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Автор: Grafiati
Опубліковано: 6 вересня 2023

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1

SISSAKIAN, ALEXEY, IGOR SOLOVTSOV, and OLEG SHEVCHENKO. "VARIATIONAL PERTURBATION THEORY." International Journal of Modern Physics A 09, no. 12 (May 10, 1994): 1929–99. http://dx.doi.org/10.1142/s0217751x94000832.

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Анотація:
A nonperturbative method — variational perturbation theory (VPT) — is discussed. A quantity we are interested in is represented by a series, a finite number of terms of which not only describe the region of small coupling constant but reproduce well the strong coupling limit. The method is formulated only in terms of the Gaussian quadratures, and diagrams of the conventional perturbation theory are used. Its efficiency is demonstrated for the quantum-mechanical anharmonic oscillator. The properties of convergence are studied for series in VPT for the [Formula: see text] model. It is shown that it is possible to choose variational additions such that they lead to convergent series for any values of the coupling constant. Upper and lower estimates for the quantities under investigation are considered. The nonperturbative Gaussian effective potential is derived from a more general approach, VPT. Various versions of the variational procedure are explored and the preference for the anharmonic variational procedure in view of convergence of the obtained series is argued. We investigate the renormalization procedure in the φ4 model in VPT. The nonperturbative β function is derived in the framework of the proposed approach. The obtained result is in agreement with four-loop approximation and has the asymptotic behavior as g3/2 for a large coupling constant. We construct the VPT series for Yang-Mills theory and study its convergence properties. We introduce coupling to spinor fields and demonstrate that they do not influence the VPT series convergence properties.
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2

Urban, Zbyněk, and Demeter Krupka. "Foundations of higher-order variational theory on Grassmann fibrations." International Journal of Geometric Methods in Modern Physics 11, no. 07 (August 2014): 1460023. http://dx.doi.org/10.1142/s0219887814600238.

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A setting for higher-order global variational analysis on Grassmann fibrations is presented. The integral variational principles for one-dimensional immersed submanifolds are introduced by means of differential 1-forms with specific properties, similar to the Lepage forms from the variational calculus on fibred manifolds. Prolongations of immersions and vector fields to the Grassmann fibrations are defined as a geometric tool for the variations of immersions, and the first variation formula in the infinitesimal form is derived. Its consequences, the Euler–Lagrange equations for submanifolds and the Noether theorem on invariant variational functionals are proved. Examples clarifying the meaning of the Noether theorem in the context of variational principles for submanifolds are given.
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3

Jackson, A. D., A. Lande, and R. A. Smith. "Planar Theory Made Variational." Physical Review Letters 54, no. 14 (April 8, 1985): 1469–71. http://dx.doi.org/10.1103/physrevlett.54.1469.

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4

Prestipino, Santi, and Erio Tosatti. "Variational theory of preroughening." Physical Review B 59, no. 4 (January 15, 1999): 3108–24. http://dx.doi.org/10.1103/physrevb.59.3108.

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5

Lekner, John. "Variational Theory of Reflection." Australian Journal of Physics 38, no. 2 (1985): 113. http://dx.doi.org/10.1071/ph850113.

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Анотація:
Schwinger's variational method for the scattering phase shift produced by a central potential is adapted to reflection by a planar potential barrier (or well). The formulation is general, for an arbitrary transition between any two media, but the application here is limited to reflection at a barrier between media of equal potential energy. The simplest variational estimate for the reflection amplitude correctly tends to -1 at grazing incidence, as it must for any finite barrier. This is in contrast to the first order perturbation reflection amplitude, which diverges at grazing incidence. The same variational estimate is also correct to second order in the ratio of the interface thickness to the wavelength of the incident wave. The theory applies also to the reflection of the electromagnetic s (or transverse electric) wave at an interface between two media.
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6

Hamad, Esam Z., and G. Ali Mansoori. "Variational theory of mixtures." Fluid Phase Equilibria 37 (January 1987): 255–85. http://dx.doi.org/10.1016/0378-3812(87)80055-9.

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7

Sasaki, Yoshi K. "Entropic Balance Theory and Variational Field Lagrangian Formalism: Tornadogenesis." Journal of the Atmospheric Sciences 71, no. 6 (May 30, 2014): 2104–13. http://dx.doi.org/10.1175/jas-d-13-0211.1.

