Search results for: lateral type of H-derivative

Authors: Ardeshir Karami Mohammadi, Mohammadreza Saee

Abstract:

A variable structure model reference adaptive control (VS-MRAC) strategy for active steering assistance of a two wheel steering car is proposed. An ideal steering system with fixed properties and moving on an ideal road is used as the reference model, and the active steering assistance system is forced to attain the same behavior as the reference model. The proposed system can treat the nonlinear relationships between the side slip angles and lateral forces on tire, and the uncertainties on friction of the road surface, whose compensation are very important under critical situations. Simulation results show improvements on yaw rate and side slip.

Keywords: Variable Structure, Adaptive Control, Model reference, Active steering assistance.

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Authors: J. Fernandez, N. Aguilar, R. Fernandez de Canete, J. C. Ramos-Diaz

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In this paper, a simulation model of the glucose-insulin system for a patient undergoing diabetes Type 1 is developed by using a causal modeling approach under system dynamics. The OpenModelica simulation environment has been employed to build the so called causal model, while the glucose-insulin model parameters were adjusted to fit recorded mean data of a diabetic patient database. Model results under different conditions of a three-meal glucose and exogenous insulin ingestion patterns have been obtained. This simulation model can be useful to evaluate glucose-insulin performance in several circumstances, including insulin infusion algorithms in open-loop and decision support systems in closed-loop.

Keywords: Causal modeling, diabetes, glucose-insulin system, diabetes, causal modeling, OpenModelica software.

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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: V.V. Lyahov, V.M. Neshchadim

Abstract:

The structural stability of the model of a nonelectroneutral current sheath is investigated. The stationary model of a current sheath represents the system of four connected nonlinear differential first-order equations and thus they should manifest structural instability property, i.e. sensitivity to the infinitesimal changes of parameters and starting conditions. Domains of existence of the solutions of current sheath type are found. Those solutions of the current sheath type are realized only in some regions of sevendimensional space of parameters of the problem. The phase volume of those regions is small in comparison with the whole phase volume of the definition range of those parameters. It is shown that the offered model of a nonelectroneutral current sheath is applicable for theoretical interpretation of the bifurcational current sheaths observed in the magnetosphere.

Keywords: Distribution function, electromagnetic field, magnetoactive plasma, nonelectroneutral current sheath, structural instability, bifurcational current sheath.

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Authors: Ramandeep Behl, S. S. Motsa

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The main focus of this manuscript is to provide a highly efficient two-point sixth-order family of super-Halley type methods that do not require any second-order derivative evaluation for obtaining simple roots of nonlinear equations, numerically. Each member of the proposed family requires two evaluations of the given function and two evaluations of the first-order derivative per iteration. By using Mathematica-9 with its high precision compatibility, a variety of concrete numerical experiments and relevant results are extensively treated to confirm t he t heoretical d evelopment. From their basins of attraction, it has been observed that the proposed methods have better stability and robustness as compared to the other sixth-order methods available in the literature.

Keywords: Basins of attraction, nonlinear equations, simple roots, Super-Halley.

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Authors: Muhammad E. Rahman, Paul J. Fanning

Abstract:

Many single or multispan arch bridges are strengthened with the addition of some kind of structural support between adjacent arches of multispan or beside the arch barrel of a single span to increase the strength of the overall structure. It was traditionally formed by either placing loose rubble masonry blocks between the arches and beside the arches or using mortar or concrete to construct a more substantial structural bond between the spans. On the other hand backing materials are present in some existing bridges. Existing arch assessment procedures generally ignore the effects of backing materials. In this paper an investigation of the effects of backing on ratings for masonry arch bridges is carried out. It is observed that increasing the overall lateral stability of the arch system through the inclusion of structural backing results in an enhanced failure load by reducing the likelihood of any tension occurring at the top of the arch.

Keywords: Arch, Backing, Bridge, Masonry

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Authors: Javier Navallas, Armando Malanda, Luis Gila, Javier Rodriguez, Ignacio Rodriguez

Abstract:

According to previous studies, some muscles present a non-homogeneous spatial distribution of its muscle fiber types and motor unit types. However, available muscle models only deal with muscles with homogeneous distributions. In this paper, a new architecture muscle model is proposed to permit the construction of non-uniform distributions of muscle fibers within the muscle cross section. The idea behind is the use of a motor unit placement algorithm that controls the spatial overlapping of the motor unit territories of each motor unit type. Results show the capabilities of the new algorithm to reproduce arbitrary muscle fiber type distributions.

