Search results for: AIMMS mathematical software

Authors: Yong-Kyu Jung

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The fast growth in information technology has led to de-mands to access/process data. CPSs heavily depend on the time of hardware/software operations and communication over the network (i.e., real-time/parallel operations in CPSs (e.g., autonomous vehicles). Since data processing is an im-portant means to overcome the issue confronting data management, reducing the gap between the technological-growth and the data-complexity and channel-bandwidth. An adaptive perpetual data approximation method is intro-duced to manage the actual entropy of the digital spectrum. An ADAC implemented as an accelerator and/or apps for servers/smart-connected devices adaptively rescales digital contents (avg.62.8%), data processing/access time/energy, encryption/decryption overheads in AI/ML applications (facial ID/recognition).

Keywords: adaptive codec, AI, ML, HPC, cyber-physical, cybersecurity

Procedia PDF Downloads 65

Authors: Abdelouaheb Rouabhi

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In order to study the plastic resource of structures, the elastic-plastic single degree of freedom model described by Prandtl diagram is widely used. The generalization of this model to tow degree of freedom beyond the scope of a simple rigid-plastic system allows investigating the plastic resource of structures under complex disproportionate by individual components of deformation (earthquake). This macro-model greatly increases the accuracy of the calculations carried out. At the same time, the implementation of the proposed macro-model calculations easier than the detailed dynamic elastic-plastic calculations existing software systems such as ANSYS.

Keywords: elastic-plastic, single degree of freedom model, rigid-plastic system, plastic resource, complex plastic deformation, macro-model

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Authors: Supattra Kanchanopast

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The purpose of this research is to develop and design a management information system for 7 eleven shop in Bangkok. The system was designed and developed to meet users’ requirements via the internet network by use of application software such as My SQL for database management, Apache HTTP Server for Web Server and PHP Hypertext Preprocessor for an interface between web server, database and users. The system was designed into two subsystems as the main system, or system for head office, and the branch system for branch shops. These consisted of three parts which are classified by user management as shop management, inventory management and Point of Sale (POS) management. The implementation of the MIS for the mini-mart shop, can lessen the amount of paperwork and reduce repeating tasks so it may decrease the capital of the business and support an extension of branches in the future as well.

Keywords: convenience store, the management information system, inventory management, 7 eleven shop

Procedia PDF Downloads 448

Authors: Ahmed A. Al-Mudhafar, Ali A. Abduljabar, Hayder Jawad Albattat

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This work suggests a new microwave resonator sensor (MRS) device for measuring the oil’s breakdown voltage of high voltage transformers. A precise high-sensitivity sensor is designed and manufactured based on a microstrip split ring resonator (SRR). To improve the sensor sensitivity, a RF amplifier of 30 dB gain is linked through a transmission line of 50Ω.The sensor operates at a microwave band (L) with a quality factor of 1.35x105 when it is loaded with an empty tube. In this work, the sensor has been tested with three samples of high voltage transformer oil of different ages (new, middle, and damaged) where the quality factor differs with each sample. A mathematical model was built to calculate the breakdown voltage of the transformer oils and the accuracy of the results was higher than 90%.

Keywords: active resonator sensor, oil breakdown voltage, transformers oils, quality factor

Procedia PDF Downloads 255

Authors: Constantinos Vayenas, Athanasios Fokas, Dimitrios Grigoriou

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We use special relativity to compute the inertial and thus gravitational mass of relativistic electron and muon neutrinos, and we find that, for neutrino kinetic energies above 150 MeV/c2, these masses are in the Planck mass range. Consequently, we develop a simple Bohr-type model using gravitational rather than electrostatic forces between the rotating neutrinos as the centripetal force in order to examine the bound rotational states formed by two or three such relativistic neutrinos. We find that the masses of the composite rotational structures formed, are in the meson and baryon mass ranges, respectively. These models contain no adjustable parameters and by comparing their predictions with the experimental values of the masses of protons and pions, we compute a mass of 0.0437 eV/c2 for the heaviest electron neutrino mass and of 1.1 x10-3 eV/c2 for the heaviest muon neutrino mass.

