi-physical domain, conduction model, port-based modeling, dynamic interaction, physical modeling.

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2568 Estimating Frequency, Amplitude and Phase of Two Sinusoids with Very Close Frequencies

Authors: Jayme G. A. Barbedo, Amauri Lopes

Abstract:

This paper presents an algorithm to estimate the parameters of two closely spaced sinusoids, providing a frequency resolution that is more than 800 times greater than that obtained by using the Discrete Fourier Transform (DFT). The strategy uses a highly optimized grid search approach to accurately estimate frequency, amplitude and phase of both sinusoids, keeping at the same time the computational effort at reasonable levels. The proposed method has three main characteristics: 1) a high frequency resolution; 2) frequency, amplitude and phase are all estimated at once using one single package; 3) it does not rely on any statistical assumption or constraint. Potential applications to this strategy include the difficult task of resolving coincident partials of instruments in musical signals.

Keywords: Closely spaced sinusoids, high-resolution parameter estimation, optimized grid search.

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2567 Wavelet and K-L Seperability Based Feature Extraction Method for Functional Data Classification

Authors: Jun Wan, Zehua Chen, Yingwu Chen, Zhidong Bai

Abstract:

This paper proposes a novel feature extraction method, based on Discrete Wavelet Transform (DWT) and K-L Seperability (KLS), for the classification of Functional Data (FD). This method combines the decorrelation and reduction property of DWT and the additive independence property of KLS, which is helpful to extraction classification features of FD. It is an advanced approach of the popular wavelet based shrinkage method for functional data reduction and classification. A theory analysis is given in the paper to prove the consistent convergence property, and a simulation study is also done to compare the proposed method with the former shrinkage ones. The experiment results show that this method has advantages in improving classification efficiency, precision and robustness.

Keywords: classification, functional data, feature extraction, K-Lseperability, wavelet.

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2566 Non–Geometric Sensitivities Using the Adjoint Method

Authors: Marcelo Hayashi, João Lima, Bruno Chieregatti, Ernani Volpe

Abstract:

The adjoint method has been used as a successful tool to obtain sensitivity gradients in aerodynamic design and optimisation for many years. This work presents an alternative approach to the continuous adjoint formulation that enables one to compute gradients of a given measure of merit with respect to control parameters other than those pertaining to geometry. The procedure is then applied to the steady 2–D compressible Euler and incompressible Navier–Stokes flow equations. Finally, the results are compared with sensitivities obtained by finite differences and theoretical values for validation.

Keywords: Adjoint method, optimisation, non–geometric sensitivities, boundary conditions.

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2565 Analysis of the Reasons behind the Deteriorated Standing of Engineering Companies during the Financial Crisis

Authors: Levan Sabauri

Abstract:

In this paper, we discuss the deteriorated standing of engineering companies, some of the reasons behind it and the problems facing engineering enterprises during the financial crisis. We show the part that financial analysis plays in the detection of the main factors affecting the standing of a company, classify internal problems and the reasons influencing efficiency thereof. The publication contains the analysis of municipal engineering companies in post-Soviet transitional economies. In the wake of the 2008 world financial crisis the issue became even more poignant. It should be said though that even before the problem had been no less acute for some post-Soviet states caught up in a lengthy transitional period. The paper highlights shortcomings in the management of transportation companies, with new, more appropriate methods suggested. In analyzing the financial stability of a company, three elements need to be considered: current assets, investment policy and structural management of the funding sources leveraging the stability, should be focused on. Inappropriate management of the three may create certain financial problems, with timely and accurate detection thereof being an issue in terms of improved standing of an enterprise. In this connection, the publication contains a diagram reflecting the reasons behind the deteriorated financial standing of a company, as well as a flow chart thereof. The main reasons behind low profitability are also discussed.

Keywords: Efficiency, financial management, financial analysis funding structure, financial sustainability, investment policy, profitability, solvency, working capital.

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2564 The Interaction between Human and Environment on the Perspective of Environmental Ethics

Authors: Mella Ismelina Farma Rahayu

Abstract:

Environmental problems could not be separated from unethical human perspectives and behaviors toward the environment. There is a fundamental error in the philosophy of people’s perspective about human and nature and their relationship with the environment, which in turn will create an inappropriate behavior in relation to the environment. The aim of this study is to investigate and to understand the ethics of the environment in the context of humans interacting with the environment by using the hermeneutic approach. The related theories and concepts collected from literature review are used as data, which were analyzed by using interpretation, critical evaluation, internal coherence, comparisons, and heuristic techniques. As a result of this study, there will be a picture related to the interaction of human and environment in the perspective of environmental ethics, as well as the problems of the value of ecological justice in the interaction of humans and environment. We suggest that the interaction between humans and environment need to be based on environmental ethics, in a spirit of mutual respect between humans and the natural world.

