Relevant bibliographies by topics / Logarithmic coordinates

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  1. Journal articles
  2. Dissertations / Theses
  3. Books
  4. Book chapters
  5. Conference papers

Academic literature on the topic 'Logarithmic coordinates'

Author: Grafiati
Published: 2 June 2025
Last updated: 31 July 2025

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Journal articles on the topic "Logarithmic coordinates"

1

Rigbi, Zvi. "Graphical representation on logarithmic triangular coordinates." Journal of Chemical Education 62, no. 10 (1985): 855. http://dx.doi.org/10.1021/ed062p855.

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2

Avakov, V. A. "Fatigue Reliability Functions in Semilogarithmic Coordinates." Journal of Mechanical Design 113, no. 3 (1991): 352–58. http://dx.doi.org/10.1115/1.2912789.

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In the previous publication [2], the transformation between fatigue life and strength distribution was established using double-logarithmic coordinate system (InN-InS). Here, a similar transformation is established using a semilogarithmic (InN-S) coordinate system. It is assumed that the set of S = Sj (N/Qj) (j = 1,2,...,p) relations, plotted in the InN-S coordinates, becomes a family of parallel straight lines. With the aid of the developed orthogonal relations, lognormal, Weibull and three-parameter logweibull life distributions have been transformed into normal, asymptotic type 1 of smalles
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Campos, L. M. B. C., and P. J. S. Gil. "On spiral coordinates with application to wave propagation." Journal of Fluid Mechanics 301 (October 25, 1995): 153–73. http://dx.doi.org/10.1017/s0022112095003843.

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We introduce a possibly new system of orthogonal curvilinear coordinates, whose coordinate curves are logarithmic spirals in the plane, supplemented by a cylindrical coordinate for three dimensions. It is shown that plane spiral coordinates form a oneparameter family, with equal scale factors along the two orthogonal coordinate curves, and constant Christoffel symbols. The equations of magnetohydrodynamics, which include those of fluid mechanics, are written in spiral coordinates and used to find a state of magnetohydrostatic equilibrium under a radial gravity field and spiral magnetic field,
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Tymofijeva, Nadiya К. "Sign Combinatorial Spaces, Finite Sequences and Logarithmic Spirals." Control Systems and Computers, no. 1 (297) (2022): 32–43. http://dx.doi.org/10.15407/csc.2022.01.032.

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Introduction. Sign combinatorial spaces that exist in two states: convolute (tranquility) and deployed (dynamics), are considered. Spaces, in particular biological, physical, informational and some others, for which the axioms of sign combinatorial spaces, are valid, have a combinatorial nature. When they are deployed, combinatorial numbers (Fibonacci numbers) are formed, through which logarithmic spirals appear in living nature. These spirals are formed due to the finite sequences that take place during the deployment of the agreed spaces and which are presented geometrically using polar coor
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Turski, Jacek. "Robotic Vision with the Conformal Camera: Modeling Perisaccadic Perception." Journal of Robotics 2010 (2010): 1–16. http://dx.doi.org/10.1155/2010/130285.

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Humans make about 3 saccades per second at the eyeball's speed of 700 deg/sec to reposition the high-acuity fovea on the targets of interest to build up understanding of a scene. The brain's visuosaccadic circuitry uses the oculomotor command of each impending saccade to shift receptive fields (RFs) to cortical locations before the eyes take them there, giving a continuous and stable view of the world. We have developed a model for image representation based on projective Fourier transform (PFT) intended for robotic vision, which may efficiently process visual information during the motion of
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Marton, Katalin. "Logarithmic Sobolev inequalities in discrete product spaces." Combinatorics, Probability and Computing 28, no. 06 (2019): 919–35. http://dx.doi.org/10.1017/s0963548319000099.

