• 호남수학학술지
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• 제38권3호
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• pp.507-552
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• 2016

For a complex number q and a divisor function ${\sigma}_1(n)$ we define $$C(q):=q{\prod_{n=1}^{\infty}}(1-q^n)^{16}(1-q^{2n})^4,\\D(q):=q^2{\prod_{n=1}^{\infty}}(1-q^n)^8(1-q^{2n})^4(1-q^{4n})^8,\\L(q):=1-24{\sum_{n=1}^{\infty}}{\sigma}_1(n)q^n$$ moreover we obtain the number of representations of $n{\in}{\mathbb{N}}$ as sum of 24 squares, which are possible for us to deduce $L(q^4)C(q)$ and $L(q^4)D(q)$.

• 대한수학회지
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• 제39권2호
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• pp.221-236
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• 2002

Using the p-adic q-integral due to T. Kim[4], we define a number B＊$_{n}$(q) and a polynomial B＊$_{n}$(q) which are p-adic q-analogue of the ordinary Bernoulli number and Bernoulli polynomial, respectively. We investigate some properties of these. Also, we give slightly different construction of Tsumura＇s p-adic function $\ell$$_{p}$(u, s, $\chi$) [14] using the p-adic q-integral in [4].n [4].

• 충청수학회지
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• 제26권1호
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• pp.147-159
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• 2013

Hamada ([8]) and Maruta ([17]) proved the minimum length $n_3(6,\;d)=g_3(6,\;d)+1$ for some ternary codes. In this paper we consider such minimum length problem for $q{\geq}4$, and we prove that $n_q(6,\;d)=g_q(6,\;d)+1$ for $d=q^5-q^3-q^2-2q+e$, $1{\leq}e{\leq}q$. Combining this result with Theorem A in [4], we have $n_q(6,\;d)=g-q(6,\;d)+1$ for $q^5-q^3-q^2-2q+1{\leq}d{\leq}q^5-q^3-q^2$ with $q{\geq}4$. Note that $n_q(6,\;d)=g_q(6,\;d)$ for $q^5-q^3-q^2+1{\leq}d{\leq}q^5$ by Theorem 1.2.

• Journal of Nutrition and Health
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• 제49권5호
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• pp.367-377
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• 2016

