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Relevant bibliographies by topics / Infinitely differentiable function

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Academic literature on the topic 'Infinitely differentiable function'

Author: Grafiati

Published: 24 April 2022

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Journal articles on the topic "Infinitely differentiable function"

1

Buczolich, Zoltán. "Functions with finite intersections with analytic functions." Proceedings of the Royal Society of Edinburgh: Section A Mathematics 112, no. 3-4 (1989): 271–75. http://dx.doi.org/10.1017/s0308210500018746.

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SynopsisWe prove that for every dense Gδ set H, there exists a continuous function f, such that f intersects every analytic function in finitely many points and f is infinitely differentiable exactly at the points of H. This answers a problem of S. Agronsky, A. M. Bruckner, M. Laczkovich and D. Preiss. They proved a result which implies that every continuous function with finite intersections with analytic functions is infinitely differentiable at the points of a dense Gδ set.

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Sekerin, A. B. "Representation of an infinitely differentiable function by a difference of plurisubharmonic functions." Mathematical Notes of the Academy of Sciences of the USSR 40, no. 5 (1986): 841–46. http://dx.doi.org/10.1007/bf01159701.

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Nemzer, Dennis. "Operational calculus and differential equations with infinitely smooth coefficients." International Journal of Mathematics and Mathematical Sciences 13, no. 2 (1990): 405–10. http://dx.doi.org/10.1155/s0161171290000618.

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A subringMFof the field of Mikusiński operators is constructed as a countable union space. Some topological properties ofMFare investigated. Then, the product of an infinitely differentiable function and an element ofMFis given and is used to investigate operational equations with infinitely smooth coefficients.

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Jolevska-Tuneska, Biljana, та Emin Özça¯g. "On the Composition of Distributionsx−sln|x|and|x|μ". International Journal of Mathematics and Mathematical Sciences 2007 (2007): 1–9. http://dx.doi.org/10.1155/2007/60129.

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LetFbe a distribution and letfbe a locally summable function. The distributionF(f)is defined as the neutrix limit of the sequence{Fn(f)}, whereFn(x)=F(x)*δn(x)and{δn(x)}is a certain sequence of infinitely differentiable functions converging to the Dirac delta-functionδ(x). The composition of the distributionsx−sIn|x|and|x|μis evaluated fors=1,2,…,μ>0andμs≠1,2,….

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Smith, Patrick Adrian Neale. "Counterexamples to Smoothing Convex Functions." Canadian Mathematical Bulletin 29, no. 3 (1986): 308–13. http://dx.doi.org/10.4153/cmb-1986-047-5.

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AbstractGreene and Wu have shown that any continuous strongly convex function on a Riemannian manifold can be uniformly approximated by infinitely differentiable strongly convex functions. This result is not true if the word “strongly” is omitted; in this paper, we give examples of manifolds on which convex functions cannot be approximated by convex functions (k = 0, 1,2,...).

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Moorthy, R. Subash, and R. Roopkumar. "Curvelet transform on tempered distributions." Asian-European Journal of Mathematics 08, no. 02 (2015): 1550031. http://dx.doi.org/10.1142/s179355711550031x.

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The curvelet transform of a tempered distribution is defined as an infinitely differentiable function of (a, b, θ) with a polynomial growth in b. An inversion formula of the curvelet transform on tempered distributions is also obtained.

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Sivak, Maria. "The research on using robust functions for neural networks." Transaction of Scientific Papers of the Novosibirsk State Technical University, no. 4 (December 18, 2020): 50–58. http://dx.doi.org/10.17212/2307-6879-2020-4-50-58.

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The paper is devoted to analyzing the ability of using robust functions for building neural networks. The research highlights different robust functions in terms of applying them for obtaining a robust modification of the back-propagation algorithm. The algorithm requires that the used loss function should be infinitely or continuously differentiable. The analysis of twelve different functions has been done. The derivate of Charbonnier function has been obtained by the author. The results of analysis shows which functions can be used for the further investigation and which ones should be exclu

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Lin, Mongkolsery. "On the neutrix composition of x−−slnmx− and ln(1 + x+)." Asian-European Journal of Mathematics 11, no. 06 (2018): 1850086. http://dx.doi.org/10.1142/s1793557118500869.