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AbstractThe aim of this paper is to prove an inequality between relative entropy and the sum of average conditional relative entropies of the following form: for a fixed probability measure q on , ( is a finite set), and any probability measure on , (*) $$D(p||q){\rm{\le}}C \cdot \sum\limits_{i = 1}^n {{\rm{\mathbb{E}}}_p D(p_i ( \cdot |Y_1 ,{\rm{ }}...,{\rm{ }}Y_{i - 1} ,{\rm{ }}Y_{i + 1} ,...,{\rm{ }}Y_n )||q_i ( \cdot |Y_1 ,{\rm{ }}...,{\rm{ }}Y_{i - 1} ,{\rm{ }}Y_{i + 1} ,{\rm{ }}...,{\rm{ }}Y_n )),} $$ where pi(· |y1, …, yi−1, yi+1, …, yn) and qi(· |x1, …, xi−1, xi+1, …, xn) denote the lo
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Das, Tuhin, and Ranjan Mukherjee. "Reconfiguration of a Rolling Sphere: A Problem in Evolute-Involute Geometry." Journal of Applied Mechanics 73, no. 4 (2005): 590–97. http://dx.doi.org/10.1115/1.2164515.

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This paper provides a new perspective to the problem of reconfiguration of a rolling sphere. It is shown that the motion of a rolling sphere can be characterized by evolute-involute geometry. This characterization, which is a manifestation of our specific selection of Euler angle coordinates and choice of angular velocities in a rotating coordinate frame, allows us to recast the three-dimensional kinematics problem as a problem in planar geometry. This, in turn, allows a variety of optimization problems to be defined and admits infinite solution trajectories. It is shown that logarithmic spira
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STARK, DUDLEY. "Explicit Limits of Total Variation Distance in Approximations of Random Logarithmic Assemblies by Related Poisson Processes." Combinatorics, Probability and Computing 6, no. 1 (1997): 87–105. http://dx.doi.org/10.1017/s0963548396002775.

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Assemblies are labelled combinatorial objects that can be decomposed into components. Examples of assemblies include set partitions, permutations and random mappings. In addition, a distribution from population genetics called the Ewens sampling formula may be treated as an assembly. Each assembly has a size n, and the sum of the sizes of the components sums to n. When the uniform distribution is put on all assemblies of size n, the process of component counts is equal in distribution to a process of independent Poisson variables Zi conditioned on the event that a weighted sum of the independe
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LI Lang, ZHOU Shiyun, GAO Chunqing, and FU Shiyao. "Log-polar transformation data decoding for orbital angular momentum shift keying." Acta Physica Sinica 74, no. 6 (2025): 0. https://doi.org/10.7498/aps.74.20241612.

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Orbital angular momentum (OAM), as a novel high-dimensional degree of freedom, offering significantly potential for optical communication in increasing the system channel capacity and addressing the scarcity of communication resources. However, the effective recognition and detection of OAM modes are the core challenges for achieving efficient communication in such systems. This paper presents an OAM decoding system based on log-polar coordinate transformation, consisting of a designed coordinate transformation device, a phase corrector, and a Fourier transform lens. The coordinate transformat
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Nakajima, Yoshitaka, Takashi Tsumura, Seiichi Matsuura, Hiroyuki Minami, and Ryunen Teranishi. "Dynamic Pitch Perception for Complex Tones Derived from Major Triads." Music Perception 6, no. 1 (1988): 1–20. http://dx.doi.org/10.2307/40285413.

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A new type of complex tone that demonstrates pitch circularity is described. For such tones, the spectral envelope is trapezoidal on the coordinates of logarithmic frequency and logarithmic amplitude, and remains constant. The components of each tone form a major triad within each octave. The component frequencies were increased by steps of 1/10 octave from tone to tone, until the first tone was obtained again. According to our paired comparison experiments for pitch, which were analyzed using the multidimensional scaling technique, two kinds of pitch circularities appear. One group of subject
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Dissertations / Theses on the topic "Logarithmic coordinates"

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Hitchcock, Yvonne Roslyn. "Elliptic curve cryptography for lightweight applications." Thesis, Queensland University of Technology, 2003. https://eprints.qut.edu.au/15838/1/Yvonne_Hitchcock_Thesis.pdf.

