Complicated Mathematical Equations Research Articles

Simulation on Motion Reliability of Five-Axis Turning-Milling Center

Five-axis turning-milling center is an important and advanced NC machine in fields of military industry, aerospace, automobile and medical machinery. The model of machining center is established by using ADAMS and designing the variable parameters. The error of machining center is simulated by Monte Carlo method. The command file is compiled to simulate the machining center and the motion reliability is computed using simulation results. The whole process avoids establishing and solving complicated mathematical equations. So, it is an effective method for the analysis and computation of motion reliability. Compared with traditional methods, this method is more accurate and quick and it is suitable for complicated mechanism.

Study and application of optimization algorithm about nonlinear partial differential equations with boundary value problem

For elliptic nonlinear partial differential equations with boundary value problem, based on difference method and dynamic design variable optimization method, by taking unknown function value on discrete net point as design variables, difference equation of all the discrete net points is constructed as an objective function. A kind of optimization algorithm about solving unknown function value on discrete net point is proposed. Universal computing program is designed. Practical example is analyzed. By comparing the computing result with the analytical solution, effectiveness and feasibility are verified. Thus complicated nonlinear mathematical physics equations can be solved by the numerical calculation method.

Design of A GUI Tool for the Prediction of Building Energy Performance

In the present study a GUI tool for the prediction of building energy performance based on a three-layered BP neural network and MATLAB was developed. The inputs for this tool are the 18 building envelope parameters. The outputs are building heating, cooling and total energy consumptions and the energy saving rate. Compared with the complicated mathematical equations, this tool provides a very easy and effective method for students to learn the effects of building envelope performance parameters on the building energy performance. Thus, this tool can be used in building physics and building energy efficiency courses for the design of energy efficient building.

A pedagogical Web service-based interactive learning environment for a digital filter design course: An evolutionary approach

The course of digital filter design in electronic/electrical engineering involves complicated mathematical equations and dynamic waveform variations. It is a consensus among educators that using simulation tools assist in improving students' learning experiences. Previous studies on system simulation seemed to lack an appropriate approach to design such a course. Few emphasized the design of an interactive learning environment by using an evolutionary approach. This study integrated the design concept of an evolutionary approach and Web service-based technology into a simulation system entitled Pedagogical Web Service-Based Interactive Learning Environment (PEWSILE) was introduced. The PEWSILE system contained two interactive learning environments—a simple system and an advanced system. It offered a total of six pedagogical Web services. The simple interactive learning environment included text/color-based services, and text/color/diagram-based services. The advanced interactive learning environment included batch-based, interval change-based, comparison-based, and scroll bar-based services. The study also assessed the students' performance in six pedagogical Web services covering interaction and overall use, usefulness, and intention to use through a questionnaire survey and subsequent interviews. Three significant findings were reported. For example, in the advanced interactive learning environment, the designs of interval change-based and comparison-based services make it easier to observe differences in the outcome of parameter change, while batch-based services lacks the element of waveform comparison. In sum, the findings in this study provide helpful implications in designing engineering educational software. © 2010 Wiley Periodicals, Inc. Comput Appl Eng Educ 18: 423–433, 2010; View this article online at wileyonlinelibrary.com; DOI 10.1002/cae.20163

Modelling nitrate pollution of groundwater using artificial neural network and genetic algorithm in an arid zone

This paper presents a hybrid approach to analyse nitrate pollution based on an Artificial Neural Network (ANN) and Genetic Algorithm (GA). This makes it possible to compute the amount of nitrate in different time-scales easily without employment of confusing complicated mathematical equations. Generally, the results of the current research could be useful in management purposes and also for beneficiaries of groundwater. Isfahan province, located in a dry region of Iran, was chosen as the study area.

Digital dice: computational solutions to practical probability problems

Some probability problems are so difficult that they stump the smartest mathematicians. But even the hardest of these problems can often be solved with a computer and a Monte Carlo simulation, in which a random-number generator simulates a physical process, such as a million rolls of a pair of dice. This is what Digital Dice is all about: how to get numerical answers to difficult probability problems without having to solve complicated mathematical equations. Popular-math writer Paul Nahin challenges readers to solve twenty-one difficult but fun problems, from determining the odds of coin-flipping games to figuring out the behavior of elevators. Problems build from relatively easy (deciding whether a dishwasher who breaks most of the dishes at a restaurant during a given week is clumsy or just the victim of randomness) to the very difficult (tackling branching processes of the kind that had to be solved by Manhattan Project mathematician Stanislaw Ulam). In his characteristic style, Nahin brings the problems to life with interesting and odd historical anecdotes. Readers learn, for example, not just how to determine the optimal stopping point in any selection process but that astronomer Johannes Kepler selected his second wife by interviewing eleven women.The book shows readers how to write elementary computer codes using any common programming language, and provides solutions and line-by-line walk-throughs of a MATLAB code for each problem.Digital Dice will appeal to anyone who enjoys popular math or computer science. In a new preface, Nahin wittily addresses some of the responses he received to the first edition.

