• Journal of the Korean Mathematical Society
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• v.58 no.5
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• pp.1279-1298
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• 2021

The aim of this paper is to prove the existence of the global attractor of the Cauchy problem for a semilinear degenerate hyperbolic equation involving strongly degenerate elliptic differential operators. The attractor is characterized as the unstable manifold of the set of stationary points, due to the existence of a Lyapunov functional.

• Communications of the Korean Mathematical Society
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• v.38 no.3
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• pp.741-754
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• 2023

In this paper, we study the existence and nonexistence of solutions for a class of Hamiltonian strongly degenerate elliptic system with subcritical growth $$\left{\array{-{\Delta}_{\lambda}u-{\mu}v={\mid}v{\mid}^{p-1}v&&\text{in }{\Omega},\\-{\Delta}_{\lambda}v-{\mu}u={\mid}u{\mid}^{q-1}u&&\text{in }{\Omega},\\u=v=0&&\text{ on }{\partial}{\Omega},}$$ where p, q > 1 and Ω is a smooth bounded domain in ℝ^N, N ≥ 3. Here Δ_λ is the strongly degenerate elliptic operator. The existence of at least a nontrivial solution is obtained by variational methods while the nonexistence of positive solutions are proven by a contradiction argument.

• Communications of the Korean Mathematical Society
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• v.37 no.2
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• pp.423-443
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• 2022

We study the existence and long-time behavior of weak solutions to a class of strongly degenerate semilinear parabolic equations with exponential nonlinearities on ℝ^N. To overcome some significant difficulty caused by the lack of compactness of the embeddings, the existence of a global attractor is proved by combining the tail estimates method and the asymptotic a priori estimate method.

• Journal of the Chungcheong Mathematical Society
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• v.33 no.1
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• pp.19-32
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• 2020

We discuss the coexistence of positive solutions to certain strongly-coupled predator-prey elliptic systems under the homogeneous Dirichlet boundary conditions. The sufficient condition for the existence of positive solutions is expressed in terms of the spectral property of differential operators of nonlinear Schrödinger type which reflects the influence of the domain and nonlinearity in the system. Furthermore, applying the obtained results, we investigate the sufficient conditions for the existence of positive solutions of a predator-prey system with degenerate diffusion rates.

• Communications of the Korean Mathematical Society
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• v.12 no.1
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• pp.193-201
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• 1997

The paper presens results on the perturbation problem of invariant manifolds of differential equations. It is well-known that if there is a pseudohyperbollic structure on an invariant manifold then one is strongly indestructible. The set of strongly inderstructible invariant manifolds is wider than the set of persistent (normally hyperbolic) manifolds. The following theorem is main result of the paper: if the condition of transversality holds on an invariant manifold, except, possibly, for the non-degenerate strong sources and non-degenerate strong sinks, then there is the pseudohyperbolic structure on the invariant manifold. From this it follows the conditions for the indestructibility of locally non-unique invariant manifolds. An example is considered.

• Journal of Microbiology and Biotechnology
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• v.9 no.6
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• pp.732-736
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• 1999

The superoxide dismutase (SOD) in Lactococcus lactis was measured quantitatively and qualitatively under various culture conditions. The L. lactis SOD was induced by oxidative stress. As the concentration of paraquat to produce superoxide radicals increased, the growth of L. lactis decreased with concomitant increase of SOD activity. The SOD activity was found to be growth-phase dependent: when aerobically grown cells entered to the stationary phase, the activity increased gradually until the late stationary phase. From inhibition studies, L. lactis SOD was found to be insensitive to KCN and $H_2O_2$ which are known to inhibit Cu/ZnSOD and FeSOD, respectively. Moreover, as the concentration of manganese in the medium increased, the activity of SOD also increased. These data strongly suggested that L. lactis possessed a single manganese-containing SOD (MnSOD). Finally, a putative sod gene fragment of 510 bp was identified in L. lactis using a polymerase chain reaction (PCR) with degenerate primers designed from the deduced DNA sequences of known SOD genes.

