• Title, Summary, Keyword: operator

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Characterization of Some Classes of Distributions Related to Operator Semi-stable Distributions

  • Joo, Sang Yeol;Yoo, Young Ho;Choi, Gyeong Suk
    • Communications for Statistical Applications and Methods
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    • v.10 no.1
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    • pp.177-189
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    • 2003
  • For a positive integer m, operator m-semi-stability and the strict operator m-semi-stability of probability measures on R^d$ are defined. The operator m-semi-stability is a generalization of the definition of operator semi-stability with exponent Q. Characterization of strictly operator na-semi-stable distributions among operator m-semi-stable distributions is given. Translation of strictly operator m-semi-stable distribution is discussed.

Characterization of some classes of distributions related to operator semi-stable distributions

  • Joo, Sang-Yeol;Choi, Gyeong-Suk
    • Proceedings of the Korean Statistical Society Conference
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    • pp.221-225
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    • 2002
  • For a positive integer m, operator m-semi-stability and the strict operator m-semi-stability of probability measures on $R^{d}$ are defined. The operator m-semi-stability is a generalization of the definition of operator semi- stability with exponent Q. Translation of strictly operator m-semi-stable distribution is discussed.

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Coefficient Inequalities for Certain Subclasses of Analytic Functions Defined by Using a General Derivative Operator

  • Bulut, Serap
    • Kyungpook Mathematical Journal
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    • v.51 no.3
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    • pp.241-250
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    • 2011
  • In this paper, we define new classes of analytic functions using a general derivative operator which is a unification of the S$\breve{a}$l$\breve{a}$gean derivative operator, the Owa-Srivastava fractional calculus operator and the Al-Oboudi operator, and discuss some coefficient inequalities for functions belong to this classes.

Operator-splitting methods respecting eigenvalue problems for shallow shelf equations with basal drag

  • Geiser, Jurgen;Calov, Reinhard
    • Coupled systems mechanics
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    • v.1 no.4
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    • pp.325-343
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    • 2012
  • We present different numerical methods for solving the shallow shelf equations with basal drag (SSAB). An alternative approach of splitting the SSAB equation into a Laplacian and diagonal shift operator is discussed with respect to the underlying eigenvalue problem. First, we solve the equations using standard methods. Then, the coupled equations are decomposed into operators for membranes stresses, basal shear stress and driving stress. Applying reasonable parameter values, we demonstrate that the operator of the membrane stresses is much stiffer than the operator of the basal shear stress. Here, we could apply a new splitting method, which alternates between the iteration on the membrane-stress operator and the basal-shear operator, with a more frequent iteration on the operator of the membrane stresses. We show that this splitting accelerates and stabilize the computational performance of the numerical method, although an appropriate choice of the standard method used to solve for all operators in one step speeds up the scheme as well.

SLANT H-TOEPLITZ OPERATORS ON THE HARDY SPACE

  • Gupta, Anuradha;Singh, Shivam Kumar
    • Journal of the Korean Mathematical Society
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    • v.56 no.3
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    • pp.703-721
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    • 2019
  • The notion of slant H-Toeplitz operator $V_{\phi}$ on the Hardy space $H^2$ is introduced and its characterizations are obtained. It has been shown that an operator on the space $H^2$ is a slant H-Toeplitz if and only if its matrix is a slant H-Toeplitz matrix. In addition, the conditions under which slant Toeplitz and slant Hankel operators become slant H-Toeplitz operators are also obtained.

QUANTITATIVE WEIGHTED BOUNDS FOR THE VECTOR-VALUED SINGULAR INTEGRAL OPERATORS WITH NONSMOOTH KERNELS

  • Hu, Guoen
    • Bulletin of the Korean Mathematical Society
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    • v.55 no.6
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    • pp.1791-1809
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    • 2018
  • Let T be the singular integral operator with nonsmooth kernel which was introduced by Duong and McIntosh, and $T_q(q{\in}(1,{\infty}))$ be the vector-valued operator defined by $T_qf(x)=({\sum}_{k=1}^{\infty}{\mid}T\;f_k(x){\mid}^q)^{1/q}$. In this paper, by proving certain weak type endpoint estimate of L log L type for the grand maximal operator of T, the author establishes some quantitative weighted bounds for $T_q$ and the corresponding vector-valued maximal singular integral operator.