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The neutrix composition [Formula: see text], [Formula: see text] is a distribution and [Formula: see text] is a locally summable function, is defined as the neutrix limit of the sequence [Formula: see text], where [Formula: see text] and [Formula: see text] is a certain sequence of infinitely differentiable functions converging to the Dirac delta-function [Formula: see text]. The neutrix composition of the distributions [Formula: see text] and [Formula: see text] is evaluated for [Formula: see text] Further related results are also deduced.

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Fisher, Brian. "On the composition of the distributions x-s+ lnmx+ and xμ+". Applicable Analysis and Discrete Mathematics 3, № 2 (2009): 212–23. http://dx.doi.org/10.2298/aadm0902212f.

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Let F be a distribution and let f be a locally summable function. The distribution F(f) is defined as the neutrix limit of the sequence {Fn(f)}, where Fn(x) = F(x)*?n(x) and {?n(x)} is a certain sequence of infinitely differentiable functions converging to the Dirac delta-function ?(x). The composition of the distributions x-s + lnm x+ and x? + is proved to exist and be equal to ?mx-s? + lnm x+ for ? > 0 and s,m = 1, 2,....

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Bartoszewicz, Artur, and Szymon Głąb. "Large Function Algebras with Certain Topological Properties." Journal of Function Spaces 2015 (2015): 1–7. http://dx.doi.org/10.1155/2015/761924.

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LetFbe a family of continuous functions defined on a compact interval. We give a sufficient condition so thatF∪{0}contains a densec-generated free algebra; in other words,Fis denselyc-strongly algebrable. As an application we obtain densec-strong algebrability of families of nowhere Hölder functions, Bruckner-Garg functions, functions with a dense set of local maxima and local minima, and nowhere monotonous functions differentiable at all but finitely many points. We also study the problem of the existence of large closed algebras withinF∪{0}whereF⊂RXorF⊂CX. We prove that the set of perfectly

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Dissertations / Theses on the topic "Infinitely differentiable function"

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Lee, Jae S. (Jae Seung). "Continuous, Nowhere-Differentiable Functions with no Finite or Infinite One-Sided Derivative Anywhere." Thesis, University of North Texas, 1994. https://digital.library.unt.edu/ark:/67531/metadc278627/.

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In this paper, we study continuous functions with no finite or infinite one-sided derivative anywhere. In 1925, A. S. Beskovitch published an example of such a function. Since then we call them Beskovitch functions. This construction is presented in chapter 2, The example was simple enough to clear the doubts about the existence of Besicovitch functions. In 1932, S. Saks showed that the set of Besicovitch functions is only a meager set in C[0,1]. Thus the Baire category method for showing the existence of Besicovitch functions cannot be directly applied. A. P. Morse in 1938 constructed Besicov

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Althubiti, Saeed. "STOCHASTIC FUNCTIONAL DIFFERENTIAL EQUATIONS WITH INFINITE MEMORY." OpenSIUC, 2018. https://opensiuc.lib.siu.edu/dissertations/1544.

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In this dissertation, we discuss the existence and uniqueness of Ito-type stochastic functional differential equations with infinite memory using fixed point theorem technique. We also address the properties of the solution which are an upper bound for the pth moments of the solution and the Lp-regularity. Then, we provide an analysis to show the local asymptotic L2-stability of the trivial solution using fixed point theorem technique, and we give an approximation of the solution using Euler-Maruyama method providing the global error followed by simulating examples.

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Nishiguchi, Junya. "Retarded functional differential equations with general delay structure." 京都大学 (Kyoto University), 2017. http://hdl.handle.net/2433/225381.

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Pelander, Anders. "A Study of Smooth Functions and Differential Equations on Fractals." Doctoral thesis, Uppsala : Department of Mathematics, Uppsala university [distributör], 2007. http://urn.kb.se/resolve?urn=urn:nbn:se:uu:diva-7590.

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Freudenberg, Johannes M. "Bayesian Infinite Mixture Models for Gene Clustering and Simultaneous Context Selection Using High-Throughput Gene Expression Data." University of Cincinnati / OhioLINK, 2009. http://rave.ohiolink.edu/etdc/view?acc_num=ucin1258660232.

