• Bulletin of the Korean Mathematical Society
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• v.52 no.3
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• pp.935-946
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• 2015

The purpose of this paper is to introduce a new class of rings that is closely related to the classes of pseudo valuation rings (PVRs) and pseudo-almost valuation domains (PAVDs). A commutative ring R is said to be ${\phi}$-ring if its nilradical Nil(R) is both prime and comparable with each principal ideal. The name is derived from the natural map ${\phi}$ from the total quotient ring T(R) to R localized at Nil(R). A prime ideal P of a ${\phi}$-ring R is said to be a ${\phi}$-pseudo-strongly prime ideal if, whenever $x,y{\in}R_{Nil(R)}$ and $(xy){\phi}(P){\subseteq}{\phi}(P)$, then there exists an integer $m{\geqslant}1$ such that either $x^m{\in}{\phi}(R)$ or $y^m{\phi}(P){\subseteq}{\phi}(P)$. If each prime ideal of R is a ${\phi}$-pseudo strongly prime ideal, then we say that R is a ${\phi}$-pseudo-almost valuation ring (${\phi}$-PAVR). Among the properties of ${\phi}$-PAVRs, we show that a quasilocal ${\phi}$-ring R with regular maximal ideal M is a ${\phi}$-PAVR if and only if V = (M : M) is a ${\phi}$-almost chained ring with maximal ideal $\sqrt{MV}$. We also investigate the overrings of a ${\phi}$-PAVR.

• Kyungpook Mathematical Journal
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• v.46 no.2
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• pp.255-260
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• 2006

Let $m$ and $k$ be any positive integers, let $\mathbb{Z}_k$ the ring of integers of modulo $k$, let $G_m(\mathbb{Z}_k)$ the group of all $m$ by $m$ nonsingular matrices over $\mathbb{Z}_k$ and let ${\phi}_m(k)$ the order of $G_m(\mathbb{Z}_k)$. In this paper, ${\phi}_m(k)$ can be computed by the following investigation: First, for any relatively prime positive integers $s$ and $t$, $G_m(\mathbb{Z}_{st})$ is isomorphic to $G_m(\mathbb{Z}_s){\times}G_m(\mathbb{Z}_t)$. Secondly, for any positive integer $n$ and any prime $p$, ${\phi}_m(p^n)=p^{m^2}{\cdot}{\phi}_m(p^{n-1})=p{^{2m}}^2{\cdot}{\phi}_m(p^{n-2})={\cdots}=p^{{(n-1)m}^2}{\cdot}{\phi}_m(p)$, and so ${\phi}_m(k)={\phi}_m(p_1^n1){\cdot}{\phi}_m(p_2^{n2}){\cdots}{\phi}_m(p_s^{ns})$ for the prime factorization of $k$, $k=p_1^{n1}{\cdot}p_2^{n2}{\cdots}p_s^{ns}$.

• Communications of the Korean Mathematical Society
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• v.32 no.3
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• pp.543-552
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• 2017

Let R be a commutative ring with identity, and ${\phi}:{\mathfrak{I}}(R){\rightarrow}{\mathfrak{I}}(R){\cup}\{{\varnothing}\}$ be a function where ${\mathfrak{I}}(R)$ is the set of all ideals of R. Following [2], a proper ideal P of R is called a ${\phi}$-prime ideal if $x,y{\in}R$ with $xy{\in}P-{\phi}(P)$ implies $x{\in}P$ or $y{\in}P$. For an ideal I of R, we define the ${\phi}$-radical ${\sqrt[{\phi}]{I}}$ to be the intersection of all ${\phi}$-prime ideals of R containing I, and show that this notion inherits most of the essential properties of the usual notion of radical of an ideal. We also investigate when the set of all ${\phi}$-prime ideals of R, denoted $Spec_{\phi}(R)$, has a Zariski topology analogous to that of the prime spectrum Spec(R), and show that this topological space is Noetherian if and only if ${\phi}$-radical ideals of R satisfy the ascending chain condition.

• Journal of applied mathematics & informatics
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• v.22 no.1_2
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• pp.361-372
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• 2006

In this paper, we consider the multi-point boundary value problems for one-dimensional p-Laplacian at resonance: $({\phi}_p(x'(t)))'=f(t,x(t),x'(t))$, subject to the boundary value conditions: ${\phi}_p(x'(0))={\sum}^{n-2}_{i=1}{\alpha}_i{\phi}_p(x'({\epsilon}i)),\;{\phi}_p(x'(1))={\sum}^{m-2}_{i=1}{\beta}_j{\phi}_p(x'({\eta}_j))$ where ${\phi}_p(s)=/s/^{p-2}s,p>1,\;{\alpha}_i(1,{\le}i{\le}n-2){\in}R,{\beta}_j(1{\le}j{\le}m-2){\in}R,0<{\epsilon}_1<{\epsilon}_2<...<{\epsilon}_{n-2}1,\;0<{\eta}1<{\eta}2<...<{\eta}_{m-2}<1$, By applying the extension of Mawhin's continuation theorem, we prove the existence of at least one solution. Our result is new.

