• Title/Summary/Keyword: ${\alpha}^{\prime}$

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POSITIVE SOLUTIONS FOR A THREE-POINT FRACTIONAL BOUNDARY VALUE PROBLEMS FOR P-LAPLACIAN WITH A PARAMETER

  • YANG, YITAO;ZHANG, YUEJIN
    • Journal of applied mathematics & informatics
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    • v.34 no.3_4
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    • pp.269-284
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    • 2016
  • In this paper, we firstly use Krasnosel'skii fixed point theorem to investigate positive solutions for the following three-point boundary value problems for p-Laplacian with a parameter $({\phi}_P(D^{\alpha}_{0}+u(t)))^{\prime}+{\lambda}f(t, u(t))=0$, 0$D^{\alpha}_{0}+u(0)=u(0)=u{\prime}{\prime}(0)=0$, $u^{\prime}(1)={\gamma}u^{\prime}(\eta)$ where ϕp(s) = |s|p−2s, p > 1, $D^{\alpha}_{0^+}$ is the Caputo's derivative, α ∈ (2, 3], η, γ ∈ (0, 1), λ > 0 is a parameter. Then we use Leggett-Williams fixed point theorem to study the existence of three positive solutions for the fractional boundary value problem $({\phi}_P(D^{\alpha}_{0}+u(t)))^{\prime}+f(t, u(t))=0$, 0$D^{\alpha}_{0}+u(0)=u(0)=u{\prime}{\prime}(0)=0$, $u^{\prime}(1)={\gamma}u^{\prime}(\eta)$ where ϕp(s) = |s|p−2s, p > 1, $D^{\alpha}_{0^+}$ is the Caputo's derivative, α ∈ (2, 3], η, γ ∈ (0, 1).

Inheritance of 7S α' - subunit Protein in Soybean Seed (콩의 7S α' - subunit 단백질의 유전)

  • Sung, Mi-Kyung;Kim, Kyung-Roc;Park, Jung-Soo;Hwang, Kyo-Jin;Chung, Jong-Il
    • Journal of agriculture & life science
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    • v.43 no.5
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    • pp.39-42
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    • 2009
  • Soybean is an important sources of plant proteins for human and animal nutrition. The use of soybean proteins has been expanded in the food industry due to their excellent nutritional benefits. But, Soybeans contain allergenic proteins that cause allergies to sensitive individuals. ${\beta}$-conglycinin(7S globulin) and glycinin(11S globulin) are the major components of storage protein in soybean. ${\beta}$-conglycinin consists of three subunits, ${\alpha}^{\prime}$, ${\alpha}$, ${\beta}$ and exhibits poorer nutritional and food processing properties than glycinin. There is a great deal of interest in the development of soybean lines with reduced amounts of ${\beta}$-conglycinin. The objective of this study was to determine the inheritance of ${\alpha}^{\prime}$-subunit protein in 7S globulin. F2 population was developed from the cross of "Jinpumkong2ho"(${\alpha}^{\prime}$-subunit presence) and PI506876(${\alpha}^{\prime}$-subunit absence) parent. Total 98 of F2 seeds were obtained and analyzed for the segregation of ${\alpha}^{\prime}$-subunit protein by SDS-PAGE. Among 98 F2 seeds, 70 F2 seeds showed ${\alpha}^{\prime}$-subunit protein and 28 F2 seeds did not show ${\alpha}^{\prime}$-subunit protein. The segregation ratios of 3 : 1 for presence and absence of ${\alpha}^{\prime}$-subunit protein were observed(${\chi}^2=0.667$, P=0.414). These data indicate that presence and absence of ${\alpha}^{\prime}$-subunit protein is controlled by a single major gene and might be useful for strain selection of 7S protein reduced soybean.

