• 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 $x{\in}R$.

• Bulletin of the Korean Mathematical Society
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• v.48 no.6
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• pp.1253-1259
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• 2011

Let R be a prime ring, I a nonzero ideal of R and n a fixed positive integer. If R admits a generalized derivation F associated with a derivation d such that c for all x, $y{\in}I$. Then either R is commutative or n = 1, d = 0 and F is the identity map on R. Moreover in case R is a semiprime ring and $(F([x,\;y]))^n=[x,\;y]$ for all x, $y{\in}R$, then either R is commutative or n = 1, $d(R){\subseteq}Z(R)$, R contains a non-zero central ideal and for all $x{\in}R$.

• Journal of the Korean Mathematical Society
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• v.52 no.1
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• pp.191-207
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• 2015

Let $\mathcal{R}$ be a prime ring of characteristic different from 2, $\mathcal{Q}_r$ be its right Martindale quotient ring and $\mathcal{C}$ be its extended centroid. Suppose that $\mathcal{G}$ is a nonzero generalized skew derivation of $\mathcal{R}$, ${\alpha}$ is the associated automorphism of $\mathcal{G}$, f($x_1$, ${\cdots}$, $x_n$) is a non-central multilinear polynomial over $\mathcal{C}$ with n non-commuting variables and $$\mathcal{S}=\{f(r_1,{\cdots},r_n)\left|r_1,{\cdots},r_n{\in}\mathcal{R}\}$$. If $\mathcal{G}$ acts as a Jordan homomorphism on $\mathcal{S}$, then either $\mathcal{G}(x)=x$ for all $x{\in}\mathcal{R}$, or $\mathcal{G}={\alpha}$.

• Communications of the Korean Mathematical Society
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• v.33 no.4
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• pp.1113-1121
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• 2018

Let R be a prime ring (or semiprime ring) with center Z(R), I a nonzero ideal of R, T an automorphism of $R,S:R^n{\rightarrow}R$ be a symmetric skew n-derivation associated with the automorphism T and ${\Delta}$ is the trace of S. In this paper, we shall prove that S($x_1,{\ldots},x_n$) = 0 for all $x_1,{\ldots},x_n{\in}R$ if any one of the following holds: i) ${\Delta}(x)=0$, ii) [${\Delta}(x),T(x)]=0$ for all $x{\in}I$. Moreover, we prove that if $[{\Delta}(x),T(x)]{\in}Z(R)$ for all $x{\in}I$, then R is a commutative ring.

• Kyungpook Mathematical Journal
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• v.47 no.1
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• pp.1-20
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• 2007

In this paper, oscillation and nonoscillation criteria are established for nonlinear neutral delay differential equations with several positive and negative coefficients $$[x(t)-R(t)x(t-r)]^{\prime}+\sum_{i=1}^{m}Pi(t)H_i(x(t-{\tau}_i))-\sum_{j=1}^{n}Q_j(t)H_j(x(t-{\sigma}_j))=0$$. Our criteria improve and extend many results known in the literature. In addition we prove that under appropriate hypotheses, if every solution of the associated linear equation with constant coefficients, $$y^{\prime}(t)+\sum_{i=1}^{m}(p_i-\sum_{k{\in}J_i}qk)y(t-{\tau}_i)=0$$, oscillates, then every solution of the nonlinear equation also oscillates.

• Communications of the Korean Mathematical Society
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• v.13 no.4
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• pp.759-764
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• 1998

We define the rational lens algebra (equation omitted)(n) as the crossed product by an action of Z on C( $S^{2n＋l}$). Assume the fibres are $M_{ k}$/(C). We prove that (equation omitted)(n) $M_{p}$ (C) is not isomorphic to C(Prim((equation omitted)(n))) $M_{kp}$ /(C) if k > 1, and that (equation omitted)(n) $M_{p{\infty}}$ is isomorphic to C(Prim((equation omitted)(n))) $M_{k}$ /(C) $M_{p{\infty}}$ if and only if the set of prime factors of k is a subset of the set of prime factors of p. It is moreover shown that if k > 1 then (equation omitted)(n) is not stably isomorphic to C(Prim(equation omitted)(n))) $M_{k}$ (c).

