• 제목/요약/키워드: Euler Number

검색결과 223건 처리시간 0.03초

The new Weakness of RSA and The Algorithm to Solve this Problem

  • Somsuk, Kritsanapong
    • KSII Transactions on Internet and Information Systems (TIIS)
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    • 제14권9호
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    • pp.3841-3857
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    • 2020
  • RSA is one of the best well-known public key cryptosystems. This methodology is widely used at present because there is not any algorithm which can break this system that has all strong parameters within polynomial time. However, it may be easily broken when at least one parameter is weak. In fact, many weak parameters are already found and are solved by some algorithms. Some examples of weak parameters consist of a small private key, a large private key, a small prime factor and a small result of the difference between two prime factors. In this paper, the new weakness of RSA is proposed. Assuming Euler's totient value, Φ (n), can be rewritten as Φ (n) = ad + b, where d is the private key and a, b ∈ ℤ, if a divides both of Φ (n) and b and the new exponent for the decryption equation is a small integer, this condition is assigned as the new weakness for breaking RSA. Firstly, the specific algorithm which is created for this weakness directly is proposed. Secondly, two equations are presented to find a, b and d. In fact, one of two equations must be implemented to find a and b at first. After that, the other equation is chosen to find d. The experimental results show that if this weakness has happened and the new exponent is small, original plaintext, m, will be recovered very fast. Furthermore, number of steps to recover d are very small when a is large. However, if a is too large, d may not be recovered because m which must be always written as m = ha is higher than modulus.

Post-buckling analysis of shear-deformable composite beams using a novel simple two-unknown beam theory

  • Kaci, Abdelhakim;Houari, Mohammed Sid Ahmed;Bousahla, Abdelmoumen Anis;Tounsi, Abdelouahed;Mahmoud, S.R.
    • Structural Engineering and Mechanics
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    • 제65권5호
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    • pp.621-631
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    • 2018
  • In this paper, an exact analytical solution is developed for the analysis of the post-buckling non-linear response of simply supported deformable symmetric composite beams. For this, a new theory of higher order shear deformation is used for the analysis of composite beams in post-buckling. Unlike any other shear deformation beam theories, the number of functions unknown in the present theory is only two as the Euler-Bernoulli beam theory, while three unknowns are needed in the case of the other beam theories. The theory presents a parabolic distribution of transverse shear stresses, which satisfies the nullity conditions on both sides of the beam without a shear correction factor. The shear effect has a significant contribution to buckling and post-buckling behaviour. The results of this analysis show that classical and first-order theories underestimate the amplitude of the buckling whereas all the theories considered in this study give results very close to the static response of post-buckling. The numerical results obtained with the novel theory are not only much more accurate than those obtained using the Euler-Bernoulli theory but are almost comparable to those obtained using higher order theories, Accuracy and effectiveness of the current theory.

발전용 소형가스터빈의 축류터빈 공력설계 (Axial Turbine Aerodynamic Design of Small Heavy-Duty Gas Turbines)

  • 김중석;이우상;류제욱
    • 대한기계학회논문집B
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    • 제37권4호
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    • pp.415-421
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    • 2013
  • 본 논문은 두산중공업(주)에서 개발 중인 소형 가스터빈의 축류 터빈 설계 과정을 기술하였다. 축류터빈의 설계 과정은 크게 유로설계, 익형설계, 3D 성능 계산의 세 단계로 구성되며. 최적의 유로를 설계하기 위해 자오면의 형상, 평균 반경, 블레이드간 간격, 유로 형상각 등 여러 형상 변수에 대해 통과유동계산 및 손실계산을 수행한다. 익형 설계는 유로 설계시 스팬 방향으로 계산된 입출구 유동각을 기준으로 실험상관식을 적용하여 최적의 블레이드 개수를 결정한 후 2D 익형 단면을 설계하며 2D NS 계산을 통해 캐스케이드 유동구조를 검토하여 설계한 단면의 설계적정성을 평가한다. 설계된 2D 익형 단면을 스팬방향으로 적층하여 3D 익형을 생성하고, 다단 Euler 계산, 단익렬, 다단 NS 계산을 수행하여 3D 유동 특성을 고찰한다.