The design and evaluation of clinical decision support systems in the area of pharmacokinetics

Gentamicin, an antibiotic drug, can be used in one-sided (unilateral) Meniere's disease to end frequent attacks of spontaneous disabling vertigo. However, with incorrect dose treatment it can profoundly damage patients' inner ear and kidney. The dosage of medication and the dosage interval will affect serum concentration that results therapeutic or damage. Pharmacokinetics is the study of managing the relationship between the dosage medication, dosing interval, and serum concentration. However, due to the complicated mathematical equations of pharmacokinetics, it is rarely used in clinics. The purpose of this study was to use a pharmacokinetics model to build a prototype of gentamicin CDSS embedded in a PDA. This system was implemented in a district teaching hospital in Chiayi area, Taiwan. Empirical data was collected under routine clinical setting with real patients and physicians to validate this CDSS. The research results showed that, considering the therapeutic effect, the pharmacokinetics-based CDSS outperforms physicians' experience. Regarding the intoxication, the pharmacokinetics-based CDSS also performed better than physicians' experience with less intoxication. The physicians using the system revealed a high degree of agreement with the perceived usefulness, perceived ease of use, and intention to use the pharmacokinetics-based CDSS.

Comparison of definitions of the lag phase and the exponential phase in bacterial growth.

Different definitions for the lag time and of the duration of the exponential phase can be used to calculate these quantities from growth models. The conventional definitions were compared with newly proposed definitions. It appeared to be possible to derive values for the lag time and the duration of the exponential phase from the growth models and differences between the various definitions could be quantified. All the different values can be calculated from the growth parameters microm, lambda and alpha. Therefore, it appeared to be unnecessary to use complicated mathematical equations; simple equations were adequate. For the Gompertz model the conventional definition of the lag time did not differ appreciably from the newly proposed definition. The end-point of the exponential phase and thus the duration of the exponential phase differed considerably for the two definitions. For the logistic model the two definitions lead to considerable differences for all quantities. It is recommended that the conventional definition is used for calculating the lag time. For the duration of the exponential phase it is recommended that the new definition is used. The value can be calculated, however, directly from the conventional growth parameters.

Load frequency control using power demand estimation and fuzzy control

AbstractNumerous control methods based on modern control theory have been proposed to improve the load frequency control (LFC) characteristics of power systems. These control methods generally regard the load frequency control system as a linear system model. Furthermore, complicated mathematical equations have to be solved to determine control laws. However, realistic power systems are nonlinear, i.e., the nonlinearities of tie‐lines connecting between the control areas and of generation rate constraints of power plants exist. Consequently, it is considered that the design of controllers is difficult.In this paper, the application of fuzzy control to the load frequency control system is proposed to solve the forementioned problems. The proposed control first, to satisfy the load frequency control requirements, estimates power demand variations of the control areas and uses them as the output set‐point values of power plants, instead of using an integral‐type controller. Next, to improve stability and optimality of the nonlinear load frequency control system using the fore‐mentioned output set‐point control method, the proportional‐type fuzzy control considering a computation time‐delay is implemented. Parameters of the proposed fuzzy controller are determined by minimizing the integral square of the area control error (ACE) to ensure optimality of the system.

負荷推定とファジー制御とを用いた負荷周波数制御

Numerous control methods based on modern control theory have been proposed to improve the load frequency control (LFC) characteristics of power systems. These control methods generally regard the load frequency control system as a linear system model. Furthermore, complicated mathematical equations have to be solved to determine control laws. However, realistic power systems are nonlinear, i.e., the nonlinearities of tie-lines connecting between the control areas and of generation rate constraints of power plants exist. Consequently, it is considered that the design of controllers is difficult. In this paper, the application of fuzzy control to the load frequency control system is proposed to solve the forementioned problems. The proposed control first, to satisfy the load frequency control requirements, estimates power demand variations of the control areas and uses them as the output set-point values of power plants, instead of using an integral-type controller. Next, to improve stability and optimality of the nonlinear load frequency control system using the fore-mentioned output set-point control method, the proportional-type fuzzy control considering a computation time-delay is implemented. Parameters of the proposed fuzzy controller are determined by minimizing the integral square of the area control error (ACE) to ensure optimality of the system.