Search results for: derivative free method

Authors: M. Eskandarighadi, C. R. McGann

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It is observed from past experiences of earthquakes that local site conditions can significantly affect the strong ground motion characteristicssuch as frequency content, amplitude, and duration of seismic waves. The most common method for investigating site response is one-dimensional seismic site response analysis. The infinite horizontal length of the model and the homogeneous characteristic of the soil are crucial assumptions of this method. One boundary condition that can be used in the sides is tying the sides horizontally for vertical 1D wave propagation. However, 1D analysis cannot account for the 2D nature of wave propagation in the condition where the soil profile is not fully horizontal or has heterogeneity within layers. Therefore, 2D seismic site response analysis can be used to take all of these limitations into account for a better understanding of local site conditions. Different types of boundary conditions can be appliedin 2D site response models, such as tied boundary condition, massive columns, and free-field boundary condition. The tied boundary condition has been used in 1D analysis, which is useful for 1D wave propagation. Employing two massive columns at the sides is another approach for capturing the 2D nature of wave propagation. Free-field boundary condition can simulate the free-field motion that would exist far from the domain of interest. The goal for free-field boundary condition is to minimize the unwanted reflection from sides. This research focuses on the comparison between these methods with examples and discusses the details and limitations of each of these boundary conditions.

Keywords: boundary condition, free-field, massive columns, opensees, site response analysis, wave propagation

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Authors: Emanuel Guariglia

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In this paper we deal with Chebyshev wavelets. We analyze their properties computing their Fourier transform. Moreover, we discuss the differential properties of Chebyshev wavelets due the connection coefficients. The differential properties of Chebyshev wavelets, expressed by the connection coefficients (also called refinable integrals), are given by finite series in terms of the Kronecker delta. Moreover, we treat the p-order derivative of Chebyshev wavelets and compute its Fourier transform. Finally, we expand the mother wavelet in Taylor series with an application both in fractional calculus and fractal geometry.

Keywords: Chebyshev wavelets, Fourier transform, connection coefficients, Taylor series, local fractional derivative, Cantor set

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Authors: Siti Sofo Ismail, Siti Noraina Wahida Mohd Alwi, Mohamad Hafiz Ameran, Masrudin M. Yusoff

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Locating clandestine cadaver is crucially important in forensic investigations. However, it requires a lot of man power, costly and time consuming. Therefore, the development of a new method to locate the clandestine graves is urgently needed as the cases involve burial of cadaver in different types of soils under tropical climates are still not well explored. This study focused on the burial in mangrove and oil palm plantation soils, comparing the fatty acid distributions in different soil acidities. A stimulated burial experiment was conducted using domestic pig (Sus scrofa) to substitute human tissues. Approximately 20g of pig fatty flesh was allowed to decompose in mangrove and oil palm plantation soils, mimicking burial in a shallow grave. The associated soils were collected at different designated sampling points, corresponding different decomposition stages. Modified Bligh-Dyer Extraction method was applied to extract the soil free fatty acids. Then, the obtained free fatty acids were analyzed with gas chromatography-flame ionization (GC-FID). A similar fatty acid distribution was observed for both mangrove and oil palm plantations soils. Palmitic acid (C₁₆) was the most abundance of free fatty acid, followed by stearic acid (C₁₈). However, the concentration of palmitic acid (C₁₆) higher in oil palm plantation compare to mangrove soils. Conclusion, the decomposition rate of cadaver can be affected by different type of soils.

