• Honam Mathematical Journal
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• v.34 no.1
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• pp.45-54
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• 2012

In this paper, we prove stabilities of multiplicative functional equations in three variables such as $r(\frac{x+y+z}{3})-r(x+y+z)$=$\frac{2r(\frac{x+y}{2})r(\frac{y+z}{2})r(\frac{z+x}{2})}{r(\frac{x+y}{2})r(\frac{y+z}{2})+r(\frac{y+z}{2})r(\frac{z+x}{2})+r(\frac{z+x}{2})r(\frac{x+y}{2})}$ and $r(\frac{x+y+z}{3})+r(x+y+z)$=$\frac{4r(\frac{x+y}{2})r(\frac{y+z}{2})r(\frac{z+x}{2})}{r(\frac{x+y}{2})r(\frac{y+z}{2})+r(\frac{y+z}{2})r(\frac{z+x}{2})+r(\frac{z+x}{2})r(\frac{x+y}{2})}$.

• Honam Mathematical Journal
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• v.46 no.3
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• pp.365-377
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• 2024

In this paper, we give some sums involving the generalized harmonic numbers H^r_n (σ) and the (q, r)-binomial coefficient $\left({L \atop k}\right)_{q,r}$ by using Euler's transform. For example, for (c, r) ∈ ℤ⁺ × ℝ⁺, $${\sum_{n=0}^{\infty}}{\sum_{k=0}^{n}}\,(-1)^k\,\left({n+r \atop n-k}\right)\frac{c^{n+1}H^{r-1}_k({\sigma})}{(n+1)(1+c)^{n+1}}=-(c+{\frac{1}{{\sigma}}})\,{\ln}\,(1+c{\sigma})+c,$$ and $${\sum_{k=0}^{n}}\left({n \atop k}\right)\left({L \atop k}\right)_{2,r}={\sum_{j=0}^{n}}{\sum_{k=0}^{j}}(-1)^k\left({j-k+2L+r \atop j-k}\right)\left({r \atop n-j}\right)\left({L \atop k}\right)_2,$$ where σ is appropriate parameter, H^r_n (σ) is the generalized hyperharmonic number of order r and $\left({L \atop k}\right)_q$ is the q-binomial coefficient.

• The Mathematical Education
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• v.12 no.2
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• pp.5-12
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• 1974

단위원을 가지는 하환환에 있어서의 Prime Spectrum에 관하여 다음 세가지 사실을 증명하였다. 1. X를 환 R의 prime spectrum, C(X)를 X에서 정의되는 실연적함수의 환, X를 C(X)의 maximal spectrum이라 하면 X는 C(X)의 prime spectrum의 부분공간으로서의 한 T-space로 된다. N을 환 R의 nilradical이라 하면, R/N이 regula 이면 X와 X는 위상동형이다. 2. f: R$\longrightarrow$R'을 ring homomorphism, P를 R의 한 Prime ideal, $R_{p}$, R'$_{p}$를 각각 S=R-P 및 f(S)에 관한 분수환(ring of fraction)이라 하고, k(P)를 local ring $R_{p}$의 residue' field라 할 때, R'의 prime spectrum의 부분공간인 $f^{*-1}$(P)는 k(P)(equation omitted)$_{R}$R'의 prime spectrum과 위상동형이다. 단 f*는 f*(Q)=$f^{-1}$(Q)로서 정의되는 함수 s*:Spec(R')$\longrightarrow$Spec(R)이다. 3. X를 환 S의 prime spectrum, N을 R의 nilradical이라 할 때, 다음 네가지 사실은 동치이다. (1) R/N 은 regular 이다. (2) X는 Zarski topology에 관하여 Hausdorff 공간이다. (3) X에서의 Zarski topology와 constructible topology와는 일치한다. (4) R의 임의의 원소 f에 대하여 f를 포함하지 않는 R의 prime ideal 전체의 집합 $X_{f}$는 Zarski topology에 관하여 개집합인 동시에 폐집합이다.폐집합이다....

• Journal of the Korean Mathematical Society
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• v.37 no.4
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• pp.521-530
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• 2000

We find the values of numerical invariants col(R) and row (R) for R=k[te, te+1, t(e-1)e-1] where k is a field and e$\geq$4. We also show that col(R) = crs (R) and row (R) = drs(R), but they are strictly less than the reduction number of R plus 1.

