×

zbMATH — the first resource for mathematics

Schrödinger wave functional in quantum Yang-Mills theory from precanonical quantization. (English) Zbl 1441.81129
Summary: A relation between the precanonical quantization of pure Yang-Mills fields and the standard functional Schrödinger representation in the temporal gauge is established. It is shown that the latter can be obtained from the former when the ultraviolet parameter \(\varkappa\) introduced in precanonical quantization goes to infinity. In this limiting case, the Schrödinger wave functional can be expressed as the trace of the Volterra product integral of Clifford-algebra-valued precanonical wave functions restricted to a field configuration, and the canonical functional derivative Schrödinger equation together with the quantum Gauss constraint is derived from the Dirac-like precanonical Schrödinger equation.
MSC:
81T70 Quantization in field theory; cohomological methods
35J10 Schrödinger operator, Schrödinger equation
81T13 Yang-Mills and other gauge theories in quantum field theory
81S08 Canonical quantization
PDF BibTeX XML Cite
Full Text: DOI
References:
[1] Feynman, R. P., The qualitative behavior of Yang-Mills theory in 2 + 1 dimensions, Nucl. Phys. B, 188, 479-512 (1981) · Zbl 1243.81112
[2] Gawędzki, K., Yang-Mills theory as Schrödinger quantum mechanics on the space of gauge-group orbits, Phys. Rev. D, 26, 3593-3610 (1982)
[3] Rossi, G. C.; Testa, M., The structure of Yang-Mills theories in the temporal gauge I-III. The structure of Yang-Mills theories in the temporal gauge I-III, Nucl. Phys. B, 163, 109 (1980); Phys. Rev. B, 176, 477 (1980); Phys. Rev. B, 237, 442 (1984); Genot, A. J.; Fujii, T.; Rondelez, Y., Scaling down DNA circuits with competitive neural networks. Scaling down DNA circuits with competitive neural networks, J. R. Soc. Interface, 10, 85 (2013), (20130212-20130212); El-Awady, R.; Saleh, E.; Hashim, A.; Soliman, N.; Dallah, A.; Elrasheed, A.; Elakraa, G., The role of eukaryotic and prokaryotic ABC transporter family in failure of chemotherapy. The role of eukaryotic and prokaryotic ABC transporter family in failure of chemotherapy, Front. Pharmacol., 7, 535 (2016); Abdellah, B.; Ahmed, E. H., Advanced Takagi-Sugeno Fuzzy Systems (2014), Springer; Potthoff, R. F.; Roy, S., A generalized multivariate analysis of variance model useful especially for growth curve problems. A generalized multivariate analysis of variance model useful especially for growth curve problems, Biometrika, 51, 3-4, 313-326 (1964); Truscott, J.; Brindley, J., Ocean plankton populations as excitable media. Ocean plankton populations as excitable media, Bull Math Biol, 56, 5, 981-998 (1994); Smith, B. R., Decompositions of Generalised Complete Graphs (2009), The University of Queensland, PhD Thesis; Oztop, H. F.; Al-Salem, K.; Varol, Y.; Pop, I., Natural convection heat transfer in a partially opened cavity filled with porous media. Natural convection heat transfer in a partially opened cavity filled with porous media, Int. J. Heat Mass Transfer, 54, 2253-2261 (2011); Rui, Z.; Zhitian, Z.; Lu, C.-D., The double charm decays of Bc meson in the perturbative QCD approach. The double charm decays of Bc meson in the perturbative QCD approach, Phys. Rev. D, 86, Article 074019 pp. (2012); Del Portillo, A.; Tripodi, J.; Najfeld, V.; Wodarz, D.; Levy, D. N.; Chen, B. K., Multiploid inheritance of HIV-1 during cell-to-cell infection. Multiploid inheritance of HIV-1 during cell-to-cell infection, J. Virol., 85, 7169-7176 (2011); Festa, P., The Shortest Path Tour Problem: Problem Definition, Modeling, and Optimization. The Shortest Path Tour Problem: Problem Definition, Modeling, and Optimization, Proceedings of INOC’2009, vol. 217, 1-7 (2009); Papastergis, E.; Shankar, F., An assessment of the “too big to fail” problem for field dwarf galaxies in view of baryonic feedback effects. An assessment of the “too big to fail” problem for field dwarf galaxies in view of baryonic feedback effects, Astron. Astrophys., 591, A58 (2016); Shen, S. Q.; Huang, T. Z.; Zhang, J. S., Augmentation block triangular preconditioners for regularized saddle point problems. Augmentation block triangular preconditioners for regularized saddle point problems, SIAM J. Matrix Anal. Appl., 33, 3, 721-741 (2012); Trostorff, S.; Waurick, M., On higher index differential-algebraic equations in infinite dimensions. (Böttcher, A.; Potts, D.; Stollmann, P.; Wenzel, D., The Diversity and Beauty of Applied Operator Theory (2018), Springer International Publishing), 477-486; Shields, A. L., A note on invariant subspaces. A note on invariant subspaces, Michigan Math. J., 17, 231-233 (1970); Taylor, M. E., Propagation, reflection, and diffraction of singularities of solutions to wave equations. Propagation, reflection, and diffraction of singularities of solutions to wave equations, Bull. Amer. Math. Soc., 84, 4, 589-611 (1978); Dorninger, D., Hamiltonian circuits determining the order of chromosomes. Hamiltonian circuits determining the order of chromosomes, Discrete Appl. Math., 50, 159-168 (1994); Schäfer, T.; Wayne, C. E., Physica D, 196, 90-105 (2004); Mishra, D.; Kulkarni, P.; Rangaswami, R., Synergy: A hypervisor managed holistic caching system. Synergy: A hypervisor managed holistic caching system, IEEE Trans. Cloud Comput., pre-print, 1-14 (2017); Bartoli, F.; Lisanti, G.; Karaman, S.; D. Bagdanov, A.; Del Bimbo, A., Unsupervised scene adaptation for faster multi-scale pedestrian detection. Unsupervised scene adaptation for faster multi-scale pedestrian detection, Proceedings of the International Conference on Pattern Recognition (2014); Albert, R.; Jeong, H.; Barabási, A.-L., Error and attack tolerance of complex networks. Error and attack tolerance of complex networks, Nature, 406, 378 (2000); Carrabs, F.; Cerrone, C.; Cerulli, R.; Silvestri, S., The rainbow spanning forest problem. The rainbow spanning forest problem, Soft. Comput., 22, 8, 2765-2776 (2018); Calladine, C. R., The theory of thin shell structures 1888-1988: love centenary lecture. The theory of thin shell structures 1888-1988: love centenary lecture, Proc. Inst. Mech. Eng., 202, 141-149 (1988); Myers, R. C.; Sachdev, S.; Singh, A., Holographic quantum critical transport without self-duality. Holographic quantum critical transport without self-duality, Phys. Rev. D, 83, Article 066017 pp. (2011); Young, A. F.; Kim, P., Nat. Phys., 5, 222 (2009); Wilkes, Gareth, Virtual pro-p properties of 3-manifold groups. Virtual pro-p properties of 3-manifold groups, J. Group Theory, 20, 5, 999-1023 (2017); Dai, M. F.; Wang, X. Q.; Zong, Y.; Zou, J. H.; Chen, Y. F.; Su, W. Y., Fractals, 25, 5, 1750049 (2017); Douglas, M. R., J. High Energy Phys., 007, 004 (1997), hep-th/9612126; Fraenkel, A. S.; Tanny, Y., A class of Wythoff-like games. A class of Wythoff-like games, Integers, 12B (2012/2013), #A7; Wilkes, Gareth, Profinite completions, cohomology and JSJ decompositions of compact 3-manifolds (2018), arXiv preprint; Hirt, C. W.; Amsden, A. A.; Cook, J. L., An arbitrary lagrangian-eulerian computing method for all flow speeds. An arbitrary lagrangian-eulerian computing method for all flow speeds, J Comput Phys, 14, 227-253 (1974); Brion, Michel, Representations of quivers. (Geometric Methods in Representation Theory I, Sémin. Congr, vol. 24 (2012), Soc. Math. France: Soc. Math. France Paris), 103-144; Wang, J.