Search results for: initial feasible solution

Authors: H. Dehghan, E. Mahdavi, M. M. Heyhat

Abstract:

In pressure vessels contain hydrogen, the role of hydrogen will be important because of hydrogen cracking problem. It is difficult to predict what is happened in metallurgical field spite of a lot of studies have been searched. The main role in controlling the mass diffusion as driving force is related to stress. In this study, finite element analysis is implemented to estimate material-s behavior associated with hydrogen embrittlement. For this purpose, one model of a pressure vessel is introduced that it has definite boundary and initial conditions. In fact, finite element is employed to solve the sequentially coupled mass diffusion with stress near a crack front in a pressure vessel. Modeling simulation intergrarnular fracture of AISI 4135 steel due to hydrogen is investigated. So, distribution of hydrogen and stress are obtained and they indicate that their maximum amounts occur near the crack front. This phenomenon is happened exactly the region between elastic and plastic field. Therefore, hydrogen is highly mobile and can diffuse through crystal lattice so that this zone is potential to trap high volume of hydrogen. Consequently, crack growth and fast fracture will be happened.

Keywords: Stress Intensity Factor, Mass Diffusion, FEM, Pressure Vessel

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Authors: Kasthurirangan Gopalakrishnan, Anshu Manik

Abstract:

Subgrade moisture content varies with environmental and soil conditions and has significant influence on pavement performance. Therefore, it is important to establish realistic estimates of expected subgrade moisture contents to account for the effects of this variable on predicted pavement performance during the design stage properly. The initial boundary soil suction profile for a given pavement is a critical factor in determining expected moisture variations in the subgrade for given pavement and climatic and soil conditions. Several numerical models have been developed for predicting water and solute transport in saturated and unsaturated subgrade soils. Soil hydraulic properties are required for quantitatively describing water and chemical transport processes in soils by the numerical models. The required hydraulic properties are hydraulic conductivity, water diffusivity, and specific water capacity. The objective of this paper was to determine isothermal moisture profiles in a soil fill and predict the soil moisture movement above the ground water table using a simple one-dimensional finite difference model.

Keywords: Fill, Hydraulic Conductivity, Pavement, Subgrade.

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Authors: Anuar Ishak

Abstract:

The mixed convection stagnation point flow toward a vertical plate is investigated. The external flow impinges normal to the heated plate and the surface temperature is assumed to vary linearly with the distance from the stagnation point. 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 mixed convection parameter. A stability analysis is performed to determine which solution is linearly stable and physically realizable.

Keywords: Dual solutions, heat transfer, mixed convection, stability analysis.

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Authors: Shuen-Tai Wang, Ying-Chuan Chen, Yu-Ching Lin

Abstract:

There has been renewal of interest in the relation between Green IT and cloud computing in recent years. Cloud computing has to be a highly elastic environment which provides stable services to users. The growing use of cloud computing facilities has caused marked energy consumption, putting negative pressure on electricity cost of computing center or data center. Each year more and more network devices, storages and computers are purchased and put to use, but it is not just the number of computers that is driving energy consumption upward. We could foresee that the power consumption of cloud computing facilities will double, triple, or even more in the next decade. This paper aims at resource allocation and scheduling technologies that are short of or have not well developed yet to reduce energy utilization in cloud computing platform. In particular, our approach relies on recalling services dynamically onto appropriate amount of the machines according to user’s requirement and temporarily shutting down the machines after finish in order to conserve energy. We present initial work on integration of resource and power management system that focuses on reducing power consumption such that they suffice for meeting the minimizing quality of service required by the cloud computing platform.

Keywords: Cloud computing, energy utilization, power consumption, resource allocation.

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Authors: Wen-Bao Qiao, Jean-Charles Créput

Abstract:

To accelerate the solution for large scale traveling salesman problems (TSP), a parallel 2-opt local search algorithm with simple implementation based on Graphics Processing Unit (GPU) is presented and tested in this paper. The parallel scheme is based on technique of data decomposition by dynamically assigning multiple K processors on the integral tour to treat K edges’ 2-opt local optimization simultaneously on independent sub-tours, where K can be user-defined or have a function relationship with input size N. We implement this algorithm with doubly linked list on GPU. The implementation only requires O(N) memory. We compare this parallel 2-opt local optimization against sequential exhaustive 2-opt search along integral tour on TSP instances from TSPLIB with more than 10000 cities.

Keywords: Doubly linked list, parallel 2-opt, tour division, GPU.

