Search results for: Linear interval systems

Authors: M. Salehi, A. A. Motie Birjandi, F. Namdari

Abstract:

Weak damping of low frequency oscillations is a frequent phenomenon in electrical power systems. These frequencies can be damped by power system stabilizers. Unified power flow controller (UPFC), as one of the most important FACTS devices, can be applied to increase the damping of power system oscillations and the more effect of this controller on increasing the damping of oscillations depends on its proper placement in power systems. In this paper, a technique based on controllability is proposed to select proper location of UPFC and the best input control signal in order to enhance damping of power oscillations. The effectiveness of the proposed technique is demonstrated in IEEE 9 bus power system.

Keywords: Unified power flow controller (UPFC), controllability, small signal analysis, eigenvalues.

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Authors: Anatoli Torokhti, Stanley Miklavcic

Abstract:

Suppose KY and KX are large sets of observed and reference signals, respectively, each containing N signals. Is it possible to construct a filter F : KY → KX that requires a priori information only on few signals, p  N, from KX but performs better than the known filters based on a priori information on every reference signal from KX? It is shown that the positive answer is achievable under quite unrestrictive assumptions. The device behind the proposed method is based on a special extension of the piecewise linear interpolation technique to the case of random signal sets. The proposed technique provides a single filter to process any signal from the arbitrarily large signal set. The filter is determined in terms of pseudo-inverse matrices so that it always exists.

Keywords: Wiener filter, filtering of stochastic signals.

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Authors: Ntokozo C. Mthembu

Abstract:

The notion of sustainable chemistry has become significant in the discourse for a global post-colonial era, including South Africa, especially when it comes to access to the general health system and related policies in relation to disease or ease of human life. In view of the stubborn vestiges of coloniality in the daily lives of indigenous African people in general, the fundamentals of present Western medical and traditional medicine systems and related policies in the democratic era were examined in this study. The situation of traditional healers in relation to current policy was also reviewed. The advent of democracy in South Africa brought about a variety of development opportunities and limitations, particularly with respect to indigenous African knowledge systems such as traditional medicine. There were high hopes that the limitations of previous narrow cultural perspectives would be rectified in the democratic era through development interventions, but some sections of society, such as traditional healers, remain marginalised. The Afrocentric perspective was explored in dissecting government interventions related to traditional medicine. This article highlights that multiple medical systems should be adopted and that health policies should be aligned in order to guarantee mutual respect and to address the remnants of colonialism in South Africa, Africa and the broader global community.

Keywords: Traditional healing system, healers, pluralist healthcare system, post-colonial era.

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Authors: M. Kowalski, M. Kastek, M. Szustakowski

Abstract:

Multispectral screening systems are becoming more popular because of their very interesting properties and applications. One of the most significant applications of multispectral screening systems is prevention of terrorist attacks. There are many kinds of threats and many methods of detection. Visual detection of objects hidden under clothing of a person is one of the most challenging problems of threats detection. There are various solutions of the problem; however, the most effective utilize multispectral surveillance imagers. The development of imaging devices and exploration of new spectral bands is a chance to introduce new equipment for assuring public safety. We investigate the possibility of long lasting detection of potentially dangerous objects covered with various types of clothing. In the article we present the results of comparative studies of passive imaging in three spectrums – visible, infrared and terahertz.

Keywords: Infrared, image processing, object detection, screening camera, terahertz.

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Authors: Fotis N. Koumboulis, Maria P. Tzamtzi

Abstract:

A supervisory scheme is proposed that implements Stepwise Safe Switching Logic. The functionality of the supervisory scheme is organized in the following eight functional units: Step- Wise Safe Switching unit, Common controllers design unit, Experimentation unit, Simulation unit, Identification unit, Trajectory cruise unit, Operating points unit and Expert system unit. The supervisory scheme orchestrates both the off-line preparative actions, as well as the on-line actions that implement the Stepwise Safe Switching Logic. The proposed scheme is a generic tool, that may be easily applied for a variety of industrial control processes and may be implemented as an automation software system, with the use of a high level programming environment, like Matlab.

Keywords: Supervisory systems, safe switching, nonlinear systems.

