Authors: Estaji, Ali Akbar, Mahmoudi Darghadam, Ahmad
Subject Terms: keyword:real measurable function, keyword:lattice-ordered ring, keyword:realcompact measurable space, keyword:real Riesz map, keyword:free ideal, msc:12J15, msc:28A20, msc:54C30
File Description: application/pdf
Relation: reference:[1] Acharyya, S., Acharyya, S.K., Bag, S., Sack, J.: Recent progress in rings and subrings of real valued measurable functions.math.GN, 6 Nov. (2018), http://arxiv.org/abs/1811.02126v1. MR 4149117; reference:[2] Aliabad, A.R., Azarpanah, F., Namdari, M.: Rings of continuous functions vanishing at infinity.Comment. Mat. Univ. Carolinae 45 (3) (2004), 519–533. MR 2103146; reference:[3] Dube, T.: On the ideal of functions with compact support in pointfree function rings.Acta Math. Hungar. 129 (3) (2010), 205–226. Zbl 1299.06021, MR 2737723, 10.1007/s10474-010-0024-8; reference:[4] Ebrahimi, M.M., Karimi Feizabadi, A.: Prime representation of real Riesz maps.Algebra Universalis 54 (2005), 291–299. MR 2219412, 10.1007/s00012-005-1945-x; reference:[5] Ebrahimi, M.M., Mahmoudi, M.: Frame.Tech. report, Shahid Beheshti University, 1996.; reference:[6] Ercan, Z., Onal, S.: A remark on the homomorphism on C(X).Amer. Math. Soc. 133 (2005), 3609–3611. MR 2163596, 10.1090/S0002-9939-05-07930-X; reference:[7] Estaji, A.A., Mahmoudi Darghadam, A.: Rings of real measurable functions vanishing at infinity on a measurable space.submitted. MR 4028813; reference:[8] Estaji, A.A., Mahmoudi Darghadam, A.: On maximal ideals of $\mathcal{R}_{\infty }$L.J. Algebr. Syst. 6 (1) (2018), 43–57. MR 3833289; reference:[9] Estaji, A.A., Mahmoudi Darghadam, A.: Rings of continuous functions vanishing at infinity on a frame.Quaest. Math. 42 (9) (2019), 1141–1157, http://dx.doi.org/10.2989/16073606.2018.1509151. MR 4028813, 10.2989/16073606.2018.1509151; reference:[10] Estaji, A.A., Mahmoudi Darghadam, A.: Rings of frame maps from $\mathcal{P}(\mathbb{R})$ to frames which vanish at infinity.Hacet. J. Math. Stat. 49 (2) (2020), 854–868, http://dx.doi.org/10.15672/hujms.624015. MR 4089915, 10.15672/hujms.624015; reference:[11] Estaji, A.A., Mahmoudi Darghadam, A., Yousefpour, H.: Maximal ideals in rings of real measurable functions.Filomat 32 (15) (2018), 5191–5203, https://doi.org/10.2298/FIL1815191E. MR 3898565, 10.2298/FIL1815191E; reference:[12] Gillman, L., Jerison, M.: Rings of continuous functions.Springer Verlag, 1976. MR 0407579; reference:[13] Hager, A.: Algebras of measurable functions.Duke Math. J. 38 (1) (1971), 21–27. MR 0273409, 10.1215/S0012-7094-71-03804-X; reference:[14] Hewitt, E.: Rings of real-valued continuous functions.Trans. Amer. Math. Soc. 64 (1948), 45–99. MR 0026239, 10.1090/S0002-9947-1948-0026239-9; reference:[15] Kohls, C.W.: Ideals in rings of continuous functions.Fund. Math. 45 (1957), 28–50. MR 0102731, 10.4064/fm-45-1-28-50; reference:[16] Rudin, W.: Real and complex analysis.3rd ed., New York: McGraw-Hill Book Co., 1987. MR 0924157
Availability:
https://doi.org/10.2989/16073606.2018.1509151
https://doi.org/10.15672/hujms.624015
https://doi.org/10.2298/FIL1815191E
https://doi.org/10.5817/AM2023-5-383
http://hdl.handle.net/10338.dmlcz/151795
Authors: Iwasa, Akira
Subject Terms: keyword:forcing, keyword:open map, keyword:closed map, keyword:quotient map, msc:54A35, msc:54C10
File Description: application/pdf
Relation: mr:MR4445739; zbl:Zbl 07584115; reference:[1] Arens R.: Note on convergence in topology.Math. Mag. 23 (1950), 229–234. MR 0037500, 10.2307/3028991; reference:[2] Engelking R.: General Topology.Sigma Series in Pure Mathematics, 6, Heldermann, Berlin, 1989. Zbl 0684.54001, MR 1039321; reference:[3] Grunberg R., Junqueira L. R., Tall F. D.: Forcing and normality.Proc. of the International Conf. on Set-theoretic Topology and Its Applications, Part 2, Matsuyama, 1994, Topology Appl. 84 (1998), no. 1–3, 145–174. MR 1611214, 10.1016/S0166-8641(97)00089-8; reference:[4] Iwasa A.: Preservation of countable compactness and pseudocompactness by forcing.Topology Proc. 50 (2017), 1–11. MR 3488498; reference:[5] Iwasa A.: Preservation of a neighborhood base of a set by ccc forcings.Topology Proc. 52 (2018), 61–72. MR 3673209; reference:[6] Jech T.: Set Theory.The Third Millennium Edition, Revised and Expanded, Springer Monographs in Mathematics, Springer, Berlin, 2003. Zbl 1007.03002, MR 1940513; reference:[7] Juhász I., Weiss W.: Omitting the cardinality of the continuum in scattered spaces.Topology Appl. 31 (1989), no. 1, 19–27. MR 0984101, 10.1016/0166-8641(89)90095-3; reference:[8] Kunen K.: Set Theory: An Introduction to Independence Proofs.Studies in Logic and the Foundations of Mathematics, 102, North-Holland Publishing, Amsterdam, 1980. Zbl 0534.03026, MR 0597342
Authors: Jun, Jaiung, Mincheva, Kalina, Rowen, Louis
Subject Terms: keyword:pair, keyword:semiring, keyword:system, keyword:triple, keyword:shallow, keyword:algebraic, keyword:integral, keyword:affine, keyword:Ore, keyword:negation map, keyword:congruence, keyword:module, msc:08A05, msc:08A30, msc:08A72, msc:12K10, msc:13C60, msc:14T10, msc:16Y60, msc:18A05, msc:18C10, msc:18E05, msc:20N20
File Description: application/pdf
Relation: mr:MR4538623; zbl:Zbl 07655857; reference:[1] Akian, M., Gaubert, S., Guterman, A.: Linear independence over tropical semirings and beyond.In: Tropical and Idempotent Mathematics (G. L. Litvinov and S. N. Sergeev, eds.), Contemp. Math. 495 (2009), 1-38. 10.1090/conm/495/09689; reference:[2] Akian, M., Gaubert, S., Rowen, L.: Linear algebra over systems.Preprint, 2022.; reference:[3] Akian, M., Gaubert, S., Rowen, L.: From systems to hyperfields and related examples.Preprint, 2022.; reference:[4] Alarcon, F., Anderson, D.: Commutative semirings and their lattices of ideals.J. Math. 20 (1994), 4.; reference:[5] Baker, M., Bowler, N.: Matroids over partial hyperstructures.Adv. Math. 343 (2019), 821-863.; reference:[6] Bell, J., Zelmanov, E.: On the growth of algebras, semigroups, and hereditary languages.Inventiones Math. 224 (2021), 683-697.; reference:[7] Connes, A., Consani, C.: From monoids to hyperstructures: in search of an absolute arithmetic.Casimir Force, Casimir Operators and the Riemann Hypothesis, de Gruyter 2010, pp. 147-198.; reference:[8] Chapman, A., Gatto, L., Rowen, L.: Clifford semialgebras.Rendiconti del Circolo Matematico di Palermo Series 2, 2022; reference:[9] Costa, A. A.: Sur la theorie generale des demi-anneaux.Publ. Math. Decebren 10 (1963), 14-29.; reference:[10] Dress, A.: Duality theory for finite and infinite matroids with coefficients.Advances Math. 93 (1986), 2, 214-250.; reference:[11] Dress, A., Wenzel, W.: Algebraic, tropical, and fuzzy geometry.Beitrage zur Algebra und Geometrie/ Contributions to Algebra und Geometry 52 (2011), 2, 431-461.; reference:[12] Elizarov, N., Grigoriev, D.: A tropical version of Hilbert polynomial (in dimension one), (2021).; reference:[13] Gatto, L., Rowen, L.: Grassman