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Authors: Min Sun, Jing Liu

Abstract:

In this article, a new inexact alternating direction method(ADM) is proposed for solving a class of variational inequality problems. At each iteration, the new method firstly solves the resulting subproblems of ADM approximately to generate an temporal point ˜xk, and then the multiplier yk is updated to get the new iterate yk+1. In order to get xk+1, we adopt a new descent direction which is simple compared with the existing prediction-correction type ADMs. For the inexact ADM, the resulting proximal subproblem has closedform solution when the proximal parameter and inexact term are chosen appropriately. We show the efficiency of the inexact ADM numerically by some preliminary numerical experiments.

Keywords: variational inequality problems, alternating direction method, global convergence

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Authors: Tomáš Bakalár, Milan Búgel, Henrieta Pavolová

Abstract:

This study deals with evaluation of influence of salinity (NaCl) onto equilibrium of Cu and Ni removal from aqueous solutions by natural sorbent – zeolite. Equilibrium data were obtained by batch experiments. The salinity of the aqueous solution was influenced by dissolving NaCl in distilled water. It was studied in the range of NaCl concentrations from 1 g.l-1 to 100g.l-1. For Cu sorption there is a significant influence of salinity. The maximum capacity of zeolite for Cu was decreasing with growing concentration of NaCl. For Ni sorption there is not so significant influence of salinity as for Cu. The maximum capacity of zeolite for Ni was slightly decreasing with growing concentration of NaCl.

Keywords: Cu, Ni, sorption, zeolite.

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Authors: Aicha Rima Cheniti, Hatem Besbes, Joseph Haggege, Christophe Sintes

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In this paper, we consider a drift flux mixture model of the blood flow. The mixture consists of gas phase which is carbon dioxide and liquid phase which is an aqueous carbon dioxide solution. This model was used to determine the distributions of the mixture velocity, the mixture pressure, and the carbon dioxide pressure. These theoretical data are used to determine a measurement method of mean gas pressure through the determination of radial velocity distribution. This method can be applicable in experimental domain.

Keywords: Mean carbon dioxide pressure, mean mixture pressure, mixture velocity, radial velocity.

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Authors: G. B. Hong, H. W. Chen

Abstract:

Liquid-Liquid Equilibrium (LLE) data are measured for the ternary mixtures of water + 1-butanol + butyl acetate and quaternary mixtures of water + 1-butanol + butyl acetate + glycerol at atmospheric pressure at 313.15 K. In addition, isothermal vapor–liquid–liquid equilibrium (VLLE) data are determined experimentally at 333.15 K. The region of heterogeneity is found to increase as the hydrophilic agent (glycerol) is introduced into the aqueous mixtures. The experimental data are correlated with the NRTL model. The predicted results from the solution model with the model parameters determined from the constituent binaries are also compared with the experimental values.

Keywords: LLE, VLLE, hydrophilic agent, NRTL.

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Authors: Anuchita Moongngarm, John E. Bronlund, Nigel Grigg, Naruemon Sriwai

Abstract:

The study aimed to investigate the effect of rice types on chewing behaviours (chewing time, number of chews, and portion size) and bolus properties (bolus moisture content, solid loss, and particle size distribution (PSD)) in human subjects. Five cooked rice types including brown rice (BR), white rice (WR), parboiled white rice (PR), high amylose white rice (HR) and waxy white rice (WXR) were chewed by six subjects. The chewing behaviours were recorded and the food boluses were collected during mastication. Rice typeswere found to significantly influence all chewing parameters evaluated. The WXR and BR showed the most pronounced differences compared with other rice types. The initial moisture content of un-chewed WXR was lowest (43.39%) whereas those of other rice types were ranged from 66.86 to 70.33%. The bolus obtained from chewing the WXR contained lowest moisture content (56.43%) whilst its solid loss (22.03%) was not significant different from those of all rice types. In PSD evaluation using Mastersizer S, the diameter of particles measured was ranged between 4 to 3500 μm. The particle size of food bolus from BR, HR, and WXR contained much finer particles than those of WR and PR.