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Authors: Irina Pyrlina

Abstract:

Author presents the results of a study conducted to identify criteria of efficient information system (IS) with serviceoriented architecture (SOA) realization and proposes a ranking method to evaluate SOA information systems using a set of architecture quality criteria before the systems are implemented. The method is used to compare 7 SOA projects and ranking result for SOA efficiency of the projects is provided. The choice of SOA realization project depends on following criteria categories: IS internal work and organization, SOA policies, guidelines and change management, processes and business services readiness, risk management and mitigation. The last criteria category was analyzed on the basis of projects statistics.

Keywords: multiple criteria threshold algorithm, serviceoriented architecture, SOA operational risks, efficiency criteria for IS architecture, projects ranking.

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Authors: Kyoung Hoon Kim, Giman Kim

Abstract:

The cycles of the steam-injection gas-turbine systems are studied. The analyses of the parametric effects and the optimal operating conditions for the steam-injection gas-turbine (STIG) system and the regenerative steam-injection gas-turbine (RSTIG) system are investigated to ensure the maximum performance. Using the analytic model, the performance parameters of the system such as thermal efficiency, fuel consumption and specific power, and also the optimal operating conditions are evaluated in terms of pressure ratio, steam injection ratio, ambient temperature and turbine inlet temperature (TIT). It is shown that the computational results are presented to have a notable enhancement of thermal efficiency and specific power.

Keywords: gas turbine, RSTIG, steam injection, STIG, thermal efficiency.

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Authors: S. Mhamdi, O. Brendel, P. Montpied, K. Ben Yahia, N. Saouyah, B. Hasnaoui, E. Dreyer

Abstract:

Leaf Life Span (LLS) is used to classify trees into two main groups: evergreen and deciduous species. It varies according to the forms of life between taxonomic groups. Co-occurrence of deciduous and evergreen oaks is common in some Mediterranean type climate areas. Nevertheless, in the Tunisian forests, there is no enough information about the functional inter-specific diversity among oak species, especially in the mixed stand marked by the simultaneous presence of Q. suber L., Q. canariensis Willd. and their hybrid (Q. afares), the latter being an endemic oak species threatened with extinction. This study has been conducted to estimate the LLS, the relative growth rate, and the count of different growth flushes of samplings in semi-controlled conditions. Our study took 17 months, with an observation's interval of 4 weeks. The aim is to characterize and compare the hybrid species to the parental ones. Differences were observed among species, both for phenology and growth. Indeed, Q. suber saplings reached higher total height and number of growth flushes then Q. canariensis, while Q. afares showed much less growth flushes than the parental species. The LLS of parental species has exceeded the duration of the experiment, but their hybrid lost all leaves on all cohorts. The short LLSs of hybrid species are in accordance with this phenology in the field, but for Q. canariensis there was a contrast with observations in the field where phenology is strictly annual. This study allowed us to differentiate the hybrid from both parental species.

Keywords: Leaf life span, growth, hybrid, evergreen, deciduous, seedlings, Q. afares Pomel, Q. suber L., Q. canariensis Willd.

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Authors: Ahed Abugabah, Louis Sanzogni

Abstract:

ERP systems are the largest software applications adopted by universities, along with quite significant investments in their implementation. However, unlike other applications little research has been conducted regarding these systems in a university environment. This paper aims at providing a critical review of previous research in ERP system in higher education with a special focus on higher education in Australia. The research not only forms the basis of an evaluation of previous research and research needs, it also makes inroads in identifying the payoff of ERPs in the sector from different perspectives with particular reference to the user. The paper is divided into two parts, the first part focuses on ERP literature in higher education at large, while the second focuses on ERP literature in higher education in Australia.

Keywords: Enterprise resource planning system, higher education, implementation, user level.

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Authors: Kyoung-jae Kim

Abstract:

Recommender systems are usually regarded as an important marketing tool in the e-commerce. They use important information about users to facilitate accurate recommendation. The information includes user context such as location, time and interest for personalization of mobile users. We can easily collect information about location and time because mobile devices communicate with the base station of the service provider. However, information about user interest can-t be easily collected because user interest can not be captured automatically without user-s approval process. User interest usually represented as a need. In this study, we classify needs into two types according to prior research. This study investigates the usefulness of data mining techniques for classifying user need type for recommendation systems. We employ several data mining techniques including artificial neural networks, decision trees, case-based reasoning, and multivariate discriminant analysis. Experimental results show that CHAID algorithm outperforms other models for classifying user need type. This study performs McNemar test to examine the statistical significance of the differences of classification results. The results of McNemar test also show that CHAID performs better than the other models with statistical significance.