비교정 영상에서의 반자동 3차원 건물 모델링 (Semi-automatic 3D Building Reconstruction from Uncalibrated Images)

  • 장경호;장재석;이석준;정순기
    • 한국멀티미디어학회논문지
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    • 제12권9호
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    • pp.1217-1232
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    • 2009
  • 본 논문에서는 실외에서 촬영된 비교정 영상으로부터 3차원 건물 구조를 복원하는 반자동화 방법론을 제안한다. 사용자는 관심있는 건물을 임의의 위치에서 촬영한다. 본 논문에서 제안하는 시스템은 먼저, 입력영상에 대하여 SIFT 알고리즘을 이용하여 특징점과 대응점을 추출한다. 두 번째로, 각 영상에 존재하는 선과 소실점을 추정하고, 추정된 소실점으로 추출한 선들을 그룹화 한다. 다음으로, 각 영상 간의 관계를 대응점의 개수로 정의한 인접 그래프를 이용하여 입력 영상에 대한 순서를 정의하여, 각 영상을 촬영한 카메라의 위치 정보를 보정한다. 최종적으로 추정한 카메라의 정보와 각 영상에서 그룹화된 선을 이용하여 건물의 대략적인 3차원 구조를 복원한다. 하프 에지(half-edge) 자료 구조와 오일러 연산자(Euler operator)를 이용한 상세 모델링을 수행함으로써 완성된 건물 구조를 복원할 수 있다. 본 논문에서는 자동으로 추출된 기하학적 정보를 이용하여 최소한의 사용자 입력으로 건물을 복원 할 수 있도록 하였다.

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판으로 나뉘어진 2차원 충류 채널유동에서 동적 유체-구조물 상호작용 수치해석 (Computation of Dynamic Fluid-Structure Interaction in a 2-Dimensional Laminar Channel Flow Divided by a Plate)

  • 남궁각;최형권;유정열
    • 대한기계학회논문집B
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    • 제26권12호
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    • pp.1738-1746
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    • 2002
  • In the FSI (Fluid-Structure Interaction) problems, two different governing equations are to be solved together. One is fur the fluid and the other for the structure. Furthermore, a kinematic constraint should be imposed along the boundary between the fluid and the structure. We use the combined formulation, which incorporates both the fluid and structure equations of motion into a single coupled variational equation so that it is not necessary to calculate the fluid force on the surface of structure explicitly when solving the equations of motion of the structure. A two-dimensional channel flow divided by a Bernoulli-Euler beam is considered and the dynamic response of the beam under the influence of channel flow is studied. The Navier-Stokes equations are solved using a P2P1 Galerkin finite element method with ALE (Arbitrary Lagrangian-Eulerian) algorithm. The internal structural damping effect is not considered in this study and numerical results are compared with a previous work fer steady case. In addition to the Reynolds number, two non-dimensional parameters, which govern this fluid-structure system, are proposed. It is found that the larger the dynamic viscosity and density of the fluid are, the larger the damping of the beam is. Also, the added mass is found to be linearly proportional to the density of the fluid.

직사각형판(直四角形板)의 진동해석(振動解析) (Vibration of Rectangular Plates)

  • 김극천;정태영
    • 대한조선학회지
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    • 제14권1호
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    • pp.1-10
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    • 1977
  • The major objects of this report are to supplement data of natural frequencies of thin elastic rectangular plates to the available data, and to give an experimental verification for natural frequencies obtained by Rayleigh-Ritz method, the generation set of which are eigenfunctions of Euler beams. For the first object the following five models, for which data only for the fundamental mode or data only for square plates are available, are adopted; (1) two opposed edges are clamped and the other two opposed edges simply supported (C-C, S-S), (2) one edge is simply supported and the other three edges clamped (C-C, C-S), (3) one edge is free and the other three edges clamped (C-C, C-F), (4) two adjacent edges are clamped and the other two adjacent edges free (C-F, C-F). For the (C-C, S-S) model the frequency equation obtained with the mode shapes assumed as of a single trigonometric series is solved. And for the other four models Rayleigh-Ritz method taking eigenfunctions of Euler beams as the generating set is applied. The numerical examples are obtained up to the fourth, the fifth or the sixth order depending on the range of the aspect ratio (0.1-10.0). The number of terms in the generating set for Rayleigh-Ritz method is fifteen for all models. For the experiment three models made of 3.2mm thickness mild steel plate for general structure use were prepared in following size; $300mm{\times}600mm,\;600mm{\times}600mm\;and\;900mm{\times}600mm$. Their boundary conditions are made to fit (C-C, C-F) condition. From the experiment mechanical impedance curves based on the frequency response method were obtained together with phase relation diagrams. The experimental data are resulted in good conformity to calculated values.