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Terrand-Jeanne, Alexandre. "Régulation des systèmes à paramètres distribués : application au forage." Thesis, Lyon, 2018. http://www.theses.fr/2018LYSE1283/document.

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Ce travail porte sur la régulation de la sortie des systèmes aux paramètres distribués. Pour ce faire, un simple contrôleur proportionnel intégral est utilisé, puis la stabilité du système en boucle fermée est démontrée à l'aide d'une fonction de Lyapunov. La principale contribution de ce travail est la construction d'un nouveau type de fonction de Lyapunov qui s'inspire d'une méthode bien connue dans le cadre des systèmes non-linéaires : le forwarding.Dans une première partie, le système est établi avec des opérateurs dont les propriétés sont données dans le cadre des semigroupes, puis la pro

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Books on the topic "Infinitely differentiable function"

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Hino, Yoshiyuki, Satoru Murakami, and Toshiki Naito. Functional Differential Equations with Infinite Delay. Springer Berlin Heidelberg, 1991. http://dx.doi.org/10.1007/bfb0084432.

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Hino, Yoshiyuki. Functional differential equations with infinite delay. Springer-Verlag, 1991.

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service), SpringerLink (Online, ed. Green's Functions and Infinite Products: Bridging the Divide. Springer Science+Business Media, LLC, 2011.

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Agarwal, Ravi P. Infinite Interval Problems for Differential, Difference and Integral Equations. Springer Netherlands, 2001.

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Anandam, Victor. Harmonic Functions and Potentials on Finite or Infinite Networks. Springer-Verlag Berlin Heidelberg, 2011.

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1886-, Watson G. N., ed. A course of modern analysis: An introduction to the general theory of infinite processes and of analytic functions, with an account of the principal transcendental functions. 4th ed. Cambridge University Press, 1992.

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Donal, O'Regan, ed. Infinite interval problems for differential, difference, and integral equations. Kluwer Academic Publishers, 2001.

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8

Mhuiris, Nessan Mac Giolla. Lyapunov exponents for infinite dimensional dynamical systems. ICASE, 1987.

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9

Balser, Werner. Formal power series and linear systems of meromorphic ordinary differential equations. Springer, 2000.

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author, Rosen Daniel 1980, ed. Function theory on symplectic manifolds. American Mathematical Society, 2014.

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Book chapters on the topic "Infinitely differentiable function"

1

Burenkov, Victor I. "Approximation by infinitely differentiable functions." In Sobolev Spaces on Domains. Vieweg+Teubner Verlag, 1998. http://dx.doi.org/10.1007/978-3-663-11374-4_3.

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Hörmander, Lars. "Classes Of Infinitely Differentiable Functions." In Unpublished Manuscripts. Springer International Publishing, 2018. http://dx.doi.org/10.1007/978-3-319-69850-2_11.

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Rubin, Herman, and Thomas M. Sellke. "Zeroes of infinitely differentiable characteristic functions." In Institute of Mathematical Statistics Lecture Notes - Monograph Series. Institute of Mathematical Statistics, 2004. http://dx.doi.org/10.1214/lnms/1196285388.

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Hale, Jack K., Luis T. Magalhães, and Waldyr M. Oliva. "Functional Differential Equations on Manifolds." In Dynamics in Infinite Dimensions. Springer New York, 2002. http://dx.doi.org/10.1007/0-387-22896-9_3.

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Becker, L. C., T. A. Burton, and S. Zhang. "Functional Differential Equations and Jensen’s Inequality." In Dynamics of Infinite Dimensional Systems. Springer Berlin Heidelberg, 1987. http://dx.doi.org/10.1007/978-3-642-86458-2_4.

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Gil’, Michael I. "Nonlinear Neutral Type Functional Differential Systems." In Stability of Finite and Infinite Dimensional Systems. Springer US, 1998. http://dx.doi.org/10.1007/978-1-4615-5575-9_12.