Keywords: clandestine grave, burial, soils, free fatty acid

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Authors: Majid Khan

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Introduction: In this era of microsurgery, free flap holds a remarkable spot in reconstructive surgery. A free flap is well suited for composite defects as it provides sufficient and well-vascularized tissue for coverage. We report our experience with the use of the free flaps for the reconstruction of composite defects. Methods: This is a retrospective case series (chart review) of patients who underwent reconstruction of composite defects with a free flap at Aga Khan University Hospital, Karachi (Pakistan) from January 01, 2015, to December 31, 2019. Data were collected for patient demographics, size of the defect, size of flap, recipient vessels, postoperative complications, and outcome of the free flap. Results: Over this period, 532 free flaps are included in this study. The overall success rate is 95.5%. The mean age of the patient was 44.86 years. In 532 procedures, there were 448 defects from tumor ablation of head and neck cancer. The most frequent free flap was the anterolateral thigh flap in 232 procedures. In this study, the risk factor hypertension (p=0.004) was found significant for wound dehiscence, preop radiation/chemotherapy (p=0.003), and malnutrition (p=0.005) were found significant for fistula formation. Malnutrition (p=0.02) and use of vein grafts (p=0.025) were significant factors for flap failure. Conclusion: Free tissue transfer is a reliable option for the reconstruction of large and composite defects. Hypertension, malnutrition, and preoperative radiotherapy can cause significant morbidity.

Keywords: free flap, free flap failure, risk factors for flap failure, free flap outcome

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Authors: Shazalina Mat Zin, Ahmad Abd. Majid, Ahmad Izani Md. Ismail, Muhammad Abbas

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The generalized wave equation models various problems in sciences and engineering. In this paper, a new three-time level implicit approach based on cubic trigonometric B-spline for the approximate solution of wave equation is developed. The usual finite difference approach is used to discretize the time derivative while cubic trigonometric B-spline is applied as an interpolating function in the space dimension. Von Neumann stability analysis is used to analyze the proposed method. Two problems are discussed to exhibit the feasibility and capability of the method. The absolute errors and maximum error are computed to assess the performance of the proposed method. The results were found to be in good agreement with known solutions and with existing schemes in literature.

Keywords: collocation method, cubic trigonometric B-spline, finite difference, wave equation

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Authors: Mamdouh Abu-Zaied, K. Mohamed, Galal A. Nawwar

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Microwave-assisted synthesis of a new class of pyridine or purine thioglycoside analogs from readily available starting materials has been described. The key step of this protocol is the formation of sodium pyridine 4-thiolate 4 and pyrazolo[1,5-a]pyrimidine-7-thiolate 5 derivatives via condensation of 1 with cyanoacetanilide derivative 2 or 5-aminopyrazole derivative 3 respectively under microwave irradiation, followed by coupling with halo sugars to give the corresponding pyridine and purine thioglycoside analogs. The obtained compounds were evaluated in vitro against lung (A549), colon (HCT116), liver (HEPG2), and MCF-7(breast) cancer cell lines. Some of them recorded promising activities.

Keywords: antitumor, cyclic sugars, pyrazoles, pyridines, pyrimidines, purines, thioglycosides

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Authors: Azher Jameel, Ghulam Ashraf Harmain

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In the recent years, the enriched techniques like the extended finite element method, the element free Galerkin method, and the Coupled finite element-element free Galerkin method have found wide application in modeling different types of discontinuities produced by cracks, contact surfaces, and bi-material interfaces. The extended finite element method faces severe mesh distortion issues while modeling large deformation problems. The element free Galerkin method does not have mesh distortion issues, but it is computationally more demanding than the finite element method. The coupled FE-EFGM proves to be an efficient numerical tool for modeling large deformation problems as it exploits the advantages of both FEM and EFGM. The present paper employs the coupled FE-EFGM to model large elastoplastic deformations in bi-material engineering components. The large deformation occurring in the domain has been modeled by using the total Lagrangian approach. The non-linear elastoplastic behavior of the material has been represented by the Ramberg-Osgood model. The elastic predictor-plastic corrector algorithms are used for the evaluation stresses during large deformation. Finally, several numerical problems are solved by the coupled FE-EFGM to illustrate its applicability, efficiency and accuracy in modeling large elastoplastic deformations in bi-material samples. The results obtained by the proposed technique are compared with the results obtained by XFEM and EFGM. A remarkable agreement was observed between the results obtained by the three techniques.