Keywords: muscle model, muscle architecture, motor unit, EMG simulation.

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Authors: S. Dhib, S. A. Addouche, T. Loukil, A. Elmhamedi

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In this paper, a reverse supply chain network is investigated for a decision making. This decision is surrounded by complex flows of returned products, due to the increasing quantity, the type of returned products and the variety of recovery option products (reuse, recycling, and refurbishment). The most important problem in the reverse logistic network (RLN) is to orient returned products to the suitable type of recovery option. However, returned products orientations from collect sources to the recovery disposition have not well considered in performance model. In this study, we propose a performance model for designing a network configuration on reverse logistics. Conceptual and analytical models are developed with taking into account operational, economic and environmental factors on designing network.

Keywords: Reverse logistics, Network design, Performance model, Open loop configuration.

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Authors: Mousa Mojarrad, Mashallah Abbasi Dezfouli, Amir Masoud Rahmani

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Detection and recognition of the Human Body Composition and extraction their measures (width and length of human body) in images are a major issue in detecting objects and the important field in Image, Signal and Vision Computing in recent years. Finding people and extraction their features in Images are particularly important problem of object recognition, because people can have high variability in the appearance. This variability may be due to the configuration of a person (e.g., standing vs. sitting vs. jogging), the pose (e.g. frontal vs. lateral view), clothing, and variations in illumination. In this study, first, Human Body is being recognized in image then the measures of Human Body extract from the image.

Keywords: Analysis of image processing, canny edge detection, classification, feature extraction, human body recognition, segmentation.

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Authors: Wei-Ju, Huang

Abstract:

It is claimed that a new style of urban planning and policy intertwined with ICT is emerging and urban planning and ICT policy are no longer considered as separate disciplines. The interactions between electronic spaces and urban spaces are so complex and uncertain that confront urban planners and policy makers with great challenges. However, the assumption about the relationship between ICT and urban planning is mainly based on North American and European experiences. In the light of empirical evidence from Taipei City, this paper shows that this new type of urban planning and policy intertwined with ICT has existed in Asian city for a decade as well. Based on these results, this paper further reviews how the Taipei City government implements this new type of urban ICT planning and the validity and realism of its underlying assumptions. Finally, it also explores the extent to which urban ICT planning could promote positive synergies between physical and electronic developments.

Keywords: ICT, Taipei City, Urban ICT Planning.

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Authors: Aqoul H. H. Alanezy, Ali M. Abdelsalam, Nouby M. Ghazaly

Abstract:

In recent years, progress has been made in increasing the renewable energy share in the power sector particularly in the wind. The experimental study conducted in this paper aims to investigate the effects of number of blades and inflow wind speed on vibration signals of a vertical axis Savonius type wind turbine. The operation of the model of Savonius type wind turbine is conducted to compare two, three and four blades wind turbines to show vibration amplitudes related with wind speed. It is found that the increase of the number of blades leads to decrease of the vibration magnitude. Furthermore, inflow wind speed has reduced effect on the vibration level for higher number of blades.

Keywords: Savonius wind turbine, number of blades, vibration amplitude, renewable energy.

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Authors: Yu-Sheng Lu, Chung-Hsin Cheng, Shuen-Shing Jan

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This paper presents the design and implementation of a sliding-mod controller for tracking servo of optical disk drives. The tracking servo is majorly subject to two disturbance sources: radial run-out and shock. The lateral run-out disturbance is mostly repeatable, and a model of such disturbance is incorporated into the controller design to effectively compensate for it. Meanwhile, as a shock disturbance is usually non-repeatable and unpredictable, the sliding-mode controller is employed for its robustness to abrupt perturbations. As a result, a sliding-mode controller design based on the internal model principle is tailored for tracking servo of optical disk drives in order to deal with these two major disturbances. Experimental comparative studies are conducted to investigate the effectiveness of the specially designed controller.

