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A New Perturbative Approach in Nonlinear Singularity Analysis

Yee
2011 Journal of Mathematics and Statistics  
Conclusion/Recommendations: In particular, for a nonprincipal but maximal Painleve family the first-order perturbed series solution is already a local representation of the general solution, whose convergence  ...  Problem statement: The study is devoted to the "mirror" method which enables one to study the integrability of nonlinear differential equations.  ...  Painleve set up the problem of determining all differential equations whose general solution are single-valued.  ... 
doi:10.3844/jmssp.2011.249.254 fatcat:66ekj4l73fduteviravoykug2a

Picard–Fuchs Uniformization and Modularity¶of the Mirror Map

Charles F. Doran
2000 Communications in Mathematical Physics  
Via the constraints of special geometry, the Picard-Fuchs equations for one parameter families of Calabi-Yau threefolds imply a differential equation criterion for automorphicity of the mirror map in terms  ...  algebraic invariants -the functional and generalized functional invariants respectively.  ...  This is our general criterion for modularity of the mirror map for Calabi-Yau threefolds.  ... 
doi:10.1007/s002200000228 fatcat:aqfkgcgy5vggpcvddy2csy7ohe

Analytical models of transient thermoelastic deformations of mirrors heated by high power cw laser beams

Patrice Hello, Jean-Yves Vinet
1990 Journal de Physique  
Abstract. 2014 We study the aberrations of massive mirrors heated by partial of intense laser beams in the coating or in the bulk.  ...  The non-uniform temperature field generated in the solid substrate induce thermoelastic deformations for which with the special assumption of axial symmetry, we give analytical models and numerical evaluations  ...  conditions reduce to : But 1} rz and 1} zz have the following expressions : We find the boundary conditions equivalent to the following linear system : where ym has already been defined in (3.15), and The solutions  ... 
doi:10.1051/jphys:0199000510200224300 fatcat:tsm22gwnu5gyjgdexk43saquzq

Designing coupled free-form surfaces

R. Andrew Hicks, Christopher Croke
2010 Optical Society of America. Journal A: Optics, Image Science, and Vision  
Example applications are given to the design of a mirror pair that increases the field of view of an observer, a similar mirror pair that also rotate the observers view, and a pair of mirrors that give  ...  The problem of designing optical systems that contain free-form surfaces is a challenging one, even in the case of designing a single surface.  ...  In sharp contrast to the case of a single mirror (where no solution is expected), in general one can expect that there exists a unique solution surface (albeit possibly very small) passing through the  ... 
doi:10.1364/josaa.27.002132 pmid:20922003 fatcat:mdshs3sdrzcjregcwetzxrtobu

A Continuous Adjoint Framework For Vehicle Aerocoustic Optimization

Kapellos, C.,, Hartmann, M.,
2018 Zenodo  
The proposed methodology is applied to compute the sensitivity map on the side mirror of a generic vehicle model, the SAE body.  ...  This work focuses on the solution of the derived adjoint systems, and the computation of the sensitivity derivatives.  ...  In Section 4, the method is applied to compute the adjoint aeroacoustic sensitivity map on the side mirror of the generic SAE vehicle.  ... 
doi:10.5281/zenodo.1442610 fatcat:jcwzhfim2rd3vj6xdmnvg7mmnq

Theory of double-chirped mirrors

N. Matuschek, F.X. Kartner, U. Keller
1998 IEEE Journal of Selected Topics in Quantum Electronics  
Solutions of the transmission line equations are given using the WKB-method. Analytic expressions for reflectivity and group delay are derived.  ...  A theory of double-chirped mirrors (DCM's) for dispersion compensation in ultrashort pulse laser sources is presented. We describe the multilayer interference coating by exact coupled-mode equations.  ...  In Section IV, we study the solutions of these Schrödinger equations qualitatively using WKB-solutions and derive an explicit expression for the complex reflection coefficient of the mirror.  ... 
doi:10.1109/2944.686724 fatcat:apyj6hi5k5hmjdwaipk6nqhqnu

Ion Temperature Effects on Plasma Flow in the Magnetic Mirror Configuration [article]

A. Sabo, A. I. Smolyakov, P. Yushmanov, S. Putvinskii
2022 arXiv   pre-print
Stationary accelerating solutions were obtained and compared with the time dependent dynamics, confirming that the solutions of the time-dependent equations converge to the stationary solutions and therefore  ...  The effects of the ion pressure anisotropy were analyzed using Chew-Goldberger-Low model and its generalization.  ...  Steady-state solutions of stationary equations obtained by the shooting method were compared with the time-dependent solutions obtained as a solution of the initial value problem for equations (3 -6),  ... 
arXiv:2109.02006v2 fatcat:voslsexp65hphbwuw7ji3cuqdm

Beyond Alhazen's problem: Analytical projection model for non-central catadioptric cameras with quadric mirrors