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Анотація:
Abstract The entropic balance theory has been applied with outstanding results to explain many important aspects of tornadic phenomena. The theory was originally developed in variational (probabilistic) field Lagrangian formalism, or in short, variational formalism, with Lagrangian density and action appropriate for supercell-storm and tornadic phenomena. The variational formalism is broadly used in in modern physics, not only in classical mechanics, with Lagrangian density and action designed for each physical problem properly. The Clebsch transformation (equation) was derived in the classical variational formalism but has not been used because of the unobservable and nonmeteorological Lagrange multiplier. The entropic balance condition is thus developed from the Clebsch transformation, changing the unobservable nonmeteorological Lagrange multiplier to observable meteorological rotational flow velocity with entropy and making it applicable to tornadic phenomena. Theoretical details of the entropic balance are presented such as the entropic right-hand rule, entropic dipole, source and sink, overshooting mechanism of hydrometeors against westerlies and the existence of single and multiple vortices and their relation to tornadogenesis. These results are in reasonable agreement with the many observations and data analysis publications. The Clebsch transformation and entropic balance are the new balance conditions, different from the known other balance conditions such as hydrostatic, (quasi-)geostrophic, cyclostrophic, Boussinesq, and anelastic balance. The variations in calculus of variations and in the classical variational formalism are hypothetical. However, this article suggests that the hypothetical variations could be physical, relating to quantum variations and their interaction with the classical systems.
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8

Yuan, Xiao, Suguru Endo, Qi Zhao, Ying Li, and Simon C. Benjamin. "Theory of variational quantum simulation." Quantum 3 (October 7, 2019): 191. http://dx.doi.org/10.22331/q-2019-10-07-191.

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Анотація:
The variational method is a versatile tool for classical simulation of a variety of quantum systems. Great efforts have recently been devoted to its extension to quantum computing for efficiently solving static many-body problems and simulating real and imaginary time dynamics. In this work, we first review the conventional variational principles, including the Rayleigh-Ritz method for solving static problems, and the Dirac and Frenkel variational principle, the McLachlan's variational principle, and the time-dependent variational principle, for simulating real time dynamics. We focus on the simulation of dynamics and discuss the connections of the three variational principles. Previous works mainly focus on the unitary evolution of pure states. In this work, we introduce variational quantum simulation of mixed states under general stochastic evolution. We show how the results can be reduced to the pure state case with a correction term that takes accounts of global phase alignment. For variational simulation of imaginary time evolution, we also extend it to the mixed state scenario and discuss variational Gibbs state preparation. We further elaborate on the design of ansatz that is compatible with post-selection measurement and the implementation of the generalised variational algorithms with quantum circuits. Our work completes the theory of variational quantum simulation of general real and imaginary time evolution and it is applicable to near-term quantum hardware.
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9

Tessarotto, Massimo, and Claudio Cremaschini. "The Principle of Covariance and the Hamiltonian Formulation of General Relativity." Entropy 23, no. 2 (February 10, 2021): 215. http://dx.doi.org/10.3390/e23020215.

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The implications of the general covariance principle for the establishment of a Hamiltonian variational formulation of classical General Relativity are addressed. The analysis is performed in the framework of the Einstein-Hilbert variational theory. Preliminarily, customary Lagrangian variational principles are reviewed, pointing out the existence of a novel variational formulation in which the class of variations remains unconstrained. As a second step, the conditions of validity of the non-manifestly covariant ADM variational theory are questioned. The main result concerns the proof of its intrinsic non-Hamiltonian character and the failure of this approach in providing a symplectic structure of space-time. In contrast, it is demonstrated that a solution reconciling the physical requirements of covariance and manifest covariance of variational theory with the existence of a classical Hamiltonian structure for the gravitational field can be reached in the framework of synchronous variational principles. Both path-integral and volume-integral realizations of the Hamilton variational principle are explicitly determined and the corresponding physical interpretations are pointed out.
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10

Laurin-Kovitz, Kirsten F., and E. E. Lewis. "Variational Nodal Transport Perturbation Theory." Nuclear Science and Engineering 123, no. 3 (July 1996): 369–80. http://dx.doi.org/10.13182/nse96-a24200.