Keywords: Customer need type, Data mining techniques, Recommender system, Personalization, Mobile user.

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Authors: Bu Seog Ju, Woo Young Jung

Abstract:

The cost of damage to the non-structural systems in critical facilities like nuclear power plants and hospitals can exceed 80% of the total cost of damage during an earthquake. The failure of nonstructural components, especially, piping systems led to leakage of water and subsequent shut-down of hospitals immediately after the event. Consequently, the evaluation of performance of these types of structural configurations has become necessary to mitigate the risk and to achieve reliable designs. This paper focuses on a methodology to evaluate the static and dynamic characteristics of complex actual piping system based on NFPA-13 and SMACNA guidelines. The result of this study revealed that current piping system subjected to design lateral force and design spectrum based on UBC-97 was failed in both cases and mode shapes between piping system and building structure were very different

Keywords: Nonstructural component, piping, hospital, seismic, bracing.

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Authors: Trung-Kien Pham, Yoonsu Nam, Hyungun Kim, Jaehoon Son

Abstract:

This paper addresses linear quadratic regulation (LQR) for variable speed variable pitch wind turbines. Because of the inherent nonlinearity of wind turbine, a set of operating conditions is identified and then a LQR controller is designed for each operating point. The feedback controller gains are then interpolated linearly to get control law for the entire operating region. Besides, the aerodynamic torque and effective wind speed are estimated online to get the gain-scheduling variable for implementing the controller. The potential of the method is verified through simulation with the help of MATLAB/Simulink and GH Bladed. The performance and mechanical load when using LQR are also compared with that when using PI controller.

Keywords: variable speed variable pitch wind turbine, multi-MW size wind turbine, wind energy conversion system, LQR control.

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Authors: Doshi N. A., Dhobale S. B., Kakade S. R.

Abstract:

As chip manufacturing technology is suddenly on the threshold of major evaluation, which shrinks chip in size and performance, LFSR (Linear Feedback Shift Register) is implemented in layout level which develops the low power consumption chip, using recent CMOS, sub-micrometer layout tools. Thus LFSR counter can be a new trend setter in cryptography and is also beneficial as compared to GRAY & BINARY counter and variety of other applications. This paper compares 3 architectures in terms of the hardware implementation, CMOS layout and power consumption, using Microwind CMOS layout tool. Thus it provides solution to a low power architecture implementation of LFSR in CMOS VLSI.

Keywords: Chip technology, Layout level, LFSR, Pass transistor

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Authors: H. A. Majid, N. Razali, M. S. Sulaiman, A. K. A'ain

Abstract:

A new interface circuit for capacitive sensor is presented. This paper presents the design and simulation of soil moisture capacitive sensor interface circuit based on phase differential technique. The circuit has been designed and fabricated using MIMOS- 0.35"m CMOS technology. Simulation and test results show linear characteristic from 36 – 52 degree phase difference, representing 0 – 100% in soil moisture level. Test result shows the circuit has sensitivity of 0.79mV/0.10 phase difference, translating into resolution of 10% soil moisture level.

Keywords: Capacitive sensor, interface, phase differential.

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Authors: Farhad Kolahan, Mahdi Abachizadeh

Abstract:

In this paper, a simulated annealing algorithm has been developed to optimize machining parameters in turning operation on cylindrical workpieces. The turning operation usually includes several passes of rough machining and a final pass of finishing. Seven different constraints are considered in a non-linear model where the goal is to achieve minimum total cost. The weighted total cost consists of machining cost, tool cost and tool replacement cost. The computational results clearly show that the proposed optimization procedure has considerably improved total operation cost by optimally determining machining parameters.

Keywords: Optimization, Simulated Annealing, Machining Parameters, Turning Operation.

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Authors: Esmaeil Asadzadeh, Mehtab Alam

Abstract:

Progressive collapse of the layered hyperbolic tower shells are studied considering the influences of changes in the supporting columns’ types and angles. 3-D time history analyses employing the finite element method are performed for the towers supported with I-type and ᴧ-type column. It is found that the inclination angle of the supporting columns is a very important parameter in optimization and safe design of the cooling towers against the progressive collapse. It is also concluded that use of Demand Capacity Ratio (DCR) criteria of the linear elastic approach recommended by GSA is un-conservative for the hyperbolic tower shells.