Amit Agrawal, Yuichi Taguchi, Srikumar Ramalingam
2011 CVPR 2011  
We derive an analytical 'forward projection' equation for the projection of a 3D point reflected by a quadric mirror on the imaging plane of a perspective camera, with no restrictions on the camera placement  ...  Catadioptric cameras are widely used to increase the field of view using mirrors.  ...  While a spherical mirror has four solutions, it is assumed that there is no closed-form or analytical solution for general mirrors.  ... 
doi:10.1109/cvpr.2011.5995596 dblp:conf/cvpr/AgrawalTR11 fatcat:tc236xstenfx3aujzkc56hgdam

Schwinger-Dyson equations for fermions self-energy in the electroweak-scale right-handed neutrino model

Nguyễn Như Lê, Phạm Quang Hưng
2017 HUE UNIVERSITY JOURNAL OF SCIENCE NATURAL SCIENCE  
Mirror quark and righthanded neutrino condensates can be determined through solutions of Schwinger-Dyson equations.  ...  Two types of condensates are considered here: that which is produced by the exchange of the fundamental Higgs double t 2 between two mirror quarks and the other which is produced by the exchange of the  ...  The solutions to the SD equations for RH neutrinos and mirror quarks self-energy We begin by considering the case of Higgs triplet.  ... 
doi:10.26459/jns.v116i2.3765 fatcat:w7gbj2cbs5anjokoaoxjlicxqy

Analytical Forward Projection for Axial Non-central Dioptric and Catadioptric Cameras [chapter]

Amit Agrawal, Yuichi Taguchi, Srikumar Ramalingam
2010 Lecture Notes in Computer Science  
-Reduces to 4 th degree equation for spherical mirror • Closed Form Solution • For refractive sphere -Solve 10 th degree equation in one unknown • 100 times speed up -3D reconstruction using  ...  Analytical Forward Projection for Non-Central Cameras • Axial Configuration -Camera lies on the axis of rotationally symmetric mirror • For conic mirrors -Solve 6 th degree equation in one unknown  ...  Results: Fast Projection of 3D Points • Project randomly generated 100,000 points (spherical mirror)  ... 
doi:10.1007/978-3-642-15558-1_10 fatcat:xyqyjl6cpvgrhivhtokweq2ega

Two-Sided Gravitational Mirror: Sealing off Curvature Singularities [article]

Aharon Davidson, Ben Yellin
2012 arXiv   pre-print
structure of a massive mirror.  ...  To demonstrate the phenomenon analytically, we derive an exact, static, radially symmetric, two-sided mirror solution, which asymptotes the massless BTZ black hole background, and then probe the local  ...  The primary role of the scalar potential V (φ) is to ensure a stable general relativistic vacuum solution.  ... 
arXiv:1201.0137v2 fatcat:jhxueelotrhivpslj6xrtgtt24

Generalized figure-control algorithm for large segmented telescope mirrors

Weiyao Zou
2001 Optical Society of America. Journal A: Optics, Image Science, and Vision  
for the figure control of a Keck-type telescope mirror.  ...  The author establishes a universal mathematical control model and provides an efficient algorithm to solve this model equation set.  ...  Establishment of a Generalized Equation Set for Segmented-Mirror Figure Control The complexity of the coefficient matrix of a generalized figure-control equation set is closely related to the sensor-actuator  ... 
doi:10.1364/josaa.18.000638 fatcat:ecm4b5wrvze4xmiuw2fpwd6t6a

Applications of the Network Simulation Method to Differential Equations with Singularities and Chaotic Behaviour

Joaquín Solano, Francisco Balibrea, José Andrés Moreno
2021 Mathematics  
others like the parabolic mirror and van der Pol non-linear equation.  ...  Additionally, we introduce also the electric-electronic circuits we have designed to be able of obtaining the solutions of the referred equations.  ...  Circuit equivalent to equation Parabolic Mirror p = y (t) Circuits to generate the values of y(t) and y'(t) Circuit equivalent to equation Parabolic Mirror.  ... 
doi:10.3390/math9121442 fatcat:dzqsf2ewajfghnxeiqwjqvewfy

Geometric optimization of magnetically actuated MEMS micromirrors

Francesco Pieri
2016 Journal of Physics, Conference Series  
We use this solutions to optimize the micromirror geometry by minimization of a linear objective function.  ...  The tradeoffs that emerge from optimization data allow simple quantitative design of low current, low size mirrors.  ...  Acknowledgments The author wishes to acknowledge the financial contribution by the ENIAC Joint Undertaking in the framework of project Lab4MEMS II under grant n. 621176-2.  ... 
doi:10.1088/1742-6596/757/1/012030 fatcat:u5ztcpjzbredxfg4zs2z5m3moa

A Comparative CFD Study of Side-view Mirror and Side-view Camera Usages on a City Bus

Duygu İPCİ
2020 International Journal of Automotive Science and Technology  
As a result of these operations, continuity equation and general momentum equations for incompressible flows may be stated as respec Fig. 3 . 3 Sub-options and constants of RSM turbulence model 2.2 Boundary  ...  [7] studied on the interference drag that is generated by the mixing of airflow streamlines between door mirrors and vehicle body.  ... 
doi:10.30939/ijastech..726376 fatcat:cjkj5et27nca7ph45aw5aczy2a
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