• East Asian mathematical journal
• /
• 제4권
• /
• pp.1-13
• /
• 1988

We consider some properties of the completely bounded representations of C*-algebras. We discuss the relation between the k-similarity and the property $D_k$ and get the result every k-similar C*-algebra has property $D_k$. Moreover we determine the similarity problem for the algebra C$\bigoplus$C precisely and constructively.

• Nonlinear Functional Analysis and Applications
• /
• 제27권2호
• /
• pp.271-287
• /
• 2022

In this article, we shall prove a common fixed point theorem for two weakly compatible self-maps 𝒫 and 𝔔 on a dislocated metric space (M, d^*) satisfying the following ξ-weakly expansive condition: d^*(𝒫c, 𝒫d) ≥ d^* (𝔔c, 𝔔d) + ξ(∧(𝔔c, 𝔔d)), ∀ c, d ∈ M, where $${\wedge}(Qc,\;Qd)=max\{d^*(Qc,\;Qd),\;d^*(Qc,\;\mathcal{P}c),\;d^*(Qd,\;\mathcal{P}d),\;\frac{d^*(Qc,\;\mathcal{P}c){\cdot}d^*(Qd,\;\mathcal{P}d)}{1+d^*(Qc,\;Qd)},\;\frac{d^*(Qc,\;\mathcal{P}c){\cdot}d^*(Qd,\;\mathcal{P}d)}{1+d^*(\mathcal{P}c,\;\mathcal{P}d)}\}$$. Also, we have proved common fixed point theorems for the above mentioned weakly compatible self-maps along with E.A. property and (CLR) property. An illustrative example is also provided to support our results.

• Korean Journal of Mathematics
• /
• 제20권3호
• /
• pp.353-360
• /
• 2012

In this paper we introduce the property (C), which is a cone metric extension of the usual metric property (E,A) and consider fixed point theorems for generalized contractive mappings under suitable conditions in cone metric spaces without normal cones.

• 대한수학회논문집
• /
• 제25권2호
• /
• pp.257-262
• /
• 2010

Let f be a $C^2$-diffeomorphism on a closed surface which satisfies the Axiom A. Then f is in the $C^2$-interior of the set of all diffeomorphisms having the inverse shadowing property with respect to the class of the continuous methods if and only if f satisfies the strong transversality condition.

• Korean Journal of Mathematics
• /
• 제14권2호
• /
• pp.169-183
• /
• 2006

In this paper, we define and study the C-integral and the strong C-integral of functions mapping an interval [a,b] into a Banach space X. We prove that the C-integral and the strong C-integral are equivalent if and only if the Banach space is finite dimensional, We also consider the property of primitives corresponding to Banach-valued functions with respect to the C-integral and the strong C-integral.

• 대한수학회지
• /
• 제57권4호
• /
• pp.893-913
• /
• 2020

Let 𝓢 be the collection of the operator matrices $\(\array{A&C\\Z&B}\)$ where the range of C is closed. In this paper, we study the properties of operator matrices in the class 𝓢. We first explore various local spectral relations, that is, the property (β), decomposable, and the property (C) between the operator matrices in the class 𝓢 and their component operators. Moreover, we investigate Weyl and Browder type spectra of operator matrices in the class 𝓢, and as some applications, we provide the conditions for such operator matrices to satisfy a-Weyl's theorem and a-Browder's theorem, respectively.

• 한국식품영양학회지
• /
• 제27권1호
• /
• pp.112-119
• /
• 2014

Ohmic heating uses electric resistance heat which occurs equally and rapidly inside food when the electrical current is transmitted into. Prior to the study, we have researched the potato starch's thermal property changes during ohmic heating. Comparing with conventional heating, the gelatinization temperature and the range of potato starch treated by ohmic heating are increased and narrowed respectively. Herein, we have studied thermal property changes of wheat, corn, potato and sweet potato starch by ohmic heating as well as conventional heating. And then we measure the water holding capacity of starches. Annealing of starch is a heat treatment method heated at 3~4% below the gelatinization point. This treatment changes the starch's thermal property. In the DSC analysis of this study, the $T_o$, $T_p$, $T_c$ of all starch levels have increased, and the $T_c$-$T_o$ narrowed. In the ohmic heating, the treatment sample is extensively changed but not with the conventional heating. From the ohmic treatment, increases from gelatinization temperature are potato ($8.3^{\circ}C$) > wheat ($5.3^{\circ}C$) > corn ($4.9^{\circ}C$) > sweet potato ($4.5^{\circ}C$), and gelatinization ranges are potato ($7.9^{\circ}C$), wheat ($7.5^{\circ}C$), corn ($6.1^{\circ}C$) and sweet potato ($6.8^{\circ}C$). In the case of conventional treatment, water holding capacity is not changed with increasing temperature but the ohmic heating is increased. Water holding capacity is related to the degree of gelatinization for starch. This result show that when treated with below gelatinization temperature, the starches are partly gelatined by ohmic treatment. When viewing the results of the above, ohmic treatment is enhanced by heating and generating electric currents to the starch structure.

