• Journal of the Korean Mathematical Society
• /
• v.33 no.4
• /
• pp.891-908
• /
• 1996

Let (X,d) be a metric space and let T be a mapping from X into itself. We say that a metric space (X,d) is T-orbitally complete if every Cauchy sequence of the form ${T^{n_i}x}_{i \in N}$ for $x \in X$ converges to a point in X.

• Nonlinear Functional Analysis and Applications
• /
• v.27 no.3
• /
• pp.569-585
• /
• 2022

A brief comparative survey of some generalizations of a metric space with three dimensional metric structures and different forms of the triangle inequality is done along with their topological properties. Then a common fixed point is obtained for reciprocally continuous and compatible self-maps in a G-metric space. Further, a common fixed point theorem is proved for a pair of weakly compatible self-maps on a G-metric space with the common limit range property.

• FLOWER RESEARCH JOURNAL
• /
• v.18 no.4
• /
• pp.284-290
• /
• 2010

This study was carried out to breed a self-compatible variety of Tiger Lily from the seedlings originated from Chinju city, Gyeongsangnam-do. The morphological characteristics, ploidy, and the resistance of seedlings to virus infection were investigated. A progeny test was also conducted to examine whether the propagated progenies had the same characteristics as the mother plant. The self-compatible diploid lily variety developed in this study showed a tall type like native triploid lily, Lilium tigrinum, and bulbils were formed on both lily varieties. The morphological characteristics of the flowers and leaves were not much different between the varieties, while the size of the bulbils and bulbs showed significant differences. The percentage of seed generation by self-pollination was 72.6% for the self-compatible variety, while there was no seed generated for native triploid lily. The number of chromosome was 2n = 26 (x = 13, diploid) for the self-compatible variety, while 2n = 39 (x = 13, triploid) in native lily variety. The progenies of the self-compatible diploid lily variety showed the same characteristics as those of its mother plant in morphology, seed germination, and polyploidy. The mother plant of the self-compatible diploid lily variety showed 58% pollen germination and the 2-year-old and 3-year-old progenies showed similar germination percentages. The pollen grains of Korean native triploid lily, however, never germinated.

• Communications of the Korean Mathematical Society
• /
• v.26 no.3
• /
• pp.339-348
• /
• 2011

A ring R is called symmetric, if abc = 0 implies acb = 0 for a, b, c ${\in}$ R. An ideal I of a ring R is called symmetric (resp. radically-symmetric) if R=I (resp. R/$\sqrt{I}$) is a symmetric ring. We first show that symmetric ideals and ideals which have the insertion of factors property are radically-symmetric. We next show that if R is a semicommutative ring, then $T_n$(R) and R[x]=($x^n$) are radically-symmetric, where ($x^n$) is the ideal of R[x] generated by $x^n$. Also we give some examples of radically-symmetric ideals which are not symmetric. Connections between symmetric ideals of R and related ideals of some ring extensions are also shown. In particular we show that if R is a symmetric (or semicommutative) (${\alpha}$, ${\delta}$)-compatible ring, then R[x; ${\alpha}$, ${\delta}$] is a radically-symmetric ring. As a corollary we obtain a generalization of [13].

• Proceedings of the Korean Institute of Electrical and Electronic Material Engineers Conference
• /
• 2008.06a
• /
• pp.168-168
• /
• 2008

Dimension of a transistor has rapidly shrunk to increase the speed of device and to reduce the power consumption. However, it is accompanied with several problems like direct tunneling through the gate dioxide layer and low conductivity characteristic of poly-Si gate in nano-region. To cover these faults, study of new materials is urgently needed. Recently, high dielectric materials like $Al_2O_3$, $ZrO_2$, and $HfO_2$ are being studied for equivalent oxide thickness (EOT). However, poly-Si gate is not compatible with high-k materials for gate-insulator. Poly Si gate with high-k material has some problems such as gate depletion and dopant penetration problems. Therefore, new gate structure or materials that are compatible with high-k materials are also needed. TiN for metal/high-k gate stack is conductive enough to allow a good electrical connection and compatible with high-k materials. According to this trend, the study on dry etching of TiN for metal/high-k gate stack is needed. In this study, the investigations of the TiN etching characteristics were carried out using the inductively coupled $BCl_3$-based plasma system and adding $Cl_2$ gas. Dry etching of the TiN was studied by varying the etching parameters including $BCl_3$/Ar gas mixing ratio, RF power, DC-bias voltage to substrate, and $Cl_2$ gas addition. The plasmas were characterized by optical emission spectroscopy analysis. Scanning electron microscopy was used to investigate the etching profile.

