Search results for: matrices of mass

Authors: G. Balakayeva, A. Aktymbayeva

Abstract:

In this paper, we consider components of discrete event imitating model, implementing a simulation model by using JAVA and performing an input analysis of the data and an output analysis of the simulation results. Was lead development of imitating model of mass service system with n (n≥1) devices of service. On the basis of the developed process of a multithreading simulated the distributed processes with presence of synchronization. Was developed the algorithm of event-oriented simulation, was received results of system functioning with n devices of service.

Keywords: Imitating modeling, Mass service system, Multi agentsystem.

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Authors: Nirmala P. Ratchagar, S. Senthamilselvi

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The heat and mass transfer characteristics of contaminants in groundwater subjected to a biodegradation reaction is analyzed by taking into account the thermal diffusion (Soret) effects. This phenomenon is modulated mathematically by a system of partial differential equations which govern the motion of fluid (groundwater) and solid (contaminants) particles. The numerical results are presented graphically for different values of the parameters entering into the problem on the velocity profiles of fluid, contaminants, temperature and concentration profile.

Keywords: Heat and mass transfer, Soret number, porous media.

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Authors: Mikhail Semenov , Svetlana Kolupaeva, Tatiana Kovalevskaya, Olga Daneyko

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An investigation of the process of deformation hardening and evolution of deformation defect medium in dispersion-hardened materials with face centered cubic matrices and nanoparticles was done. Mathematical model including balance equation for the deformation defects was used.

Keywords: deformation defects, dispersion-hardened materials, mathematical modeling, plastic deformation

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Authors: Ahmed H. Abdullah, Pavel Kroupa

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Globular clusters (GC) are important objects for tracing the early evolution of a galaxy. We study the correlation between the cluster population and the global properties of the host galaxy. We found that the correlation between cluster population (NGC) and the baryonic mass (Mb) of the host galaxy are best described as 10 −5.6038Mb. In order to understand the origin of the U -shape relation between the GC specific frequency (SN) and Mb (caused by the high value of SN for dwarfs galaxies and giant ellipticals and a minimum SN for intermediate mass galaxies≈ 1010M), we derive a theoretical model for the specific frequency (SNth). The theoretical model for SNth is based on the slope of the power-law embedded cluster mass function (β) and different time scale (Δt) of the forming galaxy. Our results show a good agreement between the observation and the model at a certain β and Δt. The model seems able to reproduce higher value of SNth of β = 1.5 at the midst formation time scale.

Keywords: Galaxies, dwarf, globular cluster, specific frequency, formation time scale.

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Authors: Ibrahim Yakubu Seini, Oluwole Daniel Makinde

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MHD chemically reacting viscous fluid flow towards a vertical surface with slip and convective boundary conditions has been conducted. The temperature and the chemical species concentration of the surface and the velocity of the external flow are assumed to vary linearly with the distance from the vertical surface. The governing differential equations are modeled and transformed into systems of ordinary differential equations, which are then solved numerically by a shooting method. The effects of various parameters on the heat and mass transfer characteristics are discussed. Graphical results are presented for the velocity, temperature, and concentration profiles whilst the skin-friction coefficient and the rate of heat and mass transfers near the surface are presented in tables and discussed. The results revealed that increasing the strength of the magnetic field increases the skin-friction coefficient and the rate of heat and mass transfers toward the surface. The velocity profiles are increased towards the surface due to the presence of the Lorenz force, which attracts the fluid particles near the surface. The rate of chemical reaction is seen to decrease the concentration boundary layer near the surface due to the destructive chemical reaction occurring near the surface.

Keywords: Boundary layer, surface slip, MHD flow, chemical reaction, heat transfer, mass transfer.

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Authors: Alan C. Lin, Tzu-Kuan Lin, Tsong Der Lin

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This paper proposes a new method to find the equations of transformation matrix for the rotation angles of the two rotational axes and the coordinates of the three linear axes of an orthogonal multi-axis milling machine. This approach provides intuitive physical meanings for rotation angles of multi-axis machines, which can be used to evaluate the accuracy of the conversion from CL data to NC data.

Keywords: CAM, multi-axis milling machining.

