• Title, Summary, Keyword: n-additive function

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COUNTING SUBRINGS OF THE RING ℤm × ℤn

  • Toth, Laszlo
    • 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.

ON THE GENERAL SOLUTION OF A QUARTIC FUNCTIONAL EQUATION

  • Chung, Jukang-K.;Sahoo, Prasanna, K.
    • 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].

The Function of Halogen Additive in $CH_4/O_2/N_2$ Flames ($CH_4/O_2/N_2$ 화염에서 할로겐 첨가제의 역할)

  • Lee, Ki-Yong;Shin, Sung-Su
    • 한국연소학회:학술대회논문집
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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.

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ON THE MULTI-DIMENSIONAL PARTITIONS OF SMALL INTEGERS

  • Kim, Jun-Kyo
    • 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.

ON THE STABILITY OF A JENSEN TYPE FUNCTIONAL EQUATION ON GROUPS

  • FAIZIEV VALERH A.;SAHOO PRASANNA K.
    • 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, $\mathbb{C}$).

On the McShane integrability

  • Kim, Jin-Yee
    • 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 $\sum$.

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The Effects of $Y_3Al_5O_{12}$ on the Mechanical Properties of Silicon Nitride (복산화물에 의한 질화규소 세라믹스의 제조와 그 기계적 특성)

  • Noh, Sang-Hoon;Kim, Bu-Ahn;Jeong, Hae-Yong;Yoon, Han-Ki
    • Proceedings of the Korea Committee for Ocean Resources and Engineering Conference
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    • pp.169-172
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    • 2006
  • In the present work, silicon nitride was fabricated with $Y_3Al_5O_{12}$ as sintering additive and its mechanical properties were investigated. Silicon nitride with 3, 5, 7wt% of $Y_3Al_5O_{12}$ was prepared and sintered by a Hot Pressing (HP) technique at 1750, $1800^{\circ}C$ for 2 hours. The Process was fulfilled under different process pressures of 30, 45MPa respectively. Mechanical properties (density, strength, hardness, fracture toughness) were investigated as a function of $Y_3Al_5O_{12}$ contents in $Si_3N_4$. $Si_3N_4-Y_3Al_5O_{12}$ ceramics showed similar mechanical properties compared with $Si_3N_4-Y_2O_3-Al_2O_3$ ceramics. But its high temperature strength was higher than $Si_3N_4-Y_2O_3-Al_2O_3$ceramics considerably.

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SOME UMBRAL CHARACTERISTICS OF THE ACTUARIAL POLYNOMIALS

  • Kim, Eun Woo;Jang, Yu Seon
    • Journal of the Chungcheong Mathematical Society
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    • v.29 no.1
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    • pp.73-82
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    • 2016
  • The utility of exponential generating functions is that they are relevant for combinatorial problems involving sets and subsets. Sequences of polynomials play a fundamental role in applied mathematics, such sequences can be described using the exponential generating functions. The actuarial polynomials ${\alpha}^{({\beta})}_n(x)$, n = 0, 1, 2, ${\cdots}$, which was suggested by Toscano, have the following exponential generating function: $${\limits\sum^{\infty}_{n=0}}{\frac{{\alpha}^{({\beta})}_n(x)}{n!}}t^n={\exp}({\beta}t+x(1-e^t))$$. A linear functional on polynomial space can be identified with a formal power series. The set of formal power series is usually given the structure of an algebra under formal addition and multiplication. This algebra structure, the additive part of which agree with the vector space structure on the space of linear functionals, which is transferred from the space of the linear functionals. The algebra so obtained is called the umbral algebra, and the umbral calculus is the study of this algebra. In this paper, we investigate some umbral representations in the actuarial polynomials.

Electrical Properties of n-type Co-doped Fe-Si Alloy (Co 첨가 Fe-Si n형 반도체의 전기적 특성)

  • Pai, Chul-Hoon;Kim, Jeung-Gon
    • 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.

Performance Analysis of FFH/MFSK System with Clipper Receiver in the Presence of Multitone Interference (다중톤 재밍 환경에서 clipper 수신기를 사용하는 FFH/MFSK 시스템의 성능 분석)

  • 전근표;곽진삼;권오주;박재돈;이재홍
    • Proceedings of the IEEK Conference
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    • pp.15-19
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    • 2003
  • In this paper, the bit error rate (BER) performance of the fast frequency hopping/M-ary frequency shift keying system using the clipper receiver is analyzed by using the characteristic function (CF) technique in the presence of n=1 band multitone jamming and additive white Gaussian noise environment. The CFs of the clipper receiver outputs are derived as a infinite series representation using Gamma function and Marcum's Q -function. The analytical results are validated with various simulation results. Performance comparisons with linear combining receiver are shown that the BER performance of the clipper receiver is much better than that of the linear combining receiver In addition, as the clipping level approaches to infinity, it is shown that the clipper receiver simply performs a linear combining without clipping and there exists an optimum value of diversity level (the number of hops per symbol) that maximizes the worst case BER performance of the clipper receiver.

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