يعرض 1 - 10 نتائج من 8,202 نتيجة بحث عن '"F', وقت الاستعلام: 1.14s تنقيح النتائج
  1. 1
    دورية أكاديمية

    المؤلفون: Chen, Xi, Tao, Xinran, Wang, Xuejun

    وصف الملف: application/pdf

    العلاقة: mr:MR4567839; zbl:Zbl 07675640; reference:[1] Adler, A., Rosalsky, A.: Some general strong laws for weighted sums of stochastically dominated random variables.Stoch. Anal. Appl. 5 (1987), 1-16. Zbl 0617.60028, MR 0882694; reference:[2] Adler, A., Rosalsky, A., Taylor, R. L.: Strong laws of large numbers for weighted sums of random elements in normed linear spaces.Int. J. Math. Math. Sci. 12 (1989), 507-530. MR 1007204, 10.1155/S0161171289000657; reference:[3] Chen, P. Y., Sung, S. H.: A Spitzer-type law of large numbers for widely orthant dependent random variables.Statist. Probab. Lett. 2054 (2019), 1-8, Article ID 108544. MR 3980503; reference:[4] Chow, Y. S.: On the rate of moment convergence of sample sums and extremes.Bull. Inst. Math., Academia Sinica 16 (1988), 177-201. MR 1089491; reference:[5] Georgiev, A. A.: Local properties of function fitting estimates with applications to system identification.In: Mathematics Statistics and Applications. Proceedings 4th Pannonian Symposium on Mathematical Statistics 1983, (W. Grossmann, ed.). vol. B, Bad Tatzmannsdorf, Austria, Reidel, Dordrecht, pp. 141-51. MR 0851050; reference:[6] Georgiev, A. A., Greblicki, W.: Nonparametric function recovering from noisy observations.J. Statist. Plann. Inference 13 (1986), 1-14. MR 0822121; reference:[7] He, Q. H.: Consistency of the Priestley-Chao estimator in nonparametric regression model with widely orthant dependent errors.J. Inequal. Appl. 2019 (2019), 1-13, Article ID 64. MR 3923002; reference:[8] Hsu, P. L., Robbins, H.: Complete convergence and the law of large numbers.Proc. National Acad. Sci. Unit. States Amer. 33 (1947), 25-31. Zbl 0030.20101, MR 0019852; reference:[9] Joag-Dev, K., Proschan, F.: Negative association of random variables with applications.Ann. Statist. 11 (1983), 286-295. MR 0684886; reference:[10] Lang, J. J., He, T. Y., Cheng, L., Lu, C., Wang, X. J.: Complete convergence for weighted sums of widely orthant-dependent random variables and its statistical application.Revista Mat. Complut. 34 (2021), 853-881. MR 4302244; reference:[11] Li, Y. M., Zhou, Y., Liu, C.: On the convergence rates of kernel estimator and hazard estimator for widely dependent samples.J. Inequal. Appl. 2018 (2018), 1-10, Article ID 71. MR 3782674; reference:[12] Liang, H. Y., Jing, B. Y.: Asymptotic properties for estimates of nonparametric regression models based on negatively associated sequences.J. Multivar. Anal. 95 (2005), 227-245. MR 2170396; reference:[13] Liang, H. Y., Zhang, J. J.: Strong convergence for weighted sums of negatively associated arrays.Chinese Annals of Mathematics 31B (2010), 273-288. MR 2607650; reference:[14] Lu, C., Chen, Z., Wang, X. J.: Complete $f$-moment convergence for widely orthant dependent random variables and its application in nonparametric models.Acta Math. Sinica, English Series 35 (2019), 1917-1936. MR 4033590; reference:[15] Hu, D. H. Qiu abd T. C.: Strong limit theorems for weighted sums of widely orthant dependent random variables.J. Math. Res. Appl. 34 (2014), 105-113. MR 3220656; reference:[16] Qiu, D. H., Chen, P. Y.: Complete and complete moment convergence for weighted sums of widely orthant dependent random variables.Acta Math. Sinica, English Series 30 (2014), 1539-1548. MR 3245935; reference:[17] Roussas, G. G., Tran, L. T., Ioannides, D. A.: Fixed design regression for time series: asymptotic.J. Multivar. Anal. 40 (1992), 262-291. MR 1150613; reference:[18] Shen, A.T.: Complete convergence for weighted sums of END random variables and its application to nonparametric regression models.J. Nonparametr. Statist. 