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Authors: Md. Nasir Uddin, M. A. Alim, M. M. K. Chowdhury

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The effect of mass transfer on MHD mixed convective flow along inclined porous plate with thermodiffusion have been analyzed on the basis of boundary layer approximations. The fluid is assumed to be incompressible and dense, and a uniform magnetic field is applied normal to the direction of the flow. A Similarity transformation is used to transform the problem under consideration into coupled nonlinear boundary layer equations which are then solved numerically using the Runge-Kutta sixth-order integration scheme together with Nachtsheim-Swigert shooting iteration technique. The behavior of velocity, temperature, concentration, local skin-friction, local Nusselt number and local Sherwood number for different values of parameters have been computed and the results are presented graphically, and analyzed thereafter. The validity of the numerical methodology and the results are questioned by comparing the findings obtained for some specific cases with those available in the literature, and a comparatively good agreement is reached.

Keywords: Mass transfer, inclined porous plate, MHD, mixed convection, thermodiffusion.

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Authors: D. R. Jain

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The aim of this paper is to use matrix representation of Fuzzy soft sets for proving some equalities connected with Fuzzy soft sets based on set-operations.

Keywords: Equality, Fuzzy soft matrix, Fuzzy soft sets, operations.

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Authors: A. Peveri

Abstract:

The interaction of mass will determine the curvature of space-time, may determine that events proceed at different rates of time at each point in space, so each has a corresponding gravitational potential time. So we can find different values ​​of gravity (g), corresponding to different times (t), thus making a "map of time in space." The space-time is curved by present mass, causing a force of attraction towards the body, but if you invest the curvature of space-time, we find that this field is repulsive: Obtaining negative gravitational forces and positive gravitational forces respectively.

Keywords: Space-time, time, positive gravitation, negative gravitation.

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Authors: Atefeh Saljooghi Khoshkar, Jafar Hassanpour

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One of the main problems of design stage relating to many tunneling projects is the lack of an appropriate standard for the provision of engineering geological data in a predefined format. In particular, this is more reflected in highway and railroad tunnels projects in which there is a number of tunnels and different professional teams involved. In this regard, a comprehensive software needs to be designed using the accepted methods in order to help engineering geologists to prepare standard reports, which contain sufficient input data for the design stage. Regarding this necessity, an applied software has been designed using macro capabilities and Visual Basic programming language (VBA) through Microsoft Excel. In this software, all of the engineering geological input data, which are required for designing different parts of tunnels such as discontinuities properties, rock mass strength parameters, rock mass classification systems, boreability classification, the penetration rate and so forth can be calculated and reported in a standard format.

Keywords: Engineering geology, rock mass classification, rock mechanic, tunnel.

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Authors: Eric Sitorus, Septian Prahastudhi, Turgod Nainggolan, Erwin Riyanto

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Mining by block or panel caving is a mining method that takes advantage of fractures within an ore body, coupled with gravity, to extract material from a predetermined column of ore. The caving column is weakened from beneath through the use of undercutting, after which the ore breaks up and is extracted from below in a continuous cycle. The nature of this method induces cyclical stresses on the pillars of excavations as stress is built up and released over time, which has a detrimental effect on both the installed ground support and the rock mass itself. Ground support capacity, especially on the production where excavation void ratio is highest, is subjected to heavy loading. Strain above threshold of the elongation of support capacity can yield resulting in damage to excavations. Geotechnical engineers must evaluate not only the remnant capacity of ground support systems but also investigate depth of rock mass yield within pillars, backs and floors. Ground Penetrating Radar (GPR) is a geophysical method that has the ability to evaluate rock mass damage using electromagnetic waves. This paper illustrates a case study from the Grasberg mining complex where non-invasive information on the depth of damage and condition of the remaining rock mass was required. GPR with 100 MHz antenna resolution was used to obtain images of the subsurface to determine rehabilitation requirements prior to recommencing production activities. The GPR surveys were used to calibrate the reflection coefficient response of varying rock mass conditions to known Rock Quality Designation (RQD) parameters observed at the mine. The calibrated GPR survey allowed site engineers to map subsurface conditions and plan rehabilitation accordingly.

Keywords: Block caving, ground penetrating radar, reflectivity, RQD.

