• Journal of Korean Ophthalmic Optics Society
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• v.5 no.1
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• pp.43-48
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• 2000

It was to adjust the luminance of light by the rotation angle of the polarizes and analyzer. The luminance value Lmax, Lmin of Contrast Sensitivity could be obtained from the rotation angle ${\theta}_m$ of the average luminance($L_m$), the rotation angle(${\theta}_{max}$, ${\theta}_{min}$) of the maximum and the minimum's amplitude. $$L_{max}=I(0)e^{-2at}{\cdot}cos^2{\theta}_m(1+C_s^{-1})$$ $$L_{min}=I(0)e^{-2at}{\cdot}cos^2{\theta}_m(1-C_s^{-1})$$ We obtained the rotation angle(${\theta}_{max}$, ${\theta}_{min}$) of the polarizes and analyzer from the rotation angle ${\theta}_m$ of the average luminance($L_m$) and the Contrast Sensitivity($C_s$). $${\theta}_{max}=cos^{-1}[cos{\theta}_m{\cdot}(1+C_s^{-1})^{1/2}]$$ $${\theta}_{min}=cos^{-1}[cos{\theta}_m{\cdot}(1-C_s^{-1})^{1/2}]$$.

• Communications of the Korean Mathematical Society
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• v.31 no.2
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• pp.229-235
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• 2016

In this paper we study the regularity of inside (or outside) (${\theta},{\phi}$)-derivations in BCI-algebras X and prove that let $d_{({\theta},{\phi})}:X{\rightarrow}X$ be an inside (${\theta},{\phi}$)-derivation of X. If there exists a ${\alpha}{\in}X$ such that $d_{({\theta},{\phi})}(x){\ast}{\theta}(a)=0$, then $d_{({\theta},{\phi})}$ is regular for all $x{\in}X$. It is also shown that if X is a BCK-algebra, then every inside (or outside) (${\theta},{\phi}$)-derivation of X is regular. Furthermore the concepts of ${\theta}$-ideal, ${\phi}$-ideal and invariant inside (or outside) (${\theta},{\phi}$)-derivations of X are introduced and their related properties are investigated. Finally we obtain the following result: If $d_{({\theta},{\phi})}:X{\rightarrow}X$ is an outside (${\theta},{\phi}$)-derivation of X, then $d_{({\theta},{\phi})}$ is regular if and only if every ${\theta}$-ideal of X is $d_{({\theta},{\phi})}$-invariant.

• Bulletin of the Korean Mathematical Society
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• v.29 no.2
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• pp.245-256
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• 1992

In this article, we study the behavior of half integral weight thetaseries under theta operators. Theta operators are very important in the study of theta-series in connection with Hecke operators. Andrianov[A1] proved that the space of integral weight theta-series is invariant under the action of theta operators. We prove that his statement can be extened for half integral weight theta-series with a slight modification. By using this result one can prove that the space of theta-series is invariant under the action of Hecke operators as Andrianov did for intrgral weight theta-series [A1].

• Kyungpook Mathematical Journal
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• v.59 no.3
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• pp.403-414
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• 2019

Theta functions are the sections of line bundles on a complex torus. Noncommutative versions of theta functions have appeared as theta vectors and quantum theta operators. In this paper we describe a super version of theta vectors and quantum theta operators. This is the natural unification of Manin's result on bosonic operators, and the author's previous result on fermionic operators.

• Journal of the Chungcheong Mathematical Society
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• v.3 no.1
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• pp.97-101
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• 1990

For testing a hypothesis $H:{\theta}={\theta}_1$, vs $A:{\theta}={\theta}_2$ (${\theta}_1$ < ${\theta}_2$, we obtain a truncated sequential bayes procedure which minimizes the average sample size between ${\theta}_1$ and ${\theta}_2$.

• Kyungpook Mathematical Journal
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• v.56 no.1
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• pp.249-256
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• 2016

There are many concepts around classical theta functions, theta vectors and quantum theta functions. Manin clarified the relation among these concepts with the symmetry of functional equations. We extend his results to the super torus.

