Equations Of Mathematical Model Research Articles

Mathematical model of mass transfer processes of pervaporation water purification

Object. Theoretical studies of pervaporation separation of water -organic mixture by mathematical modeling of process.Design. Methodology . Approach. The current state of the problem, namely the existing mathematical model of membrane processes had been analyzed. After analysis of features of pervaporation purification process the mathematical model was formulated. The mathematical model describes the pervaporation of organic liquid component through the non-porous membrane in a circular cross section channel. Initial and boundary conditions for this mathematical model had been recorded. Without these conditions the solution is impossible Conclusions. Solution of the equations of mathematical model with the initial and boundary conditions allows to determine the concentration distribution of liquid flow which passes the membrane, and also though the membrane thickness depending on the size of the membrane, the modes of motion of initial and gas-vapor mixture, the concentration of organic impurities in initial and gas-vapor mixture. A mathematical model allows to finding a mode of operating of unit at which completely realized possibilities of membranes and minimized the cost of liquid heating and condensate cooling. In further the research of experimental studies of pervaporation process are planned to continue, to confirm the results obtained by mathematical modeling.

USING OF OBJECT-ORIENTED DESIGN PRINCIPLES IN ELECTRIC MACHINES DEVELOPMENT

Purpose. To develop the theoretical basis of electrical machines object-oriented design, mathematical models and software to improve their design synthesis, analysis and optimization. Methodology. We have applied object-oriented design theory in electric machines optimal design and mathematical modelling of electromagnetic transients and electromagnetic field distribution. We have correlated the simulated results with the experimental data obtained by means of the double-stator screw dryer with an external solid rotor, brushless turbo-generator exciter and induction motor with squirrel cage rotor. Results. We have developed object-oriented design methodology, transient mathematical modelling and electromagnetic field equations templates for cylindrical electrical machines, improved and remade Cartesian product and genetic optimization algorithms. This allows to develop electrical machines classifications models, included not only structure development but also parallel synthesis of mathematical models and design software, to improve electric machines efficiency and technical performance. Originality. For the first time, we have applied a new way of design and modelling of electrical machines, which is based on the basic concepts of the object-oriented analysis. For the first time is suggested to use a single class template for structural and system organization of electrical machines, invariant to their specific variety. Practical value. We have manufactured screw dryer for coil dust drying and mixing based on the performed object-oriented theory. We have developed object-oriented software for design and optimization of induction motor with squirrel cage rotor of AIR series and brushless turbo-generator exciter. The experimental studies have confirmed the adequacy of the developed object-oriented design methodology.

A Personalized Framework for Dynamic Modeling of Disease Trajectories in Chronic Lymphocytic Leukemia.

Chronic lymphocytic leukemia (CLL) is the most common peripheral blood and bone marrow cancer in the developed world. This manuscript proposes mathematical model equations representing the disease dynamics of B-cell CLL. We interconnect delay differential cell cycle models in each of the tumor-involved disease centers using physiologically relevant cell migration. We further introduce five hypothetical case studies representing CLL heterogeneity commonly seen in clinical practice and demonstrate how the proposed CLL model framework may capture disease pathophysiology across patient types. We conclude by exploring the capacity of the proposed temporally- and spatially distributed model to capture the heterogeneity of CLL disease progression. By using global sensitivity analysis, the critical parameters influencing disease trajectory over space and time are: 1) the initial number of CLL cells in peripheral blood, the number of involved lymph nodes, the presence and degree of splenomegaly; 2) the migratory fraction of nonproliferating as well as proliferating CLL cells from bone marrow into blood and of proliferating CLL cells from blood into lymph nodes; and 3) the parameters inducing nonproliferative cells to proliferate. The proposed model offers a practical platform that may be explored in future personalized patient protocols once validated.

Dissolution profiling and its comparison of natural fruit powder effervescent tablets

The aims of the study were to observe the dissolution profile of four types of selected fruit powder fast dissolve tablet and apply different dissolution profile comparison methods, in order to select most applicable method. Spray dried powder of pitaya, pineapple, guava and mango were used as raw material. Each type of fruit powder tablet has identical dissolution profile. Dissolution profiles and dissolution rate of fruit powder tablets were different at different dissolution environment. In model-independent and statistical method pairwise comparison was performed and in model dependent method profile comparison was carried out based on best fitting of mathematical model equation. Dissolution Profile comparison methods represented that model independent method use wide range of value for profile comparison and it was direct and easy; model dependent method was indirect and complex and for critically compare the dissolution profile statistical method was the most suitable method.

