• Bulletin of the Korean Mathematical Society
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• v.30 no.1
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• pp.79-82
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• 1993

We let F be a p-adic field with ring of integers O. Suppose .THETA.$_{i}$ .mem. $F^{x}$ /( $F^{x}$ )$^{2}$ for i=1,2 and write $E^{{\theta}_{i}}$:= F(.root..THETA.$_{i}$ ). Then there appear some specific sets such as ( $E^{{\theta}_{i}}$)$^{x}$ / $F^{x}$ in [1] which we need to measure. In addition to that, nanother possible condition attached to the generalized results in [2] had better be presented even though they may not be quite so important. This paper is concerned with these matters. Most notations and conventions are standard and have been used also in [1] and [2].

• Proceedings of the Optical Society of Korea Conference
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• 1989.02a
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• pp.81-84
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• 1989

EHZP is a kind of holographic optical element, which is generated by the interference of two divergent spherical waves from point sources on the same axis. It has the spherical aberration that the focal power increases as the radial distance r increases. By using this property, optimal design of EHZP was performed for f-$\theta$ lens. As the result of optimization, the f-$\theta$ condition and the field flattening condition were well satisfied when EHZP has f0=0.803f, faR=4.076f, 1=0.406f. It was assumed for calculation of field flattening condition that the incident wave was a plane wave with the diameter of 1mm.

• Bulletin of the Korean Mathematical Society
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• v.56 no.2
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• pp.419-437
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• 2019

This paper investigates skew ${\Theta}-{\lambda}$-constacyclic codes over $R=F_0{\oplus}F_1{\oplus}{\cdots}{\oplus}F_{k-1}$, where $F{_i}^{\prime}s$ are finite fields. The structures of skew ${\lambda}$-constacyclic codes over finite commutative semi-simple rings and their duals are provided. Moreover, skew ${\lambda}$-constacyclic codes of arbitrary length are studied under a new definition. We also show that a skew cyclic code of arbitrary length over finite commutative semi-simple rings is equivalent to either a cyclic code over R or a quasi-cyclic code over R.

• Communications of the Korean Mathematical Society
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• v.37 no.1
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• pp.31-43
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• 2022

In his notebooks, Srinivasa Ramanujan recorded several modular equations that are useful in the computation of class invariants, continued fractions and the values of theta functions. In this paper, we prove some new modular equations of signature 2 by well-known and useful theta function identities of composite degrees. Further, as an application of this, we evaluate theta function identities.

• Nonlinear Functional Analysis and Applications
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• v.28 no.3
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• pp.731-751
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• 2023

If p(z) is a polynomial of degree n having all its zeros in |z| ≤ k, k ≥ 1, then for any complex number α with |α| ≥ k, and r ≥ 1, Aziz [1] proved $$\left{{\int}_{0}^{2{\pi}}\,{\left|1+k^ne^{i{\theta}}\right|^r}\,d{\theta}\right}^{\frac{1}{r}}\;{\max\limits_{{\mid}z{\mid}=1}}\,{\mid}p^{\prime}(z){\mid}\,{\geq}\,n\,\left{{\int}_{0}^{2{\pi}}\,{\left|p(e^{i{\theta}})\right|^r\,d{\theta}\right}^{\frac{1}{r}}.$$ In this paper, we obtain an improved extension of the above inequality into polar derivative. Further, we also extend an inequality on polar derivative recently proved by Rather et al. [20] into L^r-norm. Our results not only extend some known polynomial inequalities, but also reduce to some interesting results as particular cases.

• Journal of the Korean Statistical Society
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• v.10
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• pp.83-90
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• 1981

Let (X, A) be a measurable space, i.e. X is a non-empty set and A is a $\sigma$-field of subsets of X. Let $\Omega$ be a parameter space and P be a family of probability measures $P_\theta, \theta \in \Omega$ defined on (X, A).

• Journal of applied mathematics & informatics
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• v.9 no.2
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• pp.817-823
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• 2002

This paper gives some characterizations of quasi irresolute functions.

• East Asian mathematical journal
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• v.9 no.1
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• pp.157-165
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• 1993

• Applied Biological Chemistry
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• v.29 no.4
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• pp.352-358
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• 1986

The relationship between weight reduction and rehydration of dehydrofrozen potato was determined. At initial stage of dehydration sliced potato lost moisture rapidly. After drying for 2 hours weight reduction of sliced potato was 56% for Superior var., and 55% for Irish Cobbler. The empirical drying equations were obtained as follows: ${\frac{M-M_e}{M_o-M_e}}={\exp}(-0.4487\;{\theta}^{1.2328})$ and ${\frac{M-M_e}{M_o-M_e}}={\exp}\;(-0.4951\;{\theta}^{1.1949})$ for Irish Cobbler and Superior, respectively, where $M_o$, $M_e$, and M are dry base moisture content(%) of initial, equilibrium and at time ${\theta}$ in hour, respectively. With the decrease of weight above 50%, the rehydration rate decreased sharply and the color index L value also decreased while a and b increased. Lightness of dehydrofrozen potato decreased slightly and rehydration rate remained constant during storage at $-18^{\circ}C$. The sulfite treatment led to increase of L value and decrease of a and b values.

• Journal of Korean Ophthalmic Optics Society
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• v.2 no.1
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• pp.1-8
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• 1997

When a ferroelastic domain of ${\beta}-Tb_2(MoO_4)_3$ single crystal is switched from $S_k$ state to $S_p$ state by external force, the formulae that can calculate relativistic displacement of the lattice point and distribution of ferroelastic switching force were derived by this study. The formulae that can calculate threshold switching force in any direction were derived from the conservation law of enthalpy and measured value of threshold switching force in specific direction. Theoretical values of threshold switching force were in accord with measured values at (${\theta}=90^{\circ}$, ${\phi}=15^{\circ}$), (${\theta}=90^{\circ}$, ${\phi}=30^{\circ}$), (${\theta}=90^{\circ}$, ${\phi}=45^{\circ}$), (${\theta}=90^{\circ}$, ${\phi}=60^{\circ}$), (${\theta}=90^{\circ}$, ${\phi}=75^{\circ}$).