-B.; Wang, M.-Z., Single-machine scheduling with nonlinear deterioration. Single-machine scheduling with nonlinear deterioration, Optim. Lett., 6, 87-98 (2012); Sharma, P.; Kulkarni, P., Singleton: system-wide page deduplication in virtual environments. (Proceedings of the 21st international symposium on High-Performance Parallel and Distributed Computing (2012)), 15-26; Ogawa, S.; Cambon, B.; Leoncini, X.; Vittot, M.; del-Castillo-Negrete, D.; Dif-Pradalier, G.; Garbet, X., Phys. Plasmas, 23, Article 072506 pp. (2016); Baranes, A.; Oudeyer, P., Active learning of inverse models with intrinsically motivated goal exploration in robots. Active learning of inverse models with intrinsically motivated goal exploration in robots, Robot. Auton. Syst., 61, 1, 49-73 (2013); Atkinson, S. E.; Halvorsen, R., Interfuel substitution in steam-electric power generation. Interfuel substitution in steam-electric power generation, J. Political Econ., 84, 959-978 (1976); Rao, S. S.; Chen, L., Numerical solution of fuzzy linear equations in engineering analysis. Numerical solution of fuzzy linear equations in engineering analysis, Int. J. Numer. Methods Eng., 42, 829-846 (2015); Jin, Z.; Li, X., Anti-Ramsey numbers for graphs with independent cycles. Anti-Ramsey numbers for graphs with independent cycles, Electron. J. Combin., 16, R85 (2009); Zengin, G.; Mahomoodally, M. F.; Aktumsek, A.; Ceylan, R.; Uysal, S.; Mocan, A.; Yilmaz, M. A.; Picot-Allain, C. M.N.; Ćirić, A.; Glamočlija, J., Food Biosci., 23, 75-82 (2018); Knudsen, F.; Mumford, D., The projectivity of the moduli space of stable curves I: preliminaries on ‘det’ and ‘Div’. The projectivity of the moduli space of stable curves I: preliminaries on ‘det’ and ‘Div’, Math. Scand., 39, 19-55 (1976); LeVeque, R. J., Finite difference methods for ordinary and partial differential equations: steady-state and time-dependent problems (2007), SIAM; Fraenkel, A. S.; Lorberbom, M., Nimhoff games. Nimhoff games, J. Combin. Theory Ser. A, 58, 1-25 (1991); Hall, Marshall, A basis for free Lie rings and higher commutators in free groups. A basis for free Lie rings and higher commutators in free groups, Proc. Am. Math. Soc., 1, 575-581 (1950), MR0038336; Carrabs, F.; Cerrone, C.; Cerulli, R.; Silvestri, S., On the complexity of rainbow spanning forest problem. On the complexity of rainbow spanning forest problem, Optim. Lett., 12, 3, 443-454 (2018); Straughan, B., The energy method, stability, and nonlinear convection. The energy method, stability, and nonlinear convection, Series in Applied Mathematical Sciences, vol. 91 (2004), Springer; Mohammadi, A. S.; Trovão, J. P.; Dubois, M. R., Hybridisation ratio for hybrid excitation synchronous motors in electric vehicles with enhanced performance. Hybridisation ratio for hybrid excitation synchronous motors in electric vehicles with enhanced performance, IET Electr. Syst. Transp., 8, 1, 12-19 (2018); Gohberg; Sementsul, A., On the inversion of finite-section Toeplitz matrices and their continuous analogues. On the inversion of finite-section Toeplitz matrices and their continuous analogues, Mat. Issled., 7, 201-224 (1972), (in Russian); Regan, Á.; Raats, M.; Shan, L. C.; Wall, P. G.; McConnon, Á., Risk communication and social media during food safety crises: A study of stakeholders’ opinions in Ireland. Risk communication and social media during food safety crises: A study of stakeholders’ opinions in Ireland, Journal of Risk Research, 19, 1, 119-133 (2016); Ackerberg, D. A.; Caves, K.; Frazer, G., Identification properties of recent production function estimators. Identification properties of recent production function estimators, Econometrica, 83, 2411-2451 (2015); Melenk, J.; Babuska, I., The partition of unity finite element method: basic theory and applications. The partition of unity finite element method: basic theory and applications, Comput. Methods Appl. Mech. Engrg., 139, 289-314 (1996); Wei, C.-M.; Wang, J.-B.; Ji, P., Single-machine scheduling with time-and-resource-dependent processing times. Single-machine scheduling with time-and-resource-dependent processing times, Appl. Math. Modell., 62, 792-798 (2012); Delduc, F.; Magro, M.; Vicedo, B., On classical q-deformations of integrable sigma-models. On classical q-deformations of integrable sigma-models, J. High Energy Phys., 1311, Article 192 pp. (2013); Löhner, R.; Baum, J. D., Adaptive h-refinement on 3d unstructured grids for transient problems. Adaptive h-refinement on 3d unstructured grids for transient problems, Int J Numer Methods Fluids, 14, 1407-1419 (1992); Kuetche, V. K.; Youssoufa, S.; Kofane, T. C., Phys. Rev. E, 90, Article 063203 pp. (2014), 13pp; De Domenico, M.; Biamonte, J., Spectral entropies as information-theoretic tools for complex network comparison. Spectral entropies as information-theoretic tools for complex network comparison, Phys. Rev. X, 6, 4, 41062 (2016); Motter, A. E.; Lai, Y., Cascade-based attacks on complex networks. Cascade-based attacks on complex networks, Phys. Rev. E, 66, 065102(R) (2002); Wilton, Henry; Zalesskii, Pavel, Profinite properties of graph manifolds. Profinite properties of graph manifolds, Geom. Dedic., 147, 1, 29-45 (2010); Hain, Richard M., Iterated integrals, intersection theory and link groups. Iterated integrals, intersection theory and link groups, Topology, 24, 1, 45-66 (1985), MR790675; Devhare, P. B.; Ray, R. B., Extracellular vesicles: novel mediator for cell to cell communications in liver pathogenesis. Extracellular vesicles: novel mediator for cell to cell communications in liver pathogenesis, Mole. Aspects Med. (2017), doi:https://doi.org/10.1016/j.mam.2017.11.001; Motter, A. E., Cascade control and defense in complex networks. Cascade control and defense in complex networks, Phys. Rev. Lett., 93, 098701 (2004); Elad, M.; Feuer, A., Restoration of a single superresolution image from several blurred, noisy, and undersampled measured images. Restoration of a single superresolution image from several blurred, noisy, and undersampled measured images, IEEE Trans. Image Process., 6, 12, 1646-1658 (1997); Chattopadhayay, J.; Sarkar, R.; Mandal, S., Toxin-producing plankton may act as a biological control for planktonic blooms—field study and mathematical modelling. Toxin-producing plankton may act as a biological control for planktonic blooms—field study and mathematical modelling, J Theor Biol, 215, 3, 333-344 (2002); Read, C. J., The invariant subspace problem for a class of Banach spaces. II. Hypercyclic operators. The invariant subspace problem for a class of Banach spaces. II. Hypercyclic operators, Israel J. Math., 63, 1-40 (1988); Condon, A.; Kirkpatrick, B.; Maňuch, J., Reachability bounds for chemical reaction networks and strand displacement systems. Reachability bounds for chemical reaction networks and strand displacement systems, Nat. Comput., 4, 499-516 (2014); Zengin, G.; Stefanucci, A.; Rodrigues, M. J.; Mollica, A.; Custodio, L.; Aumeeruddy, M. Z.; Mahomoodally, M. F., J. Pharm. Biomed. Anal., 162, 225-233 (2019)