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Elliptic curves were first proposed as a basis for public key cryptography in the mid 1980's. They provide public key cryptosystems based on the difficulty of the elliptic curve discrete logarithm problem (ECDLP) , which is so called because of its similarity to the discrete logarithm problem (DLP) over the integers modulo a large prime. One benefit of elliptic curve cryptosystems (ECCs) is that they can use a much shorter key length than other public key cryptosystems to provide an equivalent level of security. For example, 160 bit ECCs are believed to provide about the same level of security
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Hitchcock, Yvonne Roslyn. "Elliptic Curve Cryptography for Lightweight Applications." Queensland University of Technology, 2003. http://eprints.qut.edu.au/15838/.

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Elliptic curves were first proposed as a basis for public key cryptography in the mid 1980's. They provide public key cryptosystems based on the difficulty of the elliptic curve discrete logarithm problem (ECDLP) , which is so called because of its similarity to the discrete logarithm problem (DLP) over the integers modulo a large prime. One benefit of elliptic curve cryptosystems (ECCs) is that they can use a much shorter key length than other public key cryptosystems to provide an equivalent level of security. For example, 160 bit ECCs are believed to provide about the same level of security
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Rocha, Eugénio Alexandre Miguel. "Uma Abordagem Algébrica à Teoria de Controlo Não Linear." Doctoral thesis, Universidade de Aveiro, 2003. http://hdl.handle.net/10773/21444.

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Doutoramento em Matemática<br>Nesta tese de Doutoramento desenvolve-se principalmente uma abordagem algébrica à teoria de sistemas de controlo não lineares. No entanto, outros tópicos são também estudados. Os tópicos tratados são os seguidamente enunciados: fórmulas para sistemas de controlo sobre álgebras de Lie livres, estabilidade de um sistema de corpos rolantes, algoritmos para aritmética digital, e equações integrais de Fredholm não lineares. No primeiro e principal tópico estudam-se representações para as soluções de sistemas de controlo lineares no controlo. As suas trajetórias
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Books on the topic "Logarithmic coordinates"

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Eureka math: A story of functions : Exponential and logarithmic functions. Jossey-Bass, 2015.

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Inc, Common Core. Eureka Math: A Story of Functions. Wiley & Sons, Incorporated, John, 2015.

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Inc, Common Core. Eureka Math: A Story of Functions. Wiley & Sons, Incorporated, John, 2015.

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Li͡usternik, L. A. Ten-Decimal Tables of the Logarithms of Complex Numbers and for the Transformation from Cartesian to Polar Coordinates: Volume 33 in Mathematical Tables Series. Elsevier Science & Technology Books, 2014.

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Howe, George. Mathematics for the Practical Man: Explaining Simply and Quickly All the Elements of Algebra, Geometry, Trigonometry, Logarithms, Coordinate Geometry, Calculus; With Answers to Problems,. Franklin Classics Trade Press, 2018.

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Howe, George. Mathematics for the Practical Man: Explaining Simply and Quickly All the Elements of Algebra, Geometry, Trigonometry, Logarithms, Coordinate Geometry, Calculus; with Answers to Problems,. Nabu Press, 2010.

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Mathematics for the Practical Man: Explaining Simply and Quickly All the Elements of Algebra, Geometry, Trigonometry, Logarithms, Coordinate Geometry, Calculus; with Answers to Problems,. Creative Media Partners, LLC, 2022.

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Howe, George. Mathematics for the Practical Man: Explaining Simply and Quickly All the Elements of Algebra, Geometry, Trigonometry, Logarithms, Coordinate Geometry, Calculus; With Answers to Problems,. Franklin Classics, 2018.

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Howe, George. Mathematics for the Practical Man: Explaining Simply and Quickly All the Elements of Algebra, Geometry, Trigonometry, Logarithms, Coordinate Geometry, Calculus with Answers to Problems. Independently Published, 2018.

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Mathematics for the Practical Man: Explaining Simply and Quickly All the Elements of Algebra, Geometry, Trigonometry, Logarithms, Coordinate Geometry, Calculus; with Answers to Problems,. Creative Media Partners, LLC, 2022.

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Book chapters on the topic "Logarithmic coordinates"

1

Luengo-Oroz, Miguel A., Jesús Angulo, Georges Flandrin, and Jacques Klossa. "Mathematical Morphology in Polar-Logarithmic Coordinates. Application to Erythrocyte Shape Analysis." In Pattern Recognition and Image Analysis. Springer Berlin Heidelberg, 2005. http://dx.doi.org/10.1007/11492542_25.

