• 대한수학회논문집
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• 제24권3호
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• pp.367-379
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• 2009

For a prime number p, let $\mathbb{Q}_p$ denote the p-adic field and let $\mathbb{Q}_p^d$ denote a vector space over $\mathbb{Q}_p$ which consists of all d-tuples of $\mathbb{Q}_p$. For a function f ${\in}L_{loc}^1(\mathbb{Q}_p^d)$, we define the Hardy-Littlewood maximal function of f on $\mathbb{Q}_p^d$ by $$M_pf(x)=sup\frac{1}{\gamma{\in}\mathbb{Z}|B_{\gamma}(x)|H}{\int}_{B\gamma(x)}|f(y)|dy$$, where |E|$_H$ denotes the Haar measure of a measurable subset E of $\mathbb{Q}_p^d$ and $B_\gamma(x)$ denotes the p-adic ball with center x ${\in}\;\mathbb{Q}_p^d$ and radius $p^\gamma$. If 1 < q $\leq\;\infty$, then we prove that $M_p$ is a bounded operator of $L^q(\mathbb{Q}_p^d)$ into $L^q(\mathbb{Q}_p^d)$; moreover, $M_p$ is of weak type (1, 1) on $L^1(\mathbb{Q}_p^d)$, that is to say, |{$x{\in}\mathbb{Q}_p^d:|M_pf(x)|$>$\lambda$}|$_H{\leq}\frac{p^d}{\lambda}||f||_{L^1(\mathbb{Q}_p^d)},\;\lambda$ > 0 for any f ${\in}L^1(\mathbb{Q}_p^d)$.

• 한방비만학회지
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• 제4권1호
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• pp.139-160
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• 2004

The obesity is detrimental to the health of people living in affluent societies. Individual differences in energy metabolism are caused primarily by single nucleotide polymorphisms(SNPs), some of which promote the development of obesity-related type 2 diabetes mellitus. Type 2 diabetes mellitus is a common multifactorial genetic syndrome, which is determined by several different genes and environmental factors. In this review, five major conclusions are reached: (1)To be clinically significant, SNPs must be relevant, prevalent, modifiable, and measurable. (2)Differences in SNPs may have been caused by famine, ultraviolet light, alcohol, climate, agricultural revolution. livestock, lactase persistence, and westernized lifestyle. (3)Candidate obesity genes of calorie intake restriction are SIM 1, MC3R, MC4R, AGRP, CART, CCK, CNTFR, DRD2, Ghrelin, 5-HT receptor, NPY, PON and those of energy metabolism are LEP, LEPR, UCP1, UCP2, UCP3, B2AR, B3AR, PGC-1, Androgen receptor and those of fat mobilization are AGT, ACE, ADA, APM1, Apolipoproteins, PPAR, FABP, FOXC2, GCGR, $11-{\beta}HSDI$, LDLR, Hormonal sensitive lipase, Perilipin, $TNF-{\alpha}$, $TNF-{\beta}$ (4)Candidate obesity genes in the eastern are NPY, LEP, LEPR, UCP1, UCP2, UCP3, B2AR, B3AR, ACE, APM1, PPAR, and FABP. (5)Candidate obesity genes in type 2 diabetes mellitus are MC3R, MC4R, B2AR, B3AR, ADA, APM1, PPAR, FABP, FOXC2, PC1, PC2, ABCC8, CAPN10, CYP19, CYP7, ENPP1, GCK, GYS1, IGF, IL-6, Insulin receptor, IRS, and LPL. The discovery of SNPs will lead to a greater understanding of the pathogenesis of obesity and to better diagnostics, treatment, and eventually prevention.

• KIEE International Transaction on Electrical Machinery and Energy Conversion Systems
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• 제4B권4호
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• pp.217-224
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• 2004

A novel anti-islanding method for the distributed power generation system (DPGS) is proposed in this paper. Three different islanding scenarios are explored and presented based on the analysis of real and reactive power mismatch. It is shown via investigation that islanding voltage is a function of real power alone, where its frequency is a function of both real and reactive power. Following this analysis, a robust anti-islanding algorithm is developed. The proposed algorithm continuously perturbs ($\pm$5%) the reactive power supplied by the DPGS while simultaneously monitoring the utility voltage and frequency. In the event of islanding, a measurable frequency deviation takes place, upon which the real power of the DPGS is further reduced to 80%. A drop in voltage positively confirms islanding and the DPGS is then safely disconnected. This method of control is shown to be robust: it is able to detect islanding under resonant loads and is also fast acting (operable in one cycle). Possible islanding conditions are simulated and verified through analysis. Experimental results on a 0.5kW fuel cell system connected to a utility grid are discussed.