[4] Hatfield, B. F., Gauge invariant regularization of Yang-Mills wave functions, Phys. Lett., 154B, 296-302 (1985)
[5] Jackiw, R., Analysis on infinite dimensional manifolds: Schrödinger representation for quantized fields, (Éboli, O.; Gomes, M.; Santoro, A., Field Theory and Particle Physics, (1990), World Scientific: World Scientific Singapore), 78-143
[6] Lüscher, M.; Narayanan, R.; Weisz, P.; Wolff, U., The Schrödinger functional—a renormalizable probe for nonabelian theories, Nucl. Phys. B, 384, 168-228 (1992)
[7] Kim, S. K.; Namgung, W.; Soh, K. S.; Yee, J. H., Equivalence between the Weyl, Coulomb, and unitary gauges in the functional Schrödinger picture. Equivalence between the Weyl, Coulomb, and unitary gauges in the functional Schrödinger picture, Phys. Rev. D, 41, 3792-3795 (1990); Boltje, R., Monomial resolutions. Monomial resolutions, J. Algebra, 246, 811-848 (2001); Kim, S. K.; Namgung, W.; Soh, K. S.; Yee, J. H., Equivalence between the covariant, Weyl, and Coulomb gauges in the functional Schrödinger picture. Equivalence between the covariant, Weyl, and Coulomb gauges in the functional Schrödinger picture, Phys. Rev. D, 43, 2046-2049 (1991)
[8] Hatfield, B., Quantum Field Theory of Point Particles and Strings (1992), Addison-Wesley: Addison-Wesley Reading, MA · Zbl 0984.81501
[9] Mansfield, P.; Sampaio, M., Yang-Mills beta function from the large distance expansion of the Schrödinger functional, Nucl. Phys. B, 545, 623-655 (1999), hep-th/9807163 · Zbl 0944.81021
[10] Islam, J. N., Schrödinger functional equation for Yang-Mills theory, Prog. Theor. Phys., 89, 161-185 (1993)
[11] Pachos, J., The Coulomb branch of Yang-Mills theory from the Schrödinger representation, Phys. Lett. B, 432, 187-190 (1998), hep-th/9801163
[12] Olejník, Š., The Yang-Mills vacuum wave functional thirty-five years later, J. Phys.: Conf. Ser., 631, 012057 (2015), arXiv:1503.01296 [hep-lat]
[13] Wang, J.-B.; Wang, M.-Z., Minimizing makespan in three-machine flow shops with deteriorating jobs. Minimizing makespan in three-machine flow shops with deteriorating jobs, Comput. Oper. Res., 40, 547-557 (2013); Przytycki, Piotr; Wise, Daniel T., Separability of embedded surfaces in 3-manifolds. Separability of embedded surfaces in 3-manifolds, Compos. Math., 150, 9, 1623-1630 (2014); Urtasun, R.; Darrell, T., Discriminative gaussian process latent variable model for classification. Discriminative gaussian process latent variable model for classification, Proceedings of the 24th International Conference on Machine Learning, 927-934 (2007); Gervais, J.-L., Commun. Math. Phys., 130, 257 (1990); Fox, Ralph H., Free differential calculus. I. Derivation in the free group ring. Free differential calculus. I. Derivation in the free group ring, Ann. of Math. (2), 57, 547-560 (1953); Abdulle, A.; Nonnenmacher, A., A short and versatile finite element multiscale code for homogenization problems. A short and versatile finite element multiscale code for homogenization problems, Comput. Methods Appl. Mech. Engrg., 198, 2839-2859 (2009); Krug, S., The Yang-Mills Vacuum Wave Functional in 2 + 1 Dimensions. The Yang-Mills Vacuum Wave Functional in 2 + 1 Dimensions, PhD Thesis (2014), UAB: UAB Barcelona, arXiv:1404.7005 [hep-th]. See also; Noble, B.; Daniel, J. W., Applied Linear Algebra (1977), Prentice-Hall: Prentice-Hall Englewood Cliffs, N.J; Krug, S.; Pineda, A., The regularization and determination of the Yang-Mills vacuum wave functional in three dimensions at O(e2). The regularization and determination of the Yang-Mills vacuum wave functional in three dimensions at O(e2), Nucl. Phys., 878, 82-116 (2014), arXiv:1308.2663 [hep-th] · Zbl 1284.81211
[14] Kanatchikov, I. V., Precanonical quantization of Yang-Mills fields and the functional Schrödinger representation, Rep. Math. Phys., 53, 181-193 (2004), hep-th/0301001 · Zbl 1061.81050
[15] Kanatchikov, I. V., Ehrenfest theorem in precanonical quantization, J. Geom. Symmetry Phys., 37, 43 (2015), arXiv:1501.00480 · Zbl 1316.81085
[16] Kanatchikov, I. V., Toward the Born-Weyl quantization of fields, Int. J. Theor. Phys., 37, 333-342 (1998), quant-ph/9712058 · Zbl 0947.53044
[17] Kanatchikov, I. V., De Donder-Weyl theory and a hypercomplex extension of quantum mechanics to field theory, Rep. Math. Phys., 43, 157-170 (1999), hep-th/9810165 · Zbl 0980.53103
[18] Kanatchikov, I. V., On quantization of field theories in polymomentum variables, (Rembielinski, J., Particles, Fields and Gravitation, (Proc. Int. Conf. Łódź, Poland, Apr. 1998), 453 (1998), Amer. Inst. Phys.: Amer. Inst. Phys. Woodbury (NY)), 356-367, hep-th/9811016 AIP Conf. Proc. · Zbl 0982.81028
[20] Kanatchikov, I. V., Precanonical quantization and the Schrödinger wave functional revisited, Adv. Theor. Math. Phys., 18, 1249-1265 (2014), arXiv:1112.5801 [hep-th] · Zbl 1307.81062
[21] Kanatchikov, I. V., On the precanonical structure of the Schrödinger wave functional, Adv. Theor. Math. Phys., 20, 1377-1396 (2016), arXiv:1312.4518 [hep-th] · Zbl 1366.81210
[22] Kanatchikov, I. V., Precanonical quantization and the Schrödinger wave functional, Phys. Lett. A, 283, 25-36 (2001), hep-th/0012084 · Zbl 0984.81160
[24] De Donder, Th., Théorie Invariantive du Calcul des Variations, (1935), Gauthier-Villars: Gauthier-Villars Paris; Weyl, H., Geodesic fields in the calculus of variations. Geodesic fields in the calculus of variations, Ann. Math. (2), 36, 607-629 (1935); Barucca, P.; Lillo, F., Disentangling bipartite and core-periphery structure in financial networks. Disentangling bipartite and core-periphery structure in financial networks, Chaos Solitons Fractals, 88, 244-253 (2016); Adams, K.; Agesen, O., A comparison of software and hardware techniques for x86 virtualization. A comparison of software and hardware techniques for x86 virtualization, SIGOPS Oper. Syst. Rev., 40, 5, 2-13 (2006); Velinova, M.; Sengupta, D.; Tadjer, A. V.; Marrink, S. J., Langmuir, 27, 14071-14077 (2011); Robertson, N.; Seymour, P. D., Graph minors II: algorithmic aspects of tree-width. Graph minors II: algorithmic aspects of tree-width, J. Algorithms, 7, 309-322 (1986); Wang, X.; Tang, X., Hallucinating face by eigentransformation with distortion reduction. (Zhang, D.; Jain, A. K., Biometric Authentication. Biometric Authentication, Lecture Notes in Computer Science, 3072 (2004), Springer Berlin Heidelberg), 88-94; Asheim, G., Can NNP be used for welfare comparisons?. Can NNP be used for welfare comparisons?, Environ. Dev. Econ., 12, 11-31 (2007); Rund, H., The Hamilton-Jacobi Theory in the Calculus of Variations (1966), D. van Nostrand: D. van Nostrand Toronto; Kastrup, H., Canonical theories of Lagrangian dynamical systems in physics. Canonical theories of Lagrangian dynamical systems in physics, Phys. Rep., 101, 1-167 (1983)
