The Sixth World Professional Forum “The Book. Culture. Education. Innovations” – “Crimea–2021”. The review

The work of the Sixth World Professional Forum “The Book. Culture. Education. Innovations” (June 5–13, 2021, Sudak, Republic of Crimea, Russian Federation) is reviewed; its themes and topics are discussed: library mission in the digitization era; pandemic impact on libraries; prospects for library and information community; national information systems; libraries collaboration with research and educational organizations; modern competences of library specialists; partnerships of national libraries, etc. The focus is made on the following events: The Twenty Seventh International Conference «Libraries and information resources in the modern world of science, culture, education and business», The Third Scientific and Educational Symposium “Building and developing the modern digital environment for education and science”; The Fifth Industry Conference “Book publishing and libraries: Vectors of cooperation”. The authors also give overview of discussions and presentations at the open press conference, the work and conclusions of the central discussion site, Day of Crimean Libraries, Day of Rospatent, The Third Scientific Conference “Scientometrics, bibliometrics, open data and publications in science”, The Third International Conference on the global ecological problems, the research and practice events held within the framework of the Forum, as well as the opening and closing ceremonies, and Forum plenary session.

Circumcentered reflections method for wavelet feasibility problems

We introduce a two-stage global-then-local search method for solving feasibility problems. The approach pairs the advantageous global tendency of the Douglas–Rachford method to find a basin of attraction for a fixed point, together with the local tendency of the circumcentered reflections method to perform faster within such a basin. We experimentally demonstrate the success of the method for solving nonconvex problems in the context of wavelet construction formulated as a feasibility problem. References F. J. Aragón Artacho, R. Campoy, and M. K. Tam. The Douglas–Rachford algorithm for convex and nonconvex feasibility problems. Math. Meth. Oper. Res. 91 (2020), pp. 201–240. doi: 10.1007/s00186-019-00691-9 R. Behling, J. Y. Bello Cruz, and L.-R. Santos. Circumcentering the Douglas–Rachford method. Numer. Algor. 78.3 (2018), pp. 759–776. doi: 10.1007/s11075-017-0399-5 R. Behling, J. Y. Bello-Cruz, and L.-R. Santos. On the linear convergence of the circumcentered-reflection method. Oper. Res. Lett. 46.2 (2018), pp. 159–162. issn: 0167-6377. doi: 10.1016/j.orl.2017.11.018 J. M. Borwein, S. B. Lindstrom, B. Sims, A. Schneider, and M. P. Skerritt. Dynamics of the Douglas–Rachford method for ellipses and p-spheres. Set-Val. Var. Anal. 26 (2018), pp. 385–403. doi: 10.1007/s11228-017-0457-0 J. M. Borwein and B. Sims. The Douglas–Rachford algorithm in the absence of convexity. Fixed-point algorithms for inverse problems in science and engineering. Springer, 2011, pp. 93–109. doi: 10.1007/978-1-4419-9569-8_6 I. Daubechies. Orthonormal bases of compactly supported wavelets. Commun. Pure Appl. Math. 41.7 (1988), pp. 909–996. doi: 10.1002/cpa.3160410705 N. D. Dizon, J. A. Hogan, and J. D. Lakey. Optimization in the construction of nearly cardinal and nearly symmetric wavelets. In: 13th International conference on Sampling Theory and Applications (SampTA). 2019, pp. 1–4. doi: 10.1109/SampTA45681.2019.9030889 N. D. Dizon, J. A. Hogan, and S. B. Lindstrom. Circumcentering reflection methods for nonconvex feasibility problems. arXiv preprint arXiv:1910.04384 (2019). url: https://arxiv.org/abs/1910.04384 D. J. Franklin. Projection algorithms for non-separable wavelets and Clifford Fourier analysis. PhD thesis. University of Newcastle, 2018. doi: 1959.13/1395028. D. J. Franklin, J. A. Hogan, and M. K. Tam. A Douglas–Rachford construction of non-separable continuous compactly supported multidimensional wavelets. arXiv preprint arXiv:2006.03302 (2020). url: https://arxiv.org/abs/2006.03302 D. J. Franklin, J. A. Hogan, and M. K. Tam. Higher-dimensional wavelets and the Douglas–Rachford algorithm. 13th International conference on Sampling Theory and Applications (SampTA). 2019, pp. 1–4. doi: 10.1109/SampTA45681.2019.9030823 B. P. Lamichhane, S. B. Lindstrom, and B. Sims. Application of projection algorithms to differential equations: Boundary value problems. ANZIAM J. 61.1 (2019), pp. 23–46. doi: 10.1017/S1446181118000391 S. B. Lindstrom and B. Sims. Survey: Sixty years of Douglas–Rachford. J. Aust. Math. Soc. 110 (2020), 1–38. doi: 10.1017/S1446788719000570 S. B. Lindstrom, B. Sims, and M. P. Skerritt. Computing intersections of implicitly specified plane curves. J. Nonlin. Convex Anal. 18.3 (2017), pp. 347–359. url: http://www.yokohamapublishers.jp/online2/jncav18-3 S. G. Mallat. Multiresolution approximations and wavelet orthonormal bases of L2(R). Trans. Amer. Math. Soc. 315.1 (1989), pp. 69–87. doi: 10.1090/S0002-9947-1989-1008470-5 Y. Meyer. Wavelets and operators. Cambridge University Press, 1993. doi: 10.1017/CBO9780511623820 G. Pierra. Decomposition through formalization in a product space. Math. Program. 28 (1984), pp. 96–115. doi: 10.1007/BF02612715