semialgebras and the Cayley-Hamilton theorem.Proc. American Mathematical Society, series B, 7 (2020), 183-201.; reference:[14] Gaubert, S.: Theorie des systemes lineaires dans les diodes.These, Ecole des Mines de Paris 1992.; reference:[15] Gaubert, S.: Methods and applications of (max,+) linear algebra.STACS' 97, number 1200 in LNCS, Lübeck, Springer 1997.; reference:[16] Giansiracusa, J., Jun, J., Lorscheid, O.: On the relation between hyperrings and fuzzy rings.Beitr. Algebra Geom. 58 (2017), 735-764.; reference:[17] Golan, J.: The theory of semirings with applications in mathematics and theoretical computer science.Longman Sci Tech. 54 (1992).; reference:[18] Greenfeld, B.: Growth of monomial algebras, simple rings and free subalgebras.J. Algebra 489 (2017), 427-434.; reference:[19] Hilgert, J., Hofmann, K.: Semigroups in Lie groups, semialgebras in Lie algebras.Trans. Amer. Math. Soc. 288 (1985), 2.; reference:[20] Izhakian, Z.: Tropical arithmetic and matrix algebra.Commun. Algebra 37 (2009), 4, 1445-1468.; reference:[21] Izhakian, Z., Rowen, L.: Supertropical algebra.Adv. Math. 225 (2010), 4, 2222-2286.; reference:[22] Izhakian, Z., Rowen, L.: Supertropical matrix algebra.Israel J. Math. 182 (2011), 1, 383-424.; reference:[23] Jacobson, N.: Basic Algebra II.Freeman 1980.; reference:[24] Joo, D., Mincheva, K.: Prime congruences of additively idempotent semirings and a Nullstellensatz for tropical polynomials.Selecta Mathematica 24 (2018), 3, 2207-2233.; reference:[25] Jun, J., Mincheva, K., Rowen, L.: Projective systemic modules.J. Pure Appl. Algebra 224 (2020), 5, 106-243.; reference:[26] Jun, J.: Algebraic geometry over hyperrings.Adv. Math. 323 (2018), 142-192.; reference:[27] Jun, J., Rowen, L.: Categories with negation.In: Categorical, Homological and Combinatorial Methods in Algebra (AMS Special Session in honor of S. K. Jain's 80th birthday), Contempor. Math. 751 (2020), 221-270.; reference:[28] Katsov, Y.: Tensor products of functors.Siberian J. Math. 19 (1978), 222-229, trans. from Sib. Mat. Zhurnal 19 (1978), 2, 318-327. 10.1007/BF00970503; reference:[29] Krasner, M.: A class of hyperrings and hyperfields.Int. J. Math. Math. Sci. 6 (1983), 2, 307-312. 10.1155/S0161171283000265; reference:[30] Krause, G. R., Lenagan, T. H.: Growth of algebras and Gelfand-Kirillov dimension.Amer. Math. Soc. Graduate Stud. Math. 22 (2000).; reference:[31] Ljapin, E. S.: Semigroups.AMS Translations of Mathematical Monographs 3 (1963), 519 pp.; reference:[32] Lorscheid, O.: The geometry of blueprints. Part I.Adv. Math. 229 (2012), 3, 1804-1846.; reference:[33] Lorscheid, O.: A blueprinted view on $\mathbb{F}_1$-geometry.In: Absolute Arithmetic and $\mathbb{F}_1$-geometry (Koen Thas. ed.), European Mathematical Society Publishing House 2016.; reference:[34] Rowen, L. H.: Ring Theory. Vol. I.Academic Press, Pure and Applied Mathematics 127, 1988.; reference:[35] Rowen, L. H.: Graduate algebra: Noncommutative View.AMS Graduate Studies in Mathematics 91, 2008.; reference:[36] Rowen, L. H.: Algebras with a negation map.Europ. J. Math. 8 (2022), 62-138. 10.1007/s40879-021-00499-0; reference:[37] Rowen, L. H.: An informal overview of triples and systems, 2017.; reference:[38] Smoktunowicz, A.: Growth, entropy and commutativity of algebras satisfying prescribed relations.Selecta Mathematica 20 (2014) 4, 1197-1212.; reference:[39] Shneerson, L. M.: Types of growth and identities of semigroups.Int. J. Algebra Comput., Special Issue: International Conference on Group Theory "Combinatorial, Geometric and Dynamical Aspects of Infinite Groups"; (L. Bartholdi, T. Ceccherini-Silberstein, T. Smirnova-Nagnibeda, A. Zuk, eds.), 15 (2005), 05, 1189-1204.; reference:[40] Viro, O. Y.: Hyperfields for tropical geometry I, Hyperfields and dequantization, 2010.
Authors: Le, Cong Nhan, Le, Xuan Truong
Subject Terms: keyword:Nehari manifold, keyword:fibrering maps, keyword:vanishing potential, keyword:logarithmic nonlinearity, msc:35J60, msc:47J30
File Description: application/pdf
Relation: mr:MR4387467; zbl:Zbl 07547240; reference:[1] Alves, C. O., Souto, M. A. S.: Existence of solutions for a class of elliptic equations in $\mathbb R^N$ with vanishing potentials.J. Differ. Equations 252 (2012), 5555-5568 \99999DOI99999 10.1016/j.jde.2012.01.025 . Zbl 1250.35103, MR 2902126, 10.1016/j.jde.2012.01.025; reference:[2] Alves, C. O., Souto, M. A. S.: Existence of solutions for a class of nonlinear Schrödinger equations with potential vanishing at infinity.J. Differ. Equations 254 (2013), 1977-1991 \99999DOI99999 10.1016/j.jde.2012.11.013 . Zbl 1263.35076, MR 3003299; reference:[3] Ambrosetti, A., Malchiodi, A.: Nonlinear Analysis and Semilinear Elliptic Problems.Cambridge Studies in Advanced Mathematics 104. Cambridge University Press, Cambridge (2007). Zbl 1125.47052, MR 2292344, 10.1017/CBO9780511618260; reference:[4] Ambrosetti, A., Wang, Z.-Q.: Nonlinear Schrödinger equations with vanishing and decaying potentials.Differ. Integral Equ. 18 (2005), 1321-1332 \99999MR99999 2174974 . Zbl 1210.35087, MR 2174974; reference:[5] Ardila, A. H.: Existence and stability of standing waves for nonlinear fractional Schrödinger equation with logarithmic nonlinearity.Nonlinear Anal., Theory Methods Appl. 155 (2017), 52-64 \99999DOI99999 10.1016/j.na.2017.01.006 . Zbl 1368.35242, MR 3631741; reference:[6] Benci, V., Grisanti, C. R., Micheletti, A. M.: Existence of solutions for the nonlinear Schrödinger equation with $V(\infty)=0$.Contributions to Nonlinear Analysis Progress in Nonlinear Differential Equations and Their Applications 66. Birkhäuser, Basel (2006), 53-65 \99999DOI99999 10.1007/3-7643-7401-2_4 . Zbl 1231.35225, MR 2187794; reference:[7] Berestycki, H., Lions, P.-L.: Nonlinear scalar field equations. I: Existence of a ground state.Arch. Ration. Mech. Anal. 82 (1983), 313-345 \99999DOI99999 10.1007/BF00250555 . 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Zbl 1321.35253, MR 3377693, 10.1007/s00033-014-0486-6; reference:[16] Cheng, M.: Bound state for the fractional Schrödinger equation with unbounded potential.J. Math. Phys. 53 (2012), Article ID 043507, 7 pages \99999DOI99999 10.1063/1.3701574 . Zbl 1275.81030, MR 2953151; reference:[17] Corvellec, J.-N., Degiovanni, M., Marzocchi, M.: Deformation properties for continuous functionals and critical point theory.Topol. Methods Nonlinear Anal. 1 (1993), 151-171 \99999DOI99999 10.12775/TMNA.1993.012 . Zbl 0789.58021, MR 1215263; reference:[18] D'Avenia, P., Montefusco, E., Squassina, M.: On the logarithmic Schrödinger equation.Commun. Contemp. Math. 16 (2014), Article ID 1350032, 15 pages \99999DOI99999 10.1142/S0219199713500326 . Zbl 1292.35259, MR 3195154; reference:[19] Degiovanni, M., Zani, S.: Multiple solutions of semilinear elliptic equations with one-sided growth conditions.Math. Comput. Modelling 32 (2000), 1377-1393. 