[25] Kanatchikov, I. V., Canonical structure of classical field theory in the polymomentum phase space. Canonical structure of classical field theory in the polymomentum phase space, Rep. Math. Phys., 41, 49-90 (1998), hep-th/9709229; Dang, L.; Bernard, N.; Bracikowski, N.; Berthiau, G., Design optimization with flux-weakening of High-Speed PMSM for electrical vehicle considering the driving cycle. Design optimization with flux-weakening of High-Speed PMSM for electrical vehicle considering the driving cycle, IEEE Trans. Ind. Electron., 99 (2017); Hudgins, L. B.; Primont, D., Derivative properties of directional technology distance functions. (Färe, R.; Grosskopf, S.; Primont, D., Aggregation, Efficiency, and Measurement (2007), Springer); Fu, H. Z.; Wang, M. H.; Ho, Y. S., The most frequently cited adsorption research articles in the Science Citation Index (Expanded). The most frequently cited adsorption research articles in the Science Citation Index (Expanded), J. Colloid Interface Sci., 379, 1, 148-156 (2012); Kanatchikov, I. V., On field theoretic generalizations of a Poisson algebra. On field theoretic generalizations of a Poisson algebra, Rep. Math. Phys., 40, 225-234 (1997), hep-th/9710069
[26] Hélein, F.; Kouneiher, J., The notion of observable in the covariant Hamiltonian formalism for the calculus of variations with several variables. The notion of observable in the covariant Hamiltonian formalism for the calculus of variations with several variables, Adv. Theor. Math. Phys., 8, 735-777 (2004), math-ph/0401047; Ernst, M.; Jochemsz, E.; May, A.; de Weger, B., Partial key exposure attacks on RSA up to full size exponents. (Cramer, R., Advances in Cryptology - EUROCRYPT 2005, 24th Annual International Conference on the Theory and Applications of Cryptographic Techniques. Advances in Cryptology - EUROCRYPT 2005, 24th Annual International Conference on the Theory and Applications of Cryptographic Techniques, Lecture Notes in Computer Science, vol. 3494 (2005), Springer), 371-386; Herr, N.; Nicod, J.-M.; Varnier, C.; Jardin, L.; Sorrentino, A.; Hissel, D.; Péra, M.-C., Decision process to manage useful life of multi-stacks fuel cell systems under service constraint. Decision process to manage useful life of multi-stacks fuel cell systems under service constraint, Renew. Energy, 105, 590-600 (2017), URL http://www.sciencedirect.com/science/article/pii/S0960148117300010; Gear, C. W., Numerical Initial Value Problems in Ordinary Differential Equations (1971), Prentice Hall; Bell, F. K.; Rowlinson, P., On the multiplicities of graph eigenvalues. On the multiplicities of graph eigenvalues, Bull. Lond. Math. Soc., 35, 3, 401-408 (2003); Bennett, P.; Calman, K.; Curtis, S.; Fischbacher-Smith, D., Understanding public responses to risk: Policy and practice. (Bennett, P.; Calman, K.; Curtis, S.; Fischbacher-Smith, D., Risk communication and public health (2010), Oxford University Press: Oxford University Press Oxford), 3-22; Kaschenko, S. A., Asymptotics of relaxational oscillations for systems of difference-differential equations with compactly supported nonlinearity. II. Asymptotics of relaxational oscillations for systems of difference-differential equations with compactly supported nonlinearity. II, Differ. Equ., 31, 12, 1938-1946 (1995); Chant, D., On asymptotic tests of composite hypotheses in nonstandard conditions. On asymptotic tests of composite hypotheses in nonstandard conditions, Biometrika, 61, 2, 291-298 (1974); Lipton, A., Mathematical Methods for Foreign Exchange: A Financial Engineer’s Approach (2001), World Scientific: World Scientific Singapore; Smirnov, Eugene; Rüter, ChristianE; Stepić, Milutin; Kip, Detlef; Shandarov, Vladimir, Formation and light guiding properties of dark solitons in one-dimensional waveguide arrays. Formation and light guiding properties of dark solitons in one-dimensional waveguide arrays, Phys Rev, E 74, Article 065601 pp. (2006); Dragon, P. B.; Hernandez, O. I.; Sawada, J.; Williams, A.; Wong, D., Constructing de Bruijn sequences with co-lexicographic order: The k-ary Grandmama sequence. Constructing de Bruijn sequences with co-lexicographic order: The k-ary Grandmama sequence, European J. Combin., 72, 1-11 (2018); Dorogovtsev, S. N.; Mendes, J. F.F., Evolution of networks. Evolution of networks, Adv. Phys., 51, 1079 (2002); Li, Y.; Hon, Y. L., Finite integration method with radial basis function for solving stiff problems. Finite integration method with radial basis function for solving stiff problems, Eng Anal Bound Elem, 82, 32-42 (2017); Mirsky, L., Symmetric gauge functions and unitarily invariant norms. Symmetric gauge functions and unitarily invariant norms, Quart. J. Math. Oxford Ser., 11, 2, 50-59 (1960); Stricker, J.; Cookson, S.; Bennett, M. R.; Mather, W. H.; Tsimring, L. S.; Hasty, J., A fast, robust and tunable synthetic gene oscillator. A fast, robust and tunable synthetic gene oscillator, Nature, 456, 516-519 (2008); La Scala, R., Computing minimal free resolutions of right modules over noncommutative algebras. Computing minimal free resolutions of right modules over noncommutative algebras, J. Algebra, 478, 458-483 (2017); Georgiou, G.; Panopoulos, P.; Sagkrioti, E.; Sfetsos, K.; Siampos, K., The exact C-function in integrable λ-deformed theories. The exact C-function in integrable λ-deformed theories, Phys. Lett. B, 782, 613-618 (2018); Chen, W.; Ding, H.; Feng, P.; Lin, H.; Chou, K. C., iACP: a sequence-based tool for I dentifying anticancer peptides. iACP: a sequence-based tool for I dentifying anticancer peptides, Oncotarget, 7, 16895 (2016); Kumar, S.; Jan, J. M., Mapping research collaboration in the business and management field in Malaysia, 1980-2010. Mapping research collaboration in the business and management field in Malaysia, 1980-2010, Scientometrics, 97, 3, 491-517 (2013); Zhang, X.; Martin, T.; Newman, M., Identification of core-periphery structure in networks. Identification of core-periphery structure in networks, Phys. Rev. E, 91, 0321803 (2014); Petersen, J. L.; Rasmussen, J.; Yu, M., Nucl. Phys. B, 481, 577 (1996); Duval, J. P., Factorizing words over an ordered alphabet. Factorizing words over an ordered alphabet, J. Algorithms, 4, 363-381 (1983); Blömer, J.; May, A., New partial key exposure attacks on RSA. (Boneh, D., Advances in Cryptology - CRYPTO 2003, 23rd Annual International Cryptology Conference. Advances in Cryptology - CRYPTO 2003, 23rd Annual International Cryptology Conference, Lecture Notes in Computer Science, vol. 2729 (2003), Springer), 27-43; Silva, W. T.M.; Bezerra, L. M., Performance of composite implicit time integration scheme for nonlinear dynamic analysis. Performance of composite implicit time integration scheme for nonlinear dynamic analysis, Math. Probl. Eng., 2008, 4, 267-290 (2008); Sukhatme, J.; Smith, L. M., Local and nonlocal dispersive turbulence. Local and nonlocal dispersive turbulence, Phys. Fluids, 21, 5, 056603 (2009); Mudholkar, G. S., A class of tests with monotone power functions for two problems in multivariate statistical analysis. A class of tests with monotone power functions for two problems in multivariate statistical analysis, Ann. Math. Statist., 36, 1794-1801 (1965); Hernández-Pérez, H.; Salazar-González, J. J., Heuristics for the one-commodity pickup-and-delivery traveling salesman problem. Heuristics for the one-commodity pickup-and-delivery traveling salesman problem, Transp. Sci., 38, 2, 245-255 (2004); Wang, Z.; Larson, R. G., J. Phys. Chem. B, 113, 13697-13710 (2009); Lang, U., Injective hulls of certain discrete metric spaces and groups. Injective hulls of certain discrete metric spaces and