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Waldschmidt, Michel. "Points Whose Coordinates are Logarithms of Algebraic Numbers." In Diophantine Approximation on Linear Algebraic Groups. Springer Berlin Heidelberg, 2000. http://dx.doi.org/10.1007/978-3-662-11569-5_11.

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Li, Dan, Lei Chen, Jun Tian, Dai-hong Jiang, Jin-ping Sun, and Bin Ding. "Image Mosaic Based on Improved Logarithmic Polar Coordinate Transformation and Ransac Algorithm." In Simulation Tools and Techniques. Springer International Publishing, 2019. http://dx.doi.org/10.1007/978-3-030-32216-8_59.

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Collilieux, Xavier, Zuheir Altamimi, Paul Rebischung, et al. "A Review of Space Geodetic Technique Seasonal Displacements Based on ITRF2020 Results." In International Association of Geodesy Symposia. Springer Berlin Heidelberg, 2023. http://dx.doi.org/10.1007/1345_2023_216.

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AbstractThe new release of the International Terrestrial Reference Frame, ITRF2020, differs from ITRF2014 by the addition of parametric functions describing annual and semi-annual displacements for every station. ITRF2020 coordinates are now described with piece-wise linear functions, occasional exponential and logarithmic functions modelling post-seismic displacements and the newly provided seasonal parameters. The paper first shortly presents the ITRF2020 seasonal parameters provided both in the Center of Mass (CM) and in the Center of Fig. (CF) frames. The station-specific seasonal displace
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Atesmen, M. Kemal. "Transient Heat Transfer from an Infinitely Long and Thin Heat Source used to Measure Thermal Conductivity of Soils and Soft Rocks in an Infinite Cylindrical Medium." In Case Studies in Transient Heat Transfer With Sensitivities to Governing Variables. ASME, 2023. http://dx.doi.org/10.1115/1.886786_ch23.

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Thermal conductivity of soils and soft rocks is an important thermophysical property used in models for climate change and for crop production. In this chapter, we will investigate transient heat transfer from an infinitely long and thin heat source, called the thermal needle probe, to an infinite cylindrical medium to determine the temperature rise in the medium with increasing time. We will show that the temperature-rise versus natural logarithm of time, Ln(θ), for the medium can be linearly correlated at large times. The transient heat transfer equation that applies to this case is given in
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Furbish, David Jon. "Turbulent Boundary-Layer Shear Flows." In Fluid Physics in Geology. Oxford University Press, 1997. http://dx.doi.org/10.1093/oso/9780195077018.003.0019.

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Turbulent shear flows next to solid boundaries are one of the most important types of flow in geology. In such flows, turbulence is generated primarily by boundary effects; vorticity originates near a boundary in association with the velocity gradients that arise from the no-slip condition at the boundary. Such gradients provide a ready source of vorticity for eddies and eddy-like structures to develop in response to the destabilizing effects of inertial forces, and then move outward into the adjacent flow. Eddies are also generated within the wakes of bumps that comprise boundary roughness, f
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Menshchikov, Igor A., Andrey S. Kosmodamianskiy, and Sergei I. Batashov. "INTELLIGENT ON-BOARD DIAGNOSTIC SYSTEM FOR ISOLATION OF ASYNCHRONOUS TRACTION STATOR WINDINGS ELECTRIC MOTOR TYPE DTA-1200 ELECTRIC LOCOMOTIVE EP20." In Intellectual Transport Systems. Russian University of Transport, Moscow, Russian Federation, 2023. http://dx.doi.org/10.30932/9785002182794-2023-592-599.

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The article is devoted to the development of an intelligent on-board diagnostic system for an asynchronous traction electric motor of the DTA-1200 type, a passenger mainline electric locomotive of the EP20 series. A structural mathematical model in a fixed coordinate system is proposed for diagnosing the case and inter-turn insulation of the stator windings of an asynchronous traction motor of the DTA-1200 type. The results of modeling the serviceable and emergency condition of an asynchronous traction motor of the DTA-1200 type in the MATLAB&amp;SIMULINK software package are presented. Using
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Conference papers on the topic "Logarithmic coordinates"

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Avakov, Vladimir A. "Fatigue Reliability Functions in Semilogarithmic Coordinates." In ASME 1991 Design Technical Conferences. American Society of Mechanical Engineers, 1991. http://dx.doi.org/10.1115/detc1991-0009.

