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A MODIFIED SELF-AVOIDING WALK MODEL ON THE SQUARE LATTICE WITH REFLECTING AND ABSORBING BARRIERS
SONG, JUNHO 한국산업정보응용수학회 2000 한국산업정보응용수학회 Vol.4 No.2
Well known is the directed self-avoiding walk model on the square lattice with reflecting and absorbing barriers. We consider two models, namely, a pyramid self-avoiding polygon model and a top and bottom pyramid polygon model, as sub collections of the model. We derive explicit formulas for the number of 2N-step polygons in these models.
The expected independent domination number of random directed rooted trees
Junho Song,Changwoo Lee 대한수학회 2004 대한수학회지 Vol.41 No.5
We derive a formula for the expected value µ(n) of the independent domination number of a random directed rooted tree with n labeled vertices and determine the asymptotic behavior of µ(n) as n goes to infinity.
On the Generalized Convex Functions
SONG, Huhn-Jong,SONG, Junho 釜山水産大學校 1981 釜山水産大學 硏究報告 Vol.21 No.2
The functional operations of generalized convex functions, relation between generalized convex sets and generalized convex functions, topological properties of generalized convex sets, topological propertey of supports of generalized convex functions in function space and the existence of a maximal element in the set Φ={ΓεΦ:f is Γconvex} were studied by using following property: property 1. Given any two points x₁and x₂in (a, b) and two real numbers y₁and y₂there is a unique member of ?? passing through (x₁,y₁) and (x₂,y₂). And for each ?? F is continuous on (a, b). We get following main results: 1. Let Γ be a family of functions given by F(x)=ax+β+Φ(x), (α, βεR), where is Γ convex function defined on (a, b). (1) If f and g are Γ convex, then so is f+g. (2) If λ>1 and f is Γ convex, then so is λf. 2. f is Γ convex if and only if epi f={(x, y)εR: f(x)<y} is Γ convex. 3. Let C be a non empty subset of R. If C is Γ convex, then (1) The closure of C, Cl(C) is Γ convex. (2) The non empty interior of C, Int (C) is Γ convex. 4. Let f be a Γ convex function defined on (a, b) and let (∂f)(x)={FεΓ: F supports f at xε(a, b)}. Then (∂f)(x) is closed in C((a, b): R) for each xε(a, b). 5. Let Φ be a subset of Φ with the following property: property 2. Given x₁, x₂ε(a, b) and y, yεR, there exists a continuous function g defined on (a, b) such that ?? on (x₁,x₂) and ?? out side the interval (x₁, x₂) for anx FεΓεΦ determined by (x₁,y₂) and (x₁,y₂). If f is Γ convex for some ΓεΦ, then ψ'={ΓεΦ': f is Γ convex} has a maximal element in ψ.
One Dimensional Random Walks with Reflecting Barriers
SONG,Junho 釜山水産大學校 1980 釜山水産大學 硏究報告 Vol.20 No.2
reflecting points가 2개 있는 일차원 비대칭 취보에 관한 제 성질을 조사하였다. 특히, 이 논고에서는 다른 논문에서 거의 찾아 볼 수 없는 recurrence properties, the mean recurrence time 그리고 walker가 n step 후에 방문하는 lattice points의 수등에 대한 제 성질을 Green’s function method를 사용하여 이에 대한 엄밀한 식을 유도하였다.
Artificial Intelligence in the Design of Innovative Metamaterials: A Comprehensive Review
JunHo Song,Jae Hoon Lee,Namjung Kim,Kyoungmin Min 한국정밀공학회 2024 International Journal of Precision Engineering and Vol.25 No.1
Artificial intelligence-based algorithms are becoming essential tools in materials science-related fields because of their excellent functionality in reflecting physics in the training database and predicting the properties of unexplored materials with outstanding accuracy. Designing novel materials with engineered properties, such as metamaterials, is the key to revolutionizing material discovery, and machine learning (ML) and deep learning (DL) can be powerful and indispensable tools for acceleration. This review focuses on the implementation of ML/DL-based approaches for designing metamaterials. Quantum–mechanical, atomistic, and macroscale simulation methods are also assessed as database construction processes. Forward and inverse design methods are summarized in detail, and breakthroughs in generative models are particularly introduced. Moreover, applications in fundamental property prediction and material structural design are reviewed. Finally, the remaining challenging tasks for future related work are presented.