• Title/Summary/Keyword: explicit equations

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Explicit Equations of Normal Depth for Drainage Pipes (하수관 등류수심 양해법 산정식)

  • Yoo, Dong-Hoon;Rho, Jung-Soo
    • Journal of Korea Water Resources Association
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    • v.38 no.7 s.156
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    • pp.527-535
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    • 2005
  • The computation of normal depth is very important for the design of channel and the analysis of water flow. Drainage pipe generally has the shape of curvature like circular or U-type, which is different from artificial triangular or rectangular channel. In this case, the computation of normal depth or the derivation of equations is very difficult because the change of hydraulic radius and area versus depth is not simple. If the ratio of the area to the diameter, or the hydraulic radius to the diameter of pipe is expressed as the water depth to the diameter of pipe by power law, however, the process of computing normal depth becomes relatively simple, and explicit equations can be obtained. In the present study, developed are the explicit normal depth equations for circular and U-type pipes, and the normal depth equation associated with Hagen (Manning) equation and friction factor equation of smooth turbulent flow by power law is also proposed because of its wide usage in engineering design.

Analytical Solution for Hypersonic Flow on Blunt Bodies (뭉뚝한 물체 주변에 형성된 극초음속유동해석)

  • Baik Doo Sung
    • Journal of computational fluids engineering
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    • v.8 no.4
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    • pp.1-5
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    • 2003
  • A Thin-layer Wavier-Stokes equations are applied for the hypersonic flow over blunt bodies with applications to laminar as well as turbulent flows. The equations are expressed in the forms of flux-vector splitting and explicit algorithm. The upwind schemes of Steger-Warming and Van Leer are investigated to predict accurately the heating loads along the surface of the body. A mixed scheme has been presented for the differencing the convective terms and the mixed scheme is found to be less dissipative producing accurate solutions.

ON CERTAIN NEW NONLINEAR RETARDED INTEGRAL INEQUALITIES FOR FUNCTIONS IN TWO VARIABLES AND THEIR APPLICATIONS

  • Ma, Qing-Hua;Pecaric, Josip
    • Journal of the Korean Mathematical Society
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    • v.45 no.1
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    • pp.121-136
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    • 2008
  • Some new explicit bounds on the solutions to a class of new nonlinear retarded Volterra-Fredholm type integral inequalities in two independent variables are established, which can be used as effective tools in the study of certain integral equations. Some examples of application are also indicated.

DIFFERENTIAL EQUATIONS AND ZEROS FOR NEW MIXED-TYPE HERMITE POLYNOMIALS

  • JUNG YOOG KANG
    • Journal of applied mathematics & informatics
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    • v.41 no.4
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    • pp.869-882
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    • 2023
  • In this paper, we find induced differential equations to give explicit identities of these polynomials from the generating functions of 2-variable mixed-type Hermite polynomials. Moreover, we observe the structure and symmetry of the zeros of the 2-variable mixed-type Hermite equations.

Linearized analysis of the internal pressures for a two-compartment building with leakage

  • Yu, Xianfeng;Gu, Ming;Xie, Zhuangning
    • Wind and Structures
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    • v.28 no.2
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    • pp.89-97
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    • 2019
  • The non-linear equations governing wind-induced internal pressures for a two-compartment building with background leakage are linearized based on some reasonable assumptions. The explicit admittance functions for both building compartments are derived, and the equivalent damping coefficients of the coupling internal pressure system are iteratively obtained. The RMS values of the internal pressure coefficients calculated from the non-linear equations and linearized equations are compared. Results indicate that the linearized equations generally have good calculation precision when the porosity ratio is less than 20%. Parameters are analyzed on the explicit admittance functions. Results show that the peaks of the internal pressure in the compartment without an external opening (Compartment 2) are higher than that in the compartment with an external opening (Compartment 1) at lower Helmholtz frequency. By contrast, the resonance peak of the internal pressure in compartment 2 is lower than that in compartment 1 at higher Helmholtz frequencies.

Explicit time integration algorithm for fully flexible cell simulation (외연적 적분 기법을 적용한 Fully Flexible Cell 분자 동영학 시뮬레이션)

  • Park Shi-Dong;Cho Maeng-Hyo
    • Proceedings of the Computational Structural Engineering Institute Conference
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    • 2006.04a
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    • pp.389-394
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    • 2006
  • Fully flexible cell preserves Hamiltonian in structure, so the symplectic time integrator is applied to the equations of motion. Primarily, generalized leapfrog time integration (GLF) is applicable, but the equations of motion by GLF have some of implicit formulas. The implicit formulas give rise to a complicate calculation for coding and need an iteration process. In this paper, the time integration formulas are obtained for the fully flexible cell molecular dynamics simulation by using the splitting time integration. It separates flexible cell Hamiltonian into terms corresponding to each of Hamiltonian term, so the simple and completely explicit recursion formula was obtained. The explicit formulas are easy to implementation for coding and may be reduced the integration time because they are not need iteration process. We are going to compare the resulting splitting time integration with the implicit generalized leapfrog time integration.

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On the maximum likelihood estimation for a normal distribution under random censoring

  • Kim, Namhyun
    • Communications for Statistical Applications and Methods
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    • v.25 no.6
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    • pp.647-658
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    • 2018
  • In this paper, we study statistical inferences on the maximum likelihood estimation of a normal distribution when data are randomly censored. Likelihood equations are derived assuming that the censoring distribution does not involve any parameters of interest. The maximum likelihood estimators (MLEs) of the censored normal distribution do not have an explicit form, and it should be solved in an iterative way. We consider a simple method to derive an explicit form of the approximate MLEs with no iterations by expanding the nonlinear parts of the likelihood equations in Taylor series around some suitable points. The points are closely related to Kaplan-Meier estimators. By using the same method, the observed Fisher information is also approximated to obtain asymptotic variances of the estimators. An illustrative example is presented, and a simulation study is conducted to compare the performances of the estimators. In addition to their explicit form, the approximate MLEs are as efficient as the MLEs in terms of variances.

ON j-INVARIANTS OF WEIERSTRASS EQUATIONS

  • Horiuchi, Ryutaro
    • Journal of the Korean Mathematical Society
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    • v.45 no.3
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    • pp.695-698
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    • 2008
  • A simple proof of the fact that the j-invariants for Weierstrass equations are invariant under birational transformations which keep the forms of Weierstrass equations is given by finding a non-trivial explicit birational transformation which sends a normalized Weierstrass equation to the same equation.