• Bulletin of the Korean Mathematical Society
• /
• v.54 no.3
• /
• pp.789-797
• /
• 2017

The main purpose of this paper is to present closed integral form expressions for the Mathieu-type a-series and its associated alternating version whose terms contain a (p, q)-extended Gauss' hypergeometric function. Certain upper bounds for the two series are also given.

• Bulletin of the Korean Mathematical Society
• /
• v.53 no.5
• /
• pp.1291-1308
• /
• 2016

In this paper we obtain the closed forms of some hypergeometric functions. As an application, we obtain the explicit forms of the Bergman kernel functions for intersection of two complex ellipsoids {$z{\in}\mathbb{C}^3:{\mid}z_1{\mid}^p+{\mid}z_2{\mid}^q$ < 1, ${\mid}z_1{\mid}^p+{\mid}z_3{\mid}^r$ < 1}. We consider cases p = 6, q = r = 2 and p = q = r = 2. We also investigate the Lu Qi-Keng problem for p = q = r = 2.

• Journal of the Korean Mathematical Society
• /
• v.53 no.6
• /
• pp.1211-1223
• /
• 2016

Let M be an n-dimensional $K{\ddot{a}}hler$ manifold with positive holomorphic bisectional curvature and let ${\Omega}{\Subset}M$ be a pseudoconvex domain of order $n-q$, $1{\leq}q{\leq}n$, with $C^2$ smooth boundary. Then, we study the (weighted) $\bar{\partial}$-equation with support conditions in ${\Omega}$ and the closed range property of ${\bar{\partial}}$ on ${\Omega}$. Applications to the ${\bar{\partial}}$-closed extensions from the boundary are given. In particular, for q = 1, we prove that there exists a number ${\ell}_0$ > 0 such that the ${\bar{\partial}}$-Neumann problem and the Bergman projection are regular in the Sobolev space $W^{\ell}({\Omega})$ for ${\ell}$ < ${\ell}_0$.

• Communications of the Korean Mathematical Society
• /
• v.27 no.3
• /
• pp.431-439
• /
• 2012

Characterizations of $\mathcal{N}$-subalgebra of type (${\in}$, ${\in}{\vee}q$) are provided. The notion of $\mathcal{N}$-subalgebras of type ($\bar{\in}$, $\bar{\in}{\vee}\bar{q}$) is introduced, and its characterizations are discussed. Conditions for an $\mathcal{N}$-subalgebra of type (${\in}$, ${\in}{\vee}q$) (resp. ($\bar{\in}$, $\bar{\in}{\vee}\bar{q}$) to be an $\mathcal{N}$-subalgebra of type (${\in}$, ${\in}$) are considered.

• Honam Mathematical Journal
• /
• v.40 no.4
• /
• pp.621-659
• /
• 2018

Let us consider that ${\mathbb{K}}$ be a complete ultrametric algebraically closed field and A (${\mathbb{K}}$) be the ${\mathbb{K}}$-algebra of entire functions on ${\mathbb{K}}$. In this paper we introduce the notions of (p, q)-th relative order and (p, q)-th relative type of entire functions on ${\mathbb{K}}$ where p and q are any two positive integers and then study some basic properties of p-adic entire functions on the basis of their (p, q)-th relative order and (p, q)-th relative type.

• Korean Journal of Applied Biomechanics
• /
• v.33 no.4
• /
• pp.128-136
• /
• 2023

Objective: The aim of this study was to investigate the effect of an 8-week closed kinetic chain typed Reformer and Chair Pilates exercise on static and dynamic lower limb alignment for healthy female adults. Method: Ten healthy young female adults without musculoskeletal injury history in last 6 months (Age: 29.3 ± 3.5 yrs., Height: 165 ± 3.4 cm, Body mass: 58.2 ± 5.4 kg) participated in this study. All participants asked to join the 8-week closed kinetic chain typed Reformer and Chair Pilates exercise, and the program was conducted for 60 minutes twice a week. Participants were asked to be measure a static Q-angle and performed free squat one week before and after the program. A 3-D motion analysis with 8 infrared cameras and 5 channels of EMG was executed in this study. The effectiveness of the training was evaluated by paired t-test, and the significance level was set at .05. Results: A significantly decreased in internal rotation angles was found at hip joint during free squat after the training. Also, significantly decreased in lateral rotation angles were found at knee and ankle joint during free squat after training. Finally, significantly decreased in muscle activations were found at adductor longus and peroneus longus during free squat after training. Conclusion: From results of our study, it is concluded that an 8-week closed kinetic chain typed Pilates exercise positively effect on lower limb alignment during dynamic movement.

