Search results for: break point

Authors: Yuhei Kunihiro, Sorin V. Sabau, Kazuhiro Shibuya

Abstract:

We study the molecular evolution of insulin from the metric geometry point of view. In mathematics, and particularly in geometry, distances and metrics between objects are of fundamental importance. Using a weaker notion than the classical distance, namely the weighted quasi-metrics, one can study the geometry of biological sequences (DNA, mRNA, or proteins) space. We analyze from the geometrical point of view a family of 60 insulin homologous sequences ranging on a large variety of living organisms from human to the nematode C. elegans. We show that the distances between sequences provide important information about the evolution and function of insulin.

Keywords: metric geometry, evolution, insulin, C. elegans

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Authors: K. Khaerunnisa, D. Ryangga, S. A. Pawiro

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Over the past few decades, film dosimetry has become a tool which is used in various radiotherapy modalities, either for clinical quality assurance (QA) or dose verification. The response of the film to irradiation is usually expressed in optical density (OD) or net optical density (netOD). While the film's response to radiation is not linear, then the use of film as a dosimeter must go through a calibration process. This study aimed to compare the function of the calibration curve of various measurement methods with various densitometer, using a flat bad scanner, point densitometer and spectrophotometer. For every response function, a radichromic film calibration curve is generated from each method by performing accuracy, precision and sensitivity analysis. netOD is obtained by measuring changes in the optical density (OD) of the film before irradiation and after irradiation when using a film scanner if it uses ImageJ to extract the pixel value of the film on the red channel of three channels (RGB), calculate the change in OD before and after irradiation when using a point densitometer, and calculate changes in absorbance before and after irradiation when using a spectrophotometer. the results showed that the three calibration methods gave readings with a netOD precision of doses below 3% for the uncertainty value of 1σ (one sigma). while the sensitivity of all three methods has the same trend in responding to film readings against radiation, it has a different magnitude of sensitivity. while the accuracy of the three methods provides readings below 3% for doses above 100 cGy and 200 cGy, but for doses below 100 cGy found above 3% when using point densitometers and spectrophotometers. when all three methods are used for clinical implementation, the results of the study show accuracy and precision below 2% for the use of scanners and spectrophotometers and above 3% for precision and accuracy when using point densitometers.

Keywords: Callibration Methods, Film Dosimetry EBT3, Flat Bad Scanner, Densitomete, Spectrophotometer

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Authors: S. Masoud Barakati, Mohsen Rahmani Haredasht

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Recently, the use of T-type nested neutral point clamped (T-NNPC) converter has increased in medium voltage applications. However, the T-NNPC converter architecture's reliability and continuous operation are at risk by including semiconductor switches. Semiconductor switches are a prone option for open-circuit faults. As a result, fault-tolerant converters are required to improve the system's reliability and continuous functioning. This study's primary goal is to provide a fault-tolerant T-NNPC converter configuration. In the proposed design utilizing the cold reservation approach, a redundant phase is considered, which replaces the faulty phase once the fault is diagnosed in each phase. The suggested fault-tolerant configuration can be easily implemented in practical applications due to the use of a simple PWM control mechanism. The performance evaluation of the proposed configuration under different scenarios in the MATLAB-Simulink environment proves its efficiency.

Keywords: T-type nested neutral point clamped converter, reliability, continuous operation, open-circuit faults, fault-tolerant converters

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Authors: Wafa Halfaoui Mbarek, Khir Tahar, Ben Brahim Ammar

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This study reports a comparison from an exergetic point of view between three configurations of vapor compression industrial refrigeration systems operating with R134a as working fluid. The performances of the different cycles are analyzed as function of several operating parameters such as condensing temperature and inter stage pressure. In addition, the contributions of component exergy destruction to the total exergy destruction are obtained for each system. The results are estimated to be used in the selection of the most advantageous configuration from an exergetic view point.

Keywords: vapor compression, exergy, destruction, efficiency, R134a

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Authors: Alemayehu Geremew Geremew

Abstract:

We prove the weak convergence of Mann iteration for a hybrid pair of maps to a common fixed point of a selfmap f and a multivalued f nonexpansive mapping T in Banach space E.