• Progress in Superconductivity
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• v.12 no.1
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• pp.46-50
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• 2010

In the superconducting $Sr_2VO_3FeAs$, containing bimetallic layers, with maximum $T_c{\approx}\;46\;K$ correlation effects on V ions have been investigated using LDA+U method. Within the local density approximation (LDA) this system has the one-third filled $t_{2g}$ manifold of V, decomposed into $d_{xy}$ of bandwidth W=2 eV and nearly degenerate $d_{zx}d_{yz}$ of W=1 eV. Consideration of correlation effects leads to a metal-insulator transition on V ions $t^{2\uparrow}_{2g}\;{\rightarrow}\;d^{1\uparrow}_{xz}\;d^{1\uparrow}_{yz}$ at the critical on-site Coulomb repulsion $U_c$= 3.5 eV. At U=4 eV, the electronic structure, in which V ions are insulating, leads to several van Hove singularities near $E_F$ and similar Fermiology with other pnictides. Applying U to V ions results in increasing Fe moment as well as V moment, indicating somewhat hybridization between Fe and V ions even though this system is strongly 2-dimesional. Our results show possible importance of correlation effects on this system.

• Journal of the Korean Ceramic Society
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• v.50 no.4
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• pp.288-293
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• 2013

Zn-In-Sn-O films were prepared at room temperature by combinatorial RF-magnetron co-sputtering system. The cationic contents of the films were varied using a compositionally combinatorial technique. The effects of the oxygen partial pressure and film compositionon the structural and electrical properties were investigated. The Zn-In-Sn-O films deposited at Ar gas atmosphere showed an amorphous phaseirrespective of the film composition. However, the amorphous Zn-In-Sn-O films with a Zn content below 30.0 at% were converted into a bixbyite type-ITO polycrystalline phase with an increase in the oxygen partial pressure. The resistivity, carrier concentration, and Hall mobility were strongly affected by the oxygen partial pressure and chemical composition of the film. At sufficiently high carrier densities above $5{\times}10^{18}cm^{-3}$, the conduction behavior of amorphous Zn-In-Sn-O film changes from thermally activated to degenerate band conduction accompanied with high mobility.

• Proceedings of the Korean Society of Developmental Biology Conference
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• 2003.10a
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• pp.64-64
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• 2003

The sex differentiation of fishes occurs under the control of genetic and various environmental factors. DM-domain containing genes are novel zinc finger transcription factors and play key roles in sex determination. In order to isolate the wrasse DMRT (wDMRT) cDNA from the protogynous wrasse (Halichoeres tenuispinnis), the wrasse testis cDNA library was screened using the $^{32}$ P-labeled PCR products, which were amplified with the degenerate primers from conserved DM-domain regions of several DMRT genes. Among a few positives obtained through screening, the full length wDMRT cDNA of 2.9kb size encoding a predicted 300 amino acid residues was isolated. The sequence analysis exhibited 60%, 43% sequence identity with rainbow trout and tilapia DMRT1, respectively. RT-PCR assay showed that wDMRT was expressed specifically in male testis. Also, wDMRT gene was strongly expressed in May during reproductive season, when the reproductivity of wrasse is most active. This results suggested that wDMRT gene function in testis differentiation The conserved DM-domain regions were amplified using PCR from DMRT genes of several species among Labridae, and their sequences were determined. The sequence of DM-domain region of Halichoeres. tenuispinis was identical to those of Pseudolabrus japonicus, Pteragogus flagellifera, and showed 94% identity with that of Halichoeres poecioptrerus.

• Journal of Microbiology and Biotechnology
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• v.17 no.5
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• pp.761-768
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• 2007

Serratia proteamaculans HY-3 isolated from the digestive tract of a spider produces an extracellular protease named arazyme, with an estimated molecular mass of 51.5 kDa. The purified enzyme was characterized as having high activities at wide pH and temperature ranges. We further characterized biochemical features of the enzymatic reactions under various reaction conditions. The protease efficiently hydrolyzed a broad range of protein substrates including albumin, keratin, and collagen. The dependence of enzymatic activities on the presence of metal ions such as calcium and zinc indicated that the enzyme is a metalloprotease, together with the previous observation that the proteolytic activity of the enzyme was not inhibited by aspartate, cysteine, or serine protease inhibitors, but strongly inhibited by 1,10-phenanthroline and EDTA. The araA gene encoding the exoprotease was isolated as a 5.6 kb BamHI fragment after PCR amplification using degenerate primers and subsequent Southern hybridization. The nucleotide sequence revealed that the deduced amino acid sequences shared extensive similarity with those of the serralysin family of metalloproteases from other enteric bacteria. A gene(inh) encoding a putative protease inhibitor was also identified immediately adjacent to the araA structural gene.