• The Mathematical Education
• /
• v.23 no.1
• /
• pp.35-38
• /
• 1984

• Journal of the Korean Institute of Telematics and Electronics C
• /
• v.35C no.5
• /
• pp.11-16
• /
• 1998

We analyze the software reliability growth models for the specified period from the viewpoint of theory of differential equations. we defien a genralized form of reliability growth models as follws: dN(t)/dt = b(t)f(N(t)), Where N(t) is the number of remaining faults and b(t) is the failure rate per software fault at time t. We show that the well-known three software reliability growth models - Goel - Okumoto, s-shaped, and Musa-Okumoto model- are special cases of the generalized form. We, also, extend the generalized form into an extended form being dN(t)/dt = b(t, .gamma.)f(N(t)), The genneralized form can be obtained if the distribution of failures is given. The extended form can be used to describe a software reliabilit growth model having weibull density function as a fault exposure rate. As an application of the generalized form, we classify three mentioned models according to the forms of b(t) and f(N(t)). Also, we present a case study applying the generalized form.

• Journal of Pharmaceutical Investigation
• /
• v.39 no.2
• /
• pp.117-120
• /
• 2009

Two crystal forms of ziprasidone have been isolated by recrystallization from different organic solvents and characterized by differential scanning calorimetry, powder X-ray diffractometry and thermogravimetric analysis. It was confirmed that Form 2 has the same crystal structure as Form 1.

• 제어로봇시스템학회:학술대회논문집
• /
• 1989.10a
• /
• pp.947-951
• /
• 1989

A Class of nonlinear distributed parameter control problems is first stated in a partial differential equation form in multi-index notion and then converted into an integral equation form. Necessary conditions for optimality in the form of maximum principle are then derived in Sobolev space W$^{l}$, p/(1 leq. p .leq. .inf.)..

• Journal of the Korean Chemical Society
• /
• v.63 no.1
• /
• pp.7-11
• /
• 2019

Olmutinib, N-[3-({2-[4-(4-methylpiperazine-1-yl)aniline]thieno[3,2-d]Pyrimidin-4-yl}oxy)phenyl]prop-2-enamide dihydrochloride monohydrate, $Olita^{TM}$ is an oral, third-generation epidermal growth factor receptor tyrosine kinase inhibitor (EGFR TKI) that was developed by Boehringer Ingelheim and Hanmi Pharmaceutical Co. Ltd for the treatment of non-small cell lung cancer (NSCLC). The aim of this work was to investigate the existence of polymorphs and pseudopolymorphs of olmutinib. Three crystal forms of olmutinib have been isolated by recrystallization and characterized by differential scanning calorimetry (DSC), thermogravimetric (TG) analysis and powder X-ray diffractometry (PXRD). From the DSC and TG data it was confirmed that Form 1 is monohydrate, Form 2 is dihydrate, Form 3 is 1.5 hydrate. The PXRD patterns of three crystal forms were different respectively. After storage of 1 month at $2^{\circ}C$, 24% RH (Relative Humidity), Form 1, Form 2, and Form 3 were not transformed.

• International Journal of Contents
• /
• v.11 no.4
• /
• pp.56-69
• /
• 2015

This paper proposes an efficient image encryption scheme based on quintuple encryption using two chaotic maps. The encryption process is realized with quintuple encryption by calling the encrypt(E) and decrypt(D) functions five times with five different keys in the form EDEEE. The decryption process is accomplished in the reverse direction by invoking the encrypt and decrypt functions in the form DDDED. The keys for the quintuple encryption/decryption processes are generated by using a Tent map. The chaotic values for the encrypt/decrypt operations are generated by using a Gumowski-Mira map. The encrypt function E is composed of three stages: permutation, pixel value rotation and diffusion. The permutation stage scrambles all the rows and columns to chaotically generated positions. This stage reduces the correlation radically among the neighboring pixels. The pixel value rotation stage circularly rotates all the pixels either left or right, and the amount of rotation is based on chaotic values. The last stage performs the diffusion four times by scanning the image in four different directions: Horizontally, Vertically, Principal diagonally and Secondary diagonally. Each of the four diffusion steps performs the diffusion in two directions (forward and backward) with two previously diffused pixels and two chaotic values. This stage ensures the resistance against the differential attacks. The security and performance of the proposed method is investigated thoroughly by using key space, statistical, differential, entropy and performance analysis. The experimental results confirm that the proposed scheme is computationally fast with security intact.

