• Bulletin of the Korean Mathematical Society
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• v.56 no.3
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• pp.779-787
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• 2019

In this paper, we study two functional equations with two unknown functions from an Abelian group into a commutative ring without zero divisors. The two equations are generalizations of Swiatak's functional equations with an involution. We determine the general solutions of the two functional equations and the properties of the general solutions of the two functional equations under three different hypotheses, respectively. For one of the functional equations, we establish the Hyers-Ulam stability in the case that the unknown functions are complex valued.

• Communications of the Korean Mathematical Society
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• v.37 no.3
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• pp.659-667
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• 2022

This paper treats the commutativity of prime rings with involution over which elements satisfy some specific identities involving endomorphisms. The obtained results cover some well-known results. We show, by given examples, that the imposed hypotheses are necessary.

• Bulletin of the Korean Mathematical Society
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• v.58 no.6
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• pp.1409-1418
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• 2021

In this paper, we study domination in the zero-divisor graph of a *-ring. We first determine the domination number, the total domination number, and the connected domination number for the zero-divisor graph of the product of two *-rings with componentwise involution. Then, we study domination in the zero-divisor graph of a Rickart *-ring and relate it with the clique of the zero-divisor graph of a Rickart *-ring.

• Communications of the Korean Mathematical Society
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• v.39 no.2
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• pp.279-302
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• 2024

In this paper, we summarise and present results on involution lengths and commutator lengths of certain linear groups such as special linear groups, projective linear groups, upper triangle matrix groups and Vershik-Kerov groups. Some open problems motivated by these results are also proposed.

• The Journal of Korean Medicine Ophthalmology and Otolaryngology and Dermatology
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• v.23 no.2
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• pp.1-12
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• 2010

Objective : For this study, mice on mercurial toxication were given mercuric subcutaneous injection to their abdomen factitiously. After delivering Kami- bangpungtongseong-san(KBT) extracts to the mice by oral administration, we observed changes from liver and kidney of mice. Method : The BALB/c mice were distributed into three groups: No treated group(Normal group), Mercuric chloride subcutaneous injection group(Control group), Kami-bangpungtongseong-san-treated group (Sample group). KBT Extracts were delivered orally in 7 days. We observed involution of liver, necrosis of liver and cell plate loss of liver, lipid peroxidation CYP1A1 expression. We observed involution of proximal convoluted tubules, hypertrophy of Bowman's capsule, periodic acid-Schiff(PAS)'s positive reaction of proximal convoluted tubules, heat shock protein(HSP)700's positive reaction in glomerulus. For the charting the results, image analysis was taken. The result of image analysis was verified significance by Sigmaplot 2000(P<0.05). Result : The mice' liver on mercurial toxication were relieved involution of liver, necrosis of liver, and cell plate loss of liver and also declined lipid peroxidation and CYP1A1 expression. The mice' kidney on mercurial toxication were relieved involution of proximal convoluted tubules, hypertrophy of Bowman's capsule and increasing PAS's positive reaction of proximal convoluted tubules. On the other hand it was declined HSP700's positive reaction in glomerulus. Conclusion : According to the result of study, we think that we can expect to the effect of KBT extracts' therapeutic action to tissue injuries of the mice' liver and kidney on acute mercurial toxication.

• Journal of Veterinary Clinics
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• v.12 no.1
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• pp.819-827
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• 1995

An attempt to reproduce pyometra by means of experimental uterine infection was conducted with the 10 mongrel hitches of the anestrus, proestrus, metestrus, and postpartum uterine involution stages. Organism used was hemoltic E. coli. origially isolated from uterine pus of a bitch that had the canine pyometra. One ml of broth culture containing $2{\times}10^6$ CFU was inoculated into the uterine horn with the uterine cervix ligated. Aか bitches were ovariohysterectomized at the 7th or 14th day after inoculation and the uterus was provided for macroscopic and microscopic observations. An experimental production of pyometra was successful in 7(70%) of 10 mongrel bitches, and the incidence of pyometra was seen 100% in the stage of anestrus, 100% in the stage of metestrus, 50.0% in the stage of pyomestrus, and 33.359 in the stage of uterine involution. Histologically, these uteri were characterized by the presence of cystic. endomeetrial hyperplasia(CEH) and acute endometritis superimposed on the cystic hyperplasia. And the pyometra with CEH could be seen 66.7% in metestrus 50% in anestrus, 33.3% in involution and in 0% in proestrus stage. Blood progesterone concentrations were showed as a normal range of the each stage of sexual cycle and any relationships between the progesterone concentrations and the incidence of pyometra were not observed.

