• Kyungpook Mathematical Journal
• /
• v.47 no.4
• /
• pp.501-517
• /
• 2007

In this paper, we introduce and study a new class containing absolutely summing multilinear mappings and polynomials, which we call multiple weakly summing multilinear mappings and polynomials. We investigate some interesting properties about multiple weakly ($p$; $q_1$, ${\cdots}$, $q_k$)-summing multilinear mappings and polynomials defined on Banach spaces: In particular, we prove a kind of Dvoretzky-Rogers' Theorem and an ideal property for multiple weakly ($p$; $q_1$, ${\cdots}$, $q_k$)-summing multilinear mappings and polynomials. We also prove that the Aron-Berner extensions of multiple weakly ($p$; $q_1$, ${\cdots}$, $q_k$)-summing multilinear mappings and polynomials are also multiple weakly ($p$; $q_1$, ${\cdots}$, $q_k$)-summing.

• Korean Journal of Mathematics
• /
• v.30 no.1
• /
• pp.147-154
• /
• 2022

In this article, we prove that an absolutely summing operator on 𝓛^λ₁ spaces has a lifting under the conditions that a target Banach space is a quotient of reflexive Banach subspaces.

• Journal of the Korean Society of Radiology
• /
• v.12 no.5
• /
• pp.557-563
• /
• 2018

Coincidence summing correction effects are known to be greater as the efficiency of the detector increases and as the distance between the source and the detector increases. A point source($^{60}Co$) was used to vary the distance in the direction of the detector's center axis and in the radial direction to obtain the P/T ratio for Coincidence summing correction calibration. In this study, values for coincidence summing corrected calibration of the values in the central and radial directions were applied to the mixed volume source(450 ml CRM source) to compare the overall peak efficiency change according to P/T with Geant4. In addition, the efficiency obtained from the mapping method is applied to the seaweed, a marine sample, and the compatibility of the P/T ratio with the detector and sample very dose together. The efficiency corrected to 1,836 keV was applied to the energy zone affected by the efficiency of 500 keV and the relative error of the measured and corrected values was well matcched by the 3.2 % peak efficiency correction. As with 450 mL CRM source, the larger the volume, the lower the P/T ratio was by ${\pm}5%$. This is due to the increased scattering of gamma-rays emitted as the source becomes farther away from the detector, and this change in P/T has been confirmed to affect the Coincidence summing corrected peak efficiency.

• Journal of the Korean Mathematical Society
• /
• v.47 no.5
• /
• pp.899-924
• /
• 2010

In the paper we introduce averages of each type and use these averages to construct examples of weakly compact operators on the space C ($\Omega$) for which the necessary and sufficient conditions that they be compact, absolutely summing or nuclear are distinct. A great number of concrete examples, in various situations, are given.

• Journal of Radiation Protection and Research
• /
• v.30 no.3
• /
• pp.107-112
• /
• 2005

Cascade summing occurs when two gamma-rays emitted in the decay of a single nucleus both deposit energy in a detector. The effect may cause systematic errors that can reach levels of more than ten percent for some radionuclides. A method for estimation of the effect of these coincidences was developed. It is based on direct computation of the effect by means of peak to total ratio measured for the place around the detector. It has been shown that the P/T ratio for the given energy in the working space around the detector may not be a constant value and must use its mean value. Some results from a peak to total calibration study in the presence of scattering materials are also given.

• Nuclear Engineering and Technology
• /
• v.54 no.5
• /
• pp.1754-1759
• /
• 2022

The activity of gamma-ray emitting nuclides is calculated assuming that each gamma-ray is detected individually; thus, the magnitude of the coincidence summing signal must be considered during activity calculations. Here, the correction factor for the coincidence summing effect was calculated, and the detection efficiencies of two HPGe detectors were compared. The CANBERRA Inc. GC4018 high-purity Ge detector provided an estimate for the peak-to-total ratio using a point source to determine the coincidence summing correction factor. The ORTEC Inc. GEM60 high-purity Ge detector uses EFFTRAN in LVis to obtain the parameters of the detector and source model and the gamma-gamma and gamma-X match estimates, in order to determine the coincidence summing correction factor. Nuclide analyses, radioactivity comparisons, and analyses of reference material samples were performed utilizing certified reference materials to accurately determine the detection efficiencies. For both Co-60 and Y-88, the detection efficiency for a point source increased by an average of at least 12-13%, whereas the detection efficiency determined using LVis increased by an average of at least 13-15%. The calculated radioactivity values of the certified reference material and reference material samples were accurate to within 3% and 6% of the measured values, respectively.

• Korean Journal of Mathematics
• /
• v.15 no.1
• /
• pp.13-26
• /
• 2007

We prove that every strong null sequence in a Banach space X lies inside the range of a vector measure of bounded variation if and only if the condition $\mathcal{N}_1(X,{\ell}_1)={\Pi}_1(X,{\ell}_1)$ holds. We also prove that for $1{\leq}p<{\infty}$ every strong ${\ell}_p$ sequence in a Banach space X lies inside the range of an X-valued measure of bounded variation if and only if the identity operator of the dual Banach space $X^*$ is ($p^{\prime}$,1)-summing, where $p^{\prime}$ is the conjugate exponent of $p$. Finally we prove that a Banach space X has the property that any sequence lying in the range of an X-valued measure actually lies in the range of a vector measure of bounded variation if and only if the condition ${\Pi}_1(X,{\ell}_1)={\Pi}_2(X,{\ell}_1)$ holds.

• The Transactions of the Korean Institute of Electrical Engineers A
• /
• v.50 no.8
• /
• pp.351-358
• /
• 2001

This paper deals with the PSS modeling of Ulchin N/P #1 as well as the generator and excitation system modeling by utilizing the recorded data from AVR step test, which has been performed by entering small voltage signal into the AVR summing point. In addition to it. two recorded results obtained from the AVR step test with PSS sunning and without PSS running have not only been compared each other on the time domain, but also they heve been analyzed with FFT analysis on the frequency domain; thus, the desirable effects of running PSS in Ulchin N/P #1 on power system have been explicitly confirmed. Finally, the derived PSS model parameters lead to good matches between simulation results and recorded data.

• Honam Mathematical Journal
• /
• v.37 no.4
• /
• pp.529-547
• /
• 2015

In this paper, we proved some properties of the greatest expanded numbers, and give the method to determine the greatest expanded numbers and find the integer x for which $S_{q,p}(x)-x$ is the largest. Additionally, we provide an algorithm to find the greatest expanded number.

• Korean Journal of Mathematics
• /
• v.27 no.3
• /
• pp.645-655
• /
• 2019

In this article, we show that the nuclear operator defined on Banach space has an extending and lifting operator. Also we give new proofs of the well known facts which were given $Pelcz{\acute{y}}nski$ theorem for complemented subspaces of ${\ell}_1$ and Lewis and Stegall's theorem for complemented subspaces of $L_1({\mu})$.