• Journal of applied mathematics & informatics
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• v.16 no.1_2
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• pp.251-263
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• 2004

In this paper, algorithms for computing the minimal polynomial and the common minimal polynomial of resultant matrices over any field are presented by means of the approach for the Grobner basis of the ideal in the polynomial ring, respectively, and two algorithms for finding the inverses of such matrices are also presented. Finally, an algorithm for the inverse of partitioned matrix with resultant blocks over any field is given, which can be realized by CoCoA 4.0, an algebraic system over the field of rational numbers or the field of residue classes of modulo prime number. We get examples showing the effectiveness of the algorithms.

• Carbon letters
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• v.5 no.4
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• pp.159-163
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• 2004

The polymer-ceramic hybrid, known as 'ceramer', was synthesized by a sol-gel process by incorporating different amount of alkoxide as source of silicon in resorcinol-formaldehyde in presence of basic catalyst to get different percentage of silicon in ultimate carbonized composites. FTIR of the ceramer confirms that it is a network of Si-O-Si, Si-O-$CH_2$ and Si-OH type groups linked with benzene ring. Different amount of silicon in the ceramer exhibits varying temperature of thermal stability and lower coefficient of thermal expansion as compared to pure resorcinol-formaldehyde resin. The lower value of CTE in ceramer is due to existence of silica and resorcinol -formaldehyde in co-continuous phase. Unidirectional composites prepared with ceramer matrix and high-strength carbon fibers show lower value of flexural strength at polymer stage as compared to those prepared with resorcinol-formaldehyde resin. However, after heat treatment to $1450^{\circ}C$, the ceramer matrix composites show large improvement in the mechanical properties, i.e. with 7% silicon in the ceramer, the flexural strength is enhanced by 100% and flexural modulus value by 40% as compared to that of pure resorcinol-formaldehyde resin matrix composites.

• Journal of the Korean Mathematical Society
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• v.52 no.6
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• pp.1323-1336
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• 2015

Let S be a semigroup with 0 and R be a ring with 1. We extend the definition of the zero-divisor graphs of commutative semigroups to not necessarily commutative semigroups. We define an annihilating-ideal graph of a ring as a special type of zero-divisor graph of a semigroup. We introduce two ways to define the zero-divisor graphs of semigroups. The first definition gives a directed graph ${\Gamma}$(S), and the other definition yields an undirected graph ${\overline{\Gamma}}$(S). It is shown that ${\Gamma}$(S) is not necessarily connected, but ${\overline{\Gamma}}$(S) is always connected and diam$({\overline{\Gamma}}(S)){\leq}3$. For a ring R define a directed graph ${\mathbb{APOG}}(R)$ to be equal to ${\Gamma}({\mathbb{IPO}}(R))$, where ${\mathbb{IPO}}(R)$ is a semigroup consisting of all products of two one-sided ideals of R, and define an undirected graph ${\overline{\mathbb{APOG}}}(R)$ to be equal to ${\overline{\Gamma}}({\mathbb{IPO}}(R))$. We show that R is an Artinian (resp., Noetherian) ring if and only if ${\mathbb{APOG}}(R)$ has DCC (resp., ACC) on some special subset of its vertices. Also, it is shown that ${\overline{\mathbb{APOG}}}(R)$ is a complete graph if and only if either $(D(R))^2=0,R$ is a direct product of two division rings, or R is a local ring with maximal ideal m such that ${\mathbb{IPO}}(R)=\{0,m,m^2,R\}$. Finally, we investigate the diameter and the girth of square matrix rings over commutative rings $M_{n{\times}n}(R)$ where $n{\geq} 2$.

• Transactions of the Korean Society of Mechanical Engineers
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• v.15 no.1
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• pp.1-10
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• 1991

Two-dimensional explicit finite element code was developed. The transient dynamics code can analyse large deformations of non-linear materials subjected to extremely high strain rates. The Lagrangian finite element program uses an explicit time integration operator to integrate the equations of motion, thus the stiffness matrix is not introduced. Cylinder upsetting and ring compression problems are simulated to check the effects of friction and inertia force. It is shown that (1) calculated results agree very well with experimental results, (2) constant shear friction method overestimates the decrease of inner ring radius and then underestimates after on in comparison with the Coulomb friction method, and (3) the effect of the increase in initial strain rate is similar to the effect of higher frictional coefficient.