ON A CLASS OF QUANTUM ALPHA-CONVEX FUNCTIONS

  • NOOR, KHALIDA INAYAT;BADAR, RIZWAN S.
    • Journal of applied mathematics & informatics
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    • v.36 no.5_6
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    • pp.567-574
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    • 2018
  • Let $f:f(z)=z+{\sum^{{\infty}}_{n=2}}a_nz^n$ be analytic in the open unit disc E. Then f is said to belong to the class $M_{\alpha}$ of alpha-convex functions, if it satisfies the condition ${\Re}\{(1-{{\alpha})}{\frac{zf^{\prime}(z)}{f(z)}}+{{\alpha}}{\frac{(zf^{\prime}(z))^{\prime})}{f^{\prime}(z)}}\}$ > 0, ($z{\in}E$). In this paper, we introduce and study q-analogue of the class $M_{\alpha}$ by using concepts of Quantum Analysis. It is shown that the functions in this new class $M(q,{\alpha})$ are q-starlike. A problem related to q-Bernardi operator is also investigated.

The Effect of Initial α' on Low and High Cycle Fatigue Behavior of STS 304 Stainless Steel (STS 304 강의 저주기 및 고주기 피로에 있어 초기 마르텐사이트의 영향)

  • Lee, Hyun-Seung;Sin, Hyung-Ju;Kim, Song-Hee
    • Journal of Industrial Technology
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    • v.21 no.B
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    • pp.331-339
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    • 2001
  • Zero to tension fatigue tests and strain controlled fatigue tests were carried out to find how initial strain induced martensite, ${\alpha}^{\prime}$ affects low and high cycle fatigue behavior and fatigue crack growth mechanisms. Microscopic study and phase analysis were carried out with TEM, SEM, EDAX, Optical Microscope, Ferriscope, and X-ray diffractometry. The amount of Initial ${\alpha}^{\prime}$ was controlled from 0% to 33% by controlling the temperatures for cold working and heat treatment. Lower contents of initial ${\alpha}^{\prime}$ showed higher fatigue resistance in low cycle fatigue but lower fatigue resistance in high cycle fatigue because it is ascribed to the more transformation of ${\alpha}^{\prime}$ martensite during low cycle fatigue and higher ductility. In high cycle fatigue, fatigue life is attributed to the strength and phase transformation of austenite into ${\alpha}^{\prime}$ during fatigue was negligible. ${\gamma}$ boundary, ${\gamma}/twin$ boundary, and ${\gamma}/{\alpha}^{\prime}$ boundary were found to be the preferred site of fatigue crack initiation.

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ON GENERALIZED (α, β)-DERIVATIONS AND COMMUTATIVITY IN PRIME RINGS

  • Jung, Yong-Soo;Park, Kyoo-Hong
    • Bulletin of the Korean Mathematical Society
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    • v.43 no.1
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    • pp.101-106
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    • 2006
  • Let R be a prime ring and I a nonzero ideal of R. Let $\alpha,\;\nu,\;\tau\;R{\rightarrow}R$ be the endomorphisms and $\beta,\;\mu\;R{\rightarrow}R$ the automorphisms. If R admits a generalized $(\alpha,\;\beta)-derivation$ g associated with a nonzero $(\alpha,\;\beta)-derivation\;\delta$ such that $g([\mu(x),y])\;=\;[\nu/(x),y]\alpha,\;\tau$ for all x, y ${\in}I$, then R is commutative.

Mechanical Properties Variation of Ti-6Al-4V Alloy by Microstructural Control (α+β 타이타늄 합금의 미세조직 제어에 따른 기계적 특성)

  • Hwang, Yu-Jin;Park, Yang-Kyun;Kim, Chang-Lim;Kim, Jin-Yung;Lee, Dong-Geun
    • Journal of the Korean Society for Heat Treatment
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    • v.29 no.5
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    • pp.220-226
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    • 2016
  • The mechanical properties of Ti-6Al-4V can be improved by microstructural control through the heat treatment in ${\alpha}+{\beta}$ region. The heat treatment was carried out with a variety of heat treatment temperatures and holding times to find the optimized heat treatment conditions and it was analyzed by linking the microstructural characteristics and mechanical properties. The part of ${\beta}$ phase with $10{\pm}2wt%$ vanadium was transformed into ${\alpha}^{{\prime}{\prime}}$ martensite phase after quenched, so the hardness and tensile properties were decreased below $900^{\circ}C$. The higher the heat treatment temperature is, the smaller is the vanadium-rich region, which leads to transformation into hcp ${\alpha}^{\prime}$ martensite above $900^{\circ}C$. The hardness and tensile properties were improved due to the hard ${\alpha}^{\prime}$ martensite. As the holding times were longer, the hardness and tensile properties decreased below $900^{\circ}C$ because of the softening effect by the grain growth. When varying the holding times above $900^{\circ}C$, the change of mechanical properties was slight because the softening effect of grain growth and the strengthening effect of ${\alpha}^{\prime}$ phase were counteractive. Therefore, the best conditions of heat treatment, which is in the range of $920{\sim}960^{\circ}C$, 40 min, WQ, can effectively improve the mechanical properties of Ti-6Al-4V.

