SOME RESULTS ON CONDITIONALLY UNIFORMLY STRONG MIXING SEQUENCES OF RANDOM VARIABLES

Yuan, De-Mei,Hu, Xue-Mei,Tao, Bao Korean Mathematical Society 2014 대한수학회지 Vol.51 No.3

From the ordinary notion of uniformly strong mixing for a sequence of random variables, a new concept called conditionally uniformly strong mixing is proposed and the relation between uniformly strong mixing and conditionally uniformly strong mixing is answered by examples, that is, uniformly strong mixing neither implies nor is implied by conditionally uniformly strong mixing. A couple of equivalent definitions and some of basic properties of conditionally uniformly strong mixing random variables are derived, and several conditional covariance inequalities are obtained. By means of these properties and conditional covariance inequalities, a conditional central limit theorem stated in terms of conditional characteristic functions is established, which is a conditional version of the earlier result under the non-conditional case.

SOME RESULTS ON CONDITIONALLY UNIFORMLY STRONG MIXING SEQUENCES OF RANDOM VARIABLES

De-Mei Yuan,Xue-Mei Hu,Bao Tao 대한수학회 2014 대한수학회지 Vol.51 No.3

From the ordinary notion of uniformly strong mixing for a se- quence of random variables, a new concept called conditionally uniformly strong mixing is proposed and the relation between uniformly strong mix- ing and conditionally uniformly strong mixing is answered by examples, that is, uniformly strong mixing neither implies nor is implied by condi- tionally uniformly strong mixing. A couple of equivalent definitions and some of basic properties of conditionally uniformly strong mixing ran- dom variables are derived, and several conditional covariance inequalities are obtained. By means of these properties and conditional covariance inequalities, a conditional central limit theorem stated in terms of condi- tional characteristic functions is established, which is a conditional version of the earlier result under the non-conditional case.

A Note on the Dependence Conditions for Stationary Normal Sequences

Choi, Hyemi The Korean Statistical Society 2015 Communications for statistical applications and me Vol.22 No.6

Extreme value theory concerns the distributional properties of the maximum of a random sample; subsequently, it has been significantly extended to stationary random sequences satisfying weak dependence restrictions. We focus on distributional mixing condition $D(u_n)$ and the Berman condition based on covariance among weak dependence restrictions. The former is assumed for general stationary sequences and the latter for stationary normal processes; however, both imply the same distributional limit of the maximum of the normal process. In this paper $D(u_n)$ condition is shown weaker than Berman's covariance condition. Examples are given where the Berman condition is satisfied but the distributional mixing is not.

Investigation of pressure pulsations in a reactor coolant pump with mixed-flow vaned diffuser and spherical casing

Xide Lai,Daoxing Ye,Bo Yu,Xiaoming Chen,Yaguang Heng 대한기계학회 2022 JOURNAL OF MECHANICAL SCIENCE AND TECHNOLOGY Vol.36 No.1

Pressure pulsations are an important factors that cause unstable phenomena such as vibration and noise in the reactor coolant pump (RCP), which is much more complex than inside a general mixed-flow pump due to its structure and actual operating conditions. It is necessary to figure out its characteristics at different operating conditions in order to meet the high requirements of reliability and safety in both design and operation phases. Pressure pulsations inside the impeller and diffuser vanes was carefully investigated by using 3D unsteady flow simulations of the completed pump at 5 operating conditions. To seek the relationship between the pressure pulsations characteristics and operating conditions, the timedomain and frequency-domain characteristics of pressure pulsations at different locations inside the RCP were analyzed. It has been shown that the dominant frequency of pressure pulsations is mainly governed by the blade-passing frequency due to rotor-stator interaction (RSI) between the impeller and diffuser vanes at all operating conditions, and the amplitude of pressure pulsations mainly depends on the operating discharges. The influence on the peak amplitude of its higher harmonics can be neglected when operating at the design discharge, but cannot be negligible for operating at the smaller discharge. The behavior of pressure pulsations at the inlet of the impeller in circumferential direction is not the same and more intensive on the suction side than the pressure side of a blade at different operating conditions, but it is almost the same at the outlet of the impeller as the interaction between the impeller and diffuser vanes. The maximum amplitude of pressure pulsations mainly depends on the operating discharge and reaches the smallest level at the design operating condition. Due to geometric features of the spherical casing, the vortex flow inside the spherical casing leads to the highly irregular and unsteady pressure pulsations inside flow channel of the impeller and diffuser under the smaller discharge operating conditions, and the amplitude of pressure pulsations in higher frequencies increases with the decreasing of the operating discharge. The amplitude of pressure pulsations inside the whole flow channel distinctly increases when the RCP is operating at the extreme small operating discharge. The spherical casing does have influence on the pressure pulsations inside the impeller and diffuser vanes, the effect is stronger under smaller discharge operating conditions than at larger ones.

