• Bulletin of the Korean Mathematical Society
• /
• v.50 no.6
• /
• pp.1981-1988
• /
• 2013

We say a positive integer n satisfies the Lehmer property if ${\phi}(n)$ divides n - 1, where ${\phi}(n)$ is the Euler's totient function. Clearly, every prime satisfies the Lehmer property. No composite integer satisfying the Lehmer property is known. In this article, we show that every composite integer of the form $D_{p,n}=np^n+1$, for a prime p and a positive integer n, or of the form ${\alpha}2^{\beta}+1$ for ${\alpha}{\leq}{\beta}$ does not satisfy the Lehmer property.

• The Pure and Applied Mathematics
• /
• v.5 no.1
• /
• pp.23-32
• /
• 1998

In the present paper the author studies the decomposition property ($\delta$) of the bounded linear operators.

• Journal of applied mathematics & informatics
• /
• v.24 no.1_2
• /
• pp.437-448
• /
• 2007

Suppose K is a nonempty closed convex nonexpansive retract of a real uniformly convex Banach space E with P as a nonexpansive retraction. Let $T_1,\;T_2\;and\;T_3\;:\;K{\rightarrow}E$ be nonexpansive mappings with nonempty common fixed points set. Let $\{\alpha_n\},\;\{\beta_n\},\;\{\gamma_n\},\;\{\alpha'_n\},\;\{\beta'_n\},\;\{\gamma'_n\},\;\{\alpha'_n\},\;\{\beta'_n\}\;and\;\{\gamma'_n\}$ be real sequences in [0, 1] such that ${\alpha}_n+{\beta}_n+{\gamma}_n={\alpha}'_n+{\beta'_n+\gamma}'_n={\alpha}'_n+{\beta}'_n+{\gamma}'_n=1$, starting from arbitrary $x_1{\in}K$, define the sequence $\{x_n\}$ by $$\{zn=P({\alpha}'_nT_1x_n+{\beta}'_nx_n+{\gamma}'_nw_n)\;yn=P({\alpha}'_nT_2z_n+{\beta}'_nx_n+{\gamma}'_nv_n)\;x_{n+1}=P({\alpha}_nT_3y_n+{\beta}_nx_n+{\gamma}_nu_n)$$ with the restrictions $\sum^\infty_{n=1}{\gamma}_n<\infty,\;\sum^\infty_{n=1}{\gamma}'_n<\infty,\; \sum^\infty_{n=1}{\gamma}'_n<\infty$. (i) If the dual $E^*$ of E has the Kadec-Klee property, then weak convergence of a $\{x_n\}$ to some $x^*{\in}F(T_1){\cap}{F}(T_2){\cap}(T_3)$ is proved; (ii) If $T_1,\;T_2\;and\;T_3$ satisfy condition(A'), then strong convergence of $\{x_n\}$ to some $x^*{\in}F(T_1){\cap}{F}(T_2){\cap}(T_3)$ is obtained.

• Journal of the Chungcheong Mathematical Society
• /
• v.24 no.1
• /
• pp.19-34
• /
• 2011

A bounded linear operator T on a complex Banach space X is said to have property (I) provided that T has Bishop's property (${\beta}$) and there exists an integer p > 0 such that for a closed subset F of ${\mathbb{C}}$ ${X_T}(F)={E_T}(F)=\bigcap_{{\lambda}{\in}{\mathbb{C}}{\backslash}F}(T-{\lambda})^PX$ for all closed sets $F{\subseteq}{\mathbb{C}}$, where $X_T$(F) denote the analytic spectral subspace and $E_T$(F) denote the algebraic spectral subspace of T. Easy examples are provided by normal operators and hyponormal operators in Hilbert spaces, and more generally, generalized scalar operators and subscalar operators in Banach spaces. In this paper, we prove that if T has property (I), then the quasi-nilpotent part $H_0$(T) of T is given by $$KerT^P=\{x{\in}X:r_T(x)=0\}={\bigcap_{{\lambda}{\neq}0}(T-{\lambda})^PX$$ for all sufficiently large integers p, where ${r_T(x)}=lim\;sup_{n{\rightarrow}{\infty}}{\parallel}T^nx{\parallel}^{\frac{1}{n}}$. We also prove that if T has property (I) and the spectrum ${\sigma}$(T) is finite, then T is algebraic. Finally, we prove that if $T{\in}L$(X) has property (I) and has decomposition property (${\delta}$) then T has a non-trivial invariant closed linear subspace.

• Bulletin of the Korean Mathematical Society
• /
• v.42 no.2
• /
• pp.359-367
• /
• 2005

Let A be a Banach algebra, we say that A has the strongly double limit property (SDLP) if for each bounded net $(a_\alpha)$ in A and each bounded net $(a^{\ast}\;_\beta)\;in\;A^{\ast},\;lim_\alpha\;lim_\beta=lim_\beta\;lim_\alpha$ whenever both iterated limits exist. In this paper among other results we show that if A has the SDLP and $A^{\ast\ast}$ is (n - 2)-weakly amenable, then A is n-weakly amenable. In particular, it is shown that if $A^{\ast\ast}$ is weakly amenable and A has the SDLP, then A is weakly amenable.