Keywords: XFEM, EFGM, coupled FE-EFGM, level sets, large deformation

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Authors: Hamioud Saida, Khalfallah Salah

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In this study, a spectral element method is employed to predict the free vibration of a Euler-Bernoulli beam resting on a Winkler foundation with elastically restrained ends. The formulation of the dynamic stiffness matrix has been established by solving the differential equation of motion, which was transformed to frequency domain. Non-dimensional natural frequencies and shape modes are obtained by solving the partial differential equations, numerically. Numerical comparisons and examples are performed to show the effectiveness of the SEM and to investigate the effects of various parameters, such as the springs at the boundaries and the elastic foundation parameter on the vibration frequencies. The obtained results demonstrate that the present method can also be applied to solve the more general problem of the dynamic analysis of structures with higher order precision.

Keywords: elastically supported Euler-Bernoulli beam, free-vibration, spectral element method, Winkler foundation

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Authors: Amanbek Jainakov, Abdikerim Kurbanaliev

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The work presents the results of mathematical modeling of large-scale flows in areas with a complex topographic relief. The Reynolds-averaged Navier—Stokes equations constitute the basis of the three-dimensional unsteady modeling. The well-known Volume of Fluid method implemented in the solver interFoam of the open package OpenFOAM 2.3 is used to track the free-boundary location. The mathematical model adequacy is checked by comparing with experimental data. The efficiency of the applied technology is illustrated by the example of modeling the breakthrough of the dams of the Andijan (Uzbekistan) and Papan (near the Osh town, Kyrgyzstan) reservoir.

Keywords: three-dimensional modeling, free boundary, the volume-of-fluid method, dam break, flood, OpenFOAM

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Authors: M. Bouinoun, M. Bouhadef

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The present study is concerned with the problem of determining the shape of the free surface flow in a hydraulic channel which has an uneven bottom. For the mathematical formulation of the problem, the fluid of the two-dimensional irrotational steady flow in water is assumed inviscid and incompressible. The solutions of the nonlinear problem are obtained by using the usual conformal mapping theory and Hilbert’s technique. An experimental study, for comparing the obtained results, has been conducted in a hydraulic channel (subcritical regime and supercritical regime).

Keywords: free-surface flow, experiments, numerical method, uneven bottom, supercritical regime, subcritical regime

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Authors: T. Prabakaran

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Gas Insulated Substations (GIS) are widely used as important switchgear equipment because of its high reliability, low space requirement, low risk factor and easy maintenance, yet some failures have been reported. Some of the failures are due to presence of metallic particles inside the GIS compartment. The defect can be generated in GIS during production, maintenance, installation and can be due to ageing of the component. The Ultra-High Frequency (UHF) method is used to diagnose the insulation condition of GIS by detecting the PD signals in GIS. This paper identifies PD patterns for free moving particle defect and particle fixed on cone using UHF method. As insulation failure usually starts with PD activity, this paper investigates the differences in PD characteristics in SF6 gas with different types of defects. Experimental results show that correct identification of defects can be achieved based on considered PD characteristics. The method can be applied to prove the quality of assembly work at commissioning, also on a regular basis after many years in service to detect aged and conducting particles as a part of the condition based maintenance.

Keywords: gas insulated substation, partial discharge, free moving particle defect, particle fixed on cone defect, ultra high frequency method

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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: Chiung-Ju Huang

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This study utilizes a frequency domain approach over the period of 1996 to 2013 to examine the causal relationship between governance and economic growth in ten Asian countries, which have different levels of democracy; classified as “Free”, “Partly Free”, and “Not Free” countries. The empirical results show that there is no Granger causality running from governance to economic growth in “Not Free” countries and “Partly Free” countries with the exception of Singapore. As for “Free” countries such as South Korea and Taiwan, there is a one-way causality running from governance to economic growth. The findings of this study indicate that policy makers in South Korea, Taiwan, and Singapore could use governance index to improve their predictions of the future economic growth.