Keywords: Mechatronics, optical disk drive, sliding-mode control, servo systems.

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Authors: K. Khanafer

Abstract:

The aim of this investigation was to validate the fluid-structure interaction (FSI) model of type B aortic dissection with our experimental results from a bench-top-model. Another objective was to study the relationship between the size of a septectomy that increases the outflow of the false lumen and its effect on the values of the differential of pressure between true lumen and false lumen. FSI analysis based on Galerkin’s formulation was used in this investigation to study flow pattern and hemodynamics within a flexible type B aortic dissection model using boundary conditions from our experimental data. The numerical results of our model were verified against the experimental data for various tear size and location. Thus, CFD tools have a potential role in evaluating different scenarios and aortic dissection configurations.

Keywords: Aortic dissection, fluid-structure interaction, in vitro model, numerical.

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Authors: Tayebeh Norouzi

Abstract:

This study aims to investigate the acquisition process of intonation. It examines the intonation structure of Tokyo Japanese and its realization by Iranian learners of Japanese. Seven Iranian learners of Japanese, differing in fluency, and two Japanese speakers participated in the experiment. Two sentences were used to test the phonological and phonetic characteristics of lexical pitch-accent as well as the intonation patterns produced by the speakers. Both sentences consisted of similar words with the same number of syllables and lexical pitch-accents but different syntactic structure. Speakers were asked to read each sentence three times at normal speed, and the data were analyzed by Praat. The results show that lexical pitch-accent, Accentual Phrase (AP) and AP boundary tone realization vary depending on sentence type. For sentences of type XdeYwo, the lexical pitch-accent is realized properly. However, there is a rise in AP boundary tone regardless of speakers’ level of fluency. In contrast, in sentences of type XnoYwo, the lexical pitch-accent and AP boundary tone vary depending on the speakers’ fluency level. Advanced speakers are better at grouping words into phrases and produce more native-like intonation patterns, though they are not able to realize downstep properly. The non-native speakers tried to realize proper intonation patterns by making changes in lexical accent and boundary tone.

Keywords: Intonation, Iranian learners, Japanese prosody, lexical accent, second language acquisition.

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Authors: Mohammad Hassan Heidari, Amir Hossein Goodarzi, Majid Azarniush

Abstract:

Radiation doses to tissues and organs were measured using the anthropomorphic phantom as an equivalent to the human body. When high-energy X-rays are externally applied to treat laryngeal cancer, the absorbed dose at the laryngeal lumen is lower than given dose because of air space, which it should pass through, before reaching the lesion. Specially, in case of high-energy X-rays, the loss of dose is considerable. Three-dimensional absorbed dose distributions have been computed for high-energy photon radiation therapy of laryngeal and hypopharyngeal cancers, using a coaxial pair of opposing lateral beams in fixed positions. Treatment plans obtained under various conditions of irradiation.

Keywords: 3D Treatment Planning, anthropomorphic phantom, larynx cancer, radiotherapy.

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Authors: Amid Ranjkesh, Milan Ambrožič, Samo Kralj

Abstract:

We study the typical domain size and configuration character of a randomly perturbed system exhibiting continuous symmetry breaking. As a model system we use rod-like objects within a cubic lattice interacting via a Lebwohl–Lasher-type interaction. We describe their local direction with a headless unit director field. An example of such systems represents nematic LC or nanotubes. We further introduce impurities of concentration p, which impose the random anisotropy field-type disorder to directors. We study the domain-type pattern of molecules as a function of p, anchoring strength w between a neighboring director and impurity, temperature, history of samples. In simulations we quenched the directors either from the random or homogeneous initial configuration. Our results show that a history of system strongly influences: i) the average domain coherence length; and ii) the range of ordering in the system. In the random case the obtained order is always short ranged (SR). On the contrary, in the homogeneous case, SR is obtained only for strong enough anchoring and large enough concentration p. In other cases, the ordering is either of quasi long range (QLR) or of long range (LR). We further studied memory effects for the random initial configuration. With increasing external ordering field B either QLR or LR is realized.

Keywords: Lebwohl-Lasher model, liquid crystals, disorder, memory effect, orientational order.

