• Nonlinear Functional Analysis and Applications
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• v.26 no.2
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• pp.331-345
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• 2021

Let p(z)be a polynomial of degree n. Then Bernstein's inequality [12,18] is $${\max\limits_{{\mid}z{\mid}=1}}\;{\mid}p^{\prime}(z){\mid}\;{\leq}\;n\;{\max_{{\mid}z{\mid}=1}{\mid}(z){\mid}}$$. For q > 0, we denote $${\parallel}p{\parallel}_q=\{{\frac{1}{2{\pi}}}{\normalsize\displaystyle\smashmargin{2}{\int\nolimits_{0}}^{2{\pi}}}\;{\mid}p(e^{i{\theta}}){\mid}^qd{\theta}\}^{\frac{1}{q}}$$, and a well-known fact from analysis [17] gives $${{\lim_{q{\rightarrow}{{\infty}}}}\{{\frac{1}{2{\pi}}}{\normalsize\displaystyle\smashmargin{2}{\int\nolimits_{0}}^{2{\pi}}}\;{\mid}p(e^{i{\theta}}){\mid}^qd{\theta}\}^{\frac{1}{q}}={\max\limits_{{\mid}z{\mid}=1}}\;{\mid}p(z){\mid}$$. Above Bernstein's inequality was extended by Zygmund [19] into L^q norm by proving ║p'║_q ≤ n║p║_q, q ≥ 1. Let p(z) = a₀ + ∑ⁿ_𝜈=𝜇 a_𝜈z^𝜈, 1 ≤ 𝜇 ≤ n, be a polynomial of degree n having no zero in |z| < k, k ≥ 1. Then for 0 < r ≤ R ≤ k, Aziz and Zargar [4] proved $${\max\limits_{{\mid}z{\mid}=R}}\;{\mid}p^{\prime}(z){\mid}\;{\leq}\;{\frac{nR^{{\mu}-1}(R^{\mu}+k^{\mu})^{{\frac{n}{\mu}}-1}}{(r^{\mu}+k^{\mu})^{\frac{n}{\mu}}}\;{\max\limits_{{\mid}z{\mid}=r}}\;{\mid}p(z){\mid}}$$. In this paper, we obtain the L^q version of the above inequality for q > 0. Further, we extend a result of Aziz and Shah [3] into L^q analogue for q > 0. Our results not only extend some known polynomial inequalities, but also reduce to some interesting results as particular cases.

• Transactions of the Korean Society of Mechanical Engineers A
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• v.36 no.1
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• pp.9-16
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• 2012

Recently, an optics-based concentrator for solar concentration has been a key issue in development of photovoltaic systems. In the present study, a new, simple, easily producible planar concentrator based on a light guide system is proposed. In this device, solar light is concentrated by microprism optical patterns guiding the light, mainly through total reflection and refraction. The main design variables of the concentrator are the geometric concentration ratio ($R_c$) and the ${\Theta}_1$ and ${\Theta}_2$ of the microprism pattern. Ray tracing was simulated using commercial software, SPEOS, and the optical efficiencies of the light guide solar concentrator were predicted in each case. The predicted maximum optical efficiencies are 65.60%, 54.78%, and 46.78%, respectively, for $R_c$ values of 4, 5, and 6. The variation of the optical efficiencies according to ${\Theta}_1$, ${\Theta}_2$, and the incline angle of the incident light were predicted.

