• 대한수학회지
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• 제34권3호
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• pp.731-770
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• 1997

We study Diriclet forms and related subjects for the Gibbs measures of classical unbounded sping systems interacting via potentials which are superstable and regular. For any Gibbs measure $\mu$, we construct a Dirichlet form and the associated diffusion process on $L^2(\Omega, d\mu), where \Omega = (R^d)^Z^\nu$. Under appropriate conditions on the potential we show that the Dirichlet operator associated to a Gibbs measure $\mu$ is essentially self-adjoint on the space of smooth bounded cylinder functions. Under the condition of uniform log-concavity, the Gibbs measure exists uniquely and there exists a mass gap in the lower end of the spectrum of the Dirichlet operator. We also show that under the condition of uniform log-concavity, the unique Gibbs measure satisfies the log-Sobolev inequality. We utilize the general scheme of the previous works on the theory in infinite dimensional spaces developed by e.g., Albeverio, Antonjuk, Hoegh-Krohn, Kondratiev, Rockner, and Kusuoka, etc, and also use the equilibrium condition and the regularity of Gibbs measures extensively.

• 대한수학회보
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• 제38권4호
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• pp.773-786
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• 2001

On the setting of the half-space of the Euclidean n-space, we consider harmonic Bergman spaces and we also study properties of the reproducing kernel. Using covering lemma, we find some equivalent quantities. We prove that if lim$ lim\limits_{i\rightarrow\infty}\frac{\mu(K_r(zi))}{V(K_r(Z_i))}$ then the inclusion function $I : b^p\rightarrow L^p(H_n, d\mu)$ is a compact operator. Moreover, we show that if f is a nonnegative continuous function in $L^\infty and lim\limits_{Z\rightarrow\infty}f(z) = 0, then T_f$ is compact if and only if f $\in$ $C_{o}$ (H$_{n}$ ).

• 대한수학회지
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• 제49권3호
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• pp.571-583
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• 2012

Let $G$ be a metrizable, ${\sigma}$-compact locally compact abelian group with a compact open subgroup. In this paper we define the Gramian and the dual Gramian operators for shift invariant subspaces of $L^2(G)$ and we use them to characterize shift generated dual frames for shift in- variant spaces, which forms a frame for a subspace of $L^2(G)$. We present necessary and sufficient conditions for which standard dual is a unique SG-dual frame of type I and type II.

• Advances in nano research
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• 제7권3호
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• pp.209-221
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• 2019

Graphene, with impressive electronic properties, have high potential in the microelectronic field. However, graphene itself is a zero bandgap material which is not suitable for digital logic gates and its application. Thus, much focus is on graphene nanoribbons (GNRs) that are narrow strips of graphene. During GNRs fabrication process, the occurrence of defects that ultimately change electronic properties of graphene is difficult to avoid. The modelling of GNRs with defects is crucial to study the non-idealities effects. In this work, nearest-neighbor tight-binding (TB) model for GNRs is presented with three main simplifying assumptions. They are utilization of basis function, Hamiltonian operator discretization and plane wave approximation. Two major edges of GNRs, armchair-edged GNRs (AGNRs) and zigzag-edged GNRs (ZGNRs) are explored. With single vacancy (SV) defects, the components within the Hamiltonian operator are transformed due to the disappearance of tight-binding energies around the missing carbon atoms in GNRs. The size of the lattices namely width and length are varied and studied. Non-equilibrium Green's function (NEGF) formalism is employed to obtain the electronics structure namely band structure and density of states (DOS) and all simulation is implemented in MATLAB. The band structure and DOS plot are then compared between pristine and defected GNRs under varying length and width of GNRs. It is revealed that there are clear distinctions between band structure, numerical DOS and Green's function DOS of pristine and defective GNRs.