Keywords: economic growth, frequency domain, governance, granger causality

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Authors: Sunil Kumar, Sandip Dhole, Deepak Salunke, Chung-ming Sun

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Heterocycles bearing nitrogen, oxygen, and selenium are present in innumerable biologically active compounds. For instance, coumarin containing dicoumarol acts as naturally occurring anticoagulant. 2-Acylamido selenazole works as Store-Operated Calcium (SOC) channel regulator. Therefore, due to biologically significance of selenazole and coumarin and our quest to develop efficient methodologies for the synthesis of complex heterocycles, the trisubstituted angular isocoumarinoselenazole synthesis was proposed and achieved by starting from nitrobenzoic acid derivative, available commercially. Synthetic procedure involves three steps: i) the construction of 2-aminobenzoselenazoles, ii) their regioselective N-alkylation at position-2 and iii) alkyne insertion via Ru catalyzed C-H activation. Transition metal free synthesis of benzoselenazoles was successfully brought about by the addition/elimination reaction via intramolecular C-Se bond formation. In the next step, N-alkylation of selenazole furnished two regioisomers. Both the isomers exhibited different reactivity towards [4+2] alkyne annulation reaction. The fusion of α-pyrone ring on the benzo[1,3-d]selenazole skeleton was achieved via Ru(II)-catalyzed C-H activation and alkyne insertion. As evident from mechanism, the selenazole 'N' plays an important role for the experiential selectivity.

Keywords: alkylation, alkyne insertion, coumarin, selenazole

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Authors: J. Fernandez de Canete, S. Fernandez-Calvo, I. García-Moral

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This paper presents and discusses the application of the object-oriented modelling software SIMSCAPE to hydraulic systems, with particular reference to multivariable proportional-integral-derivative (PID) control. As a result, a particular modelling approach of a double cylinder-piston coupled system is proposed and motivated, and the SIMULINK based PID tuning tool has also been used to select the proper controller parameters. The paper demonstrates the usefulness of the object-oriented approach when both physical modelling and control are tackled.

Keywords: object-oriented modeling, multivariable hydraulic system, multivariable PID control, computer simulation

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Authors: Aklilu Zeleke

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A cross-sectional study was conducted in order to understand the effect of wet and dry seasons on the free residual chlorine and bacteriological contamination of the Addis Ababa (Ethiopia) water supply system. Water samples were taken at 30 selected distribution points and analyzed for Free Residual Chlorine and bacteriological analysis total coliforms and fecal coliform). It was found that some of the bacteriological data and Free Residual Chlorine levels are below the recommended values and beyond the maximum tolerable limits recommended by World Health Organization and Ethiopian National Standards. Water quality during the dry season is better than that of the wet season. There is a strong relationship between Free Residual Chlorine levels in drinking water and its bacteriological quality.

Keywords: addis ababa, wet season, dry season, free residual chlorine

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Authors: Youssef Abdelli, Rachid Nasri

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The large amplitude free vibration analysis of three-layered symmetric sandwich beams is carried out using two different approaches. The governing nonlinear partial differential equations of motion in free natural vibration are derived using Hamilton's principle. The formulation leads to two nonlinear partial differential equations that are coupled both in axial and binding deformations. In the first approach, the method of multiple scales is applied directly to the governing equation that is a nonlinear partial differential equation. In the second approach, we discretize the governing equation by using Galerkin's procedure and then apply the shooting method to the obtained ordinary differential equations. In order to check the validity of the solutions obtained by the two approaches, they are compared with the solutions obtained by two approaches; they are compared with the solutions obtained numerically by the finite difference method.

Keywords: finite difference method, large amplitude vibration, multiple scales, nonlinear vibration

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Authors: Saeed Kamarian

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In this paper, free vibrations of Functionally Graded Sandwich (FGS) beams reinforced by randomly oriented Single-Walled Carbon Nanotubes (SWCNTs) are investigated. The Eshelby–Mori–Tanaka approach based on an equivalent fiber is used to investigate the material properties of the structure. The natural frequencies of the FGS nanocomposite beam are analyzed based on various Higher-order Shear Deformation Beam Theories (HSDBTs) and using an analytical method. The verification study represents the simplicity and accuracy of the method for free vibration analysis of nanocomposite beams. The effects of carbon nanotube volume fraction profiles in the face layers, length to span ratio and thicknesses of face layers on the natural frequency of structure are studied for the different HSDBTs. Results show that by utilizing the FGS type of structures, free vibration characteristics of structures can be improved. A comparison is also provided to show the difference between natural frequency responses of the FGS nanocomposite beam reinforced by aligned and randomly oriented SWCNT.

