• Journal of the Korean Society for Industrial and Applied Mathematics
• /
• 제9권2호
• /
• pp.1-15
• /
• 2005

In this article, a generalisation of Sard's inequality for Appell polynomials is obtained. Estimates for the remainder are also provided.

• Journal of the Korean Mathematical Society
• /
• 제51권3호
• /
• pp.443-462
• /
• 2014

Using a simple recurrence relation, we give a new method to compute the Jones polynomials of closed braids: we find a general expansion formula and a rational generating function for the Jones polynomials. The method is used to estimate the degree of the Jones polynomials for some families of braids and to obtain general qualitative results.

• Proceedings of the Korean Statistical Society Conference
• /
• 한국통계학회 2003년도 춘계 학술발표회 논문집
• /
• pp.25-30
• /
• 2003

We prove that the logarithm of the flow of stochastic differential equations is an element of the free Lie algebra generated by a finite set consisting of vector fields being coefficients of equations. As an application, we directly obtain a formula of the solution of stochastic differential equations given by Castell(1993) without appealing to an expansion for ordinary differential equations given by Strichartz (1987).

• Kyungpook Mathematical Journal
• /
• 제18권2호
• /
• pp.311-319
• /
• 1978

This paper deals with the evaluation of two definite integrals involving spheroidal wave function, H-function of two variables, and the generalized hypergeometric function. Also, an expansion formula for the product of generalized hypergeometric function and the H-function of two variables has been obtained. Since the H-function of two variables, spheroidal wave functions, and the generalized hypergeometric function may be transformed into a number of higher transcendental functions and polynomials, the results obtained in this paper include some known results as their particular cases. As an application of such results, a problem of heat conduction in a non-homogenous bar has been solved by using the generalized Legendre transform [9].

• Bulletin of the Korean Mathematical Society
• /
• 제58권5호
• /
• pp.1149-1161
• /
• 2021

In this paper, we present new bounds on the fundamental units of real quadratic fields ${\mathbb{Q}}({\sqrt{d}})$ using the continued fraction expansion of the integral basis element of the field. Furthermore, we apply these bounds to Dirichlet's class number formula. Consequently, we provide computational advantages to estimate the class numbers of such fields. We also give some numerical examples.

• Journal of the Korea institute for structural maintenance and inspection
• /
• 제28권2호
• /
• pp.1-8
• /
• 2024

The expansion joint is installed to offset the expansion of the superstructure and must ensure sufficient gap during its service life. In detailed guideline of safety inspection and precise safety diagnosis for bridge, damage due to lack or excessive gap is specified, but there are insufficient standards for determining the abnormal behavior of superstructures. In this study, a data-based maintenance was proposed by continuously monitoring the expansion-gap data of the same expansion joint. A total of 2,756 data were collected from 689 expansion joint, taking into account the effects of season. We have developed a method to evaluate changes in the expansion joint-gap that can analyze the thermal movement through four or more data at the same location, and classified the factors that affect the superstructure behavior and analyze the influence of each factor through deep learning and explainable artificial intelligence(AI). Abnormal behavior of the superstructure was classified into narrowing and functional failure through the expansion joint-gap evaluation graph. The influence factor analysis using deep learning and explainable AI is considered to be reliable because the results can be explained by the existing expansion gap calculation formula and bridge design.

• The Journal of Korean Institute for Practical Engineering Education
• /
• 제2권2호
• /
• pp.55-60
• /
• 2010

We usually encounter Electro-magnetics phenomenons and only feel some part of that, but it is hard to feel it visually. Moreover understanding physically and quantitatively is not a easy work. These electrostatic field theory, magnetostatic field theory and interchange magnetic field theory combined with electromagnetic field are formulated experimentally and theoretically by James Clerk Maxwell in 1873. Electromagnetic field takes electro-magnetic phenomenons as a expansion of formula originated in Maxwell equations. Since this is based on expansion of formula, it is hard to understand for many students not only middle school and high school students learning it at the first time but also college students studying physics as a elementary class and even majors in electromagnetic field. The program is developed as a visual aid to cope with these problems, and even to deal with complex problem to estimate solution using numerical method.