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11

Robinson, James B., and Peter J. Knowles. "Quasi-variational coupled cluster theory." Journal of Chemical Physics 136, no. 5 (February 7, 2012): 054114. http://dx.doi.org/10.1063/1.3680560.

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12

Groma, I., G. Györgyi, and P. D. Ispánovity. "Variational approach in dislocation theory." Philosophical Magazine 90, no. 27-28 (September 21, 2010): 3679–95. http://dx.doi.org/10.1080/14786430903401073.

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13

Jisha, C. P., V. C. Kuriakose, and K. Porsezian. "Variational method in soliton theory." European Physical Journal Special Topics 173, no. 1 (June 2009): 341–46. http://dx.doi.org/10.1140/epjst/e2009-01084-8.

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14

Robinson, James B., and Peter J. Knowles. "Approximate variational coupled cluster theory." Journal of Chemical Physics 135, no. 4 (July 28, 2011): 044113. http://dx.doi.org/10.1063/1.3615060.

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15

Jihuan, H. E. "Variational theory for Chandrasekharaiah thermopiezoelectricity." Communications in Nonlinear Science and Numerical Simulation 4, no. 4 (December 1999): 289–92. http://dx.doi.org/10.1016/s1007-5704(99)90044-8.

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16

Zorii, N. V. "Variational problems of potential theory." Ukrainian Mathematical Journal 43, no. 4 (April 1991): 311–17. http://dx.doi.org/10.1007/bf01670071.

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17

Sissakian, A. N., and I. L. Solovtsov. "Variational perturbation theory. Anharmonic oscillator." Zeitschrift für Physik C Particles and Fields 54, no. 2 (June 1992): 263–71. http://dx.doi.org/10.1007/bf01566655.

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18

Zhou, Xin-Wei. "Variational theory for physiological flow." Computers & Mathematics with Applications 54, no. 7-8 (October 2007): 1000–1002. http://dx.doi.org/10.1016/j.camwa.2006.12.043.

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19

Zorii, N. V. "Variational problems of potential theory." Ukrainian Mathematical Journal 43, no. 3 (March 1991): 311–17. http://dx.doi.org/10.1007/bf01060840.

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20

Balian, R., H. Flocard, and M. Vénéroni. "Variational extensions of BCS theory." Physics Reports 317, no. 5-6 (September 1999): 251–358. http://dx.doi.org/10.1016/s0370-1573(98)00134-3.

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21

PRESTON, SERGE. "VARIATIONAL THEORY OF BALANCE SYSTEMS." International Journal of Geometric Methods in Modern Physics 07, no. 05 (August 2010): 745–95. http://dx.doi.org/10.1142/s0219887810004543.

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Анотація:
In this work, we apply the Poincaré–Cartan formalism of Classical Field Theory to study the systems of balance equations (balance systems). We introduce the partial k-jet bundles [Formula: see text] of the configurational bundle π : Y → X and study their basic properties: partial Cartan structure, prolongation of vector fields, etc. A constitutive relation C of a balance system [Formula: see text] is realized as the mapping between a (partial) k-jet bundle [Formula: see text] and the extended dual bundle [Formula: see text] similar to the Legendre mapping of the Lagrangian Field Theory. The invariant (variational) form of the balance system [Formula: see text] corresponding to a constitutive relation [Formula: see text] is studied. Special cases of balance systems — Lagrangian systems of order 1 with arbitrary sources and RET (Rational Extended Thermodynamics) systems are characterized in geometrical terms. The action of automorphisms of the bundle π on the constitutive mappings [Formula: see text] is studied and it is shown that the symmetry group [Formula: see text] of [Formula: see text] acts on the sheaf of solutions [Formula: see text] of balance system [Formula: see text]. A suitable version of Noether theorem for an action of a symmetry group is presented together with the special forms for semi-Lagrangian and RET balance systems. Examples of energy momentum and gauge symmetries balance laws are provided. At the end, we introduce the secondary balance laws for a balance system and classify these laws for the Cattaneo heat propagation system.
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22

KUTZELNIGG, WERNER. "Almost variational coupled cluster theory." Molecular Physics 94, no. 1 (May 1, 1998): 65–71. http://dx.doi.org/10.1080/00268979809482295.