• Journal of the Korean Society for Industrial and Applied Mathematics
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• v.11 no.1
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• pp.13-30
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• 2007

In this paper we study the numerical solutions of the stochastic functional differential equations of the following form $$du(x,\;t)\;=\;f(x,\;t,\;u_t)dt\;+\;g(x,\;t,\;u_t)dB(t),\;t\;>\;0$$ with initial data $u(x,\;0)\;=\;u_0(x)\;=\;{\xi}\;{\in}\;L^p_{F_0}\;([-{\tau},0];\;R^n)$. Here $x\;{\in}\;R^n$, ($R^n$ is the ${\nu}\;-\;dimenional$ Euclidean space), $f\;:\;C([-{\tau},\;0];\;R^n)\;{\times}\;R^{{\nu}+1}\;{\rightarrow}\;R^n,\;g\;:\;C([-{\tau},\;0];\;R^n)\;{\times}\;R^{{\nu}+1}\;{\rightarrow}\;R^{n{\times}m},\;u(x,\;t)\;{\in}\;R^n$ for each $t,\;u_t\;=\;u(x,\;t\;+\;{\theta})\;:\;-{\tau}\;{\leq}\;{\theta}\;{\leq}\;0\;{\in}\;C([-{\tau},\;0];\;R^n)$, and B(t) is an m-dimensional Brownian motion.

• Journal of applied mathematics & informatics
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• v.12 no.1_2
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• pp.313-321
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• 2003

In this Paper we show the following: Let R be a prime ring (with characteristic different two) and a $\in$ R. Let Θ, $\phi$ : R longrightarrow R be automorphisms and let d : R longrightarrow R be a nonzero Θ-derivation. (i) if［d($\chi$), a］Θo$\phi$ = 0 (or d(［$\chi$, a］$\phi$ = 0) for all $\chi$ $\in$ R, then a+$\phi$(a) $\in$ Z, the conte. of R, (ii) if〈d($\chi$), a〉 = 0 for all $\chi$$\in$R, then d(a) =0. (iii) if [ad($\chi$), $\chi$］$\phi$= 0 for all $\chi$$\in$R, then either a = 0 or R is commutative.

• Journal of the Korean Electrochemical Society
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• v.12 no.1
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• pp.26-33
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• 2009

The phase-shift method and correlation constants, i.e., the unique electrochemical impedance spectroscopy (EIS) techniques for studying the linear relationship between the behavior ($-{\varphi}$ vs. E) of the phase shift ($90^{\circ}{\geq}-{\varphi}{\geq}0^{\circ}$) for the optimum intermediate frequency and that ($\theta$ vs. E) of the fractional surface coverage ($0{\leq}{\theta}{\leq}1$), have been proposed and verified to determine the Langmuir, Frumkin, and Temkin adsorption isotherms of H and related electrode kinetic and thermodynamic parameters at noble metal (alloy)/aqueous solution interfaces. At a Zr/0.2 M ${H_2}{SO_4}$ aqueous solution interface, the Frumkin and Temkin adsorption isotherms ($\theta$ vs. E), equilibrium constants (K = $1.401{\times}10^{-17}\exp(-3.5{\theta})mol^{-1}$ for the Frumkin and K = $1.401{\times}10^{-16}\exp(8.1{\theta})mol^{-1}$ for the Temkin adsorption isotherm), interaction parameters (g = 3.5 for the Frumkin and g = 8.1 for the Temkin adsorption isotherm), rates of change of the standard free energy (r = $8.7\;kJ\;mol^{-1}$ for g = 3.5 and r = $20\;kJ\;mol^{-1}$ for g = 8.1) of H with $\theta$, and standard free energies ($96.13{\leq}{\Delta}G^0_{\theta}{\leq}104.8\;kJ\;mol^{-1}$ for K = $1.401{\times}10^{-17}\exp(-3.5{\theta})mol^{-1}$ and $0{\leq}{\theta}{\leq}1$ and ($94.44<{\Delta}G^0_{\theta}<106.5\;kJ\;mol^{-1}$ for K = $1.401{\times}10^{-16}\exp(-8.1{\theta})mol^{-1}$ and $0.2<{\theta}<0.8$) of H are determined using the phase-shift method and correlation constants. At 0.2 < $\theta$ < 0.8, the Temkin adsorption isotherm correlating with the Frumkin adsorption isotherm, and vice versa, is readily determined using the correlation constants. The phase-shift method and correlation constants are probably the most accurate, useful, and effective ways to determine the adsorption isotherms of H and related electrode kinetic and thermodynamic parameters at highly corrosion-resistant metal/aqueous solution interfaces.