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Rev. 32(A) (1985), 1201-1204 \99999DOI99999 10.1103/PhysRevA.32.1201 .; reference:[24] Ji, C., Szulkin, A.: A logarithmic Schrödinger equation with asymptotic conditions on the potential.J. Math. Anal. Appl. 437 (2016), 241-254. Zbl 1333.35010, MR 3451965, 10.1016/j.jmaa.2015.11.071; reference:[25] Khoutir, S., Chen, H.: Existence of infinitely many high energy solutions for a fractional Schrödinger equation in $\mathbb R^N$.Appl. Math. Lett. 61 (2016), 156-162 \99999DOI99999 10.1016/j.aml.2016.06.001 . Zbl 1386.35444, MR 3518463; reference:[26] Laskin, N.: Fractional quantum mechanics and Lévy path integrals.Phys. Lett., A 268 (2000), 298-305 \99999DOI99999 10.1016/S0375-9601(00)00201-2 . Zbl 0948.81595, MR 1755089; reference:[27] Laskin, N.: Fractional Schrödinger equation.Phys. Rev. E (3) 66 (2002), Article ID 056108, 7 pages \99999DOI99999 10.1103/PhysRevE.66.056108 . MR 1948569; reference:[28] Perera, K., Squassina, M., Yang, Y.: Critical fractional $p$-Laplacian problems with possibly vanishing potentials.J. Math. Anal. Appl. 433 (2016), 818-831 \99999DOI99999 10.1016/j.jmaa.2015.08.024 . Zbl 1403.35319, MR 3398738; reference:[29] Secchi, S.: Ground state solutions for nonlinear fractional Schrödinger equations in $\mathbb R^N$.J. Math. Phys. 54 (2013), Article ID 031501, 17 pages \99999DOI99999 10.1063/1.4793990 . Zbl 1281.81034, MR 3059423; reference:[30] Shang, X., Zhang, J.: Ground states for fractional Schrödinger equations with critical growth.Nonlinearity 27 (2014), 187-207 \99999DOI99999 10.1088/0951-7715/27/2/187 . Zbl 1287.35027, MR 3153832; reference:[31] Shang, X., Zhang, J., Yang, Y.: On fractional Schrödinger equation in $\mathbb R^N$ with critical growth.J. Math. Phys. 54 (2013), Article ID 121502, 20 pages. 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Zbl 1364.35426, MR 3583517, 10.3934/cpaa.2017004; reference:[36] Zloshchastiev, K. G.: Logarithmic nonlinearity in theories of quantum gravity: Origin of time and observational consequences.Grav. Cosmol. 16 (2010), 288-297. Zbl 1232.83044, MR 2740900, 10.1134/S0202289310040067
Availability:
https://doi.org/10.1016/j.jde.2012.01.025
https://doi.org/10.1016/j.jde.2012.11.013
https://doi.org/10.1016/j.na.2017.01.006
https://doi.org/10.1007/3-7643-7401-2_4
https://doi.org/10.1007/BF00250555
https://doi.org/10.1016/0003-4916(76)90057-9
https://doi.org/10.1016/S0022-0396(03)00121-9
https://doi.org/10.1007/978-3-642-25361-4_3
https://doi.org/10.1137/S1052623499353169
https://doi.org/10.5802/afst.543
Authors: Benkartab, Aicha, Cherif, Ahmed Mohammed
Subject Terms: keyword:Riemannian geometry, keyword:Harmonic maps, keyword:Biharmonic maps, msc:53C20, msc:53C22, msc:58E20
File Description: application/pdf
Relation: mr:MR4197078; zbl:Zbl 1480.53051; reference:[1] Baird, P., Fardoun, A., Ouakkas, S.: Conformal and semi-conformal biharmonic maps.Annals of Global Analysis and Geometry, 34, 4, 2008, 403-414, Springer, MR 2447908, 10.1007/s10455-008-9118-8; reference:[2] Baird, P., Kamissoko, D.: On constructing biharmonic maps and metrics.Annals of Global Analysis and Geometry, 23, 1, 2003, 65-75, Springer, MR 1952859, 10.1023/A:1021213930520; reference:[3] Baird, P., Wood, J.C.: Harmonic morphisms between Riemannian manifolds.29, 2003, Oxford University Press, MR 2044031; reference:[4] Benkartab, A., Cherif, A.M.: New methods of construction for biharmonic maps.Kyungpook Mathematical Journal, 59, 1, 2019, 135-147, Department of Mathematics, Kyungpook National University, MR 3946694; reference:[5] Caddeo, R., Montaldo, S., Oniciuc, C.: Biharmonic submanifolds of $\mathbb {S}^{3}$.International Journal of Mathematics, 12, 08, 2001, 867-876, World Scientific, MR 1863283; reference:[6] Eells, J., Lemaire, L.: A report on harmonic maps.Bulletin of the London Mathematical Society, 10, 1, 1978, 1-68, Citeseer, Zbl 0401.58003, MR 0495450, 10.1112/blms/10.1.1; reference:[7] Eells, J., Lemaire, L.: Another report on harmonic maps.Bulletin of the London Mathematical Society, 20, 5, 1988, 385-524, Oxford University Press, Zbl 0669.58009, MR 0956352, 10.1112/blms/20.5.385; reference:[8] Eells, J., Sampson, J.H.: Harmonic mappings of Riemannian manifolds.American Journal of Mathematics, 86, 1, 1964, 109-160, JSTOR, Zbl 0122.40102, MR 0164306, 10.2307/2373037; reference:[9] K{ö}rpinar, T., Turhan, E.: Tubular surfaces around timelike biharmonic curves in Lorentzian Heisenberg group $\operatorname {Heis}^3$.Analele Universitatii ``Ovidius" Constanta -- Seria Matematica, 20, 1, 2012, 431-446, Sciendo, MR 2928433; reference:[10] Oniciuc, C.: New examples of biharmonic maps in spheres.Colloquium Mathematicum, 97, 1, 2003, 131-139, MR 2010548, 10.4064/cm97-1-12; reference:[11] Ouakkas, S.: Biharmonic maps, conformal deformations and the Hopf maps.Differential Geometry and its Applications, 26, 5, 2008, 495-502, Elsevier, MR 2458275, 10.1016/j.difgeo.2008.04.006; reference:[12] Jiang, G.Y.: 2-harmonic maps and their first and second variational formulas.Chinese Ann. Math. Ser. A, 7, 4, 1986, 389-402, MR 0886529; reference:[13] O'Neill, B.: Semi-Riemannian geometry with applications to relativity.1983, Academic Press, MR 0719023; reference:[14] Sakai, T.: Riemannian geometry.1992, Shokabo, Tokyo, (in Japanese). MR 1390760
Availability: http://hdl.handle.net/10338.dmlcz/148707
Authors: Amiri, Habib, Glöckner, Helge, Schmeding, Alexander
Subject Terms: keyword:Lie groupoid, keyword:Lie algebroid, keyword:topological groupoid, keyword:mapping groupoid, keyword:current groupoid, keyword:manifold of mappings, keyword:superposition operator, keyword:Nemytskii operator, keyword:pushforward, keyword:submersion, keyword:immersion, keyword:embedding, keyword:local diffeomorphism, keyword:\mathbbT1-cmd 1étale map, keyword:proper map, keyword:perfect map, keyword:orbifold groupoid, keyword:transitivity, keyword:local transitivity, keyword:local triviality, keyword:Stacey-Roberts Lemma, msc:22A22, msc:22E65, msc:22E67, msc:46T10, msc:47H30, msc:58D15, msc:58H05
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Relation: mr:MR4188745; zbl:Zbl 07285968; reference:[1] Alzaareer, H., Schmeding, A.: Differentiable mappings on products with different degrees of differentiability in the two factors.Expo. Math. 33 (2015), no. 2, 184–222. MR 3342623 DOI: http://dx.doi.org/10.1016/j.exmath.2014.07.002 MR 3342623, 10.1016/j.exmath.2014.07.002; reference:[2] Amiri, H.: A group of continuous self-maps on a topological groupoid.Semigroup Forum (2017), 1–12. DOI: http://dx.doi.org/10.1007/s00233-017-9857-6 MR 3750347, 10.1007/s00233-017-9857-6; reference:[3] Amiri, H., Schmeding, A.: Linking Lie groupoid representations and representations of infinite-dimensional Lie groups.2018. MR 3951756; reference:[4] Amiri, H., Schmeding, A.: A differentiable monoid of smooth maps on Lie groupoids.J. Lie Theory 29 (4) (2019), 1167–1192. MR 4022150; reference:[5] Bastiani, A.: Applications différentiables et variétés différentiables de dimension infinie.J. Analyse Math. 13 (1964), 1–114. 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Availability:
https://doi.org/10.1016/j.exmath.2014.07.002
https://doi.org/10.1007/s00233-017-9857-6
https://doi.org/10.1016/S0723-0869(04)80006-9
https://doi.org/10.1007/978-3-662-12494-9
https://doi.org/10.1142/S0219199706002246
https://doi.org/10.1090/conm/641/12857
https://doi.org/10.4007/annals.2003.157.575
https://doi.org/10.1090/S0002-9904-1966-11558-6
https://doi.org/10.1006/jfan.2002.3942
https://doi.org/10.1016/j.indag.2017.04.004
Authors: Drewnowski, Lech
Subject Terms: keyword:preimage, keyword:open map, keyword:complete metric space, keyword:$F$-space, keyword:$F$-lattice, keyword:compact set, keyword:uniformly open map, keyword:surpositive operator, keyword:lower semicontinuous set-valued map, msc:46A16, msc:46A30, msc:54C10, msc:54D65, msc:54E35, msc:54E40, msc:54E45, msc:54E50
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Relation: mr:MR4093430; zbl:Zbl 07217159; reference:[1] Aliprantis C., Burkinshaw O.: Locally Solid Riesz Spaces with Applications to Economics.Mathematical Surveys and Monographs, 105, American Mathematical Society, Providence, 2003. MR 2011364, 10.1090/surv/105; reference:[2] Bessaga C., Pełczyński A.: Selected Topics in Infinite-Dimensional Topology.Monografie Matematyczne, 58, PWN---Polish Scientific Publishers, Warsaw, 1975. MR 0478168; reference:[3] Bourbaki N.: Éléments de mathématique. I: Les structures fondamentales de l'analyse. Fascicule VIII. Livre III: Topologie générale. Chapitre 9: Utilisation des nombres réels en topologie générale.Deuxième édition revue et augmentée, Actualités Scientifiques et Industrielles, 1045, Hermann, Paris, 1958 (French). MR 0173226; reference:[4] Diestel J.: Sequences and Series in Banach Spaces.Graduate Texts in Mathematics, 92, Springer, New York, 1984. MR 0737004; reference:[5] Drewnowski L., Wnuk W.: On finitely generated vector sublattices.Studia Math. 245 (2019), no. 2, 129–167. MR 3863066, 10.4064/sm170524-23-12; reference:[6] Engelking R.: General Topology.Biblioteka Matematyczna, Tom 47, Państwowe Wydawnictwo Naukowe, Warsaw, 1975 (Polish). Zbl 0684.54001, MR 0500779; reference:[7] Jarchow H.: Locally Convex Spaces.Mathematische Leitfäden, B. G. Teubner, Stuttgart, 1981. Zbl 0466.46001, MR 0632257; reference:[8] Köthe G.: Topological Vector Spaces. I.Die Grundlehren der mathematischen Wissenschaften, 159, Springer, New York, 1969. MR 0248498; reference:[9] Michael E.: A theorem on semi-continuous set-valued functions.Duke Math. J. 26 (1959), 647–651. MR 0109343, 10.1215/S0012-7094-59-02662-6; reference:[10] Michael E.: $\aleph_0$-spaces.J. Math. Mech. 15 (1966), 983–1002. MR 0206907; reference:[11] Michael E.: $G_\delta$ sections and compact-covering maps.Duke Math. J. 36 (1969), 125–127. MR 0240790, 10.1215/S0012-7094-69-03617-5; reference:[12] Michael E., K. Nagami: Compact-covering images of metric spaces.Proc. Amer. Math. Soc. 37 (1973), 260–266. MR 0307148, 10.1090/S0002-9939-1973-0307148-4; reference:[13] Nagami K.: Ranges which enable open maps to be compact-covering.General Topology and Appl. 3 (1973), 355–367. MR 0345055, 10.1016/0016-660X(73)90023-8; reference:[14] Schaefer H. H.: Banach Lattices and Positive Operators.Die Grundlehren der mathematischen Wissenschaften, 215, Springer, New York, 1974. Zbl 0296.47023, MR 0423039
Authors: Bayer, Tomáš, Kočandrlová, Milada
Subject Terms: keyword:mathematical cartography, keyword:inverse form, keyword:map, keyword:projection, keyword:van der Grinten, keyword:GIS, msc:53A20, msc:86A30
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Relation: mr:MR4342613; zbl:Zbl 07442411; reference:[1] Bayer, T.: Estimation of an unknown cartographic projection and its parameters from the map.GeoInformatica 18 (2014), 621-669. 10.1007/s10707-013-0200-4; reference:[2] Bayer, T.: Advanced methods for the estimation of an unknown projection from a map.GeoInformatica 20 (2016), 241-284. 10.1007/s10707-015-0234-x; reference:[3] Bayer, T.: Detectproj, software for the map projection analysis.Available athttp://sourceforge.net/projects/detectproj/ (2017).; reference:[4] Bayer, T., Kočandrlová, M.: Reconstruction of map projection, its inverse and re-projection.Appl. Math., Praha 63 (2018), 455-481. Zbl 06945742, MR 3842963, 10.21136/AM.2018.0096-18; reference:[5] W. D. Brooks, C. E. Roberts, Jr.: An analysis of a modified van der Grinten equatorial arbitrary oval projection.American Cartographer 3 (1976), 143-150. 10.1559/152304076784080096; reference:[6] Evenden, G., Butler, H.: PROJ.Available at https://proj.org/ (1983-2020).; reference:[7] Fenna, D.: Cartographic Science: A Compendium of Map Projections, with Derivations.CRC Press/Taylor & Francis, Boca Raton (2007). 10.1201/b15876; reference:[8] Grossman, S. I.: Multivariable Calculus, Linear Algebra, and Differential Equations.Saunders College Pub., Portland (1995). 10.1016/c2013-0-07351-3; reference:[9] Grosvenor, G.: National Geographic Map Of World.National Geographic Society, New York (1943).; reference:[10] Lowman, P. D., Frey, H. V.: A Geophysical Atlas for Interpretation of Satellite-Derived Data.National Aeronautics and Space Administration, Washington (1979).; reference:[11] O'Keefe, J. A., Greenberg, A.: A note on the van der Grinten projection of the whole earth onto a circular disk.American Cartographer 4 (1977), 127-132. 10.1559/152304077784080392; reference:[12] Reeves, E. A.: Van der Grinten's projection.Geographical Journal 24 (1904), 670-672. 10.2307/1776259; reference:[13] Rubincam, D. P.: Inverting $x,y$ Grid Coordinates to Obtain Latitude and Longitude in the Van Der Grinten Projection.NASA Technical Memorandum 81998. National Aeronautics and Space Administration, Washington (1980).; reference:[14] Snyder, J. P.: Communications from readers: Projection notes.American Cartographer 6 (1979), 81. 10.1559/152304079784022709; reference:[15] Snyder, J. P.: Map projections: A working manual.U.S. Geological Survey Profesional Paper 1395. U.S. Government Printing Office, Washington (1987). 10.3133/pp1395; reference:[16] Snyder, J. P.: Flattening the Earth: Two Thousand Years of Map Projections.University of Chicago Press, Chicago (1997).; reference:[17] Grinten, A. J. van der: Darstellung der ganzen Erdoberfläche auf einer kreisförmigen Projektionsebene.Petermann's Mitteilungen 50 (1904), 155-159 German.; reference:[18] Grinten, A. J. van der: New circular projection of the whole Earth's surface.Am. J. Sci. 19 (1905), 357-366. 10.2475/ajs.s4-19.113.357; reference:[19] Grinten, A. J. van der: Zur Verebnung der ganzen Erdoberfläche: Nachtrag zu der Darstellung in Pet. Mitt. 1904. Heft VII, S. 155-159.Petermann's Mitteilungen 51 (1905), 237 German.; reference:[20] Zöppritz, K. J.: Leitfaden der Kartenentwurfslehre. 1 Teil. Die Projektionslehre.B. G. Teubner, Leipzig (1912), German \99999JFM99999 43.1102.07.