• Bulletin of the Korean Chemical Society
• /
• v.31 no.2
• /
• pp.315-326
• /
• 2010

This study examined the overlapping resonances in the systems involving 1 open and 2 closed channels using the phase-shifted version of multichannel quantum-defect theory (MQDT). The results showed that 21 patterns for the q reversals in the autoionization spectra are possible depending on the relative arrangements of the two simple poles and roots of the quadratic equations. Complete cases could be generated easily using the q zero planes determined using only 3 asymmetric spectral line profile indices. The transition of the spectra of the coarse interloper Rydberg series from the lines into a structured continuum by being dispersed onto the entire Rydberg series was found. The overall behavior of the time delays was found to be governed by the dense Rydberg series, which is quite different from the one of the autoionization cross sections that is governed by an interloper, indicating that different dynamics prevail for them. This is in contrast to the two channel system where both quantities behave similarly. The dynamics obtained in the presence of overlapping resonances is as follows. The absorption process is instant and dominated by a transition to the interloper line. This process is followed by rapid leakage into the dense Rydberg series, which has a longer residence time before ionization than that of the interloper state. This is because the orbiting period is proportional to $\upsilon^3$ so that an excited electron has a shorter lifetime in the interloper state belonging to a lower member of the Rydberg series.

• 제어로봇시스템학회:학술대회논문집
• /
• 1994.10a
• /
• pp.364-368
• /
• 1994

Algebraic matrix Riccati equations of the form, FP+PF$^{T}$ -PRP+Q=0. are analyzed with reference to the stability of closed-loop system F-PR. Here F, R and Q are n * n real matrices with R=R$^{T}$ and Q=Q$^{T}$ .geq.0 (nonnegative-definite). Such equations have been playing key roles in optimal control and filtering problems with R .geq. 0. and also in the solutions of in H$_{\infty}$ control problems with R taking the form R=H$_{1}$$^{T}$ H$_{1}$-H$_{2}$$^{T}$ H$_{2}$. In both cases an existence of stabilizing solution, i.e. the solution yielding asymptotically stable closed-loop system, is an important problem. First, we briefly review the typical results when R is of definite form, namely either R .geq. 0 as in LQG problems or R .leq. 0. They constitute two extrence cases of Riccati to the cases H$_{2}$=0 and H$_{1}$=0. Necessary and sufficient conditions are shown for the existence of nonnegative-definite or positive-definite stabilizing solution. Secondly, we focus our attention on more general case where R is only assumed to be symmetric, which obviously includes the case for H$_{\infty}$ control problems. Here, necessary conditions are established for the existence of nonnegative-definite or positive-definite stabilizing solutions. The results are established by employing consistently the so-called algebraic method based on an eigenvalue problem of a Hamiltonian matrix.x.ix.x.

• ETRI Journal
• /
• v.29 no.6
• /
• pp.707-715
• /
• 2007

In-phase/quadrature (I/Q) imbalances, which are generated by non-ideal transceiver components, are inevitable physical phenomena that cause the performance of practical communication systems to be degraded. In this paper, we provide a new closed-form expression for the bit error rate of hierarchical M-ary phase shift keying with I/Q phase and amplitude imbalances and analyze the effect of I/Q imbalances on BER performance over an additive white Gaussian noise channel.

• Honam Mathematical Journal
• /
• v.44 no.3
• /
• pp.447-460
• /
• 2022

We consider a closed subspace ${\tilde{A}}^{{\alpha},m}_q$ (ℂ) of the Fock space A^α,m_q (ℂ) of q-analytic functions with the weight ϕ(z) = -α log |z|²+|z|^2m for any positive integer m. We obtain the corresponding reproducing kernel K^ℂ_α,q,m(z, w) using the weighted Laguerre polynomials and the Mittag-Leffler functions. Finally, we investigate the necessary and sufficient condition on (α, q, m) such that K^ℂ_α,q,m(z, w) is zero-free.