• Communications for Statistical Applications and Methods
• /
• v.21 no.2
• /
• pp.183-191
• /
• 2014

We define a multivariate Cauchy distribution using a probability density function; subsequently, a Ferguson's definition of a multivariate Cauchy distribution can be viewed as a characterization theorem using the characteristic function approach. To clarify this characterization theorem, we construct two dependent Cauchy random variables, but their sum is not Cauchy distributed. In doing so the proofs depend on the characteristic function, but we use the cumulative distribution function to obtain the exact density of their sum. The derivation methods are relatively straightforward and appropriate for graduate level statistics theory courses.

• Nuclear Engineering and Technology
• /
• v.53 no.12
• /
• pp.3944-3951
• /
• 2021

Several reasons such as no free lunch theorem indicate that there is not a universal Feature selection (FS) technique that outperforms other ones. Moreover, some approaches such as using synthetic dataset, in presence of large number of FS techniques, are very tedious and time consuming task. In this study to tackle the issue of dependency of estimation accuracy on the selected FS technique, a methodology based on the heterogeneous ensemble is proposed. The performance of the major learning algorithms of neural network (i.e. the FFNN-BR, the FFNN-LM) in combination with the diverse FS techniques (i.e. the NCA, the F-test, the Kendall's tau, the Pearson, the Spearman, and the Relief) and different combination techniques of the heterogeneous ensemble (i.e. the Min, the Median, the Arithmetic mean, and the Geometric mean) are considered. The target parameters/transients of Bushehr nuclear power plant (BNPP) are examined as the case study. The results show that the Min combination technique gives the more accurate estimation. Therefore, if the number of FS techniques is m and the number of learning algorithms is n, by the heterogeneous ensemble, the search space for acceptable estimation of the target parameters may be reduced from n × m to n × 1. The proposed methodology gives a simple and practical approach for more reliable and more accurate estimation of the target parameters compared to the methods such as the use of synthetic dataset or trial and error methods.

• Journal for History of Mathematics
• /
• v.23 no.3
• /
• pp.57-73
• /
• 2010

Transcendental numbers are important in the history of mathematics because their study provided that circle squaring, one of the geometric problems of antiquity that had baffled mathematicians for more than 2000 years was insoluble. Liouville established in 1844 that transcendental numbers exist. In 1874, Cantor published his first proof of the existence of transcendentals in article [10]. Louville's theorem basically can be used to prove the existence of Transcendental number as well as produce a class of transcendental numbers. The number e was proved to be transcendental by Hermite in 1873, and $\pi$ by Lindemann in 1882. In 1934, Gelfond published a complete solution to the entire seventh problem of Hilbert. Within six weeks, Schneider found another independent solution. In 1966, A. Baker established the generalization of the Gelfond-Schneider theorem. He proved that any non-vanishing linear combination of logarithms of algebraic numbers with algebraic coefficients is transcendental. This study aims to examine the concept and development of transcendental numbers and to present students with its open problems promoting a research on it any further.

• Journal of applied mathematics & informatics
• /
• v.27 no.5_6
• /
• pp.1493-1499
• /
• 2009

Let $A_1$ and $A_2$ be nonzero complex idempotent and tripotent matrix, respectively. Denote a linear combination of the two matrices by A = $c_1A_1$ + $c_2A_2$, where $c_1,\;c_2$ are nonzero complex scalars. In this paper, under an assumption of $A_1A_2$ = $A_2A_1$, we characterize all situations in which the linear combination is tripotent. A statistical interpretation of this tripotent problem is also pointed out. Moreover, In [2], Baksalary characterized all situations in which the above linear combination is idem-potent by using the property of decomposition of a tripotent matrix, i.e. if $A_2$ is tripotent, then $A_2$ = $B_1-B_2$, where $B^2_i=B_i$, i = 1, 2 and $B_1B_2=B_2B_1=0$. While in this paper, by utilizing a method different from the one used by Baksalary in [2], we prove the theorem 1 in [2] again.

• Proceedings of the Korean Society for Technology of Plasticity Conference
• /
• 2003.05a
• /
• pp.176-179
• /
• 2003

The mean temperature prediction of strip is very important in hot strip finishing mill because of affecting on product quality and shape. Also, temperature can be used by basic information in other on-line control models with affecting control accuracy in factory. So, FE based on-line temperature model was developed for predicting strip mean temperature accurately in various process conditions and factory environments. There are many variables in affecting strip mean temperature in on-line states of factory. But some problems are occurred in considering all variables for making temperature model because of the bad efficiency of regression or fitting analysis. In this report, we have adopted dimensional analysis for solving these problems. We have many variables with dimensions affecting strip temperature but we are able to make non-dimensional variables less than dimensional variables from the combination of dimensional variables caused by PI-Theorem in fluid mechanics. The developed models are divided by two parts. The one is interstand temperature prediction model. The other is roll gap temperature model.