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Authors: S. A. H. Feghhi, Z. Gholamzadeh, Z. Alipoor, C. Tenreiro

Abstract:

Currently, thorium fuel has been especially noticed because of its proliferation resistance than long half-life alpha emitter minor actinides, breeding capability in fast and thermal neutron flux and mono-isotopic naturally abundant. In recent years, efficiency of minor actinide burning up in PWRs has been investigated. Hence, a minor actinide-contained thorium based fuel matrix can confront both proliferation resistance and nuclear waste depletion aims. In the present work, minor actinide depletion rate in a CANDU-type nuclear core modeled using MCNP code has been investigated. The obtained effects of minor actinide load as mixture of thorium fuel matrix on the core neutronics has been studied with comparing presence and non-presence of minor actinide component in the fuel matrix. Depletion rate of minor actinides in the MA-contained fuel has been calculated using different power loads. According to the obtained computational data, minor actinide loading in the modeled core results in more negative reactivity coefficients. The MA-contained fuel achieves less radial peaking factor in the modeled core. The obtained computational results showed 140 kg of 464 kg initial load of minor actinide has been depleted in during a 6-year burn up in 10 MW power.

Keywords: Minor actinide burning, CANDU-type reactor, MCNPX code, Neutronic parameters.

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Authors: Ashkan Shafee, Ahmad Fahimifar

Abstract:

There is a growing demand for construction of high-rise buildings and infrastructures in large cities, which sometimes require deep excavations in the vicinity of pile foundations. In this study, a two-dimensional finite element analysis is used to gain insight into the response of pile groups adjacent to deep excavations in sand. The numerical code was verified by available experimental works, and a parametric study was performed on different working load combinations, excavation depth and supporting system. The results show that the simple two-dimensional plane strain model can accurately simulate the excavation induced changes on adjacent pile groups. It was found that further excavation than pile toe level and also inclined loading on adjacent pile group can severely affect the serviceability of the foundation.

Keywords: Deep excavation, pile group, inclined loading, lateral deformation.

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Authors: Ihor Trots, Yuriy Tasinkevych, Andrzej Nowicki, Marcin Lewandowski

Abstract:

The paper presents the multi-element synthetic transmit aperture (MSTA) method with a small number of elements transmitting and all elements apertures in medical ultrasound imaging. As compared to the other methods MSTA allows to increase the system frame rate and provides the best compromise between penetration depth and lateral resolution. In the experiments a 128-element linear transducer array with 0.3 mm pitch excited by a burst pulse of 125 ns duration were used. The comparison of 2D ultrasound images of tissue mimicking phantom obtained using the STA and the MSTA methods is presented to demonstrate the benefits of the second approach. The results were obtained using SA algorithm with transmit and receive signals correction based on a single element directivity function.

Keywords: Beamforming, frame rate, synthetic aperture, ultrasound imaging

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Authors: Hassan Manouzi, Taous-Meriem Laleg-Kirati

Abstract:

In this paper we study mathematically the eigenvalue problem for stochastic elliptic partial differential equation of Wick type. Using the Wick-product and the Wiener-Itô chaos expansion, the stochastic eigenvalue problem is reformulated as a system of an eigenvalue problem for a deterministic partial differential equation and elliptic partial differential equations by using the Fredholm alternative. To reduce the computational complexity of this system, we shall use a decomposition method using the Wiener-Itô chaos expansion. Once the approximation of the solution is performed using the finite element method for example, the statistics of the numerical solution can be easily evaluated.

Keywords: Eigenvalue problem, Wick product, SPDEs, finite element, Wiener-Itô chaos expansion.

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Authors: L. Abdelmalek, M. Zerikat, M. Rahli

Abstract:

In this paper, we present a comparative study of the genetic algorithms and Hessian-s methods for optimal research of the active powers in an electric network of power. The objective function which is the performance index of production of electrical energy is minimized by satisfying the constraints of the equality type and inequality type initially by the Hessian-s methods and in the second time by the genetic Algorithms. The results found by the application of AG for the minimization of the electric production costs of power are very encouraging. The algorithms seem to be an effective technique to solve a great number of problems and which are in constant evolution. Nevertheless it should be specified that the traditional binary representation used for the genetic algorithms creates problems of optimization of management of the large-sized networks with high numerical precision.