Keywords: Chewing behavior, Mastication, Rice, Rice types, Bolus properties

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Authors: Rajib Ul Alam Uzzal, Ion Stiharu, Waiz Ahmed

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This paper presents the modeling of a MEMS based accelerometer in order to detect the presence of a wheel flat in the railway vehicle. A haversine wheel flat is assigned to one wheel of a 5 DOF pitch plane vehicle model, which is coupled to a 3 layer track model. Based on the simulated acceleration response obtained from the vehicle-track model, an accelerometer is designed that meets all the requirements to detect the presence of a wheel flat. The proposed accelerometer can survive in a dynamic shocking environment with acceleration up to ±150g. The parameters of the accelerometer are calculated in order to achieve the required specifications using lumped element approximation and the results are used for initial design layout. A finite element analysis code (COMSOL) is used to perform simulations of the accelerometer under various operating conditions and to determine the optimum configuration. The simulated results are found within about 2% of the calculated values, which indicates the validity of lumped element approach. The stability of the accelerometer is also determined in the desired range of operation including the condition under shock.

Keywords: MEMS accelerometer, Pitch plane vehicle, wheel flat.

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Authors: O. A. Akinfenwa, N.M. Yao, S. N. Jator

Abstract:

In this paper, a self starting two step continuous block hybrid formulae (CBHF) with four Off-step points is developed using collocation and interpolation procedures. The CBHF is then used to produce multiple numerical integrators which are of uniform order and are assembled into a single block matrix equation. These equations are simultaneously applied to provide the approximate solution for the stiff ordinary differential equations. The order of accuracy and stability of the block method is discussed and its accuracy is established numerically.

Keywords: Collocation and Interpolation, Continuous HybridBlock Formulae, Off-Step Points, Stability, Stiff ODEs.

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Authors: Mohammed I. Ali, Feng Fan, Peter N. Khakina, Ma H.H

Abstract:

In construction of any structure, the aesthetic and utility values should be considered in such a way as to make the structure cost-effective. Most structures are composed of elements and joints which are very critical in any skeletal space structure because they majorly determine the performance of the structure. In early times, most space structures were constructed using rigid joints which had the advantage of better performing structures as compared to pin-jointed structures but with the disadvantage of requiring all the construction work to be done on site. The discovery of semi-rigid joints now enables connections to be prefabricated and quickly assembled on site while maintaining good performance. In this paper, cost-effective is discussed basing on strength of connectors at the joints, buckling of joints and overall structure, and the effect of initial geometrical imperfections. Several existing joints are reviewed by classifying them into categories and discussing where they are most suited and how they perform structurally. Also, finite element modeling using ABAQUS is done to determine the buckling behavior. It is observed that some joints are more economical than others. The rise to span ratio and imperfections are also found to affect the buckling of the structures. Based on these, general principles that guide the design of cost-effective joints and structures are discussed.

Keywords: Buckling, Connectors, Joint stiffness, Eccentricity, Second moment of area, Semi-rigid joints.

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Authors: A. Rouili

Abstract:

Cantilever L-shaped walls are known to be relatively economical as retaining solution. The design starts by proportioning the wall dimensions for which the stability is checked for. A ratio between the lengths of the base and the stem, falling between 0.5 to 0.7 ensure in most case the stability requirements, however, the displacement pattern of the wall in terms of rotations and translations, and the lateral pressure profile, do not have the same figure for all wall’s proportioning, as it is usually assumed. In the present work the results of a numerical analysis are presented, different wall geometries were considered. The results show that the proportioning governs the equilibrium between the instantaneous rotation and the translation of the wall-toe, also, the lateral pressure estimation based on the average value between the at-rest and the active pressure, recommended by most design standards, is found to be not applicable for all walls.

Keywords: Cantilever wall, proportioning, numerical analysis.

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Authors: Praloy Kumar Biswas, Prof. Dipanwita Roy Chowdhury

Abstract:

Grobner basis calculation forms a key part of computational commutative algebra and many other areas. One important ramification of the theory of Grobner basis provides a means to solve a system of non-linear equations. This is why it has become very important in the areas where the solution of non-linear equations is needed, for instance in algebraic cryptanalysis and coding theory. This paper explores on a parallel-distributed implementation for Grobner basis calculation over GF(2). For doing so Buchberger algorithm is used. OpenMP and MPI-C language constructs have been used to implement the scheme. Some relevant results have been furnished to compare the performances between the standalone and hybrid (parallel-distributed) implementation.

Keywords: Grobner basis, Buchberger Algorithm, Distributed- Parallel Computation, OpenMP, MPI.