• The Korean Nurse
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• v.33 no.3
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• pp.79-91
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• 1994

The purpose of this study was to identify the meaningful nursing diagnosis in maternity unit and to suggest formally the basal data to the nursing service with scientific approach. The subject for this paper were 64 patients who admitted to Chung Ang University Hospital, Located in Seoul, from Mar. 10, to July 21, 1993. The results were as follows: 1. The number of nursing diagnosis from 64 patients were 892 and average number of nursing diagnosis per patient was 13.9. 2. Applying the division of nursing diagnosis to Roy's Adaptation Model, determined nursing diagnosis from the 64 patients were 621 (69.6%) in physiological adaptation mode and (Comfort, altered r/t), (Injury, potential for r/t), (Infection, potential for r/t), (Bowel elimination, altered patterns r/t), (Breathing pattern, ineffective r/t), (Nutrition, altered r/t less than body requirement) in order, and 139 (15.6%) in role function mode, (Self care deficit r/t), (Knowledge deficit r/t), (Mobility, impaired physical r/t) in order, 122 (13.7%) in interdependence adaptation mode, (Anxiety r/t), (Family Process, altered r/t) in order, 10(1.1%) in self concept adaptation mode, (Powerlessness r/t), (Grieving, dysfunctional r/t) in order. 3. Nursing diagnosis in maternity unit by the medical diagnosis, the average hospital dates were 3.8 days in normal delivery and majority of used nursing diagnosis, (Comfort, altered r/t) 64.6%, (Self care deficit r/t) 13.6% in order, and the average hospital dates were 9.6 days in cesarean section delivery and majority of used nursing diagnosis, (Comfort, altered r/t) 51.6%, (Self care deficit r/t) 15.2%, (Infection, potential for r/t) 9.9%, (Injury, potential "for r/t) 8.1%, (Anxiety r/t) 5.0%, (Mobility, impaired physical r/t) 3.3% in order, and the average hospital dates were 15.8days in preterm labor and majority of used nursing diagnosis, (Comfort, altered r/ t), (Anxiety r/t), (Injury, potential for r/t) in order, and the average short-term hospital dates were 2.5days, long-term hospital dates were 11.5days in gynecologic diseases and majority of used nursing diagnosis, (Comfort, altered r/t). (Self care deficit r/t), (Injury, potential for r/t), (Infection, potential for r/t) in order.

• Journal of the Korea Society of Computer and Information
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• v.20 no.3
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• pp.69-74
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• 2015

This paper offers solutions to unresolved $43{\leq}R(5,5){\leq}49$ and $102{\leq}R(6,6){\leq}165$ problems of Ramsey's number. The Ramsey's number R(s,t) of a complete graph $k_n$ dictates that n-1 number of incidental edges of a arbitrary vertex ${\upsilon}$ is dichotomized into two colors: (n-1)/2=R and (n-1)/2=B. Therefore, if one introduces the concept of distance to the vertex ${\upsilon}$, one may construct a partite graph $K_n=K_L+{\upsilon}+K_R$, to satisfy (n-1)/2=R of {$K_L,{\upsilon}$} and (n-1)/2=B of {${\upsilon},K_R$}. Subsequently, given that $K_L$ forms the color R of $K_{s-1)$, $K_S$ is attainable. Likewise, given that $K_R$ forms the color B of $K_{t-1}$, $K_t$ is obtained. By following the above-mentioned steps, $R(s,t)=K_n$ was obtained, satisfying necessary and sufficient conditions where, for $K_L$ and $K_R$, the maximum distance should be even and incidental edges of all vertices should be equal are satisfied. This paper accordingly proves R(5,5)=43 and R(6,6)=91.

• Asian Pacific Journal of Cancer Prevention
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• v.15 no.11
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• pp.4711-4716
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• 2014

Introduction: Adiponectin (ApN) is a complement C1q-related protein, mainly secreted from adipose tissue, that signals through ApN receptor1 (Adipo-R1) and ApN receptor 2 (Adipo-R2). Low serum ApN concentrations are associated with obesity-related malignancies. However, there are very few studies on any prognostic role of ApN receptors in gastric cancer. Objectives: The aim of this study is to investigate the relationship between AdipoR1/R2 expression and early/advanced stage gastric cancer in terms of clinicopathologic characteristics and survival. Materials and Methods: Eighteen patients with early and 39 with advanced stage gastric cancer who underwent surgical gastric resection were included in this study. Results: Adipo-R1 expression was low in 2 of the 18 patients with early stage gastric cancer (11.1%), while 4 had low Adipo-R2 expression (22.2%). In those with advanced stage gastric cancer, 7 of 39 had low Adipo-R1 expression (17.9%) and 16 had low Adipo-R2 expression (41%). Adipo-R2 expression was significantly higher (p=0.011) in moderately differentiated tumors when compared to well-differentiated tumors. While there was nearly a statistically significant relationship between TNM stage (T, tumor size; N, regional lymph node; M, whether distant metastases exist) and Adipo-R2 expression (p=0.054), there was no relationship between Adipo-R1/-R2 expression with tumor stage and survival. Conclusion: Adipo-R1/-R2 expression has no prognostic significance of in early/advanced stage gastric cancer.

