• Korean Journal of Mathematics
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• v.21 no.4
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• pp.455-462
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• 2013

Let D be an integral domain, S be a saturated multi-plicative subset of D such that $D_S$ is a factorial domain, $\{X_{\alpha}\}$ be a nonempty set of indeterminates, and $D[\{X_{\alpha}\}]$ be the polynomial ring over D. We show that S is a splitting (resp., almost splitting, t-splitting) set in D if and only if every nonzero prime t-ideal of D disjoint from S is principal (resp., contains a primary element, is t-invertible). We use this result to show that $D{\backslash}\{0\}$ is a splitting (resp., almost splitting, t-splitting) set in $D[\{X_{\alpha}\}]$ if and only if D is a GCD-domain (resp., UMT-domain with $Cl(D[\{X_{\alpha}\}]$ torsion UMT-domain).

• Communications of the Korean Mathematical Society
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• v.33 no.4
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• pp.1141-1158
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• 2018

Hahn difference operator $D_{q,{\omega}}$ which is defined by $$D_{q,{\omega}}g(t)=\{{\frac{g(gt+{\omega})-g(t)}{t(g-1)+{\omega}}},{\hfill{20}}\text{if }t{\neq}{\theta}:={\frac{\omega}{1-q}},\\g^{\prime}({\theta}),{\hfill{83}}\text{if }t={\theta}$$ received a lot of interest from many researchers due to its applications in constructing families of orthogonal polynomials and in some approximation problems. In this paper, we investigate sufficient conditions for stability of the abstract linear Hahn difference equations of the form $$D_{q,{\omega}}x(t)=A(t)x(t)+f(t),\;t{\in}I$$, and $$D^2{q,{\omega}}x(t)+A(t)D_{q,{\omega}}x(t)+R(t)x(t)=f(t),\;t{\in}I$$, where $A,R:I{\rightarrow}{\mathbb{X}}$, and $f:I{\rightarrow}{\mathbb{X}}$. Here ${\mathbb{X}}$ is a Banach algebra with a unit element e and I is an interval of ${\mathbb{R}}$ containing ${\theta}$.

• Proceedings of the Korean Society for Noise and Vibration Engineering Conference
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• 2003.05a
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• pp.846-851
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• 2003

The differential equations governing free, in-plane vibrations of non-circular arches with non-uniform cross-section, including the effects of rotatory inertia, shear deformation and axial deformation, are derived and solved numerically to obtain frequencies. The lowest four natural frequencies are calculated for the prime parabolic arches with hinged-hinged, hinged-clamped, and clamped-clamped end constraints. Three general taper types for rectangular section are considered. A wide range of arch rise to span length ratios, slenderness ratios, and section ratios are considered. The agreement with results determined by means of a finite element method is good from an engineering viewpoint.

• Advances in materials Research
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• v.5 no.2
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• pp.81-92
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• 2016

Stress concentration is an interesting and essential field of study, as it is the prime cause of failure of structural parts under static load. In the current paper, stress and strain concentration factors in unidirectional functionally graded (UDFGM) plate with central circular cutout are predicted by carrying out a finite element study on ANSYS APDL platform. The present study aims to bridge the lacuna in the understandings of stress analysis in perforated functionally graded plates. It is found that the material variation parameter is an important criterion while designing a perforated UDFGM plate. By selecting a proper material variation parameter and direction of material gradation, the stress and strain concentrations can be significantly reduced.

• Kyungpook Mathematical Journal
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• v.49 no.2
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• pp.221-233
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• 2009

In this article, we generalize a well-known result of Hebisch and Weinert that states that a finite semidomain is either zerosumfree or a ring. Specifically, we show that the class of commutative semirings S such that S has nonzero characteristic and every zero-divisor of S is nilpotent can be partitioned into zerosumfree semirings and rings. In addition, we demonstrate that if S is a finite commutative semiring such that the set of zero-divisors of S forms a subtractive ideal of S, then either every zero-sum of S is nilpotent or S must be a ring. An example is given to establish the existence of semirings in this latter category with both nontrivial zero-sums and zero-divisors that are not nilpotent.

