• Journal of applied mathematics & informatics
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• v.30 no.1_2
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• pp.327-336
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• 2012

Let {$X_{ni}$, $i{\geq}1$, $n{\geq}1$} be an array of rowwise and pairwise negatively quadrant dependent random variables with mean zero, {$a_{ni}$, $i{\geq}1$, $n{\geq}1$} an array of weights and {$b_n$, $n{\geq}1$} an increasing sequence of positive integers. In this paper we consider some results concerning complete convergence of ${\sum}_{i=1}^{bn}a_{ni}X_{ni}$.

• Journal of applied mathematics & informatics
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• v.28 no.3_4
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• pp.711-721
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• 2010

Values of the parameter $\lambda$ are determined for which there exist positive solutions of the system of boundary value problems, $u^{(n)}+{\lambda}p(t)f(\upsilon)=0$, $\upsilon^{(n)}+{\lambda}q(t)g(u)=0$, for $t\;{\in}\;[a,b]$, and satisfying, $u^{(i)}(a)=0$, $u^{(\alpha)}(b)=0$, $\upsilon^{(i)}(a)=0$, $\upsilon^{(\alpha)}(b)=0$, for $0\;{\leq}\;i\;{\leq}\;n-2$ and $1\;{\leq}\;\alpha\;\leq\;n-1$ (but fixed). A well-known Guo-Krasnosel'skii fixed point theorem is applied.

• YAKHAK HOEJI
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• v.41 no.5
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• pp.575-581
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• 1997

The 6,7-dichlorquinoline-5,8-dione was reacted with ${alpha}$-cyanoacetic acid ethyl ester in ammonia solution to yield 6-(${alpha}$-cyano-${alpha}$-ethoxycarbonyhnethyl)-7-chloroquinoline- 5,8-dione (compound I). When this compound was reacted with some alkyl amines (methylamine, ethylamine, isopropylamine, etc) 2-amino-3-ethoxycarbonyl-N-alkyl-pyridino[2,3-f]indole-4,9-diones (compounds II a-e) were obtained.

• Communications of the Korean Mathematical Society
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• v.31 no.3
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• pp.483-493
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• 2016

In this paper, we study and prove common fixed point theorems for N generalized I-asymptotically nonexpansive mappings in a Hadamard space.

• Journal of the Korean Statistical Society
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• v.13 no.2
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• pp.114-120
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• 1984

A parallel flats fraction for the $3^n$ design is defined as union of flats ${t}At=c_i(mod 3)}, i=1,2,\cdots, f$ and is symbolically written as At=C where A is rank r. The A matrix partitions the effects into n+1 alias sets where $u=(3^{n-r}-1)/2. For each alias set the f flats produce an ACPM from which a detection matrix is constructed. The set of all possible parallel flats fraction C can be partitioned into equivalence classes. In this paper, we develop some properties of a detection matrix and C.

• 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.

• Journal of the Chungcheong Mathematical Society
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• v.34 no.3
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• pp.209-219
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• 2021

A set {a₁, a₂, ⋯ , a_m} of positive integers is called a Diophantine m-tuple if a_ia_j + 1 is a perfect square for all 1 ≤ i < j ≤ m. Let F_n be the nth Fibonacci number which is defined by F₀ = 0, F₁ = 1 and F_n+2 = F_n+1 + F_n. In this paper, we find the extendibility of Diophantine pairs {F_2k, b} with some conditions.

• Journal of Gastric Cancer
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• v.5 no.3 s.19
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• pp.158-162
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• 2005

Purpose: In order to clarify the carcinogenesis mechanism from chronic atrophic gastritis toward gastric cancer, we measured the pepsinogen I and II and compared their ratio with several clinical findings. Materials and Methods: We measured the preoperative serum pepsinogen I and II by using a radio-immunoassay and compared their ratio with several clinical findings, such as tumor size, mucinous vs non-mucinous tumor, cell differentiation, tumor location, depth of invasion, lymph-node status, Lauren's classification, and peritumoral atrophy in 103 consecutive patients with gastric adenocarcinomas who had received resections at Bundang CHA Hospital during the period from July 2003 to February 2005. Results: There were significant differences in the serum pepsinogen I/II ratio between patients with mucinous vs non-mucinous tumors (n=4 vs 9 and mean pep I/II=1.29 vs. 2.99, p=0.0288), with tumor size more than and less than $10cm^2$ (n=55 vs. 48 and mean pep I/II=2.64 vs. 3.24, p=0.0491), and with or without peritumoral atrophy (n=94 vs. 9 and mean pep I/II=2.83 vs. 3.89, p=0.0466). In patients with peritomoral atrophy, the pepsinogen I/II ratio was also lower in larger tumors (n=48 vs. 46 and mean pep I/II=2.44 vs. 3.23, p=0.0083). Well-differentiated carcinomas showed significantly lower serum pep I/II ratios than signet-ring-ceil types. There was no correlation between serum pep I/II ratio and tumor location, depth of invasion, lymph-node status, or Lauren's classification Conclusion: We proved the existence of a correlation between serum pepsinogen level and musosal atrophy, but these results are not sufficient for clinical application of serum pepsinogen level as a screening tool for gastric cancer.

• Kyungpook Mathematical Journal
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• v.60 no.3
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• pp.467-475
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• 2020

Let G be a chemical graph with vertex set {v₁, v₁, …, v_n} and degree sequence d(G) = (deg_G(v₁), deg_G(v₂), …, deg_G(v_n)). The inverse degree, R(G) of G is defined as $R(G)={\sum{_{i=1}^{n}}}\;{\frac{1}{deg_G(v_i)}}$. The cyclomatic number of G is defined as γ = m - n + k, where m, n and k are the number of edges, vertices and components of G, respectively. In this paper, some upper bounds on the diameter of a chemical graph in terms of its inverse degree are given. We also obtain an ordering of connected chemical graphs with respect to the inverse degree.

• East Asian mathematical journal
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• v.16 no.1
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• pp.111-123
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• 2000

Northcott and McKerrow proved that if R is a left noetherian ring and E is an injective left R-module, then $E[x^{-1}]$ is an injective left R[xl-module. Park generalize Northcott and McKerrow's result so that if R is a left noetherian ring and E is an injective left R-module, then $E[x^{-S}]$ is an injective left $R[x^s]$-module, where S is a submonoid of N(N is the set of all natural numbers). In this paper we show $$Hom_{R[x^S]}(M[x^{-S}],\;N[x^{-S}]){\cong}Hom_R(M,\;N)[[x^S]]$$ and using the above result and this isomorphism, finally we show that $$Ext^i_{R[x^S]}(M[x^{-S}],\;N[x^{-S}]){\cong}Ext^i_R(M,\;N)[[x^S]]$$.