• Progress in Medical Physics
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• v.27 no.4
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• pp.189-195
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• 2016

This paper aims to verify the clinical feasibility of a custom-made film created by a laser cutting tool for End-to-End (E2E) quality assurance in robotic intensity modulated radiation therapy system. The custom-made film was fabricated from the Gafchromic EBT3 film with the size of $8^{{\prime}{\prime}}{\times}10^{{\prime}{\prime}}$ using a drawing that is identical to the shape and scale of the original E2E film. The drawing was created by using a computer aided design program with the image file, which is obtained by scanning original E2E film. Beam delivery and evaluations were respectively performed with the original film and the custom-made film using fixed-cone collimator on three tracking modes: 6D skull (6DS), Xsight spine (XS), and Xsight lung (XL). The differences between total targeting errors of the original and custom-made films were recorded as 0.17 mm, 0.3 mm, and 0.17 mm at 6DS, XS, and XL tracking modes, respectively. This indicates that the custom-made film could yield nearly equivalent results to those of the original E2E film, given the uncertainties caused by distortions during film scanning and vibrations associated with film cutting. By confirming the clinical feasibility of a custom-made film for E2E testing, it can be expected that economic efficiency of the testing will increase accordingly.

• Korean Journal of Community Nutrition
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• v.21 no.5
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• pp.451-462
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• 2016

Objectives: This study was designed with the goal of understanding the factors affecting the frequency of skipping meals of prime-aged mothers with children as well as their nutritional status. Methods: Utilizing data from the 2010-2011 Korea National Health and Nutrition Survey, the frequency of skipping meals of mothers aged between 30 to 49 years with children aged between 3 to 11 years during a two day period was statistically analyzed. The number of meals skipped calculated and categorized into skipping no meals, skipping one meal, skipping two meals or more. Results: Compared to subjects who corresponded to mean nutrient adequacy ratio(MAR) of 4 quartile, subjects who corresponded to MAR of 2 quartile had 2.766 (95% CI: 1.552-4.931) probability of being in the 1 meal skippers group, while the probability of being in the more than 2 meals skippers group was 2.743(95% CI: 1.353-5.564). Also, compared to subjects who corresponded to MAR of 4 quartile, subjects who corresponded to MAR of 1 quartile had 3.471 (95% CI: 1.871-6.442) probability of being in the 1 meal skippers group, while the odds ratio for being in the more than 2 meals skippers group was 5.258(95% CI: 2.642-10.466). Conclusions: The results have the advantage of being generalized because the study selected subjects from probability sampling of the female population of Korea. The research results showed that the elements influencing skipping meals of prime-aged mothers with children were mean nutrient adequacy ratio and the number of nutrients, under estimated average requirement intake, and others. Therefore, to encourage dietary behaviors in the right direction, an integrated approach that considers the associated factors must be realized. Future studies are needed to understand how the frequency of skipping meals of mothers affects their children.

• CELLMED
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• v.11 no.1
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• pp.3.1-3.6
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• 2021

Ascites is the accumulation of fluid in the peritoneal cavity, and it is generally allied with liver disease like cirrhosis of the liver. The ascites is commonly associated with liver cirrhosis, malignancy, or cardiovascular disease today. The liver cirrhosis is the most significant cause of ascites in developed countries as per the available data. In the modern medicine system, the treatment includes the restriction of sodium intake, use of diuretics, and paracentesis done in severe cases. There are many side effects of synthetic chemical diuretics, and their long-term use is not recommended. The alternative medicine like Unani system of medicine provides natural diuretics and drugs which also have protective effects on kidney, liver and other internal organs. It is well known in all drug systems that the prognosis is poor in ascites, but the use of Unani herbal medicines can minimize the side effects caused by synthetic chemical diuretics. The natural herbs used for the management of ascites have fewer side effects as compared to synthetic drugs. The natural drugs can be used for longer duration and provide some dietary supplement which improves the quality of life. This review addressed the thorough treatment of ascites by natural diet and medications.

• Journal of the Korean Mathematical Society
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• v.47 no.3
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• pp.633-643
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• 2010

Let a be an ideal of a commutative Noetherian ring R, M a finitely generated R-module and N a weakly Laskerian R-module. We show that if N has finite dimension d, then $Ass_R(H^d_a(N))$ consists of finitely many maximal ideals of R. Also, we find the least integer i, such that $H^i_a$(M, N) is not consisting of finitely many maximal ideals of R.