• Journal of applied mathematics & informatics
• /
• v.26 no.3_4
• /
• pp.689-706
• /
• 2008

In this paper, a fifth order numerical method is presented for solving singularly perturbed two point boundary value problems with a boundary layer at one end point. The two point boundary value problem is transformed into general first order ordinary differential equation system. A discrete approximation of a fifth order compact difference scheme is presented for the first order system. An asymptotically equivalent first order equation of the original singularly perturbed two point boundary value problem is obtained from the theory of singular perturbations. It is used in the fifth order compact difference scheme to get a two term recurrence relation and is solved. Several linear and non-linear singular perturbation problems have been solved and the numerical results are presented to support the theory. It is observed that the present method approximates the exact solution very well.

• Journal of the Korea Concrete Institute
• /
• v.12 no.4
• /
• pp.59-67
• /
• 2000

With increased height of structure, the effect of column shortening need special consideration in the design and construction of high-rise buildings. The shortening of each column affects nonstructural members such as partitions, cladding, and M/E systems, which are not designed to carry gravity forces. The slabs and beams will tilt due to the cumulative differential shortening of adeacent vertical members. The main purpose of estimating the total shortening of vertical structural member is to compensate the differential shortening between adeacent members. This paper presents effect of parameters for phenomenon of column shortening in vertical members. The paper presents effect of parameters for phenomenon of column shortening in vertical members. The conclusions obtained from this study are follow as ; Strength of concrete and steel ratio effected on column shortening caused by elastic and inelastic shortening. Also, it is known that Ultimate-shrinkage-Value, Specific-Creep-Value, and volume to surface ratio effected on inelastic shortening only. Particularly, Ultimate-Shrinkage-Value and Specific-Creep-Value effected considerable on the amount of total column shortening.

• International Journal of Reliability and Applications
• /
• v.7 no.2
• /
• pp.155-166
• /
• 2006

Many software reliability growth models (SRGMs) based on nonhomogeneous Poisson process (NHPP) have been developed and applied in practice. NHPP SRGMs are characterized by their mean value functions. Mean value functions are usually derived from differential equations representing the fault detection/removal process during testing. In this paper such differential equations are regarded as frameworks for generating mean value functions. Currently available frameworks are theoretically discussed with respect to capability of representing the fault detection/removal process. Then two general frameworks are proposed.

• Knowledge Management Research
• /
• v.11 no.3
• /
• pp.1-11
• /
• 2010

The importance of intangible assets have increased unprecedentedly with the advent of the knowledge-based society. Investment in R&D has contributed to the rise of productivity and firm-value in the capital markets. but it is very difficult to determine the economic benefits of R&D investment, due to elusive link between time requirements and the realization of firm value from R&D investment. This study examines the differential effects of R&D expenditure and patents on firm-value by industry. Patents are intangible, proprietary rights that develops new products, plays a crucial role in market competition and results in research and development activities. If firms get patents, their R&D expenditure is assumed to be successful. The study analyzes whether successful R&D expenditure has a significant effect on the firm-value. The study considers two industries : high-tech industries and low-tech industries. These industries are expected to have different effect on R&D expenditure and firm-vale. The results of the study indicate that the successful R&D expenditure increased the firm-value. Successful R&D expenditure in high-tech industries more increased the firm-value more than that in low-tech industries.

• Bulletin of the Korean Mathematical Society
• /
• v.40 no.2
• /
• pp.195-205
• /
• 2003

For the boundary value problem (BVP) of second order functional differential equations for the one-dimensional $\rho$-Laplaclan: ($\Phi$$_{\rho}$(y'))'(t)+m(t)f(t, $y^{t}$ )=0 for t$\in$[0,1], y(t)=η(t) for t$\in$[-$\sigma$,0], y'(t)=ξ(t) for t$\in$[1,d], suitable conditions are imposed on f(t, $y^{t}$ ) which yield the existence of at least two positive solutions. Our result generalizes the main result of Avery, Chyan and Henderson.

• Kyungpook Mathematical Journal
• /
• v.55 no.4
• /
• pp.997-1030
• /
• 2015

This paper is concerned with integral type boundary value problems of second order singular differential equations with quasi-Laplacian on whole lines. Sufficient conditions to guarantee the existence and non-existence of positive solutions are established. The emphasis is put on the non-linear term $[{\Phi}({\rho}(t)x^{\prime}(t))]^{\prime}$ involved with the nonnegative singular function and the singular nonlinearity term f in differential equations. Two examples are given to illustrate the main results.

• Journal of Korean Association for Spatial Structures
• /
• v.2 no.3 s.5
• /
• pp.115-122
• /
• 2002

It is often hard to obtain analytical solutions of boundary value problems of shells. Introducing some approximations into the governing equations may allow us to get analytical solutions of boundary value problems. Instead of an analytical procedure, we can apply a numerical method to the governing equations. Since the governing equations of shells of revolution under symmetric load are expressed by ordinary differential equations, a numerical solution of ordinary differential equations is applicable to solve the equations. In this paper, the governing equations of orthotropic spherical shells under symmetric load are derived from the classical theory based on differential geometry, and the analysis is numerically carried out by computer program of Runge-Kutta methods. The numerical results are compared to the solutions of a commercial analysis program, SAP2000, and show good agreement.

• Journal of applied mathematics & informatics
• /
• v.7 no.1
• /
• pp.183-193
• /
• 2000

In this paper we use measure theory to solve a wide range of second-order boundary value ordinary differential equations. First, we transform the problem to a first order system of ordinary differential equations(ODE's)and then define an optimization problem related to it. The new problem in modified into one consisting of the minimization of a linear functional over a set of Radon measures; the optimal measure is then approximated by a finite combination of atomic measures and the problem converted approximatly to a finite-dimensional linear programming problem. The solution to this problem is used to construct the approximate solution of the original problem. Finally we get the error functional E(we define in this paper) for the approximate solution of the ODE's problem.

• Asian Pacific Journal of Cancer Prevention
• /
• v.13 no.5
• /
• pp.2081-2085
• /
• 2012

Background: To investigate the value of ultrasound elastography (UE) in the differentiation between benign and malignant enlarged cervical lymph nodes (LNs). Methods: B-mode ultrasound, power Doppler imaging and UE were examined to determine LN characteristics. Two kinds of methods, 4 scores of elastographic classification and a strain ratio (SR) were used to evaluate the ultrasound elastograms. Results: The cutoff point of SR had high utility in differential diagnosis of benign and malignant of cervical lymph nodes, with good sensitivity, specificity and accuracy. Conclusion: UE is an important aid in differential diagnosis of benign and malignant cervical LNs.

• Journal of applied mathematics & informatics
• /
• v.27 no.3_4
• /
• pp.501-515
• /
• 2009

A second order nonlinear ordinary differential equation is obtained by solving the initial-boundary value problem of a class of elas-todynamics equations, which models the radially symmetric motion of a incompressible hyper-elastic solid sphere under a suddenly applied surface tensile load. Some new conclusions are presented. All existence conditions of nonzero solutions of the ordinary differential equation, which describes cavity formation and motion in the interior of the sphere, are presented. It is proved that the differential equation has singular periodic solutions only when the surface tensile load exceeds a critical value, in this case, a cavity would form in the interior of the sphere and the motion of the cavity with time would present a class of singular periodic oscillations, otherwise, the sphere remains a solid one. To better understand the results obtained in this paper, the modified Varga material is considered simultaneously as an example, and numerical simulations are given.