Relevant bibliographies by topics / Solvable approximation

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

Academic literature on the topic 'Solvable approximation'

Author: Grafiati
Published: 25 May 2024
Last updated: 31 July 2025

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Journal articles on the topic "Solvable approximation"

1

Hopkins, William E., and Wing Shing Wong. "Approximation of almost solvable bilinear systems." Systems & Control Letters 6, no. 2 (1985): 131–40. http://dx.doi.org/10.1016/0167-6911(85)90011-8.

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Valtancoli, P. "Exactly solvable f(R) inflation." International Journal of Modern Physics D 28, no. 07 (2019): 1950087. http://dx.doi.org/10.1142/s0218271819500871.

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Lemm, J. C. "Inhomogeneous Random Phase Approximation: A Solvable Model." Annals of Physics 244, no. 1 (1995): 201–38. http://dx.doi.org/10.1006/aphy.1995.1111.

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Co’, Giampaolo, and Stefano De Leo. "Hartree–Fock and random phase approximation theories in a many-fermion solvable model." Modern Physics Letters A 30, no. 36 (2015): 1550196. http://dx.doi.org/10.1142/s0217732315501965.

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We present an ideal system of interacting fermions where the solutions of the many-body Schrödinger equation can be obtained without making approximations. These exact solutions are used to test the validity of two many-body effective approaches, the Hartree–Fock and the random phase approximation theories. The description of the ground state done by the effective theories improves with increasing number of particles.
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Shi, Ronggang, and Barak Weiss. "Invariant measures for solvable groups and Diophantine approximation." Israel Journal of Mathematics 219, no. 1 (2017): 479–505. http://dx.doi.org/10.1007/s11856-017-1472-y.

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Burova, I. G. "The Hermite-Birkhoff Problem and Local Spline Approximation." WSEAS TRANSACTIONS ON MATHEMATICS 23 (October 2, 2024): 591–98. http://dx.doi.org/10.37394/23206.2024.23.62.

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This paper discusses the use of local spline approximations to solve the Hermite-Birkhoff problem. The solution to a specific problem using polynomial and non-polynomial local splines of the third order of approximation is considered. Here we discuss the case when the values of the function 𝑢(𝑥) and its derivative 𝑢’(𝑥) are given at the nodes of the grid in an alternative way: … , 𝑢(𝑥𝑗), 𝑢′(𝑥𝑗+1), 𝑢(𝑥𝑗+2), … . Note that when using polynomial and non-polynomial spline approximations, it is possible to obtain acceptable solutions in several interesting cases that are impossible when we use the c
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SOLENOV, DMITRY, and VLADIMIR PRIVMAN. "EVALUATION OF DECOHERENCE FOR QUANTUM COMPUTING ARCHITECTURES: QUBIT SYSTEM SUBJECT TO TIME-DEPENDENT CONTROL." International Journal of Modern Physics B 20, no. 11n13 (2006): 1476–95. http://dx.doi.org/10.1142/s0217979206034066.

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We present an approach that allows quantifying decoherence processes in an open quantum system subject to external time-dependent control. Interactions with the environment are modeled by a standard bosonic heat bath. We develop two unitarity-preserving approximation schemes to calculate the reduced density matrix. One of the approximations relies on a short-time factorization of the evolution operator, while the other utilizes expansion in terms of the system-bath coupling strength. Applications are reported for two illustrative systems: an exactly solvable adiabatic model, and a model of a r
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Liu, Yao, Yin Yin, Wenxin Qiu, Wei Cheng, Huan Lu, and Guang Luo. "The Second-Order Approximation of Superpotentials Based on SUSYQM." Symmetry 17, no. 4 (2025): 493. https://doi.org/10.3390/sym17040493.

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This paper is based on the shape invariance of the solvable superpotentials and uses the series expansion method to study the approximate expansion forms of these superpotentials. Firstly, this paper examines the differential equations satisfied by the first-order approximations of the superpotentials. Through an example, namely Rosen–Morse (trigonometric) superpotentials, the specific forms of these first-order approximations are analyzed. Based on these simple first-order approximations, this paper then delves into the ground-state wave functions of the superpotential. Secondly, this paper d
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Kudryashov, Vladimir V., and Yulian V. Vanne. "Explicit summation of the constituent WKB series and new approximate wave functions." Journal of Applied Mathematics 2, no. 6 (2002): 265–75. http://dx.doi.org/10.1155/s1110757x02112046.

