• East Asian mathematical journal
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• v.16 no.2
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• pp.169-174
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• 2000

We give an easy proof that ${\phi}(z)=\frac{z^2_1}{1-z^2_2}$ induces the bounded composition operator $C_{\phi}:\mathcal{B}{\rightarrow}{\bigcap}H^p(B_2)$ defined by $C_{\phi}f=f\;o\;{\phi}$.

• Journal of the Korean Mathematical Society
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• v.59 no.3
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• pp.439-448
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• 2022

For a natural number n, let R(n) denote the number of representations of n as the sum of one square and five cubes of primes. In this paper, it is proved that the anticipated asymptotic formula for R(n) fails for at most $O(N^{{\frac{4}{9}+{\varepsilon}})$ positive integers not exceeding N.

• Bulletin of the Korean Mathematical Society
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• v.59 no.4
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• pp.905-915
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• 2022

This paper studies the boundedness of integral operators on the Cesàro function spaces. As applications of the main result, we obtain the Hilbert inequalities, the boundedness of the Erdélyi-Kober fractional integrals and the Mellin fractional integrals on the Cesàro function spaces.

• Journal of the Korean Mathematical Society
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• v.59 no.2
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• pp.407-420
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• 2022

It is proved that every sufficiently large even integer can be represented as a sum of two squares of primes, two cubes of primes, two fourth powers of primes and 17 powers of 2.

• Nonlinear Functional Analysis and Applications
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• v.28 no.4
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• pp.1005-1015
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• 2023

In this paper, we establish the existence of at least two distinct solutions to a p-Laplacian problems involving critical exponents and singular cylindrical potential, by using the Nehari manifold.

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

• Journal of the Korean Mathematical Society
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• v.42 no.1
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• pp.111-127
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• 2005

Let B and S be the unit ball and the unit sphere in $\mathbb{C}^n$, respectively. Let ${\sigma}$ be the normalized Lebesgue measure on S. Define the Privalov spaces $N^P(B)\;(1\;<\;p\;<\;{\infty})$ by $$N^P(B)\;=\;\{\;f\;{\in}\;H(B) : \sup_{0 where H(B) is the space of all holomorphic functions in B. Let ${\varphi}$ be a holomorphic self-map of B. Let ${\mu}$ denote the pull-back measure ${\sigma}o({\varphi}^{\ast})^{-1}$. In this paper, we prove that the composition operator $C_{\varphi}$ is metrically bounded on $N^P$(B) if and only if ${\mu}(S(\zeta,\delta)){\le}C{\delta}^n$ for some constant C and $C_{\varphi}$ is metrically compact on $N^P(B)$ if and only if ${\mu}(S(\zeta,\delta))=o({\delta}^n)$ as ${\delta}\;{\downarrow}\;0$ uniformly in ${\zeta}\;\in\;S. Our results are an analogous results for Mac Cluer's Carleson-measure criterion for the boundedness or compactness of $C_{\varphi}$ on the Hardy spaces $H^P(B)$.

• Wind and Structures
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• v.8 no.2
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• pp.79-88
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• 2005

This paper deals with a unified way for calculating vortex-induced vibrations (Aeolian vibrations in transmission line parlance) of undamped single overhead conductors. The main objective of the paper is to identify reduced parameters which would unify the predicted vibration response to the largest possible extent. This is actually done by means of a simple mathematical transformation resulting, for a given terrain (associated to a given wind turbulence intensity), into a single, unified response curve that is applicable to any single multi-layered aluminium conductor. In order to further validate the above process, the predicted, unified response curve is compared with measured response curves drawn from tests run on a full-scale test line using several aluminium-conductor-steel-reinforced (ACSR), all-alloy-aluminium-conductor (AAAC) and aluminium-conductor-alloy-reinforced (ACAR) conductors strung at different tensions. On account of the expected scatter in the results from such field tests, the agreement is shown to be good. The final results are expressed by means of only four different curves pertaining to four different terrain characteristics. These curves may then be used to assess the vibration response of any undamped single, multi-layer aluminium conductor of any diameter, strung at any practical tension.

• Asian-Australasian Journal of Animal Sciences
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• v.21 no.6
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• pp.776-783
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• 2008

In this study, we investigated the genetic diversity and phylogenetic relationship of six duck populations by employing the genetic polymorphisms of 20 microsatellites. The parameters used in this study included number of alleles, average effective numbers of alleles (E) and average rates of heterozygosity of each population. The results showed that all the microsatellite loci were highly polymorphic except that the locus AJ515896 in Muscovy duck was 0. The average PIC (0.762), average h (0.7843) and average E (5.261) of the six duck populations were all high, indicating that the gene polymorphisms and genetic diversity were high. The test of Hardy-Weinberg equilibrium showed that the six populations in this study were all in Hardy-Weinberg disequilibrium. The F-statistic analysis results showed the range of FST was from 0.0205 (AJ515895) to 0.2558 (AJ515896). The mean FST was 0.0936. Phylogenetic study revealed that Peking duck (Z1 and Z4), Shaoxing duck, Cherry Valley duck and Aobaixing duck were clustered in one group, while the Muscovy duck was clustered in one group alone. The phylogenetic relationships among different populations were in accordance with their breeding history and distribution. Our data suggested that the 20 microsatellite loci were effective markers for analysis of genetic relationships among duck populations.

• Asian-Australasian Journal of Animal Sciences
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• v.21 no.11
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• pp.1535-1543
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• 2008

Microsatellites (MS) are useful for quantifying genetic variation within and between populations and for describing the evolutionary relationships of closely related populations. The main objectives of this work were to estimate genetic parameters, measure genetic distances and reconstruct phylogenetic relationships between Australian Angora/Angora_Aus/ and Cashmere/Cashmere_Aus/ populations and three Mongolian Cashmere goat (Bayandelger/BD/, Zavkhan Buural/ZB/, and Gobi Gurvan Saikhan/GGS/) populations based on variation at fourteen MS loci. The level and pattern of observed and expected heterozygosity and polymorphic information content of the fourteen loci studied across the populations were quite similar and high. Except for SRCRSP07, all studied microsatellites were in Hardy-Weinberg Equilibrium (p<0.001). Moderate genetic variation (7.5%) was found between the five goat populations with 92.5% of total genetic variation attributable to diversity existing between the individuals within each population. The greatest Nei's genetic distances were found between the Angora and four Cashmere populations (0.201-0.276) and the lowest distances were between the Mongolian Cashmere goat populations (0.026-0.031). Compared with other Cashmere goat populations, the GGS (crossbred with Russian Don Goats) population had the smallest pairwise genetic distance from the Australian Angora population (0.192). According to a three-factorial correspondence analysis (CA), the three different Mongolian Cashmere populations could hardly be distinguished from each other.