• The Journal of the Korean Society for Microbiology
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• v.11 no.1
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• pp.13-18
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• 1976

The rabbit anti-rat brain associated ${\theta}(RBA{\theta})$ serum wich was obtained by immunization of rabbit with DA rat brain tested against rat lymphoid tissues for cytotoxicity, indirect immunofluorescent staining and ability to inhibit a graft-vs-host reaction. It was founded that the antiserum was a potent anti-${\theta}$ like antiserum, and rat brain associated ${\theta}$ antigen was cross-reactive with mouse thymocytes and brain antigen. Using the RBA ${\theta}$ sera, distribution of ${\theta}$-bearing lymphocytes in rat lymphoid tissues was detected. And it was found that approximately 98% of thymocytes, 70-76% of lymph node lymphocytes, 72% of peripheral blood lymphocytes, 36-44% of spleen lymphocytes, and 4% of bone marrow were ${\theta}$-bearing.

• Journal of the Korean Society for Aeronautical & Space Sciences
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• v.39 no.4
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• pp.321-331
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• 2011

The present work is aimed to analyze the creep characteristics of a turbojet engine turbine blade using the theta projection method. The theta projection method has been widely used due to its advantages and flexibility. For the creep characteristic analysis of the turbine blade, tests are performed considering the operating conditions and the non-linear material properties. Results from the creep test are fitted using the four theta model. The predicted proprieties using the four theta model are compared with the prediction model and creep test results. To obtain an optimum value of the four theta parameters in non-linear square method, a number of computing processes in the non-linear least square method were carried out to obtain full creep curves. Results using the theta model has more than 0.95 value of $R^2$. The results between the experimental values and predicted four theta model has about 90.0% accuracy. The theta projection method can be utilized for a design purpose to predict the creep behavior.

• Communications of the Korean Mathematical Society
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• v.34 no.1
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• pp.1-16
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• 2019

Let a, b, P, and Q be real numbers with $PQ{\neq}0$ and $(a,b){\neq}(0,0)$. The Horadam sequence $\{W_n\}$ is defined by $W_0=a$, $W_1=b$ and $W_n=PW_{n-1}+QW_{n-2}$ for $n{\geq}2$. Let the sequence $\{X_n\}$ be defined by $X_n=W_{n+1}+QW_{n-1}$. In this study, we obtain some new identities between the Horadam sequence $\{W_n\}$ and the sequence $\{X_n\}$. By the help of these identities, we show that Diophantine equations such as $$x^2-Pxy-y^2={\pm}(b^2-Pab-a^2)(P^2+4),\\x^2-Pxy+y^2=-(b^2-Pab+a^2)(P^2-4),\\x^2-(P^2+4)y^2={\pm}4(b^2-Pab-a^2),$$ and $$x^2-(P^2-4)y^2=4(b^2-Pab+a^2)$$ have infinitely many integer solutions x and y, where a, b, and P are integers. Lastly, we make an application of the sequences $\{W_n\}$ and $\{X_n\}$ to trigonometric functions and get some new angle addition formulas such as $${\sin}\;r{\theta}\;{\sin}(m+n+r){\theta}={\sin}(m+r){\theta}\;{\sin}(n+r){\theta}-{\sin}\;m{\theta}\;{\sin}\;n{\theta},\\{\cos}\;r{\theta}\;{\cos}(m+n+r){\theta}={\cos}(m+r){\theta}\;{\cos}(n+r){\theta}-{\sin}\;m{\theta}\;{\sin}\;n{\theta},$$ and $${\cos}\;r{\theta}\;{\sin}(m+n){\theta}={\cos}(n+r){\theta}\;{\sin}\;m{\theta}+{\cos}(m-r){\theta}\;{\sin}\;n{\theta}$$.

• Bulletin of the Korean Mathematical Society
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• v.48 no.2
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• pp.277-290
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• 2011

We show that the ${\theta}$-prime radical of a ring R is the set of all strongly ${\theta}$-nilpotent elements in R, where ${\theta}$ is an automorphism of R. We observe some conditions under which the ${\theta}$-prime radical of coincides with the prime radical of R. Moreover we characterize elements in prime radicals of skew Laurent polynomial rings, studying (${\theta}$, ${\theta}^{-1}$)-(semi)primeness of ideals of R.