• Communications of the Korean Mathematical Society
• /
• v.18 no.2
• /
• pp.243-249
• /
• 2003

We consider weighted Bergman spaces and radial derivatives on the spaces. We also prove that for each element f in B$\^$p, r/ there is a unique f in B$\^$p, r/ such that f is the radial derivative of f and for each f$\in$B$\^$r/(i), f is the radial derivative of some element of B$\^$r/(i) if and only if, lim f(tz)= 0 for all z$\in$H.

• Bulletin of the Korean Mathematical Society
• /
• v.41 no.2
• /
• pp.307-317
• /
• 2004

In the setting of the half-plane of the complex plane, we show that for $r\geq0$, the dual space of the weighted bergman spaces B$^{1}{\gamma}$ is the Bloch space of the half-plane and we study some bounded linear operators induced by radial derivatives.

• Interaction and multiscale mechanics
• /
• v.2 no.4
• /
• pp.333-352
• /
• 2009

We introduce a radial basis collocation method to solve axially moving beam problems which involve $2^{nd}$ order differentiation in time and $4^{th}$ order differentiation in space. The discrete equation is constructed based on the strong form of the governing equation. The employment of multiquadrics radial basis function allows approximation of higher order derivatives in the strong form. Unlike the other approximation functions used in the meshfree methods, such as the moving least-squares approximation, $4^{th}$ order derivative of multiquadrics radial basis function is straightforward. We also show that the standard weighted boundary collocation approach for imposition of boundary conditions in static problems yields significant errors in the transient problems. This inaccuracy in dynamic problems can be corrected by a statically condensed semi-discrete equation resulting from an exact imposition of boundary conditions. The effectiveness of this approach is examined in the numerical examples.

• Journal of applied mathematics & informatics
• /
• v.27 no.5_6
• /
• pp.1087-1095
• /
• 2009

In this paper, we study approximation method from scattered data to the derivatives of a function f by a radial basis function $\phi$. For a given function f, we define a nearly interpolating function and discuss its accuracy. In particular, we are interested in using smooth functions $\phi$ which are (conditionally) positive definite. We estimate accuracy of approximation for the Sobolev space while the classical radial basis function interpolation applies to the so-called native space. We observe that our approximant provides spectral convergence order, as the density of the given data is getting smaller.

• Journal of the Korean Mathematical Society
• /
• v.44 no.4
• /
• pp.931-940
• /
• 2007

Holomorphic mean Lipschitz space is defined in the unit ball of $\mathbb{C}^n$. The membership of the space is expressed in terms of the growth of radial derivatives, which reduced to a classical result of Hardy and Littlewood when n = 1. The membership is also expressed in terms of the growth of tangential derivatives when $n{\ge}2$.

• Bulletin of the Korean Mathematical Society
• /
• v.24 no.1
• /
• pp.13-17
• /
• 1987

Let S denote the class of nivalent functions normalized so that f(0)=f'(0)-1=0 in vertical bar z vertical bar <1. Let $S_{\alpha}$$^{*}$, -.pi./2<.alpha.<.pi./2, denote the subclass of S that satisfies Re $e^{i{\alpha}}$zf'(z)/f(z).geq.0 in vertical bar z vertical bar <1; then f is called .alpha.-spiral-like and the case .alpha.=0 is the class of normalized starlike functions [6, pp.52]. Let T denote the class of functions f normalized as above and satisfying Im z[Im f(z)]..geq.0 in vertical bar z vertical bar <1; then f is called typically real and T contains those functions of S whose coefficients are real [6, pp.55]. Also, in view of [6, pp.231], let B(.lambda.) be the class of function normalized as above and map vertical bar z vertical bar <1 onto the complement of an arc with radial angle .lambda.(0<.lambda.<.pi./2). The radial angle is meant to be the angle between the tangent and radial vectors to the arc. This note includes a sharp version for Corollary 1 of [2] when f.mem. $S_{\alpha}$$^{*}$ as well as a logarithmic coefficient estimate.nt estimate.

• Journal of the Korean Mathematical Society
• /
• v.50 no.1
• /
• pp.189-202
• /
• 2013

On the unit ball of $\mathbb{C}^n$, the space of those holomorphic functions satisfying the mean Lipschitz condition $${\int}_0^1\;{\omega}_p(t,f)^q\frac{dt}{t^1+{\alpha}q}\;<\;{\infty}$$ is characterized by integral growth conditions of the tangential derivatives as well as the radial derivatives, where ${\omega}_p(t,f)$ denotes the $L^p$ modulus of continuity defined in terms of the unitary transformations of $\mathbb{C}^n$.

• Bulletin of the Korean Mathematical Society
• /
• v.42 no.2
• /
• pp.387-396
• /
• 2005

In the setting of the half-plane of the complex plane, we introduce a modified reproducing kernel and we show that for $r>-1/2,\;B^{1,r}-cancellation$ property holds and the Bloch space is the dual space of $B^{1,r}$.

• Journal of the Korea Institute of Military Science and Technology
• /
• v.22 no.2
• /
• pp.207-214
• /
• 2019

This paper proposes a new feature extraction method for automatically estimating the number of target and detecting the chaff using high range resolution profile(HRRP). Feature of one-dimensional range profile is expected to be limited or missing due to lack of information according to the time. The proposed method considers the dynamic movements of targets depending on the radial velocity. The observed HRRP sequence is used to construct a time-range distribution matrix, then assuming diverse radial velocities reflect the number of target and seduction chaff launch, the proposed method utilizes the characteristic of the gradient distribution on the time-range distribution matrix image, which is validated by electromagnetic computation data and dynamic simulation.

• Journal of Plant Biology
• /
• v.34 no.3
• /
• pp.191-199
• /
• 1991

This study has been conducted to investigate the developmental changes of cambial initials and their derivatives in relation to the growing girth of tree in Diosypros kaki and Firmiana simplex. In D. Kaki and F. simplex with typical storeyed cambium, increase in the girth of camium occurred by radial anticlinal division in general, however occasionally the increase was companied by pseudotransverse division. The length of fusiform initials, vessel member, and sieve tube member remained relatively constant throughout the secondary growth but that of fiber showed general tendancy to increase with growing girth of tree. During the girth increase of tree, height and number of ray remained constant in D. kaki, however in F. simplex, height of ray markedly decreased while the number of ray per unit area more or less increased. The secondary ray was originated from the segmentation or division of the side or end of fusiform initials.