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Stepanyuk, Tetiana A. "Order Estimates of Best Orthogonal Trigonometric Approximations of Classes of Infinitely Differentiable Functions." In Trigonometric Sums and Their Applications. Springer International Publishing, 2020. http://dx.doi.org/10.1007/978-3-030-37904-9_13.

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Stech, Harlan W. "A Numerical Analysis of the Structure of Periodic Orbits in Autonomous Functional Differential Equations." In Dynamics of Infinite Dimensional Systems. Springer Berlin Heidelberg, 1987. http://dx.doi.org/10.1007/978-3-642-86458-2_29.

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Motreanu, D. "Generic existence of morse functions on infinite dimensional riemannian manifolds and applications." In Global Differential Geometry and Global Analysis. Springer Berlin Heidelberg, 1991. http://dx.doi.org/10.1007/bfb0083640.

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Samoilenko, Y. S. "Differential Operators with Constant Coefficients in Spaces of Functions of Infinitely Many Variables." In Spectral Theory of Families of Self-Adjoint Operators. Springer Netherlands, 1991. http://dx.doi.org/10.1007/978-94-011-3806-2_5.

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Conference papers on the topic "Infinitely differentiable function"

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Konovalov, Ya Yu. "New Infinitely Differentiable Spline-like Basis Functions." In 2019 PhotonIcs & Electromagnetics Research Symposium - Spring (PIERS-Spring). IEEE, 2019. http://dx.doi.org/10.1109/piers-spring46901.2019.9017707.

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Hino, Yoshiyuki, and Satoru Murakami. "Total stability in abstract functional differential equations with infinite delay." In The 6'th Colloquium on the Qualitative Theory of Differential Equations. Bolyai Institute, SZTE, 1999. http://dx.doi.org/10.14232/ejqtde.1999.5.13.

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Kaasen, Karl E. "Consistent State Space Modelling of Hydrodynamic Memory." In ASME 2020 39th International Conference on Ocean, Offshore and Arctic Engineering. American Society of Mechanical Engineers, 2020. http://dx.doi.org/10.1115/omae2020-19194.

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Abstract The conventional way to model hydrodynamic memory or radiation force is to use retardation functions. These functions are usually derived from frequency-dependent damping functions that are calculated by a diffraction-radiation code using potential theory. Calculating the retardation functions can be challenging due to lack of information at high frequency. In simulation of wave-driven vessel motion the retardation function is convolved with the velocity to give the wave radiation force, which is time-consuming. The paper describes how the memory effects can be modelled consistently b

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Van Auken, R. Michael. "Development and Comparison of Laplace Domain and State-Space Models of a Half-Car With Flexible Body." In ASME 2010 10th Biennial Conference on Engineering Systems Design and Analysis. ASMEDC, 2010. http://dx.doi.org/10.1115/esda2010-24518.

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Math models of wheeled ground vehicle dynamics, including flexible body effects, have been the subject of research and development for many years. These models are typically based on a finite system of simultaneous ordinary differential equations (e.g., state-space models). Higher order models that include flexible body effects offer improved accuracy over a wider frequency range than lower order rigid body models; however higher order models are typically more sensitive to uncertainties in the model parameters and have increased computational requirements. Lower order models with the desired

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Maghami Asl, Farshid, and A. Galip Ulsoy. "Solution of Systems of Linear Delay Differential Equations Via Lambert Functions." In ASME 2005 International Design Engineering Technical Conferences and Computers and Information in Engineering Conference. ASMEDC, 2005. http://dx.doi.org/10.1115/detc2005-84076.

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A new analytic approach to obtain the complete solution for systems of delay differential equations (DDE) based on the concept of Lambert functions is presented. The similarity to the concept of the state transition matrix in linear ordinary differential equations enables the approach to be used for general classes of linear DDE’s in matrix form. The solution is in the form of an infinite series of modes written in terms of Lambert functions. Results are presented for stability criteria for the individual modes, free response, and forced response in the context of specific examples. This new a

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Daneshmehr, A., and M. Shakeri. "The Response Analysis of the Piezoelectric Shell Panel Actuators Based on the Theory of Elasticity." In ASME 7th Biennial Conference on Engineering Systems Design and Analysis. ASMEDC, 2004. http://dx.doi.org/10.1115/esda2004-58389.

