• Journal of the Korean Mathematical Society
• /
• v.34 no.3
• /
• pp.731-770
• /
• 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.

• Bulletin of the Korean Mathematical Society
• /
• v.38 no.4
• /
• pp.773-786
• /
• 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$_{n}$ ).

• Journal of the Korean Mathematical Society
• /
• v.49 no.3
• /
• pp.571-583
• /
• 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
• /
• v.7 no.3
• /
• pp.209-221
• /
• 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
• /
• v.25 no.2
• /
• pp.237-247
• /
• 1993

Activity ratio of two radioactive primary fission products which had sufficiently different half-lives was expressed as functions of cooling time and irradiation histories in which average burnup, irradiation time, cycle interval time and the dominant fissile material of the spent fuel were included. The gamma-ray spectra of 36 samples from 6 spent PWR fuel assemblies irradiated in Kori unit-1 reactor were obtained by a spectrometric system equipped with a high purity germanium gamma-ray detector. Activity ratio $^{l44}$Ce $^{l37}$Cs, analyzed from each spectrum, was used for the calculation of cooling time. The results show that the radioactive fission products $^{l44}$Ce and $^{l37}$Cs are considered as useful monitors for cooling time determination because the estimated cooling time by detection of activity ratio $^{l44}$Ce $^{l37}$Cs agreed well with the operator declared cooling time within relative difference of $\pm$5 % despite the low counting rate of the gamma-ray of $^{l44}$Ce (about 10$^{-3}$ count per second). For the samples with several different irradiation histories, the determined cooling time by modeled irradiation history showed good agreement with that by known irradiation history within time difference of $\pm$0.5 year. From this result, it would be expected to be possible to estimate reliably the cooling time of spent nuclear fuel without the exact information about irradiation history. The feasibility study on identification of and/or sorting out spent nuclear fuel by applying the technique for cooling time determination was also performed and the result shows that the detection of activity ratio $^{l44}$Ce $^{l37}$Cs by gamma-ray spectrometry would be usefully applicable to certify spent nuclear fuel for the purpose of safeguards and management in a facility in which the samples dismantled or cut from spent fuel assemblies are treated, such as the post irradiation examination facility.mination facility.

• Journal of the Korean Mathematical Society
• /
• v.43 no.5
• /
• pp.1019-1045
• /
• 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
• /
• v.55 no.2
• /
• pp.345-353
• /
• 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
• /
• v.30 no.3
• /
• pp.459-465
• /
• 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
• /
• v.16 no.1
• /
• pp.11-17
• /
• 1984

Sample calculations were done for KORI-1 to develop a better understanding of what happens after very small LOCA ($\leq$0.05 ft$^2$). For a water-side break with the break size larger than 0.006 ft$^2$, fluid-loss through break exceeds the makeup. If the break size is larger than 0.008ft$^2$, decay heat can be completely removed through break. Based on these results, it was concluded that KORI-1 is fairly safe for the whole spectrum of sizes in very small LOCA. However, for the reactor with 900 MWe or 1200 MWe, a certain spectrum of sizes in very small LOCA should be carefully considered. In the accident sequence the transition from natural circulation to pool boiling or from pool boiling to natural circulation may be troublesome to the operator or in the safety analysis. Operator's intervention was discussed; primary pump shutoff, HPI pump shutoff, break isolation, and opening relief valve. It was proved that continuous operation of HPI pumps after shutdown will not threaten the integrity of the primary system.

• Bulletin of the Korean Mathematical Society
• /
• v.53 no.4
• /
• pp.1071-1085
• /
• 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.