• Title/Summary/Keyword: Formulae

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THE ANALOGUE OF WIENER SPACE WITH VALUES IN ORLICZ SPACE

  • Ryu, Kun Sik
    • Journal of the Chungcheong Mathematical Society
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    • v.27 no.4
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    • pp.689-695
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    • 2014
  • Let M be an N-function satisfies the ${\Delta}_2$-condition and let $O_M$ be the Orlicz space associated with M. Let $C(O_M)$ be the space of all continuous functions defined on the interval [0, T] with values in $O_M$. In this note, we define the analogue of Wiener measure $m^M_{\phi}$ on $C(O_M)$, establish the Wiener integration formulae for the cylinder functions on $C(O_M)$ and give some examples related to our formulae.

Strength Evaluation Formulae for Ring-stiffened Tubular T-joints (환보강 T형 관이음부의 강도산정식)

  • 조현만;류연선
    • Proceedings of the Computational Structural Engineering Institute Conference
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    • 2002.10a
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    • pp.533-540
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    • 2002
  • Tubular joints having a large diameter are reinforced using internal ring stiffener in order to increase the load carrying capacity. In this study, the static strengths of Internally ring-stiffened tubular T-joints subjected to compressive brace loading are assessed. Nonlinear finite element analyses are used to compute the behavior of unstiffened and ring-stiffened T-joints. From the numerical results, Internal ring stiffener is found to efficient in improving the ultimate capacity, and reinforcement effect are calculated. The influence of geometric parameters for members and ring is evaluated. Based on the FE results, regression analysis is performed considering practical sizes of ring stiffener, finally strength estimation formulae for ring-stiffened T-joints are proposed.

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Investigation of Wave Resistance Performance for Ships and Offshore Structures based on Arbitrary Lagrangian Eulerian Method (ALE 기법을 기반 선박 및 해양 구조물의 내파 성능 분석)

  • Lee, Chi-Seung;Kim, Joo-Hyun;Kim, Myung-Hyun;Lee, Jae-Myung
    • Proceedings of the Computational Structural Engineering Institute Conference
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    • 2011.04a
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    • pp.553-556
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    • 2011
  • The primary aim of the present study is to propose new design formulae that can be used to evaluate the structural performance of breakwaters installed on container carriers under green water impact loads. A series of numerical analyses for green water impact loads inducing breakwater collapse have been carried out. The well-known fluid-structure interaction analysis technique has been adopted realistically to consider the phenomenon of green water impact loads. The structural behavior of these breakwaters under green water impact loads has also been carried out simultaneously throughout the transient analysis. A verification study of the numerical results was performed using the actual collapse incidents of breakwaters on container carriers. It would be expected that the proposed design formulae, based on the obtained insights, could be used as practical guidelines for the design of breakwaters on container carriers.

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COUNTING STATISTICS MODIFIED BY TWO DEAD TIMES IN SERIES

  • Choi, H.D.
    • Nuclear Engineering and Technology
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    • v.43 no.3
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    • pp.287-300
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    • 2011
  • Counting statistics modified by introducing two dead times in series under a Poisson input distribution are discussed. A previous study examined the two cases of series combinations of nonextended-extended (NE-E) and extended-extended (EE) dead times. The present study investigated the remaining two cases of extended-nonextended (E-NE) and nonextended-nonextended (NE-NE) dead times. For the three time origins of the counting processes - ordinary, equilibrium, and shifted processes - a set of formulae was newly developed from a general formulation and presented for the event time interval densities, total densities, and exact mean and variance of the counts in a given counting duration. The asymptotic expressions for the mean and variance of the counts, which are most convenient for applications, were fully listed. The equilibrium mean count rates distorted by the three dead times in series were newly derived from the information obtained in these studies. An application of the derived formulae is briefly discussed.

Disturbance analysis of hydropower station vertical vibration dynamic characteristics: the effect of dual disturbances

  • Zhi, Baoping;Ma, Zhenyue
    • Structural Engineering and Mechanics
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    • v.53 no.2
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    • pp.297-309
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    • 2015
  • The purpose of this work is to analyze the effect of structure parameter disturbance on the dynamic characteristics of a hydropower station powerhouse. A vibration model with a head-cover system is established, and then the general disturbance problem analysis methods are discussed. Two new formulae based on two types of disturbances are developed from existing methods. The correctness and feasibility of these two formulae are validated by analyzing the hydropower station powerhouse vibration model. The appropriate calculation method for disturbance of the hydropower station powerhouse vibration dynamic characteristics is derived.