Keywords: common fixed point, Mann iteration, multivalued mapping, weak convergence

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Authors: Nabil Beroual, Tewfik Sari

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We consider the Gause-type predator-prey system in the case where the response function is not smooth at the origin. We discuss the conditions under which this system has exactly one stable limit cycle or has a positive stable equilibrium point, and we describe the basin of attraction of the stable limit cycle and the stable equilibrium point, respectively. Our results correct previous results of the existing literature.

Keywords: predator-prey model, response function, singularity, basin of attraction, limit cycle

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Authors: Shahid Hussain Abro, Siamak Zohari, Lena H. M. Renström, Désirée S. Jansson, Faruk Otman, Karin Ullman, Claudia Baule

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Infectious bronchitis is an acute, highly contagious respiratory, nephropathogenic and reproductive disease of poultry that is caused by infectious bronchitis virus (IBV). The present study used a large data set of structural gene sequences, including newly generated ones and sequences available in the GenBank database to further analyze the diversity and to identify selective pressures and recombination spots. There were some deletions or insertions in the analyzed regions in isolates of the Italy-02 and D274 genotypes. Whereas, there were no insertions or deletions observed in the isolates of the Massachusetts and 4/91 genotype. The hypervariable nucleotide sequence regions spanned positions 152–239, 554–582, 686–737 and 802–912 in the S1 sub-unit of the all analyzed genotypes. The nucleotide sequence data of the E gene showed that this gene was comparatively unstable and subjected to a high frequency of mutations. The M gene showed substitutions consistently distributed except for a region between nucleotide positions 250–680 that remained conserved. The lowest variation in the nucleotide sequences of ORF5a was observed in the isolates of the D274 genotype. While, ORF5b and N gene sequences showed highly conserved regions and were less subjected to variation. Genes ORF3a, ORF3b, M, ORF5a, ORF5b and N presented negative selective pressure among the analyzed isolates. However, some regions of the ORFs showed favorable selective pressure(s). The S1 and E proteins were subjected to a high rate of mutational substitutions and non-synonymous amino acids. Strong signals of recombination breakpoints and ending break point were observed in the S and N genes. Overall, the results of this study revealed that very likely the strong selective pressures in E, M and the high frequency of substitutions in the S gene can probably be considered the main determinants in the evolution of IBV.

Keywords: IBV, avian infectious bronchitis, structural genes, genotypes, genetic diversity

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Authors: V. Sankaranarayanan, V. Amrita Sundari, Sunit P. Gopal

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This paper presents the design and implementation of a nonlinear controller for the point to point control of a mobile inverted pendulum (MIP). The controller is designed based on the kinematic model of the MIP to stabilize all the four coordinates. The stability of the closed-loop system is proved using Lyapunov stability theory. The proposed controller is validated through numerical simulations and also implemented in a laboratory prototype. The results are presented to evaluate the performance of the proposed closed loop system.

Keywords: mobile inverted pendulum, switched control, nonlinear systems, lyapunov stability

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Authors: Hudson Akewe

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We prove that the convergence of explicit Mann, explicit Ishikawa, explicit Noor, explicit SP, explicit multistep and explicit multistep-SP fixed point iterative procedures are equivalent for the classes of multi-valued phi-contraction, phi-Zamfirescu and phi-quasi-contractive mappings in the framework of modular function spaces. Our results complement equivalence results on normed and metric spaces in the literature as they elegantly cut out the triangle inequality.

Keywords: multistep iterative procedures, multivalued mappings, equivalence results, fixed point

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Authors: Gaosheng Ju

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Our empirical evidence supports a model of consumption planning behaviors with the following two characteristics. First, households formulate a rational consumption target based on their desired target, displaying a diminishing sensitivity to the discrepancy between them. Second, the established target is a reference point for their planned consumption. The diminishing sensitivity leads to opposite reactions in higher and lower quantiles of both consumption targets and consumption growth to changes in economic conditions. This phenomenon accounts for the perplexingly low correlation between consumption and other macroeconomic variables. Furthermore, the opposing movements of consumption targets offer new insights into consumption-based asset pricing.