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23

Ferrando, A., C. Milián, and D. V. Skryabin. "Variational theory of soliplasmon resonances." Journal of the Optical Society of America B 30, no. 9 (August 26, 2013): 2507. http://dx.doi.org/10.1364/josab.30.002507.

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24

Steigmann, D. J., and M. G. Faulkner. "Variational theory for spatial rods." Journal of Elasticity 33, no. 1 (October 1993): 1–26. http://dx.doi.org/10.1007/bf00042633.

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25

Scutari, Gesualdo, Daniel Palomar, Francisco Facchinei, and Jong-shi Pang. "Convex Optimization, Game Theory, and Variational Inequality Theory." IEEE Signal Processing Magazine 27, no. 3 (May 2010): 35–49. http://dx.doi.org/10.1109/msp.2010.936021.

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26

Skvortsov, V. A. "Variations and variational measures in integration theory and some applications." Journal of Mathematical Sciences 91, no. 5 (October 1998): 3293–322. http://dx.doi.org/10.1007/bf02433805.

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27

Castillo, R. C., E. Martina, M. López de Haro, J. Karkheck, and G. Stell. "Linearized kinetic-variational theory and short-time kinetic theory." Physical Review A 39, no. 6 (March 1, 1989): 3106–11. http://dx.doi.org/10.1103/physreva.39.3106.

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28

Liu, Lingyun. "Chinese Translation Discourse: Variational Translation Theory." International Journal of Education and Humanities 8, no. 1 (April 5, 2023): 91–96. http://dx.doi.org/10.54097/ijeh.v8i1.7073.

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Compared with full translation and based on a large number of translation variation phenomena, variational translation is a discourse of native translation studies with Chinese characteristics. After twenty years of development and research, the research scope of variational translation theory has gradually expanded and improved, but the literature review in recent years has lagged behind. Based on some well-known literature databases at home and abroad, Citespace, a bibliometric analysis tool, was used to review and visualize the development of variational translation theory at home and abroad in the past 20 years. The analysis data covered 760 relevant literatures. Based on the relevant data, the research frontiers and trends of variational translation theory are forecasted, and the new research fields of this theory in both theoretical and empirical research are explored. The existing problems in variational translation theory are summarized, and some feasible considerations about the construction and dissemination of Chinese native translation discourse are proposed.
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29

Pieruschka, P., S. Marčelja, and M. Teubner. "Variational theory of undulating multilayer systems." Journal de Physique II 4, no. 5 (May 1994): 763–72. http://dx.doi.org/10.1051/jp2:1994163.

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30

Bouchaud, Jean-Philippe, Marc Mézard, and Jonathan S. Yedidia. "Variational theory for disordered vortex lattices." Physical Review Letters 67, no. 27 (December 30, 1991): 3840–43. http://dx.doi.org/10.1103/physrevlett.67.3840.

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31

Gratwick, R., and M. A. Sychev. "Direct Methods in Variational Field Theory." Siberian Mathematical Journal 63, no. 5 (September 2022): 862–67. http://dx.doi.org/10.1134/s0037446622050056.

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32

Lucchese, Robert R. "Multichannel variational expressions of scattering theory." Physical Review A 33, no. 3 (March 1, 1986): 1626–30. http://dx.doi.org/10.1103/physreva.33.1626.

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33

POPŁAWSKI, NIKODEM J. "VARIATIONAL FORMULATION OF EISENHART'S UNIFIED THEORY." International Journal of Modern Physics A 24, no. 20n21 (August 20, 2009): 3975–84. http://dx.doi.org/10.1142/s0217751x09044735.

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Анотація:
Eisenhart's classical unified field theory is based on a non-Riemannian affine connection related to the covariant derivative of the electromagnetic field tensor. The sourceless field equations of this theory arise from vanishing of the torsion trace and the symmetrized Ricci tensor. We formulate Eisenhart's theory from the metric-affine variational principle. In this formulation, a Lagrange multiplier constraining the torsion becomes the source for the Maxwell equations.
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34

O'Lenick, Richard, and Y. C. Chiew. "Variational theory for Lennard-Jones chains." Molecular Physics 85, no. 2 (June 10, 1995): 257–69. http://dx.doi.org/10.1080/00268979500101091.

