• 제목/요약/키워드: sine equation

검색결과 71건 처리시간 0.024초

유한 요소 해석을 이용한 고주파 간 종양 절제술의 입력 파형 최적화를 위한 연구 (A Study For Optimizing Input Waveforms In Radiofrequency Liver Tumor Ablation Using Finite Element Analysis)

  • 임도형;남궁범석;이태우;최진승;탁계래;김한성
    • 대한의용생체공학회:의공학회지
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    • 제28권2호
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    • pp.235-243
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    • 2007
  • Hepatocellular carcinoma is significant worldwide public health problem with an estimated annually mortality of 1,000,000 people. Radiofrequency (RF) ablation is an interventional technique that in recent years has come to be used for treatment of the hepatocellualr carcinoma, by destructing tumor tissues in high temperatures. Numerous studies have been attempted to prove excellence of RF ablation and to improve its efficiency by various methods. However, the attempts are sometimes paradox to advantages of a minimum invasive characteristic and an operative simplicity in RF ablation. The aim of the current study is, therefore, to suggest an improved RF ablation technique by identifying an optimum RF pattern, which is one of important factors capable of controlling the extent of high temperature region in lossless of the advantages of RF ablation. Three-dimensional finite element (FE) model was developed and validated comparing with the results reported by literature. Four representative Rf patterns (sine, square, exponential, and simulated RF waves), which were corresponding to currents fed during simulated RF ablation, were investigated. Following parameters for each RF pattern were analyzed to identify which is the most optimum in eliminating effectively tumor tissues. 1) maximum temperature, 2) a degree of alteration of maximum temperature in a constant time range (30-40 second), 3) a domain of temperature over $47^{\circ}C$ isothermal temperature (IT), and 4) a domain inducing over 63% cell damage. Here, heat transfer characteristics within the tissues were determined by Bioheat Governing Equation. Developed FE model showed 90-95% accuracy approximately in prediction of maximum temperature and domain of interests achieved during RF ablation. Maximum temperatures for sine, square, exponential, and simulated RF waves were $69.0^{\circ}C,\;66.9^{\circ}C,\;65.4^{\circ}C,\;and\;51.8^{\circ}C$, respectively. While the maximum temperatures were decreased in the constant time range, average time intervals for sine, square, exponential, and simulated RE waves were $0.49{\pm}0.14,\;1.00{\pm}0.00,\;1.65{\pm}0.02,\;and\;1.66{\pm}0.02$ seconds, respectively. Average magnitudes of the decreased maximum temperatures in the time range were $0.45{\pm}0.15^{\circ}C$ for sine wave, $1.93{\pm}0.02^{\circ}C$ for square wave, $2.94{\pm}0.05^{\circ}C$ for exponential wave, and $1.53{\pm}0.06^{\circ}C$ for simulated RF wave. Volumes of temperature domain over $47^{\circ}C$ IT for sine, square, exponential, and simulated RF waves were 1480mm3, 1440mm3, 1380mm3, and 395mm3, respectively. Volumes inducing over 63% cell damage for sine, square, exponential, and simulated RF waves were 114mm3, 62mm3, 17mm3, and 0mm3, respectively. These results support that applying sine wave during RF ablation may be generally the most optimum in destructing effectively tumor tissues, compared with other RF patterns.

고속전철 슬레브궤도에서의 노반거동 특성에 관한 연구 (A Study on the Behavior Character of Roadbed in High-Speed Railway Slab Tract)

  • 조용권;이성혁;황선근
    • 한국지반공학회:학술대회논문집
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    • 한국지반공학회 2000년도 가을 학술발표회 논문집
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    • pp.319-326
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    • 2000
  • It is investigated character of the dynamic behavior at over excavation zone of roadbed using crushed stone instead of lean concrete. It is considered that behavior of roadbed using PENTAGON-3D and Baber's equation. Typical load of sine wave type using impact factor is compared to moving load system to examine relationship in using PENTAGON-3D case. Variations of this paper are material properties of roadbed, train velocity, subgrade bearing capacity. Using variations, safety of roadbed is estimated by dynamic behavior character.