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Authors: M. M. Bagheri, G. Doudak, M. Gong

Abstract:

The in-plane rigidity of light frame diaphragms has been investigated by researchers due to the importance of this subsystem regarding lateral force distribution between the lateral force resisting system (LFRS). Where research has lacked is in evaluating the impact of out-of-plane raigidity of the diaphragm on the deflection of shear walls. This study aims at investigating the effect of the diaphragm on the behavior of wood light-frame shear walls, in particular its out-of-plane rigidity was simulated by modeling the floors as beam. The out of plane stiffness of the diaphragm was investigated for idealized (infinitely stiff or flexible) as well as “realistic”. The results showed reductions in the shear wall deflection in the magnitude of approximately 80% considering the out of plane rigidity of the diaphragm. It was also concluded that considering conservative estimates of out-of-plane stiffness might lead to a very significant reduction in deflection and that assuming the floor diaphragm to be infinitely rigid out of plan seems to be reasonable. For diaphragms supported on multiple panels, further reduction in the deflection was observed. More work, particularly at the experimental level, is needed to verify the finding obtained in the numerical investigation related to the effect of out of plane diaphragm stiffness.

Keywords: Deflection of light-frame wood shear walls, out-of-plane stiffness of the diaphragm, initial stiffness.

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Authors: Nikola Karanovic, Aleksandar Djuric

Abstract:

This paper introduces a method of calculating the quantities of construction materials and construction waste on site in city of Novi Sad. In buildings is about 40% of the total weight of materials that are in circulation in the world economic space. The best solution for this waste is to be stored at source, at the point of generation. There are several treatment options for this type of waste, reduction at source, reuse, recycling. Beside its negative effects on the environment, construction waste can be and resource. Novi Sad is divided in 16 single family resident zones and 10 multi family resident zones. For every zone of the city, quantities of used construction materials and construction waste were obtained. Rational use of natural resources is an essential factor in applying the principles of development with savings.

Keywords: Construction materials, Construction waste, Novi Sad, Recycling

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Authors: Anita Kéri

Abstract:

Satisfying foreign student needs has been in the center of research interest in the past several years. Higher education institutions have been exploring factors influencing foreign student satisfaction to stay competitive on the educational market. Even though foreign student satisfaction and loyalty are topics investigated deeply in the literature, the academic years of 2020 and 2021 have revealed challenges never experienced before. With the COVID-19 pandemic, new factors have emerged that might influence foreign student satisfaction and loyalty in higher education. The aim of the current research is to shed lights on what factors influence foreign student satisfaction and loyalty in the post-pandemic educational era, and to reveal if the effects of factors influencing satisfaction and loyalty have changed compared to previous findings. Initial results show that students are less willing to participate in online surveys during and after the pandemic. The return rate of the survey instrument is below 5%. Results also reveal that there is a slight difference in what factors students deem important during pandemic times regarding their satisfaction and loyalty. The results of the current study help us determine what factors higher education institutions need to consider, when planning the future service affordances for their foreign students, that might influence their satisfaction and loyalty.

Keywords: COVID-19, foreign students, loyalty, pandemic, satisfaction.

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Authors: Raphael Zanella

Abstract:

This works deals with the finite element approximation of axisymmetric problems. The weak formulation of the heat equation under axisymmetry assumption is established for continuous finite elements. The weak formulation is implemented in a C++ solver with implicit time marching. The code is verified by space and time convergence tests using a manufactured solution. An example problem is solved with an axisymmetric formulation and with a 3D formulation. Both formulations lead to the same result but the code based on the axisymmetric formulation is mush faster due to the lower number of degrees of freedom. This confirms the correctness of our approach and the interest of using an axisymmetric formulation when it is possible.

Keywords: Axisymmetric problem, continuous finite elements, heat equation, weak formulation.

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Authors: Wen Po Cheng, Chi Hua Fu, Ping Hung Chen, Ruey Fang Yu

Abstract:

Recovering resources from water purification sludge (WPS) have been gradually stipulated in environmental protection laws and regulations in many nations. Hence, reusing the WPS is becoming an important topic, and recovering alum from WPS is one of the many practical alternatives. Most previous research efforts have been conducted on studying the amphoteric characteristic of aluminum hydroxide for investigating the optimum pH range to dissolve the Al(III) species from WPS, but it has been lack of reaction kinetics or mechanisms related discussion. Therefore, in this investigation, water purification sludge (WPS) solution was broken by ultrasound to make particle size of reactants smaller, specific surface area larger. According to the reaction kinetics, these phenomena let the dissolved aluminum salt quantity increased and the reaction rate go faster.

Keywords: Aluminum, Acidification, Sludge, Recovery.