본 연구는 산업체근로자들의 직무스트레스와 카페인 섭취량을 알아보고, 직무스트레스에 따른 카페인 섭취량과의 관련성에 대해 살펴보고자 실시하였다. 연구 대상자의 직무스트레스 총합은 100점 환산 기준으로 $72.7{\pm}6.8$점으로 나타났으며, 연구 대상자들의 직무스트레스 정도에 따라 스트레스를 가장 적게 받는 그룹은 Q1, 스트레스를 적게 받는 그룹은 Q2, 스트레스를 많이 받는 그룹은 Q3, 스트레스를 가장 많이 받는 그룹은 Q4로 구분 하였다. 이들이 느끼는 스트레스는 조직적 관리체계에 대한 스트레스가 $21.9{\pm}3.3$점으로 직무요구도 $19.9{\pm}5.1$점, 보상 부적절 $16.1{\pm}2.5$점, 직무자율성 결여 $14.7{\pm}2.1$점에 비해 가장 높았다. 카페인에 대한 인지도 조사결과 카페인이 건강에 미칠 영향에 대해 스트레스가 가장 높은 군 (Q4)에서 '적당히 마시면 도움이 되고 해롭지 않다' 57.1%, '적게 마실수록 좋다'고 응답한 사람들이 17.3%로 스트레스가 많을수록 카페인은 적당히 섭취하면 도움이 되고 해롭지 않으나 적게 마실수록 좋다고 하였다. 스트레스 정도에 따른 카페인 섭취량을 보면 커피믹스 (1봉 47.51 mg)는 Q3에서 $86.1{\pm}56.4mg$ (p < 0.01), 자판기 커피 (1잔 47.51 mg)는 Q2에서 $62.3{\pm}60.9mg$ (p < 0.05), 커피전문점 커피 (1잔 158.43 mg)는 Q4에서 $40.7{\pm}88.7mg$ (p < 0.001), 녹차 (1티백: 28 mg)는 Q4에서 $18.4{\pm}32.4mg$ (p < 0.01)으로 가장 높게 나타났다. 이에 따른 카페인 일일섭취량은 Q1에서 $172.0{\pm}85.3mg$, Q2에서 $179.0{\pm}83.7mg$, Q3에서 $187.9{\pm}81.4mg$, Q4에서 $214.2{\pm}147.3mg$ 으로 Q4그룹이 유의하게 높았다 (p < 0.05). 본 연구 결과 카페인 최대 일일 섭취권고량 대비 실제 카페인 섭취량 비율은 Q1에서 $43.0{\pm}21.3%$, Q2에서 $44.8{\pm}20.9%$, Q3에서 $47.1{\pm}20.4%$, Q4에서 $53.6{\pm}36.8%$로 일일섭취량과 같이 Q4그룹이 유의하게 높았다 (p < 0.05). 카페인 섭취에 따른 부작용으로는 속이 메슥거리거나 구토와 같은 부작용이 Q4에서 $2.7{\pm}0.8$로 유의하게 높았다 (p < 0.05). 대상자들의 카페인 섭취량은 직무스트레스는 유의한 양의 상관관계를 (r = 0.137, p = 0.009), 평균 근무시간과도 유의한 양의 상관성을 보였으며 (r = 0.122 p = 0.001), 수면시간 역시 유의한 양의 상관성을 보였다 (r = 0.169, p = 0.001). 반면 카페인 섭취량과 근무기간은 유의한 음의 상관관계를 나타냈다 (r = -0.114. p = 0.031). 본 연구의 결과, K 제조공장 근로자들은 스트레스 정도가 높아질수록 섭취하는 카페인 섭취량이 많았고, 스트레스를 많이 받는 군에서는 최대 일일 섭취권고량 대비 실제 카페인 섭취량 비율이 50% 정도로 나타나 한국 20세 성인남자보다 2배 이상 섭취하는 것으로 조사되었다.

• 대한수학회보
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• 제54권3호
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• pp.731-736
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• 2017

It is well-known that there exists a constant-weight $[s{\theta}_{k-1},k,sq^{k-1}]_q$ code for any positive integer s, which is an s-fold simplex code, where ${\theta}_j=(q^{j+1}-1)/(q-1)$. This gives an upper bound $n_q(k,sq^{k-1}+d){\leq}s{\theta}_{k-1}+n_q(k,d)$ for any positive integer d, where $n_q(k,d)$ is the minimum length n for which an $[n,k,d]_q$ code exists. We construct a two-weight $[s{\theta}_{k-1}+1,k,sq^{k-1}]_q$ code for $1{\leq}s{\leq}k-3$, which gives a better upper bound $n_q(k,sq^{k-1}+d){\leq}s{\theta}_{k-1}+1+n_q(k-1,d)$ for $1{\leq}d{\leq}q^s$. As another application, we prove that $n_q(5,d)={\sum_{i=0}^{4}}{\lceil}d/q^i{\rceil}$ for $q^4+1{\leq}d{\leq}q^4+q$ for any prime power q.

• Kyungpook Mathematical Journal
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• 제50권4호
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• pp.473-482
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• 2010

In the present paper we define a q-extension of the Leibniz rule for q-derivatives via Weyl type q-derivative operator. Expansions and summation formulae for the generalized basic hypergeometric functions of one and more variables are deduced as the applications of the main result.

