• 제목/요약/키워드: inverse functions

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Closed form ultimate strength of multi-rectangle reinforced concrete sections under axial load and biaxial bending

  • da Silva, V. Dias;Barros, M.H.F.M.;Julio, E.N.B.S.;Ferreira, C.C.
    • Computers and Concrete
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    • v.6 no.6
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    • pp.505-521
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    • 2009
  • The analysis of prismatic members made of reinforced concrete under inclined bending, especially the computation of ultimate loads, is a pronounced non-linear problem which is frequently solved by discretizing the stress distribution in the cross-section using interpolation functions. In the approach described in the present contribution the exact analytical stress distribution is used instead. The obtained expressions are integrated by means of a symbolic manipulation package and automatically converted to optimized Fortran code. The direct problem-computation of ultimate internal forces given the position of the neutral axis-is first described. Subsequently, two kinds of inverse problem are treated: the computation of rupture envelops and the dimensioning of reinforcement, given design internal forces. An iterative Newton-Raphson procedure is used. Examples are presented.

ON A CLASS OF GENERALIZED FUNCTIONS FOR SOME INTEGRAL TRANSFORM ENFOLDING KERNELS OF MEIJER G FUNCTION TYPE

  • Al-Omari, Shrideh Khalaf
    • Communications of the Korean Mathematical Society
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    • v.33 no.2
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    • pp.515-525
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    • 2018
  • In this paper, we investigate a modified $G^2$ transform on a class of Boehmians. We prove the axioms which are necessary for establishing the $G^2$ class of Boehmians. Addition, scalar multiplication, convolution, differentiation and convergence in the derived spaces have been defined. The extended $G^2$ transform of a Boehmian is given as a one-to-one onto mapping that is continuous with respect to certain convergence in the defined spaces. The inverse problem is also discussed.

A q-ANALOGUE OF QI FORMULA FOR r-DOWLING NUMBERS

  • Cillar, Joy Antonette D.;Corcino, Roberto B.
    • Communications of the Korean Mathematical Society
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    • v.35 no.1
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    • pp.21-41
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    • 2020
  • In this paper, we establish an explicit formula for r-Dowling numbers in terms of r-Whitney Lah and r-Whitney numbers of the second kind. This is a generalization of the Qi formula for Bell numbers in terms of Lah and Stirling numbers of the second kind. Moreover, we define the q, r-Dowling numbers, q, r-Whitney Lah numbers and q, r-Whitney numbers of the first kind and obtain several fundamental properties of these numbers such as orthogonality and inverse relations, recurrence relations, and generating functions. Hence, we derive an analogous Qi formula for q, r-Dowling numbers expressed in terms of q, r-Whitney Lah numbers and q, r-Whitney numbers of the second kind.

Numerical Inversion Technique for the One and Two-Dimensional L2-Transform Using the Fourier Series and Its Application to Fractional Partial Differential Equations

  • Aghili, Arman;Ansari, Alireza
    • Kyungpook Mathematical Journal
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    • v.52 no.4
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    • pp.383-395
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    • 2012
  • In this paper, we use a computational algorithm for the inversion of the one and two-dimensional $\mathcal{L}_2$-transform based on the Bromwich's integral and the Fourier series. The new inversion formula can evaluate the inverse of the $\mathcal{L}_2$-transform with considerable accuracy over a wide range of values of the independent variable and can be devised for the functions which are not Laplace transformable and have damping motion in small interval near origin.

A Generalized Fourier Transform Based on a Periodic Window

  • Yoo, Kyung-Yul
    • The Journal of the Acoustical Society of Korea
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    • v.15 no.4E
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    • pp.53-57
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    • 1996
  • An extension of the well-known Fourier transform is developed in this paper. It is denoted as the generalized Fourier transform(GFT), since it encompasses the Fourier transform as its special case. The first idea of this extension can be found on [1]. In the definition of the N-point discrete GFT, it first construct a passband in time which functions as a window in the time domain. An appropriate interpretation of each variables are introduced during the definition of the GFT, followed by the formal derivation of the inverse GFT. This transform pair is similar to the windowing in the frequency domain such as the subband coding technique (or filter bank approach) and could be extended to the wavelet transform.