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Authors: Hanieh Tarbiat Khosrowshahi, Mojtaba Shakeri

Abstract:

Wireless Sensor Networks (WSNs) consist of a set of sensor nodes with limited capability. WSNs may suffer from multiple node failures when they are exposed to harsh environments such as military zones or disaster locations and lose connectivity by getting partitioned into disjoint segments. Relay nodes (RNs) are alternatively introduced to restore connectivity. They cost more than sensors as they benefit from mobility, more power and more transmission range, enforcing a minimum number of them to be used. This paper addresses the problem of RN placement in a multiple disjoint network by developing a genetic algorithm (GA). The problem is reintroduced as the Steiner tree problem (which is known to be an NP-hard problem) by the aim of finding the minimum number of Steiner points where RNs are to be placed for restoring connectivity. An upper bound to the number of RNs is first computed to set up the length of initial chromosomes. The GA algorithm then iteratively reduces the number of RNs and determines their location at the same time. Experimental results indicate that the proposed GA is capable of establishing network connectivity using a reasonable number of RNs compared to the best existing work.

Keywords: Connectivity restoration, genetic algorithms, multiple-node failure, relay nodes, wireless sensor networks.

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Authors: Juyi Park, Jung-Min Kim, Hee-Hwan Park, Jin-Wook Kim, Gye-Hyung Kang, Soo-Ho Kim

Abstract:

This paper presents an iterative algorithm to find a inverse kinematic solution of 5-DOF robot. The algorithm is to minimize the iteration number. Since the 5-DOF robot cannot give full orientation of tool. Only z-direction of tool is satisfied while rotation of tool is determined by kinematic constraint. This work therefore described how to specify the tool direction and let the tool rotation free. The simulation results show that this algorithm effectively worked. Using the proposed iteration algorithm, error due to inverse kinematics converged to zero rapidly in 5 iterations. This algorithm was applied in real welding robot and verified through various practical works.

Keywords: 5-DOF manipulator, Inverse kinematics, Iterative algorithm, Wrist offset.

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Authors: Mehran Yazdi, Mehdi Seyfi, Amirhossein Rafati, Meghdad Asadi

Abstract:

Detection and tracking of the lip contour is an important issue in speechreading. While there are solutions for lip tracking once a good contour initialization in the first frame is available, the problem of finding such a good initialization is not yet solved automatically, but done manually. We have developed a new tracking solution for lip contour detection using only few landmarks (15 to 25) and applying the well known Active Shape Models (ASM). The proposed method is a new LMS-like adaptive scheme based on an Auto regressive (AR) model that has been fit on the landmark variations in successive video frames. Moreover, we propose an extra motion compensation model to address more general cases in lip tracking. Computer simulations demonstrate a fair match between the true and the estimated spatial pixels. Significant improvements related to the well known LMS approach has been obtained via a defined Frobenius norm index.

Keywords: Lip contour, Tracking, LMS-Like

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Authors: R. Kozik, A. Leśniak A., E. Plebankiewicz

Abstract:

Contracting authorities in the public sector are obligated to apply the principles provided for in the Polish law for the evaluation and selection of contractors. In order to analyse the methods of contractors selecting applied in practice by public clients, the notices of contract award results for construction works were analysed. The analysis shows that the procedure selected more and more often is open competitive bidding, where the assessment of the competence of contractors is not very precise, as well as noncompetitive bidding, i.e. single source procurement. The share of procurement procedures, where the only criterion is price, is increasing. The solution to the problems existing here might be the introduction of one of the forms of pre-selection of contractors. The article also briefly discusses verification systems for companies applying for public contracts used in EU countries.

Keywords: Certification, contractors selection, open tendering, public investors.

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Authors: Marco Antonio Cruz-Chávez, Juan Frausto-Solís, Fernando Ramos-Quintana

Abstract:

A procedure commonly used in Job Shop Scheduling Problem (JSSP) to evaluate the neighborhoods functions that use the non-deterministic algorithms is the calculation of the critical path in a digraph. This paper presents an experimental study of the cost of computation that exists when the calculation of the critical path in the solution for instances in which a JSSP of large size is involved. The results indicate that if the critical path is use in order to generate neighborhoods in the meta-heuristics that are used in JSSP, an elevated cost of computation exists in spite of the fact that the calculation of the critical path in any digraph is of polynomial complexity.

Keywords: Job Shop, CPM, critical path, neighborhood, meta-heuristic.