Keywords: Progressive collapse, cooling towers, finite element analysis, crack generation, reinforced concrete.

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Authors: Othmane Fahim, Naoual Belouaggadia. Charifa David, Mohamed Ezzine

Abstract:

To make better use of cooling resources, systems have been derived on the basis of the use of night radiator systems for heat pumping. Using the TRNSYS tool we determined the influence of the climatic characteristics of the two zones in Morocco on the temperature of the outer surface of a Photovoltaic Thermal Panel “PVT” made of aluminum. The proposal to improve the performance of the panel allowed us to have little heat absorption during the day and give the same performance of a panel made of aluminum at night. The variation in the granite-based panel temperature recorded a deviation from the other materials of 0.5 °C, 2.5 °C on the first day respectively in Marrakech and Casablanca, and 0.2 °C and 3.2 °C on the second night. Power varied between 110.16 and 32.01 W/m² marked in Marrakech, to be the most suitable area to practice night cooling by night radiation.

Keywords: Morocco, TRANSYS, radiative cooling.

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Authors: Toshinori Nawata, Hitoshi Takata

Abstract:

In this paper we consider a nonlinear feedback control called augmented automatic choosing control (AACC) for nonlinear systems with constrained input. Constant terms which arise from section wise linearization of a given nonlinear system are treated as coefficients of a stable zero dynamics.Parameters included in the control are suboptimally selectedby extremizing a combination of Hamiltonian and Lyapunov functions with the aid of the genetic algorithm. This approach is applied to a field excitation control problem of power system to demonstrate the splendidness of the AACC. Simulation results show that the new controller can improve performance remarkably well.

Keywords: Augmented Automatic Choosing Control, NonlinearControl, Genetic Algorithm, Hamiltonian, Lyapunovfunction

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Authors: Chewa Thassana, Wicharn Techitdheera

Abstract:

The spin (ms) and orbital (mo) magnetic moment of the antiferromagnetic NiO and MnO have been studied in the local spin density approximation (LSDA+U) within full potential linear muffin-tin orbital (FP-LMTO method with in the coulomb interaction U varying from 0 to 10eV, exchange interaction J, from 0 to 1.0eV, and volume compression VC in range of 0 to 80%. Our calculated results shown that the spin magnetic moments and the orbital magnetic moments increase linearly with increasing U and J. While the interesting behaviour appears when volume compression is greater than 70% for NiO and 50% for MnO at which ms collapses. Further increase of volume compression to be at 80% leads to the disappearance of both magnetic moments.

Keywords: spin-orbital magnetic moment, Coulomb interaction U and exchange interaction J, volume compression VC, LSDA+U.

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Authors: Y. Pala, M. O. Ertas

Abstract:

In this paper, the general Riccati equation is analytically solved by a new transformation. By the method developed, looking at the transformed equation, whether or not an explicit solution can be obtained is readily determined. Since the present method does not require a proper solution for the general solution, it is especially suitable for equations whose proper solutions cannot be seen at first glance. Since the transformed second order linear equation obtained by the present transformation has the simplest form that it can have, it is immediately seen whether or not the original equation can be solved analytically. The present method is exemplified by several examples.

Keywords: Riccati Equation, ordinary differential equation, nonlinear differential equation, analytical solution, proper solution.

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Authors: C. Thassana, W. Techitdheera

Abstract:

This calculation focus on the effect of exchange interaction J and Coulomb interaction U on spin magnetic moments (ms) of MnO by using the local spin density approximation plus the Coulomb interaction (LSDA+U) method within full potential linear muffin-tin orbital (FP-LMTO). Our calculated results indicated that the spin magnetic moments correlated to J and U. The relevant results exhibited the increasing spin magnetic moments with increasing exchange interaction and Coulomb interaction. Furthermore, equations of spin magnetic moment, which h good correspondence to the experimental data 4.58μB, are defined ms = 0.11J +4.52μB and ms = 0.03U+4.52μB. So, the relation of J and U parameter is obtained, it is obviously, J = -0.249U+1.346 eV.

Keywords: exchange interaction J, the Coulomb interaction U, spin magnetic moment, LSDA+U, MnO.

