• Journal of the Korean Mathematical Society
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• v.56 no.2
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• pp.475-484
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• 2019

We study the set of critical exponents of discrete groups acting on regular trees. We prove that for every real number ${\delta}$ between 0 and ${\frac{1}{2}}\;{\log}\;q$, there is a discrete subgroup ${\Gamma}$ acting without inversion on a (q+1)-regular tree whose critical exponent is equal to ${\delta}$. Explicit construction of edge-indexed graphs corresponding to a quotient graph of groups are given.

• Journal of Radiation Protection and Research
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• v.43 no.2
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• pp.75-84
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• 2018

Background: Gamma-ray spectrometry helps in radiation shielding problems and different applications of radioisotopes. Experimental arrangements including broad beam geometries are widely used. The aim is to investigate and evaluate the ${\gamma}-ray$ spectra via attenuation by environmental materials. Materials and Methods: The photo peak to nominated parts in the ${\gamma}-ray$ spectra and the attenuation coefficients ${\mu}_b/{\rho}$ from broad beam geometries are measured for the materials water, soil, sand and cement at the energies 0.662, 1.25, and 1.332 MeV with a $3{^{\prime}^{\prime}}{\times}3{^{\prime}^{\prime}}$ NaI(Tl) detector. Results and Discussion: The ${\gamma}-ray$ spectra vary according to changes in the effective atomic number $Z_{eff}$ of the attenuator, the photon energy and the solid angle. The peak to total ratios are the most sensitive parts to variations in the experimental conditions and overturn in the region 0.663 MeV to 1.332 MeV. This is indicated as inversion trend. The results are discussed in view of $Z_{eff}$ and the experimental conditions. The intensity build-up is larger at the lower energy and larger scattering angles in agreement with Klein-Nishina formula and other results. The build-up factor B is$${\sim_=}$$1 at high ${\gamma}-energies$ and small scattering angles. Conclusion: The sensitivity to material characteristics decrease gradually from peak: to total, to Compton valley, to Compton plateau ratios. Rigorous collimation is necessary at small energies. Cement, of the largest $Z_{eff}$, is characterized by the maximum broad beam mass attenuation coefficients ${\mu}_b/{\rho}$. The obtained results provide information to decide for the suitable experimental set-up based on aim of the work.

• Nuclear Engineering and Technology
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• v.56 no.5
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• pp.1747-1753
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• 2024

The accurate determination of formation density and the physical properties of rocks is the most critical logging tasks which can be obtained using gamma-ray transport and detection tools. Though the simulation works published so far have considerably improved the knowledge of the parameters that govern the responses of the detectors in these tools, recent studies have found considerable differences between the results of using a conventional model of a homogeneous mixture of formation and fluid and an inhomogeneous fractured medium. It has increased concerns about the importance of the complexity of the model used for the medium in simulation works. In the present study, we have suggested two various models for the flow of the fluid in porous media and fractured rock to be used for logging purposes. For a typical gamma-gamma logging tool containing a ¹³⁷Cs source and two NaI detectors, simulated by using the MCNPX code, a simplified porous (SP) model in which the formation is filled with elongated rectangular cubes loaded with either mineral material or oil was investigated. In this model, the oil directly reaches the top of the medium and the connection between the pores is not guaranteed. In the other model, the medium is a large 3-D matrix of 1 cm³ randomly filled cubes. The designed algorithm to fill the matrix sites is so that this realistic random (RR) model provides the continuum growth of oil flow in various disordered directions and, therefore, fulfills the concerns about modeling the rock textures consist of extremely complex pore structures. For an arbitrary set of oil concentrations and various formation materials, the response of the detectors in the logging tool has been considered as a criterion to assess the effect of modeling for the distribution of pores in the formation on simulation studies. The results show that defining a RR model for describing heterogeneities of a porous medium does not effectively improve the prediction of the responses of logging tools. Taking into account the computational cost of the particle transport in the complex geometries in the Monte Carlo method, the SP model can be satisfactory for gamma-gamma logging purposes.

• Communications of the Korean Mathematical Society
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• v.27 no.4
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• pp.843-849
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• 2012

Let G = (V, E) be a graph with chromatic number ${\chi}(G)$. dominating set D of G is called a chromatic transversal dominating set (ctd-set) if D intersects every color class of every ${\chi}$-partition of G. The minimum cardinality of a ctd-set of G is called the chromatic transversal domination number of G and is denoted by ${\gamma}_{ct}$(G). In this paper we characterize the class of trees, unicyclic graphs and cubic graphs for which the chromatic transversal domination number is equal to the connected domination number.

• Communications of the Korean Mathematical Society
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• v.32 no.1
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• pp.7-17
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• 2017

Let R be a commutative ring with zero-divisors Z(R). The extended zero-divisor graph of R, denoted by $\bar{\Gamma}(R)$, is the (simple) graph with vertices $Z(R)^*=Z(R){\backslash}\{0\}$, the set of nonzero zero-divisors of R, where two distinct nonzero zero-divisors x and y are adjacent whenever there exist two non-negative integers n and m such that $x^ny^m=0$ with $x^n{\neq}0$ and $y^m{\neq}0$. In this paper, we consider the extended zero-divisor graphs of idealizations $R{\ltimes}M$ (where M is an R-module). At first, we distinguish when $\bar{\Gamma}(R{\ltimes}M)$ and the classical zero-divisor graph ${\Gamma}(R{\ltimes}M)$ coincide. Various examples in this context are given. Among other things, the diameter and the girth of $\bar{\Gamma}(R{\ltimes}M)$ are also studied.

