• Korean Journal of Mathematics
• /
• v.26 no.3
• /
• pp.537-544
• /
• 2018

There is a standard construction of lifting cyclic codes over the prime finite field ${\mathbb{Z}}_p$ to the rings ${\mathbb{Z}}_{p^e}$ and to the ring of p-adic integers. We generalize this construction for arbitrary finite fields. This will naturally enable us to lift codes over finite fields ${\mathbb{F}}_{p^r}$ to codes over Galois rings GR($p^e$, r). We give concrete examples with all of the lifts.

• Kyungpook Mathematical Journal
• /
• v.51 no.2
• /
• pp.177-185
• /
• 2011

A right ideal I of a ring R is small in case for every proper right ideal K of R, K + I ${\neq}$ = R. A right R-module M is called PS-injective if every R-homomorphism f : aR ${\rightarrow}$ M for every principally small right ideal aR can be extended to R ${\rightarrow}$ M. A ring R is called right PS-injective if R is PS-injective as a right R-module. We develop, in this article, PS-injectivity as a generalization of P-injectivity and small injectivity. Many characterizations of right PS-injective rings are studied. In light of these facts, we get several new properties of a right GPF ring and a semiprimitive ring in terms of right PS-injectivity. Related examples are given as well.

• Applied Biological Chemistry
• /
• v.43 no.2
• /
• pp.95-99
• /
• 2000

A series of hetero ring (X) substitued chalcone derivatives with farnesyl protein transferase (FPTase) inhibition activities $(pI_{50})$ values determined in vitro is analyzed by modified Free-Wilson (F-W) and Hansch method for quantitative structure activity relationship (QSARs). On the basis of F-W analysis on the FPTase inhibitory activity of a training set of the compounds, none of the (X)-substituents were not contribute the activity. But the net charge of ${\alpha}$ carbon atom is contribute the activity than that of ${\beta}$ carbon atom. And the relative orders of the (Y)-substituents on the activity are ortho>meta>para-substituents. According to Hansch approach, the activities would depend largely on the optimal, $(R_{opt.}=-0.35)$ resonance effect with ortho substituted $(I_o>0)$ electron donating group (R<0) and STERIMOL parameter, $B_1$ constant. The inhibition activity between hetro ring substituents have been a proportioned with each others and none substituent(H), 45 showed the highest FPTase inhibition $(pI_{50}=4.30)$ activity.

• Communications of the Korean Mathematical Society
• /
• v.39 no.1
• /
• pp.31-43
• /
• 2024

Let $R_e\,=\,\frac{{\mathbb{F}}_{p^m}[u]}{{\langle}u^e{\rangle}}$, where p is a prime number, e is a positive integer and u^e = 0. In this paper, we first characterize the structure of cyclic codes of length p^s over R_e. These codes will be classified into 2^e distinct types. Among other results, in the case that e = 4, the torsion codes of cyclic codes of length p^s over R₄ are obtained. Also, we present some examples of cyclic codes of length p^s over R_e.

• Bulletin of the Korean Chemical Society
• /
• v.10 no.2
• /
• pp.132-133
• /
• 1989

To probe the geometrical effects of cyclopropyl moiety on the stabilization of an adjacent cation center, chemical shift of 2-p-fluorophenyl-8,9-dehydro-2-adamantyl cation (3) was compared with that of 5-p-fluorophenyl-2,4-dehydro-5-homoadamantyl cation (4). Difference between the chemical shift of 8,9-dehydro-2-adamantyl cation 3 and that of 2,4-dehydro-5-adamantyl cation 4 is 5.1 ppm (${\Delta}{\Delta}{\delta}$). We conclude, therefore, that ion 3 is about 3.82 kcal more stadble than ion 4 of which rigid carbon skeleton requires significant distortion of the cyclopropane ring from the ideal bisected conformation. The energy difference between these cations can be calculated by Taft-Relationship$^8$ on the basis of chemical shift.

• Bulletin of the Korean Mathematical Society
• /
• v.56 no.1
• /
• pp.131-150
• /
• 2019

In this paper, we consider the structure of ${\gamma}$-constacyclic codes of length $2p^s$ over the Galois ring $GR(p^a,m)$ for any unit ${\gamma}$ of the form ${\xi}_0+p{\xi}_1+p^2z$, where $z{\in}GR(p^a,m)$ and ${\xi}_0$, ${\xi}_1$ are nonzero elements of the set ${\mathcal{T}}(p,m)$. Here ${\mathcal{T}}(p,m)$ denotes a complete set of representatives of the cosets ${\frac{GR(p^a,m)}{pGR(p^a,m)}}={\mathbb{F}}p^m$ in $GR(p^a,m)$. When ${\gamma}$ is not a square, the rings ${\mathcal{R}}_p(a,m,{\gamma})=\frac{GR(p^a,m)[x]}{{\langle}x^2p^s-{\gamma}{\rangle}}$ is a chain ring with maximal ideal ${\langle}x^2-{\delta}{\rangle}$, where ${\delta}p^s={\xi}_0$, and the number of codewords of ${\gamma}$-constacyclic code are provided. Furthermore, the self-orthogonal and self-dual ${\gamma}$-constacyclic codes of length $2p^s$ over $GR(p^a,m)$ are also established. Finally, we determine the Rosenbloom-Tsfasman (RT) distances and weight distributions of all such codes.