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35

Otero-Espinar, M. Victoria, Juan J. Nieto, Donal O'Regan, and Kanishka Perera. "Variational Methods and Critical Point Theory." Abstract and Applied Analysis 2012 (2012): 1–2. http://dx.doi.org/10.1155/2012/894769.

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36

Kennedy, W. L. "Modified variational calculations in quantum theory." Physical Review A 38, no. 5 (September 1, 1988): 2657–59. http://dx.doi.org/10.1103/physreva.38.2657.

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37

Bachmann, Michael, Hagen Kleinert, and Axel Pelster. "Variational perturbation theory for density matrices." Physical Review A 60, no. 5 (November 1, 1999): 3429–43. http://dx.doi.org/10.1103/physreva.60.3429.

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38

Montgomery, H. E. "One-electron wavefunctions: variational perturbation theory." Chemical Physics Letters 311, no. 5 (October 1999): 367–71. http://dx.doi.org/10.1016/s0009-2614(99)00894-5.

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39

Khavinson, Dmitry, Mihai Putinar, and Harold S. Shapiro. "Poincaré’s Variational Problem in Potential Theory." Archive for Rational Mechanics and Analysis 185, no. 1 (October 18, 2006): 143–84. http://dx.doi.org/10.1007/s00205-006-0045-1.

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40

Galli, D. E., L. Reatto, and S. A. Vitiello. "Variational theory of rotons in superfluid4He." Journal of Low Temperature Physics 101, no. 3-4 (November 1995): 755–60. http://dx.doi.org/10.1007/bf00753386.

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41

Putrino, Anna, Daniel Sebastiani, and Michele Parrinello. "Generalized variational density functional perturbation theory." Journal of Chemical Physics 113, no. 17 (November 2000): 7102–9. http://dx.doi.org/10.1063/1.1312830.

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42

Dua, A., and T. A. Vilgis. "Self-consistent variational theory for globules." Europhysics Letters (EPL) 71, no. 1 (July 2005): 49–55. http://dx.doi.org/10.1209/epl/i2005-10062-x.

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43

Kang, Hong Seok, and Francis H. Ree. "A variational theory of classical solids." Journal of Chemical Physics 99, no. 4 (August 15, 1993): 2985–91. http://dx.doi.org/10.1063/1.465205.

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44

Lakshmikantham, V., X. Liu, and S. Leela. "Variational Lyapunov method and stability theory." Mathematical Problems in Engineering 3, no. 6 (1998): 555–71. http://dx.doi.org/10.1155/s1024123x97000689.

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Анотація:
By unifying the method of variation of parameters and Lyapunov's second method, we develop a fruitful technique which we call variational Lyapunov method. We then consider the stability theory in this new framework showing the advantage of this unification.
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45

Donskoi, I. G. "VARIATIONAL PROBLEMS FOR COMBUSTION THEORY EQUATIONS." Journal of Applied Mechanics and Technical Physics 63, no. 5 (November 2022): 773–81. http://dx.doi.org/10.1134/s0021894422050054.

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46

Pollak, Eli, and Dmitry Proselkov. "Quantum variational transition state theory revisited." Chemical Physics 170, no. 3 (March 1993): 265–73. http://dx.doi.org/10.1016/0301-0104(93)85113-m.

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47

Korsun, L. D., A. N. Sisakyan, and I. L. Solovtsov. "Variational perturbation theory. The? 2k oscillator." Theoretical and Mathematical Physics 90, no. 1 (January 1992): 22–34. http://dx.doi.org/10.1007/bf01018815.

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48

Penot, Jean-Paul. "Variational Analysis for the Consumer Theory." Journal of Optimization Theory and Applications 159, no. 3 (February 28, 2013): 769–94. http://dx.doi.org/10.1007/s10957-013-0289-5.

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49

Sellers, Harrell. "Variational energy derivatives and perturbation theory." International Journal of Quantum Chemistry 33, no. 4 (April 1988): 271–77. http://dx.doi.org/10.1002/qua.560330403.

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50

Sissakian, A. N., I. L. Solovtsov, and O. Yu Shevchenko. "Convergent series in variational perturbation theory." Physics Letters B 297, no. 3-4 (December 1992): 305–8. http://dx.doi.org/10.1016/0370-2693(92)91267-d.

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