• 대한수학회지
• /
• 제42권4호
• /
• pp.773-793
• /
• 2005

We consider interesting conditions, one of which will be called the disjoint $(A^2,\;D^2)-pair$ property, on genus $g{\geq}2$ Heegaard splittings of compact orient able 3-manifolds. Here a Heegaard splitting $(C_1,\;C_2;\;F)$ admits the disjoint $(A^2,\;D^2)-pair$ property if there are an essential annulus Ai normally embedded in $C_i$ and an essential disk $D_j\;in\;C_j((i,\;j)=(1,\;2)\;or\;(2,\;1))$ such that ${\partial}A_i$ is disjoint from ${\partial}D_j$. It is proved that all genus $g{\geq}2$ Heegaard splittings of toroidal manifolds and Seifert fibered spaces admit the disjoint $(A^2,\;D^2)-pair$ property.

• Journal of applied mathematics & informatics
• /
• 제39권3_4호
• /
• pp.487-496
• /
• 2021

In this paper we show that if A ∈ L(X) and B ∈ L(Y), X and Y complex Banach spaces, then A ⊕ B ∈ L(X ⊕ Y) is subscalar if and only if both A and B are subscalar. We also prove that if A, Q ∈ L(X) satisfies AQ = QA and Q^p = 0 for some nonnegative integer p, then A has property (C) (resp. property (𝛽)) if and only if so does A + Q (resp. property (𝛽)). Finally, we show that A ∈ L(X, Y) and B, C ∈ L(Y, X) satisfying operator equation ABA = ACA and BA ∈ L(X) is subscalar with property (𝛿) then both Lat(BA) and Lat(AC) are non-trivial.

• 한국정보디스플레이학회:학술대회논문집
• /
• 한국정보디스플레이학회 2002년도 International Meeting on Information Display
• /
• pp.1053-1055
• /
• 2002

Recently CRT is getting large-sized, Flatness and High Fine Pitched in the meantime the raw material for shadow mask is in rapid progress of thinness, Low Thermal Expansion and high strength.Until now we have used AK(Aluminum Killed) & Invar(Fe-Ni alloy) materials for main raw material of shadow mask component. However recently Nb and Co addition and Nb+Co addition, which has advantage of Low Thermal Expansion and High Strength. has been developed as well as applying in mass production as CRT's trend has become more flat and fine pitch. Among of them, Co addition has been mass production as forming type (Flat CRT) with the beneficial effect of low thermal expansion & high strength for the first time. Since then Nb+Co addition has been used in mass production by the request of much higher strength of shadow mask component. In case of Nb addition, It's thermal expansion coefficient is a little lower than normal Invar and a little higher than Co addition, meanwhile Its Mechanical property is almost similar to Co Addition. The used samples of this experiment are 36%Ni + Fe, 32%Ni + 5%Co + Fe, 32%Ni + 5%Co + 0.3%Nb + Fe, 32%Ni + 0.3%Nb + Fe with heat treatment temperature of 600$^{\circ}C$, 650$^{\circ}C$, 700$^{\circ}C$, 750$^{\circ}C$, 800$^{\circ}C$, 850$^{\circ}C$, 900$^{\circ}C$ respectively under the condition of 15min holding time. After heat treatment, we have observed the change of mechanical property with addition of small elements through mechanical property investigation and metal structure observation as well as transition of thermal expansion coefficient by measuring of thermal expansion coefficient at 850$^{\circ}C$. In conclusion, 5%Co addition indicates that its thermal expansion coefficient is very similar under the condition of at 850$^{\circ}C$ for 15min 's heat treatment. From the experimental result it is suggested that Co addition is mostly suitable for Doming property and Nb addition is mostly suitable for Drop property.