Search results for: mathematical discussion.
Commenced in January 2007
Frequency: Monthly
Edition: International
Paper Count: 1350

Search results for: mathematical discussion.

840 Disparity in Socio-Economic Development and Its Implications on Communal Conflicts: A Study on India's North-Eastern Region

Authors: Debasis Neogi

Abstract:

India-s North-Eastern part, comprising of seven states, is a lowly developed, tribal population dominated region in India. Inspite of the common Mongoloid origin and lifestyle of majority of the population residing here, sharp differences exist in the status of their socio-economic development. The present paper, through a state-wise analysis, makes an attempt to find out the extent of this disparity, especially on the socio-economic front. It illustrates the situations prevailing in health, education, economic and social cohesion sector. Discussion on the implications of such disparity on social stability finds that the causes of frequent insurgency activities, that have been penetrating the region for a long time, thereby creating communal conflicts, can be traced in the economic deprivation and disparity. In the last section, the paper makes policy prescription and suggests how by taking care of disparity and deprivation both poverty and the problem of communal conflicts can be controlled.

Keywords: Disparity, development, deprivation, communal conflicts.

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839 A Study of Distinctive Models for Pre-hospital EMS in Thailand: Knowledge Capture

Authors: R. Sinthavalai, N. Memongkol, N. Patthanaprechawong, J. Viriyanantavong, C. Choosuk

Abstract:

In Thailand, the practice of pre-hospital Emergency Medical Service (EMS) in each area reveals the different growth rates and effectiveness of the practices. Those can be found as the diverse quality and quantity. To shorten the learning curve prior to speed-up the practices in other areas, story telling and lessons learnt from the effective practices are valued as meaningful knowledge. To this paper, it was to ascertain the factors, lessons learnt and best practices that have impact as contributing to the success of prehospital EMS system. Those were formulized as model prior to speedup the practice in other areas. To develop the model, Malcolm Baldrige National Quality Award (MBNQA), which is widely recognized as a framework for organizational quality assessment and improvement, was chosen as the discussion framework. Remarkably, this study was based on the consideration of knowledge capture; however it was not to complete the loop of knowledge activities. Nevertheless, it was to highlight the recognition of knowledge capture, which is the initiation of knowledge management.

Keywords: Emergency Medical Service, Modeling, MBNQA, Thailand.

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838 Behavior of RC Buildings to Tsunami Action

Authors: Carlos H. Cuadra

Abstract:

The present report describes the characteristics of damages and behavior of reinforced concrete buildings during the tsunami action. The discussion is based on the field damage survey in selected cities located on the coast of the zone affected by the Great East Japan Earthquake on March 11, 2011. This earthquake is the most powerful know earthquake that has hit Japan with a magnitude 9.0 and with epicenter located at 129 km of Sendai city (off the coast). The earthquake triggered a destructive tsunami with run up height of up to 40 meters that mainly affect cities located on the Pacific Ocean coast of the Tohoku region (north-east region of Japan). Reinforced concrete buildings in general resist the tsunami without collapse however the non-structural elements like panels and ceilings were severely damaged. The analysis of damages has permitted to understand the behavior of RC buildings under tsunami attack, and has also permitted to establish recommendations for their use to take refuge from tsunami in places where natural topography makes impossible to reach hilltops or other safer places.

Keywords: tsunami, RC buildings, East Japan Earthquake, seismic damage

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837 Dynamic Safety-Stock Calculation

Authors: Julian Becker, Wiebke Hartmann, Sebastian Bertsch, Johannes Nywlt, Matthias Schmidt

Abstract:

In order to ensure a high service level industrial enterprises have to maintain safety-stock that directly influences the economic efficiency at the same time. This paper analyses established mathematical methods to calculate safety-stock. Therefore, the performance measured in stock and service level is appraised and the limits of several methods are depicted. Afterwards, a new dynamic approach is presented to gain an extensive method to calculate safety-stock that also takes the knowledge of future volatility into account.

Keywords: Inventory dimensioning, material requirement planning, safety-stock calculation.

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836 Problems of Boolean Reasoning Based Biclustering Parallelization

Authors: Marcin Michalak

Abstract:

Biclustering is the way of two-dimensional data analysis. For several years it became possible to express such issue in terms of Boolean reasoning, for processing continuous, discrete and binary data. The mathematical backgrounds of such approach — proved ability of induction of exact and inclusion–maximal biclusters fulfilling assumed criteria — are strong advantages of the method. Unfortunately, the core of the method has quite high computational complexity. In the paper the basics of Boolean reasoning approach for biclustering are presented. In such context the problems of computation parallelization are risen.

