• East Asian mathematical journal
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• v.21 no.2
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• pp.233-240
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• 2005

Let $CS^{\alpha}(\beta)$ denote the class of normalized strongly $\alpha$-logarithmic close-to-convex functions of order $\beta$, defined in the open unit disk $\mathbb{U}$ by $$\|arg\{\(\frac{f(z)}{g(z)}\)^{1-\alpha}\(\frac{zf'(z)}{g(z)\)^{\alpha}\}\|\leq\frac{\pi}{2}\beta,\;(\alpha,\beta\geq0)$$ where $g{\in}S^*$ the class of normalized starlike functions. In this paper, we prove sharp $Fekete-Szeg\"{o}$ inequalities for functions $f{\in}CS^{\alpha}(\beta)$.

• The Pure and Applied Mathematics
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• v.17 no.1
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• pp.87-92
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• 2010

Let R be a 2-torsion free $\sigma$-prime ring with an involution $\sigma$, U a nonzero square closed $\sigma$-Lie ideal, Z(R) the center of Rand d a derivation of R. In this paper, it is proved that d = 0 or $U\;{\subseteq}\;Z(R)$ if one of the following conditions holds: (1) $d(xy)\;-\;xy\;{\in}\;Z(R)$ or $d(xy)\;-\;yx\;{\in}Z(R)$ for all x, $y\;{\in}\;U$. (2) $d(x)\;{\circ}\;d(y)\;=\;0$ or $d(x)\;{\circ}\;d(y)\;=\;x\;{\circ}\;y$ for all x, $y\;{\in}\;U$ and d commutes with $\sigma$.

• Bulletin of the Korean Chemical Society
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• v.15 no.6
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• pp.469-473
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• 1994

The E-and Z-isomers of 1-methyl-l-phenyl-2-neopentylsilene, generated by the sealed tube thermolyses of their anthracene adducts are stereospecifically trapped by trimethylmethoxysilane to give diastereomeric adducts. The temperature dependence of the ratio of the two diastereomers obtained when the silene formed from the pure E-or Z-anthracene adduct was trapped at higher temperatures permitted the determination of an activation energy for the silene isomerization. The activation energies for the E-to Z-and Z-to E-silene isomerization are $45{\pm}$6 and $20{\pm}4$ kcal $mol^{-1}$, respectively. The significance of these values is discussed.

• Bulletin of the Korean Chemical Society
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• v.21 no.5
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• pp.477-482
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• 2000

Phenyl group migration within protonated 1,2-diphenyl hydrazines has been studied theoretically using the semi-empirical AM1 method. This reaction proceeds through a 3-membered cyclic transition state and requires high activation energy. In the reactant, there was no resonance stabilization for the moving Z-ring, however, hammett $p_Z^+$ values are large due to the direct involvement of the Z-ring inthe reaction, and the development of a negative charge on the reaction center gives them a posifive value. In the case of the non-moving ring, $p_Y^+$ values are small and negative owing to the smaller positive charge increase in the reaction center. The cross-interaction constant, $p_YZ^+$, was obtained from the activation enthalpies, using the multipe linear regression methdo, and the interaction between two substituents, Y and Z, is examined.

• Bulletin of the Korean Chemical Society
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• v.18 no.11
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• pp.1179-1182
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• 1997

The rates for the reaction of (Z)-phenacyl (X)-benzenesulfonates with (Y)-pyridines in acetone were measured by an electrical conductivity method at 1-2000 bars and 45 ℃. The magnitudes of the Hammett reaction constants, ρX, ρY and ρZ, represent the degree of Nu-C bond formation and that of C-L bond breaking. The magnitude of correlation interaction term ρij can be used to determine the structure of the transition state (TS) for the SN reaction. As the pressure is increased, the Hammett reaction constants, ρX, |ρY| and ρZ are increased, but correlation interaction coefficient, |ρXZ| and ρYZ, are decreased. The results indicate that the reaction of (Z)-phenacyl (X)-benzenesulfonates with (Y)-pyridines probably moves from an associative SN2 to late-type SN2 mechanism by increasing pressure.