Keywords: sandwich beam, nanocomposite beam, functionally graded materials, higher-order beam theories, Mori-Tanaka approach

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Authors: Afaf Bouchoucha, Karima Si Larbi, Mohamed Amine Bourouaia, Salah.Boulanouar, Safia.Djabbar

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The synthesis, characterization and comparative biological study of manganese (II) and copper (II) complexes with an heterocyclic ligand used in pharmaceutical field (Scheme 1), were reported. Two kinds of complexes were obtained with derivative sulfonamide, [M (L)₂ (H₂O)₂].H₂O and [M (L)₂ (Cl)₂]3H₂O. These complexes have been prepared and characterized by elemental analysis, FAB mass, ESR magnetic measurements, FTIR, UV-Visible spectra and conductivity. Their stability constants have been determined by potentiometric methods in a water-ethanol (90:10 v/v) mixture at a 0.2 mol l-1 ionic strength (NaCl) and at 25.0 ± 0.1 ºC using Sirko program. DFT calculations were done using B3LYP/6-31G(d) and B3LYP/LanL2DZ. The antimicrobial activity of ligand and complexes against the species Escherichia coli, P. aeruginosa, Klebsiella pneumoniae, S. aureus, Bacillus subtilisan, Candida albicans, Candida tropicalis, Saccharomyces, Aspergillus fumigatus and Aspergillus terreus has been carried out and compared using agar-diffusion method. Also, the toxicity study was evaluated on synchesis complexes using Mice of NMRI strain.

Keywords: hetterocyclic ligand, complex, stability constant, antimicrobial activity, DFT, acute and genotoxicity study

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Authors: S. Khardazi, H. Zaitouni, A. Neqali, S. Lyubchyk, D. Mezzane, M. Amjoud, E. Choukri, S. Lyubchyk, Z. Kutnjak

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In the present paper, structural, dielectric, ferroelectric, and energy storage properties of pure perovskite lead-free BCZT, BTSn, and BTSn-BCZT ferroelectric ceramics have been investigated. Rietveld refinement of XRD data confirms the coexistence of the rhombohedral and orthorhombic phases at room temperature in the composite BCZT–BTSn ceramic. Remarkably, an improved recoverable energy density of 137.86 mJ/cm³ and a high energy storage efficiency of 86.19 % at 80°C under a moderate applied electric field of 30 kV/cm were achieved in the designed BCZT–BTSn ceramic. Besides, the sample exhibits excellent thermal stability of the energy storage efficiency (less than 3%) in the temperature range of 70 to 130 °C under 30 kV/cm. Such results make the pb-free BCZT–BTSn ferroelectric ceramic a very promising potential matrix for energy storage capacitor applications.

Keywords: sol-gel, ferroelectrics, lead-free, perovskites, energy storage

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Authors: Yiping Meng, Yiming Sun

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The traditional construction industry is unable to meet the requirements for novel fabrication and construction. Automated construction and digital design have emerged as industry development trends that compensate for this shortcoming under the backdrop of Industrial Revolution 4.0. Benefitting from more flexible working space and more various end-effector tools compared to CNC methods, robot fabrication and construction techniques have been used in irregular architectural design. However, there is a lack of a systematic and comprehensive design and optimisation workflow considering geometric form, material, and fabrication methods. This paper aims to propose a design optimisation workflow for improving the rationality of a free-form timber structure fabricated by the robotic arm. Firstly, the free-form surface is described by NURBS, while its structure is calculated using the finite element analysis method. Then, by considering the characteristics and limiting factors of robotic timber fabrication, strain energy and robustness are set as optimisation objectives to optimise structural morphology by gradient descent method. As a result, an optimised structure with axial force as the main force and uniform stress distribution is generated after the structure morphology optimisation process. With the decreased strain energy and the improved robustness, the generated structure's bearing capacity and mechanical properties have been enhanced. The results prove the feasibility and effectiveness of the proposed optimisation workflow for free-form timber structure morphology design.