Keywords: consumption planning, reference point, diminishing sensitivity, quantile regression, asset pricing puzzles

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Authors: M. A. Sedghamiz, S. Raeissi

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This study presents three different approaches to estimate bubble point pressures for the binary system of CO2 and ethyl palmitate fatty acid ethyl ester. The first method involves the Peng-Robinson (PR) Equation of State (EoS) with the conventional mixing rule of Van der Waals. The second approach involves the PR EOS together with the Wong Sandler (WS) mixing rule, coupled with the Uniquac Ge model. In order to model the bubble point pressures with this approach, the volume and area parameter for ethyl palmitate were estimated by the Hansen group contribution method. The last method involved the Peng-Robinson, combined with the Wong-Sandler Method, but using NRTL as the GE model. Results using the Van der Waals mixing rule clearly indicated that this method has the largest errors among all three methods, with errors in the range of 3.96–6.22 %. The Pr-Ws-Uniquac method exhibited small errors, with average absolute deviations between 0.95 to 1.97 percent. The Pr-Ws-Nrtl method led to the least errors where average absolute deviations ranged between 0.65-1.7%.

Keywords: bubble pressure, Gibbs excess energy model, mixing rule, CO2 solubility, ethyl palmitate

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Authors: Kapse Swapnil, K. Shankar

Abstract:

Aiming at optimizing the weight and deflection of cantilever beam subjected to maximum stress and maximum deflection, Multi-objective Particle Swarm Optimization (MOPSO) with Utopia Point based local search is implemented. Utopia point is used to govern the search towards the Pareto Optimal set. The elite candidates obtained during the iterations are stored in an archive according to non-dominated sorting and also the archive is truncated based on least crowding distance. Local search is also performed on elite candidates and the most diverse particle is selected as the global best. This method is implemented on standard test functions and it is observed that the improved algorithm gives better convergence and diversity as compared to NSGA-II in fewer iterations. Implementation on practical structural problem shows that in 5 to 6 iterations, the improved algorithm converges with better diversity as evident by the improvement of cantilever beam on an average of 0.78% and 9.28% in the weight and deflection respectively compared to NSGA-II.

Keywords: Utopia point, multi-objective particle swarm optimization, local search, cantilever beam

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Authors: Andrey V. Osipov, Sergey A. Kukushkin, Andrey V. Luk’yanov

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A method is developed for the solid-phase synthesis of epitaxial layers when the substrate itself is involved into a topochemical reaction and the reaction product grows in the interior of substrate layer. It opens up new possibilities for the relaxation of the elastic energy due to the attraction of point defects formed during the topochemical reaction in anisotropic media. The presented method of silicon carbide (SiC) formation employs a topochemical reaction between the single-crystalline silicon (Si) substrate and gaseous carbon monoxide (CO). The corresponding theory of interaction of point dilatation centers in anisotropic crystals is developed. It is eliminated that the most advantageous location of the point defects is the direction (111) in crystals with cubic symmetry. The single-crystal SiC films with the thickness up to 200 nm have been grown on Si (111) substrates owing to the topochemical reaction with CO. Grown high-quality single-crystal SiC films do not contain misfit dislocations despite the huge lattice mismatch value of ~20%. Also the possibility of growing of thick wide-gap semiconductor films on these templates SiC/Si(111) and, accordingly, its integration into Si electronics, is demonstrated. Finally, the ab initio theory of SiC formation due to the topochemical reaction has been developed.

Keywords: epitaxy, silicon carbide, topochemical reaction, wide-bandgap semiconductors

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Authors: Jiahe Liu, HongyangYu, Feng Qian, Miao Luo

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The aim of this study was to improve the effects of human body 3D reconstruction. The MvP algorithm was adopted to obtain key point information from multiple perspectives. This algorithm allowed the capture of human posture and joint positions from multiple angles, providing more comprehensive and accurate data. The study also incorporated the SMPL-X model, which has been widely used for human body modeling, to achieve more accurate 3D reconstruction results. The use of the MvP algorithm made it possible to observe the reconstructed object from multiple angles, thus reducing the problems of blind spots and missing information. This algorithm was able to effectively capture key point information, including the position and rotation angle of limbs, providing key data for subsequent 3D reconstruction. Compared with traditional single-view methods, the method of multi-view fusion significantly improved the accuracy and stability of reconstruction. By combining the MvP algorithm with the SMPL-X model, we successfully achieved better human body 3D reconstruction effects. The SMPL-X model is highly scalable and can generate highly realistic 3D human body models, thus providing more detail and shape information.

Keywords: 3D human reconstruction, multi-view, joint point, SMPL-X

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Authors: Mai Al-Subaie

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This research suggests that women in traditional families of Saudi Arabia are divided into two groups, the one who conform to the society and the new type of women that has been emerged due to the changing and development of the culture, who do not want to conform to the rules. The factors underlying the differences were explored by using a test and an interview. That concluded some of the main factors that were a real effect of why some women still want to follow the society and traditional rules, and other want to break free.