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Analysis of Probabilities of Failure and Partial Safety Factors of Armor Units on Tranding and Coastal Harbors (무역항 및 연안항 피복재의 파괴확률과 부분안전계수 해석)

  • Lee, Cheol-Eung;Park, Dong-Heon
    • Journal of Industrial Technology
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    • v.28 no.B
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    • pp.157-165
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    • 2008
  • Level II AFDA and Level III MCS reliability models are applied to analyze the stability of armor units on trading and coastal harbors in Korea. Hudson's formula and Van der Meer's formula are used in this reliability analysis. Also, probability density functions of reliability index and probability of failure are derived by the additional analysis. In addition, the partial safety factors of all harbors related to armor units can be straightforwardly evaluated by the inverse-reliability method. The upper and lower limits and average level of partial safety factors can be statistically investigated with the results of all cases applied in this paper. Therefore, it may be possible to design armor units of new breakwaters including the uncertainty of random variable and target level by using the present results.

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A Novel Digital Automatic Gain Control for a WCDMA Receiver

  • Kim, Kyusheob;Sungbin Im;Kim, Chonghoon
    • Proceedings of the IEEK Conference
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    • 2002.07b
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    • pp.1358-1361
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    • 2002
  • In this paper, we propose a new architecture of digital automatic gain control (AGC) for a wideband code division multiple access (WCDMA) receiver. The feature of the proposed architecture is simplicity, in that it does not utilize complicated mathematical functions such as log and its inverse. When the proposed algorithm is implemented using a field programmable gate array (FPGA) device, the number of slices used to implement is 130 over the total of 5120 slices (less than 3%) with 61.44 ㎒ clock. This algorithm has been successfully applied to commercial WCDMA base stations.

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Calculation of Impact Forces of an Arbitrary Force Applied Vibro-Impact system (임의 하중이 작용하는 진동-충격시스템에서의 충격력계산)

  • 이창희
    • Journal of KSNVE
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    • v.10 no.4
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    • pp.679-685
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    • 2000
  • A procedure is presented for calculating the magnitude and shape of impact pulses in a vibro-impact system when an arbitrary input force is applied to a point in the system. The procedure utilizes the condition that the displacements of two contacting point in the primary and secondary system are the same during a contacting period. The displacements of those points are calculated numerically through the convolution integral which involve the impulse response functions and applied forces. The validity of the calculation procedure is demonstrated by using it to calculated the impact forces of a simple system where a theoretical solution is known and also of systems for which other researchers have published results. The agreement between the results derived by the numerical method and the theoretical and also some published results is good.

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RELATIONSHIPS BETWEEN INTEGRAL TRANSFORMS AND CONVOLUTIONS ON AN ANALOGUE OF WIENER SPACE

  • Cho, Dong Hyun
    • Honam Mathematical Journal
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    • v.35 no.1
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    • pp.51-71
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    • 2013
  • In the present paper, we evaluate the analytic conditional Fourier-Feynman transforms and convolution products of unbounded function which is the product of the cylinder function and the function in a Banach algebra which is defined on an analogue o Wiener space and useful in the Feynman integration theories and quantum mechanics. We then investigate the inverse transforms of the function with their relationships and finally prove that th analytic conditional Fourier-Feynman transforms of the conditional convolution products for the functions, can be expressed in terms of the product of the conditional Fourier-Feynman transforms of each function.

Visual servoing of robot manipulator by fuzzy membership function based neural network (퍼지 신경망에 의한 로보트의 시각구동)

  • 김태원;서일홍;조영조
    • 제어로봇시스템학회:학술대회논문집
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    • 1992.10a
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    • pp.874-879
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    • 1992
  • It is shown that there exists a nonlinear mappping which transforms features and their changes to the desired camera motion without measurement of the relative distance between the camera and the part, and the nonlinear mapping can eliminate several difficulties encountered when using the inverse of the feature Jacobian as in the usual feature-based visual feedback controls. And instead of analytically deriving the closed form of such a nonlinear mapping, a fuzzy membership function (FMF) based neural network is then proposed to approximate the nonlinear mapping, where the structure of proposed networks is similar to that of radial basis function neural network which is known to be very useful in function approximations. The proposed FMF network is trained to be capable of tracking moving parts in the whole work space along the line of sight. For the effective implementation of proposed IMF networks, an image feature selection processing is investigated, and required fuzzy membership functions are designed. Finally, several numerical examples are illustrated to show the validities of our proposed visual servoing method.

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