• 호남수학학술지
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• 제1권1호
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• pp.21-25
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• 1979

Abelian군(群)의 presheaf에 관한 직적(直積)과 직화(直和)를 Category 입장에서 정의(定義)하고 presheaf $F_{\lambda}\;({\lambda}{\epsilon}{\Lambda})$들의 두 직적(直積)(또는 直和)은 서로 동형적(同型的) 관계(關係)에 있으며, 특히 ${\phi}:X{\rightarrow}Y$가 homeomorphism이라 하고 ${\phi}_*F$를 X상(上)의 presheaf F의 direct image이라 하면 (1) $({\phi}_*F, \;{\phi}_*(f_{\lambda})_{{\lambda}{\epsilon}{\Lambda}})$가 $({\phi}_*F_{\lambda})_{{\lambda}{\epsilon}{\Lambda}}$의 직적(直積)일 때 오직 그때 한하여 $(F,\;(f_{\lambda})_{{\lambda}{\epsilon}{\Lambda}})$는 $(F_{\lambda})_{{\lambda}{\epsilon}{\Lambda}})$의 직적(直積)이다. (2) $({\phi}_*F,\;{\phi}_*(l_{\lambda})_{{\lambda}{\epsilon}{\Lambda}})$가 $({\phi}_*F_{\lambda})_{{\lambda}{\epsilon}{\Lambda}}$의 직화(直和)일 때 오직 그때 한하여 $(F,\;(l_{\lambda})_{{\lambda}{\epsilon}{\Lambda}})$는 $(F_{\lambda})_{{\lambda}{\epsilon}{\Lambda}})$의 직화(直和)이다. Let $(F_{\lambda})_{{\lambda}{\epsilon}{\Lambda}})$ be an indexed set of presheaves of abelian group on topological space X. We can define the cartesian product $$\prod_{{\lambda}{\epsilon}{\Lambda}}\;F_{\lambda}$$ of $(F_{\lambda})_{{\lambda}{\epsilon}{\Lambda}})$ by $$(\prod_{{\lambda}{\epsilon}{\Lambda}}\;F_{\lambda})(U)=\prod_{{\lambda}{\epsilon}{\Lambda}}(F_{\lambda}(U))$$ for U open in X $${\rho}_v^u:\;(\prod_{{\lambda}{\epsilon}{\Lambda}}\;F_{\lambda})(U){\rightarrow}(\prod_{{\lambda}{\epsilon}{\Lambda}}\;F_{\lambda})(V)((s_{\lambda})_{{\lambda}{\epsilon}{\Lambda}}{\rightarrow}(_{\lambda}{\rho}_v^u(s_{\lambda}))_{{\lambda}{\epsilon}{\Lambda}})$$ for $V{\subseteq}U$ open in X where $_{\lambda}{\rho}^U_V$ is a restriction of $F_{\lambda}$, And we have natural presheaf morphisms ${\pi}_{\lambda}$ and ${\iota}_{\lambda}$ such that ${\pi}_{\lambda}(U):\;({\prod}_\;F_{\lambda})(U){\rightarrow}F_{\lambda}(U)((s_{\lambda})_{{\lambda}{\epsilon}{\Lambda}}{\rightarrow}s_{\lambda})$ ${\iota}_{\lambda}(U):\;F_{\lambda}(U){\rightarrow}({\prod}\;F_{\lambda})(U)(s_{\lambda}{\rightarrow}(o,o,{\cdots}\;{\cdots}o,s_{\lambda},o,{\cdots}\;{\cdots}o)$ for $(s_{\lambda}){\epsilon}{\prod}_{\lambda}\;F_{\lambda}(U)$ and $(s_{\lambda}){\epsilon}F_{\lambda}(U)$.

• 한국수학교육학회지시리즈B:순수및응용수학
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• 제13권4호
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• pp.295-301
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• 2006

We Investigate the relation between the multi-variable bi-additive functional equation f(x+y+z,u+v+w)=f(x,u)+f(x,v)+f(x,w)+f(y,u)+f(y,v)+f(y,w)+f(z,u)+f(z,v)+f(z,w) and the multi-variable quadratic functional equation g(x+y+z)+g(x-y+z)+g(x+y-z)+g(-x+y+z)=4g(x)+4g(y)+4g(z). Furthermore, we find out the general solution of the above two functional equations.

