• Journal of the Korean Mathematical Society
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• v.58 no.3
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• pp.633-642
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• 2021

In this paper we consider the following strongly damped wave equation with variable-exponent nonlinearity u_tt(x, t) - ∆u(x, t) - ∆u_t(x, t) = |u(x, t)|^p(x)-2u(x, t), where the exponent p(·) of nonlinearity is a given measurable function. We establish finite time blow-up results for the solutions with non-positive initial energy and for certain solutions with positive initial energy. We extend the previous results for strongly damped wave equations with constant exponent nonlinearity to the equations with variable-exponent nonlinearity.

• Transactions of Materials Processing
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• v.1 no.1
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• pp.42-51
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• 1992

The ring compression test has been widely employed as an experimental means to determine the friction factor. The calibration curves are obtained by the rigid-plastic finite element analysis for various work-hardening exponent and strain-rate hardening exponent. The effects of work-hardening exponent and strain-rate hardening exponent are thoroughly studied and discussed from the finite element computation. The change of friction factor during height reduction in ring compression is also discussed. Then, the method to estimate the change of friction factor during ring compression is proposed.

• Asian Journal of Atmospheric Environment
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• v.6 no.4
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• pp.304-313
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• 2012

In this study, the ${\AA}$ngstrom exponent for polydispersed aerosol during dynamic processes was investigated. Log-normal aerosol size distribution was assumed, and a sensitivity analysis of the ${\AA}$ngstrom exponent with regards the coagulation and condensation process was performed. The ${\AA}$ngstrom exponent is expected to decrease because of the particle growth due to coagulation and condensation. However, it is difficult to quantify the degree of change. In order to understand quantitatively the change in the ${\AA}$ngstrom exponent during coagulation and condensation, different real and imaginary parts of the refractive index were considered. The results show that the ${\AA}$ngstrom exponent is sensitive to changes in size distribution and refractive index. The total number concentration decreases and the geometric mean diameter of aerosols increase during coagulation. On the while, the geometric standard deviation approaches monodispersed size distribution during the condensation process, and this change in size distribution affects the ${\AA}$ngstrom exponent. The degree of change in the ${\AA}$ngstrom exponent depends on the refractive index and initial size distribution, and the size parameter changes with the ${\AA}$ngstrom exponent for a given refractive index or chemical composition; this indicates that the size distribution plays an important role in determining the ${\AA}$ngstrom exponent as well as the chemical composition. Subsequently, this study shows how the ${\AA}$ngstrom exponent changes quantitatively during the aerosol dynamics processes for a log-normal aerosol size distribution for different refractive indices; the results showed good agreement with the results for simple analytic size distribution solutions.

• Nuclear Engineering and Technology
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• v.10 no.2
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• pp.73-78
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• 1978

The effect of temperature and strain rate on the deformation behavior of $\alpha$-uranium was investigated in the temperature ranged 300$^{\circ}$ to 55$0^{\circ}C$ by strain, rate change test. Strain rate sensitivity, activation volume, strain rate sensitivity exponent and dislocation velocity exponent were determined. The strain rate sensitivity exponent and dislocation velocity exponent were determined. The strain rate sensitivity exponent increases with strain below 40$0^{\circ}C$, while the exponent decreases with strain above 50$0^{\circ}C$. It is believed that the increase of strain rate sensitivity exponent with strain below 40$0^{\circ}C$ can be attributed to an increase in internal stress as a result of work hardening while decrease of the exponent with strain above 50$0^{\circ}C$ is due to predominance of thermal softening over work hardening because more slip, system are active in deformation above about 50$0^{\circ}C$.

• Bulletin of the Korean Mathematical Society
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• v.57 no.6
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• pp.1427-1449
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• 2020

In this paper, we establish the boundedness of the m-linear Calderón-Zygmund operators on product of central Morrey spaces with variable exponent. The corresponding boundedness properties of their commutators with λ-central BMO symbols are also considered. Finally, we prove that the multilinear commutators of Calderón-Zygmund singular integrals introduced by Pérez and Trujillo-Gonález are bounded on central Morrey spaces with variable exponent. Our results improve and generalize some previous classical results to the variable exponent setting.

