• Journal of the Chungcheong Mathematical Society
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• v.32 no.1
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• pp.1-14
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• 2019

We prove the generalized Hyers-Ulam-Rassias stability problem of the quadratic functional equation with involution in the fuzzy quasi ${\beta}$-normed space by using the fixed point method.

• Asian-Australasian Journal of Animal Sciences
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• v.20 no.2
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• pp.153-159
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• 2007

In our previous study, overexpression of extracellular proteinase inhibitor (Expi) gene accelerated apoptosis of mammary epithelial cells, and induced expression of B cell activating factor (BAFF) gene. In this study, we found induction of BAFF-receptor (BAFF-R) gene expression in the Expi-transfected cells. A proliferation-inducing ligand (APRIL) gene is another TNF family member and the closest known relative of BAFF. We found induction of APRIL gene expression in the Expi-overexpressed apoptotic cells. NF-${\kappa}$B gene was also induced in the Expi-overexpressed cells. Expression patterns of BAFF and APRIL pathway-related genes were examined in in vivo mouse mammary gland at various reproductive stages. Expression levels of BAFF gene were very low at early pregnancy, increased from mid-pregnancy, and peaked at lactation, and thereafter decreased at involution stages of mammary gland. Expression of BAFF-R gene was highly induced in involution stages compared to lactation stages. Thus, expression patterns of BAFF-R gene were correlated to apoptotic status of mammary gland: active apoptosis of mammary epithelial cells occurs at involution stage of mammary gland. Expression levels of NF-${\kappa}$B gene were higher in involution stages compared to lactation stages. We analyzed mRNA levels of bcl-2 family genes from different stages of mammary development. Bcl-2 gene expression was relatively constant during lactation and involution stages. There was a slight increase in bcl-xL gene expression in involution stages compared to lactation state. Bax gene expression was highly induced in involution stage. Our results suggest that signaling pathways activated by both BAFF and ARRIL in mammary gland point towards NF-${\kappa}$B activation which causes upregulation of bax.

• Proceedings of the KSAR Conference
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• 2001.03a
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• pp.59-59
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• 2001

Interleukin-10 (IL-10) is known as a regulator of inflammation and pathogenesis in mammalian organs, but its precise role is little known in the mammary gland. Our initial experiment showed that IL-10 expression levels in mice decreased at the lactation stage otherwise increased at the involution stage. To reveal the effects of IL-10 on the involution of mammary gland, expression profiles of the apoptosis-related genes were examined in transgenic mice expressing human IL-10 as well as in knock-out mice (IL-10-/-). Mild inflammatory legions by lymphocytes were observed in the mammary glands of transgenic lines at the lactation stage. The expression of TRAIL (Tumor necrosis factor-Related Apoptosis-Inducing Ligand) among the apoptosis-related genes was highly elevated in the transgenic mice while others were not significantly changed. Furthermore, TRAIL was down regulated by four fold in the IL-10-/- mice at the involution stage. The expression of DR4 was elevated at the involution stage of normal mice. DR4 was detected in the milk of transgenic mice but absent in that of normal mice. Our results proposed that the elevated IL-10 at the involution stage recruit lymphocytes and induce TRAIL and DR4 genes, therefore, lead to enter involution stage of mammary glands.

• Asian-Australasian Journal of Animal Sciences
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• v.14 no.4
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• pp.462-466
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• 2001

To understand molecular mechanisms of mouse mammary gland involution, clones were isolated by differential screening of a cDNA library. Partial sequences of a clone showed 100% identity to cDNA sequences of mouse lysozyme P gene. Northern analysis was performed to examine expression levels of lysozyme mRNA in mammary gland at several physiological states. Expression of lysozyme gene was induced at involution day 5 compared with lactating stage. High levels of lysozyme mRNA were also detected at virgin tissues. Two types of separate genes, P and M lysozyme, have been known in mouse, and we found that both lysozyme P and M genes were expressed in mammary tissues by reverse transcriptase-polymerase chain reaction. The lysozyme enzyme activity determined by lysoplate assay was also higher in involuted mammary tissues compared with lactating tissues, showing a similar trend to its mRNA levels. Lysozyme is an antimicrobial protein and involved in host defense mechanism. The increase in lysozyme gene expression may help to prevent microbial infection during mammary gland involution at which stage the residual milk in the mammary gland provides good nutritional sources for microbial growth.

• Korean Journal of Mathematics
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• v.18 no.3
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• pp.289-298
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• 2010

E$\breve{g}$ecio$\breve{g}$lu and Remmel [1] gave a combinatorial interpretation for the entries of the inverse Kostka matrix $K^{-1}$. Using this interpretation Sagan and Lee [8] constructed a sign reversing involution on special rim hook tableaux. In this paper we generalize Sagan and Lee's algorithm on special rim hook tableaux to give a combinatorial partial proof of $K^{-1}K=I$.

• Korean Journal of Mathematics
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• v.24 no.1
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• pp.41-49
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• 2016

In this paper, using xed point method, we prove the Hyers-Ulam stability of the following functional equation $$\hspace{15}f+(x+y+z)+f({\sigma}(x)+y+z)+f(x+{\sigma}(y)+z)+f(x+y+{\sigma}(z))\\=4f(x)+4f(y)+4f(z)$$ with involution in paranormed spaces.

• Journal of the Korean Mathematical Society
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• v.44 no.4
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• pp.757-766
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• 2007

In this note we construct an anti-symplectic involution on the non-$K\ddot{a}hler$, symplectic 4-manifold which is constructed by Thurston and show that the quotient of the Thurston's 4-manifold is not symplectic. Also we construct a non-$K\ddot{a}hler$, symplectic 4-manifold using the Gomph's symplectic sum method and an anti-symplectic involution on the non-$K\ddot{a}hler$, symplectic 4-manifold.

• Bulletin of the Korean Mathematical Society
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• v.56 no.3
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• pp.659-666
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• 2019

In this paper, we consider a conjecture of I. N. Herstein for local commutators of symmetric elements and unitary elements of division rings. For example, we show that if D is a finite dimensional division ring with involution ${\star}$ and if $a{\in}D^*=D{\setminus}\{0\}$ such that local commutators $axa^{-1}x^{-1}$ at a are radical over the center F of D for every $x{\in}D^*$ with $x^{\star}=x$, then either $a{\in}F$ or ${\dim}_F\;D=4$.

• Communications of the Korean Mathematical Society
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• v.39 no.1
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• pp.1-10
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• 2024

In this paper we will demonstrate some results on a prime ring with involution by introducing two generalized derivations acting on symmetric and skew symmetric elements. This approach allows us to generalize some well known results. Furthermore, we provide examples to show that various restrictions imposed in the hypotheses of our theorems are not superfluous.

• Communications of the Korean Mathematical Society
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• v.39 no.1
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• pp.79-91
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• 2024

This article examines the connection between 3-derivations and the commutativity of a prime ring R with an involution * that fulfills particular algebraic identities for symmetric and skew symmetric elements. In practice, certain well-known problems, such as the Herstein problem, have been studied in the setting of three derivations in involuted rings.