Modelling of Thermal Behavior of Borehole Heat Exchangers of Geothermal Heat Pump Heating Systems

This article reports results of comparing the accuracy of the software package “INSOLAR.GSHP.12”, modeling non-steady thermal behavior of geothermal heat pump heating systems (GHCS) and of the similar model “conventional” using finite difference methods for solving spatial non-steady problems of heat conductivity. The software package is based on the method of formulating mathematical models of thermal behavior of ground low-grade heat collection systems developed by INSOLAR group of companies. Equations of mathematical model of spatial non-steady thermal behavior of ground mass of low-grade heat collection system obtained by the developed method have been solved analytically that significantly reduced computing time spent by the software complex “INSOLAR.GSHP.12” for calculations. The method allows to turn aside difficulties associated with information uncertainty of mathematical models of the ground thermal behavior and approximation of external factors affecting the ground. Use of experimentally obtained information about the ground natural thermal behavior in the software package allows to partially take into account the whole complex of factors (such as availability of groundwater, their velocity and thermal behavior, structure and arrangement of ground layers, the Earth’s thermal background, precipitation, phase transformations of moisture in the pore space, and more), significantly influencing the formation of thermal behavior of the ground mass of a low-grade geothermal heat collection system. Numerical experiments presented in the article confirmed the high convergence of the results obtained through the software package “INSOLAR.GSHP.12” with solutions obtained by conventional finite-difference methods.

Optimization the machining parameters by using VIKOR and Entropy Weight method during EDM process of Al–18% SiCp Metal matrix composite

Article history: Received June 25, 2015 Received in revised format: October 12, 2015 Accepted November 15, 2015 Available online November 16 2015 The objective of this paper is to optimize the process parameters by combined approach of VIKOR and Entropy weight measurement method during Electrical discharge machining (EDM) process of Al-18wt.%SiCp metal matrix composite (MMC). The central composite design (CCD) method is considered to evaluate the effect of three process parameters; namely pulse on time (Ton), peak current (Ip) and flushing pressure (Fp) on the responses like material removal rate (MRR), tool wear rate (TWR), Radial over cut (ROC) and surface roughness (Ra). The Entropy weight measurement method evaluates the individual weights of each response and, using VIKOR method, the multi-objective responses are optimized to get a single numerical index known as VIKOR Index. Then the Analysis of Variance (ANOVA) technique is used to determine the significance of the process parameters on the VIKOR Index. Finally, the result of the VIKOR Indexed is validated by conformation test using the liner mathematical model equation develop by responses surface methodology to identify the effectiveness of the proposed method. Growing Science Ltd. All rights reserved. 6 © 201

Optimisation Of Process Parameters In High Energy Mixing As A Method Of Cohesive Powder Flowability Improvement

Abstract Flowability of fine, highly cohesive calcium carbonate powder was improved using high energy mixing (dry coating) method consisting in coating of CaCO3 particles with a small amount of Aerosil nanoparticles in a planetary ball mill. As measures of flowability the angle of repose and compressibility index were used. As process variables the mixing speed, mixing time, and the amount of Aerosil and amount of isopropanol were chosen. To obtain optimal values of the process variables, a Response Surface Methodology (RSM) based on Central Composite Rotatable Design (CCRD) was applied. To match the RSM requirements it was necessary to perform a total of 31 experimental tests needed to complete mathematical model equations. The equations that are second-order response functions representing the angle of repose and compressibility index were expressed as functions of all the process variables. Predicted values of the responses were found to be in a good agreement with experimental values. The models were presented as 3-D response surface plots from which the optimal values of the process variables could be correctly assigned. The proposed, mechanochemical method of powder treatment coupled with response surface methodology is a new, effective approach to flowability of cohesive powder improvement and powder processing optimisation.

