• Journal of the Korean Mathematical Society
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• v.59 no.2
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• pp.299-309
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• 2022

Let k ⩾ 2 be an integer, S^k = {1^k, 2^k, 3^k, …} and B = {b₁, b₂, b₃, …} be an additive complement of S^k, which means all sufficiently large integers can be written as the sum of an element of S^k and an element of B. In this paper we prove that $${{\lim}\;{\sup}}\limits_{n{\rightarrow}{\infty}}\;{\frac{{\Gamma}(2-{\frac{1}{k}})^{\frac{k}{k-1}}{\Gamma}(1+{\frac{1}{k}})^{\frac{k}{k-1}}n^{\frac{k}{k-1}}-b_n}{n}}\;{\geqslant}\;{\frac{k}{2(k-1)}}\;{\frac{{\Gamma}(2-{\frac{1}{k}})^2}{{\Gamma}(2-{\frac{2}{k}})}},$$ where 𝚪(·) is Euler's Gamma function.

• Journal of the Chungcheong Mathematical Society
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• v.25 no.4
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• pp.771-777
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• 2012

We give a result on the density of certain additive arithmetic functions which count the number of restricted irreducible polynomials on the polynomial ring.

• Journal of the Chungcheong Mathematical Society
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• v.25 no.1
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• pp.51-63
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• 2012

In this paper, we prove the stability in random normed spaces via fixed point method for the functional equation $$f(2x+y)+f(2x-y)+2f(x)-f(x+y)-f(x-y)-2f(2x)=0$$.

• Journal of the Korean Mathematical Society
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• v.56 no.6
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• pp.1599-1611
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• 2019

Let $m,n{\in}{\mathbb{N}}$. We represent the additive subgroups of the ring ${\mathbb{Z}}_m{\times}{\mathbb{Z}}_n$, which are also (unital) subrings, and deduce explicit formulas for $N^{(s)}(m,n)$ and $N^{(us)}(m,n)$, denoting the number of subrings of the ring ${\mathbb{Z}}_m{\times}{\mathbb{Z}}_n$ and its unital subrings, respectively. We show that the functions $(m,n){\mapsto}N^{u,s}(m,n)$ and $(m,n){\mapsto}N^{(us)}(m,n)$ are multiplicative, viewed as functions of two variables, and their Dirichlet series can be expressed in terms of the Riemann zeta function. We also establish an asymptotic formula for the sum $\sum_{m,n{\leq}x}N^{(s)}(m,n)$, the error term of which is closely related to the Dirichlet divisor problem.

• Bulletin of the Korean Mathematical Society
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• v.40 no.4
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• pp.565-576
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• 2003

In this paper, we determine the general solution of the quartic equation f(x+2y)+f(x-2y)+6f(x) = 4[f(x+y)+f(x-y)+6f(y)] for all x, $y\;\in\;\mathbb{R}$ without assuming any regularity conditions on the unknown function f. The method used for solving this quartic functional equation is elementary but exploits an important result due to M. Hosszu [3]. The solution of this functional equation is also determined in certain commutative groups using two important results due to L. Szekelyhidi [5].

• 한국연소학회:학술대회논문집
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• 2003.12a
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• pp.209-214
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• 2003

Numerical simulations are performed at atmospheric pressure in order to understand the effect of additives on flame speed, flame temperature, the radical concentration, the NOx formation in freely propagating $CH_4/O_2/N_2$ flames. The additives used are carbon dioxide and hydrogen chloride which have a combination of physical and chemical behavior on hydrocarbon flame. In the flame established with the same mole of methane and additive, $CO_2$ addition significantly contributes toward the reduction of flame speed and flame temperature by the physical effect, whereas addition of HCl mainly does by the chemical effect. The impact of HCl addition on the decrease of the radical concentration is about 1.6-1.8 times as large as $CO_2$ addition. Hydrogen chloride addition is higher on the reduction of EINO than $CO_2$ addition because of the chemical effect of HCl.

• East Asian mathematical journal
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• v.28 no.1
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• pp.101-107
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• 2012

For each dimension exceeds 1, determining the number of multi-dimensional partitions of a positive integer is an open question in combinatorial number theory. For n ${\leq}$ 14 and d ${\geq}$ 1 we derive a formula for the function ${\wp}_d(n)$ where ${\wp}_d(n)$ denotes the number of partitions of n arranged on a d-dimensional space. We also give an another definition of the d-dimensional partitions using the union of finite number of divisor sets of integers.

• Bulletin of the Korean Mathematical Society
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• v.42 no.4
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• pp.757-776
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• 2005

In this paper we establish the stability of a Jensen type functional equation, namely f(xy) - f($xy^{-1}$) = 2f(y), on some classes of groups. We prove that any group A can be embedded into some group G such that the Jensen type functional equation is stable on G. We also prove that the Jensen type functional equation is stable on any metabelian group, GL(n, $\mathbb{C}$), SL(n, $\mathbb{C}$), and T(n, $\mathbb{C}$).

• Communications of the Korean Mathematical Society
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• v.11 no.2
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• pp.377-383
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• 1996

For a given separable space X which contains no copy of $C_0$ and a weakly compact T, we show that a Dunford integrable function $f : [a,b] \to X$ is intrinsically-separable valued if and only if f is McShane integrable. Also, for a given separable space X which contains no copy of $C_0$, a weakly compact T and a Dunford integrable function f we show that if there exists a sequence $(f_n)$ of McShane integrable functions from [a,b] to X such that for each $x^* \in X^*, x^*f_n \to x^*f$ a.e., then f is McShane integrable. Finally, let X contain no copy of $C_0$. If $f : [a,b] \to X$ is McShane integrable, then F is a countably additive on $\sum$.

• Korean Journal of Metals and Materials
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• v.47 no.12
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• pp.860-865
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• 2009

The effect of Co additive on the electrical properties of Fe-Si alloys prepared by a RF inductive furnace was investigated. The electrical conductivity and Seebeck coefficient were measured as a function of the temperature under an Ar atmosphere to evaluate their applicability to thermoelectric energy conversion. The electrical conductivity of the specimens increased as the temperature increased, showing typical semiconducting behavior. The electrical conductivity of Co-doped specimens was higher than that of undoped specimens and increased slightly as the amount of Co additive increased. This is most likely due to the difference in the carrier concentration and the amount of residual metallic phase ${\varepsilon}$-FeSi (The ${\varepsilon}$-FeSi was detected in spite of an annealing treatment of 100 h at $830^{\circ}C$). Additionally, metallic conduction increased slightly as the amount of Co additive increased. On the other hand, Co-doped specimens showed a lower Seebeck coefficient due to the metallic phase. The power factor of Co-doped specimens was higher than that of undoped specimens. This would be affected more by the electrical conductivity compared to the Seebeck coefficient.