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Authors: Ambra Giovannelli, Erika Maria Archilei

Abstract:

The amount of the electrical power required by refrigeration systems is relevant worldwide. It is evaluated in the order of 15% of the total electricity production taking refrigeration and air-conditioning into consideration. For this reason, in the last years several energy saving techniques have been proposed to reduce the power demand of such plants. The paper deals with the development of an innovative internal recovery system for cryogenic cooling plants. Such a system consists in a Compressor-Expander Group (CEG) designed on the basis of the automotive turbocharging technology. In particular, the paper is focused on the design of the expander, the critical component of the CEG system. Due to the low volumetric flow entering the expander and the high expansion ratio, a commercial turbocharger expander wheel was strongly modified. It was equipped with a transonic nozzle, designed to have a radially inflow full admission. To verify the performance of such a machine and suggest improvements, two different set of nozzles have been designed and modelled by means of the commercial Ansys-CFX software. steady-state 3D CFD simulations of the second-generation prototype are presented and compared with the initial ones.

Keywords: Energy saving, organic fluids, radial turbine, refrigeration plant, vapor compression systems.

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Authors: Daesung Moon, Woo-Yong Choi, Kiyoung Moon

Abstract:

Fuzzy fingerprint vault is a recently developed cryptographic construct based on the polynomial reconstruction problem to secure critical data with the fingerprint data. However, the previous researches are not applicable to the fingerprint having a few minutiae since they use a fixed degree of the polynomial without considering the number of fingerprint minutiae. To solve this problem, we use an adaptive degree of the polynomial considering the number of minutiae extracted from each user. Also, we apply multiple polynomials to avoid the possible degradation of the security of a simple solution(i.e., using a low-degree polynomial). Based on the experimental results, our method can make the possible attack difficult 2192 times more than using a low-degree polynomial as well as verify the users having a few minutiae.

Keywords: Fuzzy vault, fingerprint recognition multiple polynomials.

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Authors: Alexander V. Libin, Manon Schladen, Assya Pascalev, Nawar Shara, Miriam Philmon, Yuri Millo, Joseph Verbalis

Abstract:

Chronic conditions carry with them strong emotions and often lead to charged relationships between patients and their health providers and, by extension, patients and health researchers. Persons are both autonomous and relational and a purely cognitive model of autonomy neglects the social and relational basis of chronic illness. Ensuring genuine informed consent in research requires a thorough understanding of how participants perceive a study and their reasons for participation. Surveys may not capture the complexities of reasoning that underlies study participation. Contradictory reasons for participation, for instance an initial claim of altruism as rationale and a subsequent claim of personal benefit (therapeutic misconception), affect the quality of informed consent. Individuals apply principles through the filter of personal values and lived experience. Authentic autonomy, and hence authentic consent to research, occurs within the context of patients- unique life narratives and illness experiences.

Keywords: ethical dilemmas, open source technology, patient education, psychology of decision making

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Authors: Yayun Hsu, Henry Horng-Shing Lu

Abstract:

This paper proposes a data-driven, biology-inspired neural segmentation method of 3D drosophila Brainbow images. We use Bayesian Sequential Partitioning algorithm for probabilistic modeling, which can be used to detect somas and to eliminate crosstalk effects. This work attempts to develop an automatic methodology for neuron image segmentation, which nowadays still lacks a complete solution due to the complexity of the image. The proposed method does not need any predetermined, risk-prone thresholds, since biological information is inherently included inside the image processing procedure. Therefore, it is less sensitive to variations in neuron morphology; meanwhile, its flexibility would be beneficial for tracing the intertwining structure of neurons.

Keywords: Brainbow, 3D imaging, image segmentation, neuron morphology, biological data mining, non-parametric learning.

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Authors: Jose William Porras Ferreira

Abstract:

This paper presents two solutions to the Fermat’s Last Theorem (FLT). The first one using some algebraic basis related to the Pythagorean theorem, expression of equations, an analysis of their behavior, when compared with power  and power  and using " the “Well Ordering Principle” of natural numbers it is demonstrated that in Fermat equation . The second one solution is using the connection between  and power  through the Pascal’s triangle or  Newton’s binomial coefficients, where de Fermat equation do not fulfill the first coefficient, then it is impossible that:

zⁿ=xⁿ+yⁿ for n>2 and (x, y, z) E Z⁺ - {0}

 

Keywords: Fermat’s Last Theorem, Pythagorean Theorem, Newton Binomial Coefficients, Pascal’s Triangle, Well Ordering Principle.

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