Keywords: geons, gravitational confinement, neutrino masses, special relativity

Procedia PDF Downloads 252

Authors: Mengjie Shen, Jianhua Wu, Chun Gan, Lifeng Zhang, Qingguo Sun

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Switching flux permanent magnet (SFPM) motor has doubly salient structure which lead to high torque ripple, and also has cogging torque as a permanent magnet motor. Torque ripple and cogging torque have impact on the motor performance. A novel stator structure SFPM motor is presented in this paper. A triangular shape silicon steel sheet is put in the stator slot to reduce the torque ripple, which will not deteriorate the cogging torque. The simulation of proposed motor is analyzed using 2-D finite element method (FEM) based on Ansoft and Simplorer software, and the result show a good performance of the proposed SFPM motor.

Keywords: switching flux permanent magnet (SFPM) motor, torque ripple, Ansoft, FEM

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Authors: Muna Tabuni

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The paper contains an investigation of the notion of Q algebras. A brief introduction to quantum mechanics is given, in that systems the state defined by a vector in a complex vector space H which have Hermitian inner product property. H may be finite or infinite-dimensional. In quantum mechanics, operators must be hermitian. These facts are saved by Lie algebra operators but not by those of quantum algebras. A Hilbert space H consists of a set of vectors and a set of scalars. Lie group is a differentiable topological space with group laws given by differentiable maps. A Lie algebra has been introduced. Q-algebra has been defined. A brief introduction to BCI-algebra is given. A BCI sub algebra is introduced. A brief introduction to BCK=BCH-algebra is given. Every BCI-algebra is a BCH-algebra. Homomorphism maps meanings are introduced. Homomorphism maps between two BCK algebras are defined. The mathematical formulations of quantum mechanics can be expressed using the theory of unitary group representations. A generalization of Q algebras has been introduced, and their properties have been considered. The Q- quantum algebra has been studied, and various examples have been given.

Keywords: Q-algebras, BCI, BCK, BCH-algebra, quantum mechanics

Procedia PDF Downloads 185

Authors: Mohammad Khodaei, Mahmood Meratien, Alireza Valanezhad, Serdar Pazarlioglu, Serdar Salman, Ikuya Watanabe

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Pore size and morphology plays a crucial role on mechanical properties of porous scaffolds. In this research, titanium scaffold was prepared using space holder technique. Sodium chloride and ammonium bicarbonate were utilized as spacer agent separately. The effect of the hardness of spacer on the cell morphology was investigated using scanning electron microscopy (SEM) and optical stereo microscopy. Image analyzing software was used to interpret the microscopic images quantitatively. It was shown that sodium chloride, due to its higher hardness, maintain its morphology during cold compaction, and cause better replication in porous scaffolds.

Keywords: Spacer, Titanium Scaffold, Pore Morphology, Space Holder Technique

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Authors: Sun Fan, Wu Xiaoguang, Fang Miaomiao, Wei Chi

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The degree of damage to the support is simulated by finite element software, and its influence on the static and dynamic effects of the bridge structure is analyzed. Four working conditions are selected for the study of bearing damage impact: the bearing is intact (condition 1), the bearing damage coefficient is 0.8 (condition 2), the bearing damage coefficient is 0.6 (condition 3), and the bearing damage coefficient is 0.4 (Working Condition 4). The effect value of the bridge structure under each working condition is calculated, and the simple-supported girder bridge and continuous girder bridge with typical spans are taken as examples to analyze the overall change of the bridge structure after the bearing completely fails.

Keywords: bridge bearing damage, dynamic response, finite element analysis, load conditions

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Authors: Sachin Kumar

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Fuzzy fractional diffusion equation is widely useful to depict different physical processes arising in physics, biology, and hydrology. The motive of this article is to deal with the fuzzy fractional diffusion equation. We study a mathematical model of fuzzy space-time fractional diffusion equation in which unknown function, coefficients, and initial-boundary conditions are fuzzy numbers. First, we find out a fuzzy operational matrix of Legendre polynomial of Caputo type fuzzy fractional derivative having a non-singular Mittag-Leffler kernel. The main advantages of this method are that it reduces the fuzzy fractional partial differential equation (FFPDE) to a system of fuzzy algebraic equations from which we can find the solution of the problem. The feasibility of our approach is shown by some numerical examples. Hence, our method is suitable to deal with FFPDE and has good accuracy.