Keywords: robotic fabrication, free-form timber structure, Multi-objective optimisation, Structural morphology, rational design

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Authors: Alexander Matrosov, Guriy Shirunov

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A superposition method based on Lame's idea is used to get a general analytical solution to analyze a stress and strain state of a rectangular isotropjc elastic thick plate. The solution is built by using three solutions of the method of initial functions in the form of double trigonometric series. The results of bending of a thick plate under normal stress on its top face with two opposite sides clamped while others free of load are presented and compared with FEM modelling.

Keywords: general solution, method of initial functions, superposition method, thick isotropic plates

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Authors: Benchalak Muangmeesri

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The purpose of this paper is to discuss how to test the best control performance of a ceramics. Hydraulic press machine (HPM) is the most common shaping of advanced ceramic with products, dimensions, and ceramic products mainly from synthetic powders. A microcontroller can be achieved to control process and has set high standards in the shaping of raw materials in powder form. HPM was proposed to develop a position control system that linked to the embedded controller PIC16F877 via Proportional and Derivative (PD) controller. The model is performed using MATLAB/SIMULINK and the best control performance of an HPM. Finally, PD controller results, showing the best performance as it had the smallest overshoot and highest quality using a microcontroller control.

Keywords: ceramics, hydraulic press, microcontroller, PD controller

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Authors: Benghezel Hichem

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Thyroid dysfunction in hemodialysis subjects is represented mainly by hypothyroidism. The objective of our work is to determine the thyroid profile of our hemodialysis patients and to highlight the prevalence of different thyroid disorders. Methods: This is a retrospective study performed on a mono centric 2 months (February and March 2013) on 42 hemodialysis patients (11 male and 31 female). We made the dosage of thyroid hormones Thyrotropin (TSH) ((free thyroxin ) FT4 and free Triodothyronin ) FT3) by chemiluminescence immunoassay method on cobas 6000 Roche Diagnostics. The results: The prevalence of biological hypothyroidism was 18% (7% with a high TSH isolated and a mean +/- SD 9.44 +/- 6.29, 5% with high TSH, and with low FT4 a mean +/- SD is 8.18 +/- 0.53 for TSH and 9.69 +/- 0.22 for FT4, One patient with a high TSH, and low FT4, FT3. 4% of patients with a low T3 syndrome with a mean +/- SD of 3.93 +/- 0,3 for FT3), we notice that 5% of patients with hyperthyroidism TSH collapsed and mean +/- SD of TSH is 0.017 +/- 0,001. Conclusion: The biological Hypothyroidism is a common endocrine disorder in chronic hemodialysis.

Keywords: hypothyroidism, hemodialysis, thyréostimulin, free thyroxin, triodothyronin

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Authors: Hesamoddin Abdollahpour, Roghayeh Abdollahpour, Elham Rahgozar

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This paper we deal with an analysis of the free vibrations of the governing partial differential equation that it is Danel equation in the shells. The problem considered represents the governing equation of the nonlinear, large amplitude free vibrations of the hinged shell. A new implementation of the new method is presented to obtain natural frequency and corresponding displacement on the shell. Our purpose is to enhance the ability to solve the mentioned complicated partial differential equation (PDE) with a simple and innovative approach. The results reveal that this new method to solve Danel equation is very effective and simple, and can be applied to other nonlinear partial differential equations. It is necessary to mention that there are some valuable advantages in this way of solving nonlinear differential equations and also most of the sets of partial differential equations can be answered in this manner which in the other methods they have not had acceptable solutions up to now. We can solve equation(s), and consequently, there is no need to utilize similarity solutions which make the solution procedure a time-consuming task.

