• 대한수학회보
• /
• 제53권6호
• /
• pp.1651-1670
• /
• 2016

In this paper, we investigate exponentially biharmonic maps u : (M, g) ${\rightarrow}$ (N, h) from a Riemannian manifold into a Riemannian manifold with non-positive sectional curvature. We obtain that if $\int_{M}e^{\frac{p{\mid}r(u){\mid}^2}{2}{\mid}{\tau}(u){\mid}^pdv_g$ < ${\infty}$ ($p{\geq}2$), $\int_{M}{\mid}{\tau}(u){\mid}^2dv_g$ < ${\infty}$ and $\int_{M}{\mid}d(u){\mid}^2dv_g$ < ${\infty}$, then u is harmonic. When u is an isometric immersion, we get that if $\int_{M}e^{\frac{pm^2{\mid}H{\mid}^2}{2}}{\mid}H{\mid}^qdv_g$ < ${\infty}$ for 2 ${\leq}$ p < ${\infty}$ and 0 < q ${\leq}$ p < ${\infty}$, then u is minimal. We also obtain that any weakly convex exponentially biharmonic hypersurface in space form N(c) with $c{\leq}0$ is minimal. These results give affirmative partial answer to conjecture 3 (generalized Chen's conjecture for exponentially biharmonic submanifolds).

• Bulletin of the Korean Chemical Society
• /
• 제32권5호
• /
• pp.1625-1629
• /
• 2011

Kinetic studies of the reactions of O,O-diphenyl Z-S-aryl phosphorothioates with X-benzylamines have been carried out in dimethyl sulfoxide at 55.0 $^{\circ}C$. The Hammett (log $k_2$ vs ${\sigma}_X$) and Bronsted [log $k_2$ vs $pK_a(X)$] plots for substituent X variations in the nucleophiles are biphasic concave downwards with a maximum point at X = H, and the unusual positive ${\rho}_X$ and negative ${\beta}_X$ values are obtained for the strongly basic benzylamines. The sign of the cross-interaction constant (${\rho}_{XZ}$) is negative for both the strongly and weakly basic nucleophiles. Greater magnitude of ${\rho}_{XZ}$ value is observed with the weakly basic nucleophiles (${\rho}_{XZ}$ = -2.35) compared to with the strongly basic nucleophiles (${\rho}_{XZ}$ = -0.03). The deuterium kinetic isotope effects ($k_H/k_D$) involving deuterated benzylamines [$XC_6H_4CH_2ND_2$] are primary normal ($k_H/k_D$ > 1). The proposed mechanism is a concerted $S_N2$ involving a frontside nucleophilic attack with a hydrogen bonded, four-center-type transition state for both the strongly and weakly basic nucleophiles. The unusual positive ${\rho}_X$ and negative ${\beta}_X$ values with the strongly basic benzylamines are rationalized by through-space interaction between the ${\pi}$-clouds of the electron-rich phenyl ring of benzylamine and the phenyl ring of the leaving group thiophenoxide.

• 한국수학교육학회지시리즈B:순수및응용수학
• /
• 제22권3호
• /
• pp.199-214
• /
• 2015

We establish a common coupled fixed point theorem for hybrid pair of mappings under generalized Mizoguchi-Takahashi contraction on a noncomplete metric space, which is not partially ordered. It is to be noted that to find coupled oincidence point, we do not employ the condition of continuity of any mapping involved therein. An example is also given to validate our results. We improve, extend and generalize several known results.