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Bayesian estimation of tension in bridge hangers using modal frequency measurements

  • Papadimitriou, Costas;Giakoumi, Konstantina;Argyris, Costas;Spyrou, Leonidas A.;Panetsos, Panagiotis
    • Structural Monitoring and Maintenance
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    • 제3권4호
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    • pp.349-375
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    • 2016
  • The tension of an arch bridge hanger is estimated using a number of experimentally identified modal frequencies. The hanger is connected through metallic plates to the bridge deck and arch. Two different categories of model classes are considered to simulate the vibrations of the hanger: an analytical model based on the Euler-Bernoulli beam theory, and a high-fidelity finite element (FE) model. A Bayesian parameter estimation and model selection method is used to discriminate between models, select the best model, and estimate the hanger tension and its uncertainty. It is demonstrated that the end plate connections and boundary conditions of the hanger due to the flexibility of the deck/arch significantly affect the estimate of the axial load and its uncertainty. A fixed-end high fidelity FE model of the hanger underestimates the hanger tension by more than 20 compared to a baseline FE model with flexible supports. Simplified beam models can give fairly accurate results, close to the ones obtained from the high fidelity FE model with flexible support conditions, provided that the concept of equivalent length is introduced and/or end rotational springs are included to simulate the flexibility of the hanger ends. The effect of the number of experimentally identified modal frequencies on the estimates of the hanger tension and its uncertainty is investigated.

정익과 동익의 상호작용에 의한 비정상 천이 경계층 유동의 수치해석에 관한 연구 (II) (Numerical Prediction of Unsteady Transitional Boundary Layer Flows due to Rotor-Stator Interaction(II)-Characteristics of Unsteady Transitional Boundary Layer Flow-)

  • 강동진
    • 대한기계학회논문집B
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    • 제22권6호
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    • pp.771-787
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    • 1998
  • A Navier-Stokes code with a modified low Reynolds number k-.epsilon. turbulence model was used to study the unsteady transitional boundary layer flow due to rotor-stator interaction. The modification, proposed by Launder, to improve prediction of stagnation flows was incorporated to the low Reynolds number k-.epsilon. turbulence model by Fan-Lakshminarayana-Barnett. Numerical solution is shown to capture well the calmed laminar flow as well as the wake induced transitional strip due to rotor-stator interaction and shows improvement, in terms of onset of transition and its length, over previous Euler/boundary layer solution. The turbulent kinetic energy shows local maximum along the upstream rotor wake in the wake induced transitional strip and this characteristics is observed untill the end of transition. The wake induced strip also shown apparent even in the laminar sublayer as the upstream rotor wake penetrates inside the boundary layer.

두 평행한 관의 출구로부터 방출되는 트윈파에 관한 연구 (A Study of the Twin Impulse Wave Discharged from the Exit of Two Parallel Tubes)

  • 강성황;김재호;김희동
    • 한국소음진동공학회논문집
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    • 제15권8호
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    • pp.962-967
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    • 2005
  • The twin-impulse wave discharged from two parallel tubes is investigated to see flow patterns, compared with the single impulse wave. In the present study, the merging phenomena and propagation characteristics of the impulse waves are investigated by experiment and numerical computation. The Harten-Yee's total variation diminishing scheme is used to solve the unsteady, two-dimensional, compressible, Euler equations. The Mach number Ms of incident shock wave is lower than 1.5 and the distance between the tubes is between 1.2 and 4.0. In the shock tube experiment, the twin impulse waves are visualized by a Schlieren optical system in order to validate the computational result. It is shown that on the symmetric axis between two parallel tubes, the peak pressure produced by the twin impulse waves and its location strongly depend upon the tube distance and the incident shock Mach number, Ms. The predicted Schlieren images show a good agreement with the measured twin-impulse wave.

불규칙 이동분포하중을 받는 차량 타이어의 구조 진동소음 제어를 위한 음향방사 해석 (Sound Radiation Analysis for Structure Vibration Noise Control of Vehicle Tire under The Action of Random Moving Line Forces)

  • 김병삼
    • 한국음향학회:학술대회논문집
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    • 한국음향학회 2004년도 추계학술발표대회논문집 제23권 2호
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    • pp.221-224
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    • 2004
  • A theoretical model has been studied to describe the sound radiation analysis for structure vibration noise of vehicle tires under the action of random moving line forces. When a tire is analyzed, it had been modeled as curved beams with distributed springs and dash pots that represent the radial , tangential stiffness and damping of tire, respectively. The reaction due to fluid loading on the vibratory response of the curved beam is taken into account. The curved beam is assumed to occupy the plane y=0 and to be axially infinite. The curved beam material and elastic foundation are assumed to be lossless Bernoulli-Euler beam theory including a tension force, damping coefficient and stiffness of foundation will be employed. The expression for sound power is integrated numerically and the results examined as a function of Mach number, wave-number ratio and stiffness factor. The experimental investigation for structure vibration noise of vehicle tire under the action of random moving line forces has been made. Based on the Spatial Transformation of Sound Field techniques, the sound power and sound radiation are measured. Results strongly suggest that operation condition in the tire material properties and design factors of the tire govern the sound power and sound radiation characteristics.

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