Sensitivity of friction condition in finite element investigations of equal channel angular extrusion

Son, I.H.,Jin, Y.G.,Im, Y.T.,Chon, S.H.,Park, J.K. Elsevier Sequoia 2007 Materials science & engineering. properties, micro Vol.445 No.-

Equal channel angular extrusion (ECAE) is an effective forming technique that increases the material strength by accumulating plastic strain into the workpiece without changing its cross-sectional shape in the multi-pass processing. This study concentrates on the investigation of interface contact phenomenon between the workpiece and channel in terms of forming load and material flow predictions. The change of contact conditions during remeshing was also investigated in terms of variation of load requirements and volume losses. In order to validate the numerical algorithm proposed, simulation results were compared with the experimentally measured data of the ECAE with the CP-Ti Gr-1 cylindrical specimen. Numerical simulations were obtained by applying the mixed finite element formulation with tetrahedral elements under the non-isothermal condition. For determination of the material data, compression test was carried out and the tested data was interpolated as a function of strain, strain rate and temperature. The current investigation clearly showed the importance of proper handling of the friction boundary condition during numerical simulations to guarantee the solution accuracy of the ECAE.

FREQUENCY-DOMAIN APPROACH TO PARABOLIC DIFFERENTIAL EQUATIONS WITH MIXED BOUNDARY CONDITION

LEE, JONGWOO 광운대학교 기초과학연구소 1998 기초과학연구소논문집 Vol.27 No.-

We consider a numerical method to approximate solutions for parabolic problems with mixed boundary condition. We solve an indefinite complex elliptic problem for each frequency instead of an elliptic problem for each time, by taking the Fourier transformation of given equations in the space-time domain into the space-frequency domain. Fourier inversion will then recover the solution of the original problem in the space-time domain. This method turns out to be naturally parallelizable. Existence and uniqueness of the solution for the transformed problem corresponding to each frequency are established. Fourier invertibility of the solution in the frequency-domain is also examined. Error estimates for a finite element approximation to the solution of each transformed problem corresponding to each frequency and full error estimates for solving the given problem using a discrete Fourier inverse transform are presented.

Buckling of rectangular plates with mixed edge supports

Xiang, Y.,Su, G.H. Techno-Press 2002 Structural Engineering and Mechanics, An Int'l Jou Vol.14 No.4

This paper presents a domain decomposition method for buckling analysis of rectangular Kirchhoff plates subjected to uniaxial inplane load and with mixed edge support conditions. A plate is decomposed into two rectangular subdomains along the change of the discontinuous support conditions. The automated Ritz method is employed to derive the governing eigenvalue equation for the plate system. Compatibility conditions are imposed for transverse displacement and slope along the interface of the two subdomains by modifying the Ritz trial functions. The resulting Ritz function ensures that the transverse displacement and slope are continuous along the entire interface of the two subdomains. The validity and accuracy of the proposed method are verified with convergence and comparison studies. Buckling results are presented for several selected rectangular plates with various combination of mixed edge support conditions.

기포벽면에 혼합경계조건을 이용한 소노루미네센스 현상에 대한 분자동력학 시뮬레이션

임찬수(Chansoo Im),김기영(Ki Young Kim),곽호영(Ho-Young Kwak) 대한기계학회 2007 대한기계학회 춘추학술대회 Vol.2007 No.10

Sonolumincescence is light emission associated with the catastrophic collapse of a trapped micro gas bubble under periodic ultrasonic field. Molecular dynamics (MD) simulation of collapsing bubble in sulfuric acid solution was performed with the various boundary conditions such as adiabatic, heat bath and mixed boundary conditions. The molecules inside the gas bubble were assumed by hard sphere ones and the instantaneous bubble radius, velocity, pressure and temperature at the bubble wall which were used in the simulation were obtained from the Keller-Miksis equation with pressure data taken from MD simulation. With a proper boundary condition at the bubble wall, the MD simulation results for the bubble wall velocity, the gas temperature and pressure around the collapse point for the sonoluminescing bubbles are in acceptable agreement with the theoretical predictions. Our study has revealed that the collapsing process of sonoluminescing gas bubble proceeds almost adiabatically.

DISCONTINUOUS GALERKIN METHOD FOR NONLINEAR PARABOLIC PROBLEMS WITH MIXED BOUNDARY CONDITION

엄미례,이현영,신준용 한국전산응용수학회 2014 Journal of applied mathematics & informatics Vol.32 No.5

In this paper we consider the nonlinear parabolic problems with mixed boundary condition. Under comparatively mild conditions of the coefficients related to the problem, we construct the discontinuous Galerkin approximation of the solution to the nonlinear parabolic problem. We discretize spatial variables and construct the finite element spaces consisting of discontinuous piecewise polynomials of which the semidiscrete approximations are composed. We present the proof of the convergence of the semidiscrete approximations in L∞(H¹) and L∞(L²) normed spaces.

DISCONTINUOUS GALERKIN METHOD FOR NONLINEAR PARABOLIC PROBLEMS WITH MIXED BOUNDARY CONDITION

Ohm, Mi Ray,Lee, Hyun Yong,Shin, Jun Yong The Korean Society for Computational and Applied M 2014 Journal of applied mathematics & informatics Vol.32 No.5

In this paper we consider the nonlinear parabolic problems with mixed boundary condition. Under comparatively mild conditions of the coefficients related to the problem, we construct the discontinuous Galerkin approximation of the solution to the nonlinear parabolic problem. We discretize spatial variables and construct the finite element spaces consisting of discontinuous piecewise polynomials of which the semidiscrete approximations are composed. We present the proof of the convergence of the semidiscrete approximations in $L^{\infty}(H^1)$ and $L^{\infty}(L^2)$ normed spaces.