• Journal of the Chungcheong Mathematical Society
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• v.33 no.2
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• pp.271-285
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• 2020

In this paper, we have introduced a new type of covering property ${\beta}^t_{({\omega}_r,s)}$-closedness, stronger than $P^t_{({\omega}_r,s)}$-closedness [3] in terms of (r, s)-β-open sets [9] and β-ω_t-closures in bitopological spaces along with its several characterizations via filter bases and grills [15] and various properties. Further grill generalizations of ${\beta}^t_{({\omega}_r,s)}$-closedness (namely, ${\beta}^t_{({\omega}_r,s)}$-closedness modulo grill) and associated concepts have also been investigated.

• Korean journal of applied entomology
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• v.24 no.4 s.65
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• pp.231-238
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• 1986

Molecular orbital theoretical study on the stability of conformations and chemical reactivity of 0,0-diethylphenylphosphate derivatives were carried out by EHT and CNDO/2 molecular orbital calculation method. The results shown that the dipole moment(${\mu}$) and total energies of the ${\theta}=90^{\circ}$ conformer were ${\mu}=3.185D\;&\;E_t=-162.6479(au)$ and also that of the ${\theta}=0^{\circ}$ conformer were ${\mu}=5.596D\;&\;E_t=-162.4013(au)$, respectively. Therefore, the values of ${\mu}\;&\;E_t$ of the ${\theta}=90^{\circ}$ conformer were much smaller than that of the ${\theta}=0^{\circ}$ conformer. The form with angle of rotation ${\theta}=90^{\circ}$ of phenyl ring was shown to be most stable and this was interpreted in terms of electrostatic and steric effect. 0,0-diethylphenylphosphate derivatives are predicted to increase both charge and orbital controlled $SN_2$ reactivity of the electron withdrawing substituent reduces the HOMO & LUMO energy, while the electron withdrawing substituent due to increase in positive charge of phosphorus atom of phosphate molecule.

• East Asian mathematical journal
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• v.24 no.4
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• pp.329-338
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• 2008

The aim of this paper is to introduce a new generalization of fuzzy faintly continuous functions called fuzzy faintly pre-continuous functions and also we have introduced and studied weakly fuzzy pre-continuous functions. Several characterizations of fuzzy faintly pre-continuous functions are given and some interesting properties of the above functions are discussed.

• Proceedings of the KAIS Fall Conference
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• 2004.06a
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• pp.321-323
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• 2004

자연의 세계에서 나뭇잎, 돌기물, 구름, 해안선, 곤충의 모습 등에 내재하고 있는 아름다움은 흔히 균형성, 대칭성, 다양성 등으로부터 비롯된다. 자연 현상은 복소수를 활용하여 극좌표 표현으로 묘사되는 경우가 많다. 본 논문에서는 1989년 Temple H. Fay가 Amer. Math. Monthly 96(5)호에서 발표한 나비곡선 $r=e^{cos{\theta}}-2cos4{\theta}+sin^5(\frac{\theta}{12})$의 기하학적 성질을 분석하고, 수학전문 소프트웨어인 매스매티카를 활용하여 나비곡선의 작도하고자 한다.

• Journal of applied mathematics & informatics
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• v.7 no.3
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• pp.875-886
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• 2000

Let G denote either of the groups $GL_2(q)$ or $SL_2(q)$. Then ${\theta}$:G -> G given by ${\theta}(A)$ = ${(A^t)}^{-l}$, where $A^t$ denotes the transpose of the matrix A, is an automorphism of G. Therefore we may form the group G.$<{\theta}>$ which is the split extension of the group G by the cyclic group $<{\theta}>$ of order 2. Our aim in this paper is to find the complex irreducible character table of G.$<{\theta}>$.