• Nonlinear Functional Analysis and Applications
• /
• v.27 no.2
• /
• pp.309-322
• /
• 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.

• Journal of the Korean Mathematical Society
• /
• v.31 no.4
• /
• pp.633-643
• /
• 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)$.

• Journal of the korean academy of Pediatric Dentistry
• /
• v.11 no.1
• /
• pp.181-189
• /
• 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.

• Textile Coloration and Finishing
• /
• v.27 no.1
• /
• pp.1-10
• /
• 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.

• Communications of the Korean Mathematical Society
• /
• v.24 no.3
• /
• pp.367-379
• /
• 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 ${\in}L^1(\mathbb{Q}_p^d)$.

• Communications of the Korean Mathematical Society
• /
• v.12 no.2
• /
• pp.311-324
• /
• 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 $M_2={f \in L^2(D^2, m \times m)\midBf = f$.

• Journal of the Korean Ceramic Society
• /
• v.40 no.7
• /
• pp.677-682
• /
• 2003

The physical properties of sintered body made from 3 kinds of slip, F (Flocculated), M (Moderate), and D (Dispersed) for coal fly ash 70-clay 30 (wt%) were studied in terms of slip states and pore size distribution of sintered bodies. The floc particle size distribution for slip F was wider than slip D and the slip F contained flocs larger than 11 $\mu\textrm{m}$. The pore size distribution of the green body of all slips ranged over 1∼4 $\mu\textrm{m}$. The pores smaller than 1 $\mu\textrm{m}$ almost disappeared during the sintering process, while the larger pore of 2.5∼3 $\mu\textrm{m}$ growed by 1 $\mu\textrm{m}$. The pore distribution for the green body of slip F became a narrow in width and high in height after sintering and the large pore limit in a slip F sintered body was 5.1 $\mu\textrm{m}$ which is smaller than that of other slip. The slip F rather flocculated was favorable over slip D well dispersed, in offering a higher compressive strength. From these results, the mechanical strength of sintered body is dependent on the pore distribution which could be controlled by dispersion state of the slips.

• Bulletin of the Korean Mathematical Society
• /
• v.20 no.1
• /
• pp.9-13
• /
• 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
• /
• v.62 no.1
• /
• pp.1-28
• /
• 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.

• Communications of the Korean Mathematical Society
• /
• v.32 no.3
• /
• pp.779-787
• /
• 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.