Keywords: fractional PDE, fuzzy valued function, diffusion equation, Legendre polynomial, spectral method

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Authors: Edward Hage, Pieter Lietaert, Gabriel Abedrabbo

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Musculoskeletal disorders are an important category of work-related diseases. They are often caused by working in non-ergonomic postures and are preventable with proper workplace design, possibly including human-machine collaboration. This paper presents a methodology and a supporting software prototype to design a simple assembly cell with minimal ergonomic risk. The methodology helps to determine the optimal position and orientation of workpieces and workplace resources for specific operator assembly actions. The methodology is tested on an industrial use case: a collaborative robot (cobot) assisted assembly of a clamping device. It is shown that the automated methodology results in a workplace design with significantly reduced ergonomic risk to the operator compared to a manual design of the cell.

Keywords: ergonomics optimization, design for ergonomics, workplace design, pose generation

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Authors: Talal Hasan, Akram Mohammad

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Carbon-free combustion has great attention in today’s research for its unlimited benefits regarding various factors, and ammonia is considered a potential carbon-free alternative gas despite its flame characteristics. The Shrestha mechanism and Chemkin-Pro software will be used for numerical data. Firstly, experimental and numerical results should show good agreement to move for studying the laminar flame speed of ammonia under various conditions. Ammonia flame speed will be investigated under normal conditions (298 K, 1 atm) as well as under the influence of a range of equivalence ratios (0.6-1.8), elevated temperatures (298,323,373,423, and 473), elevated pressures (1 atm- 70 atm) and finally at varying hydrogen content (0-100%). Therefore, this work will understand the ammonia laminar flame speed characteristics and how and to what extent hydrogen can improve ammonia combustion intensity.

Keywords: laminar burning velocity, ammonia, hydrogen, combustion

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Authors: Han Joo Choe, Soon-Ho Kwon, Jung-Joong Lee

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Tin particles of various size and distribution were self-assembled by plasma treating tin film deposited on silicon oxide substrates. Plasma treatment was conducted using an inductively coupled plasma (ICP) source. A range of ICP power and topographic templated substrates were evaluated to observe changes in particle size and particle distribution. Scanning electron microscopy images of the particles were analyzed using computer software. The evolution of tin film dewetting into particles initiated from the hole nucleation in grain boundaries. Increasing ICP power during plasma treatment produced larger number of particles per area and smaller particle size and particle-size distribution. Topographic templates were also effective in positioning and controlling the size of the particles. By combining the effects of ICP power and topographic templates, particles of similar size and well-ordered distribution were obtained.

Keywords: dewetting, particles, plasma, tin

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Authors: Hameed B. Mahood, Ali Sh. Baqir

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Vaporization of a single n-pentane drop in a direct contact with another flowing immiscible liquid (warm water) has been experimentally investigated. The experiments were carried out utilising a cylindrical Perspex tube of diameter 10 cm and height and 150 cm. Saturated liquid n-pentane and warm water at 45oC were used as the dispersed and continuous phases, respectively. Photron FASTCAM SA 1.1high speed camera (75,000f/s) with software V. 321 was implemented during the experiments. Five different continuous phase flow rates (warm water) (10, 20, 30, 40, and 46 L⁄h) were used in the study. The results indicated that the increase of the continuous phase (warm water) flow rate results in increasing of the drop/bubble diameter.

Keywords: drop evaporation, direct contact heat transfer, drop/bubble growth, experimental technique

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Authors: A. Ghenaim, A. Terfous

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In this work, degradation phenomena in fluvial beds having uniform sediments are explored experimentally under extreme flow conditions. Laboratory experiments were conducted in a rectangular cross-section channel for different flow conditions, channel characteristics, and sediment properties at the National Institute of Applied Sciences (Strasbourg, France). Tests were carried out in two conditions: (1) equilibrium condition, where, once the steady and uniform flow conditions were achieved for a given slope and discharge, the channel was fed with variable sediment discharges until the bed-load sediment transport achieved an equilibrium condition; and (2) nonequilibrium condition, where the sediment feeding was instantaneously stopped, and the bed levels were measured over time. Experimental results enabled assessing the erosion rates and determining the empirical mathematical model to predict the bed level changes.

Keywords: fluvial beds, sediment, uniform flow conditions, nonequilibrium condition, sediment disposition, erosion

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Authors: Rutusha Bhutada, Gaurav Chavan, Sarvesh Kasat, Varsha Mujumdar

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This software system will be an Augmented Reality application designed to maximize the doctor’s productivity by providing tools to assist in automating the patient recognition and updating patient’s records using face and voice recognition features, which would otherwise have to be performed manually. By maximizing the doctor’s work efficiency and production, the application will meet the doctor’s needs while remaining easy to understand and use. More specifically, this application is designed to allow a doctor to manage his productive time in handling the patient without losing eye-contact with him and communicate with a group of other doctors for consultation, for in-place treatments through video streaming, as a video study. The system also contains a relational database containing a list of doctor, patient and display techniques.