• Nuclear Engineering and Technology
• /
• v.33 no.4
• /
• pp.409-422
• /
• 2001

The dynamic character of a system of the governing differential equations for the one- dimensional two-fluid model, where the momentum flux parameters are employed to consider the velocity and void fraction distribution in a flow channel, is investigated. In response to a perturbation in the form of a＇traveling wave, a linear stability analysis is peformed for the governing differential equations. The expression for the growth factor as a function of wave number and various flow parameters is analytically derived. It provides the necessary and sufficient conditions for the stability of the one-dimensional two-fluid model in terms of momentum flux parameters. It is demonstrated that the one-dimensional two-fluid model employing the physical momentum flux parameters for the whole range of dispersed flow regime, which are determined from the simplified velocity and void fraction profiles constructed from the available experimental data and $C_{o}$ correlation, is stable to the linear perturbations in all wave-lengths. As the basic form of the governing differential equations for the conventional one-dimensional two-fluid model is mathematically ill posed, it is suggested that the velocity and void distributions should be properly accounted for in the one-dimensional two-fluid model by use of momentum flux parameters.s.

• The Journal of Korean Institute of Communications and Information Sciences
• /
• v.15 no.1
• /
• pp.21-28
• /
• 1990

In this paper, the effects of Intersymbol Interference(ISI) of Gaussian filtered minimum shift Keying (GMSK) with two-bit differential defection on the probability of error is analyzed theoretically in fast Rayleigh fading characterizing land mobile radio channels and a closed form for the probability of error is derived. Numerical results are presented for cased of interest, BT=0.25 to 0.4, taking fading rate $f_\rho$T as a parameter. It is shown that the probability of error taking the ISI of the only one adjacent bit into consideration is accurate enough to evaluate the performance of GMSK with two-bit differential detetion.

• Journal of Advanced Marine Engineering and Technology
• /
• v.8 no.1
• /
• pp.100-111
• /
• 1984

The methods solving the 2nd order linear ordinary differential equations of the form y"+H(x)y'+G(x)y=P(x) using Fourier series are presented in this paper. These methods are applied to the differential equations of which the exact solutions are known, and the solutions by Fourier series are compared with the exact solutions. The main results obtained in these studies are summarized as follows; 1) The product and the quotient of two functions expressed in Fourier series can be expressed also in Fourier series and the relations between the Fourier coefficients of the series are obtained by multiplying term by term. 2) If the solution of the 2nd order lindar ordinary differential equation exists in a certain interval, the solution can be obtained using Fourier series and can be expressed in Fourier series. 3) The absolute errors of Fourier series solutions are generally less in the center of the interval than in the end of the interval. 4) The more terms are considered in Fourier series solutions, the less the absolute errors.rors.

• Bulletin of the Korean Mathematical Society
• /
• v.57 no.4
• /
• pp.1061-1073
• /
• 2020

In this paper, the expressions of meromorphic solutions of the following nonlinear complex differential equation of the form $$f^n+Qd(z,f)=\sum\limits_{i=1}^{3}pi(z)e^{{\alpha}_i(z)}$$ are studied by using Nevanlinna theory, where n ≥ 5 is an integer, Q_d(z, f) is a differential polynomial in f of degree d ≤ n - 4 with rational functions as its coefficients, p₁(z), p₂(z), p₃(z) are non-vanishing rational functions, and α₁(z), α₂(z), α₃(z) are nonconstant polynomials such that α'₁(z), α'₂(z), α'₃(z) are distinct each other. Moreover, examples are given to illustrate the accuracy of the condition.