• East Asian mathematical journal
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• v.14 no.2
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• pp.259-268
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• 1998

In this paper, for a commutative ring R with an identity, considering the endomorphism ring $End_R$(M) of left R-module $_RM$ which is (quasi-)injective or (quasi-)projective, some discriminations of prime endomorphism were found as follows: each epimorphism with the irreducible(or simple) kernel on a (quasi-)injective module and each monomorphism with maximal image on a (quasi-)projective module are prime. It was shown that for a field F, any given square matrix in $Mat_{n{\times}n}$(F) with maximal image and irreducible kernel is a prime matrix, furthermore, any given matrix in $Mat_{n{\times}n}$(F) for any field F can be factored into a product of prime matrices.

• Kyungpook Mathematical Journal
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• v.60 no.3
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• pp.477-484
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• 2020

For a non-zero complex number b and for m and n in 𝒩₀ = {0, 1, 2, …} let Ψ_n,m(b) denote the class of normalized univalent functions f satisfying the condition ${\Re}\;\[1+{\frac{1}{b}}\(\frac{D^{n+m}f(z)}{D^nf(z)}-1\)\]\;>\;0$ in the unit disk U, where Dⁿ f(z) denotes the Salagean operator of f. Sharp bounds for the Fekete-Szegö functional |a₃ - 𝜇a²₂| are obtained.

• Journal of electromagnetic engineering and science
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• v.13 no.2
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• pp.127-133
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• 2013

We examined the scaling effects of a number of gate_fingers (N) and gate_widths (w) on the high-frequency characteristics of $0.1-{\mu}m$ metamorphic high-electron-mobility transistors. Functional relationships of the extracted small-signal parameters with total gate widths ($w_t$) of different N were proposed. The cut-off frequency ($f_T$) showed an almost independent relationship with $w_t$; however, the maximum frequency of oscillation ($f_{max}$) exhibited a strong functional relationship of gate-resistance ($R_g$) influenced by both N and $w_t$. A greater $w_t$ produced a higher $f_{max}$; but, to maximize $f_{max}$ at a given $w_t$, to increase N was more efficient than to increase the single gate_width.

• The Journal of Korean Institute of Communications and Information Sciences
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• v.27 no.1A
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• pp.35-41
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• 2002

In this paper, we generalize the family of binary bent sequences introduced by Olsen, Scholtz and Welch [2] to obtain the generalized binary bent sequences with optimal correlation and balance properties. The modified trace transform is introduced and it enables us to use linear function from ${F_{2^n}}$ to the intermediate field ${F_{2^e}}$, where e|n. If we choose e=1, our method becomes the conventional binary bent sequence case. Also, some examples are given which show that our construction gives the family of simple binary sequences with optimal correlation and balance properties.

• Journal of the Institute of Convergence Signal Processing
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• v.13 no.4
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• pp.194-200
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• 2012

In this paper we analyze the code sequence generating algorism defined on $GF(2^n)$ proposed by S.Bostas and V.Kumar[7] and derive the implementation functions of code sequence generator using Boolean functions which can map the vector space $F_2^n$ of all binary vectors of length n, to the finite field with two elements $F_2$. We find the code sequence generating boolean functions based on two kinds of the primitive polynomials of degree, n=5 and n=7 from trace function. We then design and implement the code sequence generators using these functions, and produce two code sequence groups. The two groups have the period 31 and 127 and the magnitudes of out of phase(${\tau}{\neq}0$) autocorrelation and crosscorrelation functions {-9, -1, 7} and {-17, -1, 15}, satisfying the period $L=2^n-1$ and the correlation functions $R_{ij}({\tau})=\{-2^{(n+1)/2}-1,-1,2^{(n+l)/2}-1\}$ respectively. Through these results, we confirm that the code sequence generators using boolean functions are designed and implemented correctly.

• Journal of the Korean Society for Industrial and Applied Mathematics
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• v.8 no.2
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• pp.1-5
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• 2004

A multiplicative plane partition is a two-dimensional array of positive integers larger than 1 that are nonincreasing both from left to right and top to bottom and whose multiple is a given number n. For a natural number n, let $f_2(n)$ be the number of multiplicative plane partitions of n. In this paper, we prove $f_2(n)\;{\leq}\;n^2$ and a table of them up to $10^5$ is provided.