Keywords: large amplitude, free vibrations, analytical solution, Danell Equation, diagram of phase plane

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Authors: Temesgen Takele Kasa

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The main aim of this paper is to suggest one active slip based continuum dislocation approach to matrix dominated MMC plasticity analysis. The approach centered the free energy principles through the continuum behavior of dislocations combined with small strain continuum kinematics. The analytical derivation of this method includes the formulation of one active slip system, the thermodynamic approach of dislocations, determination of free energy, and evolution of dislocations. In addition zero and non-zero energy dissipation analysis of dislocation evolution is also formulated by using varational energy minimization method. In general, this work shows its capability to analyze the plasticity of matrix dominated MMC with inclusions. The proposed method is also found to be capable of handling plasticity of MMC.

Keywords: active slip, continuum dislocation, distortion, dominated, energy dissipation, matrix dominated, plasticity

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Authors: Ishak Hashim, Ammar Alsabery

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The problem of conjugate free convection in a square cavity filled with nanofluid and heated from below by spatial wall temperature is studied numerically using the finite difference method. Water-based nanofluid with copper nanoparticles are chosen for the investigation. Governing equations are solved over a wide range of nanoparticle volume fraction (0 ≤ φ ≤ 0.2), wave number ((0 ≤ λ ≤ 4) and thermal conductivity ratio (0.44 ≤ Kr ≤ 6). The results presented for values of the governing parameters in terms of streamlines, isotherms and average Nusselt number. It is found that the flow behavior and the heat distribution are clearly enhanced with the increment of the non-uniform heating.

Keywords: conjugate free convection, square cavity, nanofluid, spatial temperature

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Authors: J. J. Peña, J. Morales, J. García-Ravelo, L. Arcos-Díaz

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The Point canonical transformation method is applied for solving the Schrödinger equation with position-dependent mass. This class of problem has been solved for continuous mass distributions. In this work, a staggered mass distribution for the case of a free particle in an infinite square well potential has been proposed. The continuity conditions as well as normalization for the wave function are also considered. The proposal can be used for dealing with other kind of staggered mass distributions in the Schrödinger equation with different quantum potentials.

Keywords: free particle, point canonical transformation method, position-dependent mass, staggered mass distribution

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Authors: Virag Vass, Ilona Bereczki, Erzsebet Szabo, Nora Debreczeni, Aniko Borbas, Pal Herczegh, Arpad Tosaki

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Hydrogen sulfide (H₂S) is a toxic gas, but it is produced by certain tissues in a small quantity. According to earlier studies, ibuprofen and H₂S has a protective effect against damaging heart tissue caused by ischemia-reperfusion. Recently, we have been investigating the effect of a new water-soluble H₂S releasing ibuprofen molecule administered after artificially generated ischemia-reperfusion on isolated rat hearts. The H₂S releasing property of the new ibuprofen derivative was investigated in vitro in medium derived from heart endothelial cell isolation at two concentrations. The ex vivo examinations were carried out on rat hearts. Rats were anesthetized with an intraperitoneal injection of ketamine, xylazine, and heparin. After thoracotomy, hearts were excised and placed into ice-cold perfusion buffer. Perfusion of hearts was conducted in Langendorff mode via the cannulated aorta. In our experiments, we studied the dose-effect of the H₂S releasing molecule in Langendorff-perfused hearts with the application of gradually increasing concentration of the compound (0- 20 µM). The H₂S releasing ibuprofen derivative was applied before the ischemia for 10 minutes. H₂S concentration was measured with an H₂S detecting electrochemical sensor from the coronary effluent solution. The 10 µM concentration was chosen for further experiments when the treatment with this solution was occurred after the ischemia. The release of H₂S is occurred by the hydrolyzing enzymes that are present in the heart endothelial cells. The protective effect of the new H₂S releasing ibuprofen molecule can be confirmed by the infarct sizes of hearts using the Triphenyl-tetrazolium chloride (TTC) staining method. Furthermore, we aimed to define the effect of the H₂S releasing ibuprofen derivative on autophagic and apoptotic processes in damaged hearts after investigating the molecular markers of these events by western blotting and immunohistochemistry techniques. Our further studies will include the examination of LC3I/II, p62, Beclin1, caspase-3, and other apoptotic molecules. We hope that confirming the protective effect of new H₂S releasing ibuprofen molecule will open a new possibility for the development of more effective cardioprotective agents with exerting fewer side effects. Acknowledgment: This study was supported by the grants of NKFIH- K-124719 and the European Union and the State of Hungary co- financed by the European Social Fund in the framework of GINOP- 2.3.2-15-2016-00043.