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W UMa형 접촉쌍성 AB And의 주기변화 (PERIOD CHANGE OF W UMa TYPE CONTACT BINARY AB And)

  • 진호;한원용;김천휘;이재우;이우백
    • Journal of Astronomy and Space Sciences
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    • 제14권2호
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    • pp.242-250
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    • 1997
  • W UMa형 접촉쌍성 AB And의 BVR CCD 측광 관측을 1994년 9월부터 1996년 10까지 4일간 수행하여 4개의 새로운 극심 시간을 결정하였다. 이 극심 시각과 이제까지 발표된 모든 극심 시각을 분석하여 AB And의 주기변화의 양상을 연구하였다. AB And의 주기변화를 sine 함수와 같이 규칙적으로 변한다고 가정하여, 관측된 극심 시간을 가장 잘 맞추는 광도 요소를 구하였다. 이 광도요소의 sine 항으로부터 계산된 AB And의 공전주기 변화는 약 0.059일의 진폭으로 약 92년 주기로 규칙적으로 변화하고 있다. 그러나 가장 최근에 관측된 이 연구의 극심 시각들은 이 광도요소에서 예측한 극심 시각들보다 다소 크게 나타나고 있다. 따라서, 우리는 AB An의 공전주기가 sine 함수 외에도 포물선 형태로 변한다고 가정하고 관측된 극심 시각을 가장 잘 맞추는 광도요소를 구하였다. 이 광도요소의 이차항으로 계산된 AB And의 공전주기는 100년에 약 0.73초만큼 영 년 증가하는 동시에, sine 항으로부터 약 62.9년 주기와 0.024일의 진폭으로 규칙적으로 변화한다는 것을 알 수 있었다. 따라서 향후 10년 이내에는 AB And의 공전주기는 sine 항만을 고려하면 주기 감소를 해야하고, 이차항까지 고려하면, 주기 증가가 예측되므로, AB And의 주기변화에 대한 명확한 해답을 위해서 지속적인 관측이 요구된다.

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사행하천(蛇行河川)의 횡방향(橫方向) 하상경사(河床傾斜)의 예측모형(豫測模型) (A Prediction Model of Transverse Bed Slope in Meandering Rivers)

  • 홍창선;정용태
    • 대한토목학회논문집
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    • 제11권4호
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    • pp.81-89
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    • 1991
  • 사행하천형의 특성은 유로의 한쪽제방을 침식시키고, 다른 쪽은 퇴적을 일으키므로써 유로위치에 따라 천천히 형성되는데, 본 연구에서는 Odgaard(1986)가 제안한 횡방향 하상경사에 관한 선형 2차 미분방정식에 Langbein & Leopold(1966)가 제안한 sine-generated curve를 도입하므로써 위상차 및 폭-수심비의 영향을 고려한 새로운 하상형을 제시하고, 금강유역에 위치한 청원과 연기지역을 대상하천으로 하상변동조사보고서의 자료를 이용하여 비교분석한 결과 실측치와 잘 일치하였다.

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$SiC_p$ 크기를 달리한 $SiC_p$/Al2024 복합재료의 열간 변형특성에 관한연구 (A Study on Hot Deformation Behavior of $SiC_p$/AI2024 Composites Reinforced with Different Sizes of $SiC_p$)

  • 고병철;홍흥기;유연철
    • 소성∙가공
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    • 제7권2호
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    • pp.158-167
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    • 1998
  • Hot restoration mechanism flow stress and stain of the Al2024 composites reinforced with 1,8,15,36, and $44{\mu}m\;SiC_p$(10 vol. %) were studied by hot torsion tests. The hot restoration mechanism of all the composites was found to be dynamic recrystallization(DRX) at $320^{\circ}C$ while that of the composites reinforced with 1 and $8{\mu}m\;SiC_p$ was found to be dynamic recovery(DRX) at $480^{\circ}C$. It was found that the Al2024 composite with $15{\mu}m\;SiC_p$ showed the highest flow stress(${\sim}$223 MPa) at $320^{\circ}C$ under a strain rate of 1.0/sec. Also the highest flow strain of the composites was obtained at $430^{\circ}C$. The com-posites reinforced with 1 and $8{\mu}m\;SiC_p$ showed lower flow stress and higher flow strain at $480^{\circ}C$ than those of the composites reinforced with 15, 36, and $44\;{\mu}m\;SiC_p$ These result were discussed in relation to the transition of the hot restoration mechanism. $DRX{\leftrightarrow}DRV$. The dependence of flow stress on strain rate and temperature was attempted to fit with the hyperbolic sine equation ($\dot{\varepsilon}=A[sinh({\alpha}{\cdot}{\sigma}_p]^n$ exp(-Q/RT)and Zener-Hollomon parameter($Z=\;\dot{\varepsilon}\;exp(Q/RT))$.

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FOURIER'S TRANSFORM OF FRACTIONAL ORDER VIA MITTAG-LEFFLER FUNCTION AND MODIFIED RIEMANN-LIOUVILLE DERIVATIVE

  • Jumarie, Guy
    • Journal of applied mathematics & informatics
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    • 제26권5_6호
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    • pp.1101-1121
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    • 2008
  • One proposes an approach to fractional Fourier's transform, or Fourier's transform of fractional order, which applies to functions which are fractional differentiable but are not necessarily differentiable, in such a manner that they cannot be analyzed by using the so-called Caputo-Djrbashian fractional derivative. Firstly, as a preliminary, one defines fractional sine and cosine functions, therefore one obtains Fourier's series of fractional order. Then one defines the fractional Fourier's transform. The main properties of this fractal transformation are exhibited, the Parseval equation is obtained as well as the fractional Fourier inversion theorem. The prospect of application for this new tool is the spectral density analysis of signals, in signal processing, and the analysis of some partial differential equations of fractional order.