• Journal of applied mathematics & informatics
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• 제27권5_6호
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• pp.1157-1163
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• 2009

Let G be a graph with vertex set V(G) and let f be a nonnegative integer-valued function defined on V(G). A spanning subgraph F of G is called a fractional f-factor if $d^h_G$(x)=f(x) for all x $\in$ for all x $\in$ V (G), where $d^h_G$ (x) = ${\Sigma}_{e{\in}E_x}$ h(e) is the fractional degree of x $\in$ V(F) with $E_x$ = {e : e = xy $\in$ E|G|}. In this paper it is proved that if ${\delta}(G){\geq}{\frac{b^2(k-1)}{a}},\;n>\frac{(a+b)(k(a+b)-2)}{a}$ and $|N_G(x_1){\cup}N_G(x_2){\cup}{\cdots}{\cup}N_G(x_k)|{\geq}\frac{bn}{a+b}$ for any independent subset ${x_1,x_2,...,x_k}$ of V(G), then G has a fractional f-factor. Where k $\geq$ 2 be a positive integer not larger than the independence number of G, a and b are integers such that 1 $\leq$ a $\leq$ f(x) $\leq$ b for every x $\in$ V(G). Furthermore, we show that the result is best possible in some sense.

• 대한수학회지
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• 제45권6호
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• pp.1613-1622
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• 2008

Let G be a graph with vertex set V(G) and edge set E(G), and let g, f be two nonnegative integer-valued functions defined on V(G) such that $g(x)\;{\leq}\;f(x)$ for every vertex x of V(G). We use $d_G(x)$ to denote the degree of a vertex x of G. A (g, f)-factor of G is a spanning subgraph F of G such that $g(x)\;{\leq}\;d_F(x)\;{\leq}\;f(x)$ for every vertex x of V(F). In particular, G is called a (g, f)-graph if G itself is a (g, f)-factor. A (g, f)-factorization of G is a partition of E(G) into edge-disjoint (g, f)-factors. Let F = {$F_1$, $F_2$, ..., $F_m$} be a factorization of G and H be a subgraph of G with mr edges. If $F_i$, $1\;{\leq}\;i\;{\leq}\;m$, has exactly r edges in common with H, we say that F is r-orthogonal to H. If for any partition {$A_1$, $A_2$, ..., $A_m$} of E(H) with $|A_i|=r$ there is a (g, f)-factorization F = {$F_1$, $F_2$, ..., $F_m$} of G such that $A_i\;{\subseteq}E(F_i)$, $1\;{\leq}\;i\;{\leq}\;m$, then we say that G has (g, f)-factorizations randomly r-orthogonal to H. In this paper it is proved that every (0, mf - (m - 1)r)-graph has (0, f)-factorizations randomly r-orthogonal to any given subgraph with mr edges if $f(x)\;{\geq}\;3r\;-\;1$ for any $x\;{\in}\;V(G)$.

• 대한수학회논문집
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• 제31권3호
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• pp.495-505
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• 2016

Let $f:{\mathbb{R}}^3{\rightarrow}{\mathbb{R}}$. In this paper we prove the stability of functional inequalities ${\mid}f(ux+vy,uy-vx,zw)-f(x,y,z)f(u,v,w){\mid}{\leq}{\phi}(u,v,w)$ or ${\phi}(x,y,z)$, ${\mid}f(ux-vy,uy-vx,zw)-f(x,y,z)f(u,v,w){\mid}{\leq}{\phi}(u,v,w)$ or ${\phi}(x,y,z)$ for all $x,y,z,u,v,w{\in}{\mathbb{R}}$. Furthermore, we give refined descriptions of bounded functions satisfying the inequalities as in Albert and Baker [1].

• 대한화학회지
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• 제51권3호
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• pp.265-269
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• 2007

국부적인 결정구조와 에너지 띠 간격 간 상관관계를 고찰하기 위하여 Nb를 포함하는 일련의 불소 산화물에 대하여 결정구조와 자외선-가시광선 확산 반사율 스펙트럼을 비교, 연구하였다. 이 실험에서 다룬 RbSrNb2O6F와 RbCaNb2O6F, RbNb2O5F는 공통적으로, 꼭지점 공유를 하고 있는 NbO5F 팔면체로 구성되어 있 다. 구조적 뒤틀림 정도의 척도로 볼 수 있는 Nb-O(F)-Nb 평균 결합각은 RbSrNb2O6F에서 158.6°, RbCaNb2O6F 에서 149.6° 그리고 RbNb2O5F에서 139.5o이다. 확산 반사율 스펙트럼으로부터 구한 에너지 띠 간격은 Nb-O(F)-Nb 결합각이 감소할수록 증가하는 경향을 보였다. 즉 RbSrNb2O6F, RbCaNb2O6F, RbNb2O5F 각각의 화합물에 대해 서 3.48 eV, 3.75 eV, 4.03 eV 의 값을 나타내었다. 이러한 실험적 결과는 Nb를 포함하는 불소 산화물에서 국 부구조의 변화를 통해 띠 간격을 약 0.6 eV의 범위에서 조절할 수 있음을 의미한다.