• Journal of applied mathematics & informatics
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• 제25권1_2호
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• pp.155-167
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• 2007

A graph G is called to be a 2-degree integral subgraph of a q-tree if it is obtained by deleting an edge e from an integral subgraph that is contained in exactly q - 1 triangles. An added-vertex q-tree G with n vertices is obtained by taking two vertices u, v (u, v are not adjacent) in a q-trees T with n - 1 vertices such that their intersection of neighborhoods of u, v forms a complete graph $K_{q}$, and adding a new vertex x, new edges xu, xv, $xv_{1},\;xv_{2},\;{\cdots},\;xv_{q-4}$, where $\{v_{1},\;v_{2},\;{\cdots},\;v_{q-4}\}\;{\subseteq}\;K_{q}$. In this paper we prove that a graph G with minimum degree not equal to q - 3 and chromatic polynomial $$P(G;{\lambda})\;=\;{\lambda}({\lambda}-1)\;{\cdots}\;({\lambda}-q+2)({\lambda}-q+1)^{3}({\lambda}-q)^{n-q-2}$$ with $n\;{\geq}\;q+2$ has and only has 2-degree integral subgraph of q-tree with n vertices and added-vertex q-tree with n vertices.

• 대한수학회보
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• 제44권4호
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• pp.817-823
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• 2007

In this paper, we develop a simple method for computing the stabilizer subgroup of a subgroup of $$D(g)={{\alpha}{\in}\mathbb{F}_q|there\;is\;a\;{\beta}{\in}{\mathbb{F}}^x_q\;such\;that\;{\beta}^n=g(\alpha)}$$ in $PSL_2(\mathbb{F}_q)$, where q is a large odd prime power, n is a positive integer dividing q-1, and $g(x){\in}\mathbb{F}_q[x]$. As an application, we construct new infinite families of 3-designs (cf. Examples 3.4 and 3.5).

• Journal of Microbiology and Biotechnology
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• 제29권3호
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• pp.357-366
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• 2019

We first confirmed the involvement of MalQ (4-${\alpha}$-glucanotransferase) in Escherichia coli glycogen breakdown by both in vitro and in vivo assays. In vivo tests of the knock-out mutant, ${\Delta}malQ$, showed that glycogen slowly decreased after the stationary phase compared to the wild-type strain, indicating the involvement of MalQ in glycogen degradation. In vitro assays incubated glycogen-mimic substrate, branched cyclodextrin (maltotetraosyl-${\beta}$-CD: G4-${\beta}$-CD) and glycogen phosphorylase (GlgP)-limit dextrin with a set of variable combinations of E. coli enzymes, including GlgX (debranching enzyme), MalP (maltodextrin phosphorylase), GlgP and MalQ. In the absence of GlgP, the reaction of MalP, GlgX and MalQ on substrates produced glucose-1-P (glc-1-P) 3-fold faster than without MalQ. The results revealed that MalQ led to disproportionate G4 released from GlgP-limit dextrin to another acceptor, G4, which is phosphorylated by MalP. In contrast, in the absence of MalP, the reaction of GlgX, GlgP and MalQ resulted in a 1.6-fold increased production of glc-1-P than without MalQ. The result indicated that the G4-branch chains of GlgP-limit dextrin are released by GlgX hydrolysis, and then MalQ transfers the resultant G4 either to another branch chain or another G4 that can immediately be phosphorylated into glc-1-P by GlgP. Thus, we propose a model of two possible MalQ-involved pathways in glycogen degradation. The operon structure of MalP-defecting enterobacteria strongly supports the involvement of MalQ and GlgP as alternative pathways in glycogen degradation.

• 호남수학학술지
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• 제40권4호
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• pp.681-689
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• 2018

In this paper, we defined new subclasses of Spirallike and Robertson functions by using concept of q-derivative operator. We investigate convolution properties and coefficient estimates for both classes q-Spirallike and q-Robertson functions denoted by ${\mathcal{S}}^{\lambda}_q[A,\;B]$ and ${\mathcal{C}}^{\lambda}_q[A,\;B]$, respectively.