Keywords: conformity, non conformity, females, Saudi Arabia

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Authors: Diqin Qi, Jiaming Li, Siman Li

Abstract:

Based on the use of the three-point smoothing method for selectively processing original data columns, this paper establishes a group of grey GM(1,1) models to predict the concentration ranges of four major air pollutants in Shanghai from 2023 to 2024. The results indicate that PM₁₀, SO₂, and NO₂ maintain the national Grade I standards, while the concentration of PM₂.₅ has decreased but still remains within the national Grade II standards. Combining the forecast results, recommendations are provided for the Shanghai municipal government's efforts in air pollution prevention and control.

Keywords: atmospheric pollutant prediction, Grey GM(1, 1), model group, three-point smoothing method

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Authors: F. M. Ali, R. Nazar, N. M. Arifin, I. Pop

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In this paper, the problem of unsteady stagnation-point flow and heat transfer induced by a shrinking sheet in the presence of radiation effect is studied. The transformed boundary layer equations are solved numerically by the shooting method. The influence of radiation, unsteadiness and shrinking parameters, and the Prandtl number on the reduced skin friction coefficient and the heat transfer coefficient, as well as the velocity and temperature profiles are presented and discussed in detail. It is found that dual solutions exist and the temperature distribution becomes less significant with radiation parameter.

Keywords: heat transfer, radiation effect, shrinking sheet unsteady flow

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Authors: Ashkan Golgoon, Arash Yavari

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In this paper, we present some analytical solutions for the stress fields of nonlinear anisotropic solids with line and point defects distributions. In particular, we determine the induced stress fields of a parallel cylindrically-symmetric distribution of screw dislocations in infinite orthotropic and monoclinic media as well as a cylindrically-symmetric distribution of parallel wedge disclinations in an infinite orthotropic medium. For a given distribution of edge dislocations, the material manifold is constructed using Cartan's moving frames and the stress field is obtained assuming that the medium is orthotropic. Also, we consider a spherically-symmetric distribution of point defects in a transversely isotropic spherical ball. We show that for an arbitrary incompressible transversely isotropic ball with the radial material preferred direction, a uniform point defect distribution results in a uniform hydrostatic stress field inside the spherical region the distribution is supported in. Finally, we find the stresses induced by a discombination in an orthotropic medium.

Keywords: defects, disclinations, dislocations, monoclinic solids, nonlinear elasticity, orthotropic solids, transversely isotropic solids

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Authors: A. Mimaroglu, H. Unal

Abstract:

In this study, the mechanical properties of nano filled epoxy composites were evaluated. The matrix material is epoxy. nano fillers are Al2O3, TiO2 and clay added in 2.5- 10 wt% by weight ratio. Test samples were prepared using an open mould type die. Mechanical tests were carried out. The tensile strength, elastic modulus, elongation at break and the hardness of the composite materials were obtained and evaluated. It was seen from the results that the filler content had a high influence on the level of the mechanical properties of the epoxy composites.

Keywords: nano, epoxy, composite, fillers, clay

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Authors: Michael Tupý, Alice Tesaříková-Svobodová, Dagmar Měřínská, Vít Petránek

Abstract:

Polyethylene (PE), Polypropylene (PP), Polyethylene (vinyl acetate) (EVA) and Surlyn (modif-PE) nano composite samples were prepared with montmorillonite fillers Cloisite 93A and Dellite 67G. The amount of modified Na+ montmorillonite (MMT) was fixed to 5 % (w/w). For the compounding of polymer matrix and chosen nano fillers twin-screw kneader was used. The level of MMT intercalation or exfoliation in the nano composite systems was studied by transmission electron microscopy (TEM) observations. The properties of samples were evaluated by dynamical mechanical analysis (E* modulus at 30 °C) and by the measurement of tensile properties (stress and strain at break).

Keywords: polyethylene, polypropylene, polyethylene(vinyl acetate), clay, nanocomposite, montmorillonite

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Authors: Samra Isadounene, Amar Boukerrou, Dalila Hammiche

Abstract:

In this work, the composites were prepared with poly(lactic acid) (PLA) and olive husk flour (OHF) with different percentages (10, 20 and 30%) using extrusion method followed by injection molding. The morphological, mechanical properties and thermal behavior of composites were investigated. Tensile strength and elongation at break of composites showed a decreasing trend with increasing fiber content. On the other hand, Young modulus and storage modulus were increased. The addition of OHF resulted in a decrease in thermal stability of composites. The presence of OHF led to an increase in percentage of crystallinity (Xc) of PLA matrix.

