• 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.

• Journal of the Korean Institute of Landscape Architecture
• /
• v.26 no.2
• /
• pp.194-206
• /
• 1998

In 1977, Local governments' planting regulations for the development projects were established in accordance with the revised building law in Korea. A landscaped area, planting densities of trees and shrubs, a percentage of evergreen plants, minimum tree size and species were prescribed in the planting regulations. But the clauses for an excessive planting density and a high ratio of evergreen trees that the regulations includes, have been gradually in the way to a creative planting design, and raise a problem of poor growth of trees an a disordered planting landscape. Therefore, in this study the present planting regulations of 124 local governments throughout the country were analyzed and compared with 13 foreign local governments' of 4 countries ; Japan, the United States of America, Canada and Singapore. And the linitations and characteristics of the regulations are drawn as follows ; 1. The regulations focus on controlling the green spaces and plantings by quantitative methods such as controlling the number of trees and the landscaped area, which are inadequate for estimating the crown coverage of mature trees, and which areinadequate for estimating the crown coverage of mature trees, and implementing the function of polantings and the use of green spaces. 2. Minimums of tree densities are higher than those of foreign countries, especially higher about 10 times to 100 times than those of the United States of America. 3.Excessive number of evergreen trees and fruit trees should be planted under the present planting regulations, that results in constricting the creativity in planting design. 4. An article for using specific tree size, 2.0ms over in height makes it difficult to use a wide variety of different sizes of trees. And there is no incentive measures when larger trees are planted. To enhance the quality of green spaces and plantings, it is needed that the function and locating of green spaces and plantings have to be emphasized, and the planting density should be concerned about the mature tree size. The incentive measure to use various sizes of trees is also needed, and the regulations to use excessive number of evergreen trees or fruit trees should be loosened.

• Journal of Environmental Science International
• /
• v.28 no.12
• /
• pp.1147-1156
• /
• 2019

The purpose of this study was to analyze examples of green infrastructure presented by the American Society of Landscape Architects as a part of basic research to assess hub green spaces in cities. With the specific goal of green infrasturcture in mind, the study samples were classified according to their purpose: 'humanities', 'hydrology', 'ecology', and 'environment'. Based on this we assessed the elements of planning for the target sites and obtained the following results. With regard to the aspect of humanities, planning urban hub green spaces was related to the satisfaction in leisure activities and the 'quality of life' that people expect to enjoy at parks or other green areas in general. Rather than focusing on direct and visible benefits, which might come from green infrastructure's technological elements, people hoped that parks and green areas have macroscopic values. For hydrological characteristics, the 'ecologically manages stormwater' was applied the most in planning hub green spaces in cities, and it mainly took the form of technological elements or factors. Third, the planning elements pertaining to ecological characteristics were identified as a combination of strategies and technological elements that 'reintroduces native plants' and 'habitat for wildlife'. As for the plans to instill eco-friendly aspects, the study found that the research on air, climate, weather, heat reaction, soil, energy efficiency, and use and application of resources is important. However, it was difficult to measure the potential quantitative benefits of 'reusing or recycling materials', 'reducing urban heat', and 'cooling air temperature'. The result of this study is meaningful in that it can be used for the assessment of urban hub green spaces in the future.

• Bulletin of the Korean Mathematical Society
• /
• v.49 no.6
• /
• pp.1275-1289
• /
• 2012

In this manuscript we solve in the positive a question informally proposed by Enflo on the measure of the set of isometric reflection vectors in non-Hilbert 2-dimensional real Banach spaces. We also reformulate equivalently the separable quotient problem in terms of isometric reflection vectors. Finally, we give a new and easy example of a real Banach space whose dual has a non-trivial L-summand that does not come from an M-ideal in the predual.

• Bulletin of the Korean Mathematical Society
• /
• v.50 no.3
• /
• pp.901-914
• /
• 2013

Kwon and Bae gave an interpolation for a continuous form of H$\ddot{o}$lder's inequality for a real-valued bounded measurable function on a product of measure spaces. It is given some generalizations of their result.

• Journal of the Korean Mathematical Society
• /
• v.57 no.1
• /
• pp.61-88
• /
• 2020

In this paper, we investigate the existence of mild solutions for a class of fractional impulsive evolution equation with periodic boundary condition by means of the method of upper and lower solutions and monotone iterative method. Using the theory of Kuratowski measure of noncompactness, a series of results about mild solutions are obtained. Finally, two examples are given to illustrate our results.

• The Pure and Applied Mathematics
• /
• v.2 no.1
• /
• pp.1-8
• /
• 1995

Since the concept of Pettis integral was introduced in 1938 [10], the Pettis integrability of weakly measurable functions has been studied by many authors [5, 6, 7, 8, 9, 11]. It is known that there is a bounded function that is not Pettis integrable [10, Example 10. 8]. So it is natural to raise the question: when is a bounded function Pettis integrable\ulcorner(omitted)

• Journal of the Korean Society for Industrial and Applied Mathematics
• /
• v.16 no.2
• /
• pp.93-105
• /
• 2012

In this paper, we consider the controllability of a certain class of impulsive neutral evolution differential equations in Banach spaces. Sufficient conditions for controllability are obtained by using the Hausdorff measure of noncompactness and Monch fixed point theorem under the assumption of noncompactness of the evolution system.

• Journal of applied mathematics & informatics
• /
• v.23 no.1_2
• /
• pp.489-496
• /
• 2007

Let g be a continuous function on an interval I which is not constant on any subinterval of I, and let ${\mu}$ be a Borel measure on I. In this paper we give a necessary and sufficient conditions guaranteeing, for the strongly measurable function f on I with values in a Banach space X, the existence of a continuous primitive function F on I with respect to g.

• Journal of the Korean Mathematical Society
• /
• v.38 no.2
• /
• pp.283-296
• /
• 2001

The Heisenberg inequality associated with the uncertainty principle is extended to an infinite dimensional abstract Wiener space (H, B) with an abstract Wiener measure p$_1$. For $\phi$ $\in$ L$^2$(p$_1$) and T$\in$L(B, H), it is shown that (※Equations, See Full-text), where F(sub)$\phi$ is the Fourier-Wiener transform of $\phi$. The conditions when the equality holds also discussed.