• Archives of Plastic Surgery
• /
• 제43권2호
• /
• pp.197-203
• /
• 2016

Background The aim of unilateral breast reconstruction after mastectomy is to craft a natural-looking breast with symmetry. The latissimus dorsi (LD) flap with implant is an established technique for this purpose. However, it is challenging to obtain adequate volume and satisfactory aesthetic results using a one-stage operation when considering factors such as muscle atrophy, wound dehiscence and excessive scarring. The two-stage reconstruction addresses these difficulties by using a tissue expander to gradually enlarge the skin pocket which eventually holds an appropriately sized implant. Methods We analyzed nine patients who underwent unilateral two-stage LD reconstruction. In the first stage, an expander was placed along with the LD flap to reconstruct the mastectomy defect, followed by gradual tissue expansion to achieve overexpansion of the skin pocket. The final implant volume was determined by measuring the residual expander volume after aspirating the excess saline. Finally, the expander was replaced with the chosen implant. Results The average volume of tissue expansion was 460 mL. The resultant expansion allowed an implant ranging in volume from 255 to 420 mL to be placed alongside the LD muscle. Seven patients scored less than six on the relative breast retraction assessment formula for breast symmetry, indicating excellent breast symmetry. The remaining two patients scored between six and eight, indicating good symmetry. Conclusions This approach allows the size of the eventual implant to be estimated after the skin pocket has healed completely and the LD muscle has undergone natural atrophy. Optimal reconstruction results were achieved using this approach.

• Journal of the Korean Society of Manufacturing Process Engineers
• /
• 제19권10호
• /
• pp.52-58
• /
• 2020

Bellows are corrugated mechanical elements used to absorb displacements or vibrations caused by temperature changes, pressure, earthquakes, waves, etc., which are welded to flanges or directly connected to pipes. Expansion joint bellows must not only be designed to sufficiently withstand the internal pressure of the pipes but also accommodate axial, transverse, and rotational deformations to minimize the transfer of forces to the sensitive components of the system. Bellows have various types of corrugations, but U-type bellows are most commonly used in general piping systems. In this study, the behavior of U-shaped one-, two-, and three-ply bellows with the same inner diameter under pressure and forced displacement was analyzed using the finite element method. The results were compared with the design formula in the Expansion Joint Manufacturers Association (EJMA)'s code. Manufacturer data were used for the applied pressure and force displacement. The behavioral characteristics of the three cases were compared via structural analysis because the stress levels will be different for each model, even if they have the same inner diameter. Since the analytical model has an axisymmetric shape but displacement occurs in the transverse direction, the finite element model was composed of 1/2 of the whole model, and ANSYS Workbench 17.2 was employed for the analysis.

• Transactions of the Korean Society of Mechanical Engineers
• /
• 제11권1호
• /
• pp.132-144
• /
• 1987

This paper presents the theroetical analysis of the crack tip stress intensity factor for a center crack in a finite width plate with variable thickness. The analyses were based on Laurent's expansions of complex stress potentials where the expansion coefficients are determined from the boundary conditions. The perturbation method was employed in numerical calculations. The correction factor F(.lambda.)is given in the form of power series of .lambda. [a numerical formula] where .lambda.=a/w$^{1}$; Dimensionless crack length, .betha.=t$_{2}$/t; Thickness ratio .omega.=w$_{2}$/w$_{1}$; width ratio The correction factor values vary with the width ratio .omega. and the maximum variation occurs around .betha.=1. For the case of .betha.=1 or .betha.=0 (uniform thickness plate0, the correction factor values agree well with Feddersen's formula. In all cases, as .lambda. approaches to 1 (thickness interface), the correction factor values are decreased rapidly for .betha.>1, and increased rapidly for .betha.<1.