A Geometrical Structural Model of 2:1 Trioctahedral Clay Minerals (2:1 삼팔면체 점토광물의 기하학적 구조모델)

  • 유재영
    • Journal of the Mineralogical Society of Korea
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    • v.4 no.2
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    • pp.90-98
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    • 1991
  • This study introduces a new structural model of 1M 2:1 trioctahedral clay minerals or, more generally, 2:1 trioctahedral phyllosilicates. The structural model requires only the chemical formulae of the clay minerals as an input and uses the regression relation (Radoslovich, 1962) to calculate the a- and b-dimensions of the phyllosilicates with the given chemical formulae. The atomic coordinates of the constituent atoms are geometrically calculated for C2/m space group under the assumption that the interatomic distances are constant. To determine the c-dimension, this study calculates the binding energies of 1M 2:1 trioctahedral phyllosilicates as a function of d(001) and find the minimum energy producing d(001). The structural model generates the cell dimensions, interaxial angles, interatomic distances, octahedral, tetrahedral and interlayer thickness, polyhedron deformation angles and atomic coordinates in the unit cell. The simulated structural parameters of phlogopite and annite are very close to the reported data by Hazen and Burnham (1973), suggesting that the structure simulation using only the chemical formule is successful, and thus, that the structural model of this study overcomes the difficulties in the previous models by other investigators.

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Updating algorithms in statistical computations (통계계산에서의 갱신 알고리즘에 관한 연구)

  • 전홍석
    • The Korean Journal of Applied Statistics
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    • v.5 no.2
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    • pp.283-292
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    • 1992
  • Updating algorithms are studied for the basic statistics (mean, variance). For a linear model, a recursive formulae for least squares estimators of regression coefficients, residual sum of squares and variance-covariance matrix are also studied. Hotelling's $T^2$ statistics can be calculated recursively using the recursive formulae of mean vector and variance-covariance matrix without computing the sample variance-covariance matrix at each stage.

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A Study on the Accuracy of Convergent Photographs Using Non-Metric Camera (비측량용 사진기에 의한 수렴사진의 정확도에 관한 연구)

  • Yeu, Bock-Mo;Kwon, Hyon;Yu, Ki-Yun
    • Journal of the Korean Society of Surveying, Geodesy, Photogrammetry and Cartography
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    • v.7 no.2
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    • pp.63-68
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    • 1989
  • This study was to develope the methmatic prediction model of accuracy for the convergent photographs using nonmetric camera in close range photogrammetry. By analyzing positioning error on object distance and convergent angles, the validity of the new formulae for prediction of accuracy were proved. Rational design of camera systems and convergent angles according to accuracy demands in plane and height were developed using these formulae.

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The Shape and Virial Theorem of a Star Cluster in the Galactic Tidal Force Field

  • Lee, See-Woo;Rood, Herbert J.
    • Journal of The Korean Astronomical Society
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    • v.2 no.1
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    • pp.1-9
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    • 1969
  • On the instantaneous tidal relaxation approximation, formulae are derived for the ellipticities and virial theorem of a slightly flattened homogeneous rotating cluster (the largest axis of the cluster is directed towards the Galactic center), in terms of the Galactic tidal force and the characteristic intrinsic plus orbital angular velocity. The expression for a purely tidally-determined ellipticity is identical to that for an incompressible fluid body of uniform density. Orbital motion generally contributes significantly to the shape of the cluster. The virial theorem is identical to that for an isolated cluster except that the gravitational potential energy is multiplied by (1-${\chi}$), where ${\chi}$ is a positive tidal correction term. To obtain the actual mass of a cluster, the virial theorem mass based on an isolated cluster should be multiplied by the factor 1/(1-${\chi}$). The formulae are applied to open star clusters, the globular cluster ${\omega}$ Centauri, and dwarf elliptical galaxies in the Local Group.

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Formulae for the frequency equations of beam-column system carrying a fluid storage tank

  • El-Sayed, Tamer. A.;Farghaly, Said. H.
    • Structural Engineering and Mechanics
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    • v.73 no.1
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    • pp.83-95
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    • 2020
  • In this work, a mathematical model of beam-column system carrying a double eccentric end mass system is investigated, and solved analytically based on the exact solution analysis. The model considers the case in which the double eccentric end mass is a rigid storage tank containing fluid. Both Timoshenko and Bernoulli-Euler beam bending theories are considered. Equation of motion, general solution and boundary conditions for the present system model are developed and presented in dimensional and non-dimensional format. Several important non-dimensional design parameters are introduced. Symbolic and/or explicit formulae of the frequency and mode shape equations are formulated. To the authors knowledge, the present reduced closed form symbolic and explicit frequency equations have not appeared in literature. For different applications, the results are validated using commercial finite element package, namely ANSYS. The beam-column system investigated in this paper is significant for many engineering applications, especially, in mechanical and structural systems.