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American Mathematical Society, Providence (1997)\nAmburg, I., et al.: Stern sequences for a family of multidimensional continued fractions: TRIP-Stern sequences. J. Integer Seq. 20(1), Article 17.1.7 (2017)\nBingham, N.H., Goldie, C.M., Teugels, J.L.: “Regular Variation”, Encyclopedia of Mathematics and Its Applications, vol. 27. Cambridge University Press, Cambridge (1989)\nBonanno, C., Del Vigna, A.: Representation and coding of rational pairs on a triangular tree and Diophantine approximation in \\({\\mathbb{R}}^{2}\\). arXiv:2007.05958 [math.NT]\nBonanno, C., Isola, S.: Orderings of the rationals and dynamical systems. Colloq. Math. 116(2), 165–189 (2009)\nBrentjes, A.J.: “Multidimensional Continued Fraction Algorithms”. Mathematical Centre Tracts, vol. 145. Mathematisch Centrum, Amsterdam (1981)\nGarrity, T.: On periodic sequences for algebraic numbers. J. Number Theory 88(1), 86–103 (2001)\nGarrity, T.: On Gauss–Kuzmin statistics and the transfer operator for a multidimensional continued fraction algorithms: the triangle map. arXiv: 1509.01840v1 [math.NT]\nGarrity, T., Mcdonald, P.: Generalizing the Minkowski question mark function to a family of multidimensional continued fractions. Int. J. Number Theory 14(9), 2473–2516 (2018)\nIosifescu, M., Kraaikamp, C.: “Metrical Theory of Continued Fractions”. Mathematics and Its Applications, vol. 547. Kluwer Academic Publishers, Dordrecht (2002)\nIsola, S.: From infinite ergodic theory to number theory (and possibly back). Chaos Solitons Fractals 44(7), 467–479 (2011)\nKesseböhmer, M., Munday, S., Stratmann, B.O.: Infinite Ergodic Theory of Numbers. De Gruyter Graduate. De Gruyter, Berlin (2016)\nKesseböhmer, M., Stratmann, B.O.: Fractal analysis for sets of non-differentiability of Minkowski’s question mark function. J. Number Theory 128(9), 2663–2686 (2008)\nLenci, M.: On infinite-volume mixing. Commun. Math. Phys. 298(2), 485–514 (2010)\nLenci, M.: Exactness, K-property and infinite mixing. Publ. Mat. Urug. 14, 159–170 (2013)\nLenci, M., Munday, S.: Pointwise convergence of Birkhoff averages for global observables. Chaos 28(8), 083111 (2018)\nMessaoudi, A., Nogueira, A., Schweiger, F.: Ergodic properties of triangle partitions. Monatsh. Math. 157(3), 283–299 (2009)\nMinkowski, H.: Geometrie der Zahlen, Gesammelte Abhandlungen, vol. 2, 1911; reprinted by Chelsea, New York, pp. 43–52 (1967)\nMiao, J.J., Munday, S.: Derivatives of slippery Devil’s staircases. Discrete Contin. Dyn. Syst. Ser. S 10(2), 353–365 (2017)\nMunday, S.: On the derivative of the \\(\\alpha \\)-Farey–Minkowski function. Discrete Contin. Dyn. Syst. 34(2), 709–732 (2014)\nNakada, H., Natsui, R.: On the metrical theory of continued fraction mixing fibred systems and its application to Jacobi–Perron algorithm. Monatsh. Math. 138(4), 267–288 (2003)\nPanti, G.: Multidimensional continued fractions and a Minkowski function. Monatsh. Math. 154(3), 247–264 (2008)\nSchweiger, F.: Kuzmin’s theory revisited. Ergodic Theory Dyn. Syst. 20(2), 557–565 (2000)\nSchweiger, F.: Multidimensional Continued Fractions. Oxford University Press, Oxford (2000)\nVeech, W.A.: Interval exchange transformations. J. Anal. Math. 33, 222–272 (1978)\nVernon, R.P.: Relationships between Fibonacci-type sequences and Golden-type ratios. 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Comm. Alg. 44, 4177–4184 (2016)\nBastos, R., Shumyatsky, P.: On profinite groups with Engel-like conditions. J. Algebra 427, 215–225 (2015)\nBastos, R., Rocco, N.R.: Non-abelian tensor square of finite-by-nilpotent groups, preprint available at arXiv:1509.05114 [math.GR] (2015)\nBastos, R., Shumyatsky, P., Tortora, A., Tota, M.: On groups admitting a word whose values are Engel. Int. J. Algebra Comput. 23(1), 81–89 (2013)\nBrown, R., Loday, J.L.: Excision homotopique en basse dimension. CR. Acad. Sci. Paris Sr. I 298(15), 353–356 (1984)\nBrown, R., Loday, J.