• Journal of the Chungcheong Mathematical Society
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• v.22 no.2
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• pp.149-153
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• 2009

Let {$X_{n},\;n\;\geq\;1$} be a sequence of independent and identically distributed random variables with absolutely continuous cumulative distribution function (cdf) F(x) and probability density function (pdf) f(x). Suppose $X_{U(m)},\;m = 1,\;2,\;{\cdots}$ be the upper record values of {$X_{n},\;n\;\geq\;1$}. It is shown that the linearity of the conditional expectation of $X_{U(n+2)}$ given $X_{U(n)}$ characterizes the lomax, exponential and pareto distributions.

• Communications of the Korean Mathematical Society
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• v.20 no.2
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• pp.351-358
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• 2005

We study asymptotic equivalence between nonlinear difference system $$\Delta\chi(n)=f(n,\chi(n))$$ and its variational system $${\Delta}v(n)=f_{\chi}(n,0)v(n)$$.

• Korean Journal of Materials Research
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• v.22 no.8
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• pp.439-444
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• 2012

To compare the photocatalytic performances of titania for purification of waste water according to applied voltages and doping, $TiO_2$ films were prepared in a 1.0 M $H_2SO_4$ solution containing $NH_4F$ at different anodic voltages. Chemical bonding states of F-N-codoped $TiO_2$ were analyzed using surface X-ray photoelectron spectroscopy (XPS). The photocatalytic activity of the co-doped $TiO_2$ films was analyzed by the degradation of aniline blue solution. Nanotubes were formed with thicknesses of 200-300 nm for the films anodized at 30 V, but porous morphology was generated with pores of 1-2 ${\mu}m$ for the $TiO_2$ anodized at 180 V. The phenomenon of spark discharge was initiated at about 98 V due to the breakdown of the oxide films in both solutions. XPS analysis revealed the spectra of F1s at 684.3 eV and N1s at 399.8 eV for the $TiO_2$ anodized in the $H_2SO_4-NH_4F$ solution at 180 V, suggesting the incorporation of F and N species during anodization. Dye removal rates for the pure $TiO_2$ anodized at 30 V and 180 V were found to be 14.0% and 38.9%, respectively, in the photocatalytic degradation test of the aniline blue solution for 200 min irradiation; the rates for the F-N-codoped $TiO_2$ anodized at 30 V and 180 V were found to be 21.2% and 65.6%, respectively. From the results of diffuse reflectance absorption spectroscopy (DRS), it was found that the absorption edge of the F-N-codoped $TiO_2$ films shifted toward the visible light region up to 412 nm, indicating that the photocatalytic activity of $TiO_2$ is improved by appropriate doping of F and N by the addition of $NH_4F$.

• Journal of the Korean Mathematical Society
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• v.48 no.2
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• pp.397-420
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• 2011

In this paper we study the structure of closed weakly dense ideals in Privalov spaces $N^p$ (1 < p < $\infty$) of holomorphic functions on the disk $\mathbb{D}$ : |z| < 1. The space $N^p$ with the topology given by Stoll's metric [21] becomes an F-algebra. N. Mochizuki [16] proved that a closed ideal in $N^p$ is a principal ideal generated by an inner function. Consequently, a closed subspace E of $N^p$ is invariant under multiplication by z if and only if it has the form $IN^p$ for some inner function I. We prove that if $\cal{M}$ is a closed ideal in $N^p$ that is dense in the weak topology of $N^p$, then $\cal{M}$ is generated by a singular inner function. On the other hand, if $S_{\mu}$ is a singular inner function whose associated singular measure $\mu$ has the modulus of continuity $O(t^{(p-1)/p})$, then we prove that the ideal $S_{\mu}N^p$ is weakly dense in $N^p$. Consequently, for such singular inner function $S_{\mu}$, the quotient space $N^p/S_{\mu}N^p$ is an F-space with trivial dual, and hence $N^p$ does not have the separation property.