Authors: Baird, Paul, Ventura, Jade
Subject Terms: keyword:Einstein manifold, keyword:conformal foliation, keyword:semi-conformal map, keyword:biconformal deformation, msc:53C12, msc:53C18, msc:53C25
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Relation: mr:MR4346113; zbl:Zbl 07442414; reference:[1] Baird, P., Wood, J.C.: Harmonic morphisms between Riemannian manifolds.London Math. Soc. Monographs, New Series, vol. 29, Oxford Univ. Press, 2003. MR 2044031; reference:[2] Besse, A.: Einstein Manifolds.Springer-Verlag, 1987. Zbl 0613.53001; reference:[3] Danielo, L.: Structures Conformes, Harmonicité et Métriques d’Einstein.Ph.D. thesis, Université de Bretagne Occidentale, 2004.; reference:[4] Danielo, L.: Construction de métriques d’Einstein à partir de transformations biconformes.Ann. Fac. Sci. Toulouse (6) 15 (3) (2006), 553–588. MR 2246414, 10.5802/afst.1129; reference:[5] Dieudonné, J.: Foundations of Modern Analysis.Academic Press, 1969.; reference:[6] Hebey, E.: Scalar curvature type problems in Riemannian geometry.Notes of a course given at the University of Rome 3. http://www.u-cergy.fr/rech/pages/hebey/.; reference:[7] Hebey, E.: Introduction à l’analyse non linéaire sur les variétés.Diderot, Paris, 1997.; reference:[8] Hilbert, D.: Die Grundlagen der Physik.Nachr. Ges. Wiss. Göttingen (1915), 395–407.; reference:[9] Hitchin, N.J.: On compact four-dimensional Einstein manifolds.J. Differential Geom. 9 (1974), 435–442. 10.4310/jdg/1214432419; reference:[10] Schoen, R.: Conformal deformation of a Riemannian metric to constant scalar curvature.J. Differential Geom. 20 (1984), 479–495. Zbl 0576.53028, 10.4310/jdg/1214439291; reference:[11] Spivak, M.: A Comprehensive Introduction to Riemannian Geometry.2nd ed., Publish or Perish, Wilmongton DE, 1979.; reference:[12] Thorpe, J.A.: Some remarks on the Gauss-Bonnet formula.J. Math. Mech. 18 (1969), 779–786.; reference:[13] Vaisman, I.: Conformal foliations.Kodai Math. J. 2 (1979), 26–37. 10.2996/kmj/1138035963; reference:[14] Yamabe, H.: On a deformation of Riemannian structures on compact manifolds.Osaka Math. J. 12 (1960), 21–37. Zbl 0096.37201
Authors: Godefroy, Gilles
Subject Terms: keyword:compact approximation property, keyword:Lipschitz map, keyword:Lipschitz-free Banach space, msc:46B20, msc:47A15
File Description: application/pdf
Relation: mr:MR4143704; zbl:Zbl 07286000; reference:[1] Borel-Mathurin L.: Approximation properties and non-linear geometry of Banach spaces.Houston J. Math. 38 (2012), no. 4, 1135–1148. MR 3019026; reference:[2] Casazza P.: Approximation Properties.Handbook of the Geometry of Banach Spaces, Vol. 1, North-Holland, Amsterdam, 2001, pages 271–316. MR 1863695, 10.1016/S1874-5849(01)80009-7; reference:[3] Cho C.-M., Johnson W. B.: A characterization of subspaces $X$ of $l_p$ for which $K(X)$ is an $M$-ideal in $L(X)$.Proc. Amer. Math. Soc. 93 (1985), no. 3, 466–470. MR 0774004; reference:[4] Godefroy G.: A survey on Lipschitz-free Banach spaces.Comment. Math. 55 (2015), no. 2, 89–118. MR 3518958; reference:[5] Godefroy G.: Extensions of Lipschitz functions and Grothendieck's bounded approximation property.North-West. Eur. J. Math. 1 (2015), 1–6. MR 3417417; reference:[6] Godefroy G., Kalton N. J.: Lipschitz-free Banach spaces.Studia Math. 159 (2003), no. 1, 121–141. MR 2030906, 10.4064/sm159-1-6; reference:[7] Godefroy G., Lancien G., Zizler V.: The non-linear geometry of Banach spaces after Nigel Kalton.Rocky Mountain J. Math. 44 (2014), no. 5, 1529–1584. MR 3295641, 10.1216/RMJ-2014-44-5-1529; reference:[8] Godefroy G., Ozawa N.: Free Banach spaces and the approximation properties.Proc. Amer. Math. Soc. 142 (2014), no. 5, 1681–1687. MR 3168474, 10.1090/S0002-9939-2014-11933-2; reference:[9] Jiménez-Vargas A., Sepulcre J. M., Villegas-Vallecillos M.: Lipschitz compact operators.J. Math. Anal. Appl. 415 (2014), no. 2, 889–901. MR 3178297, 10.1016/j.jmaa.2014.02.012; reference:[10] Kalton N. J.: Spaces of Lipschitz and Hölder functions and their applications.Collect. Math. 55 (2004), no. 2, 171–217. MR 2068975; reference:[11] Kalton N. J.: The uniform structure of Banach spaces.Math. Ann. 354 (2012), no. 4, 1247–1288. MR 2992997, 10.1007/s00208-011-0743-3; reference:[12] Oja E.: On bounded approximation properties of Banach spaces.Banach algebras 2009, Banach Center Publ., 91, Polish Acad. Sci. Inst. Math., Warsaw, 2010, pages 219–231. MR 2777497; reference:[13] Pernecka E., Smith R. J.: The metric approximation property and Lipschitz-free spaces over subsets of $\mathbb{R}^n$.J. Approx. Theory 199 (2015), 29–44. MR 3389905, 10.1016/j.jat.2015.06.003; reference:[14] Thele R. L.: Some results on the radial projection in Banach spaces.Proc. Amer. Math. Soc. 42 (1974), 483–486. MR 0328550, 10.1090/S0002-9939-1974-0328550-1; reference:[15] Willis G.: The compact approximation property does not imply the approximation property.Studia Math. 103 (1992), no. 1, 99–108. MR 1184105, 10.4064/sm-103-1-99-108
Subject Terms: keyword:bimatrix game, keyword:nash equilibrium, keyword:${\bf Z}$-transformation, keyword:semi positive map, msc:15A63, msc:90C33, msc:91A05
