• Nonlinear Functional Analysis and Applications
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• 제27권2호
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• pp.309-322
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• 2022

In this paper, we introduce the notion of a new generalized type of rational F-contraction mapping. Further, the concept is used to obtain fixed points in a complete b-metric space. We also prove another unique fixed point theorem in the context of b-metric space. Our results are verified with example.

• 대한수학회지
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• 제31권4호
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• pp.633-643
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• 1994

Let us consider the initial-value problem of dimension m: $$ \frac{d\tau}{d}y(\tau) = f(\tau, Y(\tau)), y(0) = y_0, \tau \geq 0, (1.1) $$ Where $ = (f_1, f_2, \cdots, f_m) and y = (y_1, y_2, \cdots, y_m)$.

• 대한소아치과학회지
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• 제11권1호
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• pp.181-189
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• 1984

1,840 school children aged 6 to 13 years who live in inland area in CHOONG CHUNG BUK DO were surveyed epidemiologically on the dental caries prevalence. The results were as follows; 1. The prevalence of dental carries was 76.35 percentage in male, 76.15 percentage in female, and 76.25 percentage in both sexes. 2. d.m.f rate was 77.72 percentage in male, 80.07 percentage in female, and 78.86 percentage in both sexes. D.M.F rate was 30.73 percentage in male, 38.52 percentage in female, and 34.51 percentage in both sexes. 3. d.m.f.t. rate and index was 27.94 percentage,2.55T, and d.m.f.s. rate & index was 13.62 percentage, 6.22T. 4. D.M.F.T rate & index in permanent teeth was 4.86 percentage,0.72T, and D.M.F.S. rate & index was 1.20 percentage,0.89T. 5. The filling rate was 3.90 percentage in decidious teeth, 2,00 percentage in permanent teeth.

• 한국염색가공학회지
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• 제27권1호
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• pp.1-10
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• 2015

The aim of the current study is to identify the dimerization and decomposition kinetics of the F-$D_M$ type. The regeneration of F-VS from $F_iF_j-D_M$ or the reversibility of the dimerizations were investigated. The order of real rate constants of the dimerization('$K_D{^{ij}}$) would seem to be similar to that of rate constants of a dimerization($K_D{^{ij}}$) for VS dyes at a given pH because of the constancy of the equilibrium constants($K_a{^j}$-value). The reverse reactions of the $D_M$ types are appeared to occur in two steps, the deprotonation of ${\alpha}$-carbon of the $D_M$ types and disproportionation. The ratio of the decomposition of the $D_M$ type to F-Hy and F-VS appears to be related with the ratio of $K_i/K_j$. Similarities were also found among various other reactions, including homo- and mixed dimerization. VS dyes undergoing fast hydrolysis have difficulty in forming a dimer. The higher the reactivity with cellulose or hydroxide ion, the smaller the dimerization. The easiness of the dimerization was thus found to be inversely proportional to the rate of hydrolysis.

• 대한수학회논문집
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• 제24권3호
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• pp.367-379
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• 2009

For a prime number p, let $\mathbb{Q}_p$ denote the p-adic field and let $\mathbb{Q}_p^d$ denote a vector space over $\mathbb{Q}_p$ which consists of all d-tuples of $\mathbb{Q}_p$. For a function f ${\in}L_{loc}^1(\mathbb{Q}_p^d)$, we define the Hardy-Littlewood maximal function of f on $\mathbb{Q}_p^d$ by $$M_pf(x)=sup\frac{1}{\gamma{\in}\mathbb{Z}|B_{\gamma}(x)|H}{\int}_{B\gamma(x)}|f(y)|dy$$, where |E|$_H$ denotes the Haar measure of a measurable subset E of $\mathbb{Q}_p^d$ and $B_\gamma(x)$ denotes the p-adic ball with center x ${\in}\;\mathbb{Q}_p^d$ and radius $p^\gamma$. If 1 < q $\leq\;\infty$, then we prove that $M_p$ is a bounded operator of $L^q(\mathbb{Q}_p^d)$ into $L^q(\mathbb{Q}_p^d)$; moreover, $M_p$ is of weak type (1, 1) on $L^1(\mathbb{Q}_p^d)$, that is to say, |{$x{\in}\mathbb{Q}_p^d:|M_pf(x)|$>$\lambda$}|$_H{\leq}\frac{p^d}{\lambda}||f||_{L^1(\mathbb{Q}_p^d)},\;\lambda$ > 0 for any f ${\in}L^1(\mathbb{Q}_p^d)$.

• 대한수학회논문집
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• 제12권2호
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• pp.311-324
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• 1997

We show that if $f \in L^{\infty}(D^n)$ satisfies Sf = rf for some r in the unit circle, where S is any convex combination of the iterations of Berezin operator, then f is n-harmonic. And we give some remarks and a conjecture on the space $M_2={f \in L^2(D^2, m \times m)\midBf = f$.

