• Journal of the Korean Mathematical Society
• /
• v.56 no.6
• /
• pp.1529-1560
• /
• 2019

We are concerned with the following elliptic equations: $$(-{\Delta})^s_pu+V (x){\mid}u{\mid}^{p-2}u={\lambda}g(x,u){\text{ in }}{\mathbb{R}}^N$$, where $(-{\Delta})_p^s$ is the fractional p-Laplacian operator with 0 < s < 1 < p < $+{\infty}$, sp < N, the potential function $V:{\mathbb{R}}^N{\rightarrow}(0,{\infty})$ is a continuous potential function, and $g:{\mathbb{R}}^N{\times}{\mathbb{R}}{\rightarrow}{\mathbb{R}}$ satisfies a $Carath{\acute{e}}odory$ condition. We show the existence of at least one weak solution for the problem above without the Ambrosetti and Rabinowitz condition. Moreover, we give a positive interval of the parameter ${\lambda}$ for which the problem admits at least one nontrivial weak solution when the nonlinearity g has the subcritical growth condition.

• Journal of the Korean Mathematical Society
• /
• v.59 no.5
• /
• pp.911-926
• /
• 2022

Let u be a function on a locally finite graph G = (V, E) and Ω be a bounded subset of V. Let 𝜀 > 0, p > 2 and 0 ≤ λ < λ₁(Ω) be constants, where λ₁(Ω) is the first eigenvalue of the discrete Laplacian, and h : V → ℝ be a function satisfying h ≥ 0 and $h{\not\equiv}0$. We consider a perturbed Yamabe equation, say $$\{\begin{array}{lll}-{\Delta}u-{\lambda}u={\mid}u{\mid}^{p-2}u+{\varepsilon}h,&&\text{ in }{\Omega},\\u=0,&&\text{ on }{\partial}{\Omega},\end{array}$$ where Ω and ∂Ω denote the interior and the boundary of Ω, respectively. Using variational methods, we prove that there exists some positive constant 𝜀₀ > 0 such that for all 𝜀 ∈ (0, 𝜀₀), the above equation has two distinct solutions. Moreover, we consider a more general nonlinear equation $$\{\begin{array}{lll}-{\Delta}u=f(u)+{\varepsilon}h,&&\text{ in }{\Omega},\\u=0,&&\text{ on }{\partial}{\Omega},\end{array}$$ and prove similar result for certain nonlinear term f(u).

• Interaction and multiscale mechanics
• /
• v.6 no.3
• /
• pp.287-300
• /
• 2013

In this paper, the effect of impulsive line on the propagation of shear waves in non-homogeneous elastic layer is investigated. The rigidity and density in the intermediate layer is assumed to vary quadratic as functions of depth. The dispersion equation is obtained by using the Fourier transform and Green's function technique. The study ends with the mathematical calculations for transmitted wave in the layer. These equations are in complete agreement with the classical results when the non-homogeneity parameters are neglected. Various curves are plotted to show the effects of non-homogeneities on shear waves in the intermediate layer.

• Earthquakes and Structures
• /
• v.9 no.2
• /
• pp.305-320
• /
• 2015

The present paper is devoted to study SH-wave propagation in heterogeneous layer laying over an inhomogeneous isotropic elastic half-space. The dispersion relation for propagation of said waves is derived with Green's function method and Fourier transform. As a special case when the upper layer and lower half-space are homogeneous, our derived equation is in agreement with the general equation of Love wave. Numerically, it is observed that the velocity of SH-wave increases with the increase of inhomogeneity parameter.

• Journal of the Chungcheong Mathematical Society
• /
• v.20 no.4
• /
• pp.349-353
• /
• 2007

In this paper, we obtain some coefficient bounds of harmonic univalent mappings by using properties of the analytic univalent function on ${\Delta}$={z : |z| > 1}.

• Korean Journal of Microbiology
• /
• v.46 no.2
• /
• pp.122-126
• /
• 2010

RAD53 functions as an effector kinase of checkpoint pathways in Saccharomyces cerevisiae, which plays a central role to regulate many downstream cellular processes in response to DNA damage. It also involves in transcriptional activation of various genes including RNR genes which encode the key enzyme required for dNTP synthesis. In this study, we identified CYC8 as a suppressor for the hydroxyurea sensitivity of $rad53{\Delta}$ mutation. $Rad53{\Delta}$ mutant transformed with a multi-copy plasmid containing CYC8 showed increased hydroxyurea resistance. In contrast, TUP1 which forms a complex with CYC8 did not function as a suppressor. In the case of mutations, both $cyc8{\Delta}$ and $tup1{\Delta}$ suppressed hydroxyurea sensitivity of $rad53{\Delta}$. Since CYC8 can propagate as a prion in yeast, overexpression of CYC8 induced misfolding of the normal CYC8 proteins, resulting in dominant cyc8-phenotype. Therefore, it is suggested that CYC8 can act as a multi-copy suppressor due to its prion property. It was observed that the levels of RNR transcription were increased in the yeast strains containing either multi-copies of CYC8 gene or $cyc8{\Delta}$ mutation, suggesting that the increased level of RNR will elevate the intracellular pools of dNTPs, which, in turn, suppress the phenotype of $rad53{\Delta}$ mutation.