• Journal of applied mathematics & informatics
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• 제34권3_4호
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• pp.227-237
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• 2016

In this paper we introduce a new graph labeling called k-prime cordial labeling. Let G be a (p, q) graph and 2 ≤ p ≤ k. Let f : V (G) → {1, 2, . . . , k} be a map. For each edge uv, assign the label gcd (f(u), f(v)). f is called a k-prime cordial labeling of G if |v_f (i) − v_f (j)| ≤ 1, i, j ∈ {1, 2, . . . , k} and |e_f (0) − e_f (1)| ≤ 1 where v_f (x) denotes the number of vertices labeled with x, e_f (1) and e_f (0) respectively denote the number of edges labeled with 1 and not labeled with 1. A graph with a k-prime cordial labeling is called a k-prime cordial graph. In this paper we investigate the k-prime cordial labeling behavior of a star and we have proved that every graph is a subgraph of a k-prime cordial graph. Also we investigate the 3-prime cordial labeling behavior of path, cycle, complete graph, wheel, comb and some more standard graphs.

• Kyungpook Mathematical Journal
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• 제58권4호
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• pp.747-759
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• 2018

A graph G = (V (G), E(G) of order n = |V (G)| and size m = |E(G)| is said to be odd harmonious if there exists an injection $f:V(G){\rightarrow}\{0,\;1,\;2,\;{\ldots},\;2m-1\}$ such that the induced function $f^*:E(G){\rightarrow}\{1,\;3,\;5,\;{\ldots},\;2m-1\}$ defined by $f^*(uv)=f(u)+f(v)$ is bijection. While a bipartite graph G with partite sets A and B is said to be bigraceful if there exist a pair of injective functions $f_A:A{\rightarrow}\{0,\;1,\;{\ldots},\;m-1\}$ and $f_B:B{\rightarrow}\{0,\;1,\;{\ldots},\;m-1\}$ such that the induced labeling on the edges $f_{E(G)}:E(G){\rightarrow}\{0,\;1,\;{\ldots},\;m-1\}$ defined by $f_{E(G)}(uv)=f_A(u)-f_B(v)$ (with respect to the ordered partition (A, B)), is also injective. In this paper we prove that odd harmonious graphs and bigraceful graphs are equivalent. We also prove that the number of distinct odd harmonious labeled graphs on m edges is m! and the number of distinct strongly odd harmonious labeled graphs on m edges is [m/2]![m/2]!. We prove that the Cartesian product of strongly odd harmonious trees is strongly odd harmonious. We find some new disconnected odd harmonious graphs.

• Asian Pacific Journal of Cancer Prevention
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• 제16권16호
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• pp.7327-7330
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• 2015

Background: Essential thrombocythemia (ET) is a clonal hemopoietic stem cell myeloproliferative neoplasm characterized by persistent thrombocytosis along with megakaryocytic hyperplasia. In the last decade following the identification of an acquired JAK2 V617F mutation, there has been acceleration in our understanding of this disease. The rational of this study was to determine the mutational profile of JAK2 V617F in Pakistan patients with ET. Materials and Methods: In this retrospective cross sectional study, 21 patients with ET were enrolled from January 2011 to December 2014. Patients were diagnosed based on WHO criteria for essential thrombocythemia. Complete blood count was done on an automated hematology analyzer, while JAK2 V617F expression was evaluated by polymerase chain reaction. Results: The mean age was $56.7{\pm}19.0$ years (range 18-87) and the male to female ratio was 1:1.1. The frequency of JAK2 V617F positivity in our ET patients was found to be 61.9%. The mean hemoglobin was $11.7{\pm}2.4$ g/dl with a total leukocyte count of $13.3{\pm}8.1{\times}109/l$ and a platelet count of $1188{\pm}522{\times}109/l$. Positive correlations for JAK2 V617F mutation were established with high TLC count and raised LDH (P<0.05). No correlation of JAK2 V617F could be established with age and gender (P>0.05). Conclusions: JAK2 V617F mutation frequency in our ET patients was similar to those reported previously. Screening for the mutation in all suspected essential thrombocythemia cases could be beneficial in differentiating patients with reactive and clonal thrombocytosis.

• 전자공학회논문지T
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• 제35T권1호
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• pp.48-58
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• 1998

본 논문은 센서에서 수반되는 기생용량과 온도 드리프트 및 누설전류의 영향을 경감하기 위한 C-V변환회로 및 C-V변환회로에 관한 실험결과를 제시하고, 또한 논문에서 제안한 센싱 주파수를 기준주파수로 나누어줌으로써 상기 영향들을 줄일 수 있는 새로운 인터페이스 회로를 제시한다 이 회로는 용량비의 출력신호를 디지털 방식으로 16진수로 계수 함으로써 신호의 전송이나 컴퓨터 처리가 쉬울 뿐 아니라 비트수의 증가에 따라 분해 능을 향상시킬 수 있는 이점도 있다. 시작한 인터페이스 회로의 C-V 및 C-F 변환회로에서 전원전압 4.0V, 피이드백 커패시턴스10pF, 압력 0∼10 KPa범위에서 감도는 각각 28 ㎷/㎪·V, -6.6 ㎐/㎩로서 양호하였고, 온도 드리프트 특성은 0.051 %F.S./℃ 및 0.078 %F.S./℃로서 크게 개선되었다.