Keywords: The environment, environmental ethics, the interaction, value.

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2563 Detection of Power Quality Disturbances using Wavelet Transform

Authors: Sudipta Nath, Arindam Dey, Abhijit Chakrabarti

Abstract:

This paper presents features that characterize power quality disturbances from recorded voltage waveforms using wavelet transform. The discrete wavelet transform has been used to detect and analyze power quality disturbances. The disturbances of interest include sag, swell, outage and transient. A power system network has been simulated by Electromagnetic Transients Program. Voltage waveforms at strategic points have been obtained for analysis, which includes different power quality disturbances. Then wavelet has been chosen to perform feature extraction. The outputs of the feature extraction are the wavelet coefficients representing the power quality disturbance signal. Wavelet coefficients at different levels reveal the time localizing information about the variation of the signal.

Keywords: Power quality, detection of disturbance, wavelet transform, multiresolution signal decomposition.

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2562 Flow and Heat Transfer of a Nanofluid over a Shrinking Sheet

Authors: N. Bachok, N. L. Aleng, N. M. Arifin, A. Ishak, N. Senu

Abstract:

The problem of laminar fluid flow which results from the shrinking of a permeable surface in a nanofluid has been investigated numerically. The model used for the nanofluid incorporates the effects of Brownian motion and thermophoresis. A similarity solution is presented which depends on the mass suction parameter S, Prandtl number Pr, Lewis number Le, Brownian motion number Nb and thermophoresis number Nt. It was found that the reduced Nusselt number is decreasing function of each dimensionless number.

Keywords: Boundary layer, Nanofluid, Shrinking sheet, Brownian motion, Thermophoresis, Similarity solution.

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2561 Simulation Modeling of Fire Station Locations under Traffic Obstacles

Authors: Mehmet Savsar

Abstract:

Facility location problem involves locating a facility to optimize some performance measures. Location of a public facility to serve the community, such as a fire station, significantly affects its service quality. Main objective in locating a fire station is to minimize the response time, which is the time duration between receiving a call and reaching the place of incident. In metropolitan areas, fire vehicles need to cross highways and other traffic obstacles through some obstacle-overcoming points which delay the response time. In this paper, fire station location problem is analyzed. Simulation models are developed for the location problems which involve obstacles. Particular case problems are analyzed and the results are presented.

Keywords: Public Facility Location, Fire Stations, Response Time, Fire Vehicle Delays.

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2560 Instability of Electron Plasma Waves in an Electron-Hole Bounded Quantum Dusty Plasma

Authors: Basudev Ghosh, Sailendranath Paul, Sreyasi Banerjee

Abstract:

Using quantum hydrodynamical (QHD) model the linear dispersion relation for the electron plasma waves propagating in a cylindrical waveguide filled with a dense plasma containing streaming electron, hole and stationary charged dust particles has been derived. It is shown that the effect of finite boundary and stream velocity of electrons and holes make some of the possible modes of propagation linearly unstable. The growth rate of this instability is shown to depend significantly on different plasma parameters.

Keywords: Electron Plasma wave, Quantum plasma, Quantum Hydrodynamical model.

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2559 Management by Sufficient Economy Philosophy for Hospitality Business in Samut Songkram

Authors: Krisada Sungkhamanee

Abstract:

The objectives of this research are to know the management form of Samut Songkram lodging entrepreneurs with sufficient economy framework, to know the threat that affect this business and drawing the fit model for this province in order to sustain their business with Samut Songkram style. What will happen if they do not use this philosophy? Will they have a cash short fall? The data and information are collected by informal discussion with 8 managers and 400 questionnaires. We will use a mix of methods both qualitative research and quantitative research for our study. Bent Flyvbjerg’s phronesis is utilized for this analysis. Our research will prove that sufficient economy can help small and medium business firms 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 use to practice in other areas of our country. 

Keywords: Samut Songkram, Hospitality Business, Sufficient Economy Philosophy.

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2558 Relation between Roots and Tangent Lines of Function in Fractional Dimensions: A Method for Optimization Problems

Authors: Ali Dorostkar

Abstract:

In this paper, a basic schematic of fractional dimensional optimization problem is presented. As will be shown, a method is performed based on a relation between roots and tangent lines of function in fractional dimensions for an arbitrary initial point. It is shown that for each polynomial function with order N at least N tangent lines must be existed in fractional dimensions of 0 < α < N+1 which pass exactly through the all roots of the proposed function. Geometrical analysis of tangent lines in fractional dimensions is also presented to clarify more intuitively the proposed method. Results show that with an appropriate selection of fractional dimensions, we can directly find the roots. Method is presented for giving a different direction of optimization problems by the use of fractional dimensions.

Keywords: Tangent line, fractional dimension, root, optimization problem.

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