• 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.

• Journal of the Korean Mathematical Society
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• v.48 no.3
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• pp.513-527
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• 2011

The paper deals with the degenerate parabolic system with nonlinear boundary flux. By constructing the self-similar supersolution and subsolution, we obtain the critical global existence curve. The critical Fujita curve is conjectured with the aid of some new results.

• 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.

• Bulletin of the Korean Mathematical Society
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• v.51 no.5
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• pp.1503-1510
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• 2014

The aim of this work is to construct a general family of two dimensional differential systems which admits homoclinic solutions near a non-hyperbolic fixed point, such that a Jacobian matrix at this point is zero. We then discretize it by using Euler's method and look after the persistence of the homoclinic solutions in the obtained discrete system.

• Journal of the Korean Mathematical Society
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• v.53 no.1
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• pp.27-43
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• 2016

This paper deals with a degenerate parabolic system with coupled nonlinear localized sources subject to weighted nonlocal Dirichlet boundary conditions. We obtain the conditions for global and blow-up solutions. It is interesting to observe that the weight functions for the nonlocal Dirichlet boundary conditions play substantial roles in determining not only whether the solutions are global or blow-up, but also whether the blowing up occurs for any positive initial data or just for large ones. Moreover, we establish the precise blow-up rate.

• Journal of the Korean Institute of Telematics and Electronics
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• v.25 no.4
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• pp.460-466
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• 1988

In this paper, the theory and experiments on the one-way optical image transmission through optical fiber by using degenerate four wave mixing in BSO single crystal are demonstrated. From the theoretical analysis, the diffraction efficiency of phase conjugate wave in BSO single crystal is greatly dependent on applied electric field intensity, diffraction grating period formed in the crystal and incident beam ratio, those are also in good agreement with the experimental results. Based on the experimental results, we have arranged the typical degenerate four wave mixing system in the optimal conditions (applied electric field, E. = 5kV/cm` diffraction grating period, 3\ulcorner` beam ratio of backward pump wave versus signal wave, 2.7) and realized one-way optical image transmission system through optical fiber using BSO single crystal.

• The Bulletin of The Korean Astronomical Society
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• v.46 no.2
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• pp.50.3-51
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• 2021

The progenitor of Type Ia supernovae is largely expected as a close binary system of a carbon/oxygen white dwarf (WD) primary and its secondary non-degenerate (single degenerate; SD) or degenerate companion (double degenerate; DD). Here we present a high-cadence monitoring observation of SN 2021hpr in a spiral galaxy, NGC 3147. SN 2021hpr shows typical characteristics as a normal type Ia supernova from its photometric (Δm₁₅(B)=1.01±0.03, dust free M_B,max=-19.45±0.02) and spectroscopic data. To investigate its progenitor system, we fit the early part of BVRI-band light curve simultaneously with a combined version of ejecta-companion and simple power-law model. As a result, we found a significant feature of an early excess possibly from a 7.63±0.52R_⊙-sized companion at the optimal viewing angle while the fit is not successful at the common viewing angle. No possible red sources brighter than F555W=-7.01 AB mag is detected at the SN location in Hubble Space Telescope (HST) pre-explosion images, excluding massive stars with initial mass of >16M_⊙ as companions. We suggest the progenitor system of SN 2021hpr can be a fairly large companion such as a main sequence, a low mass subgiant, and a helium giant star. In addition, a possibility of the ejecta-Disk Originated Matter (DOM) interaction for the DD scenario considering linearly-rising early flux still remains.

• Journal of Microbiology
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• v.33 no.3
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• pp.252-259
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• 1995

The PCR was employed to detect and characterize the bovine immunodeficiency-like virus (BIV), which is a newly recognized member of the I entivirinae of the retroviruses. Degenerate primers representing the conserved regions in the pol genes of the Lentivirinae, were used to detect proviral DNA obtained from the bovine embryonic spleen cell cultures infected with BIV. The PCR amplified DNA fragment was molecularly cloned and sequenced. The BIV DNA fragment contained a sequence identical to that reported by Garvey et al. (Garvey et al., 1990. Virology, 175, 391-409). With the degenerate primers, peripheral blood mononuclear cells (PBMCs) of sick cattle and cells cultured with BIV were tested to determine genetic variation of BIV pol conserved sequence. We found the sequence heterogeneity within cultures and most variations occurred at the third base of codons that would not lead to amino acid substitutions. Another change was GAG (Glu) to AAG (Lys) within the BIV isolates. Interestingly, the altered sequence is also found in other lentiviruses such as HIV-2, SIV mac, CAEV and EIAV.

• Bulletin of the Korean Mathematical Society
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• v.50 no.3
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• pp.811-821
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• 2013

We study the initial value problem of the exponential wave equation in $\math{R}^{n+1}$ for small initial data. We shows, in the case of $n=1$, the global existence of solution by applying the formulation of first order quasilinear hyperbolic system which is weakly linearly degenerate. When $n{\geq}2$, a vector field method is applied to show the stability of a trivial solution ${\phi}=0$.

• The Bulletin of The Korean Astronomical Society
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• v.46 no.1
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• pp.55.2-56
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• 2021

The progenitor of Type Ia supernovae (SNe Ia) is mainly believed to be a close binary system of acarbon-oxygen white dwarf (CO WD) and non-degenerate companion (single degenerate) or another WD (double degenerate). However, it is unclear which system is more prevalent. Here, we present a high cadence optical/Near-IR light curve of normal but slightly faint type Ia SN 2019ein from IMSNG project. We fit the early light curve (t <+8.3 days from the first detection) with various models to find the shock-heated cooling emission from SN ejecta-companion interaction. No significant shock-heated cooling emission is found, from which we constrain the progenitor star size as the following. The upper limit (R_upper,*) of the companion size in R-band is ~0.2R_⊙ when forcing the first light time (t_fl) to have one value and ~0.9R_⊙ when using the mean value of tfl from the fitting in each band. Assuming the source of the I-band curve is almost powered from the radioactive decay, we obtained R_upper,*~1.2R_⊙. The early B-V color curve is in agreement with the model color curve of the 2M_⊙ main sequence companion. These results allow us to at least rule out large stars like red giants as a companion star of the binary progenitor system of this supernova. B-R and V-R color do not show any significant signs of a red bump, which shows a thin helium shell (MHe<0.1M_⊙) for the sub-Mch WD (double detonation model). In addition, we estimated the distance to NGC 5353 as 37.098±0.028Mpc.