Keywords: Genetic algorithm, Flow of optimum loadimpedances, Hessians method, Optimal distribution.

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Authors: Davide Fuscà, Kanan Rahimli, Roberto Leuzzi

Abstract:

Prevent abuse and illegal activities in a given area of the sea is a very difficult and expensive task. Artificial intelligence offers the possibility to implement new methods to identify the vessel class type from the kinematic features of the vessel itself. The task strictly depends on the quality of the data. This paper explores the application of a deep Long Short-Term Memory model by using AIS flow only with a relatively low quality. The proposed model reaches high accuracy on detecting nine vessel classes representing the most common vessel types in the Ionian-Adriatic Sea. The model has been applied during the Adriatic-Ionian trial period of the international EU ANDROMEDA H2020 project to identify vessels performing behaviours far from the expected one, depending on the declared type.

Keywords: maritime surveillance, artificial intelligence, behaviour analysis, LSTM

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Authors: M. Abdulkawi, Z. K. Eshkuvatov, N. M. A. Nik Long

Abstract:

This manuscript presents a method for the numerical solution of the Cauchy type singular integral equations of the first kind, over a finite segment which is bounded at the end points of the finite segment. The Chebyshev polynomials of the second kind with the corresponding weight function have been used to approximate the density function. The force function is approximated by using the Chebyshev polynomials of the first kind. It is shown that the numerical solution of characteristic singular integral equation is identical with the exact solution, when the force function is a cubic function. Moreover, it also shown that this numerical method gives exact solution for other singular integral equations with degenerate kernels.

Keywords: Singular integral equations, Cauchy kernel, Chebyshev polynomials, interpolation.

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Authors: Imali T. Jayamanne, K. P. Asoka Ramanayake

Abstract:

Transition from tertiary level education to employment is one of the challenges that many fresh university graduates face after graduation. The transition period or the waiting time to obtain the first employment varies with the socio-economic factors and the general characteristics of a graduate. Compared to other fields of study, Arts graduates in Sri Lanka, have to wait a long time to find their first employment. The objective of this study is to identify the determinants of the transition from higher education to employment of these graduates using survival models. The study is based on a survey that was conducted in the year 2016 on a stratified random sample of Arts graduates from Sri Lankan universities who had graduated in 2012. Among the 469 responses, 36 (8%) waiting times were interval censored and 13 (3%) were right censored. Waiting time for the first employment varied between zero to 51 months. Initially, the log-rank and the Gehan-Wilcoxon tests were performed to identify the significant factors. Gender, ethnicity, GCE Advanced level English grade, civil status, university, class received, degree type, sector of first employment, type of first employment and the educational qualifications required for the first employment were significant at 10%. The Cox proportional hazards model was fitted to model the waiting time for first employment with these significant factors. All factors, except ethnicity and type of employment were significant at 5%. However, since the proportional hazard assumption was violated, the lognormal Accelerated failure time (AFT) model was fitted to model the waiting time for the first employment. The same factors were significant in the AFT model as in Cox proportional model.

Keywords: AFT model, first employment, proportional hazard, survey design, waiting time.

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Authors: Osama H. Ghazal

Abstract:

The intension in this work is to investigate the effect of different fuels type on engine performance for different engine speed. Brake Power, Brake Torque, and specific fuel consumption were calculated and presented to show the effect of varying fuel type on them for all cases considered. A special program used to carry out the calculations. A simulation model for one-cylinder spark ignition engine has been built and calculated.

The analysis of the results shows that for methanol the power increases about 30% at 1000 rpm and 16% at 6000 rpm comparing with methane. For the same compared fuels the increment in fuel consumption is about 100% at 1000 rpm and 115% at 6000 rpm. The increment in brake thermal efficiency for gasoline is around 11% comparing with methane at 1000 rpm and 7% for methanol comparing with methane at 4000 rpm.

Keywords: Natural gas fuel, spark ignition engines, performance, engine simulation.