File Description: application/pdf
Relation: mr:MR4160787; zbl:07285951; reference:[1] Berman, A., Plemmons, R. J.: Nonnegative Matrices in the Mathematical Sciences.Classics in Applied Mathematics 9. SIAM, Philadelphia (1994). Zbl 0815.15016, MR 1298430, 10.1137/1.9781611971262; reference:[2] Cottle, R. W., Pang, J.-S., Stone, R. E.: The Linear Complementarity Problem.Computer Science and Scientific Computing. Academic Press, Boston (1992). Zbl 0757.90078, MR 1150683, 10.1137/1.9780898719000; reference:[3] Ferris, M. C., Pang, J. S.: Engineering and economic applications of complementarity problems.SIAM Rev. 39 (1997), 669-713. Zbl 0891.90158, MR 1491052, 10.1137/S0036144595285963; reference:[4] Fiedler, M., Pták, V.: On matrices with non-positive off-diagonal elements and positive principal minors.Czech. Math. J. 12 (1962), 382-400. Zbl 0131.24806, MR 0142565, 10.21136/CMJ.1962.100526; reference:[5] Gale, D., Nikaidô, H.: The Jacobian matrix and global univalence of mappings.Math. Ann. 159 (1965), 81-93. Zbl 0158.04903, MR 0204592, 10.1007/BF01360282; reference:[6] Gowda, M. S., Ravindran, G.: On the game-theoretic value of a linear transformation relative to a self-dual cone.Linear Algebra Appl. 469 (2015), 440-463. Zbl 1309.91008, MR 3299071, 10.1016/j.laa.2014.11.032; reference:[7] Gowda, M. S., Tao, J.: Z-transformations on proper and symmetric cones.Math. Program. 117 (2009), 195-221. Zbl 1167.90022, MR 2421305, 10.1007/s10107-007-0159-8; reference:[8] Isac, G.: Complementarity Problems.Lecture Notes in Mathematics 1528. Springer, Berlin (1992). Zbl 0795.90072, MR 1222647, 10.1007/BFb0084653; reference:[9] Kaneko, I.: A linear complementarity problem with an $n$ by $2n$ ``$P$''-matrix.Math. Program. Study 7 (1978), 120-141. Zbl 0378.90054, MR 0483316, 10.1007/BFb0120786; reference:[10] Kaneko, I.: Linear complementarity problems and characterizations of Minkowski matrices.Linear Algebra Appl. 20 (1978), 111-129. Zbl 0382.15011, MR 0480554, 10.1016/0024-3795(78)90045-9; reference:[11] Karamardian, S.: The complementarity problem.Math. Program. 2 (1972), 107-129. Zbl 0247.90058, MR 295762, 10.1007/BF01584538; reference:[12] Murty, K. G.: Linear Complementarity, Linear and Nonlinear Programming.Sigma Series in Applied Mathematics 3. Heldermann Verlag, Berlin (1988). Zbl 0634.90037, MR 0949214; reference:[13] Nikaidô, H.: Convex Structures and Economic Theory.Mathematics in Science and Engineering 51. Academic Press, New York (1968). Zbl 0172.44502, MR 0277233, 10.1016/S0076-5392(08)63326-3; reference:[14] Orlitzky, M. J.: Positive Operators, Z-Operators, Lyapunov Rank, and Linear Games on Closed Convex Cones: Ph.D. Thesis.University of Maryland, Baltimore County (2017). MR 3697664; reference:[15] Parthasarathy, T., Raghavan, T. E. S.: Some Topics in Two-Person Games.American Elsevier, New York (1971). Zbl 0225.90049, MR 0277260; reference:[16] Schneider, H., Vidyasagar, M.: Cross-positive matrices.SIAM J. Numer. Anal. 7 (1970), 508-519. Zbl 0245.15008, MR 0277550, 10.1137/0707041; reference:[17] Varga, R. S.: Matrix Iterative Analysis.Springer Series in Computational Mathematics 27. Springer, Berlin (2000). Zbl 0998.65505, MR 1753713, 10.1007/978-3-642-05156-2
Authors: Sakkalis, Takis
Subject Terms: keyword:ordinary polynomials, regular polynomials, Jacobians, degrees of maps, msc:11R52, msc:12E15, msc:26B10
File Description: application/pdf
Relation: mr:MR4124289; zbl:Zbl 1470.26021; reference:[1] Baez, J.C.: The octonions.Bull. Amer. Math. Soc., 39, 2002, 145-205, MR 1886087, 10.1090/S0273-0979-01-00934-X; reference:[2] Bourbaki, N.: General Topology, Part 2.1966, Hermann, Paris, MR 0141067; reference:[3] Eilenberg, S., Niven, I.: The ``fundamental theorem of algebra'' for quaternions.Bull. Amer. Math. Soc., 50, 4, 1944, 246-248, MR 0009588, 10.1090/S0002-9904-1944-08125-1; reference:[4] Gentili, G., Struppa, D.C.: On the multiplicity of zeros of polynomials with quaternionic coefficients.Milan J. Math., 76, 1, 2008, 15-25, MR 2465984, 10.1007/s00032-008-0093-0; reference:[5] Gentili, G., Struppa, D.C., Vlacci, F.: The fundamental theorem of algebra for Hamilton and Cayley numbers.Mathematische Zeitschrift, 259, 4, 2008, 895-902, Springer, MR 2403747, 10.1007/s00209-007-0254-9; reference:[6] Gordon, B., Motzkin, T.S.: On the zeros of polynomials over division rings.Transactions of the American Mathematical Society, 116, 1965, 218-226, JSTOR, MR 0195853, 10.1090/S0002-9947-1965-0195853-2; reference:[7] Milnor, J., Weaver, D.W.: Topology from the differentiable viewpoint.1997, Princeton University Press, MR 1487640; reference:[8] Rodríguez-Ordóñez, H.: A note on the fundamental theorem of algebra for the octonions.Expositiones Mathematicae, 25, 4, 2007, 355-361, Elsevier, MR 2360922, 10.1016/j.exmath.2007.02.005; reference:[9] Topuridze, N.: On the roots of polynomials over division algebras.Georgian Math. Journal, 10, 4, 2003, 745-762, Walter de Gruyter, MR 2037774, 10.1515/GMJ.2003.745
Availability: http://hdl.handle.net/10338.dmlcz/148260
Authors: Perktaş, Selcen Y., Acet, Bilal E., Blaga, Adara M.