• 한국세라믹학회지
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• 제40권7호
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• pp.677-682
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• 2003

석탄회.점토의 무게비가 7 : 3인 슬립에 대하여 그 해교정도에 따라 slip을 F(Flocculated), M(Moderate) 및 D(Dispersed)의 3종류로 제조하고 이로부터 소결체를 합성하여 시편의 물성과 슬립 특성과의 관계를 분석하였다. Slip F는 응집입자의 크기분포가 넓은 반면 slip D는 입도분포가 좁고 11 $\mu\textrm{m}$ 이상의 큰 응집입자가 거의 존재하지 않았다. 성형체의 기공은 슬립의 종류에 관계없이 1~4 $\mu\textrm{m}$ 범위 내에 분포하며 소결 후에는 1 $\mu\textrm{m}$ 이하의 미세기공은 거의 소멸된 반면, 큰 기공은 1 $\mu\textrm{m}$ 정도 더 성장하였다. Slip F의 경우에 소결 후 기공분포는 slip M과 D에 비하여 주피크의 높이가 높고 폭이 좁았으며, large pore limit (가장 큰 기공 크기)가 5.1 $\mu\textrm{m}$로 다른 슬립 성형체보다 작았다. 입자가 잘 분산된 슬립(slip D)보다는 약간 응집된 슬립(slip F)이 소결시 시편내 거대기공의 생성을 억제함으로서 높은 압축강도를 얻는데 유리하였다. 이상의 결과로부터 소결체의 기계적 특성은 기공분포에 크게 의존하며, 이는 슬립의 분산특성을 제어함으로서 가능함을 알 수 있다.

• 대한수학회보
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• 제20권1호
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• pp.9-13
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• 1983

M$_{n}$(F) denotes the set of all n*n matrices over F={0, 1}. For a, b.mem.F, define a+b=max{a, b} and ab=min{a, b}. Under these operations a+b and ab, M$_{n}$(F) forms a multiplicative semigroup (see [1], [4]) and we call it the semigroup of the n*n boolean matrices over F={0, 1}. Since the semigroup M$_{n}$(F) is the matrix representation of the semigroup B$_{n}$ of the binary relations on the set X with n elements, we may identify M$_{n}$(F) with B$_{n}$ for finding all D-classes.l D-classes.

• Kyungpook Mathematical Journal
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• 제62권1호
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• pp.1-28
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• 2022

In this paper, we define the G-Brauer algebras $D^G_f(x)$, where G is a cyclic group, called cyclic G-Brauer algebras, as the linear span of r-signed 1-factors and the generalized m, k signed partial 1-factors is to analyse the multiplication of basis elements in the quotient $^{\rightarrow}_{I_f}^G(x,2k)$. Also, we define certain symmetric matrices $^{\rightarrow}_T_{m,k}^{[\lambda]}(x)$ whose entries are indexed by generalized m, k signed partial 1-factor. We analyse the irreducible representations of $D^G_f(x)$ by determining the quotient $^{\rightarrow}_{I_f}^G(x,2k)$ of $D^G_f(x)$ by its radical. We also find the eigenvalues and eigenspaces of $^{\rightarrow}_T_{m,k}^{[\lambda]}(x)$ for some values of m and k using the representation theory of the generalised symmetric group. The matrices $T_{m,k}^{[\lambda]}(x)$ whose entries are indexed by generalised m, k signed partial 1-factors, which helps in determining the non semisimplicity of these cyclic G-Brauer algebras $D^G_f(x)$, where G = ℤ_r.

• 대한수학회논문집
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• 제32권3호
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• pp.779-787
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• 2017

Let m be the Lebesgue measure on ${\mathbb{C}}$ normalized to $m(D)=1,{\mu}$ be an invariant measure on D defined by $d_{\mu}(z)=(1-{\mid}z{\mid}^2)^{-2}dm(z)$. For $f{\in}L^1(D^n,m{\times}{\cdots}{\times}m)$, Bf the Berezin transform of f is defined by, $$(Bf)(z_1,{\ldots},z_n)={\displaystyle\smashmargin{2}{\int\nolimits_D}{\cdots}{\int\nolimits_D}}f({\varphi}_{z_1}(x_1),{\ldots},{\varphi}_{z_n}(x_n))dm(x_1){\cdots}dm(x_n)$$. We prove that if $f{\in}L^1(D^2,{\mu}{\times}{\mu})$ is radial and satisfies ${\int}{\int_{D^2}}fd{\mu}{\times}d{\mu}=0$, then for every bounded radial function ${\ell}$ on $D^2$ we have $$\lim_{n{\rightarrow}{\infty}}{\displaystyle\smashmargin{2}{\int\int\nolimits_{D^2}}}(B^nf)(z,w){\ell}(z,w)d{\mu}(z)d{\mu}(w)=0$$. Then, using the above property we prove n-harmonicity of bounded function which is invariant under the Berezin transform. And we show the same results for the weighted the Berezin transform in the polydisc.