STRUCTURE OF 3-PRIME NEAR-RINGS SATISFYING SOME IDENTITIES

  • Boua, Abdelkarim
    • Communications of the Korean Mathematical Society
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    • v.34 no.1
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    • pp.17-26
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    • 2019
  • In this paper, we investigate commutativity of 3-prime near-rings ${\mathcal{N}}$ in which (1, ${\alpha}$)-derivations satisfy certain algebraic identities. Some well-known results characterizing commutativity of 3-prime near-rings have been generalized. Furthermore, we give some examples show that the restriction imposed on the hypothesis is not superfluous.

OSCILLATION AND NONOSCILLATION CRITERIA FOR DIFFERENTIAL EQUATIONS OF SECOND ORDER

  • Kim, RakJoong
    • Korean Journal of Mathematics
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    • v.19 no.4
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    • pp.391-402
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    • 2011
  • We give necessary and sufficient conditions such that the homogeneous differential equations of the type: $$(r(t)x^{\prime}(t))^{\prime}+q(t)x^{\prime}(t)+p(t)x(t)=0$$ are nonoscillatory where $r(t)$ > 0 for $t{\in}I=[{\alpha},{\infty})$, ${\alpha}$ > 0. Under the suitable conditions we show that the above equation is nonoscillatory if and only if for ${\gamma}$ > 0, $$(r(t)x^{\prime}(t))^{\prime}+q(t)x^{\prime}(t)+p(t)x(t-{\gamma})=0$$ is nonoscillatory. We obtain several comparison theorems.

COVERING AND INTERSECTION CONDITIONS FOR PRIME IDEALS

  • Chang, Gyu Whan;Hwang, Chul Ju
    • Korean Journal of Mathematics
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    • v.17 no.1
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    • pp.15-23
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    • 2009
  • Let D be an integral domain, P be a nonzero prime ideal of D, $\{P_{\alpha}{\mid}{\alpha}{\in}{\mathcal{A}}\}$ be a nonempty set of prime ideals of D, and $\{I_{\beta}{\mid}{\beta}{\in}{\mathcal{B}}\}$ be a nonempty family of ideals of D with ${\cap}_{{\beta}{\in}{\mathcal{B}}}I_{\beta}{\neq}(0)$. Consider the following conditions: (i) If $P{\subseteq}{\cup}_{{\alpha}{\in}{\mathcal{A}}}P_{\alpha}$, then $P=P_{\alpha}$ for some ${\alpha}{\in}{\mathcal{A}}$; (ii) If ${\cap}_{{\beta}{\in}{\mathcal{B}}}I_{\beta}{\subseteq}P$, then $I_{\beta}{\subseteq}P$ for some ${\beta}{\in}{\mathcal{B}}$. In this paper, we prove that D satisfies $(i){\Leftrightarrow}D$ is a generalized weakly factorial domain of ${\dim}(D)=1{\Rightarrow}D$ satisfies $(ii){\Leftrightarrow}D$ is a weakly Krull domain of dim(D) = 1. We also study the t-operation analogs of (i) and (ii).

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PRIME IDEALS IN LIPSCHITZ ALGEBRAS OF FINITE DIFFERENTIABLE FUNCTIONS

  • EBADIAN, ALI
    • Honam Mathematical Journal
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    • v.22 no.1
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    • pp.21-30
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    • 2000
  • Lipschitz Algebras Lip(X, ${\alpha}$) and lip(X, ${\alpha}$) were first studied by D. R. Sherbert in 1964. B. Pavlovic in 1995 shown that in these algebras, the prime ideals containing a given prime ideal form a chain. In this paper, we show that the above property holds in $Lip^n(X,\;{\alpha})$ and $lip^n(X,\;{\alpha})$, the Lipschitz algebras of finite differentiable functions on a perfect compact place set X.

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