Keywords: biopolymers, composites, mechanical properties, poly(lactic acid)

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Authors: H. Niranjan, S. Sivasankaran

Abstract:

Heat and mass transfer near a steady stagnation point boundary layer flow of viscous incompressible fluid through porous media investigates along a vertical plate is thoroughly studied under the presence of magneto hydrodynamic (MHD) effects. The fluid flow is steady, laminar, incompressible and in two-dimensional. The nonlinear differential coupled parabolic partial differential equations of continuity, momentum, energy and specie diffusion are converted into the non-similar boundary layer equations using similarity transformation, which are then solved numerically using the Runge-Kutta method along with shooting method. The effects of the conjugate heat transfer parameter, the porous medium parameter, the permeability parameter, the mixed convection parameter, the magnetic parameter, and the thermal radiation on the velocity and temperature profiles as well as on the local skin friction and local heat transfer are presented and analyzed. The validity of the methodology and analysis is checked by comparing the results obtained for some specific cases with those available in the literature. The various parameters on local skin friction, heat and mass transfer rates are presented in tabular form.

Keywords: MHD, porous medium, slip, convective boundary condition, stagnation point

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Authors: M. Pramila Devi, N. V. N. Indra Kiran

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Control charts, predominantly in the form of X-bar chart, are important tools in statistical process control (SPC). They are useful in determining whether a process is behaving as intended or there are some unnatural causes of variation. A process is out of control if a point falls outside the control limits or a series of point’s exhibit an unnatural pattern. In this paper, a study is carried out on four training algorithms for CCPs recognition. For those algorithms optimal structure is identified and then they are studied for type I and type II errors for generalization without early stopping and with early stopping and the best one is proposed.

Keywords: control chart pattern recognition, neural network, backpropagation, generalization, early stopping

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Authors: Maria Ahmadnezhad, Seyedgharani Ghoreishi ‎

Abstract:

Electrohydraulic servo system have been used in industry in a wide ‎number of applications. Its ‎dynamics are highly nonlinear and also ‎have large extent of model uncertainties and external ‎disturbances. ‎In this thesis, a robust back-stepping control (RBSC) scheme is ‎proposed to overcome ‎the problem of disturbances and system ‎uncertainties effectively and to improve the set-point ‎performance ‎of EHS systems. In order to implement the proposed control ‎scheme, the system ‎uncertainties in EHS systems are considered as ‎total leakage coefficient and effective oil volume. In ‎addition, in ‎order to obtain the virtual controls for stabilizing system, the ‎update rule for the ‎system uncertainty term is induced by the ‎Lyapunov control function (LCF). To verify the ‎performance and ‎robustness of the proposed control system, computer simulation of ‎the ‎proposed control system using Matlab/Simulink Software is ‎executed. From the computer ‎simulation, it was found that the ‎RBSC system produces the desired set-point performance and ‎has ‎robustness to the disturbances and system uncertainties of ‎EHS systems.‎

Keywords: electro hydraulic servo system, back-stepping control, robust back-‎stepping control, Lyapunov redesign‎

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Authors: M. Khouil, N. Saber, M. Mestari

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In this paper, a different architecture of a collision detection neural network (DCNN) is developed. This network, which has been particularly reviewed, has enabled us to solve with a new approach the problem of collision detection between two convex polyhedra in a fixed time (O (1) time). We used two types of neurons, linear and threshold logic, which simplified the actual implementation of all the networks proposed. The study of the collision detection is divided into two sections, the collision between a point and a polyhedron and then the collision between two convex polyhedra. The aim of this research is to determine through the AMAXNET network a mini maximum point in a fixed time, which allows us to detect the presence of a potential collision.

Keywords: collision identification, fixed time, convex polyhedra, neural network, AMAXNET

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Authors: Muhammad Rafiq, Lamae Zulfiqar, Nazish Idrees Chaudhary

Abstract:

A growing number of research focuses on healthy and unhealthy eating behaviors and their impact on health. It was intended to study the Islamic point of view on eating behavior, its impact on mental health and preventative strategies in the light of the Quran and Sunnah. Different articles and Islamic sayings related to eating behaviors and mental health were reviewed in detail. It was also revealed scientifically and through Islamic point of view that appropriate quantity, quality and timings of food have positive effects on mental health. Therefore, a 3Rs model of eating behaviors has been proposed.