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Authors: L. Al Ahmad, C. Latrille, D. Hainos, D. Blanc, M. Clausse

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A two-dimensional finite volume axisymmetric model is developed to predict the simultaneous heat and mass transfers during the drying of industrial sludge. The simulations were run using COMSOL-Multiphysics 3.5a. The input parameters of the numerical model were acquired from a preliminary experimental work. Results permit to establish correlations describing the evolution of the various parameters as a function of the drying temperature and the sludge water content. The selection and coupling of the equation are validated based on the drying kinetics acquired experimentally at a temperature range of 45-65 °C and absolute pressure range of 200-1000 mbar. The model, incorporating the heat and mass transfer mechanisms at different operating conditions, shows simulated values of temperature and water content. Simulated results are found concordant with the experimental values, only at the first and last drying stages where sludge shrinkage is insignificant. Simulated and experimental results show that sludge drying is favored at high temperatures and low pressure. As experimentally observed, the drying time is reduced by 68% for drying at 65 °C compared to 45 °C under 1 atm. At 65 °C, a 200-mbar absolute pressure vacuum leads to an additional reduction in drying time estimated by 61%. However, the drying rate is underestimated in the intermediate stage. This rate underestimation could be improved in the model by considering the shrinkage phenomena that occurs during sludge drying.

Keywords: Industrial sludge drying, heat transfer, mass transfer, mathematical modelling.

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Authors: Ahmed Abdulghani Taha, Mohammad Abdulghani Taha

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This study aims at being acquainted with the using the body fat percentage (%BF) with body Mass Index (BMI) as input parameters in fuzzy logic decision support system to predict properly the lifted weight for students at weightlifting class lift according to his abilities instead of traditional manner. The sample included 53 male students (age = 21.38 ± 0.71 yrs, height (Hgt) = 173.17 ± 5.28 cm, body weight (BW) = 70.34 ± 7.87.6 kg, Body mass index (BMI) 23.42 ± 2.06 kg.m-2, fat mass (FM) = 9.96 ± 3.15 kg and fat percentage (% BF) = 13.98 ± 3.51 %.) experienced the weightlifting class as a credit and has variance at BW, Hgt and BMI and FM. BMI and % BF were taken as input parameters in FUZZY logic whereas the output parameter was the lifted weight (LW). There were statistical differences between LW values before and after using fuzzy logic (Diff 3.55± 2.21, P > 0.001). The percentages of the LW categories proposed by fuzzy logic were 3.77% of students to lift 1.0 fold of their bodies; 50.94% of students to lift 0.95 fold of their bodies; 33.96% of students to lift 0.9 fold of their bodies; 3.77% of students to lift 0.85 fold of their bodies and 7.55% of students to lift 0.8 fold of their bodies. The study concluded that the characteristic changes in body composition experienced by students when undergoing weightlifting could be utilized side by side with the Fuzzy logic decision support system to determine the proper workloads consistent with the abilities of students.

Keywords: Fuzzy logic, body mass index, body fat percentage, weightlifting.

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Authors: Thulane Paepae, Tumisang Seodigeng

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This paper demonstrates the use of a method of synthesizing process flowsheets using a graphical tool called the GH-plot and in particular, to look at how it can be used to compare the reactions of a combined simultaneous process with regard to their thermodynamics. The technique uses fundamental thermodynamic principles to allow the mass, energy and work balances locate the attainable region for chemical processes in a reactor. This provides guidance on what design decisions would be best suited to developing new processes that are more effective and make lower demands on raw material and energy usage.

Keywords: Attainable region, dimethyl ether synthesis, mass balance, optimal reaction networks.

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Authors: Khalide Jbilou

Abstract:

In the present paper, we propose numerical methods for solving the Stein equation AXC - X - D = 0 where the matrix A is large and sparse. Such problems appear in discrete-time control problems, filtering and image restoration. We consider the case where the matrix D is of full rank and the case where D is factored as a product of two matrices. The proposed methods are Krylov subspace methods based on the block Arnoldi algorithm. We give theoretical results and we report some numerical experiments.

Keywords: IEEEtran, journal, LATEX, paper, template.