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Authors: Dawit Burusie Abdi, Mamidala Jagadesh Kumar

Abstract:

In this paper, using 2D TCAD simulations, the application of a dual material gate (DMG) for suppressing ambipolar conduction in a tunnel field effect transistor (TFET) is demonstrated. Using the proposed DMG concept, the ambipolar conduction can be effectively suppressed even if the drain doping is as high as that of the source doping. Achieving this symmetrical doping, without the ambipolar conduction in TFETs, gives the advantage of realizing both n-type and p-type devices with the same doping sequences. Furthermore, the output characteristics of the DMG TFET exhibit a good saturation when compared to that of the gate-drain underlap approach. This improved behavior of the DMG TFET makes it a good candidate for inverter based logic circuits.

Keywords: Dual material gate, suppressing ambipolar current, symmetrically doped TFET, tunnel FETs, PNPN TFET.

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Authors: N. Feroze, M. Aslam

Abstract:

The article is concerned with analysis of failure rate (shape parameter) under the Topp Leone distribution using a Bayesian framework. Different loss functions and a couple of noninformative priors have been assumed for posterior estimation. The posterior predictive distributions have also been derived. A simulation study has been carried to compare the performance of different estimators. A real life example has been used to illustrate the applicability of the results obtained. The findings of the study suggest  that the precautionary loss function based on Jeffreys prior and singly type II censored samples can effectively be employed to obtain the Bayes estimate of the failure rate under Topp Leone distribution.

Keywords: loss functions, type II censoring, posterior distribution, Bayes estimators.

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Authors: František Včelař, Zuzana Pátíková

Abstract:

Recently a new type of very general relational structures, the so called (L-)complete propelattices, was introduced. These significantly generalize complete lattices and completely lattice L-ordered sets, because they do not assume the technically very strong property of transitivity. For these structures also the main part of the original Tarski’s fixed point theorem holds for (L-fuzzy) isotone maps, i.e., the part which concerns the existence of fixed points and the structure of their set. In this paper, fundamental properties of (L-)complete propelattices are recalled and the so called L-fuzzy relatively isotone maps are introduced. For these maps it is proved that they also have fixed points in L-complete propelattices, even if their set does not have to be of an awaited analogous structure of a complete propelattice.

Keywords: Fixed point, L-complete propelattice, L-fuzzy (relatively) isotone map, residuated lattice, transitivity.

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Authors: Rama Shanker, Anil Kumar Sachan

Abstract:

Basic ingredients of concrete are cement, fine aggregate, coarse aggregate and water. To produce a concrete of certain specific properties, optimum proportion of these ingredients are mixed. The important factors which govern the mix design are grade of concrete, type of cement and size, shape and grading of aggregates. Concrete mix design method is based on experimentally evolved empirical relationship between the factors in the choice of mix design. Basic draw backs of this method are that it does not produce desired strength, calculations are cumbersome and a number of tables are to be referred for arriving at trial mix proportion moreover, the variation in attainment of desired strength is uncertain below the target strength and may even fail. To solve this problem, a lot of cubes of standard grades were prepared and attained 28 days strength determined for different combination of cement, fine aggregate, coarse aggregate and water. An artificial neural network (ANN) was prepared using these data. The input of ANN were grade of concrete, type of cement, size, shape and grading of aggregates and output were proportions of various ingredients. With the help of these inputs and outputs, ANN was trained using feed forward back proportion model. Finally trained ANN was validated, it was seen that it gave the result with/ error of maximum 4 to 5%. Hence, specific type of concrete can be prepared from given material properties and proportions of these materials can be quickly evaluated using the proposed ANN.

Keywords: Aggregate Proportions, Artificial Neural Network, Concrete Grade, Concrete Mix Design.

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Authors: M. Movahedi Rad

Abstract:

In this study, a general approach to the reliability based limit analysis of laterally loaded piles is presented. In engineering practice the uncertainties play a very important role. The aim of this study is to evaluate the lateral load capacity of free-head and fixed-head long pile when plastic limit analysis is considered. In addition to the plastic limit analysis to control the plastic behaviour of the structure, uncertain bound on the complementary strain energy of the residual forces is also applied. This bound has significant effect for the load parameter. The solution to reliability-based problems is obtained by a computer program which is governed by the reliability index calculation.

Keywords: Reliability, laterally loaded pile, residual strain energy, probability, limit analysis.

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