• Bulletin of the Korean Mathematical Society
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• v.56 no.3
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• pp.745-756
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• 2019

We obtain Lipschitz type characterization and double integral characterization for Fock-type spaces with the norm $${\parallel}f{\parallel}^p_{F^p_{m,{\alpha},t}}\;=\;{\displaystyle\smashmargin{2}{\int\nolimits_{{\mathbb{C}}^n}}\;{\left|{f(z){e^{-{\alpha}}{\mid}z{\mid}^m}}\right|^p}\;{\frac{dV(z)}{(1+{\mid}z{\mid})^t}}$$, where ${\alpha}>0$, $t{\in}{\mathbb{R}}$, and $m{\in}\mathbb{N}$. The results of this paper are the extensions of the classical weighted Fock space $F^p_{2,{\alpha},t}$.

• Bulletin of the Korean Chemical Society
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• v.19 no.2
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• pp.189-193
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• 1998

Carboxypeptidase-B (CPB) is involved in the biosynthesis of numerous peptide hormones and neurotransmitters. CPB catalyzes hydrolysis of the basic amino acids from the C-terminal position in polypeptides during posttranslational prohormonal processing. Various peptides containing thiaarginine residue at C-terminal position were synthesized and tested for their hydrolysis by CPB. A colorimetric assay, employing Ellman's reagent to detect the thioguanidine released upon hydrolysis of the dipeptide substrates, showed that thiaarginine is a suitable mimetic for arginine. Kinetic studies on the four substrates, Z-L-Ala-DL-thia-Lys, Z-L-Ala-DL-thia-Arg, Z-L-Lys-DL-thia-Arg, and Z-L-Lys(Boc)-DL-thia-Arg, gave Km (mM) of 0.66, 5.08, 0.024, and 0.006 and kcat (min-1) of 340, 5200, 151 and 335, respectively.

• Kyungpook Mathematical Journal
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• v.61 no.1
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• pp.99-110
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• 2021

In the present paper, we determine new characterisations of the subclasses ����∗��(α, β; γ) and ������(α, β; γ) of analytic functions associated with Pascal distribution series ${\Phi}^m_q(z)=z-{\sum_{n=2}^{\infty}}(^{n+m-2}_{m-1})q^{n-1}(1-q)^mz^n$. Further, we give necessary and sufficient conditions for an integral operator related to Pascal distribution series ${\mathcal{G}}^m_qf(z)={\int_{0}^{z}}{\frac{{\Phi}^m_q(t)}{t}}dt$ to belong to the above classes. Several corollaries and consequences of the main results are also considered.

• Kyungpook Mathematical Journal
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• v.62 no.2
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• pp.243-256
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• 2022

In 1914, Bohr proved that there is an r₀ ∈ (0, 1) such that if a power series ∑^∞_m=0 c_mz^m is convergent in the open unit disc and |∑^∞_m=0 c_mz^m| < 1 then, ∑^∞_m=0 |c_mz^m| < 1 for |z| < r₀. The largest value of such r₀ is called the Bohr radius. In this article, we find Bohr radius for some univalent harmonic mappings having different dilatations. We also compute the Bohr radius for functions that are convex in one direction.

• Nonlinear Functional Analysis and Applications
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• v.28 no.3
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• pp.731-751
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• 2023

If p(z) is a polynomial of degree n having all its zeros in |z| ≤ k, k ≥ 1, then for any complex number α with |α| ≥ k, and r ≥ 1, Aziz [1] proved $$\left{{\int}_{0}^{2{\pi}}\,{\left|1+k^ne^{i{\theta}}\right|^r}\,d{\theta}\right}^{\frac{1}{r}}\;{\max\limits_{{\mid}z{\mid}=1}}\,{\mid}p^{\prime}(z){\mid}\,{\geq}\,n\,\left{{\int}_{0}^{2{\pi}}\,{\left|p(e^{i{\theta}})\right|^r\,d{\theta}\right}^{\frac{1}{r}}.$$ In this paper, we obtain an improved extension of the above inequality into polar derivative. Further, we also extend an inequality on polar derivative recently proved by Rather et al. [20] into L^r-norm. Our results not only extend some known polynomial inequalities, but also reduce to some interesting results as particular cases.