• Journal of applied mathematics & informatics
• /
• v.24 no.1_2
• /
• pp.357-366
• /
• 2007

Let G(V, E) be a simple graph, and let f be an integer function on V with $1{\leq}f(v){\leq}d(v)$ to each vertex $v{\in}V$. An f-edge cover-coloring of a graph G is a coloring of edge set E such that each color appears at each vertex $v{\in}V$ at least f(v) times. The f-edge cover chromatic index of G, denoted by ${\chi}'_{fc}(G)$, is the maximum number of colors such that an f-edge cover-coloring of G exists. Any simple graph G has an f-edge cover chromatic index equal to ${\delta}_f\;or\;{\delta}_f-1,\;where\;{\delta}_f{=}^{min}_{v{\in}V}\{\lfloor\frac{d(v)}{f(v)}\rfloor\}$. Let G be a connected and not complete graph with ${\chi}'_{fc}(G)={\delta}_f-1$, if for each $u,\;v{\in}V\;and\;e=uv{\nin}E$, we have ${\chi}'_{fc}(G+e)>{\chi}'_{fc}(G)$, then G is called an f-edge covered critical graph. In this paper, some properties on f-edge covered critical graph are discussed. It is proved that if G is an f-edge covered critical graph, then for each $u,\;v{\in}V\;and\;e=uv{\nin}E$ there exists $w{\in}\{u,v\}\;with\;d(w)\leq{\delta}_f(f(w)+1)-2$ such that w is adjacent to at least $d(w)-{\delta}_f+1$ vertices which are all ${\delta}_f-vertex$ in G.

• Journal of the Korean Chemical Society
• /
• v.33 no.2
• /
• pp.156-163
• /
• 1989

The $ν_a+amide II$ combination band of thiopropionamide has been recorded for investigation of Hydrogen bonding between thiopropionamide (TPA) and N,N-dimethylalkylamide (DMF, DMA and DMP) in carbon tetrachloride over the range of $5^{\circ}$ to $55^{\circ}$. The combination band of monomeric TPA and hydrogen-bonded TPA can be resolved by Lorentzian-Gaussian product function into monomeric TPA and hydrogen-bonded TPA with amides. The association constants ($K_1$) for the hydrogen-bonded TPA were calculated by the concentrations of the monomeric TPA and the hydrogen-bonded TPA obtained from the computer resolved absorption bands. Thermodynamic parameters for the Hydrogen bonding have been evaluated by the analysis of the temperature dependent spectra. The ${\Delta}$$H^{\circ}$ of hydrogen-bonded TPA with DMF, DMA and DMP have been found to be-12.5, -13.5 and -14.1 kJ/mol, respectively. The corresponding ${\Delta}$$S^{\circ}$for the above system were -15.2, -17.9 and -22.3 J/mol${\cdot}$deg, respectively.

• Journal of the Korea society of information convergence
• /
• v.7 no.2
• /
• pp.25-29
• /
• 2014

In this study, it examined the effects of alcohol on the physiology of the eye and ocular function. It was measured to IOP(intraocular pressure), tear secretion, stereoscopic parallax, AC A ratio, convergence ability, divergence ability alcohol intake before and after. The results were as follows. The mean IOP before alcohol intake 15.14mmHg and the mean IOP after alcohol intake 12.8mmHg. Average decreased 15.44%. The mean tear secretion before alcohol intake 17.125mm and the mean secretion after alcohol intake 9.875mm. Average decreased 42.33%. Stereoscopic parallax has increased by about four times that 40' before alcohol intake to 165' after that. AC/A ratio has increased by 14.6% that $5.40{\Delta}/D$ before alcohol intake to $6.19{\Delta}/D$ after that. Convergence and divergence ability was no significant change in both distance and close range.

• Development and Reproduction
• /
• v.7 no.2
• /
• pp.69-80
• /
• 2003

The zebrafish(Danio rerio) is a pre-eminent vertebrate model system for clarification of the roles of specific genes and signaling pathways in development. We show examples of positional cloning in two developmental mutants in zebrafish. headless: The severe head defects in headless(hdl) mutants are due to a mutation in T-cell factor-3(Tcf3). Loss of Tcf3 function in the hdl mutant reveals that Hdl represses Wnt target genes. The results provide genetic evidence that a component of the Wnt signaling pathway is essential in vertebrate head formation and patterning. mind bomb: Reduced lateral inhibition in mind bomb(mib) mutants permits too many neural precursors to differentiate as neurons. Positional cloning of mib revealed that it is a gene in the Notch pathway that encodes a ubiquitin E3 ligase. Mib interacts with the intracellular domain of Delta to promote its internalization. The results suggest a model for Notch activation where the Delta-Notch interaction is followed by endocytosis of Delta and transendocytosis of the Notch extracellular domain by the signaling cell.