Subject Terms: keyword:$f$-biharmonic maps, keyword:$f$-biharmonic hypersurface, msc:53C25, msc:53C43, msc:58E20
File Description: application/pdf
Relation: mr:MR4093434; zbl:Zbl 07217163; reference:[1] Caddeo R., Montaldo S., Oniciuc C.: Biharmonic submanifolds of $S^3$.Internat. J. Math. 12 (2001), no. 8, 867–876. MR 1863283; reference:[2] Chen B.-Y.: Some open problems and conjectures on submanifolds of finite type.Soochow J. Math. 17 (1991), no. 2, 169–188. MR 1143504; reference:[3] Cieśliński J., Sym A., Wesselius W.: On the geometry of the inhomogeneous Heisenberg ferromagnet: nonintegrable case.J. Phys. A. 26 (1993), no. 6, 1353–1364. MR 1212007, 10.1088/0305-4470/26/6/017; reference:[4] Eells J., Lemaire L.: A report on harmonic maps.Bull. London Math. Soc. 10 (1978), no. 1, 1–68. Zbl 0401.58003, MR 0495450, 10.1112/blms/10.1.1; reference:[5] Eells J. Jr., Sampson J. H.: Harmonic mappings of the Riemannian manifolds.Amer. J. Math. 86 (1964), 109–160. MR 0164306, 10.2307/2373037; reference:[6] Jiang G. Y.: $2$-harmonic isometric immersions between Riemannian manifolds.Chinese Ann. Math. Ser. A 7 (1986), no. 2, 130–144 (Chinese); English summary in Chinese Ann. Math. Ser. B 7 (1986), no. 2, 255. MR 0858581; reference:[7] Jiang G. Y.: $2$-harmonic maps and their first and second variation formulas.Chinese Ann. Math. Ser. A. 7 (1986), no. 4, 389–402 (Chinese); English summary in Chinese Ann. Math. Ser. B 7 (1986), no. 4, 523. MR 0886529; reference:[8] Keleş S., Perktaş S. Y., Kiliç E.: Biharmonic curves in Lorentzian para-Sasakian manifolds.Bull. Malays. Math. Sci. Soc. (2) 33 (2010), no. 2, 325–344. MR 2666434; reference:[9] Li Y., Wang Y.: Bubbling location for $F$-harmonic maps and inhomogeneous Landau-Lifshitz equations.Comment. Math. Helv. 81 (2006), no. 2, 433–448. MR 2225633; reference:[10] Lu W.-J.: On $f$-bi-harmonic maps and bi-$f$-harmonic maps between Riemannian manifolds.Sci. China Math. 58 (2015), no. 7, 1483–1498. MR 3353985, 10.1007/s11425-015-4997-1; reference:[11] Montaldo S., Oniciuc C.: A short survey on biharmonic maps between Riemannian manifolds.Rev. Un. Mat. Argentina 47 (2006), no. 2, 1–22. MR 2301373; reference:[12] Ou Y.-L.: Biharmonic hypersurfaces in Riemannian manifolds.Pacific J. Math. 248 (2010), no. 1, 217–232. MR 2734173, 10.2140/pjm.2010.248.217; reference:[13] Ou Y.-L.: Some constructions of biharmonic maps and Chen's conjecture on biharmonic hypersurfaces.J. Geom. Phys. 62 (2012), no. 4, 751–762. MR 2888980, 10.1016/j.geomphys.2011.12.014; reference:[14] Ou Y.-L.: On $f$-biharmonic maps and $f$-biharmonic submanifolds.Pacific J. Math. 271 (2014), no. 2, 461–477. MR 3267537, 10.2140/pjm.2014.271.461; reference:[15] Ou Y.-L., Tang L.: On the generalized Chen's conjecture on biharmonic submanifolds.Michigan Math. J. 61 (2012), no. 3, 531–542. MR 2975260, 10.1307/mmj/1347040257; reference:[16] Ou Y.-L., Wang Z.-P.: Constant mean curvature and totally umbilical biharmonic surfaces in $3$-dimensional geometries.J. Geom. Phys. 61 (2011), no. 10, 1845–1853. MR 2822453, 10.1016/j.geomphys.2011.04.008; reference:[17] Perktaş S. Y., Kiliç E.: Biharmonic maps between doubly warped product manifolds.Balkan J. Geom. Appl. 15 (2010), no. 2, 159–170. MR 2608547; reference:[18] Perktaş S. Y., Kiliç E., Keleş S.: Biharmonic hypersurfaces of LP-Sasakian manifolds.An. Ştiinţ. Univ. Al. I. Cuza Iaşi Mat. (N.S.) 57 (2011), no. 2, 387–408. MR 2933391; reference:[19] Rimoldi M., Veronelli G.: Topology of steady and expanding gradient Ricci solitons via $f$-harmonic maps.Differetial. Geom. Appl. 31 (2013), no. 5, 623–638. MR 3093493, 10.1016/j.difgeo.2013.06.001
Subject Terms: keyword:harmonic vector field, keyword:harmonic map, keyword:oscillator group, msc:53C25, msc:53C43
File Description: application/pdf
Relation: mr:MR4039609; zbl:07144864; reference:[1] Boeckx, E., Vanhecke, L.: Harmonic and minimal vector fields on tangent and unit tangent bundles.Differ. Geom. Appl. 13 (2000), 77-93. Zbl 0973.53053, MR 1775222, 10.1016/s0926-2245(00)00021-8; reference:[2] Boeckx, E., Vanhecke, L.: Harmonic and minimal radial vector fields.Acta Math. Hung. 90 (2001), 317-331. Zbl 1012.53040, MR 1910716, 10.1023/a:1010687231629; reference:[3] Boothby, W. M.: An Introduction to Differentiable Manifolds and Riemannian Geometry.Pure and Applied Mathematics 120, Academic Press, Orlando (1986). Zbl 0596.53001, MR 0861409, 10.1016/S0079-8169(08)61173-3; reference:[4] Boucetta, M., Medina, A.: Solutions of the Yang-Baxter equations on quadratic Lie groups: the case of oscillator groups.J. Geom. Phys. 61 (2011), 2309-2320. Zbl 1226.53070, MR 2838508, 10.1016/j.geomphys.2011.07.004; reference:[5] Calvaruso, G.: Harmonicity of vector fields on four-dimensional generalized symmetric spaces.Cent. Eur. J. Math. 10 (2012), 411-425. Zbl 1246.53083, MR 2886549, 10.2478/s11533-011-0109-9; reference:[6] Díaz, R. D., Gadea, P. M., Oubiña, J. A.: Reductive decompositions and Einstein-Yang-Mills equations associated to the oscillator group.J. Math. Phys. 40 (1999), 3490-3498. Zbl 0978.53095, MR 1696968, 10.1063/1.532902; reference:[7] Gadea, P. M., Oubiña, J. A.: Homogeneous Lorentzian structures on the oscillator groups.Arch. Math. 73 (1999), 311-320. Zbl 0954.53029, MR 1710084, 10.1007/s000130050403; reference:[8] Gil-Medrano, O.: Relationship between volume and energy of vector fields.Differ. Geom. Appl. 15 (2001), 137-152. Zbl 1066.53068, MR 1857559, 10.1016/s0926-2245(01)00053-5; reference:[9] González-Dávila, J. C., Vanhecke, L.: Examples of minimal unit vector fields.Ann. Global Anal. Geom. 18 (2000), 385-404. Zbl 1005.53026, MR 1795104, 10.1023/a:1006788819180; reference:[10] González-Dávila, J. C., Vanhecke, L.: Minimal and harmonic characteristic vector fields on three-dimensional contact metric manifolds.J. Geom. 72 (2001), 65-76. Zbl 1005.53039, MR 1891456, 10.1007/s00022-001-8570-4; reference:[11] González-Dávila, J. C., Vanhecke, L.: Energy and volume of unit vector fields on three-dimensional Riemannian manifolds.Differ. Geom. Appl. 16 (2002), 225-244. Zbl 1035.53089, MR 1900746, 10.1016/s0926-2245(02)00060-8; reference:[12] Levichev, A. V.: Chronogeometry of an electromagnetic wave given by a bi-invariant metric on the oscillator group.Sib. Math. J. 27 (1986), 237-245 English. Russian original translation from Sib. Mat. Zh. 27 1986 117-126. Zbl 0602.53057, MR 0890307, 10.1007/bf00969391; reference:[13] Medina, A.: Groupes de Lie munis de métriques bi-invariantes.Tohoku Math. J. 2 37 French (1985), 405-421. Zbl 0583.53053, MR 0814072, 10.2748/tmj/1178228586; reference:[14] Milnor, J. W.: Curvatures of left invariant metrics on Lie groups.Adv. Math. 21 (1976), 293-329. Zbl 0341.53030, MR 0425012, 10.1016/s0001-8708(76)80002-3; reference:[15] Onda, K.: Examples of algebraic Ricci solitons in the pseudo-Riemannian case.Acta Math. Hung. 144 (2014), 247-265. Zbl 1324.53063, MR 3267185, 10.1007/s10747-014-0426-0; reference:[16] Tsukada, K., Vanhecke, L.: Minimality and harmonicity for Hopf vector fields.Ill. J. Math. 45 (2001), 441-451. Zbl 0997.53040, MR 1878613, 10.1215/ijm/1258138349; reference:[17] Vanhecke, L., González-Dávila, J. C.: Invariant harmonic unit vector fields on Lie groups.Boll. Unione Mat. Ital., Sez. B, Artic. Ric. Mat. (8) 5 (2002), 377-403. Zbl 1097.53033, MR 1911197; reference:[18] Wiegmink, G.: Total bending of vector fields on Riemannian manifolds.Math. Ann. 303 (1995), 325-344. Zbl 0834.53034, MR 1348803, 10.1007/bf01460993