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Authors: Xingyuan Qu, Shouming Zhong

Abstract:

In this paper, the problem of stability criteria of neural networks (NNs) with two-additive time-varying delay compenents is investigated. The relationship between the time-varying delay and its lower and upper bounds is taken into account when estimating the upper bound of the derivative of Lyapunov functional. As a result, some improved delay stability criteria for NNs with two-additive time-varying delay components are proposed. Finally, a numerical example is given to illustrate the effectiveness of the proposed method.

Keywords: Delay-dependent stability, time-varying delays, Lyapunov functional, linear matrix inequality (LMI).

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Authors: Jadwiga Królikowska, Andrzej Królikowski, Jarosław Bajer

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The work delineates the threats of maladjustment of the capacity of rain canals, designed and built in the early 20th century, in connection to heavy rainfall, especially in summer. This is the cause of the so called 'urban floods.' It directly relates to fierce raise of paving in the cities. Resolving this problem requires a change in philosophy of draining the rainfall by wider use of retention, infiltration and usage of rainwater.

In systemic approach to managing the safety of urban drainage systems the risk, which is directly connected to safety failures, has been accepted as a measure. The risk level defines the probability of occurrence of losses greater than the ones forecast for a given time frame. The procedure of risk modelling, enabling its numeric analysis by using appropriate weights, is a significant issue in this paper.

Keywords: Drainage system, urban areas, risk measurement.

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Authors: David E. Culler, Noah D. Anderson

Abstract:

Integrated systems for product design, manufacturing, and lifecycle management are difficult to implement and customize. Commercial software vendors, including CAD/CAM and third party PDM/PLM developers, create user interfaces and functionality that allow their products to be applied across many industries. The result is that systems become overloaded with functionality, difficult to navigate, and use terminology that is unfamiliar to engineers and production personnel. For example, manufacturers of automotive, aeronautical, electronics, and household products use similar but distinct methods and processes. Furthermore, each company tends to have their own preferred tools and programs for controlling work and information flow and that connect design, planning, and manufacturing processes to business applications. This paper presents a methodology and a case study that addresses these issues and suggests that in the future more companies will develop personalized applications that fit to the natural way that their business operates. A functioning system has been implemented at a highly competitive U.S. aerospace tooling and component supplier that works with many prominent airline manufacturers around the world including The Boeing Company, Airbus, Embraer, and Bombardier Aerospace. During the last three years, the program has produced significant benefits such as the automatic creation and management of component and assembly designs (parametric models and drawings), the extensive use of lightweight 3D data, and changes to the way projects are executed from beginning to end. CATIA (CAD/CAE/CAM) and a variety of programs developed in C#, VB.Net, HTML, and SQL make up the current system. The web-based platform is facilitating collaborative work across multiple sites around the world and improving communications with customers and suppliers. This work demonstrates that the creative use of Application Programming Interface (API) utilities, libraries, and methods is a key to automating many time-consuming tasks and linking applications together.

Keywords: CAD/CAM, CAPP, PDM, PLM, Scalable Systems.

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Authors: Caihong Sun, Xizi Zhang

Abstract:

Rating prediction is an important problem for recommender systems. The task is to predict the rating for an item that a user would give. Most of the existing algorithms for the task ignore the effect of negative ratings rated by users on items, but the negative ratings have a significant impact on users’ purchasing decisions in practice. In this paper, we present a rating prediction algorithm based on factorization machines that consider the effect of negative ratings inspired by Loss Aversion theory. The aim of this paper is to develop a concave and a convex negative disgust function to evaluate the negative ratings respectively. Experiments are conducted on MovieLens dataset. The experimental results demonstrate the effectiveness of the proposed methods by comparing with other four the state-of-the-art approaches. The negative ratings showed much importance in the accuracy of ratings predictions.

Keywords: Factorization machines, feature engineering, negative ratings, recommendation systems.

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Authors: B. Moaveni, S. Morovati

Abstract:

In recent years, increasing the usage of railway transportations especially in developing countries caused more attention to control systems railway vehicles. Consequently, designing and implementing the modern control systems to improve the operating performance of trains and locomotives become one of the main concerns of researches. Dynamic braking systems is an important safety system which controls the amount of braking torque generated by traction motors, to keep the adhesion coefficient between the wheel-sets and rail road in optimum bound. Adhesion force has an important role to control the braking distance and prevent the wheels from slipping during the braking process. Cascade control structure is one of the best control methods for the wide range of industrial plants in the presence of disturbances and errors. This paper presents cascade control structure based on two forward simple controllers with two feedback loops to control the slip ratio and braking torque. In this structure, the inner loop controls the angular velocity and the outer loop control the longitudinal velocity of the locomotive that its dynamic is slower than the dynamic of angular velocity. This control structure by controlling the torque of DC traction motors, tries to track the desired velocity profile to access the predefined braking distance and to control the slip ratio. Simulation results are employed to show the effectiveness of the introduced methodology in dynamic braking system.