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Authors: F. Gholami, M. Torabi Angaji, Z. Gholami

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Fischer-Tropsch synthesis is one of the most important catalytic reactions that convert the synthetic gas to light and heavy hydrocarbons. One of the main issues is selecting the type of reactor. The slurry bubble reactor is suitable choice for Fischer- Tropsch synthesis because of its good qualification to transfer heat and mass, high durability of catalyst, low cost maintenance and repair. The more common catalysts for Fischer-Tropsch synthesis are Iron-based and Cobalt-based catalysts, the advantage of these catalysts on each other depends on which type of hydrocarbons we desire to produce. In this study, Fischer-Tropsch synthesis is modeled with Iron and Cobalt catalysts in a slurry bubble reactor considering mass and momentum balance and the hydrodynamic relations effect on the reactor behavior. Profiles of reactant conversion and reactant concentration in gas and liquid phases were determined as the functions of residence time in the reactor. The effects of temperature, pressure, liquid velocity, reactor diameter, catalyst diameter, gasliquid and liquid-solid mass transfer coefficients and kinetic coefficients on the reactant conversion have been studied. With 5% increase of liquid velocity (with Iron catalyst), H2 conversions increase about 6% and CO conversion increase about 4%, With 8% increase of liquid velocity (with Cobalt catalyst), H2 conversions increase about 26% and CO conversion increase about 4%. With 20% increase of gas-liquid mass transfer coefficient (with Iron catalyst), H2 conversions increase about 12% and CO conversion increase about 10% and with Cobalt catalyst H2 conversions increase about 10% and CO conversion increase about 6%. Results show that the process is sensitive to gas-liquid mass transfer coefficient and optimum condition operation occurs in maximum possible liquid velocity. This velocity must be more than minimum fluidization velocity and less than terminal velocity in such a way that avoid catalysts particles from leaving the fluidized bed.

Keywords: Modeling, Fischer-Tropsch Synthesis, Slurry Bubble Column Reactor.

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Authors: Zuan-De Wang, Hou-biao Li, Zhong-xi Gao

Abstract:

In this paper, the backward Ussor iterative matrix is proposed. The relationship of convergence between the backward Ussor iterative matrix and Jacobi iterative matrix is obtained, which makes the results in the corresponding references be improved and refined.Moreover,numerical examples also illustrate the effectiveness of these conclusions.

Keywords: Backward USSOR iterative matrix, Jacobi iterative matrix, convergence, spectral radius

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Authors: Gyu-Jin Shim, Seung-Moon Baek, Choon-Geun Moon, Ho-Saeng Lee, Jung-In Yoon

Abstract:

The experimental thermal performance of two heat exchangers in closed-wet cooling tower (CWCT) was investigated in this study. The test sections are heat exchangers which have multi path that is used as the entrance of cooling water and are consisting of bare-type copper tubes between 15.88mm and 19.05mm. The process fluids are the cooling water that flows from top part of heat exchanger to bottom side in the inner side of tube, and spray water that flows gravitational direction in the outer side of it. Air contacts its outer side of that as it counterflows. Heat and mass transfer coefficients and cooling capacity were calculated with variations of process fluids, multi path and different diameter tubes to figure out the performance of characteristics of CWCT. The main results were summarized as follows: The results show this experiment is reliable with values of heat and mass transfer coefficients comparing to values of correlations. Heat and mass transfer coefficients and cooling capacity of two paths are higher than these with one path using 15.88 and 19.05mm tubes. Cooling capacity per unit volume with 15.88mm tube using one and two paths are higher than 19.05mm tube due to increase of surface area per unit volume.

Keywords: Closed–Wet Cooling Tower, Cooling Capacity, Heatand Mass Transfer Coefficients.

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Authors: Kezia Amanda Kurniadi, Emre Islamoglu, Kwangyeol Ryu

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As there has been a recognizable transition in automotive industry from mass production to mass customization, automobile manufacturers and their suppliers have been seeking ways for more flexible and efficient processes. Eventually, modular production is currently being applied to manage the changing orders of the industry. In this paper, two different modular assembly line concepts were studied: conveyor line and box assembly line. Mathematical model for two assembly line concepts were developed and their production line efficiency were compared as a performance measure to improve their assembly line balancing.

Keywords: Line Efficiency, Box assembly line, Conventional conveyor line

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Authors: S. GhaffariTooran, H. Abolghasemi, H. Bahmanyar, M. Esmaeili, A. Safari

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Using plug flow model in conjunction with experimental solute concentration profiles, overall volumetric mass transfer coefficient based on continuous phase (Koca), in a packed liquid-liquid extraction column has been optimized. Number of 12 experiments has been done using standard system of water/acid acetic/toluene in a 6 cm diameter, 120 cm height column. Thorough consideration of influencing parameters we intended to correlate dimensionless parameters in term of overall Sherwood number which has an acceptable average error of about 15.8%.

Keywords: Packed column, mass transfer coefficient, solvent extraction, Sherwood number.