Application of central composite design and rank annihilation factor analysis for optimization of mixed chelate of UO2 2+ complex with ammonium-N,N-tetramethylenedithiocarbamate and estimation of Kf value

Abstract The interaction between UO2 2+ and ammonium-N,N-tetramethylenedithiocarbamate (ATMDTC) was investigated experimentally by means of UV-Vis spectrophotometry. Central Composite Design (CCD) was applied to optimisation of reaction with 54 runs in duplicate. This design type was also used to developed mathematical model equation. Analysis of Variance (ANOVA) indicates that the terms of the model are significant within the 95% confident interval. Remarkably initial solution pH, initial ATMDTC concentration, initial Cu2+ concentration and temperature have effect on the reaction. Formation constant (log K f) was calculated as 2.917 by using Rank Annihilation Factor Analysis (RAFA).

Adaptation and Enhancement of Generalized Polynomial Chaos for Industrial Applications

AbstractThis contribution presents ideas, how to adapt stochastic elements to industrial applications and reduce the number of simulations in comparison to Monte Carlo. Especially when the mathematical model equations are not known and just an input/output interface is given. For this so called black box model which can be generated by many simulation tools the generalized polynomial chaos based on the idea of Wiener [1], and extended by Xiu and Karniadakis [2] is a suitable technique. One main advantage of this concept can be seen in the ability to produce functional representations of stochastic variability. This yields in a reduction of the simulation number compared to classical methods and can intensified by using a sparse grids approach [3]. Looking at industrial applications the concept can be applied to a huge amount of systems. For example, components including electronic drives, fuel injection valves, and mechanical parts. As an example of use, a simplified model of a DC drive with six uncertain parameters is taken into account. (© 2015 Wiley‐VCH Verlag GmbH & Co. KGaA, Weinheim)

Using ecological reducing agents instead of sodium sulphide in dyeing with CI Sulphur Black 1

Although low‐cost sodium sulphide is used as a reducing agent in most sulphur dyeing processes, it is considered to be environmentally unfavourable because of the resultant contaminated wastewater and the toxic hydrogen sulphide generated during the dyeing process. In the present paper, hydrazine sulphate, glucose, and sodium borohydride in the presence of sodium hydroxide were used as ecologically safe reduction systems for the CI Sulphur Black 1 dyeing of cotton fabric, and results were compared with those obtained using sodium sulphide. Dyeing processes were carried out at 90 °C for 60 min, and the colour yield (the K/S value), dyeing fastness, and breaking strength of dyed fabrics after soaping were measured. Response surface methodology was employed for experimental design and optimisation of results. Mathematical model equations were derived and statistical analysis carried out by computer simulation programming using Minitab v.15. At a dosage of 0.8 g l−1 of CI Sulphur Black 1, the optimum sodium borohydride reduction system (sodium borohydride 0.47 g l−1, sodium hydroxide 0.65 g l−1) exhibited the highest colour yield and the lowest chemical oxygen demand of the residual dyebath.

PREDICTING THERMAL PERFORMANCE OF ROOFING SYSTEMS IN SURABAYA

Traditional roofing systems in the developing country likes Indonesia are still be dominated by the 30o, 45o, and more pitched angle roofs; the roofing cover materials are widely used to traditional clay roof tiles, then modern concrete roof tiles, and ceramic roof tiles. In the 90’s decay, shop houses are prosperous built with flat concrete roofs dominant. Green roofs and roof ponds are almost rarely built to meet the sustainable environmental issues. Some tested various roof systems in Surabaya were carried out to observe the roof thermal performances. Mathematical equation model from three references are also performed in order to compare with the real project tested. Calculated with equation (Kabre et al.), the 30o pitched concrete-roof-tile, 30o clay-roof-tile, 45o pitched concrete-roof-tile are the worst thermal heat flux coming to room respectively. In contrast, the bare soil concrete roof and roof pond system are the least heat flux streamed onto room. Based on predicted calculation without insulation and cross-ventilation attic space, the roof pond and bare soil concrete roof (greenery roof) are the appropriate roof systems for the Surabaya’s climate; meanwhile the most un-recommended roof is pitched 30o or 45o angle with concrete-roof tiles roofing systems.