• Structural Engineering and Mechanics
• /
• v.25 no.1
• /
• pp.107-126
• /
• 2007

The problem related to the computation of bounds on plastic deformations for structures in plastic shakedown condition (alternating plasticity) is studied. In particular, reference is made to structures discretized by finite elements constituted by elastic perfectly plastic material and subjected to a special combination of fixed and cyclic loads. The load history is known during the steady-state phase, but it is unknown during the previous transient phase; so, as a consequence, it is not possible to know the complete elastic plastic structural response. The interest is therefore focused on the computation of bounds on suitable measures of the plastic strain which characterizes just the first transient phase of the structural response, whatever the real load history is applied. A suitable structural model is introduced, useful to describe the elastic plastic behaviour of the structure in the relevant shakedown conditions. A special bounding theorem based on a perturbation method is proposed and proved. Such theorem allows us to compute bounds on any chosen measure of the relevant plastic deformation occurring at the end of the transient phase for the structure in plastic shakedown; it represents a generalization of analogous bounding theorems related to the elastic shakedown. Some numerical applications devoted to a plane steel structure are effected and discussed.

• Journal of Power System Engineering
• /
• v.19 no.6
• /
• pp.60-67
• /
• 2015

While designing and operating machines, it is very important to understand the dynamic characteristic of the machines. Authors developed the Sylvester-transfer stiffness coefficient method in order to analyze effectively the free vibration of machines or structures. The Sylvester-transfer stiffness coefficient method was derived from the combination of the Sylvester's inertia theorem and the transfer stiffness coefficient method. In this paper, the authors formulate the computational algorithm for flexural free vibration analysis of axisymmetric annular plate using the Sylvester-transfer stiffness coefficient method. To confirm the usefulness of the Sylvester-transfer stiffness coefficient method, the natural frequencies and modes for two computational models computed using the Sylvester-transfer stiffness coefficient method are compared with those computed using the exact solution and the finite element method.

• Proceedings of the Korean Geotechical Society Conference
• /
• 2008.10a
• /
• pp.508-518
• /
• 2008

Reliability and sensitivity analysis of the design parameters for a section of caisson type quaywall which is the most applicable in Korea were performed. It was tried to estimate probabilities of failure for the system of the multiple failure modes and to analyze LCC in the quaywall structure. The reliability analysis was performed by FORM. Also, sensitivity indices were estimated using the reliability indices, which may be used inferring effects of each design parameter on the reliability indices. As a result, the coefficient of friction between caisson and rubble, the moment by self weight and the moment of resistance mostly affected on the reliability indices in the sliding, overturning and foundation failure, respectively. System reliability theorem was applied in order to estimate the probabilities of failure for the system of the multiple failure modes. As the results of estimation of the probabilities of failure for the system, all cases were more conservative than those for the elements, according to both failure mode and load combination applied to series system. It entirely exceeded the target reliability index, but it was consistent with the theorem. According to the optimum LCC with the width of the caisson, the probability of failure exceeded the target probability of failure at then time. Therefore, it was judged to be insufficient to the practical application.

• Communications for Statistical Applications and Methods
• /
• v.24 no.5
• /
• pp.481-492
• /
• 2017

This paper investigates a convergence rate of a test statistics given by two scale sampling method based on $A\ddot{i}t$-Sahalia and Jacod (Annals of Statistics, 37, 184-222, 2009). This statistics tests for longitudinal data having the existence of long memory dependence driven by fractional Brownian motion with Hurst parameter $H{\in}(1/2,\;1)$. We obtain an upper bound in the Kolmogorov distance for normal approximation of this test statistic. As a main tool for our works, the recent results in Nourdin and Peccati (Probability Theory and Related Fields, 145, 75-118, 2009; Annals of Probability, 37, 2231-2261, 2009) will be used. These results are obtained by employing techniques based on the combination between Malliavin calculus and Stein's method for normal approximation.

• Transactions on Control, Automation and Systems Engineering
• /
• v.3 no.3
• /
• pp.139-145
• /
• 2001

In this paper, we consider the H$_2$(or guaranteed cost control) and H$_{\infty}$ controller design methods for singular(or descriptor) systems with input time delay. Also, a mixed H$_2$and H$_{\infty}$ controller design algorithm is treated by combination of the proposed H$_2$and H$_{\infty}$ controller design method. The sufficient conditions for the existence of controllers and controller design methods are introduced at each Lemma and Theorem. Furthermore, we present optimization problems to get the upper bound of performance measures. The proposed methods are checked by examples.