Sequential operator-valued function space integral as an $L({L_p},{L_p'})$ theory

  • Ryu, K.S.
    • Journal of the Korean Mathematical Society
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    • v.31 no.3
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    • pp.375-391
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    • 1994
  • In 1968k Cameron and Storvick introduced the analytic and the sequential operator-valued function space integral [2]. Since then, the theo교 of the analytic operator-valued function space integral has been investigated by many mathematicians - Cameron, Storvick, Johnson, Skoug, Lapidus, Chang and author etc. But there are not that many papers related to the theory of the sequential operator-valued function space integral. In this paper, we establish the existence of the sequential operator-valued function space integral as an operator from $L_p$ to $L_p'(1 and investigated the integral equation related to this integral.

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Analysis on the Regularization Parameter in Image Restoration (영상복원에서의 정칙화 연산자 분석)

  • 전우상;이태홍
    • Journal of Korea Multimedia Society
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    • v.2 no.3
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    • pp.320-328
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    • 1999
  • The Laplacian operator is usually used as a regularization operator which may be used as any differential operator in the regularization iterative restoration. In this paper, several kinds of differential operator and 1-H operator that has been used in our lab as well, as a regularization operator, were compared with each other. In the restoration of noisy motion-blurred images, 1-H operator worked better than Laplacian operator in flat region, but in the edge the Laplacian operator operated better. For noisy gaussian-blurred image, 1-H operator worked better in the edge, while in flat region the Laplacian operator resulted better. In regularization, smoothing the noise and resorting the edges should be considered at the same time, so the regions divided into the flat, the middle, and the detailed, which were processed in separate and compared their MSE. Laplacian and 1-H operator showed to be suitable as the regularization operator, while the other differential operators appeared to be diverged as iterations proceeded.

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Extracting Flick Operator for Predicting Performance by GOMS Model in Small Touch Screen

  • Choi, Mikyung;Lee, Bong Geun;Oh, Hyungseok;Myung, Rohae
    • Journal of the Ergonomics Society of Korea
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    • v.32 no.2
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    • pp.179-187
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    • 2013
  • Objective: The purpose of this study is to extract GOMS manual operator, except for an experiment with participants. Background: The GOMS model has advantage of rapid modeling which is suitable for the environment of technology development which has a short life cycle products with a fast pace. The GOMS model was originally designed for desktop environment so that it is not adequate for implementing into the latest HCI environment such as small touch screen device. Therefore, this research proposed GOMS manual operator extraction methodology which is excluded experimental method. And flick Gesture was selected to explain application of proposed methodology to extract new operator. Method: Divide into start to final step of hand gesture needed to extract as an operator through gesture task analysis. Then apply the original GOMS operator to each similar step of gesture and modify the operator for implementation stage based on existing Fitts' law research. Steps that are required to move are modified based on the Fitts' law developed in touch screen device. Finally, new operator can be derived from using these stages and a validation experiment, performed to verify the validity of new operator and methodology by comparing human performance. Results: The average movement times of the participants' performance and the operator which is extracted in case study are not different significantly. Also the average of movement times of each type of view study is not different significantly. Conclusion: In conclusion, the result of the proposed methodology for extracting new operator is similar to the result of the experiment with their participants. Furthermore the GOMS model included the operator by the proposed methodology in this research could be applied successfully to predict the user's performance. Application: Using this methodology could be applied to develop new finger gesture in the touch screen. Also this proposed methodology could be applied to evaluate the usability of certain system rapidly including the new finger gesture performance.