• Bulletin of the Korean Chemical Society
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• v.15 no.12
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• pp.1108-1112
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• 1994

25-Acetoxy-26,27,28-trimethoxycalix[4]arene was synthesized by the treatment of calix[4]arene trimethyl ether with acetyl chloride in the presence of NaH. The solution conformation was inferred as a partial cone conformation based on the $^1H$-and $^{13}C$ NMR spectra. The crystal structure has been determined by X-ray diffraction method. The crystals are monoclinic, space group $P2_1$/n, a=8.186 (1), b=17.137 (2), c=19.878 (3) ${\AA}$, ${\beta}$=95.67 (1)$^{\circ}$, Z=4, V=2774.90 ${\AA}^3$, $D_c$= 1.22 g $cm^{-3}$, $D_m$=1.23 g $cm^{-3}$. The intensity data were collected on an Enraf-Noninus CAD-4 Diffractometer with a graphite monochromated $Cu-K{\alpha}$ radiation. The structure was solved by direct method and refined by full-matrix least-squares methods to a final R value of 0.054 for 3675 observed reflections. The molecule possesses a partial cone conformation with one flattened phenyl unit, in which one anisol ring, distal to the ester ring, is inverted. The acetoxyphenyl ring is flattened.

• Journal of the Korean Mathematical Society
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• v.48 no.2
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• pp.301-309
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• 2011

Let R = $Mat_2(F)$ be the ring of all 2 by 2 matrices over a finite field F, X the set of all nonzero, nonunits of R and G the group of all units of R. After investigating some properties of orbits under the left (and right) regular action on X by G, we show that the graph automorphisms group of $\Gamma(R)$ (the zero-divisor graph of R) is isomorphic to the symmetric group $S_{|F|+1}$ of degree |F|+1.

• Communications of the Korean Mathematical Society
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• v.20 no.2
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• pp.275-290
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• 2005

Let $S\;=\;R[\chi_{ij}\mid1\;{\le}\;i\;{\le}\;m,\;1\;{\le}\;j\;{\le}\;n]$ be the polynomial ring over a noetherian commutative ring R and $I_p$ be the determinantal ideal generated by the $p\;\times\;p$ minors of the generic matrix $(\chi_{ij})(1{\le}P{\le}min(m,n))$. We describe a minimal free resolution of $S/I_{p}$, in the case m = n = p + 2 over $\mathbb{Z}$.

• Bulletin of the Korean Chemical Society
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• v.3 no.1
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• pp.9-13
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• 1982

Sulfametrole, $C_9H_{10}N_4O_3S_2$, crystallizes in the monoclinic system, space group $P2_1/n$ , with a = 8.145(2), b = 16.505(4), c = 9.637(1)${\AA},{\beta}=103.72(1)^{\circ},D_m=1.52gcm^{-3}$,Z=4.Intensities for 3594(2143 observed) unique reflections were measured on a four-circle diffractometer with Mo $K{\alpha}$ radiation $({\lambda}=0.71069{\AA})$. The structure was solved by direct method and refined by full-matrix least squares to a final R of 0.070. The geometrical features of the thiadiazole ring indicate some ${pi}$-electron delocalization inside the ring. The least squares planes defined by the benzene and thiadiazole rings are nearly perpendicular to each other(dihedral angle; $93.9^{\circ}$ ). All the potential hydrogen-bond donor atoms in the molecule, N(1) and N(2), are included in the hydrogen bonding. The molecules through hydrogen bonding form three dimensional network.

• Bulletin of the Korean Chemical Society
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• v.6 no.4
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• pp.222-224
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• 1985

The crystal structure of sulindac, $C_{20}H_{17}Fo_3S$, one of the nonsteroid antiinflammatory agents, has been determined by the X-ray diffraction techniques using diffractometer data obtained by the $\varpi-2{\theta}$ scan technique with Cu $$K_{\alpha}$$ radiation from a crystal with space group symmetry Pbca and unit cell parameters a = 8.166(1), b = 18.291(8), c = 23.245(10) ${\AA}.$ The structure was solved by direct methods and refined by full-matrix least-squares to a final R = 0.11 for the 1153 observed reflections. The carboxyl group is nearly perpendicular to the indenyl ring as observed in indomethacin. The dihedral angle between the indenyl and phenyl rings is $35^{\circ}while$ the corresponding angle in indomethacin is $67^{\circ}.$ Crystal packing consists of a hydrogen bond and partial ring stacking between the indenyl rings.

• Transactions of the Korean Society of Mechanical Engineers
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• v.19 no.9
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• pp.2122-2132
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• 1995

There are some cases which require to grasp the abrasion resistance property in the fields of the high-technology to be required the high specific strength and modulus. In this study, wear test with the various test temperature and velocity were performed in the SiCw/A16061 composite and A16061 matrix using the wear test machine of the ring-on-disc type. As the results, the friction and wear properties by various test temperature and velocity were examined. The worn surface has observed by scanning electron microscope in order to examine the wear mechanism.