• Journal of international Conference on Electrical Machines and Systems
• /
• 제2권3호
• /
• pp.260-268
• /
• 2013

Based on classical Berotti discrete iron loss calculation model, the iron loss analysis mathematical model of alternator was proposed in this paper. Considering characteristics of high speed and changing frequency of the alternator, Maxwell 3-D model was built to analyze iron loss corresponding to each running speed in alternator. Based on iron loss model of alternator at rated speed, the rotor claw pole size was made an optimization design. The optimization results showed that alternator's output performance had been improved. A new idea was explored in size optimization design of claw pole alternator.

• Structural Engineering and Mechanics
• /
• 제11권4호
• /
• pp.373-392
• /
• 2001

The main idea behind the paper is to present two alternative methods of homogenization of the heat conduction problem in composite materials, where the heat conductivity coefficients are assumed to be random variables. These two methods are the Monte-Carlo simulation (MCS) technique and the second order perturbation second probabilistic moment method, with its computational implementation known as the Stochastic Finite Element Method (SFEM). From the mathematical point of view, the deterministic homogenization method, being extended to probabilistic spaces, is based on the effective modules approach. Numerical results obtained in the paper allow to compare MCS against the SFEM and, on the other hand, to verify the sensitivity of effective heat conductivity probabilistic moments to the reinforcement ratio. These computational studies are provided in the range of up to fourth order probabilistic moments of effective conductivity coefficient and compared with probabilistic characteristics of the Voigt-Reuss bounds.

• Earthquakes and Structures
• /
• 제5권3호
• /
• pp.359-378
• /
• 2013

The problem of identification of multi-component and (or) spatially varying earthquake support motions based on measured responses in instrumented structures is considered. The governing equations of motion are cast in the state space form and a time domain solution to the input identification problem is developed based on the Kalman and particle filtering methods. The method allows for noise in measured responses, imperfections in mathematical model for the structure, and possible nonlinear behavior of the structure. The unknown support motions are treated as hypothetical additional system states and a prior model for these motions are taken to be given in terms of white noise processes. For linear systems, the solution is developed within the Kalman filtering framework while, for nonlinear systems, the Monte Carlo simulation based particle filtering tools are employed. In the latter case, the question of controlling sampling variance based on the idea of Rao-Blackwellization is also explored. Illustrative examples include identification of multi-component and spatially varying support motions in linear/nonlinear structures.

• Communications for Statistical Applications and Methods
• /
• 제22권4호
• /
• pp.321-331
• /
• 2015

The K-means clustering algorithm is a popular and widely used method for clustering. For covariance matrices, we consider a geodesic clustering algorithm based on the K-means clustering framework in consideration of symmetric positive definite matrices as a Riemannian (non-Euclidean) manifold. This paper considers a geodesic clustering algorithm for data consisting of symmetric positive definite (SPD) matrices, utilizing the Riemannian geometric structure for SPD matrices and the idea of a K-means clustering algorithm. A K-means clustering algorithm is divided into two main steps for which we need a dissimilarity measure between two matrix data points and a way of computing centroids for observations in clusters. In order to use the Riemannian structure, we adopt the geodesic distance and the intrinsic mean for symmetric positive definite matrices. We demonstrate our proposed method through simulations as well as application to real financial data.

• Asia pacific journal of information systems
• /
• 제1권1호
• /
• pp.49-62
• /
• 1991

This paper examines the problems of database partitioning and file allocation in a fixed topology distributed computer network. The design objective is to make files as collections of attributes and to allocate these files to network nodes so that a minimum total transmission cost is achieved subject to storage capacity constraints. A mathematical model for solving the problem is formulated and, the resulting optimization problem is shown to fall in a class of NP-complete problems. A new heuristic algorithm is developed which uses the idea of allocating attributes according to the transaction requirements at each computer node and then making files using the allocated attributes. Numerical results indicate that the heuristic algorithm yields practicable low cost solutions in comparison with the existing methods which deal with the file allocation problems and database partitioning problems independently.