Subject Terms: keyword:antilinear map, keyword:$\ast $-structure, keyword:Hopf $\ast $-algebra, msc:16G99, msc:16T05
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Authors: Iacono, Donatella, Manetti, Marco
Subject Terms: keyword:differential graded Lie algebras, keyword:adjoint map, keyword:cofibrant resolutions, msc:17B70, msc:18G55
File Description: application/pdf
Relation: mr:MR3939059; zbl:Zbl 07088753; reference:[1] Bandiera, R.: Nonabelian higher derived brackets.J. Pure Appl. Algebra 219 (2015), 3292–3313. MR 3320220, 10.1016/j.jpaa.2014.10.015; reference:[2] Bandiera, R.: Homotopy abelian $L_\infty $ algebras and splitting property.Rend. Mat. Appl. 37 (2016), 105–122, http://www1.mat.uniroma1.it/ricerca/rendiconti/37_1-2_(2016)_105-122.html. MR 3622306; reference:[3] Hinich, V.: Homological algebra of homotopy algebras.Comm. Algebra 25 (1997), 3291–3323. MR 1465117, 10.1080/00927879708826055; reference:[4] Iacono, D.: On the abstract Bogomolov-Tian-Todorov theorem.Rend. Mat. Appl. 38 (2017), 175–198, http://www1.mat.uniroma1.it/ricerca/rendiconti/38_2_(2017)_175-198.html. MR 3762711; reference:[6] Manetti, M.: On some formality criteria for DG-Lie algebras.J. Algebra 438 (2015), 90–118. MR 3353026, 10.1016/j.jalgebra.2015.04.029
Authors: Bennouar, Abdelmadjid, Ouakkas, Seddik
Subject Terms: keyword:harmonic map, keyword:biharmonic map, keyword:warped product, msc:31B30, msc:53C25, msc:58E20, msc:58E30
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Relation: mr:MR3737120; zbl:Zbl 06837081; reference:[1] Baird P.: Harmonic maps with symmetry, harmonic morphisms and deformation of metrics.Pitman Books Limited, Boston, MA, 1983, pp. 27–39. MR 0716320; reference:[2] Baird P., Eells J.: A conservation law for harmonic maps.Lecture Notes in Math., 894, Springer, Berlin-New York, 1981, pp. 1–25. Zbl 0485.58008, MR 0655417, 10.1007/BFb0096222; reference:[3] Baird P., Wood J.C.: Harmonic Morphisms between Riemannian Manifolds.London Mathematical Society Monographs, 29, Oxford University Press, Oxford, 2003. Zbl 1055.53049, MR 2044031; reference:[4] Baird P., Kamissoko D.: On constructing biharmonic maps and metrics.Ann. Global Anal. Geom. 23 (2003), 65–75. Zbl 1027.31004, MR 1952859, 10.1023/A:1021213930520; reference:[5] Baird P., Fardoun A., Ouakkas S.: Conformal and semi-conformal biharmonic maps.Ann. Global Anal. Geom. 34 (2008), 403–414. Zbl 1158.53049, MR 2447908, 10.1007/s10455-008-9118-8; reference:[6] Balmus A.: Biharmonic properties and conformal changes.An. Stiint. Univ. Al. I. Cuza Iasi Mat. (N.S.) 50 (2004), 361–372. Zbl 1070.58016, MR 2131943; reference:[7] Balmus A., Montaldo S., Oniciuc C.: Biharmonic maps between warped product manifolds.J. Geom. Phys. 57 (2008), 449–466. Zbl 1108.58011, MR 2271198, 10.1016/j.geomphys.2006.03.012; reference:[8] Bertola M., Gouthier D.: Lie triple systems and warped products.Rend. Mat. Appl. (7) 21 (2001), 275–293. Zbl 1057.53020, MR 1884948; reference:[9] Eells J., Lemaire L.: A report on harmonic maps.Bull. London Math. Soc. 16 (1978), 1–68. Zbl 0401.58003, MR 0495450, 10.1112/blms/10.1.1; reference:[10] Eells J., Lemaire L.: Another report on harmonic maps.Bull. London Math. Soc. 20 (1988), 385–524. Zbl 0669.58009, MR 0956352, 10.1112/blms/20.5.385; reference:[11] Eells J., Lemaire L.: Selected Topics in Harmonic Maps.CNMS Regional Conference Series of the National Sciences Foundation, November 1981. Zbl 0515.58011, MR 0703510; reference:[12] Eells J., Ratto A.: Harmonic Maps and Minimal Immersions with Symmetries.Princeton University Press, Princeton, NJ, 1993. Zbl 0783.58003, MR 1242555; reference:[13] Jiang G.Y.: $2$-harmonic maps and their first and second variational formulas.Chinese Ann. Math. Ser. A 7 (1986), 389–402. Zbl 1200.58015, MR 0886529; reference:[14] Djaa N.E.H., Boulal A., Zagane A.: Generalized warped product manifolds and biharmonic maps.Acta Math. Univ. Comenian. 81 (2012), no. 2, 283–298. Zbl 1274.53093, MR 2975295; reference:[15] Lu W.J.: Geometry of warped product manifolds and its five applications.PhD Thesis, Zhejiang University, 2013.; reference:[16] Lu W.J.: $f$-Harmonic maps of doubly warped product manifolds.Appl. Math. J. Chinese Univ. Ser. B 28 (2013), no. 2, 240–252. MR 3066461, 10.1007/s11766-013-2969-1; reference:[17] Oniciuc C.: New examples of biharmonic maps in spheres.Colloq. Math. 97 (2003), 131–139. Zbl 1058.58003, MR 2010548, 10.4064/cm97-1-12; reference:[18] Ouakkas S.: Biharmonic maps, conformal deformations and the Hopf maps.Diff. Geom. Appl. 26 (2008), 495–502. Zbl 1159.58009, MR 2458275, 10.1016/j.difgeo.2008.04.006; reference:[19] Ou Y.-L.: p-harmonic morphisms, biharmonic morphisms, and non-harmonic biharmonic maps.J. Geom. Phys. 56 (2006), no. 3, 358–374. MR 2171890, 10.1016/j.geomphys.2005.02.005; reference:[20] Perktas S.Y., Kilic E.: Biharmonic maps between doubly warped product manifolds.Balkan J. Geom. Appl. 15 (2010), no. 2, 159–170. Zbl 1225.58008, MR 2608547
Authors: Havelka, Jan, Sýkora, Jan
Subject Terms: keyword:Calderón problem, keyword:finite element method, keyword:diffusion equation, keyword:boundary inverse value method, keyword:Neumann-to-Dirichlet map, msc:35K05, msc:65M32
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Authors: Bayer, Tomáš, Kočandrlová, Milada
Subject Terms: keyword:mathematical cartography, keyword:inverse projection, keyword:analysis, keyword:nonlinear least squares, keyword:partial differential equation, keyword:optimization, keyword:hybrid BFGS, keyword:early map, keyword:re-projection, msc:34B16, msc:34C25, msc:35F50, msc:35R30, msc:65K10
File Description: application/pdf
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Authors: Kozerenko, Sergiy
Subject Terms: keyword:Markov graph, keyword:Sharkovsky's theorem, keyword:maps on trees, msc:05C05, msc:05C20, msc:37E15
File Description: application/pdf
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