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HYERS-ULAM-RASSIAS STABILITY OF THE BANACH SPACE VALUED LINEAR DIFFERENTIAL EQUATIONS y′ = λy
Miura, Takeshi Miura,Jung, Soon-Mo,Takahasi, Sin-Ei Korean Mathematical Society 2004 대한수학회지 Vol.41 No.6
The aim of this paper is to prove the stability in the sense of Hyers-Ulam- Rassias of the Banach space valued differentialequation y' = λy, where λ is a complex constant. That is, suppose f is a Banach space valued strongly differentiable function on an open interval. If f is an approximate solution of the equation y' = λy, then there exists an exact solution of the equation near to f.
Takeshi Miura,Soon-Mo Jung,Sin-Ei Takahasi 대한수학회 2004 대한수학회지 Vol.41 No.6
The aim of this paper is to prove the stability in the sense of Hyers-Ulam-Rassias of the Banach space valued differential equation y = λy, where λ is a complex constant. That is, suppose f is a Banach space valued strongly differentiable function on an open interval. If f is an approximate solution of the equation y = λy, then there exists an exact solution of the equation near to f.
A perturbation of ring derivations on Banach algebras
Miura, Takeshi,Hirasawa, Go,Takahasi, Sin-Ei Elsevier 2006 Journal of mathematical analysis and applications Vol.319 No.2
<P><B>Abstract</B></P><P>Suppose <I>A</I> is a Banach algebra and suppose f:A→A is an approximate ring derivation in the sense of Hyers–Ulam–Rassias. This stability phenomenon was introduced for the first time in the subject of functional equations by Th.M. Rassias [Th.M. Rassias, On the stability of the linear mapping in Banach spaces, Proc. Amer. Math. Soc. 72 (1978) 297–300]. If <I>A</I> has an approximate identity, or if <I>A</I> is semisimple and commutative, then we prove that <I>f</I> is an exact ring derivation.</P>
The Effect of L-Ornithine on the Phosphorylation of mTORC1 Downstream Targets in Rat Liver
Takeshi Kokubo,Shyuichi Maeda,Kyoko Tazumi,Hajime Nozawa,Yutaka Miura,Takayoshi Kirisako 한국식품영양과학회 2015 Preventive Nutrition and Food Science Vol.20 No.4
A non-protein amino acid, L-ornithine (Orn), has been shown to stimulate the urea cycle and tissue protein synthesis in the liver. The purpose of the current study was to assess whether Orn affects the mammalian target of rapamycin (mTOR) complex 1 (mTORC1) pathway, which is involved in protein synthesis. Primary cultured cells isolated from Wistar rat liver were incubated in an amino acid-free medium, followed by addition of Orn for 3 h. The cell lysate was subjected to immunoblotting to evaluate the phosphorylation of downstream targets of mTORC1, including p70S6K, S6, and 4EBP1. To assess the involvement of mTORC1 for the effect of Orn, the cells were pretreated with the mTOR inhibitor rapamycin before the addition of Orn and the cell lysate was subjected to immunoblotting. We next examined whether the effects of Orn were exerted in vivo. Orn was orally administered to 18 h food-deprived rats, the blood and the livers were collected at 1 and 3 h after administration for immunoblotting. Orn treatment for primary cultured cells for 3 h enhanced the phosphorylation of p70S6K, S6, and 4EBP1. In addition, rapamycin blocked the effects of Orn completely (p70S6K and S6) or partially (4EBP1). The oral administration of Orn to the rat also augmented the phosphorylation of mTORC1 downstream targets notably in S6 at 1 h. Our findings demonstrate that Orn has the potential to induce the phosphorylation of downstream targets of mTORC1 in the rat liver. This may be mediated by the augmentation of mTORC1 activity.
The Effect of L-Ornithine on the Phosphorylation of mTORC1 Downstream Targets in Rat Liver
Kokubo, Takeshi,Maeda, Shyuichi,Tazumi, Kyoko,Nozawa, Hajime,Miura, Yutaka,Kirisako, Takayoshi The Korean Society of Food Science and Nutrition 2015 Preventive Nutrition and Food Science Vol.20 No.4
A non-protein amino acid, L-ornithine (Orn), has been shown to stimulate the urea cycle and tissue protein synthesis in the liver. The purpose of the current study was to assess whether Orn affects the mammalian target of rapamycin (mTOR) complex 1 (mTORC1) pathway, which is involved in protein synthesis. Primary cultured cells isolated from Wistar rat liver were incubated in an amino acid-free medium, followed by addition of Orn for 3 h. The cell lysate was subjected to immunoblotting to evaluate the phosphorylation of downstream targets of mTORC1, including p70S6K, S6, and 4EBP1. To assess the involvement of mTORC1 for the effect of Orn, the cells were pretreated with the mTOR inhibitor rapamycin before the addition of Orn and the cell lysate was subjected to immunoblotting. We next examined whether the effects of Orn were exerted in vivo. Orn was orally administered to 18 h food-deprived rats, the blood and the livers were collected at 1 and 3 h after administration for immunoblotting. Orn treatment for primary cultured cells for 3 h enhanced the phosphorylation of p70S6K, S6, and 4EBP1. In addition, rapamycin blocked the effects of Orn completely (p70S6K and S6) or partially (4EBP1). The oral administration of Orn to the rat also augmented the phosphorylation of mTORC1 downstream targets notably in S6 at 1 h. Our findings demonstrate that Orn has the potential to induce the phosphorylation of downstream targets of mTORC1 in the rat liver. This may be mediated by the augmentation of mTORC1 activity.
Pressure Effect on the Phase Transition Temperatures of Ni2Mn1−xCuxGa
Tomoya Miura,Yoshiya Adachi,Keita Endo,Ryosuke Kainuma,Takeshi Kanomata 한국물리학회 2013 THE JOURNAL OF THE KOREAN PHYSICAL SOCIETY Vol.62 No.12
The martensitic transition temperature TM and the Curie temperature TC of the ferromagneticalloys Ni2Mn1−xCuxGa (0 ≤ x ≤ 0.40) were measured under pressure. We estimated the pressurederivatives dTM/dp and dTC/dp from the results. The values of dTM/dp and dTC/dp for Ni2MnGa(x = 0) were -4.5 K/GPa and +3.9 K/GPa, respectively. The values of dTM/dp increased fromnegative to positive with increasing x in Ni2Mn1−xCuxGa. The values of dTC/dp approached zerowith increasing x.
Hyers-Ulam stability of a closed operator in a Hilbert space
Go Hirasawa,Takeshi Miura 대한수학회 2006 대한수학회보 Vol.43 No.1
sufficient conditions in order that a closed operator in a Hilbertspace into another have the Hyers-Ulam stability. Moreover, weprove the existence of the stability constant for a closedoperator. We also determine the stability constant in terms of the lower bound.
Essential norms and stability constants of weighted composition
Hiroyuki Takagi,Takeshi Miura,Sin-Ei Takahasi 대한수학회 2003 대한수학회보 Vol.40 No.4
For a weighted composition operator uC_{varphi} on C(X), wedetermine its essential norm and the constant for its Hyers-Ulamstability, in terms of the set varphi ( { x in X : |u(x)| geqr } ) (r > 0).