Keywords: Cascade control, dynamic braking system, DC traction motors, slip control.

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Authors: Lāsma Cielava, Daina Jonkus, Līga Paura

Abstract:

The age of first calving (AFC) is one of the most important factors that have a significant impact on cow productivity in different lactations and its whole life. A belated AFC leads to reduced reproductive performance and it is one of the main reasons for reduced longevity. Cows that calved in time period from 2001-2007 and in this time finished at least four lactations were included in the database. Data were obtained from 68841 crossbred Holstein Black and White (HM), crossbred Latvian Brown (LB), and Latvian Brown genetic resources (LBGR) cows. Cows were distributed in four groups depending on age at first calving. The longest lifespan was conducted for LBGR cows, but they were also characterized with lowest lifetime milk yield and life day milk yield. HM breed cows had the shortest lifespan, but in the lifespan of 2862.2 days was obtained in average 37916.4 kg milk accordingly 13.2 kg milk in one life day. HM breed cows were also characterized with longer calving intervals (CI) in first four lactations, but LBGR cows had the shortest CI in the study group. Age at first calving significantly affected the length of CI in different lactations (p<0.05). HM cows that first time calved >30 months old in the fourth lactation had the longest CI in all study groups (421.4 days). The LBGR cows were characterized with the shortest CI, but there was slight increase in second and third lactation. Age at first calving had a significant impact on cows’ age in each calving time. In the analysis, cow group was conducted that cows with age at first calving <24 months or in average 580.5 days at the time of fifth calving were 2156.7 days (5.9 years) old, but cows with age at first calving >30 months (932.6 days) at the time of fifth calving were 2560.9 days (7.3 years) old.

Keywords: Age at first calving, calving interval, longevity, milk yield.

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Authors: U. Mutman, S. B. Coskun

Abstract:

In this study Homotopy Perturbation Method (HPM) is employed to investigate free vibration of an Euler beam with variable stiffness resting on an elastic foundation. HPM is an easy-to-use and very efficient technique for the solution of linear or nonlinear problems. HPM produces analytical approximate expression which is continuous in the solution domain. This work shows that HPM is a promising method for free vibration analysis of nonuniform Euler beams on elastic foundation. Several case problems have been solved by using the technique and solutions have been compared with those available in the literature.

Keywords: Homotopy Perturbation Method, Elastic Foundation, Vibration, Beam

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Authors: Christina G. Siontorou

Abstract:

This paper presents an integrated knowledge-based approach to multi-scale modeling of aquatic systems, with a view to enhancing predictive power and aiding environmental management and policy-making. The basic phases of this approach have been exemplified in the case of a bay in Saronicos Gulf (Attiki, Greece). The results showed a significant problem with rising phytoplankton blooms linked to excessive microbial growth, arisen mostly due to increased nitrogen inflows; therefore, the nitrification/denitrification processes of the benthic and water column sub-systems have provided the quality variables to be monitored for assessing environmental status. It is thereby demonstrated that the proposed approach facilitates modeling choices and implementation option decisions, while it provides substantial support for knowledge and experience capitalization in long-term water management.

Keywords: Aquatic ecosystem, integrated modeling, multi-scale modeling, ontological platform.

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Authors: A. M. Sagir

Abstract:

This paper derived four newly schemes which are combined in order to form an accurate and efficient block method for parallel or sequential solution of third order ordinary differential equations of the form y''' = f(x, y, y', y''), y(α)=y₀, y'(α)=β, y''(α)=η with associated initial or boundary conditions. The implementation strategies of the derived method have shown that the block method is found to be consistent, zero stable and hence convergent. The derived schemes were tested on stiff and non – stiff ordinary differential equations, and the numerical results obtained compared favorably with the exact solution.

Keywords: Block Method, Hybrid, Linear Multistep, Self starting, Third Order Ordinary Differential Equations.

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