groups, J. Topol. Anal., 5, 297-331 (2013); Gao, L.; Wang, D.; Wang, G., Further results on exponential stability for impulsive switched nonlinear time delay systems with delayed impulse effects. Further results on exponential stability for impulsive switched nonlinear time delay systems with delayed impulse effects, Appl. Math. Comput., 268, 186-200 (2018); Chen, Y.; Wang, X.; Li, H.; Xi, H.; Zhu, W.; Yan, Y., IEEE Trans. Very Large Scale Integr. (VLSI) Syst., 18, 1724 (2010); Pang, B.; Lee, L.; Vaithyanathan, S., Thumbs up?: sentiment classification using machine learning techniques. Thumbs up?: sentiment classification using machine learning techniques, Proceedings of the ACL-02 conference on Empirical methods in natural language processing-Volume 10, 79-86 (2002), Association for Computational Linguistics; La Scala, R., Monomial right ideal and the Hilbert series of noncommutative modules. Monomial right ideal and the Hilbert series of noncommutative modules, J. Symbolic Comput., 80, 403-415 (2017); Qiu, Z.; Wu, B.; Wang, B.; Shi, C.; Yu, L., Collapsed gibbs sampling for latent dirichlet allocation on spark. Collapsed gibbs sampling for latent dirichlet allocation on spark, J. Mach. Learn. Res., 36, 17-28 (2014); Arrow, K. J.; Dasgupta, P.; Mäler, K. G., Evaluating projects and assessing sustainable development in imperfect economies. Evaluating projects and assessing sustainable development in imperfect economies, Environ. Resour. Econ., 26, 4, 647-685 (2003); de Montgolfier, F.; Soto, M.; Viennot, L., Treewidth and hyperbolicity of the internet. (IEEE Networks Computing and Applications 2011 (2011), IEEE); Stallings, John, Homology and central series of groups. Homology and central series of groups, J. Algebra, 2, 170-181 (1965), MR0175956; Diao, Z.; Pakala, M.; Panchula, A.; Ding, Y.; Apalkov, D.; Wang, L. C.; Chen, E.; Huai, Y., J. Appl. Phys., 99, Article 08G510 pp. (2006); Bächle, A.; Margolis, L., Rational conjugacy of torsion units in integral group rings of non-solvable groups. Rational conjugacy of torsion units in integral group rings of non-solvable groups, Proc. Edinb. Math. Soc. (2), 60, 4, 813-830 (2017); Huang, J.-B.; Singh, A.; Ahuja, N., Single image super-resolution from transformed self-exemplars. Single image super-resolution from transformed self-exemplars, Proceedings of the IEEE Conference on Computer Vision and Pattern Recognition (CVPR), 5197-5206 (2015); Albert, R.; Barabási, A.-L., Statistical mechanics of complex networks. Statistical mechanics of complex networks, Rev. Modern Phys., 74, 47-97 (2002); Hernandez-Torres, D.; Sename, O.; Riu, D.; Druart, F., On the robust control of DC-DC converters: Application to a hybrid power generation system. On the robust control of DC-DC converters: Application to a hybrid power generation system, IFAC Proc. Vol., 43, 21, 123-130 (2010); Makar-Limanov, L., On the hypersurface x+x2y+z2+t3 in C4, or a C3-like threefold which is not C3. On the hypersurface x+x2y+z2+t3 in C4, or a C3-like threefold which is not C3, Isr. J. Math., 96, 419-429 (1996); Chen, W.; Feng, P. M.; Lin, H.; Chou, K. C., iSS-PseDNC: identifying splicing sites using pseudo dinucleotide composition. iSS-PseDNC: identifying splicing sites using pseudo dinucleotide composition, BioMed Res. Int., 2014 (2014); Samsonovich, A.; McNaughton, B. L., Path integration and cognitive mapping in a continuous attractor neural network model. Path integration and cognitive mapping in a continuous attractor neural network model, J. Neurosci., 17, 15, 5900-5920 (1997); Hélein, F.; Kouneiher, J., Covariant Hamiltonian formalism for the calculus of variations with several variables. Covariant Hamiltonian formalism for the calculus of variations with several variables, Adv. Theor. Math. Phys., 8, 565-601 (2004), math-ph/0211046 · Zbl 1113.70023
[27] Kanatchikov, I. V., On the Duffin-Kemmer-Petiau formulation of the covariant Hamiltonian dynamics in field theory, Rev. Math. Phys., 46, 107-112 (2000), hep-th/9911175 · Zbl 0984.81067
[28] Forger, M.; Paufler, C.; Römer, H., The Poisson bracket for Poisson forms in multisymplectic field theory, Rev. Math. Phys., 15, 705 (2003), math-ph/0202043 · Zbl 1113.70017
[29] Kanatchikov, I., On a generalization of the Dirac bracket in the De Donder-Weyl Hamiltonian formalism, (Kowalski, O.; Krupka, D.; Krupková, O.; Slovák, J., Differential Geometry and its Applications (2008), World Scientific: World Scientific Singapore), 615-625, arXiv:0807.3127 · Zbl 1350.70046
[30] Kanatchikov, I. V., Precanonical quantum gravity: quantization without the space-time decomposition, Int. J. Theor. Phys., 40, 1121-1149 (2001), gr-qc/0012074. See also: I. V. Kanatchikov: gr-qc/9810076; gr-qc/9912094; gr-qc/0004066 · Zbl 0984.83026
[31] Laffont, Jean-Jacques; Rey, Patrick; Tirole, Jean, Network competition: II. Price discrimination. Network competition: II. Price discrimination, Rand J. Econ., 29, 1, 38-56 (1998); Zhang, L.; Liu, T.; Li, Q., A robust and efficient composite time integration algorithm for nonlinear structural dynamic analysis. A robust and efficient composite time integration algorithm for nonlinear structural dynamic analysis, Math. Probl. Eng., 2015 (2015); Corsi, F.; Marmi, S.; Lillo, F., When micro prudence increases macro risk: The destabilizing effects of financial innovation, leverage, and diversification. When micro prudence increases macro risk: The destabilizing effects of financial innovation, leverage, and diversification, Oper. Res., 64, 5, 1073-1088 (2016); Brooks, A. M.; Zolotov, A., Why baryons matter: The kinematics of dwarf spheroidal satellites. Why baryons matter: The kinematics of dwarf spheroidal satellites, Astrophys. J., 786, 87 (2014); Novák, B.; Tyson, J. J., Design principles of biochemical oscillators. Design principles of biochemical oscillators, Nat. Rev. Mol. Cell Biol., 9, 981-991 (2008); Macdonald, I. G., The Poincaré polynomial of a symmetric product. The Poincaré polynomial of a symmetric product, Proc. Camb. Philos. Soc., 58, 563-568 (1962); Uchic, M. D.; Dimiduk, D. M.; Florando, J. N.; Nix, W. D., Sample dimensions influence strength and crystal plasticity. Sample dimensions influence strength and crystal plasticity, Science, 305, 986-989 (2004); Georgiou, G.; Sfetsos, K.; Siampos, K., All-loop anomalous dimensions in integrable λ-deformed σ-models. All-loop anomalous dimensions in integrable λ-deformed σ-models, Nucl. Phys. B, 901, 40 (2015); Kanatchikov, I. V., On the “spin-connection foam” picture of quantum gravity from precanonical quantization. (Bianchi, M.; Jantzen, R. T.; Ruffini, R., The Fourteenth Marcel Grossmann Meeting on Recent Developments in Theoretical and Experimental General Relativity, Astrophysics, and Relativistic Field Theories, Part D (2018), World Scientific: World Scientific Singapore), 3907-3915, arXiv:1512.09137 [gr-qc]; Watson, G. S., Smooth regression analysis. Smooth regression analysis, Sankhya Series A, 26, 359-372 (1964); Boonklurb, R.; Duangpan, A.; Treeyaprasert, T., Modified finite integration method using Chebyshev polynomial for solving linear differential equations. Modified finite integration method using Chebyshev polynomial for solving linear differential equations, JNAIAM J