• East Asian mathematical journal
• /
• 제25권2호
• /
• pp.179-196
• /
• 2009

Let E be a uniformly convex Banach space and K a nonempty closed convex subset which is also a nonexpansive retract of E. For i = 1, 2, 3, let $T_i:K{\rightarrow}E$ be an asymptotically nonexpansive mappings with sequence ${\{k_n^{(i)}\}\subset[1,{\infty})$ such that $\sum_{n-1}^{\infty}(k_n^{(i)}-1)$ < ${\infty},\;k_{n}^{(i)}{\rightarrow}1$, as $n{\rightarrow}\infty$ and F(T)=$\bigcap_{i=3}^3F(T_i){\neq}{\phi}$ (the set of all common xed points of $T_i$, i = 1, 2, 3). Let {$a_n$},{$b_n$} and {$c_n$} are three real sequences in [0, 1] such that $\in{\leq}\;a_n,\;b_n,\;c_n\;{\leq}\;1-\in$ for $n{\in}N$ and some ${\in}{\geq}0$. Starting with arbitrary $x_1{\in}K$, define sequence {$x_n$} by setting {$$x_{n+1}=P((1-a_n)x_n+a_nT_1(PT_1)^{n-1}y_n)$$ $$y_n=P((1-b_n)x_n+a_nT_2(PT_2)^{n-1}z_n)$$ $$z_n=P((1-c_n)x_n+c_nT_3(PT_3)^{n-1}x_n)$$. Assume that one of the following conditions holds: (1) E satises the Opial property, (2) E has Frechet dierentiable norm, (3) $E^*$ has Kedec -Klee property, where $E^*$ is dual of E. Then sequence {$x_n$} converges weakly to some p${\in}$F(T).

• East Asian mathematical journal
• /
• 제26권3호
• /
• pp.429-440
• /
• 2010

In this paper, we study a new one-step iterative scheme with error for approximating common fixed points of non-self asymptotically nonexpansive in the intermediate sense mappings in uniformly convex Banach spaces. Also we have proved weak and strong convergence theorems for above said scheme. The results obtained in this paper extend and improve the recent ones, announced by Zhou et al. [27] and many others.

• 대한수학회보
• /
• 제22권1호
• /
• pp.23-29
• /
• 1985

Let H be an arbitrary complex Hilbert space. We constructed an extension K of H by means of weakly convergent sequences in H and the Banach limit. Let .phi. be the faithful *-representation of L(H) on K. In this note, we investigated the relations between spectra of T in L(H) and .phi.(T) in L(K) and we obtained the following results: 1) If T is a compact operator on H, then .phi.(T) is also a compact operator on K (Proposition 6), 2) .sigma.$_{l}$ (.phi.(T)).contnd..sigma.$_{l}$ (T) for any operator T.mem.L(H) (Corollary 10), 3) For every operator T.mem.L(H), .sigma.$_{ap}$ (.phi.(T))=.sigma.$_{ap}$ (T))=.sigma.$_{ap}$ (T)=.sigma.$_{p}$(.phi.(T)) (Lemma 12, 13) and .sigma.$_{c}$(.phi.(T))=.sigma.(Theorem 15).15).

• 한국수학교육학회지시리즈B:순수및응용수학
• /
• 제26권3호
• /
• pp.111-131
• /
• 2019

We introduce (CLRg) property for hybrid pair $F:X{\times}X{\rightarrow}2^X$ and $g:X{\rightarrow}X$. We also introduce joint common limit range (JCLR) property for two hybrid pairs $F,G:X{\times}X{\rightarrow}2^X$ and $f,g:X{\rightarrow}X$. We also establish some common coupled fixed point theorems for hybrid pair of mappings under generalized (${\psi},{\theta},{\varphi}$)-contraction on a noncomplete metric space, which is not partially ordered. It is to be noted that to find coupled coincidence point, we do not employ the condition of continuity of any mapping involved therein. As an application, we study the existence and uniqueness of the solution to an integral equation. We also give an example to demonstrate the degree of validity of our hypothesis. The results we obtain generalize, extend and improve several recent results in the existing literature.

• 터널과지하공간
• /
• 제5권2호
• /
• pp.134-143
• /
• 1995

Effects of blasting vibrations on curing concrete have not been well studied. As a result, unreasonable and strong blasting vibration constraints have been placed on blasting when it occurs in the vicinity of curing concrete. To study the effects of blasting on curing concrete blocks of 33.3X27.7X16.2 cm were molded and placed on the quarry. Several sets of concrete blocks were subjected separately to peak vibrations of 0.25, 0.5. 1.0, 5.0, and 10cm/sec. The impulses of blasting vibrations were applied with thirty-minute intervals. Along with unvibrated concrete blocks, the vibrated concrete samples cored with 60.3 mm in diameter were measured for elastic moduli, sonic velocity and uniaxial compressive strength. Test results can be summarized as follows; 1. The blasting vibrations between 6 and 8 hours after pour generally lowered on the uniaxial compressive strength of the concrete. 2. A low blasting vibration of 0.25 cm/sec did not affect the uniaxial compressive strength. As the magnitude of the blasting vibration increases, compressive strength of concrete is decreased. 3. Physical properties of the P-wave velocity, Young's modulus, and Poisson's ratio showed a weakly decreasing trend in the concrete blocks vibrated between 6 and 8 hours after pour.

