Search results for: integral boundary conditions.

Authors: Adil Al-Rammahi

Abstract:

Laplace transformations have wide applications in engineering and sciences. All previous studies of modified Laplace transformations depend on differential equation with initial conditions. The purpose of our paper is to solve the linear differential equations (not initial value problem) and then find the general solution (not particular) via the Laplace transformations without needed any initial condition. The study involves both types of differential equations, ordinary and partial.

Keywords: Differential Equations, Laplace Transformations.

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Authors: Chinlun Lai, Lunjyh Jiang

Abstract:

Due to the heavy burden and pressure of caring for infants, an integrated automatic baby watching system based on IoT smart sensing and deep learning machine vision techniques is proposed in this paper. By monitoring infant body conditions such as heartbeat, breathing, body temperature, sleeping posture, as well as the surrounding conditions such as dangerous/sharp objects, light, noise, humidity and temperature, the proposed system can analyze and predict the obvious/potential dangerous conditions according to observed data and then adopt suitable actions in real time to protect the infant from harm. Thus, reducing the burden of the caregiver and improving safety efficiency of the caring work. The experimental results show that the proposed system works successfully for the infant care work and thus can be implemented in various life fields practically.

Keywords: Baby care system, internet of things, deep learning, machine vision.

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Authors: Bin Su

Abstract:

The 'wind-rain' house has a courtyard with glazed roof, which allows more direct sunlight to come into indoor spaces during the winter. The glazed roof can be partially opened or closed and automatically controlled to provide natural ventilation in order to adjust for indoor thermal conditions and the roof area can be shaded by reflective insulation materials during the summer. Two field studies for evaluating indoor thermal conditions of the two 'windrain' houses have been carried out by author in 2009 and 2010. Indoor and outdoor air temperature and relative humidity adjacent to floor and ceiling of the two sample houses were continuously tested at 15-minute intervals, 24 hours a day during the winter months. Based on field study data, this study investigates relationships between building design and indoor thermal condition of the 'windrain' house to improve the future house design for building thermal comfort and energy efficiency

Keywords: Courtyard, house design, indoor thermal comfort, 'wind-rain' house

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Authors: Abdenour Bourabaa, Malika Fekih, Mohamed Saighi

Abstract:

A numerical investigation of the fin efficiency and temperature distribution of an annular fin under dehumidification has been presented in this paper. The non-homogeneous second order differential equation that describes the temperature distribution from the fin base to the fin tip has been solved using the central finite difference method. The effects of variations in parameters including relative humidity, air temperature, air face velocity on temperature distribution and fin efficiency are investigated and compared with those under fully dry fin conditions. Also, the effect of fin pitch on the dimensionless temperature has been studied.

Keywords: Annular fin, Dehumidification, Fin efficiency, Heat and mass transfer, Wet fin.

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Authors: Ravinesh C. Deo

Abstract:

This article reviews the role of nozzle-exit conditions on the flow field of a plane jet. The jet issuing from a sharp-edged orifice plate at a Reynolds number (Re=18000) with nozzle aspect ratio (AR=72) exhibits the greatest shear-layer instabilities, highest entrainment and jet-spreading rates compared to the radially contoured nozzle. The growth rate of the shear-layer is the highest for the orifice-jet although this property could be amplified for larger Re or AR. A local peak in turbulent energy is found at x»10h. The peak appears to be elevated for an orifice-jet with lower Re or AR. The far-field energy sustained by the orifice-jet exceeds the contoured case although a higher Re and AR may enhance this value. The spectra demonstrated the largest eddy structures for the contoured nozzle. However, the frequency of coherent eddies is higher for the orifice-jet, with a larger magnitude achievable for lower Re and AR. 

Keywords: Plane jet, Reynolds number, nozzle-exit conditions, nozzle geometry, aspect ratio.