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A study on the elasticity solution of shell panel piezoelectric actuators is presented. In this paper, the structure is infinitely long, simply-supported, orthotropic and under pressure and electrostatic excitation. The equations of equilibrium, which are coupled partial differential equations, are reduced to ordinary differential equations with variable coefficients by means of trigonometric function expansion in circumferential direction. The resulting ordinary differential equations are solved by Galerkin finite element method. Numerical results are presented for [0/90/P] lamination. Finall

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Lahr, Derek F., and Dennis W. Hong. "Contact Stress Reduction Mechanisms for the CAM-Based Infinitely Variable Transmission." In ASME 2007 International Design Engineering Technical Conferences and Computers and Information in Engineering Conference. ASMEDC, 2007. http://dx.doi.org/10.1115/detc2007-34601.

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The Cam-based Infinitely Variable Transmission (IVT) is a new type of ratcheting IVT based on a three dimensional cam and follower system which provides unique characteristics such as generating specific functional speed ratio outputs including dwells, for a constant velocity input. This paper presents several mechanisms and design approaches used to improve the torque and speed capacity of this unique transmission. A compact, lightweight, and capable differential mechanism based on a cord and pulley system is developed to double the number of followers in contact with the cam at any time, the

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Sharma, Kal Renganathan. "On Relativistic Transformation of Coordinates and Exact Solution of Damped Wave Conduction and Relaxation Equation." In ASME 2008 Heat Transfer Summer Conference collocated with the Fluids Engineering, Energy Sustainability, and 3rd Energy Nanotechnology Conferences. ASMEDC, 2008. http://dx.doi.org/10.1115/ht2008-56121.

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Analytical solution to the hyperbolic damped wave conduction and relaxation equation is developed by a novel method called the relativistic transformation method. The hyperbolic PDE is decomposed into a time decaying damping component and a Klein-Gardon type equation for the wave temperature. The PDE that describes the wave temperature is transformed to a Bessel differential equation by using the relativistic transformation. The relativistic transformation, η = τ2 − X2 is symmetric in space and time. The solution obtained for the transient temperature to a semi-infinite medium was compared wit

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Kobus, Chris J. "Utilizing the Integral Technique to Determine the Similarity Variable in Classical Heat Transfer Problems: One Dimensional Heat Conduction in a Finite or Semi-Infinite Solid." In ASME 2013 Heat Transfer Summer Conference collocated with the ASME 2013 7th International Conference on Energy Sustainability and the ASME 2013 11th International Conference on Fuel Cell Science, Engineering and Technology. American Society of Mechanical Engineers, 2013. http://dx.doi.org/10.1115/ht2013-17097.

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In advanced heat transfer courses, a technique exists for reducing a partial differential equation where the dependent variable is a function of two independent variables, to an ordinary differential equation where that same dependent variable becomes a function of only one independent variable. The key to this technique is finding out what the similarity variable to make this transformation is. The difficulty is that the form of the similarity variable is not intuitive, and many heat transfer textbooks do not reveal how this variable is found in classical problems such as viscous and thermal

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Yi, Sun, Patrick W. Nelson, and A. Galip Ulsoy. "Chatter Stability Analysis Using the Matrix Lambert Function and Bifurcation Analysis." In ASME 2006 International Manufacturing Science and Engineering Conference. ASMEDC, 2006. http://dx.doi.org/10.1115/msec2006-21130.

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We investigate the stability of the regenerative machine tool chatter problem, in a turning process modeled using delay differential equations (DDEs). An approach using the matrix Lambert function for the analytical solution to systems to delay differential equations is applied to this problem and compared with the result obtained using a bifurcation analysis. The Lambert function, known to be useful for solving scalar first order DDEs, has recently been extended to a matrix Lambert function approach to solve systems of DDEs. The essential advantage of the matrix Lambert approach is not only t

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Reports on the topic "Infinitely differentiable function"

1

Dyn, N., and A. Ron. Multiresolution Analysis by Infinitely Differentiable Compactly Supported Functions. Defense Technical Information Center, 1992. http://dx.doi.org/10.21236/ada256526.

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