• Bulletin of the Korean Mathematical Society
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• v.30 no.1
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• pp.71-77
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• 1993

Every ring considered in the paper will be assumed to be commutative and have a unit element. An ideal A of a ring R will be called primal if the elements of R which are zero divisors modulo A, form an ideal of R, say pp. If A is a primal ideal of R, P is called the adjoint ideal of A. The adjoint ideal of a primal ideal is prime [2]. The definition of primal ideals may also be formulated as follows: An ideal A of a ring R is primal if in the residue class ring R/A the zero divisors form an ideal of R/A. If Q is a primary idel of a ring R then every zero divisor of R/Q is nilpotent; therefore, Q is a primal ideal of R. That a primal ideal need not be primary, is shown by an example in [2]. Let R[X], and R[[X]] denote the polynomial ring and formal power series ring in an indeterminate X over a ring R, respectively. Let S be a multiplicative system in a ring R and S$^{-1}$ R the quotient ring of R. Let Q be a P-primary ideal of a ring R. Then Q[X] is a P[X]-primary ideal of R[X], and S$^{-1}$ Q is a S$^{-1}$ P-primary ideal of a ring S$^{-1}$ R if S.cap.P=.phi., and Q[[X]] is a P[[X]]-primary ideal of R[[X]] if R is Noetherian [1]. We search for analogous results when primary ideals are replaced with primal ideals. To show an ideal A of a ring R to be primal, it sufficies to show that a-b is a zero divisor modulo A whenever a and b are zero divisors modulo A.

• Journal of Sasang Constitutional Medicine
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• v.1 no.1
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• pp.139-151
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• 1989

In order to investigate the effects of Raw, Dried and Steamed Roots of Rehmanniae Radix (R.R.: from Wonju province, Korea) on cell-mediated arid humoral immune response, the author performed this experimental study. Delayed type hypersensitivity (DTH) and rosette forming cells (RFC) for cell-mediated immune response, hemagglutinin (HA) titers, hemolysin (HL) titers were maeasured in ICR mice. The results were summarized as follows: 1) DTH was increased with the order of Steamed Roots of R.R., Raw Roots of R.R., Dried Roots of R.R.-treated group, as compared with the control group, with statistical significance. 2) RFC were increased with the order of Raw Roots of R.R., Steamed Roots of R.R., Dried Roots of R.R.-treated group, as compared with the control group, with statistical significance. 5) HA titers were increased with the order of Steamed Roots of R.R., Row Roots of R.R., Dried Roots of R.R.treated group, as compared with the control group, with statistical significance. 4) HL. titers were increased with the order of Raw Roots of R.R., Steamed Roots of R.R., Dried Roots of R.R.-treated group, as compared with the control group, with statistical significance. Through in the experimental study in ICR mice, these findings suggest that all of the treated group was increased in cell-mediated immune reaponse, Raw, Steamed Roots of R.R. were increased more as compared with the Dried Roots of R.R., and all of the treated group was increased in humoral immune response, Raw, Steamed Roots of R.R. were increased more as compared with the dried Roots of R.R.

• Asian Pacific Journal of Cancer Prevention
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• v.15 no.21
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• pp.9385-9390
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• 2014

Introduction: Human adiponectin (ApN) is a 30 kDa glycoprotein of 244-amino acids which is extensively produced by adipocytes. ApN acts via two receptors, namely adiponectin receptor-1 (Adipo-R1) and adiponectin receptor-2 (Adipo-R2). Studies have shown the presence of Adipo-R1 and Adipo-R2 expression immunohistochemically in human colorectal cancers (CRCs). However, only a few studies exist which investigated effects of adiponectin receptor expression on CRC characteristics. Objectives: In the present study, we aimed to explore Adipo-R1/-R2 expression in human colorectal cancers and any association with clinicopathological characteristics and survival. Materials and Methods: The study enrolled 58 colorectal cancer patients with tumor resection and a control group of 30 subjects with normal colon mucosa. Results: Positivity for Adipo-R1/-R2 expression was significantly more common in the control group in comparison to the patient group (both p<0.001). There was no significant association between Adipo-R1/-R2 expression and clinicopathological characteristics including age, sex tumor location, pTNM stage, Duke's stage, metastasis, histological differentiation, perineural invasion, venous invasion sex, lymphatic invasion, cancer-related mortality, tumor size and recurrence. Adipo- R1/-R2 positivity was also not significantly linked to progression-free or overall survival [p values (0.871, 0.758) and (0.274, 0.232), respectively]. Conclusions: Although significantly reduced Adipo-R1/-R2 expression was found in colorectal cancer patients, it had no influence on survival.