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Authors: A. Al-Shyyab, A. F. Khadrawi

Abstract:

The hydrodynamics behavior of fluid flow in microconverging plates is investigated analytically. Effects of Knudsen number (
) on the microchannel hydrodynamics behavior and the coefficient of friction are investigated. It is found that as
 increases the slip in the hydrodynamic boundary condition increases. Also, the coefficient of friction decreases as
 increases.

Keywords: Converging plates, hydrodynamic behavior, microplates, microchannel, slip velocity

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Authors: Farai Nyabadza

Abstract:

Malaria is by far the world-s most persistent tropical parasitic disease and is endemic to tropical areas where the climatic and weather conditions allow continuous breeding of the mosquitoes that spread malaria. A mathematical model for the transmission of malaria with prophylaxis prevention is analyzed. The stability analysis of the equilibria is presented with the aim of finding threshold conditions under which malaria clears or persists in the human population. Our results suggest that eradication of mosquitoes and prophylaxis prevention can significantly reduce the malaria burden on the human population.

Keywords: Prophylaxis prevention, basic reproductive number, stability.

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Authors: Chanhoe Kang, Changhyun Lee, Seock-Hee Jun, Yeong-Tae Oh

Abstract:

Offshore floating structure under the various environmental conditions maintains a fixed position by mooring system. Environmental conditions, vessel motions and mooring loads are applied to mooring lines as the dynamic tension. Because global responses of mooring system in deep water are specified as wave frequency and low frequency response, they should be calculated from the time-domain analysis due to non-linear dynamic characteristics. To take into account all mooring loads, environmental conditions, added mass and damping terms at each time step, a lot of computation time and capacities are required. Thus, under the premise that reliable fatigue damage could be derived through reasonable analysis method, it is necessary to reduce the analysis cases through the sensitivity studies and appropriate assumptions. In this paper, effects in fatigue are studied for spread mooring system connected with oil FPSO which is positioned in deep water of West Africa offshore. The target FPSO with two Mbbls storage has 16 spread mooring lines (4 bundles x 4 lines). The various sensitivity studies are performed for environmental loads, type of responses, vessel offsets, mooring position, loading conditions and riser behavior. Each parameter applied to the sensitivity studies is investigated from the effects of fatigue damage through fatigue analysis. Based on the sensitivity studies, the following results are presented: Wave loads are more dominant in terms of fatigue than other environment conditions. Wave frequency response causes the higher fatigue damage than low frequency response. The larger vessel offset increases the mean tension and so it results in the increased fatigue damage. The external line of each bundle shows the highest fatigue damage by the governed vessel pitch motion due to swell wave conditions. Among three kinds of loading conditions, ballast condition has the highest fatigue damage due to higher tension. The riser damping occurred by riser behavior tends to reduce the fatigue damage. The various analysis results obtained from these sensitivity studies can be used for a simplified fatigue analysis of spread mooring line as the reference.

Keywords: Mooring system, fatigue analysis, time domain, non-linear dynamic characteristics.

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Authors: H. Abaali

Abstract:

The power buck converter is the most widely used DC/DC converter topology. They have a very large application area such as DC motor drives, photovoltaic power system which require fast transient responses and high efficiency over a wide range of load current. This work proposes, the modelling of DC/DC power buck converter using state-space averaging method and the current-mode control using a proportional-integral controller. The efficiency of the proposed model and control loop are evaluated with operating point changes. The simulation results proved the effectiveness of the linear model of DC/DC power buck converter.

Keywords: DC/DC power buck converter, Linear current control, State-space averaging method.

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Authors: P. Bhramara, V. D. Rao, K. V. Sharma , T. K. K. Reddy

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In designing of condensers, the prediction of pressure drop is as important as the prediction of heat transfer coefficient. Modeling of two phase flow, particularly liquid – vapor flow under diabatic conditions inside a horizontal tube using CFD analysis is difficult with the available two phase models in FLUENT due to continuously changing flow patterns. In the present analysis, CFD analysis of two phase flow of refrigerants inside a horizontal tube of inner diameter, 0.0085 m and 1.2 m length is carried out using homogeneous model under adiabatic conditions. The refrigerants considered are R22, R134a and R407C. The analysis is performed at different saturation temperatures and at different flow rates to evaluate the local frictional pressure drop. Using Homogeneous model, average properties are obtained for each of the refrigerants that is considered as single phase pseudo fluid. The so obtained pressure drop data is compared with the separated flow models available in literature.