• Journal of applied mathematics & informatics
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• v.37 no.5_6
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• pp.329-339
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• 2019

The Banach spaces $m^p(\phi)$ and $n^p(\phi)$ are very important sequence spaces related to $l_p$, which were defined to fill the gaps between $l_p(1{\leq}p{\leq}{\infty})$. In this paper, we investigated the solubility of the infinite system of differential equations in $m^p(\phi)$ and $n^p(\phi)$ by proving related theorems. Moreover, one example has been included for the justification of the claim of this paper.

• Bulletin of the Korean Mathematical Society
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• v.48 no.5
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• pp.1093-1103
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• 2011

We give the characterizations of the classes of matrix trans-formations ($m(\phi),{\ell}_p$), ($n(\phi),{\ell}_p$) ([5, Theorem 2]), (${\ell}_p,m(\phi)$) ([5, Theorem 1]) and (${\ell}_p,n(\phi)$) for $1{\leq}p{\leq}{\infty}$, establish estimates for the norms of the bounded linear operators defined by those matrix transformations and characterize the corresponding subclasses of compact matrix operators.

• KSBB Journal
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• v.10 no.5
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• pp.575-581
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• 1995

A plasmid pTTY2, containing the lipase-producing gene, was used to transform an E. coli phage lysogen, P90c/$\phi$434, into the lipase-producing lysogen, P90c/$\phi$434/pTTY2. After the overproduction of lipase by the isopropylthio-${\beta}$-D-galactoside induction, the prophage $\phi$434 in the chromosome of the host cell was induced by the milomycin C addition or ultraviolet irradiation to lyse the host cell. The optimum operating conditions, such as the isopropylthio-${\beta}$-D-galactoside induction period and the phage induction timing, were sought for the efficient cell lysis in the same fermenter. Effective cell lysis occurred at the earlier exponential growth phase with the isopropylthio-${\beta}$-D-galactoside induction period of 1 hour. The amount of the lipase production was qualitatively measured by the halo size in Luria-Bertani agar medium containing tributyrin and Rhodamine B plate.

• 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 $C_{\phi}f=f\;o\;{\phi}$.

• The Plant Pathology Journal
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• v.34 no.5
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• pp.445-450
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• 2018

Bacteriophages, bacteria-infecting viruses, have been recently reconsidered as a biological control tool for preventing bacterial pathogens. Erwinia amylovora and E. pyrifoliae cause fire blight and black shoot blight disease in apple and pear, respectively. In this study, the bacteriophage phiEaP-8 was isolated from apple orchard soil and could efficiently and specifically kill both E. amylovora and E. pyrifoliae. This bacteriophage belongs to the Podoviridae family. Whole genome analysis revealed that phiEaP-8 carries a 75,929 bp genomic DNA with 78 coding sequences and 5 tRNA genes. Genome comparison showed that phiEaP-8 has only 85% identity to known bacteriophages at the DNA level. PhiEaP-8 retained lytic activity up to $50^{\circ}C$, within a pH range from 5 to 10, and under 365 nm UV light. Based on these characteristics, the bacteriophage phiEaP-8 is novel and carries potential to control both E. amylovora and E. pyrifoliae in apple and pear.

• Journal of Applied Biological Chemistry
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• v.62 no.3
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• pp.287-292
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• 2019

Pseudomonas tolaasii causes brown blotch disease on the oyster mushroom (Pleurotus ostreatus). Various pathogenic strains of P. tolaasii were isolated and divided into three subtypes, $P1{\alpha}$, $P1{\beta}$, and $P1{\gamma}$. For phage therapy, bacteriophages against to these subtype strains were applied to mushroom cultivation and very successful to prevent from the disease. In this study, bacteriophages were isolated against the representative strains of subtype pathogens and their polyclonal antibodies were synthesized to investigate structural relationship among capsid proteins of phages. Phage preparations over $10^{10}pfu/mL$ were injected to rabbit thigh muscle and polyclonal antibodies were obtained after three times of boost injection. Titers of the antibodies obtained were over $2{\times}10^7Ab/mL$ for the phage ${\phi}6264$, $1{\times}10^6Ab/mL$ for the phage ${\phi}HK2$, and $1{\times}10^7Ab/mL$ for the phage ${\phi}HK19$ and phage ${\phi}HK23$. High specific activities were observed between antibodies and the corresponding bacteriophages. Some cross-reactivities between the antibodies and non-corresponding bacteriophages were also measured. Antibody $Ab{\phi}6264$ inactivated all phages of $P1{\alpha}$ subtype and only phage ${\phi}HK16$ among $P1{\beta}$ subtype phages. Antibody $Ab{\phi}HK23$ of $P1{\gamma}$ subtype neutralized all phages of $P1{\beta}$ subtype as well as the phage ${\phi}HK23$, showing the widest phage-inactivation range. When the structural-similarity studies of phages were investigated by using phage antibodies, closeness obtained by phylogenetic analysis of 16S rRNA genes of pathogenic strains were quite different from that of polyclonal antibody-specific structural similarity of phage capsid proteins. In conclusion, there is weak correlation between the host strain specificity of bacteriophage and its capsid structural similarity measured by phage antibodies.