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The independent solutions of the one-dimensional Schrödinger equation are approximated by means of the explicit summation of the leading constituent WKB series. The continuous matching of the particular solutions gives the uniformly valid analytical approximation to the wave functions. A detailed numerical verification of the proposed approximation is performed for some exactly solvable problems arising from different kinds of potentials.
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Mota, V., and E. S. Hern�ndez. "A solvable version of the collisional random phase approximation." Zeitschrift f�r Physik A Atomic Nuclei 328, no. 2 (1987): 177–87. http://dx.doi.org/10.1007/bf01290660.

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Dissertations / Theses on the topic "Solvable approximation"

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Manríquez, Peñafiel Ronald. "Local approximation by linear systems and Almost-Riemannian Structures on Lie groups and Continuation method in rolling problem with obstacles." Electronic Thesis or Diss., université Paris-Saclay, 2022. https://theses.hal.science/tel-03716186.

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L'objectif de cette thèse est d'étudier deux sujets en géométrie sub-Riemannienne. D'une part, l'approximation locale d'une structure presque riemannienne aux points singuliers, et d'autre part, le système cinématique d’une variété à 2 dimensions roulant (sans torsion ni glissement) sur le plan euclidien avec des régions interdites. Une structure presque riemannienne de dimension n peut être définie localement par n champs vectoriels satisfaisant la condition de rang de l'algèbre de Lie, jouant le rôle d'un cadre orthonormé. L'ensemble des points où ces champs vectoriels sont colinéaires est a
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Books on the topic "Solvable approximation"

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Research Institute for Advanced Computer Science (U.S.), ed. Explicitly solvable complex Chebyshev approximation problems related to sine polynomials. Research Institute for Advanced Computer Science, NASA Ames Research Center, 1989.

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2

Christensen, Jens Gerlach. Trends in harmonic analysis and its applications: AMS special session on harmonic analysis and its applications : March 29-30, 2014, University of Maryland, Baltimore County, Baltimore, MD. American Mathematical Society, 2015.

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Combinatorics and Random Matrix Theory. American Mathematical Society, 2016.

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Book chapters on the topic "Solvable approximation"

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Lobbe, Alexander. "Deep Learning for the Benes Filter." In Mathematics of Planet Earth. Springer International Publishing, 2022. http://dx.doi.org/10.1007/978-3-031-18988-3_12.

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AbstractThe filtering problem is concerned with the optimal estimation of a hidden state given partial and noisy observations. Filtering is extensively studied in the theoretical and applied mathematical literature. One of the central challenges in filtering today is the numerical approximation of the optimal filter. Here, accurate and fast methods are actively sought after, especially for such high-dimensional settings as numerical weather prediction, for example. In this paper we present a brief study of a new numerical method based on the mesh-free neural network representation of the densi
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Sikorski, Krzysztof A. "Fixed Points- Noncontractive Functions." In Optimal Solution of Nonlinear Equations. Oxford University Press, 2001. http://dx.doi.org/10.1093/oso/9780195106909.003.0007.

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In this chapter we consider the approximation of fixed points of noncontractive functions with respect to the absolute error criterion. In this case the functions may have multiple and/or whole manifolds of fixed points. We analyze methods based on sequential function evaluations as information. The simple iteration usually does not converge in this case, and the problem becomes much more difficult to solve. We prove that even in the two-dimensional case the problem has infinite worst case complexity. This means that no methods exist that solve the problem with arbitrarily small error toleranc
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Mussardo, Giuseppe. "Approximate Solutions." In Statistical Field Theory. Oxford University Press, 2020. http://dx.doi.org/10.1093/oso/9780198788102.003.0003.

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Chapter 3 discusses the approximation schemes used to approach lattice statistical models that are not exactly solvable. In addition to the mean field approximation, it also considers the Bethe–Peierls approach to the Ising model. Moreover, there is a thorough discussion of the Gaussian model and its spherical version, both of which are two important systems with several points of interest. A chapter appendix provides a detailed analysis of the random walk on different lattices: apart from the importance of the subject on its own, it explains how the random walk is responsible for the critical
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Rodriguez, Ricardo, Ivo Bukovsky, and Noriyasu Homma. "Potentials of Quadratic Neural Unit for Applications." In Advances in Abstract Intelligence and Soft Computing. IGI Global, 2013. http://dx.doi.org/10.4018/978-1-4666-2651-5.ch023.