Keywords: Adiabatic conditions, CFD analysis, Homogeneousmodel and Liquid – Vapor flow.

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Authors: H. Abaali, M. T. Lamchich, M. Raoufi

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In this paper, we propose the Modified Synchronous Detection (MSD) Method for determining the reference compensating currents of the shunt active power filter under non sinusoidal voltages conditions. For controlling the inverter switching we used the PI regulator. The numerical simulation results, using Power System Blockset Toolbox PSB of Matlab, from a complete structure, are presented and discussed.

Keywords: Distorted, harmonic, Modified Synchronous Detection Method, PI regulator, Shunt Active Power Filter, unbalanced.

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Authors: Karan Modi, Rajesh Kumar, Jyoti Katiyar, Shreya Thusoo

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This paper presents Finite Element Method (FEM) for analyzing the internal responses generated in thin rectangular plates with various edge conditions and rigidity conditions. Comparison has been made between the FEM (ANSYS software) results for displacement, stresses and moments generated with and without the consideration of hole in plate and different aspect ratios. In the end comparison for responses in plain and composite square plates has been studied.

Keywords: ANSYS, Finite Element Method, Plates, Static Analysis.

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Authors: Felipe Azocar Simonet, Luis Acosta Espejo

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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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Authors: F. Amin, S. Feizi

Abstract:

Big data has the potential to improve the quality of services; enable infrastructure that businesses depend on to adapt continually and efficiently; improve the performance of employees; help organizations better understand customers; and reduce liability risks. Analytics and marketing models of fixed and mobile operators are falling short in combating churn and declining revenue per user. Big Data presents new method to reverse the way and improve profitability. The benefits of Big Data and next-generation network, however, are more exorbitant than improved customer relationship management. Next generation of networks are in a prime position to monetize rich supplies of customer information—while being mindful of legal and privacy issues. As data assets are transformed into new revenue streams will become integral to high performance.

Keywords: Big Data, Next Generation Networks, Network Transformation.

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Authors: Manisha Kankarej

Abstract:

The purpose of this paper is to show a relation between CR structure and F-structure satisfying polynomial equation. In this paper, we have checked the significance of CR structure and F-structure on Integrability conditions and Nijenhuis tensor. It was proved that all the properties of Integrability conditions and Nijenhuis tensor are satisfied by CR structures and F-structure satisfying polynomial equation.

Keywords: CR-submainfolds, CR-structure, Integrability condition & Nijenhuis tensor.

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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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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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Authors: Ali Bakhtiari Gharibdosti, Mohammad Hosein Bijeh Keshavarzi, Samira Alijani

Abstract:

To understand internal characteristics relationships and determine factors which explain under consideration characteristics in rapeseed varieties, 10 rapeseed genotypes were implemented in complete accidental plot with three-time repetitions under drought stress in 2009-2010 in research field of agriculture college, Islamic Azad University, Karaj branch. In this research, 11 characteristics include of characteristics related to growth, production and functions stages was considered. Variance analysis results showed that there is a significant difference among rapeseed varieties characteristics. By calculating simple correlation coefficient under both conditions, normal and drought stress indicate that seed function characteristics in plant and pod number have positive and significant correlation in 1% probable level with seed function and selection on the base of these characteristics was effective for improving this function. Under normal and drought stress, analyzing the main factors showed that numbers of factors which have more than one amount, had five factors under normal conditions which were 82.72% of total variance totally, but under drought stress four factors diagnosed which were 76.78% of total variance. By considering total results of this research and by assessing effective characteristics for factor analysis and selecting different components of these characteristics, they can be used for modifying works to select applicable and tolerant genotypes in drought stress conditions.

Keywords: Correlation, drought stress, factor analysis, rapeseed.