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Authors: M. Ben Othmen, M. Sayadi, F. Fnaiech

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Wavelet transform provides several important characteristics which can be used in a texture analysis and classification. In this work, an efficient texture classification method, which combines concepts from wavelet and co-occurrence matrices, is presented. An Euclidian distance classifier is used to evaluate the various methods of classification. A comparative study is essential to determine the ideal method. Using this conjecture, we developed a novel feature set for texture classification and demonstrate its effectiveness

Keywords: Classification, Wavelet, Co-occurrence, Euclidian Distance, Classifier, Texture.

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Authors: S. Djebali, S. Larbi, A. Bilek

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The present work aims at contributing to the study of the complex phenomenon of wear of pin on disc contact in dry sliding friction between two material couples (bronze/steel and unsaturated polyester virgin and charged with graphite powder/steel). The work consists of the determination of the coefficient of friction, the study of the influence of the tribological parameters on this coefficient and the determination of the mass loss and the wear rate of the pin. This study is also widened to the highlighting of the influence of the addition of graphite powder on the tribological properties of the polymer constituting the pin. The experiments are carried out on a pin-disc type tribometer that we have designed and manufactured. Tests are conducted according to the standards DIN 50321 and DIN EN 50324. The discs are made of annealed XC48 steel and quenched and tempered XC48 steel. The main results are described here after. The increase of the normal load and the sliding speed causes the increase of the friction coefficient, whereas the increase of the percentage of graphite and the hardness of the disc surface contributes to its reduction. The mass loss also increases with the normal load. The influence of the normal load on the friction coefficient is more significant than that of the sliding speed. The effect of the sliding speed decreases for large speed values. The increase of the amount of graphite powder leads to a decrease of the coefficient of friction, the mass loss and the wear rate. The addition of graphite to the UP resin is beneficial; it plays the role of solid lubricant.

Keywords: Friction coefficients, mass loss, wear rate, bronze, polyester, graphite.

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Authors: Salma Parvin, M. A. Alim

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The convective and radiative heat transfer performance and entropy generation on forced convection through a direct absorption solar collector (DASC) is investigated numerically. Four different fluids, including Cu-water nanofluid, Al₂O₃-waternanofluid, TiO₂-waternanofluid, and pure water are used as the working fluid. Entropy production has been taken into account in addition to the collector efficiency and heat transfer enhancement. Penalty finite element method with Galerkin’s weighted residual technique is used to solve the governing non-linear partial differential equations. Numerical simulations are performed for the variation of mass flow rate. The outcomes are presented in the form of isotherms, average output temperature, the average Nusselt number, collector efficiency, average entropy generation, and Bejan number. The results present that the rate of heat transfer and collector efficiency enhance significantly for raising the values of m up to a certain range.

Keywords: DASC, forced convection, mass flow rate, nanofluid.

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Authors: W. Chattinnawat

Abstract:

Consider a mass production of HDD arms where hundreds of CNC machines are used to manufacturer the HDD arms. According to an overwhelming number of machines and models of arm, construction of separate control chart for monitoring each HDD arm model by each machine is not feasible. This research proposed a strategy to optimize the SPC management on shop floor. The procedure started from identifying the clusters of the machine with similar manufacturing performance using clustering technique. The three way control chart ( I - MR - R ) is then applied to each clustered group of machine. This proposed research has advantageous to the manufacturer in terms of not only better performance of the SPC but also the quality management paradigm.

Keywords: Three way control chart. I - MR - R , between/within variation, HDD arm.

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Authors: Mohammad Reza Naghavi, Farzad Alaeimoghadam, Hossein Ghafoori

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Artemisia species, which are medically beneficial, are widespread in temperate regions of both Northern and Southern hemispheres among which Iran is located. About 35 species of Artemisia are indigenous in Iran among them some are widespread in all or most provinces, yet some are restricted to some specific regions. In this review paper, initially, GC-Mass results of some experiments done in different provinces of Iran are mentioned among them some compounds are common among species, some others are mostly restricted to other species; after that, medical advantages based on some researches on species of this genus are reviewed; different qualities such as anti-leishmania, anti-bacteria, antiviral as well as anti-proliferative could be mentioned.

Keywords: Artemisia, GC-Mass analysis, medical advantage.