Numer Anal Ind Appl Math, 12, 3-4, 1-19 (2018); Sferra, G.; Fratini, F.; Ponzi, M.; Pizzi, E., Phylo_dcor: distance correlation as a novel metric for phylogenetic profiling. Phylo_dcor: distance correlation as a novel metric for phylogenetic profiling, BMC Bioinform., 18, 1, 396 (2017); Chou, K. C., Low-frequency collective motion in biomacromolecules and its biological functions. Low-frequency collective motion in biomacromolecules and its biological functions, Biophys. Chem., 30, 3-48 (1988); Uchic, M. D.; Dimiduk, D. M.; Florando, J. N.; Nix, W. D., Exploring specimen size effects in plastic deformation of Ni 3 (Al, Ta). Exploring specimen size effects in plastic deformation of Ni 3 (Al, Ta), Proceedings of the MRS, 753 (2002), Cambridge University Press; Hilfer, R., Fractional diffusion based on Riemann-Liouville fractional derivative. Fractional diffusion based on Riemann-Liouville fractional derivative, J. Phys. Chem, 104, 3914-3917 (2000); Rubin, D. B., The calculation of posterior distributions by data augmentation. The calculation of posterior distributions by data augmentation, J. Amer. Statist. Assoc., 82, 543-546 (1987); Majewska, M.; Skrzycki, M.; Podsiad, M.; Czeczot, H., Acta Pol. Pharm., 68, 611-615 (2011); Harish, B. S.; Guru, D. S.; Manjunath, S., Representation and classification of text documents: a brief review. Representation and classification of text documents: a brief review, IJCA, Special Issue on RTIPPR, 2, 110-119 (2010); Holsapple, R.; Iyer, R.; Doman, D., Variable step-size selection methods for implicit integration schemes for ODES. Variable step-size selection methods for implicit integration schemes for ODES, Int. J. Numer. Anal. Model., 4, 2, 210-240 (2007); Kleiner, B.; Lott, J., Notes on Perelman’s papers. Notes on Perelman’s papers, Geom. Topol., 12, 2587-2855 (2008); Cully, B.; Lefebvre, G.; Meyer, D.; Feeley, M.; Hutchinson, N.; Warfield, A., Remus: High availability via asynchronous virtual machine replication. (Proceedings of the 5th USENIX Symposium on Networked Systems Design and Implementation. Proceedings of the 5th USENIX Symposium on Networked Systems Design and Implementation, NSDI’08 (2008)), 161-174; Nadaraya, E. A., On estimating regression. On estimating regression, Theory of Probability and its Applications, 9, 141-142 (1964); Feyzmahdavian, H. R.; Charalambous, T.; Johansson, M., Exponential stability of homogeneous positive systems of degree one with time-varying delays. Exponential stability of homogeneous positive systems of degree one with time-varying delays, IEEE Trans. Autom. Control, 59, 1594-1599 (2014); Burton, J. D.; Jaswal, S. S.; Tsymbal, E. Y.; Mryasov, O. N.; Heinonen, O. G., Appl. Phys. Lett., 89, Article 142507 pp. (2006); Lin, J. R.; Hwang, C. C., Lubrication of short porous journal bearings-use of the Brinkman-extended Darcy model. Lubrication of short porous journal bearings-use of the Brinkman-extended Darcy model, Wear, 161, 93-104 (1993); Chen, Y.; Hu, B.; Keogh, E. J.; Batista, G., DTW-D: time series semi-supervised learning from a single example. DTW-D: time series semi-supervised learning from a single example, Proceedings of the 19th ACM SIGKDD International Conference on Knowledge Discovery and Data Mining, 383-391 (2013); Zolotov, A.; Brooks, A. M.; Willman, B.; Governato, F.; Pontzen, A.; Christensen, C.; Dekel, A.; Quinn, T.; Shen, S.; Wadsley, J., Baryons matter: Why luminous satellite galaxies have reduced central masses. Baryons matter: Why luminous satellite galaxies have reduced central masses, Astrophys. J., 761, 71 (2012); Sarkar, S., Small secret exponent attack on RSA variant with modulus N=prq. Small secret exponent attack on RSA variant with modulus N=prq, Des. Codes Cryptogr., 73, 2, 383-392 (2014); Kanatchikov, I. V., Ehrenfest theorem in precanonical quantization of fields and gravity. (Bianchi, M.; Jantzen, R. T.; Ruffini, R., The Fourteenth Marcel Grossmann Meeting on Recent Developments in Theoretical and Experimental General Relativity, Astrophysics, and Relativistic Field Theories, Part C (2018), World Scientific: World Scientific Singapore), 2828-2835, arXiv:1602.01083 [gr-qc]; Kanatchikov, I. V., On precanonical quantization of gravity in spin connection variables. On precanonical quantization of gravity in spin connection variables, AIP Conf. Proc., 1514, 73-76 (2012), arXiv:1212.6963 [gr-qc]; Dokuchaev, M. A.; Juriaans, S. O., Finite subgroups in integral group rings. Finite subgroups in integral group rings, Canad. J. Math., 48, 6, 1170-1179 (1996); Bernanke, B. S.; Gertler, M.; Gilchrist, S., The financial accelerator in a quantitative business cycle framework. (Taylor, J. B.; Woodford, M., Handbook of Macroeconomics, vol 1 (1999), Elsevier Science B.V.), 1341-1393, Chapter 21; Myerson, R., Optimal auction design. Optimal auction design, Math. Oper. Res., 6, 58-73 (1981); Dmitriev, A.; Kislov, V. Y., Stochastic Oscillations in Radiophysics and Electronics (1989), Nauka: Nauka Moscow; Caflisch, R. E.; Sammartino, M., Existence and singularities for the Prandtl boundary layer equations. Existence and singularities for the Prandtl boundary layer equations, Z. Angew. Math. Mech., 80, 11-12, 733-744 (2000); Wilson, A.; Nickisch, H., Kernel interpolation for scalable structured gaussian processes (kiss-gp). Kernel interpolation for scalable structured gaussian processes (kiss-gp), Proceedings of the 32nd International Conference on Machine Learning, 1775-1784 (2015); Pope, R. D.; Just, R. E., Empirical implementation of ex ante cost functions. Empirical implementation of ex ante cost functions, J. Econometrics, 72, 231-249 (1996); Papazyan, R.; Zhang, Y.; Lazar, M. A., Genetic and epigenomic mechanisms of mammalian circadian transcription. Genetic and epigenomic mechanisms of mammalian circadian transcription, Nat. Struct. Mol. Biol., 23, 1045-1052 (2016); Beale, N.; Rand, D. G.; Battey, H.; Croxson, K.; May, R. M.; Nowak, M. A., Individual versus systemic risk and the Regulator’s Dilemma. Individual versus systemic risk and the Regulator’s Dilemma, Proc. Natl. Acad. Sci., 108, 31, 12647-12652 (2011); Kubo, Y., Experimental and numerical study of topographic effects on deposition from two-dimensional, particle-driven density currents. Experimental and numerical study of topographic effects on deposition from two-dimensional, particle-driven density currents, Sediment Geol, 164, 311-326 (2004); Kubert, D. S.; Lang, S., Modular Units. Modular Units, Grundlehren Math. Wiss., vol. 244 (1981), Springer: Springer New York; Chou, K. C.; Chen, N. Y.; Forsen, S., The biological functions of low-frequency phonons. 2. Cooperative effects. The biological functions of low-frequency phonons. 