Keywords: autophagy, hydrogen sulfide, ibuprofen, ischemia, reperfusion

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Authors: Jeremie Coullon, Robert J. Webber

Abstract:

We introduce a Markov chain Monte Carlo (MCMC) sam-pler for infinite-dimensional inverse problems. Our sam-pler is based on the affine invariant ensemble sampler, which uses interacting walkers to adapt to the covariance structure of the target distribution. We extend this ensem-ble sampler for the first time to infinite-dimensional func-tion spaces, yielding a highly efficient gradient-free MCMC algorithm. Because our ensemble sampler does not require gradients or posterior covariance estimates, it is simple to implement and broadly applicable. In many Bayes-ian inverse problems, Markov chain Monte Carlo (MCMC) meth-ods are needed to approximate distributions on infinite-dimensional function spaces, for example, in groundwater flow, medical imaging, and traffic flow. Yet designing efficient MCMC methods for function spaces has proved challenging. Recent gradi-ent-based MCMC methods preconditioned MCMC methods, and SMC methods have improved the computational efficiency of functional random walk. However, these samplers require gradi-ents or posterior covariance estimates that may be challenging to obtain. Calculating gradients is difficult or impossible in many high-dimensional inverse problems involving a numerical integra-tor with a black-box code base. Additionally, accurately estimating posterior covariances can require a lengthy pilot run or adaptation period. These concerns raise the question: is there a functional sampler that outperforms functional random walk without requir-ing gradients or posterior covariance estimates? To address this question, we consider a gradient-free sampler that avoids explicit covariance estimation yet adapts naturally to the covariance struc-ture of the sampled distribution. This sampler works by consider-ing an ensemble of walkers and interpolating and extrapolating between walkers to make a proposal. This is called the affine in-variant ensemble sampler (AIES), which is easy to tune, easy to parallelize, and efficient at sampling spaces of moderate dimen-sionality (less than 20). The main contribution of this work is to propose a functional ensemble sampler (FES) that combines func-tional random walk and AIES. To apply this sampler, we first cal-culate the Karhunen–Loeve (KL) expansion for the Bayesian prior distribution, assumed to be Gaussian and trace-class. Then, we use AIES to sample the posterior distribution on the low-wavenumber KL components and use the functional random walk to sample the posterior distribution on the high-wavenumber KL components. Alternating between AIES and functional random walk updates, we obtain our functional ensemble sampler that is efficient and easy to use without requiring detailed knowledge of the target dis-tribution. In past work, several authors have proposed splitting the Bayesian posterior into low-wavenumber and high-wavenumber components and then applying enhanced sampling to the low-wavenumber components. Yet compared to these other samplers, FES is unique in its simplicity and broad applicability. FES does not require any derivatives, and the need for derivative-free sam-plers has previously been emphasized. FES also eliminates the requirement for posterior covariance estimates. Lastly, FES is more efficient than other gradient-free samplers in our tests. In two nu-merical examples, we apply FES to challenging inverse problems that involve estimating a functional parameter and one or more scalar parameters. We compare the performance of functional random walk, FES, and an alternative derivative-free sampler that explicitly estimates the posterior covariance matrix. We conclude that FES is the fastest available gradient-free sampler for these challenging and multimodal test problems.

Keywords: Bayesian inverse problems, Markov chain Monte Carlo, infinite-dimensional inverse problems, dimensionality reduction

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