-L.: Van Kampen theorems for diagrams of spaces. Topology 26, 311–335 (1987)\nDeryabina, G.S., Kozevnikov, P.A.: The derived subgroup of a group with commutators of bounded order can be non-periodic. Commun. Algebra 27, 4525–4530 (1999)\nLazard, M.: Sur les groupes nilpotents et les anneaux de Lie. Ann. Sci. École Norm. Sup. 71, 101–190 (1954)\nLazard, M.: Groupes analytiques \\(p\\)-adiques. IHES Publ. Math. 26, 389–603 (1965)\nLongobardi, P., Maj, M., Smith, H.: A note on locally graded groups. Rend. Sem. Mat. Univ. Padova 94, 275–277 (1995)\nMoravec, P.: The exponents of nonabelian tensor products of groups. J. Pure Appl. Algebra 212, 1840–1848 (2008)\nNakaoka, I.N., Rocco, N.R.: A survey of non-abelian tensor products of groups and related constructions. Bol. Soc. Paran. Mat. 30, 77–89 (2012)\nRobinson, D.J.S.: A course in the theory of groups, 2nd edn. Springer, New York (1996)\nRocco, N.R.: On a construction related to the non-abelian tensor square of a group. Bol. Soc. Brasil Mat. 22, 63–79 (1991)\nRocco, N.R.: A presentation for a crossed embedding of finite solvable groups. Commun. Algebra 22, 1975–1998 (1994)\nShumyatsky, P.: Groups with commutators of bounded order. Proc. Am. Math. Soc. 127, 2583–2586 (1999)\nShumyatsky, P.: On residually finite groups in which commutators are Engel. Commun. Algebra 27, 1937–1940 (1999)\nShumyatsky, P.: Applications of Lie ring methods to group theory, in Nonassociative algebra and its applications. In: Costa, R., Grishkov, A., Guzzo Jr H., Peresi, L.A. (eds.) Lecture Notes in Pure and Appl. Math., vol. 211 (Dekker, New York, 2000), pp. 373–395 (2000)\nShumyatsky, P.: Elements of prime power order in residually finite groups. Int. J. Algebra Comput. 15, 571–576 (2005)\nShumyatsky, P., Tortora, A., Tota, M.: On locally graded groups with a word whose values are Engel. Proc. Edinb. Math. Soc. (Series 2) 59, 533–539 (2016)\nTits, J.: Free subgroups in linear groups. J. Algebra 20, 250–270 (1972)\nWilson, J.S.: Two-generator conditions for residually finite groups. Bull. Lond. Math. Soc. 23, 239–248 (1991)\nWilson, J.S., Zelmanov, E.I.: Identities for Lie algebras of pro-\\(p\\) groups. J. Pure Appl. Algebra 81, 103–109 (1992)\nZelmanov, E.I.: On the restricted Burnside problem. In: Proceedings of the International Congress of Mathematicians. pp. 395–402 (1990)\nZel’manov, E.: The solution of the restricted Burnside problem for groups of odd exponent. Math. USSR Izv. 36, 41–60 (1991)\nZel’manov, E.: The solution of the restricted Burnside problem for 2-groups. Math. Sb. 182, 568–592 (1991)",{"EN":1055},"Let m, n be positive integers and p a prime. We denote by \n                  \n                    \n                  \n                  $$\\nu (G)$$\n                  \n                    \n                  \n                 an extension of the non-abelian tensor square \n                  \n                    \n                  \n                  $$G \\otimes G$$\n                  \n                    \n                  \n                 by \n                  \n                    \n                  \n                  $$G \\times G$$\n                  \n                    \n                  \n                . 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S., Lakshmikantham, V.: Generalized quasilinearization method for reaction-diffusion equation under nonlinear and nonlocal flux conditions. J. Math. Anal. Appl. 271(1), 182–205 (2002)\nCortazar, C., del Pino, M., Elgueta, M.: On the short-time behaviour of the free boundary of a porous medium equation. Duke J. Math. 87(1), 133–149 (1997)\nCui, Z., Yang, Z.: Roles of weight functions to a nonlinear porous medium equation with nonlocal source and nonlocal boundary condition. J. Math. Anal. Appl. 342(1), 559–570 (2008)\nCui, Z., Yang, Z., Zhang, R.: Blow-up of solutions for nonlinear parabolic equation with nonlocal source and nonlocal boundary condition. Appl. Math. Comput. 224(1), 1–8 (2013)\nDeng, K.: Comparison principle for some nonlocal problems. Quart. Appl. Math. 50(3), 517–522 (1992)\nFang, Z.B., Zhang, J.: Global and blow-up solutions for the nonlocal p-Laplacian evolution equation with weighted nonlinear nonlocal boundary condition. J. Integral Equat. 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Value Probl. 143, 14 (2018)\nYang, L., Fan, C.: Global existence and blow-up of solutions to a degenerate parabolic system with nonlocal sources and nonlocal boundaries. Monatsh. Math. 174(3), 493–510 (2014)\nYe, Z., Xu, X.: Global existence and blow-up for a porous medium system with nonlocal boundary conditions and nonlocal sources. Nonlinear Anal. 82, 115–126 (2013)\nZheng, S., Kong, L.: Roles of weight functions in a nonlinear nonlocal parabolic system. Nonlinear Anal. 68(8), 2406–2416 (2008)",{"EN":1135},"In this paper we consider initial boundary value problem for nonlinear nonlocal parabolic equation with absorption under nonlinear nonlocal boundary condition and nonnegative initial datum. 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