Keywords: augmented reality, hand-held devices, head-mounted devices, marker based systems, speech recognition, face detection

Procedia PDF Downloads 422

Authors: Emmanuel Omokhuale

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A mathematical model is presented to study free convective boundary layer flow in a semi-infinite vertical cylinder with heat sink effect in a porous medium. The governing dimensional governing partial differential equations (PDEs) with corresponding initial and boundary conditions are approximated and solved numerically employing finite difference method (FDM) the implicit type. Stability and convergence of the scheme are also established. Furthermore, the influence of significant physical parameters on the flow characteristics was analysed and shown graphically. The obtained results are benchmarked with previously published works in order to access the accuracy of the numerical method and found to be in good agreement.

Keywords: free convection flow, vertical cylinder, implicit finite difference method, heat sink and porous medium

Procedia PDF Downloads 127

Authors: O. S. Omorogiuwa, E. J. Omozusi

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The monitoring of spectrum usage and signal identification, using cognitive radio, is done to identify frequencies that are vacant for reuse. It has been established that ‘internet of things’ device uses secondary frequency which is free, thereby facing the challenge of interference from other users, where some primary frequencies are not being utilised. The design was done by analysing a specific frequency spectrum, checking if all the frequency stations that range from 87.5-108 MHz are presently being used in Benin City, Edo State, Nigeria. From the results, it was noticed that by using Software Defined Radio/Simulink, we were able to identify vacant frequencies in the range of frequency under consideration. Also, we were able to use the significance of energy detection threshold to reuse this vacant frequency spectrum, when the cognitive radio displays a zero output (that is decision H0), meaning that the channel is unoccupied. Hence, the analysis was able to find the spectrum hole and identify how it can be reused.

Keywords: spectrum, interference, telecommunication, cognitive radio, frequency

Procedia PDF Downloads 213

Authors: H. Medoukali, B. Zegnini

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Insulation techniques in high-voltage cables rely heavily on chemically synapsed polyethylene. The latter may contain manufacturing defects such as small cavities, for example. The presence of the cavity affects the distribution of the electric field at the level of the insulating layer; this change in the electric field is affected by the presence of different space charge densities within the insulating material. This study is carried out by performing simulations to determine the distribution of the electric field inside the insulator. The simulations are based on the creation of a two-dimensional model of a high-voltage cable of 154 kV using the COMSOL Multiphysics software. Each time we study the effect of changing the space charge density of on the electromechanical Constraints.

Keywords: COMSOL multiphysics, electric field, HVDC, microcavities, space charges, XLPE

Procedia PDF Downloads 115

Authors: Abdelazim Makki Ibrahim, Esamaldeen Ali

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This study aims at analysing the load settlement behavior and predict the bearing capacity of piled raft foundation a series of finite element models with different foundation configurations and stiffness were established. Numerical modeling is used to study the behavior of the piled raft foundation due to the complexity of piles, raft, and soil interaction and also due to the lack of reliable analytical method that can predict the behavior of the piled raft foundation system. Simple analytical models are developed to predict the average settlement and the load sharing between the piles and the raft in piled raft foundation system. A simple example to demonstrate the applications of these charts is included.

Keywords: finite element, pile-raft foundation, method, PLAXIS software, settlement

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Authors: Ravi Raj, Louis Chiu, Deepak Marla, Aijun Huang