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Authors: Ammar S. M. Moohialdin, Bambang T. Suhariadi, Mohsin Siddiqui

Abstract:

This paper addresses the application of physiological status monitoring (PSM) for assessing the impact of harsh weather conditions on sports activities in universities in Saudi Arabia. Real sports measurement was conducted during sports activities such that the physiological status (HR and BR) of five students were continuously monitored by using Zephyr BioHarness^TM 3.0 sensors in order to identify the physiological bonds and zones. These bonds and zones were employed as indicators of the associated physiological risks of the performed sports activities. Furthermore, a short yes/no questionnaire was applied to collect information on participants’ health conditions and opinions of the applied PSM sensors. The results show the absence of a warning system as a protective aid for the hazardous levels of extremely hot and humid weather conditions that may cause dangerous and fatal circumstances. The applied formulas for estimating maximum HR provides accurate estimations for Maximum Heart Rate (HR_max). The physiological results reveal that the performed activities by the participants are considered the highest category (90–100%) in terms of activity intensity. This category is associated with higher HR, BR and physiological risks including losing the ability to control human body behaviors. Therefore, there is a need for immediate intervention actions to reduce the intensity of the performed activities to safer zones. The outcomes of this study assist the safety improvement of sports activities inside universities and athletes performing their sports activities. To the best of our knowledge, this is the first paper to represent a special case of the application of PSM technology for assessing sports activities in universities considering the impacts of harsh weather conditions on students’ health and safety.

Keywords: PSM, heart rate, HR, breathing rate, BR.

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Authors: Miriam Sosa-Díaz, Faustino Sánchez-Garduño

Abstract:

In population dynamics the study of both, the abundance and the spatial distribution of the populations in a given habitat, is a fundamental issue a From ecological point of view, the determination of the factors influencing such changes involves important problems. In this paper a mathematical model to describe the temporal dynamic and the spatiotemporal dynamic of the interaction of three populations (pollinators, plants and herbivores) is presented. The study we present is carried out by stages: 1. The temporal dynamics and 2. The spatio-temporal dynamics. In turn, each of these stages is developed by considering three cases which correspond to the dynamics of each type of interaction. For instance, for stage 1, we consider three ODE nonlinear systems describing the pollinator-plant, plant-herbivore and plant-pollinator-herbivore, interactions, respectively. In each of these systems different types of dynamical behaviors are reported. Namely, transcritical and pitchfork bifurcations, existence of a limit cycle, existence of a heteroclinic orbit, etc. For the spatiotemporal dynamics of the two mathematical models a novel factor are introduced. This consists in considering that both, the pollinators and the herbivores, move towards those places of the habitat where the plant population density is high. In mathematical terms, this means that the diffusive part of the pollinators and herbivores equations depend on the plant population density. The analysis of this part is presented by considering pairs of populations, i. e., the pollinator-plant and plant-herbivore interactions and at the end the two mathematical model is presented, these models consist of two coupled nonlinear partial differential equations of reaction-diffusion type. These are defined on a rectangular domain with the homogeneous Neumann boundary conditions. We focused in the role played by the density dependent diffusion term into the coexistence of the populations. For both, the temporal and spatio-temporal dynamics, a several of numerical simulations are included.

Keywords: Bifurcation, heteroclinic orbits, steady state, traveling wave.

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Authors: I. Szer, J. Szer, M. Pieńko, A. Robak, P. Jamińska-Gadomska

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Work at height, such as construction works on scaffoldings, is associated with a considerable risk. Scaffolding workers are usually exposed to changing weather conditions what can additionally increase the risk of dangerous situations. Therefore, it is very important to foresee the risk of adverse conditions to which the worker may be exposed. The data from meteorological stations may be used to asses this risk. However, the dependency between weather conditions on a scaffolding and in the vicinity of meteorological station, should be determined. The paper presents an analysis of two selected environmental parameters which have influence on the behavior of workers – air temperature and wind speed. Measurements of these parameters were made between April and November of 2016 on ten scaffoldings located in different parts of Poland. They were compared with the results taken from the meteorological stations located closest to the studied scaffolding. The results gathered from the construction sites and meteorological stations were not the same, but statistical analyses have shown that they were correlated.