• Bulletin of the Korean Mathematical Society
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• v.61 no.1
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• pp.83-92
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• 2024

Let R be a commutative ring with nonzero identity and M be an R-module. In this paper, we first introduce the concept of S-idempotent element of R. Then we give a relation between S-idempotents of R and clopen sets of S-Zariski topology. After that we define S-pure ideal which is a generalization of the notion of pure ideal. In fact, every pure ideal is S-pure but the converse may not be true. Afterwards, we show that there is a relation between S-pure ideals of R and closed sets of S-Zariski topology that are stable under generalization.

• Journal of applied mathematics & informatics
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• v.42 no.3
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• pp.663-680
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• 2024

The zero divisor graph is the most basic way of representing an algebraic structure as a graph. For any commutative ring R, each element is a vertex on the zero divisor graph and two vertices are defined as adjacent if and only if the product of those vertices equals zero. In this research, we determine some topological indices such as the Wiener index, the edge-Wiener index, the hyper-Wiener index, the Harary index, the first Zagreb index, the second Zagreb index, and the Gutman index of zero divisor graph of integers modulo prime power and its direct product.

• Bulletin of the Korean Mathematical Society
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• v.61 no.3
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• pp.785-796
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• 2024

Let p be a prime. A group G is said to be residually p-finite if for each non-trivial element x of G, there exists a normal subgroup N of index a power of p in G such that x is not in N. In this note we shall prove that certain HNN extensions of free abelian groups of finite rank are residually p-finite. In addition some of these HNN extensions are subgroup separable. Characterisations for certain one-relator groups and similar groups including the Baumslag-Solitar groups to be residually p-finite are proved.

• Tuberculosis and Respiratory Diseases
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• v.48 no.6
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• pp.879-886
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• 2000

Background : Thyroid Transcription Factor-1(TTF-1) acts as a tissue specific transcription factor in the regulation of lung specific gene expression and as morphogenic protein during lung organogenesis. Currently, there is very little information on the cis-acting sequences and transcription factors that direct the TTF-1 gene expression. DNAse 1 hypersensitive (DH) sites represent a marker for active or potentially active chromatin and are likely to be especially important in gene regulation, being associated with many DNA sequences that regulate gene expression. It is clear that DH regions correlate with genetic regulatory loci and binding for sequence-specific DNA-binding proteins. Methods : We have used DH site assays to identify putative distal regulatory elements in H441 lung adenocarcinoma cells, which express the TTF-1 gene and HeLa cells. Results : There are four DH sites 5' of the TTF-1 gene. These sites are located at base pair approximately +150, -450, -800, and -1500 from the start of transcription. Conclusion : These data suggest that there may be at least one intragenic site and regulatory region 5' prime to the promotor region.

• The Bulletin of The Korean Astronomical Society
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• v.39 no.2
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• pp.90-90
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• 2014

The Immersion Grating Infrared Spectrometer (IGRINS) is the first astronomical spectrograph that uses a silicon immersion grating as its dispersive element. IGRINS fully covers the H and K band atmospheric transmission windows in a single exposure. It is a compact high-resolution cross-dispersion spectrometer whose resolving power R is 40,000. An individual volume phase holographic grating serves as a secondary dispersing element for each of the H and K spectrograph arms. On the 2.7m Harlan J. Smith telescope at the McDonald Observatory, the slit size is $1^{{\prime}{\prime}}{\times}15^{{\prime}{\prime}}$. IGRINS has a plate scale of 0.27" pixel-1 on a $2048{\times}2048$ pixel Teledyne Scientific & Imaging HAWAII-2RG detector with a SIDECAR ASIC cryogenic controller. The instrument includes four subsystems; a calibration unit, an input relay optics module, a slit-viewing camera, and nearly identical H and K spectrograph modules. The use of a silicon immersion grating and a compact white pupil design allows the spectrograph collimated beam size to be 25mm, which permits the entire cryogenic system to be contained in a moderately sized ($0.96m{\times}0.6m{\times}0.38m$) rectangular Dewar. The fabrication and assembly of the optical and mechanical components were completed in 2013. From January to July of this year, we completed the system optical alignment and carried out commissioning observations on three runs to improve the efficiency of the instrument software and hardware. We describe the major design characteristics of the instrument including the system requirements and the technical strategy to meet them. We also present the instrumental performance test results derived from the commissioning runs at the McDonald Observatory.