• 대한수학회보
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• 제30권2호
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• pp.179-185
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• 1993

In this article S is a topologically complete subspace of $R^{1}$i.e., the relativized topology on S may be metrized so as to make S complete. B(S) is the Borel .sigma.-field of S. For .GAMMA. one takes a set of measurable monotone (increasing or dereasing) functions on S into itself. Make the assumption of pp. There exists $x_{0}$ and a positive integer $n_{0}$ such that (Fig.) It is then shown that there exists a unique inveriant probability to which $p^{(n)}$ (x,dy) converges exponentially fast in a metric (stronger than the Kolmogorov distance); this convergence is uniform for all x .mem. S. This generalizes an earlier result of Bhattacharya and Lee (1988) who considered monotone nondecreasing maps on S.

• 대한수학회보
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• 제55권6호
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• pp.1869-1889
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• 2018

We are concerned with the following fractional p-Laplacian inclusion: $$(-{\Delta})^s_pu+V(x){\mid}u{\mid}^{p-2}u{\in}{\lambda}[{\underline{f}}(x,u(x)),\;{\bar{f}}(s,u(x))]$$ in ${\mathbb{R}}^N$, where $(-{\Delta})^s_p$ is the fractional p-Laplacian operator, 0 < s < 1 < p < $+{\infty}$, sp < N, and $f:{\mathbb{R}}^N{\times}{\mathbb{R}}{\rightarrow}{\mathbb{R}}$ is measurable with respect to each variable separately. We show that our problem with the discontinuous nonlinearity f admits at least one or two nontrivial weak solutions. In order to do this, the main tool is the Berkovits-Tienari degree theory for weakly upper semicontinuous set-valued operators. In addition, our main assertions continue to hold when $(-{\Delta})^s_pu$ is replaced by any non-local integro-differential operator.

• 대한수학회논문집
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• 제26권1호
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• pp.23-35
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• 2011

In the present work we construct a composite implicit random iterative process with errors for a finite family of asymptotically nonexpansive random operators and discuss a necessary and sufficient condition for the convergence of this process in an arbitrary real Banach space. It is also proved that this process converges to the common random fixed point of the finite family of asymptotically nonexpansive random operators in the setting of uniformly convex Banach spaces. The present work also generalizes a recently established result in Banach spaces.

• 대한수학회보
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• 제53권4호
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• pp.1157-1169
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• 2016

We find the distributional solutions of the Wilson's functional equations $$u{\circ}T+u{\circ}T^{\sigma}-2u{\otimes}v=0,\\u{\circ}T+u{\circ}T^{\sigma}-2v{\otimes}u=0,$$ where $u,v{\in}{\mathcal{D}}^{\prime}({\mathbb{R}}^n)$, the space of Schwartz distributions, T(x, y) = x + y, $T^{\sigma}(x,y)=x+{\sigma}y$, $x,y{\in}{\mathbb{R}}^n$, ${\sigma}$ an involution, and ${\circ}$, ${\otimes}$ are pullback and tensor product of distributions, respectively. As a consequence, we solve the $Erd{\ddot{o}}s$' problem for the Wilson's functional equations in the class of locally integrable functions. We also consider the Ulam-Hyers stability of the classical Wilson's functional equations $$f(x+y)+f(x+{\sigma}y)=2f(x)g(y),\\f(x+y)+f(x+{\sigma}y)=2g(x)f(y)$$ in the class of Lebesgue measurable functions.

• 한국수학교육학회지시리즈B:순수및응용수학
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• 제7권1호
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• pp.41-47
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• 2000

Johnson and Skoug [Pacific J. Math. 83(1979), 157-176] introduced the concept of scale-invariant measurability in Wiener space. And the applied their results in the theory of the Feynman integral. A converse measurability theorem for Wiener space due to the $K{\ddot{o}}ehler$ and Yeh-Wiener space due to Skoug[Proc. Amer. Math. Soc 57(1976), 304-310] is one of the key concept to their discussion. In this paper, we will extend the results on converse measurability in Wiener space which Chang and Ryu[Proc. Amer. Math, Soc. 104(1998), 835-839] obtained to abstract Wiener space.

• 한국건축시공학회:학술대회논문집
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• 한국건축시공학회 2018년도 추계 학술논문 발표대회
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• pp.85-86
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• 2018

In this study, we previously conducted a quick evaluation of cement powder map using mesiline and hydrometer. The experiment also confirmed the possibility of rapid quality evaluation of cement powder. In this study, further studies have been conducted to apply speed and cost more economical than conventional methods, and the possibility of applying this research is to be analyzed. The result of the experiment was 500 mL of a bottled water bottle with a solid edge for measurement convenience, and the hydrometer was determined to be B type. In addition, density values of each other by powder during the same time period are considered to be measurable, indicating large differences.

• KIEE International Transaction on Electrical Machinery and Energy Conversion Systems
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• 제2B권4호
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• pp.149-155
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• 2002

This paper presents magnetic field analysis technology that uses a vector magnetic characteristic. Recently the magnetic material was found to be measurable using the vector quantity technique. Therefore considering the anisotropy of the magnetic material in the vector field analysis is necessary. The magnetic field analysis method, which is considered the anisotropy by combining the finite element method with the E&$S^2$ (Enokizono, Soda, and Shimoji) modeling, is applied to a permanent magnet motor model.