2. Cooperative effects, Chemic. Scr., 18, 126-132 (1981); Chandra, Y.; Zhou, Y.; Stanciulescu, I.; Eason, T.; Spottswood, S., A robust composite time integration scheme for snap-through problems. A robust composite time integration scheme for snap-through problems, Comput. Mech., 55, 5, 1041-1056 (2015); Székely, G. J.; Rizzo, M. L., Brownian distance covariance. Brownian distance covariance, Ann. Appl. Stat., 1236-1265 (2009); Cheng, X.; Xiao, X.; Chou, K. C., pLoc-mEuk: predict subcellular localization of multi- label eukaryotic proteins by extracting the key GO information into general PseAAC. pLoc-mEuk: predict subcellular localization of multi- label eukaryotic proteins by extracting the key GO information into general PseAAC, Genomics, 110, 50-58 (2018); Mosheiov, G., The travelling salesman problem with pick-up and delivery. The travelling salesman problem with pick-up and delivery, Eur. J. Oper. Res., 79, 2, 299-310 (1994); Purcell, O.; Savery, N. J.; Grierson, C. S.; di Bernardo, M., A comparative analysis of synthetic genetic oscillators. A comparative analysis of synthetic genetic oscillators, J. R. Soc. Interface, 7, 1503-1524 (2010); Zaslavsky, T., Signed graph coloring. Signed graph coloring, Discrete Math., 39, 2, 215-228 (1982); Weigel, Thomas, Graded Lie algebras of type FP. Graded Lie algebras of type FP, Isr. J. Math., 205, 1, 185-209 (2015), MR3314587; Haslhofer, R.; Naber, A., Weak solutions for the Ricci flow I; Nicolau, F.; Respondek, W., Multi-input control-affine systems linearizable via one-fold prolongation and their flatness. Multi-input control-affine systems linearizable via one-fold prolongation and their flatness, Proceedings of the IEEE 52nd Annual Conference on Decision and Control (CDC), 3249-3254 (2013), IEEE; Khan, A.; Baharudin, B.; Lee, L. H.; Khan, K., A review of machine learning algorithms for text-documents classification. A review of machine learning algorithms for text-documents classification, J. Adv. Inf. Technol., 1, 1, 4-20 (2010); Haq, S.; Ishaq, M., Solution of coupled Whitham-Broer-Kaup equations using optimal homotopy asymptotic method. Solution of coupled Whitham-Broer-Kaup equations using optimal homotopy asymptotic method, Ocean Eng., 84, 81-88 (2014); Tsui, T. Y.; Oliver, W. C.; Pharr, G. M., Influences of stress on the measurement of mechanical properties using nanoindentation: Part I. experimental studies in an aluminum alloy. Influences of stress on the measurement of mechanical properties using nanoindentation: Part I. experimental studies in an aluminum alloy, J. Mater. Res., 11, 752-759 (1996); Li, K.; Liu, Z. L.; Zhang, Y. Y., Finite integration methods for isospectral flows. Finite integration methods for isospectral flows, Math Theory Appl (Changsha), 35, 1 (2015); Das, D.; Hati, C.; Kumar, G.; Mahajan, N.; Djayaprawira, D. D.; Tsunekawa, K.; Nagai, M.; Maehara, H.; Yamagata, S.; Watanabe, N.; Yuasa, S.; Suziki, Y.; Ando, K., Appl. Phys. Lett., 86, Article 092502 pp. (2005); Kanatchikov, I. V., De Donder-Weyl Hamiltonian formulation and precanonical quantization of vielbein gravity. De Donder-Weyl Hamiltonian formulation and precanonical quantization of vielbein gravity, J. Phys. Conf. Ser., 442, 012041 (2013), arXiv:1302.2610 [gr-qc]; Kanatchikov, I. V., On precanonical quantization of gravity. On precanonical quantization of gravity, Nonlin. Phenom. Complex Sys. (NPCS), 17, 372-376 (2014), arXiv:1407.3101 [gr-qc]; Zhao, W., Some open problems on locally finite or locally nilpotent derivations and E-derivations. Some open problems on locally finite or locally nilpotent derivations and E-derivations, Commun. Contemp. Math., 20, 4, Article 1750056 pp. (2018), See also; Székely, G. J.; Rizzo, M. L.; Bakirov, N. K.; etal., Measuring and testing dependence by correlation of distances. Measuring and testing dependence by correlation of distances, Ann. Statist., 35, 6, 2769-2794 (2007); Durfee, G.; Nguyen, P. Q., Cryptanalysis of the RSA schemes with short secret exponent from Asiacrypt ’99. (Okamoto, T., Advances in Cryptology - ASIACRYPT 2000, 6th International Conference on the Theory and Application of Cryptology and Information Security. Advances in Cryptology - ASIACRYPT 2000, 6th International Conference on the Theory and Application of Cryptology and Information Security, Lecture Notes in Computer Science, vol. 1976 (2000), Springer), 14-29; Bankó, Z.; Abonyi, J., Correlation based dynamic time warping of multivariate time series. Correlation based dynamic time warping of multivariate time series, Expert Syst. Appl., 39, 17, 12814-12823 (2012); del Río, Á.; Sehgal, S. K., Zassenhaus conjecture (ZC1) on torsion units of integral group rings for some metabelian groups. Zassenhaus conjecture (ZC1) on torsion units of integral group rings for some metabelian groups, Arch. Math. (Basel), 86, 5, 392-397 (2006)
[32] Castrillón López, M.; Marsden, J. E., Some remarks on Lagrangian and Poisson reduction for field theories, J. Geom. Phys., 48, 52-83 (2003) · Zbl 1037.70016
[33] Cianci, R.; Vignolo, S.; Bruno, D., Geometrical aspects in Yang-Mills gauge theories, J. Phys., A 37, 2519-2526 (2004) · Zbl 1116.58301
[35] Berra-Montiel, J.; del Río, E.; Molgado, A., Polysymplectic formulation for topologically massive Yang-Mills field theory, Int. J. Mod. Phys. A, 32, 1750101 (2017), arXiv:1702.03076 · Zbl 1371.81215
[36] Berra-Montiel, J.; Molgado, A.; Serrano-Blanco, D., De Donder-Weyl Hamiltonian formalism of MacDowell-Mansouri gravity, Class. Quant. Grav., 34, 235002 (2017) · Zbl 1381.83096
[37] Gaset, J.; Román-Roy, N., Multisymplectic unified formalism for Einstein-Hilbert gravity, J. Math. Phys., 59, 032502 (2018) · Zbl 1387.83006
[38] Vey, D., Multisymplectic formulation of vielbein gravity: I. De Donder-Weyl formulation, Hamiltonian (n - 1)-forms. Multisymplectic formulation of vielbein gravity: I. De Donder-Weyl formulation, Hamiltonian (n - 1)-forms, Class. Quant. Grav., 32, 095005 (2015), arXiv:1404.3546 [math-ph]; Hewitt, R. H., Measuring critical gap. Measuring critical gap, Transp. Sci., 17, 1, 87-109 (1983); Hélein, F.; Vey, D., Curved space-times by crystallization of liquid fiber bundles. Curved space-times by crystallization of liquid fiber bundles, Found. Phys., 47, 1-41 (2017), arXiv:1508.07765 [math-ph] · Zbl 1328.83036
[39] Kanatchikov, I. V., On the spectrum of DW Hamiltonian of quantum SU(2) gauge field, Int. J. Geom. Meth. Mod. Phys., 14, 1750123 (2017), arXiv:1706.01766 [hep-th] · Zbl 1373.81361
[40] Karp, R. L.; Mansouri, F.; Rno, J. S., Product integral representations of Wilson lines and Wilson loops, and Non-Abelian Stokes theorem. Product integral representations of Wilson lines and Wilson loops, and Non-Abelian Stokes theorem, Turk. J. Phys., 24, 365-384 (2000), hep-th/9903221; Georgiou, G.; Sfetsos, K., A new class of integrable deformations of CFTs. A new class of integrable deformations of CFTs, J. High Energy Phys., 1703, Article 083 pp. (2017); Guo, X.; Zhang, Y.; Hu, W.; Tan, H.; Wang, X., Inferring nonlinear gene regulatory networks from gene expression data based on distance correlation. Inferring nonlinear gene regulatory networks from gene expression data based on distance correlation, PLoS One, 9, 2, Article e87446 pp. (2014); Li, F.; Long, T.; Lu, Y.; Ouyang, Q.; Tang, C., The yeast cell-cycle network is robustly designed. The yeast cell-cycle network is robustly designed, Proc. Natl. Acad. Sci., 101, 4781-4786 (2004); Kunihiro, N., On optimal bounds of small inverse problems and approximate GCD problems with higher degree. (Gollmann, D.; Freiling, F. C., Information Security - 15th International Conference, ISC 2012. Information Security - 15th International Conference, ISC 2012, Lecture Notes in Computer Science, vol. 7483 (2012), Springer), 55-69; Massei, M.; Tremori, A.; Poggi, S.; Nicoletti, L., HLA-based real time distributed simulation of a marine port for training purposes. HLA-based real time distributed simulation of a marine port for training purposes, International Journal of Simulation and Process Modelling, 8, 1, 42-51 (2013); Li, J.; Yu, K., Noniterative integration algorithms with controllable numerical dissipations for structural dynamics. Noniterative integration algorithms with controllable numerical dissipations for structural dynamics, Int. J. Comput. Methods, 15, 3, 1850111 (2018); Cecotti, S.; Ferrara, S., Phys. Lett., 187B, 335 (1987); Zhang, P.; Wu, T. W., A hyper singular integral formulation for acoustic radiation in moving flows. A hyper singular integral formulation for acoustic radiation in moving flows, J Sound Vib, 206, 3, 309-326 (1997); Bentmann, Rasmus, Kirchberg X-algebras with real rank zero and intermediate cancellation. Kirchberg X-algebras with real rank zero and intermediate cancellation, J. Noncommut. Geom., 8, 4, 1061-1081 (2014); Bathe, K. J., Conserving energy and momentum in nonlinear dynamics: a simple implicit time integration scheme. Conserving energy and momentum in nonlinear dynamics: a simple implicit time integration scheme, Comput. Struct., 85, 78, 437-445 (2007); Han, M. Y.; Zyilmaz, B. O.; Zhang, Y.; Kim, P., Phys. Rev. Lett., 98, Article 206805 pp. (2007); Gan, J.; Feng, J.; Fang, Q.; Ng, W., Locality-sensitive hashing scheme based on dynamic collision counting. Locality-sensitive hashing scheme based on dynamic collision counting, Proceedings of the 2012 ACM SIGMOD International Conference on Management of Data, 541-552 (2012); Gérard-Varet, D.; Nguyen, T., Remarks on the ill-posedness of the Prandtl equation. Remarks on the ill-posedness of the Prandtl equation, Asymptot. Anal., 77, 1-2, 71-88 (2012); Devolder, T.; Kim, Joo-Von; Garcia-Sanchez, F.; Swerts, J.; Kim, W.; Couet, S.; Kar, G.; Furnemont, A., Phys. Rev. B, 93, Article 024420 pp. (2016); Nadaraya, E. A., Remarks on nonparametric estimates for density functions and regression curves. Remarks on nonparametric estimates for density functions and regression curves, Theory of Probability and its Applications, 15, 134-137 (1970); Lin, J. R., Surface roughness effect on the dynamic stiffness and damping characteristics of compensated hydrostatic thrust bearings. Surface roughness effect on the dynamic stiffness and damping characteristics of compensated hydrostatic thrust bearings, Int. J. Mach. Tools Manuf., 40, 1671-1689 (2000); Fileviez Perez, P.; Murgui, C.; Furfine, C. H., Interbank exposures: Quantifying the risk of contagion. Interbank exposures: Quantifying the risk of contagion, J. Money Credit Bank., 35, 1, 111-128 (2003); Angermann, L.; Wang, S., Convergence of a fitted finite volume method for the penalized Black-Scholes equation governing European and American Option pricing. Convergence of a fitted finite volume method for the penalized Black-Scholes equation governing European and American Option pricing, Numer. Math., 106, 1, 1-40 (2007); Chou, K. C.; Shen, H. B., Recent advances in developing web-servers for predicting protein attributes. Recent advances in developing web-servers for predicting protein attributes, Nat. Sci., 1, 63 (2009); Balint, D. S.; Deshpande, V. S.; Needleman, A.; Giessen, E. V.d., Discrete dislocation plasticity analysis of the wedge indentation of films. Discrete dislocation plasticity analysis of the wedge indentation of films, J. Mech. Phys. Solids, 54, 2281-2303 (2006); Sampson, P. D., Fitting conic sections to “very scattered” data: an iterative refinement of the bookstein algorithm. Fitting conic sections to “very scattered” data: an iterative refinement of the bookstein algorithm, Comput. Graph. Image Process., 18, 1, 97-108 (1982); Zhao, F.; Li, S.; Sun, J.; Mei, D., Genetic algorithm for the one-commodity pickup-and-delivery traveling salesman problem. Genetic algorithm for the one-commodity pickup-and-delivery traveling salesman problem, Comput. Indus. Eng., 56, 4, 1642-1648 (2009); Beauchamp, D. L.; Khajehpour, M., Biophys. Chem., 161, 29-38 (2012); Georgiou, G.; Sfetsos, K., Integrable flows between exact CFTs. Integrable flows between exact CFTs, J. High Energy Phys., 1711, Article 078 pp. (2017); Dybvig, Philip H.; Spatt, Chester S., Adoption externalities as public goods. Adoption externalities as public goods, J. Public Econ., 20, 231-247 (1983); Podlubny, I.; San Diego, U., Fractional Differential Equations (1999), Academic Press; Yang, L.; Jin, R.; Sukthankar, R., Bayesian active distance metric learning. Bayesian active distance metric learning, Proceedings of the 23rd Conference on Uncertainty in Artificial Intelligence, 442-449 (2007); Gomme, P.; Kydland, F.; Rupert, P., Home production meets time to build. Home production meets time to build, J. Political Econ., 109, 1115-1131 (2001); de Bondt, M., Quasi-translations and counterexamples to the homogeneous dependence problem. Quasi-translations and counterexamples to the homogeneous dependence problem, Proc. Am. Math. Soc., 134, 1, 2849-2856 (2006); Tacchella, A.; Cristelli, M.; Caldarelli, G.; Gabrielli, A.; Pietronero, L., Economic complexity: conceptual grounding of a new metrics for global competitiveness. Economic complexity: conceptual grounding of a new metrics for global competitiveness, J. Econ. Dyn. Control, 37, 8, 1683-1691 (2013); Wang, J.; Liang, K.; Huang, X.; Wang, Z.; Shen, H., Dissipative fault-tolerant control for nonlinear singular perturbed systems with Markov jumping parameters based on slow state feedback. Dissipative fault-tolerant control for nonlinear singular perturbed systems with Markov jumping parameters based on slow state feedback, Appl. Math. Comput., 328, 247-262 (2018); Karp, R. L.; Mansouri, F.; Rno, J. S., Product integral formalism and non-Abelian Stokes theorem. Product integral formalism and non-Abelian Stokes theorem, J. Math. Phys., 40, 6033-6043 (1999), hep-th/9910173 · Zbl 0968.81056
[41] Kahneman, D., Thinking, Fast and Slow (2011), Farrar, Straus and Giroux: Farrar, Straus and Giroux New York, NY; McCann, R.; Topping, P., Ricci flow, entropy and optimal transportation. Ricci flow, entropy and optimal transportation, Amer. J. Math., 132, 711-730 (2010); Volterra, V.; Hostinský, B., Opérations Infinitésimales Linéaires (1938), Gauthier-Villars: Gauthier-Villars Paris; Slavík, A., Product Integration, its History and Applications (2007), Matfyzpress: Matfyzpress Prague
[42] Akhmedov, E. T., Toward a theory of non-Abelian tensor fields. Toward a theory of non-Abelian tensor fields, Theor. Math. Phys., 145, 1664-1665 (2005); Hinze, J. O., Turbulence, 790 (1959), McGraw-Hill; Mohapatra, R. N.; Pati, J. C., Phys. Rev. D, 11, 2558 (1975); Fog, A., Lists of Instruction Latencies, Throughputs and Micro-Operation Breakdowns for Intel, AMD and VIA CPUs, Technical University of Denmark (2018); Akhmedov, E. T., The theory of non-Abelian tensor fields: Gauge transformations and curvature. The theory of non-Abelian tensor fields: Gauge transformations and curvature, Theor. Math. Phys., 147, 509-523 (2006) · Zbl 1178.81176
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.