• 대한화학회지
• /
• 제63권6호
• /
• pp.453-458
• /
• 2019

Synthesis of ZnCo₂O₃ oxide is performed by sol-gel method via nitrate-citrate route. Powder X-ray diffraction (XRD) study shows monoclinic unit cell having lattice parameters: a = 5.721(1) Å, b = 8.073(2) Å, c = 5.670(1) Å, β = 93.221(8)°, space group P_2/m and Z = 4. Average crystallite sizes determined by Scherrer equation are the range ~14-32 nm, whereas SEM micrographs show nano-micro meter size particles formed in ZnCo₂O₃. Endothermic peak at ~798 K in the Differential scanning calorimetric (DSC) trace without weight loss could be due to structural transformation and the endothermic peak ~1143 K with weight loss is due to reversible loss of O₂ in air atmosphere. Energy Dispersive X-ray (EDX) analysis profile shows the presence of elements Zn, Co and O which indicates the purity of the sample. Magnetic measurements in the range of +12 kOe to -12 kOe at 10 K, 77 K, 120 K and at 300 K by PPMS-II Physical Property Measurement System (PPMS) shows hysteresis loops having very low values of the coercivity and retentivity which indicates the weakly ferromagnetic nature of the oxide. Observed X-band EPR isotropic lineshapes at 300 K and 77 K show positive g-shift at g_iso ~2.230 and g_iso ~2.217, respectively which is in agreement with the presence of paramagnetic site Co²⁺(3d⁷) in the oxide. DC conductivity value of 2.875 ×10^-8 S/cm indicates very weakly semiconducting nature of ZnCo₂O₃ at 300 K. DRS absorption bands ~357 nm, ~572 nm, ~619 nm and ~654 nm are due to the d-d transitions ⁴T_1g(⁴F)→²E_g(²G), ⁴T_1g(⁴F)→⁴T_1g(⁴P), ⁴T_1g(⁴F)→⁴A_2g(⁴F), ⁴T_1g(⁴F)→⁴T_2g(⁴F), respectively in octahedral ligand field around Co²⁺ ions. Direct band gap energy, E_g~ 1.5 eV in the oxide is obtained by extrapolating the linear part of the Tauc plot to the energy axis indicates fairly strong semiconducting nature of ZnCo₂O₃.

• 천문학회지
• /
• 제53권2호
• /
• pp.49-57
• /
• 2020

We present numerical simulations of decaying hydrodynamic turbulence initially driven by solenoidal (divergence-free) and compressive (curl-free) drivings. Most previous numerical studies for decaying turbulence assume an isothermal equation of state (EOS). Here we use a polytropic EOS, P ∝ ρ^γ, with polytropic exponent γ ranging from 0.7 to 5/3. We mainly aim at determining the effects of γ and driving schemes on the decay law of turbulence energy, E ∝ t^-α. We additionally study probability density function (PDF) of gas density and skewness of the distribution in polytropic turbulence driven by compressive driving. Our findings are as follows. First of all, we find that even if γ does not strongly change the decay law, the driving schemes weakly change the relation; in our all simulations, turbulence decays with α ≈ 1, but compressive driving yields smaller α than solenoidal driving at the same sonic Mach number. Second, we calculate compressive and solenoidal velocity components separately and compare their decay rates in turbulence initially driven by compressive driving. We find that the former decays much faster so that it ends up having a smaller fraction than the latter. Third, the density PDF of compressively driven turbulence with γ > 1 deviates from log-normal distribution: it has a power-law tail at low density as in the case of solenoidally driven turbulence. However, as it decays, the density PDF becomes approximately log-normal. We discuss why decay rates of compressive and solenoidal velocity components are different in compressively driven turbulence and astrophysical implication of our findings.