28 (2016), 702-715. MR 3555453; reference:[19] Shen, A. T., Wu, C. Q.: Complete $q$th moment convergence and its statistical applications.RACSAM 114 (2019), 1-25, Article ID 35. MR 4042305; reference:[20] Shen, A. T., Yao, M., Wang, W. J., Volodin, A.: Exponential probability inequalities for WNOD random variables and their applications.RACSAM 110 (2016), 251-268. MR 3462086; reference:[21] Shen, A. T., Zhang, S. Y.: On complete consistency for the estimator of nonparametric regression model based on asymptotically almost negatively associated errors.Methodol. Comput. Appl. Probab. 23 (2021), 1285-1307. MR 4335161; reference:[22] Shen, A. T., Zhang, Y., Volodin, A.: Applications of the Rosenthal-type inequality for negatively super-additive dependent random variables.Metrika 78 (2015), 295-311. MR 3320899; reference:[23] Stout, W. F.: Almost Sure Convergence.Academic Press, New York 1974. MR 0455094; reference:[24] Stone, C. J.: Consistent nonparametric regression regression.Ann. Statist. 5 (1977), 595-620. MR 0443204, 10.1214/aos/1176343886; reference:[25] Tran, L., Roussas, G., Yakowitz, S., Truong, V. B.: Fixed design regression for linear time series.Ann. Statist. 24 (1996), 975-991. MR 1401833; reference:[26] Wang, Y., Wang, X. J.: Complete $f$-moment convergence for Sung's type weighted sums and its application to the EV regression models.Statist. Papers 62 (2021), 769-793. MR 4232917; reference:[27] Wang, K. Y., Wang, Y. B., Gao, Q. W.: Uniform asymptotics for the finite-time ruin probability of a dependent risk model with a constant interest rate.Methodol. Comput. Appl. Probab. 15 (2013), 109-124. MR 3030214; reference:[28] Xi, M. M., Wang, R., Cheng, Z. Y., Wang, X. J.: Some convergence properties for partial sums of widely orthant dependent random variables and their statistical applications.Statist. Papers 61 (2020), 1663-1684. MR 4127491; reference:[29] Wu, Q. Y.: Probability Limit Theory for Mixing Sequences.Science Press of China, Beijing 2006.; reference:[30] Wu, Y., Wang, X. J., Hu, S. H.: Complete moment convergence for weighted sums of weakly dependent random variables and its application in nonparametric regression model.Statist. Probab. Lett. 127 (2017), 56-66. MR 3648295; reference:[31] Wu, Y., Wang, X. J., Hu, T. C., Volodin, A.: Complete $f$-moment convergence for extended negatively dependent random variables.RACSAM 113 (2019), 333-351. MR 3942340, 10.1007/s13398-017-0480-x; reference:[32] Wu, Y., Wang, X. J., Rosalsky, A.: Complete moment convergence for arrays of rowwise widely orthant dependent random variables.Acta Math. Sinica, English Series 34 (2018), 1531-1548. MR 3854379; reference:[33] Wu, Y., Wang, X. J., Shen, A. T.: Strong convergence properties for weighted sums of m-asymptotic negatively associated random variables and statistical applications.Statist. Papers 62 (2021), 2169-94. MR 4314255; reference:[34] Yang, W. Z., Xu, H. Y., Chen, L., Hu, aand S. H.: Complete consistency of estimators for regression models based on extended negatively dependent.Statist. Papers 59 (2018), 449-465. MR 3800809; reference:[35] Zhang, S. L., Qu, C., Hou, T. T.: Limit behaviors of the estimator of nonpar ametric regression model based on extended negatively dependent errors.Commun. Statist. - Theory Methods, 2022, in press. MR 4198622; reference:[36] Zhou, X. C., Lin, J. G., Yin, C. M.: Asymptotic properties of wavelet-based estimator in nonparametric regression model with weakly dependent processes.J. Inequal. Appl. 2013 (2013), 1-18, Article ID 261. MR 3068636; reference:[37] Wang, X. J., Xu, C., Hu, T. C., Volodin, A., Hu, S. H.: On complete convergence for widely orthant-dependent random variables and its applications in nonparametric regression models.TEST 23 (2014), 607-629. MR 3252097