• Proceedings of the IEEK Conference
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• 1998.10a
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• pp.1215-1218
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• 1998

본 논문은 Digital Audio Compression(AC-3) Standard 인 A-52를 기반으로 하였으며 Borland C++3.1 Compiler를 사용하여 AC-3 Decoding Algorithm 구현하였다. Input Stream은 DVD VOB File에서 AC-3 Stream만을 분리하여 사용하며 최종 출력은 16 Bit PCM File이다. AC-3의 Frame구조는 Synchronization Information, Bit Stream Information, Audio Block, Auxiliary Data, Error Check로 구성된다. Aduio Block 은 모두 6개의 Block으로 나뉘어져 있다. BSI와 Side Information을 참조하여 Exponent를 추출하여 Exponent Strategy에 따라 Exponent를 복원한다. 복원된 Exponent 정보를 이용하여 Bit Allocation을 수행하여 각각의 Mantissa에 할당된 Bit수를 계산하고 Stream으로부터 Mantissa를 추출한다. Coupling Parameter를 참조하ㅕ Coupling Channel을 Original Channel로 복원시킨다. Stereo Mode에 대해서는 Rematrixing을 수행한다. Dynamic Range는 Mantissa와 Exponent의 Magnitude를 바꾸는 것으로 선택적으로 사용할 수 있다. Mantissa와 Exponent를 결합하여 Floating Point coefficient로 만든 후 Inverse Transform을 수행하면 PCM Data를 얻을 수 있다. PC에서 듣기 위해서는 Multi Channel을 Stereo나 Mono로 Downmix를 수행한다. 이렇게 만들어진 PCM data는 PCM Data를 재생하는 프로그램으로 재생할 수 있다.

• Proceedings of the Korean Society for Noise and Vibration Engineering Conference
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• 2001.11b
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• pp.1182-1188
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• 2001

The objective of this paper is to show the effectiveness of the wavelet transform by means of its capability to estimate the Lipschitz exponent. In particular, we show that the magnitude of the Lipschitz exponent can be used as a useful tool estimating the damage extent. An effective method based on the Lipschitz exponent is proposed and we present the results investigated both numerically and experimentally. The continuous wavelet transform by a Mexican hat wavelet having two vanishing moments is utilized for the estimation of the Lipschitz exponent.

• Structural Engineering and Mechanics
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• v.17 no.3_4
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• pp.409-428
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• 2004

In this paper, a Holder exponent, a measure of the degree to which a signal is differentiable, is presented to detect the presence of a discontinuity and when the discontinuity occurs in a dynamic signal. This discontinuity detection has potential applications to structural health monitoring because discontinuities are often introduced into dynamic response data as a result of certain types of damage. Wavelet transforms are incorporated with the Holder exponent to capture the time varying nature of discontinuities, and a classification procedure is developed to quantify when changes in the Holder exponent are significant. The proposed Holder exponent analysis is applied to various experimental signals to reveal underlying damage causing events from the signals. Signals being analyzed include acceleration response of a mechanical system with a rattling internal part, acceleration signals of a three-story building model with a loosing bolt, and strain records of an in-situ bridge during construction. The experimental results presented in this paper demonstrate that the Holder exponent can be an effective tool for identifying certain types of events that introduce discontinuities into the measured dynamic response data.

• The Pure and Applied Mathematics
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• v.7 no.2
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• pp.87-100
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• 2000

In this paper, we try to approach chasos with numerical method. After investigating nonlinear dynamcis (chaos) theory, we introduce Lyapunov exponent as chaos\`s index. To look into the existence of chaos in 2-dimensional difference equation we computes Lypunov exponent and examine the various behaviors of solutions by difurcation map.

• Korean Journal of Mathematics
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• v.19 no.4
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• pp.367-379
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• 2011

In this paper, we find the maximum exponent of primitive simple graphs G under the restriction $deg(v){\geq}3$ for all vertex $v$ of G. Our result is also an answer of a Klee and Quaife type problem on exponent to find minimum number of vertices of graphs which have fixed even exponent and the degree of whose vertices are always at least 3.