• Journal of Radiation Protection and Research
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• v.19 no.2
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• pp.147-156
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• 1994

On-line gamma monitoring system around KAERI-site was set up to monitor the radiation fluctuations in environment. Data on gamma exposure rates measured by the ionication chamber in the monitoring posts are transmitted to a computer of central control station with. radio telemetry transmission modem and monitored in real time. Radio telemetry transmission system is economical and reliable on handling and storing of data. This monitroing system can triger an early warning system in the event of abnormal radiation levels.

• Journal of the Korean Mathematical Society
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• v.49 no.1
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• pp.85-98
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• 2012

Let R be a commutative ring and I its proper ideal, let S(I) be the set of all elements of R that are not prime to I. Here we introduce and study the total graph of a commutative ring R with respect to proper ideal I, denoted by T(${\Gamma}_I(R)$). It is the (undirected) graph with all elements of R as vertices, and for distinct x, y ${\in}$ R, the vertices x and y are adjacent if and only if x + y ${\in}$ S(I). The total graph of a commutative ring, that denoted by T(${\Gamma}(R)$), is the graph where the vertices are all elements of R and where there is an undirected edge between two distinct vertices x and y if and only if x + y ${\in}$ Z(R) which is due to Anderson and Badawi [2]. In the case I = {0}, $T({\Gamma}_I(R))=T({\Gamma}(R))$; this is an important result on the definition.

• Journal of Radiation Protection and Research
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• v.36 no.4
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• pp.174-182
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• 2011

With the reactor operation conditions - 4.3 wt% $^{235}U$ initial enrichment, burn-up 55,000 MWd/MTU, average power 34 MW/MTU for three periods burned time for 539.2 days per period and cooling time for 100 hours after shut down, to set up the condition to determine the minimum height (depth) of spent fuel storage pool to shut off the radiation out of the spent fuel storage pool and to store spent fuels safely, the dose rate on the specific position directed to the surface of spent fuel storage pool induced by the neutron and gamma-ray from spent fuels are evaluated. The length of spent fuel is 381 cm, and as the result of evaluation on each position from the top of spent fuel to the surface of spent fuel storage pool, it is difficult for neutrons from spent fuels to pass through the water layer of maximum 219 cm (600 cm from the floor of spent fuel storage pool) and 419 cm (800 cm from the floor of spent fuel storage pool) for gamma-ray. Therefore, neutron and gamma-ray from spent fuels can pass through below 419 cm (800 cm from the floor) water layer directed to the surface of spent fuel storage pool.

• Nuclear Engineering and Technology
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• v.53 no.9
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• pp.3058-3067
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• 2021

Sodium zinc borate glasses doped with dysprosium and modified with different concentrations of barium oxide (0-50 mol %) were fabricated using the melting quenching technique. The structural properties of the prepared glass systems were characterized using XRD and FTIR methods. The absorption spectra of the prepared glasses were measured to determine their energy gap and their related optical properties. The density of the glasses and other physical parameters were also reported. Additionally, with the help of Photon Shielding and Dosimetry (PSD) software, we investigated the radiation shielding parameters of the prepared glass systems at different energy values. It was found that an increase in the density of the glasses by increasing the concentration of BaO significantly improved the gamma ray shielding ability of the samples. For practical results, a compatible irradiation set up was designed to check the shielding capability of the obtained glasses using a gamma ray source at 662 keV. The experimentally obtained results strongly agreed with the data obtained by PDS software at the same energy. These results demonstrated that the investigated glass system is a good candidate for several radiation shielding applications when comparing it with other commercial shielding glasses and concretes.

• Journal of Astronomy and Space Sciences
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• v.36 no.3
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• pp.115-119
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• 2019

This paper is a part of the series on positron annihilation spectroscopy of two-phase diffuse gas-and-dust aggregates, such as interstellar medium and the young remnants of type II supernovae. The results obtained from prior studies were applied here to detect the relationship between the processes of the annihilation of the K-shell electrons and incident positrons, and the effects of these processes on the optical spectra of their respective atoms. Particular attention was paid to the Doppler broadening of their optical lines. The relationship between the atomic mass of the elements and the Doppler broadening, ${\Delta}{\lambda}_D$ (${\AA}$), of their emission lines as produced in these processes was established. This relationship is also illustrated for isotope sets of light elements, namely $^3_2He$, $^6_3Li$, $^7_3Be$, $^{10}_5B$ and $^{11}_5B$. A direct correlation between the ${\gamma}-line$ luminosity ( $E_{\gamma}=1.022MeV$) and ${\Delta}{\lambda}_D$ (${\AA}$) was proved virtually. Qualitative estimates of the structure of such lines depending on the positron velocity distribution function, f(E), were made. The results are presented in tabular form and can be used to set up the objectives of further studies on active galactic nuclei and young remnants of type II supernovae.