Keywords: Scaffoldings, health and safety at work, temperature, wind speed.

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Authors: Totok R. Biyanto, Sonny Irawan, Hiskia J. Ginting, Matradji, Ya’umar, A. I. Fitri

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Steam injection is the most suitable of Enhanced Oil Recovery (EOR) methods to recover high viscosity oil. This is due to the capabilities of steam to reduce oil viscosity and increase the sweep capability of oil from the injection well toward the production well. Oil operating conditions in production should be match well with the operating condition target at the bottom of the production well. It is influenced by oil properties and reservoir rock properties. Hence, the operating condition should be optimized. Optimization requires three components i.e., objective function, model, and optimization technique. In this paper, the objective function is to obtain the optimum operating condition at the production well. The model was built using Darcy equation and mass-energy balance. The optimization technique utilizes Duelist Algorithm due to the effectiveness of its algorithm to obtain the desirable optimization results at the optimum operating condition.

Keywords: Enhanced oil recovery, steam injection, operating conditions, modeling, optimization, Duelist algorithm.

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Authors: Abdullah Alotaiq

Abstract:

The transition to low-carbon power generation is essential for mitigating climate change and achieving sustainability. This process, however, entails considerable costs, and understanding the factors influencing these costs is critical. This is necessary to cater to the increasing demand for low-carbon electricity across heating, industry, and transportation sectors. A crucial aspect of this transition is identifying cost-effective and feasible paths for decarbonization, which is integral to global climate mitigation efforts. It is concluded that hybrid solutions, combining different low-carbon technologies, are optimal for minimizing costs and enhancing flexibility. These solutions also address the challenges associated with phasing out existing fossil fuel-based power plants and broadening the spectrum of low-carbon power generation options.

Keywords: Review, power generation, energy transition, decarbonization.

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Authors: Seyedeh Belin Tavakoly Sany, H. Rosli, R. Majid, S. Aishah

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In this study, water monitoring was performed from Nov. 2012 to Oct. 2013 to assess water quality and evaluate the spatial and temporal distribution of physicochemical and biological variables in water. Water samples were collected from 10 coastal water stations of West Port. In the case of water-quality assessment, multi-metric indices and operational indicators have been proposed to classify the trophic status at different stations. The trophic level of West Port coastal water ranges from eutrophic to hypertrophic. Chl-a concentration was used to estimate the biological response of phytoplankton biomass and indicated eutrophic conditions in West Port and mesotrophic conditions at the control site. During the study period, no eutrophication events or secondary symptoms occurred, which may be related to hydrodynamic turbulence and water exchange, which prevent the development of eutrophic conditions in the West Port.

Keywords: Water quality, multi-metric indices, operational indicator, Malaysia, West Port.

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Authors: Daniele Losanno, H. A. Hadad, Giorgio Serino

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This paper presents a numerical investigation on the seismic performance of a benchmark bridge with different optimal isolation systems under near fault ground motion. Usually, very large displacements make seismic isolation an unfeasible solution due to boundary conditions, especially in case of existing bridges or high risk seismic regions. Hence, near-fault ground motions are most likely to affect either structures with long natural period range like isolated structures or structures sensitive to velocity content such as viscously damped structures. The work is aimed at analyzing the seismic performance of a three-span continuous bridge designed with different isolation systems having different levels of damping. The case study was analyzed in different configurations including: (a) simply supported, (b) isolated with lead rubber bearings (LRBs), (c) isolated with rubber isolators and 10% classical damping (HDLRBs), and (d) isolated with rubber isolators and 70% supplemental damping ratio. Case (d) represents an alternative control strategy that combines the effect of seismic isolation with additional supplemental damping trying to take advantages from both solutions. The bridge is modeled in SAP2000 and solved by time history direct-integration analyses under a set of six recorded near-fault ground motions. In addition to this, a set of analysis under Italian code provided seismic action is also conducted, in order to evaluate the effectiveness of the suggested optimal control strategies under far field seismic action. Results of the analysis demonstrated that an isolated bridge equipped with HDLRBs and a total equivalent damping ratio of 70% represents a very effective design solution for both mitigation of displacement demand at the isolation level and base shear reduction in the piers also in case of near fault ground motion.