Stability Analysis of a Three Species Syn-Eco-System with Mortality Rate for Commensal

The main objective of the present paper is to examine the stability of three species syn-eco-system. The system comprises of a commensal (S1) common to two hosts S2 and S3 with mortality rate for commensal. Further S2 is a commensal of S3 and S3 is a host of both S1, S2. Here all three species are having limited resources. The mathematical model equations constitute a set of three first order non-linear simultaneous coupled differential equations in the strengths N1, N2, N3 of S1, S2, S3 respectively. Criteria for the asymptotic stability of all the eight equilibrium points are established. Trajectories of the perturbations over the equilibrium points are illustrated. Further the global stability of a three species syneco system is established with the aid of suitably constructed Liapunov’s functionpair. Also the growth rates of the species are numerically estimated using RungeKutta fourth order scheme.Key words Commensal; Equilibrium state; Global stability; Host; Mortality rate; Stable; Trajectories.

Inverse Kinematics Simulation for a Surgical Robot Using CATIA

Robotic arm with six degrees of freedom can be successfully used to do a surgical task through a small incision called (RCM point) on the patient's body. Inverse Kinematics modeling and simulating of a 6 DOF surgical robot is developed in this paper. The mathematical model equations are built using geometric approach and the Denavit-Hartenberg convention. The 3D model of the robot is created by CATIA5 to simulate the motion of the robot in surgical environments. The inverse kinematics equations model is validated through the simulating model. Result confirms that the proposed robot mechanism is applicable for minimally invasive surgery applications.

English

This study aims to analyze the effect of variables determining mathematics interest, mathematics self- concept, mathematics anxiety, teacher-student relation, classroom management and sense of belonging on the Mathematics achievement of Turkish students in the Programme for International Student Assessment (PISA) 2012. Structural equation modeling (SEM) was employed in this research study. The research population is represented by 15 year 3 month and 16 year 2 month old students receiving education in Turkey.  The research sample, on the other hand, is composed of 4848 students randomly selected from 170 schools in 12 geographical regions where PISA is implemented. When the Mathematical structural equation model is analyzed, it has been seen that there is a medium and positive relationship between mathematics achievement and mathematics interest of students with mathematics self-concept. It has also been determined that the variable mathematics anxiety has a negative and medium effect on mathematics achievement. According to the results of the research study there is no meaningful relationship between variables of teacher-student relation, classroom management, sense of belonging and mathematics achievement of Turkish students. Key words: PISA 2012, Mathematics literacy, structural equation model.

The state of and prospects for using hardware—software simulators of electrotechnical complexes

A review of publications on simulation of electromechanical devices and electric power systems is given in the present article. Examples of structures are considered. A technique for creation and design features of software-hardware simulators for various purposes are discussed. It is noted that the practical interest in the simulator n electricity and electrical engineering is caused by the complexity of experimental research and commissioning, as well as their cost and possible risks of damage to equipment during setting up and testing. It is shown that modern information processing equipment, including programmable logic devices (PLDs), allow one to solve the equations of mathematical models of complicated electrotechnical complexes and a real time system, which makes it possible to construct software and hardware simulators that can be effectively used in design, commissioning, and training students and staff of enterprises.

Тиражна стабільність офсетних друкарських форм

The complex research for the changes in the properties of the printing plates’ printing and gap elements influenced by the printing process was conducted, that allowed to determine the change of printing and gap elements’ surface microgeometry, also to determine the change of the oxide layer stability, and to explain the decrease of the ink receptivity coefficient. The mathematical regression equation model of the printing plates’ elements’ impact onto the imprints’ optical density in offset printing was developed, that allows estimating and predicting properties of modern brand of printing plate.

Computer System for Diagnostics of Disease Condition of an Organism Taking into Account the Basic Levels of Biosystem Organization

In the given work the results of working out of theobject-oriented software for analyzing mechanisms of occurrence, development and consequences of illnesses of an organism by examples of follicular cancer of thyroid gland and hepatitis B based on the modeling backup for quantitative research of regulatory mechanisms functioning developed by authors at molecular-genetic, cellular, organ-tissue and organismal levels of living system organization and experience of construction of corresponding mathematical and computer models are considered.Applying methods of the qualitative analysis offunctional-differential equations of mathematical models, the conditions for abnormalities occurrence in hormonal regulation of thyroid gland functions and in regulatorika of the interconnected activity of molecular-genetic systems between hepatocytes and hepatitis B virus are defined. Software complexes for diagnostics, treatment and forecasting of diseases outcome are constructed taking into account the structurally-functional organization of cells, intercellular mutual relations and organismal regulation on concrete sites of considered organ and tissues. It allows to conduct computing experiments on habitual object for medical officers, to effectively interpret results ofcomputer modeling organism functioning at norm and anomalies, to develop the real scientifically-proved recommendations about improvement of organism condition at diseases.