Keywords: Boolean reasoning, biclustering, parallelization, prime implicant.

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835 Toward an Open Network Business Approach

Authors: Valentina Ndou, Laura Schina, Giuseppina Passiante, Pasquale Del Vecchio, Marco De Maggio

Abstract:

The aim of this paper is to propose a dynamic integrated approach, based on modularity concept and on the business ecosystem approach, that exploit different eBusiness services for SMEs under an open business network platform. The adoption of this approach enables firms to collaborate locally for delivering the best product/service to the customers as well as globally by accessing international markets, interrelate directly with the customers, create relationships and collaborate with worldwide actors. The paper will be structured as following: We will start by offering an overview of the state of the art of eBusiness platforms among SME of food and tourism firms and then we discuss the main drawbacks that characterize them. The digital business ecosystem approach and the modularity concept will be described as the theoretical ground in which our proposed integrated model is rooted. Finally, the proposed model along with a discussion of the main value creation potentialities it might create for SMEs will be presented.

Keywords: component, Complexity; Digital Business Ecosystem, e Business Platforms, Modularity, Networks.

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834 H∞ State Estimation of Neural Networks with Discrete and Distributed Delays

Authors: Biao Qin, Jin Huang

Abstract:

In this paper, together with some improved Lyapunov-Krasovskii functional and effective mathematical techniques, several sufficient conditions are derived to guarantee the error system is globally asymptotically stable with H∞ performance, in which both the time-delay and its time variation can be fully considered. In order to get less conservative results of the state estimation condition, zero equalities and reciprocally convex approach are employed. The estimator gain matrix can be obtained in terms of the solution to linear matrix inequalities. A numerical example is provided to illustrate the usefulness and effectiveness of the obtained results.

Keywords: H∞ performance, Neural networks, State estimation.

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833 Optical Fiber Data Throughput in a Quantum Communication System

Authors: Arash Kosari, Ali Araghi

Abstract:

A mathematical model for an optical-fiber communication channel is developed which results in an expression that calculates the throughput and loss of the corresponding link. The data are assumed to be transmitted by using of separate photons with different polarizations. The derived model also shows the dependency of data throughput with length of the channel and depolarization factor. It is observed that absorption of photons affects the throughput in a more intensive way in comparison with that of depolarization. Apart from that, the probability of depolarization and the absorption of radiated photons are obtained.

Keywords: Absorption, data throughput, depolarization, optical fiber.

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832 Comparative Analysis of Two Modeling Approaches for Optimizing Plate Heat Exchangers

Authors: Fábio A. S. Mota, Mauro A. S. S. Ravagnani, E. P. Carvalho

Abstract:

In the present paper the design of plate heat exchangers is formulated as an optimization problem considering two mathematical modelling. The number of plates is the objective function to be minimized, considering implicitly some parameters configuration. Screening is the optimization method used to solve the problem. Thermal and hydraulic constraints are verified, not viable solutions are discarded and the method searches for the convergence to the optimum, case it exists. A case study is presented to test the applicability of the developed algorithm. Results show coherency with the literature.

Keywords: Plate heat exchanger, optimization, modeling, simulation.

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831 Numerical Modeling of the Depth-Averaged Flow Over a Hill

Authors: Anna Avramenko, Heikki Haario

Abstract:

This paper reports the development and application of a 2D1 depth-averaged model. The main goal of this contribution is to apply the depth averaged equations to a wind park model in which the treatment of the geometry, introduced on the mathematical model by the mass and momentum source terms. The depth-averaged model will be used in future to find the optimal position of wind turbines in the wind park. κ − ε and 2D LES turbulence models were consider in this article. 2D CFD2 simulations for one hill was done to check the depth-averaged model in practise.

Keywords: Depth-averaged equations, numerical modeling, CFD

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830 Application of Particle Swarm Optimization Technique for an Optical Fiber Alignment System

Authors: Marc Landry, Azeddine Kaddouri, Yassine Bouslimani, Mohsen Ghribi

Abstract:

In this paper, a new alignment method based on the particle swarm optimization (PSO) technique is presented. The PSO algorithm is used for locating the optimal coupling position with the highest optical power with three-degrees of freedom alignment. This algorithm gives an interesting results without a need to go thru the complex mathematical modeling of the alignment system. The proposed algorithm is validated considering practical tests considering the alignment of two Single Mode Fibers (SMF) and the alignment of SMF and PCF fibers.