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The paper discusses the quadratic neural unit (QNU) and highlights its attractiveness for industrial applications such as for plant modeling, control, and time series prediction. Linear systems are still often preferred in industrial control applications for their solvable and single solution nature and for the clarity to the most application engineers. Artificial neural networks are powerful cognitive nonlinear tools, but their nonlinear strength is naturally repaid with the local minima problem, overfitting, and high demands for application-correct neural architecture and optimization techni
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Tuck, Adrian F. "Non-Equilibrium Statistical Mechanics." In Atmospheric Turbulence. Oxford University Press, 2008. http://dx.doi.org/10.1093/oso/9780199236534.003.0010.

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The Earth’s atmosphere is far from equilibrium; it is constantly in motion from the combined effects of gravity and planetary rotation, is constantly absorbing and emitting radiation, and hosts ongoing chemical reactions which are ultimately fuelled by solar photons. It has fluxes of material and energy across its boundaries with the planetary surface, both terrestrial and marine, and also emits a continual outward flux of infrared photons to space. The gaseous atmosphere is manifestly a kinetic system, meaning that its evolution must be described by time dependent differential equations. The
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Kalyuzhnyi, Yu V., and P. T. Cummings. "6 Equations of state from analytically solvable integral equation approximations." In Equations of State for Fluids and Fluid Mixtures. Elsevier, 2000. http://dx.doi.org/10.1016/s1874-5644(00)80017-x.

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Juan Peña, José, Jesús Morales, and Jesús García-Ravelo. "Perspective Chapter: Relativistic Treatment of Spinless Particles Subject to a Class of Multiparameter Exponential-Type Potentials." In Schrödinger Equation - Fundamentals Aspects and Potential Applications [Working Title]. IntechOpen, 2023. http://dx.doi.org/10.5772/intechopen.112184.

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By using the exactly-solvable Schrödinger equation for a class of multi-parameter exponential-type potential, the analytical bound state solutions of the Klein-Gordon equation are presented. The proposal is based on the fact that the Klein-Gordon equation can be reduced to a Schrödinger-type equation when the Lorentz-scalar and vector potential are equal. The proposal has the advantage of avoiding the use of a specialized method to solve the Klein-Gordon equation for a specific exponential potential due that it can be derived by means of an appropriate choice of the involved parameters. For th
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Conference papers on the topic "Solvable approximation"

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Todorov, Emanuel. "Eigenfunction approximation methods for linearly-solvable optimal control problems." In 2009 IEEE Symposium on Adaptive Dynamic Programming and Reinforcement Learning (ADPRL). IEEE, 2009. http://dx.doi.org/10.1109/adprl.2009.4927540.

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Pedram, Ali Reza, and Takashi Tanaka. "Linearly-Solvable Mean-Field Approximation for Multi-Team Road Traffic Games." In 2019 IEEE 58th Conference on Decision and Control (CDC). IEEE, 2019. http://dx.doi.org/10.1109/cdc40024.2019.9029579.

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Elperin, Tov, Andrew Fominykh, and Boris Krasovitov. "Modeling of Simultaneous Gas Absorption and Evaporation of Large Droplet." In ASME 2005 International Mechanical Engineering Congress and Exposition. ASMEDC, 2005. http://dx.doi.org/10.1115/imece2005-79924.

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In this study we investigated numerically simultaneous heat and mass transfer during evaporation/condensation on the surface of a stagnant droplet in the presence of inert admixtures containing non-condensable solvable gas. The performed analysis is pertinent to slow droplet evaporation/condensation when Mach number is small (M≪1). The system of transient conjugate nonlinear energy and mass conservation equations was solved using anelastic approximation. Transport coefficients of the gaseous phase were calculated as functions of temperature and concentrations of gaseous species. Thermophysical
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Elperin, Tov, Andrew Fominykh, and Boris Krasovitov. "Simultaneous Heat and Mass Transfer During Evaporation/Condensation on the Surface of a Stagnant Droplet in the Presence of Inert Admixtures Containing Non-Condensable Solvable Gas." In ASME 2005 Summer Heat Transfer Conference collocated with the ASME 2005 Pacific Rim Technical Conference and Exhibition on Integration and Packaging of MEMS, NEMS, and Electronic Systems. ASMEDC, 2005. http://dx.doi.org/10.1115/ht2005-72493.

