• Current Applied Physics
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• v.18 no.11
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• pp.1174-1181
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• 2018

In nanomagnetism, one of the crucial scientific questions is whether magnetic behaviors are deterministic or stochastic on a nanoscale. Apart from the exciting physical issue, this question is also of paramount highest relevance for using magnetic materials in a wealth of technological applications such as magnetic storage and sensor devices. In the past, the research on the stochasticity of a magnetic process has been mainly done by macroscopic measurements, which only offer ensemble-averaged information. To give more accurate answer for the question and to fully understand related underlying physics, the direct observation of statistical behaviors in magnetic structures and magnetic phenomena utilizing advanced characterization techniques is highly required. One of the ideal tools for such study is a full-field soft X-ray microscope since it enables imaging of magnetic structures on the large field of view within a few seconds. Here we review the stochastic behaviors of various magnetic processes including magnetization reversal process in thin films, magnetic domain wall motions in nanowires, and magnetic vortex formations in nanodisks studied by full-field soft X-ray microscopy. The origin triggering the stochastic nature witnessed in each magnetic process and the way to control the intrinsic nature are also discussed.

• Journal of the Korean Mathematical Society
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• v.33 no.2
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• pp.319-332
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• 1996

Many authors have studied multiple stochastic integrals in pursuit of the existence of product processes in terms of multiple integrals. But there has not been much research into the structure of the product processes themselves. In this direction, a study which gives emphasis on sample path continuity and boundedness properties was initiated in Pyke[9]. For details of problem set-ups and necessary notations, see [9]. Recently the weak limits of U-processes are shown to be chaos processes, which is product of the same Brownian measures, see [2] and [7].

• Transactions of the Korean Society for Noise and Vibration Engineering
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• v.13 no.1
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• pp.48-55
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• 2003

Hidden Markov Model(HMM) has a doubly embedded stochastic process with an underlying stochastic process that can be observed through another set of stochastic processes. This structure of HMM is useful for modeling vector sequence that doesn't look like a stochastic process but has a hidden stochastic process. So, HMM approach has become popular in various areas in last decade. The increasing popularity of HMM is based on two facts : rich mathematical structure and proven accuracy on critical application. In this paper, we applied continuous HMM (CHMM) approach with AR coefficient to detect and predict the chatter of lathe bite and to diagnose the wear of oil Journal bearing using rotor shaft displacement. Our examples show that CHMM approach is very efficient method for machine health monitoring and prediction.

• Structural Engineering and Mechanics
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• v.52 no.3
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• pp.525-540
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• 2014

The Lyapunov exponent and moment Lyapunov exponents of Hill's equation with frequency and damping coefficient fluctuated by correlated wideband random processes are studied in this paper. The method of stochastic averaging, both the first-order and the second-order, is applied. The averaged $It\hat{o}$ differential equation governing the pth norm is established and the pth moment Lyapunov exponents and Lyapunov exponent are then obtained. This method is applied to the study of the almost-sure and the moment stability of the stationary solution of the thin simply supported beam subjected to time-varying axial compressions and damping which are small intensity correlated stochastic excitations. The validity of the approximate results is checked by the numerical Monte Carlo simulation method for this stochastic system.

• Communications for Statistical Applications and Methods
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• v.2 no.1
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• pp.201-208
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• 1995

In the last years there has been growing interest in concepts of positive dependence for families of random variables such that concepts are considerable us in deriving inequalities in probability and statistics. Lehman introdued various concepts of positive dependence for bivariate random variables. A much stronger notions of positive dependence were later considered by Esary, Proschan, and Walkup. Ahmed et al and Ebrahimi and Ghosh also obtained multivariate versions of various bivariate positive dependence as descrived by Lehman. See also Block al. Glaz and Johnson an Barlow and Proschan and the references there. Multivariate processes arise when instead of observing a single process we observe several processes, say $X_19t), \cdots, X_n(t)$ simultaneously. For example, in an engineering context we may want to study the simultaneous variation of current and voltage, or temperature, pressure and volume over time. In economics we may be interested in studying inflation rates and money supply, unemployment and interest rates. We could of course, study each quantity on its own and treat each as a separate univariate process. Although this would give us some information about each quantity it could never give information about the interrelationship between various quantities. This leads us to introduce some concepts of positive and for multivariate stochastic processes. The concepts of positive dependence have subsequently been extended to stochastic processes in different directions by many authors.

• Structural Engineering and Mechanics
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• v.20 no.1
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• pp.85-110
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• 2005

This paper aims at formulating various statistical models for the study of a ten year Weigh-in-Motion (WIM) data collected from various WIM stations in Hong Kong. In order to study the bridge live load model it is important to determine the mathematical distributions of different load affecting parameters such as gross vehicle weights, axle weights, axle spacings, average daily number of trucks etc. Each of the above parameters is analyzed by various stochastic processes in order to obtain the mathematical distributions and the Maximum Likelihood Estimation (MLE) method is adopted to calculate the statistical parameters, expected values and standard deviations from the given samples of data. The Kolmogorov-Smirnov (K-S) method of approach is used to check the suitability of the statistical model selected for the particular parameter and the Monte Carlo method is used to simulate the distributions of maximum value stochastic processes of a series of given stochastic processes. Using the statistical analysis approach the maximum value of gross vehicle weight and axle weight in bridge design life has been determined and the distribution functions of these parameters are obtained under both free-flowing traffic and dense traffic status. The maximum value of bending moments and shears for wide range of simple spans are obtained by extrapolation. It has been observed that the obtained maximum values of the gross vehicle weight and axle weight from this study are very close to their legal limitations of Hong Kong which are 42 tonnes for gross weight and 10 tonnes for axle weight.

• Bulletin of the Korean Mathematical Society
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• v.21 no.2
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• pp.138-138
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• 1984

• Proceedings of the Korean Operations and Management Science Society Conference
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• 1993.04a
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• pp.302-302
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• 1993

• Journal of applied mathematics & informatics
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• v.6 no.3
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• pp.959-968
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• 1999

In this paper we are obtained new results for bivariate pro-cesses which help us to tell the dependent structure among hitting times of the processes. We are proposed both dependence properties and the-oretical results among the processes and certain kinds of dependence properties when we are imposed on processes are reflected as analo-gous properties of corresponding hitting times. Finlly we are given some examples to illustrate these concepts.

• Communications for Statistical Applications and Methods
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• v.3 no.3
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• pp.235-245
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• 1996

In this paper, a partial ordering of positive quadrant dependence(PQD) for bivariate stochastic processes are introduced and basic properties and closure under certain statistical operations are derived. Examples are given to illustrate these concepts