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Abstract In the previous publication [2], the transformation between fatigue life and strength distribution was established using double-logarithmic coordinate system (lnN-lnS). Here, a similar transformation is established using a semi logarithmic (lnN-S) coordinate system. With the aid of the developed orthogonal relations, lognormal, Weibull and three-parameter logweibull life distributions have been transformed into normal, asymptotic type 1 of smallest value, and three-parameter Weibull strength distributions, respectively. This procedure may be applied to other types of fatigue life dist
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Roy Frieden, B. "Integral logarithmic transform: theory and applications." In OSA Annual Meeting. Optica Publishing Group, 1991. http://dx.doi.org/10.1364/oam.1991.wv6.

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Mathematical properties and potential uses of a new class of integral transforms are described. Its input functions f(x) or f(x,w) must have limited support, as is true of any image. For a 1-D input f(x), the 1-D integral logarithmic transform is defined as F(y) = ∫f(xy)d(logx). For a 2-D input function f(x,w) the alternative 2-D transforms F(y,z) = ∫∫f(xy,wz)d(logx)d(logw) or G(y,z) = ∫∫fρ(yr, zθ)d(logr)dθ are defined. In the latter, function fρ (r,0) is the 1:1 polar remapping of input function f(x,w). Mathematically, it is found that transforms F(y) and F(y,z) are invariant to linear change
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Hareyama, Soichi, Satoshi Kobayashi, Kazumi Ozawa, Kenji Tsuji, and Shinya Yamamoto. "Formulation of Loosening Phenomena in Actual Machines and a Consideration of Loosening Visibility." In ASME 2024 International Mechanical Engineering Congress and Exposition. American Society of Mechanical Engineers, 2024. https://doi.org/10.1115/imece2024-144611.

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Abstract The results of the previous study showed that the loosening phenomenon of bolted joints used in actual equipment has a strong linear relationship on both logarithmic coordinates. This linear relationship is also observed in the tendency of axial tension reduction in Junker-type loosening test machine. This relationship can be displayed as a regression line and regression equation, and can be utilized for loosening lifetime estimation. The axial tension reduction phenomenon usually can’t be measured without using ultrasonic measurement methods or strain gauges etc. Therefore, measureme
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Epple, Philipp, Michael Steppert, and Andreas Malcherek. "Wall Bounded Flows and a General Proof of the Validity of the Universal Logarithmic Law of the Wall." In ASME 2021 Fluids Engineering Division Summer Meeting. American Society of Mechanical Engineers, 2021. http://dx.doi.org/10.1115/fedsm2021-65733.

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Abstract The logarithmic law of the wall is usually derived for the flat plate assuming stationary, two-dimensional fully developed flow with no external pressure gradient. The Prandtl mixing length model for the turbulence is applied, which assumes homogeneous turbulence and two empirical constants, and the logarithmic wall law is derived. It is than stated in the textbooks that it is universally valid without a proof. As a justification experimental evidence is shown. First this proof will be shown in detail. Than a more general approach based on similarity considerations is made to show the
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Hareyama, Soichi, Kenichi Manabe, and Satoshi Kobayashi. "Evaluation for Residual Lifetime and Remaining Axial Tension to Loosening Failure on Bolted Joints Used in Long-Life Machine and Plant Equipment." In ASME 2022 Pressure Vessels & Piping Conference. American Society of Mechanical Engineers, 2022. http://dx.doi.org/10.1115/pvp2022-80082.

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Abstract The bolted joints used in mechanical structures loosen owing to, for example, a decrease in the initial axial tension (clamping force) and repeated external forces in the direction perpendicular to the axis. A Junker-type loosening test used to evaluate the performance of various types of locking devices in a short period of time has been established. In such a test, it is possible to compare the loosening performance characteristics of various bolted joints and locking devices. However, it has not been possible to absolutely determine the period of time that they can maintain their i
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Voorhees, Howard R., H. Chong Rhee, and Michael K. Baker. "Long-Term Creep Life Estimation for Manaurite XM Material, Using a Constrained Monkman-Grant Plot and Proportional Similitude." In ASME 2011 Pressure Vessels and Piping Conference. ASMEDC, 2011. http://dx.doi.org/10.1115/pvp2011-57402.