Синтез разностных алгоритмов управления цифровыми следящими электроприводами мобильных роботов Е-операторным методом

The mathematical Е-operating method is intended for transformation of the of differential equations system to the tracking electric drive mathematical model equations system. In contrast to the known algorithms for numerical integration, for example, in the Matlab-Simulink, E-method allows to synthesize of the transfer function of tracking electric drives for both sequential and parallel differential algorithms for working in real time on the basis of both software and hardware shifting registers. It is important to note that these algorithms cannot be implemented using Matlab-Simulink. Parallel algorithm provides greater performance than serial algorithm. Parallel algorithm can be implemented "conveyor" method of using multiple coprocessors at the same time. Method is an alternative of the means available in Matlab-Simulink programme for description and analysis of the tracking electric drive model. In the first part of the article the synthesis algorithm using traditional means of differential calculus and Laplace transforms describes. In the second part of the article a solution of the same problem with the use of the Е-operating method presents. The results obtained can be used in mechatronics, robotics, automatic control theory, in the practice of building looking for tracking electric drive.

ОПТИМИЗАЦИЯ ТЕХНИЧЕСКИХ ПАРАМЕТРОВ ПРИ РЕШЕНИИ ИНЖЕНЕРНЫХ ЗАДАЧ

There are two radically different approaches to the engineering problems solving. The essence of one approach consists of the optimization of engineering solutions parameters using some known algorithm, for example, mathematical or some other modeling. The other approach is based on the creation of a new engineering solution using technical creativity. While solving challenging tasks both approaches are applicable. The aim of this research is to identify the correct balance of technical skills with regard to optimization and technical creativity. Optimization of technical object parameters can be reduced to the search of their best combinations at the objective function extreme values and meeting the requirements of the defined engineering constraints. As a result, a task comes to the solution of the system of mathematical model equations and inequations. However, the solution of mathematical model allows determining the object optimal parameters only in terms of specified constraints. The expansion of the constraints boundaries is possible only by the creation of new engineering decisions. It can be achieved through the identification and resolution of contradictions contained in the problem, in other words, by applying the methodology of technical creativity. The examples show that the most effective solutions to engineering problems result from the combination of the object parameters optimization and the technical creativity methods. The described approach to the problems solving is applicable to the standard engineering activity. The authors suggest applying the received data in the higher educational institutions and in training centers of industrial enterprises for training technical engineering personnel. The application of the proposed study will increase the qualitative approach of engineers while solving engineering problems, as well as improve the level of training of specialists.

Optimization of sustained release aceclofenac microspheres using response surface methodology.

Polymeric microspheres containing aceclofenac were prepared by single emulsion (oil-in-water) solvent evaporation method using response surface methodology (RSM). Microspheres were prepared by changing formulation variables such as the amount of Eudragit® RS100 and the amount of polyvinyl alcohol (PVA) by statistical experimental design in order to enhance the encapsulation efficiency (E.E.) of the microspheres. The resultant microspheres were evaluated for their size, morphology, E.E., and in vitro drug release. The amount of Eudragit® RS100 and the amount of PVA were found to be significant factors respectively for determining the E.E. of the microspheres. A linear mathematical model equation fitted to the data was used to predict the E.E. in the optimal region. Optimized formulation of microspheres was prepared using optimal process variables setting in order to evaluate the optimization capability of the models generated according to IV-optimal design. The microspheres showed high E.E. (74.14±0.015% to 85.34±0.011%) and suitably sustained drug release (minimum; 40% to 60%; maximum) over a period of 12h. The optimized microspheres formulation showed E.E. of 84.87±0.005 with small error value (1.39). The low magnitudes of error and the significant value of R(2) in the present investigation prove the high prognostic ability of the design. The absence of interactions between drug and polymers was confirmed by Fourier transform infrared (FTIR) spectroscopy. Differential scanning calorimetry (DSC) and X-ray powder diffractometry (XRPD) revealed the dispersion of drug within microspheres formulation. The microspheres were found to be discrete, spherical with smooth surface. The results demonstrate that these microspheres could be promising delivery system to sustain the drug release and improve the E.E. thus prolong drug action and achieve the highest healing effect with minimal gastrointestinal side effects.