• Honam Mathematical Journal
• /
• v.37 no.1
• /
• pp.135-147
• /
• 2015

Owing to the notion of a normal adjacency for a digital product in [8], the study of product properties of digital topological properties has been substantially done. To explain a normal adjacency of a digital product more efficiently, the recent paper [22] proposed an S-compatible adjacency of a digital product. Using an S-compatible adjacency of a digital product, we also study product properties of digital topological properties, which improves the presentations of a normal adjacency of a digital product in [8]. Besides, the paper [16] studied the product property of two digital covering maps in terms of the $L_S$- and the $L_C$-property of a digital product which plays an important role in studying digital covering and digital homotopy theory. Further, by using HS- and HC-properties of digital products, the paper [18] studied multiplicative properties of a digital fundamental group. The present paper compares among several kinds of adjacency relations for digital products and proposes their own merits and further, deals with the problem: consider a Cartesian product of two simple closed $k_i$-curves with $l_i$ elements in $Z^{n_i}$, $i{\in}\{1,2\}$ denoted by $SC^{n_1,l_1}_{k_1}{\times}SC^{n_2,l_2}_{k_2}$. Since a normal adjacency for this product and the $L_C$-property are different from each other, the present paper address the problem: for the digital product does it have both a normal k-adjacency of $Z^{n_1+n_2}$ and another adjacency satisfying the $L_C$-property? This research plays an important role in studying product properties of digital topological properties.

• Kyungpook Mathematical Journal
• /
• v.59 no.4
• /
• pp.603-615
• /
• 2019

Let R be an associative unital ring with an endomorphism α and α-derivation δ. The constant products of elements in Ore extension rings, when the coefficient ring is reversible, is investigated. We show that if f(x) = ∑ⁿ_i=0 a_ixⁱ and g(x) = ∑^m_j=0 b_jx^j be nonzero elements in Ore extension ring R[x; α, δ] such that g(x)f(x) = c ∈ R, then there exist non-zero elements r, a ∈ R such that rf(x) = ac, when R is an (α, δ)-compatible ring which is reversible. Among applications, we give an exact characterization of the unit elements in R[x; α, δ], when the coeficient ring R is (α, δ)-compatible. Furthermore, it is shown that if R is a weakly 2-primal ring which is (α, δ)-compatible, then J(R[x; α, δ]) = N iℓ(R)[x; α, δ]. Some other applications and examples of rings with this property are given, with an emphasis on certain classes of NI rings. As a consequence we obtain generalizations of the many results in the literature. As the final part of the paper we construct examples of rings that explain the limitations of the results obtained and support our main results.

• Proceedings of the Korean Institute of Electrical and Electronic Material Engineers Conference
• /
• 2010.06a
• /
• pp.239-239
• /
• 2010

This paper describes the design and analysis of AlN piezoelectric micro generator. The generator was designed to convert ambient vibration energy to electrical power as a AlN piezoelectric material compatible with integataion process. From the simulation results, the resonance frequency of designed model is about 360 Hz and analyzed the bending mode, displacement and expectation output.

• The Transactions of the Korean Institute of Electrical Engineers C
• /
• v.55 no.2
• /
• pp.72-75
• /
• 2006

A CMOS compatible Super Junction LDMOS (SJ-LDMOS) structure, which reduces substrate-assisted depletion effects, is reported. The proposed structure uses a N-buffer layer between the pillars and P-substrate to achieve global charge balance between the pillars, the N-buffer layer and the P-substrate. The new structure features high breakdown voltage, low on-resistance, and reduced sensitivity to doping imbalance in the pillars.

• The Pure and Applied Mathematics
• /
• v.21 no.3
• /
• pp.165-181
• /
• 2014

We establish a common n-tupled fixed point theorem for hybrid pair of mappings under new contractive condition. It is to be noted that to find n-tupled coincidence point, we do not use the condition of continuity of any mapping involved. An example supporting to our result has also been cited. We improve, extend and generalize several known results.