• 충청수학회지
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• 제23권1호
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• pp.119-126
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• 2010

In this paper, we find the formula for the analogue of Wiener measure over the subset of C[0, T] bounded by the sectionally differentiable functions, which is a generalization of Park and Skoug's results in [2].

• Journal of applied mathematics & informatics
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• 제26권5_6호
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• pp.901-910
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• 2008

For some generalized N-function ${\Phi}$, some Holder type inequalities and bounded operators on spaces of type $W_M^{\Omega,\Phi}$ generalizing the $W^p$-spaces due to Pathak and Upadhyay are obtained.

• Korean Journal of Mathematics
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• 제16권4호
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• pp.499-509
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• 2008

In this paper we introduce the concepts of the generalized bounded variation in the restricted sense with respect to a strictly increasing function and $Denjoy_*$-Stieltjes integral of real-valued functions and investigate their properties.

• East Asian mathematical journal
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• 제16권2호
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• pp.169-174
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• 2000

We give an easy proof that ${\phi}(z)=\frac{z^2_1}{1-z^2_2}$ induces the bounded composition operator $C_{\phi}:\mathcal{B}{\rightarrow}{\bigcap}H^p(B_2)$ defined by $C_{\phi}f=f\;o\;{\phi}$.

• Kyungpook Mathematical Journal
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• 제45권4호
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• pp.571-577
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• 2005

The aim of this paper is to establish the rate of convergence of Baskakov-Durrmeyer operators for bounded variation function. We have given the better estimate over the results due to Guo ([4]), Anial and Teberska ([1]) and Gupta and Srivastava ([8]).

• Kyungpook Mathematical Journal
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• 제47권3호
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• pp.341-345
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• 2007

In this paper we show that the second order mock theta function, given by Hikami, is bounded and satisfies the second condition for the mock theta functions.

• Kyungpook Mathematical Journal
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• 제45권3호
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• pp.423-431
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• 2005

Some recent inequalities for expectation and cumulative distribution function are improved.

• Coupled systems mechanics
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• 제12권2호
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• pp.127-149
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• 2023

A theoretical method is developed to analyze the free vibration of an elastic annular plate in contact with an ideal liquid. The displacement potential functions of the contained liquid are expressed as a combination of the Bessel functions that satisfy the Laplace equation and the liquid boundary conditions. The compatibility condition along the interface between the annular plate and the contained liquid is taken into account to consider the fluid-structure coupling. The dynamic displacement of the wet annular plate is assumed to be a combination of dry eigenfunctions, allowing for prediction of the natural frequencies using the Rayleigh-Ritz method. The study investigates the effect of radial liquid boundary conditions on the natural frequencies of the wet annular plate, considering four types of liquid bounding: outer container bounded, outer and inner bounded, inner bounded, and radially unbounded. The proposed theoretical method is validated by comparing the predicted wet natural frequencies with those obtained from finite element analysis, showing excellent accuracy. The results indicate that the radial liquid bounding effect on the natural frequencies is negligible for the axisymmetric vibrational mode, but relatively significant for the mode with one nodal diameter (n =1) and no nodal circle (m' = 0). Furthermore, the study reveals that the wet natural frequencies are the largest for the plate with an inner bounded cylinder among the radial liquid boundary cases, regardless of the vibration mode.

• 대한수학회지
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• 제34권3호
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• pp.581-598
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• 1997

This paper is concerned with the impulsive control problem $$ \dot{x}(t) = f(t, x) + g(t, x)\dot{u}(t), t \in [0, T], x(0) = \overline{x}, $$ where u is a possibly discontinuous control function of bounded variation, $f : R \times R^n \mapsto R^n$ is a bounded and Lipschitz continuous function, and $g : R \times R^n \mapsto R^n$ is continuously differentiable w.r.t. the variable x and satisfies $\mid$g(t,\cdot) - g(s,\cdot)$\mid$ \leq \phi(t) - \phi(s)$, for some increasing function $\phi$ and every s < t. We show that the map $u \mapsto x_u$ is Lipschitz continuous when u ranges in the set of step functions whose total variations are uniformly bounded, where $x_u$ is the solution of the impulsive control system corresponding to u. We also define the generalized solution of the impulsive control system corresponding to a measurable control functin of bounded variation.

• 한국수학교육학회지시리즈B:순수및응용수학
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• 제6권2호
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• pp.59-66
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• 1999

We introduce a new class of functions $H_{k}[A,{\;}B]$ described by subordination and we derive a few geometric properties for the class $H_{k}[A,{\;}B]$.