• Communications of the Korean Mathematical Society
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• v.34 no.4
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• pp.1105-1115
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• 2019

For positive integers n and k, let $S_k(n)$ and $S^{\prime}_k(n)$ be the sums of the elements in the finite sets {$x^k:1{\leq}x{\leq}n$, (x, n) = 1} and {$x^k:1{\leq}x{\leq}n/2$, (x, n) = 1}respectively. The formulae for both $S_k(n)$ and $S^{\prime}_k(n)$ are established. The explicit formulae when k = 1, 2, 3 are also given.

• The Journal of Korean Physical Therapy
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• v.19 no.4
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• pp.25-32
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• 2007

Purpose: The purpose of this study was to evaluate the effect of computerized neurocognitive function program on cognitive function about memory and attention with stroke. Methods: 24subjects with stroke were recruited. Twelve of subjects received conventional therapy including physical therapy, occupational therapy and language therapy. Another subjects received additional computer assisted cognitive training using Computer-aided Cognitive rehabilitation training system(COMCOG, MaxMedica Inc., 2004). All patients were assessed their cognitive function of memory and attention using Computerized Neurocognitive Function Test(CNT, MaxMedica Inc., 2004) before treatment and 6 weeks after treatment. Results: Before the treatment, two groups showed no difference in cognitive function(p>0.05). After 6 weeks, two groups showed significantly difference in digit span (forward, backward), verbal learning(A5, $A1{\sim}A5$), auditory CPT(n), visual CPT(n)(p<0.05). After treatment, the experimental group showed a significant improvement of digit span(forward, backward), verbal learning(A5, $A1{\sim}A5$), visual span (forward, backward), auditory CPT(n, sec), visual CPT(n, sec), and trail-making (A, B)(p<0.05). Conclusion: Computerized neurocognitive function program would be improved cognitive function of memory and attention in patients with stoke.

• Honam Mathematical Journal
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• v.37 no.4
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• pp.513-527
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• 2015

In this paper, we first introduce and study new concepts of ($k_1,{\cdots},k_n$)-convexity and k-segment. Secondly, we shall discuss some properties of nonisotropically starlike domains in $\mathbb{R}^n$ with respect to the origin.

• Honam Mathematical Journal
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• v.29 no.4
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• pp.535-542
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• 2007

In this paper, for each natural number n, we construct a polynomial $p_n$(x) of degree n so that $p_n(x)\;\leq\;p_{n+1}(x)\;\leq\;e^x$ for $x\;\geq\;-1$. These polynomials are optimal in the sense that if p(x) is a polynomial of degree n with $p_{n-l}(x)\;\leq\;p(x)\;\leq\;e^x$, then $p(x)\;\leq\;p_n(x)$.

• The Pure and Applied Mathematics
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• v.2 no.1
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• pp.31-34
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• 1995

Let R$^n$be n-th Euclidean space. Let be the n-th spere embeded as a subspace in R$\^$n+1/ centered at the origin. In this paper, we are going to consider the function space F = {f│f : S$^n$\longrightarrow S$^n$} metrized by as follow D(f,g)=d(f($\chi$), g($\chi$)) where f, g $\in$ F and d is the metric in S$^n$. Finally we want to find certain relation these spaces.(omitted)

• Honam Mathematical Journal
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• v.36 no.3
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• pp.531-542
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• 2014

Recently, Srivastava et al. [18] introduced the incomplete Pochhammer symbol and studied some fundamental properties and characteristics of a family of potentially useful incomplete hypergeometric functions. Here we introduce the incomplete Lauricella function ${\gamma}_D^{(n)}$ and ${\Gamma}_D^{(n)}$ of n variables, and investigate certain properties of the incomplete Lauricella functions, for example, their various integral representations, differential formula and recurrence relation, in a rather systematic manner. Some interesting special cases of our main results are also considered.

• Journal of the Chungcheong Mathematical Society
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• v.28 no.1
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• pp.119-125
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• 2015

We find a necessary and sufficient condition for which a point star-configuration in $\mathbb{P}^n$ has generic Hilbert function. More precisely, a point star-configuration in $\mathbb{P}^n$ defined by general forms of degrees $d_1,{\ldots},d_s$ with $3{\leq}n{\leq}s$ has generic Hilbert function if and only if $d_1={\cdots}=d_{s-1}=1$ and $d_s=1,2$. Otherwise, the Hilbert function of a point star-configuration in $\mathbb{P}^n$ is NEVER generic.

• Kyungpook Mathematical Journal
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• v.54 no.1
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• pp.73-86
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• 2014

In the present paper we introduce difference paranormed sequence spaces $c_0(\mathcal{M},{\Delta}^n_m,p,u,{\parallel}{\cdot},{\cdots},{\cdot}{\parallel})$, $c(\mathcal{M},{\Delta}^n_m,p,u,{\parallel}{\cdot},{\cdots},{\cdot}{\parallel})$ and $l_{\infty}(\mathcal{M},{\Delta}^n_m,p,u,{\parallel}{\cdot},{\cdots},{\cdot}{\parallel})$ defined by a Musielak-Orlicz function $\mathcal{M}$ = $(M_k)$ over n-normed spaces. We also study some topological properties and some inclusion relations between these spaces.

• Communications of the Korean Mathematical Society
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• v.39 no.2
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• pp.345-352
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• 2024

We introduce a new class of bi-partition function c_k(n), which counts the number of bi-color partitions of n in which the second color only appears at the parts that are multiples of k. We consider two partitions to be the same if they can be obtained by switching the color of parts that are congruent to zero modulo k. We show that the generating function for c_k(n) involves the partial theta function and obtain the following congruences: c₂(27n + 26) ≡ 0 (mod 3) and c₃(4n + 2) ≡ 0 (mod 2).

• Journal of Korea Society of Industrial Information Systems
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• v.17 no.3
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• pp.9-17
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• 2012

In this paper, we propose a SPN 256 bit block cipher so called XSB(eXtended SPN Block cipher) which has a symmetric structure in encryption and decryption. The proposed XSB is composed of the even numbers of N rounds where the first half of them, 1 to N/2-1 round, applies a pre-function and the last half of them, N/2+1 to N round, employs a post-function. Each round consists of a round key addition layer, a substiution layer, a byte exchange layer and a diffusion layer. And a symmetry layer is located in between the pre-function layer and the post-function layer. The symmetric layer is composed with a multiple simple bit slice involution S-Boxes. The bit slice involution S-Box symmetric layer increases difficult to attack cipher by Square attack, Boomerang attack, Impossible differentials cryptanalysis etc.