Keywords: Particle-swarm optimization, optical fiber, automatic alignment.

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829 Transfer Function of Piezoelectric Material

Authors: C. Worakitjaroenphon, A. Oonsivilai

Abstract:

The study of piezoelectric material in the past was in T-Domain form; however, no one has studied piezoelectric material in the S-Domain form. This paper will present the piezoelectric material in the transfer function or S-Domain model. S-Domain is a well known mathematical model, used for analyzing the stability of the material and determining the stability limits. By using S-Domain in testing stability of piezoelectric material, it will provide a new tool for the scientific world to study this material in various forms.

Keywords: Piezoelectric, Stability, S-Domain, Transfer function

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828 Considering Assembly Operations and Product Structure for Manufacturing Cell Formation

Authors: M.B. Aryanezhad, J. Aliabadi

Abstract:

This paper considers the integration of assembly operations and product structure to Cellular Manufacturing System (CMS) design so that to correct the drawbacks of previous researches in the literature. For this purpose, a new mathematical model is developed which dedicates machining and assembly operations to manufacturing cells while the objective function is to minimize the intercellular movements resulting due to both of them. A linearization method is applied to achieve optimum solution through solving aforementioned nonlinear model by common programming language such as Lingo. Then, using different examples and comparing the results, the importance of integrating assembly considerations is demonstrated.

Keywords: Assembly operations and Product structure, CellFormation, Genetic Algorithm.

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827 Social Business Process Management and Business Process Management Maturity

Authors: Dalia Suša Vugec, Vesna Bosilj Vukšić, Ljubica Milanović Glavan

Abstract:

Business process management (BPM) is a well-known holistic discipline focused on managing business processes with the intention of achieving higher level of BPM maturity and better organizational performance. In recent period, traditional BPM faced some of its limitations like model-reality divide and lost innovation. Following latest trends, as an attempt to overcome the issues of traditional BPM, there has been an introduction of applying the principles of social software in managing business processes which led to the development of social BPM. However, there are not many authors or studies dealing with this topic so this study aims to contribute to that literature gap and to examine the link between the level of BPM maturity and the usage of social BPM. To meet these objectives, a survey within the companies with more than 50 employees has been conducted. The results reveal that the usage of social BPM is higher within the companies which achieved higher level of BPM maturity. This paper provides an overview, analysis and discussion of collected data regarding BPM maturity and social BPM within the observed companies and identifies the main social BPM principles.

Keywords: Business process management, BPM maturity, process performance index, social BPM.

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826 The Use of Minor Setups in an EPQ Model with Constrained Production Period Length

Authors: Behrouz Afshar Nadjafi

Abstract:

Extensive research has been devoted to economic production quantity (EPQ) problem. However, no attention has been paid to problems where production period length is constrained. In this paper, we address the problem of deciding the optimal production quantity and the number of minor setups within each cycle, in which, production period length is constrained but a minor setup is possible for pass the constraint. A mathematical model is developed and Iterated Local Search (ILS) is proposed to solve this problem. Finally, solution procedure illustrated with a numerical example and results are analyzed.

Keywords: EPQ, Inventory control, minor setup, ILS.

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825 Effective Density for the Classification of Transport Activity Centers

Authors: Dubbale Daniel A., Tsutsumi J.

Abstract:

This research work takes a different approach in the discussion of urban form impacts on transport planning and auto dependency. Concentrated density represented by effective density explains auto dependency better than the conventional density and it is proved to be a realistic density representative for the urban transportation analysis. Model analysis reveals that effective density is influenced by the shopping accessibility index as well as job density factor. It is also combined with the job access variable to classify four levels of Transport Activity Centers (TACs) in Okinawa, Japan. Trip attraction capacity and levels of the newly classified TACs was found agreeable with the amount of daily trips attracted to each center. The trip attraction data set was drawn from a 2007 Okinawa personal trip survey. This research suggests a planning methodology which guides logical transport supply routes and concentrated local development schemes.