Keywords: Isolated bridges, optimal design, near-fault motion, supplemental damping.

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Authors: D. I. De Souza, D. R. Fonseca, G. P. Azevedo

Abstract:

Sometimes the amount of time available for testing could be considerably less than the expected lifetime of the component. To overcome such a problem, there is the accelerated life-testing alternative aimed at forcing components to fail by testing them at much higher-than-intended application conditions. These models are known as acceleration models. One possible way to translate test results obtained under accelerated conditions to normal using conditions could be through the application of the “Maxwell Distribution Law.” In this paper we will apply a combined approach of a sequential life testing and an accelerated life testing to a low alloy high-strength steel component used in the construction of overpasses in Brazil. The underlying sampling distribution will be three-parameter Inverse Weibull model. To estimate the three parameters of the Inverse Weibull model we will use a maximum likelihood approach for censored failure data. We will be assuming a linear acceleration condition. To evaluate the accuracy (significance) of the parameter values obtained under normal conditions for the underlying Inverse Weibull model we will apply to the expected normal failure times a sequential life testing using a truncation mechanism. An example will illustrate the application of this procedure.

Keywords: Sequential Life Testing, Accelerated Life Testing, Underlying Three-Parameter Weibull Model, Maximum Likelihood Approach, Hypothesis Testing.

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Authors: Travis Wiens, Greg Schoenau, Rich Burton

Abstract:

It is well known that a linear dynamic system including a delay will exhibit limit cycle oscillations when a bang-bang sensor is used in the feedback loop of a PID controller. A similar behaviour occurs when a delayed feedback signal is used to train a neural network. This paper develops a method of predicting this behaviour by linearizing the system, which can be shown to behave in a manner similar to an integral controller. Using this procedure, it is possible to predict the characteristics of the neural network driven limit cycle to varying degrees of accuracy, depending on the information known about the system. An application is also presented: the intelligent control of a spark ignition engine.

Keywords: Control and automation, artificial neural networks, limit cycle

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Authors: Erika J. Ruíz, Jairo R. Cortes, Willian A. Aperador

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In this article was evaluated the protective effect of the alternative concrete obtained from the binary mixture of fly ash, and iron and steel slag. After mixing the cement with aggregates, structural steel was inserted in the matrix cementitious. The study was conducted comparatively with specimens exposed to natural conditions free of chloride ion. The chloride ion effect on the specimens accelerated under controlled conditions (3.5% NaCl and 25°C temperature). The impedance data were acquired in a range of 1 mHz to 100 kHz.

Keywords: Alternative concrete, corrosion, alkaline activation.

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

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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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Authors: Abdul Rauf, Muhammad Irfan, Muhammad Nadeem, Ishtiaq Ahmed, Hafiz Muhammad Nasir Iqbal

Abstract:

Rhizopus oligosporus was used in the present study for the production of protease enzyme under SSF. Sunflower meal was used as by-product of oil industry incorporated with organic salts was employed for the production of protease enzyme. The main purpose of the present was to study different parameters of protease productivity, its yields and to optimize basal fermentation conditions. The optimal conditions found for protease production using sunflower meal as a substrate in the present study were inoculum size (1%), substrate (Sunflower meal), substrate concentration (20 g), pH (3), cultivation period (72 h), incubation temperature (35oC), substrate to diluent-s ratio (1:2) and tween 81 (1 mL). The maximum production of protease in the presence of cheaper substrate at low concentration and stability at acidic pH, these characteristics make the strain and its enzymes useful in different industry.

Keywords: Acidic protease, Rhizopus oligosporus, Mediaoptimization, Solid state Fermentation

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