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The present paper revisits a constrained use of Monkman-Grant coordinates, a relatively little employed or appreciated method for estimation of long-term creep life. This method is based on a logarithmic plot of remaining life versus the steady creep rate. A procedure, here called proportional similitude, is also discussed as a means to estimate the steady creep rate or time to rupture at an early stage of a test. Numerous studies as yet mostly unpublished increasingly demonstrate for many steel samples from prior creep service that a combination of these two methods permits extrapolations at
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Raninen, Antti, Rauli Franssila, and Jyrki Rovamo. "Critical flicker frequency as a function of photopic luminous flux across the human visual field." In OSA Annual Meeting. Optica Publishing Group, 1989. http://dx.doi.org/10.1364/oam.1989.wm4.

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Using the method of adjustment and a panel of 256 LEDs (dominant wavelength 640 nm) mounted in a solid, black enclosure and covered with a white diffusion screen, we measured CFF to cone stimuli (sinusoidal luminance modulation of 30%) across the temporal visual field at three different levels of retinal illuminance (1970,123, and 25.0 phot, td) produced by inserting neutral density filters (Lee) in front of the panel. Retinal illuminance was constant at all eccentricities studied because retinal area per one solid degree of visual field and effective pupillary area decrease similarly when ecc
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Poursina, Mohammad. "An Efficient Application of Polynomial Chaos Expansion for the Dynamic Analysis of Multibody Systems With Uncertainty." In ASME 2014 International Design Engineering Technical Conferences and Computers and Information in Engineering Conference. American Society of Mechanical Engineers, 2014. http://dx.doi.org/10.1115/detc2014-35226.

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In this paper the mathematical framework of an advanced algorithm is presented to efficiently form and solve the equations of motion of a multibody system involving uncertainty in the system parameters and/or the excitations. The uncertainty is introduced to the system through the application of the polynomial chaos expansion. In this scheme, states of the system, nondeterministic parameters, and the constraint loads are expanded using modal values as well as orthogonal basis functions. Computational complexity of the application of traditional methods to solve the stochastic equations of moti
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Hareyama, Soichi, Ken-ichi Manabe, and Makoto Nakashima. "The Absolute Evaluation and Loosening Life Prediction Method on Self-Loosening of Bolted Joints During Actual Machine Operation." In ASME 2012 International Mechanical Engineering Congress and Exposition. American Society of Mechanical Engineers, 2012. http://dx.doi.org/10.1115/imece2012-86415.

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This paper presents a method for estimating the absolute lock effect in bolted joints during actual machine operation. The absolute evaluation on self-loosening is indispensable for the prediction of the life of locking devices (parts)/method at actual machine operation. The loosening phenomenon of bolted joint can be viewed as the decrease tendency of the initial axial tension or residual axial tension. According to the author’s previous report, there is a good linear relation on logarithmic coordinates (log-log paper) between the decrease of axial tension (measured tension/initial axial tens
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Baratta, Mirko, Stefano d’Ambrosio, Ezio Spessa, and Alberto Vassallo. "Cycle-Resolved Detection of Combustion Start in SI Engines by Means of Different In-Cylinder Pressure Data Reduction Techniques." In ASME 2006 Internal Combustion Engine Division Spring Technical Conference. ASMEDC, 2006. http://dx.doi.org/10.1115/ices2006-1367.

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An original technique for the detection of combustion start in SI engines on a cycle-by-cycle basis was proposed and applied to the analysis of pressure time-histories taken on a bi-fuel engine fueled by either gasoline or CNG. Such a technique locates the onset of combustion on the basis of the earliest release of chemical energy. It stems from the fact that, during the compression stroke, changes in the charge sensible energy, and thus in the cylinder pressure, are ruled only by work and heat exchanges with the combustion chamber walls. Hence, an imbalance in these three energies indicates t
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