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Authors: N. Moradian, E. Timofeev, R. Tahir

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In this work, startability of the Busemann intake family with weak/strong conical shock, as most efficient intakes, via overboard mass spillage method is theoretically analyzed. Masterix and Candifix codes are used to numerically simulate few models of this type of intake and verify the theoretical results. Portions of the intake corresponding to various flow capture angles are considered to have mass spillage in the starting process of this intake. This approach allows for overboard mass spillage via a V-shaped slot with the tip of V coinciding with the focal point of the Busemann flow. The theoretical results, achieved using two different theories, of self-started Busemann takes with weak/strong conical shock show that significant improve in intake startability using overboard spillage technique. The starting phenomena of Busemann intakes with weak conical shock and seven different capture angles are numerically simulated at freestream Mach number of 3 to find the minimum area ratios of self-started intakes. The numerical results confirm the theoretical ones achieved by authors.

Keywords: Busemann intake, conical shock, overboard spillage, startability.

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Authors: Zhuan-de Wang, Hou-biao Li, Zhong-xi Gao

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In this paper, the backward MPSD (Modified Preconditioned Simultaneous Displacement) iterative matrix is firstly proposed. The relationship of eigenvalues between the backward MPSD iterative matrix and backward Jacobi iterative matrix for block p-cyclic case is obtained, which improves and refines the results in the corresponding references.

Keywords: Backward MPSD iterative matrix, Jacobi iterative matrix, eigenvalue, p-cyclic matrix.

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Authors: Peter Ndichu Muriuki

Abstract:

Assassination of politicians, school mass murders, purported suicides, aircraft crash, mass shootings by police, sinking of sea ferries, mysterious car accidents, mass fire deaths and horrificterror attacks are some of the cases that bring forth scientific and legal conflicts. Questions about truth, justice and human rights are raised by both victims and perpetrators/offenders as they seek to understand why and how it happened to them. This kind of questioning manifests itself in medical-criminological-legalpsychological and scientific realms. An agreement towards truthinvestigations for possible legal-political-psychological transitory issues such as prosecution, victim-offender mediation, healing, reconciliation, amnesty, reparation, restitution, and policy formulations is seen as one way of transforming these conflicts. Forensic scientists and pathologists in particular have formed professional groups where the complexities between legal truth and scientific truth are dramatized and elucidated within the anatomy of courtrooms. This paper focuses on how pathological truth and legal truth interact with each other in Kenya’s criminal justice system. 

Keywords: Forensic pathology, forensic science, pathological truth, truth investigations.

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Authors: Konstantinos Sotiriadis, Michael Tupý, Nikol Žižková, Vít Petránek

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The acid attack on cement mortars modified with rubber aggregates and EVA polymer binder was studied. Mortar specimens were prepared using a type CEM I 42.5 Portland cement and siliceous sand, as well as by substituting 25% of sand with shredded used automobile tires, and by adding EVA polymer in two percentages (5% and 10% of cement mass). Some specimens were only air cured, at laboratory conditions, and their compressive strength and water absorption were determined. The rest specimens were stored in acid solutions (HCl, H₂SO₄, HNO₃) after 28 days of initial curing, and stored at laboratory temperature. Compressive strength tests, mass measurements and visual inspection took place for 28 days. Compressive strength and water absorption of the air-cured specimens were significantly decreased when rubber aggregates are used. The addition of EVA polymer further reduced water absorption, while had no important impact on strength. Compressive strength values were affected in a greater extent by hydrochloric acid solution, followed by sulfate and nitric acid solutions. The addition of EVA polymer decreased compressive strength loss for the specimens with rubber aggregates stored in hydrochloric and nitric acid solutions. The specimens without polymer binder showed similar mass loss, which was higher in sulfate acid solution followed by hydrochloric and nitric acid solutions. The use of EVA polymer delayed mass loss, while its content did not affect it significantly.

Keywords: Acid attack, mortar, EVA polymer, rubber aggregates.

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Authors: Guangbin Wang, Deyu Sun, Fuping Tan

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In this paper, we present new preconditioned modified accelerated overrelaxation (MAOR) method for solving linear systems. We compare the spectral radii of the iteration matrices of the preconditioned and the original methods. The comparison results show that the preconditioned MAOR method converges faster than the MAOR method whenever the MAOR method is convergent. Finally, we give one numerical example to confirm our theoretical results.

Keywords: preconditioned, MAOR method, linear system, convergence, comparison.

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