• Nuclear Engineering and Technology
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• 제25권2호
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• pp.237-247
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• 1993

반감기가 서로 크게 다른 두 종류의 방사성 직접핵분열생성물의 방사능비(activity ratio)를 핵연료의 냉각기간 및 연소이력의 함수로 표현하였으며 연소이력에는 사용후핵연료의 평균연소도, 연소기간, 연소주기간의 간격 그리고 주 핵분열물질등이 포함되었다. 고리 1호기에서 연소된 6개의 사용후 가압경수로(PWR) 핵연료 집합체로 부터 36개의 시료를 제작하여 이들 시료에 대한 감마선 스펙트럼을 고순도(HP) Ge 검출기를 사용하여 수집한 후, 각 스펙트럼을 분석하여 얻은 방사능비 $^{l44}$Ce $^{l37}$ Cs를 이용하여 냉각기간을 계산하였다. 그 결과 $^{l44}$Ce 감마선 검출계수율이 $10^{-3}$ cps(count per second) 정도로 아주 낮았음에도 불구하고 검출된 방사능비 $^{l44}$Ce $^{l37}$ Cs를 사용하여 구한 냉각기간은 원자로 운전기록에 의한 냉각기간 (operator declared cooling time)과 상대적인 차이가 $\pm$5% 이내로 잘 일치한 것으로 부터 핵 분열 생성물 $^{l44}$Ce 및 $^{l37}$ Cs은 냉각기간 결정을 위한 좋은 모니터가 됨을 확인하였다. 여러가지의 연소 이력을 갖는 핵연료를 대상으로 한 본 실험의 경우, 단순하게 모델화한 연소이력을 대입하여 얻은 냉각기간은 실제 연소이력을 대입하여 얻은 냉각기간과 시간차이가 $\pm$0.5년 이내에서 잘 맞았으며 이로부터 연소이력에 대한 정확한 정보 없이도 신뢰할 수 있는 정도의 냉각기간을 추정하는 것이 가능할 것으로 생각되었다. 아울러 냉각기간 결정을 위한 본 기술을 활용한 사용후 핵연료의 증명 및/또는 분류에 대한 타당성 연구를 한 결과 감마선 분광분석 방법으로 검출한 방사능비 $^{l44}$Ce $^{l37}$ Cs에 의해서 결정된 냉각기간은, 조사후시험시설 (post irradiation examination facility)등과 같이 사용후핵연료 집합체를 해체 또는 절단하여 만든 시료를 취급하는 시설등에서,사용후핵연료에 대한 안전관리 및 계량관리를 위하여 유용하게 활용될 수 있을 것으로 사료되었다.것으로 사료되었다.

• 대한수학회지
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• 제43권5호
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• pp.1019-1045
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• 2006

As a natural generalization of a Sasakian space form, we define a contact strongly pseudo-convex CR-space form (of constant pseudo-holomorphic sectional curvature) by using the Tanaka-Webster connection, which is a canonical affine connection on a contact strongly pseudo-convex CR-manifold. In particular, we classify a contact strongly pseudo-convex CR-space form $(M,\;\eta,\;\varphi)$ with the pseudo-parallel structure operator $h(=1/2L\xi\varphi)$, and then we obtain the nice form of their curvature tensors in proving Schurtype theorem, where $L\xi$ denote the Lie derivative in the characteristic direction $\xi$.

• Kyungpook Mathematical Journal
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• 제55권2호
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• pp.345-353
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• 2015

Subnormality of bounded weighted composition operators on $L^2({\Sigma})$ of the form $Wf=uf{\circ}T$, where T is a nonsingular measurable transformation on the underlying space X of a ${\sigma}$-finite measure space (X, ${\Sigma}$, ${\mu}$) and u is a weight function on X; is studied. The standard moment sequence characterizations of subnormality of weighted composition operators are given. It is shown that weighted composition operators are subnormal if and only if $\{J_n(x)\}^{+{\infty}}_{n=0}$ is a moment sequence for almost every $x{{\in}}X$, where $J_n=h_nE_n({\mid}u{\mid}^2){\circ}T^{-n}$, $h_n=d{\mu}{\circ}T^{-n}/d{\mu}$ and $E_n$ is the conditional expectation operator with respect to $T^{-n}{\Sigma}$.