Keywords: food intake, mental health, quality of food, quantity of food

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Authors: Shunsuke Saito, Kazuho Yoshimoto, Shunichi Ohmori, Sirawadee Arunyanart

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In this paper, we suggest a mechanism of assessment that rater and Ratee (or employees) to convince. There are many problems exist in the personnel assessment. In particular, we were focusing on the three. (1) Raters are not sufficiently recognized assessment point. (2) Ratee are not convinced by the mechanism of assessment. (3) Raters (or Evaluators) and ratees have empathy. We suggest 1: Setting of "understanding of the assessment points." 2: Setting of "relative assessment ability." 3: Proposal of two-way assessment mechanism to solve these problems. As a prerequisite, it is assumed that there are multiple raters. This is because has been a growing importance of multi-faceted assessment. In this model, it determines the weight of each assessment point evaluators by the degree of understanding and assessment ability of raters and ratee. We used the ANP (Analytic Network Process) is a theory that an extension of the decision-making technique AHP (Analytic Hierarchy Process). ANP can be to address the problem of forming a network and assessment of Two-Way is possible. We apply this technique personnel assessment, the weights of rater of each point can be reasonably determined. We suggest absolute assessment for Two-Way assessment by ANP. We have verified that the consent of the two approaches is higher than conventional mechanism. Also, human resources consultant we got a comment about the application of the practice.

Keywords: personnel evaluation, pairwise comparison, analytic network process (ANP), two-ways

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Authors: K. Jafar, R. Nazar, A. Ishak, I. Pop

Abstract:

The present analysis considers the steady stagnation point flow and heat transfer towards a permeable sheet in an upper-convected Maxwell (UCM) electrically conducting fluid, with a constant magnetic field applied in the transverse direction to flow, and a local heat generation within the boundary layer with a heat generation rate proportional to (T-T_inf)^p. Using a similarity transformation, the governing system of partial differential equations is first transformed into a system of ordinary differential equations, which is then solved numerically using a finite-difference scheme known as the Keller-box method. Numerical results are obtained for the flow and thermal fields for various values of the shrinking/stretching parameter lambda, the magnetic parameter M, the elastic parameter K, the Prandtl number Pr, the suction parameter s, the heat generation parameter Q, and the exponent p. The results indicate the existence of dual solutions for the shrinking sheet up to a critical value lambda_c whose value depends on the value of M, K, and s. In the presence of internal heat absorbtion (Q<0), the surface heat transfer rate decreases with increasing p but increases with parameter Q and s, when the sheet is either stretched or shrunk.

Keywords: magnetohydrodynamic (MHD), boundary layer flow, UCM fluid, stagnation point, shrinking sheet

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Authors: Boonyarat Chaleephay

Abstract:

The purpose of this research paper was to describe the relationship of acupressure points on the anterior surface of the upper limb in accordance with Applied Thai Traditional Massage (ATTM) and the deep structures located at those acupressure points. There were 2 population groups; normal subjects and cadaver specimens. Eighteen males with age ranging from 20-40 years old and seventeen females with ages ranging from 30-97 years old were studies. This study was able to obtain a fundamental knowledge concerning acupressure point and the deep structures that related to those acupressure points. It might be used as the basic knowledge for clinically applying and planning treatment as well as teaching in ATTM.

Keywords: acupressure point (AP), applie Thai traditional medicine (ATTM), paresthesia, numbness

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Authors: Song Ni, Junxiang Xu

Abstract:

This paper concerns quasi-periodic perturbations with parameters of 2-dimensional degenerate systems. If the equilibrium point of the unperturbed system is elliptic-type degenerate. Assume that the perturbation is real analytic quasi-periodic with diophantine frequency. Without imposing any assumption on the perturbation, we can use a path of equilibrium points to tackle with the Melnikov non-resonance condition, then by the Leray-Schauder Continuation Theorem and the Kolmogorov-Arnold-Moser technique, it is proved that the equation has a small response solution for many sufficiently small parameters.

Keywords: quasi-periodic systems, KAM-iteration, degenerate equilibrium point, response solution

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