• 한국음향학회:학술대회논문집
• /
• 한국음향학회 1994년도 FIFTH WESTERN PACIFIC REGIONAL ACOUSTICS CONFERENCE SEOUL KOREA
• /
• pp.830-835
• /
• 1994

In this paper, a new method of statistically evaluating an output response probability distribution of a memory type non-linear system is practically derived based on a zero-memory type non-linear equivalent system. That is, first, the objective system is approximately and functionally separated into two functional parts, i.e., a zero-memory type non-linear part and a memory type linear part according to the well-known Wiener's idea. A whole mathematical frame of the output probability distribution is evaluated in an approximate but generalized form, based on the equivalent zero-memory type non-linear part. The memory effects between the input and the output of the system are reflected in the statistical parameters and the expansion coefficients.

• Computers and Concrete
• /
• 제28권6호
• /
• pp.605-619
• /
• 2021

Building Information Modeling (BIM) models are a powerful tool for preserving and using architectural history. Manually creating information models for such a significant number and variety of architectural monuments as Dong drum towers is challenging. The building logic based on "actual measurement construction" was investigated using the metamodel idea, and a metamodel-based automated modeling approach for the wood framework of Dong drum towers was presented utilizing programmable algorithms. Metamodels of fundamental frame kinds were also constructed. Case studies were used to verify the automated modeling's correctness, completeness, and efficiency using metamodel. The results suggest that, compared to manual modeling, automated modeling using metamodel may enhance the model's integrity and correctness by 5-10% while also reducing time efficiency by 10-20%. Metamodel and construction logic offer a novel way to investigate data-driven autonomous information-based modeling.

• Journal of applied mathematics & informatics
• /
• 제41권3호
• /
• pp.553-567
• /
• 2023

There are real life situations in our lives where the things are changing continuously or from time to time. It is a very important problem for one whether to continue the existing relationship or to form a new one after some occasions. That is, people, companies, cities, countries, etc. may change their opinion or position rapidly. In this work, we think of the problem of changing relationships from a mathematical point of view and think of an answer. In some sense, we comment these changes as power changes. Our number theoretical model will be based on this idea. Using the convolution sum of the restricted divisor function E, we obtain the answer to this problem.

• Korean Journal of Mathematics
• /
• 제31권4호
• /
• pp.485-494
• /
• 2023

The degree of hesitancy of a vertex in a hesitancy fuzzy graph depends on the degree of membership and non-membership of the vertex. We define a new class of hesitancy fuzzy graph, the intuitionistic hesitancy fuzzy graph in which the degree of hesitancy of a vertex is independent of the degree of its membership and non-membership. We introduce the idea of β-product of a pair of hesitancy fuzzy graphs and intuitionistic hesitancy fuzzy graphs and prove certain results based on this product.

• 한국수학사학회지
• /
• 제31권5호
• /
• pp.251-269
• /
• 2018

Empirical probability and classical probability, which are two interpretations of Kolmogorov's axiom, are two ways to recognize the chances of events occurring in the real world. In this paper, I analyzed and suggested the contents of the high school textbooks ${\ll}$Probability and Statistics${\gg}$, associated with two interpretations of probability and experiments on which two interpretations are based. By presenting the cases required expressly stating what the experiment is for supporting students' understanding of some concepts, it was discussed that stating or not stating what the experiment is should be carefully determined by the educational intent. Especially, I suggested that in the textbooks we contrast the good idea of calculating the ratios of two possibilities in the imaginary world of the classical probability with the normal idea of grasping the chances of events through the frequencies in the real world of the empirical probability, with distinguishing the experiments in two interpretations of probability. I also suggested that in the textbooks we make it clear that the Weak Law of Large Numbers justifies our expectations of the frequencies' reflecting the chances of events occurring in the real world under ideal conditions. Teaching and learning about the aesthetic elements and the practicality of imaginary mathematical thinking supported by these textbooks statements could be one form of Humanities education in mathematics as STEAM education.