• Korean Journal of Mathematics
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• 제30권3호
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• pp.459-465
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• 2022

We exhibit various properties of the weighted Berezin operator T_α and its iteration T^k_α on L^p(𝜏), where α > -1 and 𝜏 is the invariant measure on the complex unit ball B_n. Iterations of T_α on L¹_R(𝜏) the space of radial integrable functions have performed important roles in proving 𝓜-harmonicity of bounded functions with invariant mean value property. We show differences between the case of 1 < p < ∞ and p = 1, ∞ under the infinite iteration of T_α or the infinite summation of iterations, most of which are extensions or related assertions to the propositions of the previous results.

• Nuclear Engineering and Technology
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• 제16권1호
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• pp.11-17
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• 1984

매우 작은 규모의 냉각재 상실 사고후($\leq$0.05ft$^2$) 어떤 일이 일어나는 가를 더 잘 이해하기 위해 고리 1호기에 대한 샘플 계산을 수행하였다 깨진 크기가 0.006 ft$^2$ 보다 큰 사고에 대해서는 냉각재 상실이 보충되는 양을 초과한다. 0.008 ft$^2$ 보다 큰 깨진 크기에 대해서는 잔열은 깨진 곳을 통해 완전히 제거된다. 이와 같은 결과에 비추어 고리 1호기는 매우 작은 규모의 냉각재 상실 사고의 전 영역에 걸쳐 비교적 안전하다고 결론지었다. 하지만, 900MWe 나 1200MWe 를 가진 원자로에 있어서, 어떤 깨진 크기에 대해서는 이 사고가 주의깊게 고려되어야 한다. 자연 순환에서 pool boiling 으로 또는 pool boiling에서 자연 순환으로 천이할때, 특별히 운전자와 안전 분석에 문제점을 남긴다. Primary pump shutoff, HPI pump shutoff, break isolation, opening relief valve의 운전자 간섭에 대해서도 논의 되었다. Shutoff 후 HPI pump의 연속적인 운전은 primary system의 건전성을 위협하지 않는다는 것이 증명되었다.

• 대한수학회보
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• 제53권4호
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• pp.1071-1085
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• 2016

For $b{\in}L^1_{loc}({\mathbb{R}}^n)$, let ${\mathcal{I}}_{\alpha}$ be the bilinear fractional integral operator, and $[b,{\mathcal{I}}_{\alpha}]_i$ be the commutator of ${\mathcal{I}}_{\alpha}$ with pointwise multiplication b (i = 1, 2). This paper shows that if the commutator $[b,{\mathcal{I}}_{\alpha}]_i$ for i = 1 or 2 is bounded from the product Morrey spaces $L^{p_1,{\lambda}_1}({\mathbb{R}}^n){\times}L^{p_2,{\lambda}_2}({\mathbb{R}}^n)$ to the Morrey space $L^{q,{\lambda}}({\mathbb{R}}^n)$ for some suitable indexes ${\lambda}$, ${\lambda}_1$, ${\lambda}_2$ and $p_1$, $p_2$, q, then $b{\in}BMO({\mathbb{R}}^n)$, as well as that the compactness of $[b,{\mathcal{I}}_{\alpha}]_i$ for i = 1 or 2 from $L^{p_1,{\lambda}_1}({\mathbb{R}}^n){\times}L^{p_2,{\lambda}_2}({\mathbb{R}}^n)$ to $L^{q,{\lambda}}({\mathbb{R}}^n)$ implies that $b{\in}CMO({\mathbb{R}}^n)$ (the closure in $BMO({\mathbb{R}}^n)$of the space of $C^{\infty}({\mathbb{R}}^n)$ functions with compact support). These results together with some previous ones give a new characterization of $BMO({\mathbb{R}}^n)$ functions or $CMO({\mathbb{R}}^n)$ functions in essential ways.