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In this study we investigated numerically simultaneous heat and mass transfer during evaporation/condensation on the surface of a stagnant droplet in the presence of inert admixtures containing non-condensable solvable gas. The performed analysis is pertinent to slow droplet evaporation/condensation when Mach number is small (M≪1). The system of transient conjugate nonlinear energy and mass conservation equations was solved using anelastic approximation. Transport coefficients of the gaseous phase were calculated as functions of temperature and concentrations of gaseous species. Thermophysical
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Herkenrath, Maike, Till Fluschnik, Francesco Grothe, and Leon Kellerhals. "Placing Green Bridges Optimally, with Habitats Inducing Cycles." In Thirty-First International Joint Conference on Artificial Intelligence {IJCAI-22}. International Joint Conferences on Artificial Intelligence Organization, 2022. http://dx.doi.org/10.24963/ijcai.2022/531.

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Choosing the placement of wildlife crossings (i.e., green bridges) to reconnect animal species' fragmented habitats is among the 17 goals towards sustainable development by the UN. We consider the following established model: Given a graph whose vertices represent the fragmented habitat areas and whose weighted edges represent possible green bridge locations, as well as the habitable vertex set for each species, find the cheapest set of edges such that each species' habitat is connected. We study this problem from a theoretical (algorithms and complexity) and an experimental perspective, while
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Singh, Rituraj, and Krishna M. Singh. "Iterative Solvers for Meshless Petrov Galerkin (MLPG) Method Applied to Large Scale Engineering Problems Challenges." In ASME 2015 International Mechanical Engineering Congress and Exposition. American Society of Mechanical Engineers, 2015. http://dx.doi.org/10.1115/imece2015-53343.

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In recent years, significant research effort has been invested in development of mesh-free methods for different types of continuum problems. Prominent amongst these methods are element free Galerkin (EFG) method, RKPM, and mesh-less Petrov Galerkin (MLPG) method. Most of these methods employ a set of nodes for discretization of the problem domain, and use a moving least squares (MLS) approximation to generate shape functions. Of these methods, MLPG method is seen as a pure meshless method since it does not require any background mesh. Accuracy and flexibility of MLPG method is well establishe
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Zhong, Mingyuan, and Emanuel Todorov. "Moving least-squares approximations for linearly-solvable MDP." In 2011 Ieee Symposium On Adaptive Dynamic Programming And Reinforcement Learning. IEEE, 2011. http://dx.doi.org/10.1109/adprl.2011.5967383.

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Manko, D. J., and W. L. Whittaker. "Inverse Dynamic Models Used for Force Control of Compliant, Closed-Chain Mechanisms." In ASME 1989 Design Technical Conferences. American Society of Mechanical Engineers, 1989. http://dx.doi.org/10.1115/detc1989-0106.

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Abstract A general inverse dynamic model is presented that is applicable to mechanisms incorporating member, joint and base compliance. Previous approaches for defining inverse dynamic models of compliant mechanisms have been approximations or limited to simple mechanism geometries and open-chain mechanisms. Hence, the motivation for a more general approach. Inverse dynamic equations for compliant mechanisms modeled with and without constraint equations are shown to be solvable sets of differential/algebraic equations (DAE’s); relevant characteristics and solutions of DAE systems are discussed
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Wilde, Douglass J. "Monotonicity Analysis of Taguchi’s Robust Circuit Design Problem." In ASME 1990 Design Technical Conferences. American Society of Mechanical Engineers, 1990. http://dx.doi.org/10.1115/detc1990-0052.

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Abstract A recent article showed how to formulate Taguchi’s robust circuit design problem rigorously as an optimization problem. A necessary condition for optimality was found to be that the control range be centered about the target value. This generates a constraint on the two design variables which cannot be solved for either variable. The present article shows that by approximating this unsolvable constraint with a simpler constraint that is solvable, one variable can be eliminated and the problem reduced to an unconstrained one in a single variable. Since this reduced objective turns out
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Xiros, Nikolaos I. "Investigation of a Nonlinear Control Model for Marine Propulsion Power-Plants." In ASME 2011 International Mechanical Engineering Congress and Exposition. ASMEDC, 2011. http://dx.doi.org/10.1115/imece2011-63797.

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A cycle-mean-value, quasi-steady, thermodynamic model of slow-speed, two-stroke marine Diesel engines, used for performance prediction and engine-propeller/turbocharger matching, is converted into a power-plant analytic model. The dynamic part of the cycle-mean model consists of the two first-order differential equations for the cycle-mean crankshaft and turbocharger shaft rotational accelerations. This form implies a state-space formulation of the power-plant modeling approach. However, engine, turbine and compressor torques have to be calculated through the solution of the algebraic part of
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