• Journal of Korean society of Dental Hygiene
• /
• v.16 no.6
• /
• pp.1023-1031
• /
• 2016

Objectives: The purpose of the study was to investigate the related factors of learning ethics of dental hygiene students. Methods: A self-reported questionnaire was completed by 278 dental hygiene students in G metropolitan city from June 9 to July 29, 2016. The data were analyzed by frequency analysis, percentage and stepwise multiple regression analysis using SPSS 12.0 program. The questionnaire comprised learning ethics (10 items), condition of learning ethics (10 items), reason of plagiarism (8 items), intellectual property right consciousness (8 items), internet ethics consciousness (20 items), individual ethics consciousness (2 items). Results: Condition of learning ethics was higher in mosaic plagiarism (33.9%). The main reason of plagiarism was higher in lack of time (52.7%). Related factors with the intellectual property right consciousness was use of reference (${\beta}=0.424$), internet expectancy (${\beta}=0.228$) and parental rearing attitude (${\beta}=0.229$) (Adjusted $R^2=0.336$). Related factors with the internet ethics consciousness were parental rearing attitude (${\beta}=-0.241$), academic achievements (${\beta}=0.420$), internet expectancy (${\beta}=-0.368$) and grade (${\beta}=-0.154$)(Adjusted $R^2=0.390$). Related factor with the individual ethics consciousness was academic achievements (${\beta}=0.445$) (Adjusted $R^2=0.192$). Conclusions: To increase the learning ethics and preventing plagiarism, it is necessary to have essential understanding and practice to make the liberal arts education and extracurricular program of institutions.

• Fisheries and Aquatic Sciences
• /
• v.7 no.1
• /
• pp.34-38
• /
• 2004

The heterotrophic production method for Tetraselmis suecica, a suggested alternative to photoautotrophic one in the economic sense, was studied in terms of cell growth and sterolic property. The alga in the 10 mM organic carbon (glucose) manifested cell growth. However, the alga produced by the heterotrophic method showed a unique property of sterol determined with an aid of GC and GC-MS. The photoautotrophic control T. suecica contained 6 detectable sterol species: $cholesta-5,\;22-dien-3\beta-o1$, $ergost-5-en-3\beta-o1$, cholest-5-en-3\beta-o1$, $24-methyl-cholesta-5,\;22-dien-3\beta-o1$, $24-methylcholesta-5,\;24-dien-3\beta-o1$, $24-ethylchlolesta-5,\;24-dien-3\beta­o1$, $24-methylcholesta-5-en-3\beta-o1$, and $24-ethylchlolesta-5en-3\beta-o1$. We discuss the sterolic properties of the alga along the heterotrophic progress, particularly focusing on the availability of the method in the aquaculture of bivalves which normally need sterols as a dietary source.

• Journal of the Korean Mathematical Society
• /
• v.41 no.1
• /
• pp.39-50
• /
• 2004

In [25] Taskinen shows that if $\{E_n\}_n\;and\;\{F_n\}_n$ are two sequences of Frechet spaces such that ($E_m,\;F_n$) has the BB-property for all m and n then (${\Pi}_m\;E_m,\;{\Pi}_n\;F_n$) also has the ΒΒ-property. Here we investigate when this result extends to (i) arbitrary products of Frechet spaces, (ii) countable products of DFN spaces, (iii) countable direct sums of Frechet nuclear spaces. We also look at topologies properties of ($H(U),\;\tau$) for U balanced open in a product of Frechet spaces and $\tau\;=\;{\tau}_o,\;{\tau}_{\omega}\;or\;{\tau}_{\delta}$.

• Bulletin of the Korean Mathematical Society
• /
• v.43 no.4
• /
• pp.813-820
• /
• 2006

We consider a MAR model with ARCH type conditional heteroscedasticity. MAR-ARCH model can be derived as a smoothed version of the double threshold AR-ARCH model by adding a random error to the threshold parameters. Easy to check sufficient conditions for strict stationarity, ${\beta}-mixing$ property and existence of moments of the model are given via Markovian representation technique.

• Journal of applied mathematics & informatics
• /
• v.40 no.3_4
• /
• pp.785-794
• /
• 2022

In this paper we show that if A ∈ L(X) and R ∈ L(X) is a quasinilpotent operator commuting with A then X_A(F) = X_A+R(F) for all subset F ⊆ ℂ and 𝜎_loc(A) = 𝜎_loc(A + R). Moreover, we show that A and A + R share many common local spectral properties such as SVEP, property (C), property (𝛿), property (𝛽) and decomposability. Finally, we show that quasisimility preserves local spectrum.