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Hybridization of the directed laser deposition (DLD) process using an in-situ micro-roller to impart a vertical compressive load on the deposited bead at elevated temperatures can relieve tensile residual stresses incurred in the process. To investigate this stress relief mechanism and its relationship with the in-situ rolling parameters, a fully coupled dynamic thermo-mechanical model is presented in this study. A single bead deposition of Ti-6Al-4V alloy with an in-situ roller made of mild steel moving at a constant speed with a fixed nominal bead reduction is simulated using the explicit solver of the finite element software, Abaqus. The thermal model includes laser heating during the deposition process and the heat transfer between the roller and the deposited bead. The laser heating is modeled using a moving heat source with a Gaussian distribution, applied along the pre-formed bead’s surface using the VDFLUX Fortran subroutine. The bead’s cross-section is assumed to be semi-elliptical. The interfacial heat transfer between the roller and the bead is considered in the model. Besides, the roller is cooled internally using axial water flow, considered in the model using convective heat transfer. The mechanical model for the bead and substrate includes the effects of rolling along with the deposition process, and their elastoplastic material behavior is captured using the J2 plasticity theory. The model accounts for strain, strain rate, and temperature effects on the yield stress based on Johnson-Cook’s theory. Various aspects of this material behavior are captured in the FE software using the subroutines -VUMAT for elastoplastic behavior, VUHARD for yield stress, and VUEXPAN for thermal strain. The roller is assumed to be elastic and does not undergo any plastic deformation. Also, contact friction at the roller-bead interface is considered in the model. Based on the thermal results of the bead, the distance between the roller and the deposition nozzle (roller o set) can be determined to ensure rolling occurs around the beta-transus temperature for the Ti-6Al-4V alloy. It is identified that roller offset and the nominal bead height reduction are crucial parameters that influence the residual stresses in the hybrid process. The results obtained from a simulation at roller offset of 20 mm and nominal bead height reduction of 7% reveal that the tensile residual stresses decrease to about 52% due to in-situ rolling throughout the deposited bead. This model can be used to optimize the rolling parameters to minimize the residual stresses in the hybrid DLD process with in-situ micro-rolling.

Keywords: directed laser deposition, finite element analysis, hybrid in-situ rolling, thermo-mechanical model

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Authors: Kholod Hajo

Abstract:

In this study COMSOL Multiphysics was used to design lateral flow biosensors (LFBs) which provide advantages in low cost, simplicity, rapidity, stability and portability thus making LFBs popular in biomedical, agriculture, food and environmental sciences. This study was focused on simulation model of biosensor based on gold nanoparticles (GNPs) designed using software package (COMSOL Multiphysics), the magnitude of the laminar velocity field in the flow cell, concentration distribution in the analyte stream and surface coverage of adsorbed species and average fractional surface coverage of adsorbed analyte were discussed from the model and couples of suggestion was given in order to functionalize GNPs and to increase the accuracy of the biosensor design, all above were obtained acceptable results.

Keywords: model, gold nanoparticles, biosensor, COMSOL Multiphysics

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Authors: A. M. Sagir

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The aim of this paper is to investigate the performance of the developed linear multistep block method for solving first order initial value problem of Ordinary Differential Equations (ODEs). The method calculates the numerical solution at three points simultaneously and produces three new equally spaced solution values within a block. The continuous formulations enable us to differentiate and evaluate at some selected points to obtain three discrete schemes, which were used in block form for parallel or sequential solutions of the problems. A stability analysis and efficiency of the block method are tested on ordinary differential equations involving practical applications, and the results obtained compared favorably with the exact solution. Furthermore, comparison of error analysis has been developed with the help of computer software.

Keywords: block method, first order ordinary differential equations, linear multistep, self-starting

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Authors: Aleksandar Dedic, Dusko Salemovic, Milorad Danilovic, Radomir Kuzmanovic

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This paper takes into consideration the influence of bonding energy of water on energy demand of vacuum wood drying using the specific method of obtaining sorption isotherms. The experiment was carried out on oak wood at vacuum pressures of: 0.7 bar, 0.5bar and 0.3bar. The experimental work was done to determine a mathematical equation between the moisture content and energy of water-bonding. This equation helps in finding the average amount of energy of water-bonding necessary in calculation of energy consumption by use of the equation of heat balance in real drying chambers. It is concluded that the energy of water-bonding is large enough to be included into consideration. This energy increases at lower values of moisture content, when drying process approaches to the end, and its average values are lower on lower pressure.

Keywords: bonding energy, drying, isosters, oak, vacuum

Procedia PDF Downloads 259

Authors: Ahmed Amin Mousa, M. Abd El Salam

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The current study presents a proposed program for acquisition the skills and techniques needed to produce concept cartoon. The proposed program has been prepared for non-specialist students who have never used neither graphics nor animating software. It was presented to postgraduates in Faculty of Education for Early Childhood, Cairo University, during the spring term of the 2014-2015 academic year. The program works in three different aspects: Drawing and images editing, sound manipulation, and creating animation. In addition, the researchers have prepared a questionnaire for measuring the quality of the concept cartoons produced by the students. The questionnaire was used as a pre-test and post-test, and at the end of the study, a significant difference was determined in favour of post-test results.