Keywords: Effective density, urban form, auto-dependency, transport activity centers

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824 Mechanical Structure Design Optimization by Blind Number Theory: Time-dependent Reliability

Authors: Zakari Yaou, Lirong Cui

Abstract:

In a product development process, understanding the functional behavior of the system, the role of components in achieving functions and failure modes if components/subsystem fails its required function will help develop appropriate design validation and verification program for reliability assessment. The integration of these three issues will help design and reliability engineers in identifying weak spots in design and planning future actions and testing program. This case study demonstrate the advantage of unascertained theory described in the subjective cognition uncertainty, and then applies blind number (BN) theory in describing the uncertainty of the mechanical system failure process and the same time used the same theory in bringing out another mechanical reliability system model. The practical calculations shows the BN Model embodied the characters of simply, small account of calculation but betterforecasting capability, which had the value of macroscopic discussion to some extent.

Keywords: Mechanical structure Design, time-dependent stochastic process, unascertained information, blind number theory.

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823 Sliding Mode Control of a Bus Suspension System

Authors: Mujde Turkkan, Nurkan Yagiz

Abstract:

The vibrations, caused by the irregularities of the road surface, are to be suppressed via suspension systems. In this paper, sliding mode control for a half bus model with air suspension system is presented. The bus is modelled as five degrees of freedom (DoF) system. The mathematical model of the half bus is developed using Lagrange Equations. For time domain analysis, the bus model is assumed to travel at certain speed over the bump road. The numerical results of the analysis indicate that the sliding mode controllers can be effectively used to suppress the vibrations and to improve the ride comfort of the busses.

Keywords: Sliding mode control, bus model, air suspension.

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822 A Time-Reducible Approach to Compute Determinant |I-X|

Authors: Wang Xingbo

Abstract:

Computation of determinant in the form |I-X| is primary and fundamental because it can help to compute many other determinants. This article puts forward a time-reducible approach to compute determinant |I-X|. The approach is derived from the Newton’s identity and its time complexity is no more than that to compute the eigenvalues of the square matrix X. Mathematical deductions and numerical example are presented in detail for the approach. By comparison with classical approaches the new approach is proved to be superior to the classical ones and it can naturally reduce the computational time with the improvement of efficiency to compute eigenvalues of the square matrix.

Keywords: Algorithm, determinant, computation, eigenvalue, time complexity.

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821 Balanced k-Anonymization

Authors: Sabah S. Al-Fedaghi

Abstract:

The technique of k-anonymization has been proposed to obfuscate private data through associating it with at least k identities. This paper investigates the basic tabular structures that underline the notion of k-anonymization using cell suppression. These structures are studied under idealized conditions to identify the essential features of the k-anonymization notion. We optimize data kanonymization through requiring a minimum number of anonymized values that are balanced over all columns and rows. We study the relationship between the sizes of the anonymized tables, the value k, and the number of attributes. This study has a theoretical value through contributing to develop a mathematical foundation of the kanonymization concept. Its practical significance is still to be investigated.

Keywords: Balanced tables, k-anonymization, private data

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820 Throughput Optimization on Wireless Networks by Increasing the Maximum Transmission Unit

Authors: Edward Guillén, Stephanne Rodríguez, Jhordany Rodríguez

Abstract:

Throughput enhancement can be achieved with two main approaches. The first one is by the increase of transmission rate and the second one is reducing the control traffic. This paper focuses on how the throughput can be enhanced by increasing Maximum Transmission Unit -MTU. Transmission of larger packets can cause a throughput improvement by reducing IP overhead. Analysis results are obtained by a mathematical model and simulation tools with a main focus on wireless channels.

Keywords: 802.11, Maximum Transfer Unit, throughput enhancement, wireless networks.

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819 Adaptation Actions in Companies as Theoretical and Practical Aspects: A Case Study of a Food Ingredients and Additives Producer

Authors: Maja Sajdak

Abstract:

The aim of this article is to identify the measures companies undertake in order to adapt to the environment as well as discussing their diversity and effectiveness. The research methods used in the study include an in-depth analysis of the literature and a case study, which helps to illustrate the issue in question. Referring to the concept of agility, which is firmly embedded in the theory of strategic management and has been developed with the aim of adapting to the environment and its changes, the paper first examines different types of adaptation measures for companies. Then the issue under discussion is illustrated with the example of the company Hortimex. This company is an eminent representative of the world’s leading manufacturers of food additives and ingredients. The company was established in 1988 and is a family business, which in practice means that it conducts business in a responsible manner, observing the law and respecting the interests of society and the environment. The company’s mission is to develop a market in Poland for the products and solutions offered by their partners and to share their knowledge of additives in food production and consumption.