• Kyungpook Mathematical Journal
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• v.59 no.1
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• pp.1-11
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• 2019

Let R be a prime ring with involution of the second kind and centre Z(R). Suppose R admits a generalized derivation $F:R{\rightarrow}R$ associated with a derivation $d:R{\rightarrow}R$. The purpose of this paper is to study the commutativity of a prime ring R satisfying any one of the following identities: (i) $F(x){\circ}x^*{\in}Z(R)$ (ii) $F([x,x^*]){\pm}x{\circ}x^*{\in}Z(R)$ (iii) $F(x{\circ}x^*){\pm}[x,x^*]{\in}Z(R)$ (iv) $F(x){\circ}d(x^*){\pm}x{\circ}x^*{\in}Z(R)$ (v) $[F(x),d(x^*)]{\pm}x{\circ}x^*{\in}Z(R)$ (vi) $F(x){\pm}x{\circ}x^*{\in}Z(R)$ (vii) $F(x){\pm}[x,x^*]{\in}Z(R)$ (viii) $[F(x),x^*]{\mp}F(x){\circ}x^*{\in}Z(R)$ (ix) $F(x{\circ}x^*){\in}Z(R)$ for all $x{\in}R$.

• The Journal of the Korea institute of electronic communication sciences
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• v.6 no.2
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• pp.171-179
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• 2011

Feistel and SPN are the two main structures in a block cipher. Feistel is a symmetric structure which has the same structure in encryption and decryption, but SPN is not a symmetric structure. Encrypt round function and decrypt round function in SPN structure have three parts, round key addition and substitution layer with S-box for confusion and permutation layer for defusion. Most SPN structure for example ARIA and AES uses 8 bit S-Box at substitution layer, which is vulnerable to Square attack, Boomerang attack, Impossible differentials cryptanalysis etc. In this paper, we propose a SPN which has a symmetric structure in encryption and decryption. The whole operations of proposed algorithm are composed of the even numbers of N rounds where the first half of them, 1 to N/2 round, applies a right function and the last half of them, (N+1)/2 to N round, employs an inverse function. And a symmetry layer is located in between the right function layer and the inverse function layer. The symmetric layer is composed with a multiple simple bit slice involution S-Boxes. The bit slice involution S-Box symmetric layer increases difficult to attack cipher by Square attack, Boomerang attack, Impossible differentials cryptanalysis etc. The proposed symmetric SPN block cipher with bit slice involution S-Box is believed to construct a safe and efficient cipher in Smart Card and RFID environments where electronic chips are built in.

• Journal of Veterinary Clinics
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• v.22 no.3
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• pp.233-238
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• 2005

This study was undertaken to determine the normal serial ultrasonographic appearance of the postpartum uterine involution. Postpartum changes in uterine shape, architecture, echogenicity and diameter were monitored by ultrasonography in 10 Shih-tzu bitches. Serial ultrasonographic examination was done daily during the first week, 3 days interval from 8 to 30 days, and weekly from 31 to 100 days postpartum. All 10 postpartum bitches had normal involution by gross finding, vaginal discharges, and by ultrasonographic findings, uterine shape and echogenicity. The uterine diameter in the placental sites was decreased from $23.56{\pm}1.45$ mm at 1 day to $14.08{\pm}1.55$ mm at 7 day, and in the interplacental sites was decreased from $14.64{\pm}1.28$mm at 1day to $9.61{\pm}1.46$mm at 7 day postpartum. At 65 days postpartum the uterine diameter was 5-6 mm both placental and interplacental sites, and the uterine horns were uniform hypoechic, tubular structures without enlargement. Therefore, complete involution of the uterus occured 65 days. It was concluded that normal postpartum uterine involution in Shih-tzu bitches appeared to be completed 65 days postpartum by gross findings such as vaginal discharges, and ultrasonographic findings. And ultrasonographic characteristics of the postpartum uterine involution were described. Therefore, these result suggest that ultrasonographic assessment is a reliable method for diagnosing the subinvolution of placental sites and uterine dysfunction, such as pyometra in the bitch.

• Journal of the Korean Mathematical Society
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• v.14 no.1
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• pp.33-40
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• 1977