Keywords: cartoon, concept cartoon, kindergarten, animation

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Authors: Shruti Soudi, Anushka Nayak

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Altruism is a voluntary helping behavior that is not motivated by rewards. The empathy-altruism hypothesis states that altruistic behavior results from empathy, a constant emotional response between the helper and the individual in need. Individual variances in familiar ways of thinking, feeling, and acting are called personalities. The personality of an individual determines their behavior. More importantly, Adler was among the first psychologists to document the importance of birth order on personality. The present study aims to understand the influence of personality and birth order on altruism. A questionnaire consisting of standardized tools to measure altruism (Hindi Self Report Altruism Scale) and personality (Big Five Personality Inventory) will aid in studying the relationship between these variables among young adults in India. A statistical analysis of the data will be completed using ANOVA and T-Test in the SPSS Software.

Keywords: altruism, personality, birth order, ANOVA, young adults

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Authors: Mustapha Mahmoud Dif, Fouzia Benali-Toumi, Mohamed Benyahia, Sofiane Bouazza, Abbes Dellal, Slimane Baha

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L. multifida is applied to treat rheumatism and cold and has hypoglycemic and anti-inflammatory properties. The present study is to optimize the extraction of phenolic compounds in Algerian Lavandula multifida. The influences of parameters including temperature (decoction and maceration) and extraction time (15min to 45 min) on the flavonoids concentration are studied. The optimal conditions are determined and the quadratic response surfaces draw from the mathematical models. Total phenols were evaluated using Folin sicaltieu methods, total flavonoids were estimated using the Tri chloral aluminum method. The maximum concentration extracted, for total flavonoids, equal to 0.043 mg/g was achieved with decoction and extraction time of 41.55 min. However, for total phenol compounds highest concentration of 0.218 mg/g, is obtained with 45 min at 49.99°C.

Keywords: L multifidi, phenolic content, optimization, time, temperature

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Authors: Hayrettin Eroglu, Adem Kara

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Recently there has been significant attention given to imaging of the biological tissues via microwave imaging techniques. In this study, a phantom for the test and calibration of Microwave imaging used in detecting unhealthy breast structure or tumors was produced by using sol gel method. The liquid and gel phantoms being used nowadays are not durable due to evaporation and their organic ingredients, hence a new design was proposed. This phantom was fabricated from materials that were widely available (water, salt, gelatin, and glycerol) and was easy to make. This phantom was aimed to be better from the ones already proposed in the literature in terms of its durability and stability. S Parameters of phantom was measured with 1-18 GHz Probe Kit and permittivity was calculated via Debye method in “85070” commercial software. One, three, and five-week measurements were taken for this phantom. Finally, it was verified that measurement results were very close to the real biological tissue measurement results.

Keywords: phantom, breast tissue, cancer, microwave imaging

Procedia PDF Downloads 335

Authors: Luis Javier Serrano Tamayo

Abstract:

This research on technology makes a first approach to the selection of an amphibious landing ship with strategic capabilities, through the implementation of a multi-criteria model using Analytical Hierarchical Process (AHP), in which a significant group of alternatives of latest technology has been considered. The variables were grouped at different levels to match design and performance characteristics, which affect the lifecycle as well as the acquisition, maintenance and operational costs. The model yielded an overall measure of effectiveness and an overall measure of cost of each kind of ship that was compared each other inside the model and showed in a Pareto chart. The modeling was developed using the Expert Choice software, based on AHP method.

Keywords: analytic hierarchy process, multi-criteria decision-making, Pareto analysis, Colombian Marine Corps, projection operations, expert choice, amphibious landing ship

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Authors: Edward J. Kansa, Pavel Holoborodko

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Continuously differentiable radial basis functions (RBFs) are meshfree, converge faster as the dimensionality increases, and is theoretically spectrally convergent. When implemented on current single and double precision computers, such RBFs can suffer from ill-conditioning because the systems of equations needed to be solved to find the expansion coefficients are full. However, the Advanpix extended precision software package allows computer mathematics to resemble asymptotically ideal Platonic mathematics. Additionally, full systems with extended precision execute faster graphical processors units and field-programmable gate arrays because no branching is needed. Sparse equation systems are fast for iterative solvers in a very limited number of cases.

Keywords: partial differential equations, Meshfree radial basis functions, , no restrictions on spatial dimensions, Extended arithmetic precision.

Procedia PDF Downloads 137