Keywords: Adaptation measures, agile company, flexibility, unanticipated changes.

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818 Effects of Thermal Radiation on Mixed Convection in a MHD Nanofluid Flow over a Stretching Sheet Using a Spectral Relaxation Method

Authors: Nageeb A. H. Haroun, Sabyasachi Mondal, Precious Sibanda

Abstract:

The effects of thermal radiation, Soret and Dufour parameters on mixed convection and nanofluid flow over a stretching sheet in the presence of a magnetic field are investigated. The flow is subject to temperature dependent viscosity and a chemical reaction parameter. It is assumed that the nanoparticle volume fraction at the wall may be actively controlled. The physical problem is modelled using systems of nonlinear differential equations which have been solved numerically using a spectral relaxation method. In addition to the discussion on heat and mass transfer processes, the velocity, nanoparticles volume fraction profiles as well as the skin friction coefficient are determined for different important physical parameters. A comparison of current findings with previously published results for some special cases of the problem shows an excellent agreement.

Keywords: Non-isothermal wedge, thermal radiation, nanofluid, magnetic field, Soret and Dufour effects.

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817 Current Status of Industry 4.0 in Material Handling Automation and In-house Logistics

Authors: Orestis Κ. Efthymiou, Stavros T. Ponis

Abstract:

In the last decade, a new industrial revolution seems to be emerging, supported -once again- by the rapid advancements of Information Technology in the areas of Machine-to-Machine (M2M) communication permitting large numbers of intelligent devices, e.g. sensors to communicate with each other and take decisions without any or minimum indirect human intervention. The advent of these technologies have triggered the emergence of a new category of hybrid (cyber-physical) manufacturing systems, combining advanced manufacturing techniques with innovative M2M applications based on the Internet of Things (IoT), under the umbrella term Industry 4.0. Even though the topic of Industry 4.0 has attracted much attention during the last few years, the attempts of providing a systematic literature review of the subject are scarce. In this paper, we present the authors’ initial study of the field with a special focus on the use and applications of Industry 4.0 principles in material handling automations and in-house logistics. Research shows that despite the vivid discussion and attractiveness of the subject, there are still many challenges and issues that have to be addressed before Industry 4.0 becomes standardized and widely applicable.

Keywords: Industry 4.0, internet of things, manufacturing systems, material handling, logistics.

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816 Minimizing Fresh and Wastewater Using Water Pinch Technique in Petrochemical Industries

Authors: W. Mughees, M. Al-Ahmad, M. Naeem

Abstract:

This research involves the design and analysis of pinch-based water/wastewater networks to minimize water utility in the petrochemical and petroleum industries. A study has been done on Tehran Oil Refinery to analyze feasibilities of regeneration, reuse and recycling of water network. COD is considered as a single key contaminant. Amount of freshwater was reduced about 149m3/h (43.8%) regarding COD. Re-design (or retrofitting) of water allocation in the networks was undertaken. The results were analyzed through graphical method and mathematical programming technique which clearly demonstrated that amount of required water would be determined by mass transfer of COD.

Keywords: Minimization, Water Pinch, Water Management, Pollution Prevention.

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815 A New Method for Extracting Ocean Wave Energy Utilizing the Wave Shoaling Phenomenon

Authors: Shafiq R. Qureshi, Syed Noman Danish, Muhammad Saeed Khalid

Abstract:

Fossil fuels are the major source to meet the world energy requirements but its rapidly diminishing rate and adverse effects on our ecological system are of major concern. Renewable energy utilization is the need of time to meet the future challenges. Ocean energy is the one of these promising energy resources. Threefourths of the earth-s surface is covered by the oceans. This enormous energy resource is contained in the oceans- waters, the air above the oceans, and the land beneath them. The renewable energy source of ocean mainly is contained in waves, ocean current and offshore solar energy. Very fewer efforts have been made to harness this reliable and predictable resource. Harnessing of ocean energy needs detail knowledge of underlying mathematical governing equation and their analysis. With the advent of extra ordinary computational resources it is now possible to predict the wave climatology in lab simulation. Several techniques have been developed mostly stem from numerical analysis of Navier Stokes equations. This paper presents a brief over view of such mathematical model and tools to understand and analyze the wave climatology. Models of 1st, 2nd and 3rd generations have been developed to estimate the wave characteristics to assess the power potential. A brief overview of available wave energy technologies is also given. A novel concept of on-shore wave energy extraction method is also presented at the end. The concept is based upon total energy conservation, where energy of wave is transferred to the flexible converter to increase its kinetic energy. Squeezing action by the external pressure on the converter body results in increase velocities at discharge section. High velocity head then can be used for energy storage or for direct utility of power generation. This converter utilizes the both potential and kinetic energy of the waves and designed for on-shore or near-shore application. Increased wave height at the shore due to shoaling effects increases the potential energy of the waves which is converted to renewable energy. This approach will result in economic wave energy converter due to near shore installation and more dense waves due to shoaling. Method will be more efficient because of tapping both potential and kinetic energy of the waves.

Keywords: Energy Utilizing, Wave Shoaling Phenomenon

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814 Experimental Validation of the Predicted Performance of a Wind Driven Venturi Ventilator

Authors: M. A. Serag-Eldin

Abstract:

The paper presents the results of simple measurements conducted on a model of a wind-driven venturi-type room ventilator. The ventilator design is new and was developed employing mathematical modeling. However, the computational model was not validated experimentally for the particular application considered. The paper presents the performance of the ventilator model under laboratory conditions, for five different wind tunnel speeds. The results are used to both demonstrate the effectiveness of the new design and to validate the computational model employed to develop it.

Keywords: Venturi-flow, ventilation, Wind-energy, Wind flow.

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813 Predictive Models for Compressive Strength of High Performance Fly Ash Cement Concrete for Pavements

Authors: S. M. Gupta, Vanita Aggarwal, Som Nath Sachdeva

Abstract:

The work reported through this paper is an experimental work conducted on High Performance Concrete (HPC) with super plasticizer with the aim to develop some models suitable for prediction of compressive strength of HPC mixes. In this study, the effect of varying proportions of fly ash (0% to 50% @ 10% increment) on compressive strength of high performance concrete has been evaluated. The mix designs studied were M30, M40 and M50 to compare the effect of fly ash addition on the properties of these concrete mixes. In all eighteen concrete mixes that have been designed, three were conventional concretes for three grades under discussion and fifteen were HPC with fly ash with varying percentages of fly ash. The concrete mix designing has been done in accordance with Indian standard recommended guidelines. All the concrete mixes have been studied in terms of compressive strength at 7 days, 28 days, 90 days, and 365 days. All the materials used have been kept same throughout the study to get a perfect comparison of values of results. The models for compressive strength prediction have been developed using Linear Regression method (LR), Artificial Neural Network (ANN) and Leave-One-Out Validation (LOOV) methods.

Keywords: ANN, concrete mixes, compressive strength, fly ash, high performance concrete, linear regression, strength prediction models.

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812 Pattern Recognition of Biological Signals

Authors: Paulo S. Caparelli, Eduardo Costa, Alexsandro S. Soares, Hipolito Barbosa

Abstract:

This paper presents an evolutionary method for designing electronic circuits and numerical methods associated with monitoring systems. The instruments described here have been used in studies of weather and climate changes due to global warming, and also in medical patient supervision. Genetic Programming systems have been used both for designing circuits and sensors, and also for determining sensor parameters. The authors advance the thesis that the software side of such a system should be written in computer languages with a strong mathematical and logic background in order to prevent software obsolescence, and achieve program correctness.

Keywords: Pattern recognition, evolutionary computation, biological signal, functional programming.

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811 The Global Stability Using Lyapunov Function

Authors: R. Kongnuy, E. Naowanich, T. Kruehong

Abstract:

An important technique in stability theory for differential equations is known as the direct method of Lyapunov. In this work we deal global stability properties of Leptospirosis transmission model by age group in Thailand. First we consider the data from Division of Epidemiology Ministry of Public Health, Thailand between 1997-2011. Then we construct the mathematical model for leptospirosis transmission by eight age groups. The Lyapunov functions are used for our model which takes the forms of an Ordinary Differential Equation system. The globally asymptotically for equilibrium states are analyzed.

Keywords: Age Group, Leptospirosis, Lyapunov Function, Ordinary Differential Equation.

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