• Journal of the Korean Chemical Society
• /
• v.29 no.3
• /
• pp.213-219
• /
• 1985

The relative stability as a function of geometry in rigid cyclopropylcarbinyl cations was examined by $^{19}$F-nmr spectroscopy. 8-p-Fluorophenyl-tricyclo[3.3.1.0$^{2,7}$]octane-8-yl-(I), 9-p-fluorophenyl-tricyclo[3.3.1.0$^{2,8}$]nonane-9-yl (II), and 10-p-fluorophenyl-tricyclo[4.3.1.0$^{2,9}$]decane-10-yl cation(Ⅲ) were prepared from the corresponding carbinols in FSO$_3$H-SO$_2$ClF solution at -120$^{\circ}C$. $^{19}$F-nmr data indicate that the symmetrical bisected geometry of cyclopropane ring for ${\sigma}$-conjugation is a very impotant factor in charge delocalization. However, varied orientation of the bond angle ${\theta}$ within the bisected conformation does not affect the charge delocalization into the cyclopropane ring.

• Archives of Pharmacal Research
• /
• v.12 no.1
• /
• pp.52-57
• /
• 1989

The structure of cinmetacin was determined by single crystal X-ray diffraction analysis. The compound was recrystallized from a mixture of acetone and water in orthorhombic, space group $P2_12_12_1$, with Z=4, a=35.681(8), b=9.482(2), c:5.071(1) ${\AA}$, $D_x=1.352 g/cm^3$, and $D_m=1.35g/cm^3$. The structure was solved by direct method and refined by least-squares procedure to the final R value of 0.036 for 1441 observed reflections ($F{\geq}3{\sigma}(F)$). The carboxyl group of the molecule is nearly perpendicular to the indole ring. The dihedral angle between indole ring and phenyl group is $64.5^{\circ}$. The molecules are linked together via O(1)-H ----O(3) hydrogen bonds, and arranged along 2-fold screw axis in the crystal. The intermolecular contacts are the normal van der Waals' forces.

• Food Science of Animal Resources
• /
• v.43 no.2
• /
• pp.359-373
• /
• 2023

This study examined the α-glucosidase inhibitory, and apoptosis- and anti-muscular-related factors of goat meat extracts from forelegs, hind legs, loin, and ribs. The goat meat extracts were evaluated for their α-glucosidase inhibitory activity. The gene and protein expression levels of Bcl-2-associated X (bax), p53, and p21 were examined by reverse transcription polymerase chain reaction (RT-PCR) and immunoblotting in AGS and HT-29 cells. The expression levels of Atrogin-1 and MHC1b were examined by RT-PCR in C2C12 myoblasts, and the expression levels of Atrogin-1, muscle atrophy F-box (MAFbx), muscle RING-finger protein-1 (MuRF-1), and myosin heavy chain-7 were investigated by immunoblotting. α-Glucosidase inhibitory activity was higher in ethanol extract than in hydrous and hot water extracts. BAX and p53 expression levels were higher (p<0.05) in AGS cells treated with goat meat extract than those of cells treated with no goat meat extract. In HT-29 cells, the protein expression levels of BAX, p53, and p21 were higher (p<0.05) in the cells treated with goat meat extract than those of cells not treated with goat meat extract. In dexamethasone-treated C2C12 cells, goat meat extract treatment lower (p<0.05) the expression of Atrogin-1 and lower (p<0.05) the expression of MAFbx and MuRF-1. The results of the present study indicate that goat meat extracts have α-glucosidase inhibitory activity in vitro. In addition, apoptosis was induced in AGS cells and HT-29 cells treated with goat meat extract, and anti-muscular atrophy activity was also observed in C2C12 cells treated with goat meat extract.

• Korean Journal of Optics and Photonics
• /
• v.11 no.4
• /
• pp.221-226
• /
• 2000

We observed the spatial distributions of atom in a magneto-optical trap. These distributions include sphere, stick, ring, ring with core, sphere-sphere, sphere-ring etc. Coordinate-dependent asymmetry radiation force (CDARF) that arises due to laser beams misalignment and transverse profile of the laser beams is exerted on atoms, and the shape of trapped cloud is changed with the misalignment parameter. We use equations of motion that takes into account the Zeeman sublevels of the 87Rb atom, magnitude and direction of magnetic field, polarization of trapping lasers, and transverse profile of the laser beams. A theoretical analysis of the equation of motion for the trapped atom explained all the experimental observations.