• Honam Mathematical Journal
• /
• v.38 no.3
• /
• pp.507-552
• /
• 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 $L(q^4)D(q)$.

• Journal of the Korean Mathematical Society
• /
• v.39 no.2
• /
• pp.221-236
• /
• 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].

• Journal of the Chungcheong Mathematical Society
• /
• v.26 no.1
• /
• pp.147-159
• /
• 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
• /
• v.49 no.5
• /
• pp.367-377
• /
• 2016

Purpose: This study analyzed the degree of job stress and caffeine intake in workers in industrial positions in order to determine the relationships between job stress and caffeine intake. Methods: For this purpose, this study conducted a survey targeting 361 blue collar workers working for K manufacturing company, Gwangju. Results: The total score for job stress in subjects was $72.7{\pm}6.8points$/100points. According to job stress, subjects were categorized as follows: Q1 for the group who had the least stress; Q2 for the group who had little stress; Q3 for the group who had a lot of stress, and Q4 for the group who had the most stress. As for the effects of caffeine on health, 57.1% thought that caffeine is helpful and not harmful if taken properly while 17.3% responded that less caffeine consumption is better. Daily intake of caffeine according to stress was presented as: $172.0{\pm}85.3mg$ in Q1, $179.0{\pm}83.7mg$ in Q2, $187.9{\pm}81.4mg$ in Q3, and $214.2{\pm}147.3mg$ in Q4 (p < 0.05). The percentages of caffeine consumption compared to the daily safe limit in subjects were: $43.0{\pm}21.3$, $44.8{\pm}20.9$, $47.1{\pm}20.4$, and $53.6{\pm}36.8%$ in Q1, Q2, Q3, and Q4, respectively (p < 0.05). Adverse effects such as nausea or vomiting from caffeine were most common in Q4 (p < 0.05). Conclusion: As a result, higher stress in blue collar workers working for K manufacturing company was associated with more caffeine consumption. Groups with a lot of stress (Q4) consumed approximately 50% of daily safe limit of caffeine. Considering the results above, this study suggests that further research on more precise caffeine intake and its effects is needed.

• Bulletin of the Korean Mathematical Society
• /
• v.54 no.3
• /
• pp.731-736
• /
• 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
• /
• v.50 no.4
• /
• pp.473-482
• /
• 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
• /
• v.25 no.1_2
• /
• pp.155-167
• /
• 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.

• Bulletin of the Korean Mathematical Society
• /
• v.44 no.4
• /
• pp.817-823
• /
• 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
• /
• v.29 no.3
• /
• pp.357-366
• /
• 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.

• Honam Mathematical Journal
• /
• v.40 no.4
• /
• pp.681-689
• /
• 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.