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원통형 쉘의 휨 좌굴 거동에 대한 연구 (A Study on the Bending Buckling Behavior of Circular Cylindrical Shells)

  • 정진환;김성도;하지명
    • 한국전산구조공학회:학술대회논문집
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    • 한국전산구조공학회 1998년도 가을 학술발표회 논문집
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    • pp.208-215
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    • 1998
  • A stability problems of isotropic shells under pure bending is investigated based on the classical shells theory. The governing equations of stability problem presented by Donnell and Love, are developed and the solutions for the cylindrical shells are obtained by using Galerkin method. Bending moment is applied at the ends of the cylindrical shell as a from of distributed load in the shape of sine curve. For the isotropic materials, the result of the general purpose structural analysis program based on the finite element method are compared with the critical moment obtained from the classical shell theories. The critical loads for the cylindrical shells with various geometry can not be evaluated with a simple equation. However, accurate solutions for the stability problems of cylindrical shells can be obtained through the equilibrium equation developed in the study.

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수문학적 물리적 특성치의 변화에 따른 지하수 수문곡선 분석 (The Analysis of Groundwater Hydrograph According to the Variation of Hydrologic Physical Characteristics)

  • 김재한
    • 한국수자원학회:학술대회논문집
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    • 한국수자원학회 1987년도 제29회 수공학연구발표회논문초록집
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    • pp.123-137
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    • 1987
  • The groundwater hydrographs due to the recharge of water table aquifer resulting from rainfall are simulated by relating the existing linearized method, which is originally the non-linear equation suggested by Boussinesq, to the basin charcteristics. To thes end, the recharge curve is assumed as the skewed distribution of sine curve, and the parameters contained in the equation are determined from the geomorphologic and soil maps. The whole drainage area is divied in order to consider the spatial variation of parameters. The obtained parameters are tried for several cases with different values given arbitrarily to study the aspects of hydrographs according to their variation. This procedures are applied to the natural basin of Bocheong watershed(area:475.5$\textrm{km}^2$) in Korea. As a result, it is shown that considerable uncertainty is expressed for the results obtained with the given values of parameters. Thus, such uncertainty should be precluded to a certain extent by examining and observing the physical characteristics as much as possible for the determination of groundwater flows.

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The Rheological and Mechanical Model for Relaxation Spectra of Polydisperse Polymers

  • Kim, Nam Jeong;Kim, Eung Ryul;Hahn Sang Joon
    • Bulletin of the Korean Chemical Society
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    • 제13권4호
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    • pp.413-419
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    • 1992
  • The theoretical equation for the relaxation spectrum of nonlinear viscoelastic polymeric material was derived from the Ree-Eyring and Maxwell non-Newtonian model. This model consists of infinite number of hyperbolic sine law Maxwell elements coupled in parallel plus a spring without a dashpot. Infinite number of nonlinear viscoelastic Maxwell elements can be used by specifying distribution of relaxation times, hole volumes, molecular weights, crystallite size and conformational size, etc. The experimentals of stress relaxation were carried out using the tensile tester with the solvent chamber. The relaxation spectra of nylon 6 filament fibers in various electrolytic solutions were obtained by applying the experimental stress relaxation curves to the theoretical equation of relaxation spectrum. The determination of relaxation spectra was performed from computer calculation.

SOLUTIONS AND STABILITY OF TRIGONOMETRIC FUNCTIONAL EQUATIONS ON AN AMENABLE GROUP WITH AN INVOLUTIVE AUTOMORPHISM

  • Ajebbar, Omar;Elqorachi, Elhoucien
    • 대한수학회논문집
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    • 제34권1호
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    • pp.55-82
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    • 2019
  • Given ${\sigma}:G{\rightarrow}G$ an involutive automorphism of a semigroup G, we study the solutions and stability of the following functional equations $$f(x{\sigma}(y))=f(x)g(y)+g(x)f(y),\;x,y{\in}G,\\f(x{\sigma}(y))=f(x)f(y)-g(x)g(y),\;x,y{\in}G$$ and $$f(x{\sigma}(y))=f(x)g(y)-g(x)f(y),\;x,y{\in}G$$, from the theory of trigonometric functional equations. (1) We determine the solutions when G is a semigroup generated by its squares. (2) We obtain the stability results for these equations, when G is an amenable group.