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SPATIAL NUMERICAL RANGES OF ELEMENTS OF $C^*$-ALGEBRAS
Takahasi, Sin-Ei Korean Mathematical Society 2000 대한수학회보 Vol.37 No.3
When A is a subalgebra of a $C^*$-algebra, the spatial numerical range of element of A can be described in terms of positive linear functionals on the $C^*$-algebra.
New Science and Unification Thought
Takahasi, Iwaro 선문대학교 통일사상연구원 1997 통일사상 연구논총 Vol.2 No.-
In the modern science beginning with Newton Dynamics, the basic recognition of reality of bodies is a particle. Every body can be divided into final particles, called atoms; that is, every body is composed by several atoms which can not be further divided. The fluid matter such as air and water is also composed moving particles. This congnition is Democritus atominism, and conventional common sense of human is also based on this recognition of reality.
ON THE HYERS-ULAM STABILITY OF THE BANACH SPACE-VALUED DIFFERENTIAL EQUATION y'=λy
Takahasi, Sin-Ei,Miura, Takeshi,Miyajima, Shizuo Korean Mathematical Society 2002 대한수학회보 Vol.39 No.2
Let I be an open interval and X a complex Banach space. Let$\varepsilon\geq0\;and\;\lambda$ a non-zero complex number with Re $\lambda\neq0$. If $\varphi$ is a strongly differentiable map from I to X with $\parallel\varphi^'(t)-\lambda\varphi(t)\parallel\leq\varepsilon\;for\;all\;t\in\;I$, then we show that the distance between $\varphi$ and the set of all solutions to the differential equation y'=$\lambda$y is at most $\varepsilon/$\mid$Re\lambda$\mid$$.
On the Hyers-Ulam stability of the Banach space-valued differential equation y' = lambda y
Sin-Ei Takahasi,Takeshi Miura,Shizuo Miyajima 대한수학회 2002 대한수학회보 Vol.39 No.2
Let I be an open interval and X a complex Banach space.Let varepsilon geq 0 and lambda a non-zero complexnumber with text{rm Re},lambda neq 0. If varphi is astrongly differentiable map from I to X with Vertvarphi'(t)-lambda varphi(t) Vert leq varepsilon for allt in I, then we show that the distance between varphi and the set ofall solutions to the differential equation y' = lambda y is at mostvarepsilon/ vert text{rm Re},lambda vert.
Komoto Tatiana Takahasi,Lee Jaehak,Lertpatipanpong Pattawika,Ryu Junsun,Marins Mozart,Fachin Ana Lúcia,Baek Seung Joon 한국독성학회 2021 Toxicological Research Vol.37 No.4
Despite intensive research efforts in recent decades, cancer remains a leading cause of death worldwide. The chalcone family is a promising group of phytochemicals for therapeutic use against cancer development. Naturally-occurring chalcones, as well as synthetic chalcone analogues, have shown many beneficial biological properties, including anti-inflammatory, antioxidant, and anti-cancer activities. In this report, trans-chalcone (TChal) was found to increase cell death in breast cancer cells, assessed using high content screening. Subsequently, using antibody array analysis, TChal was found to increase heme oxygenase-1 (HO-1) expression in TChal-treated breast cancer cells. Blocking of HO-1 by siRNA in breast cancer cells diminished the effect of TChal on cell growth inhibition. TChal-fed mice also showed less tumor growth compared to vehicle-fed mice. Overall, we found that TChal increases HO-1 expression in breast cancer cells, thereby enhancing anti-tumorigenesis. Our results suggest that HO-1 expression could be a potential new target of TChal for anti-tumorigenesis in breast cancer.