  2. 2
    دورية أكاديمية

    المؤلفون: Xu, Chunxu, Yu, Tao

    وصف الملف: application/pdf

    العلاقة: reference:[1] Abreu, L. D., Faustino, N.: On Toeplitz operators and localization operators.Proc. Am. Math. Soc. 143 (2015), 4317-4323. Zbl 1321.47055, MR 3373930, 10.1090/proc/12211; reference:[2] Coburn, L. A.: The Bargmann isometry and Gabor-Daubechies wavelet localization operators.Systems, Approximation, Singular Integral Operators, and Related Topics Operator Theory: Advances and Applications 129. Birkhäuser, Basel (2001), 169-178. Zbl 1005.47033, MR 1882695, 10.1007/978-3-0348-8362-7_7; reference:[3] Cordero, E., Gröchenig, K.: Time-frequency analysis of localization operators.J. Funct. Anal. 205 (2003), 107-131. Zbl 1047.47038, MR 2020210, 10.1016/S0022-1236(03)00166-6; reference:[4] Daubechies, I.: Time-frequency localization operators: A geometric phase space approach.IEEE Trans. Inf. Theory 34 (1988), 605-612. Zbl 0672.42007, MR 0966733, 10.1109/18.9761; reference:[5] Engliš, M.: Toeplitz operators and group representations.J. Fourier Anal. 13 (2007), 243-265. Zbl 1128.47029, MR 2334609, 10.1007/s00041-006-6009-x; reference:[6] Engliš, M.: Toeplitz operators and localization operators.Trans. Am. Math. Soc. 361 (2009), 1039-1052. Zbl 1165.47019, MR 2452833, 10.1090/S0002-9947-08-04547-9; reference:[7] Feichtinger, H. G., Nowak, K.: A Szegö-type theorem for Gabor-Toeplitz localization operators.Mich. Math. J. 49 (2001), 13-21. Zbl 1010.47021, MR 1827072, 10.1307/mmj/1008719032; reference:[8] Hu, Z., Lv, X.: Toeplitz operators from one Fock space to another.Integral Equations Oper. Theory 70 (2011), 541-559. Zbl 1262.47044, MR 2819157, 10.1007/s00020-011-1887-y; reference:[9] Isralowitz, J., Zhu, K.: Toeplitz operators on the Fock space.Integral Equations Oper. Theory 66 (2010), 593-611. Zbl 1218.47046, MR 2609242, 10.1007/s00020-010-1768-9; reference:[10] Lo, M.-L.: The Bargmann transform and windowed Fourier localization.Integral Equations Oper. Theory 57 (2007), 397-412. Zbl 1141.47025, MR 2307818, 10.1007/s00020-006-1462-0; reference:[11] Luecking, D. H.: Trace ideal criteria for Toeplitz operators.J. Funct. Anal. 73 (1987), 345-368. Zbl 0618.47018, MR 0899655, 10.1016/0022-1236(87)90072-3; reference:[12] Rudin, W.: Functional Analysis.International Series in Pure and Applied Mathematics. McGraw-Hill, New York (1991). Zbl 0867.46001, MR 1157815; reference:[13] Suárez, D.: Approximation and symbolic calculus for Toeplitz algebras on the Bergman space.Rev. Mat. Iberoam. 20 (2004), 563-610. Zbl 1057.32005, MR 2073132, 10.4171/RMI/401; reference:[14] Suárez, D.: A generalization of Toeplitz operators on the Bergman space.J. Oper. Theory 73 (2015), 315-332. Zbl 1399.32010, MR 3346124, 10.7900/jot.2013nov28.2023; reference:[15] Wang, X., Cao, G., Zhu, K.: Boundedness and compactness of operators on the Fock space.Integral Equations Oper. Theory 77 (2013), 355-370. Zbl 1317.47026, MR 3116663, 10.1007/s00020-013-2066-0; reference:[16] Xu, C., Yu, T.: Schatten class generalized Toeplitz operators on the Bergman space.Czech. Math. J. 71 (2021), 1173-1188. Zbl 07442483, MR 4339120, 10.21136/CMJ.2021.0336-20; reference:[17] Zhu, K.: Positive Toeplitz operators on the weighted Bergman spaces of bounded symmetric domains.J. Oper. Theory 20 (1988), 329-357. Zbl 0676.47016, MR 1004127; reference:[18] Zhu, K.: Operator Theory in Function Spaces.Mathematical Surveys and Monographs 138. AMS, Providence (2007). Zbl 1123.47001, MR 2311536, 10.1090/surv/138; reference:[19] Zhu, K.: Analysis on Fock Spaces.Graduate Texts in Mathematics 263. Springer, New York (2012). Zbl 1262.30003, MR 2934601, 10.1007/978-1-4419-8801-0

  3. 3
    دورية أكاديمية

    المؤلفون: Chen, Zhiqi, Li, Jifu, Ding, Ming

    وصف الملف: application/pdf

    العلاقة: mr:MR4517607; zbl:Zbl 07655794; reference:[1] Bai, C., Meng, D.: The classification of Novikov algebras in low dimensions.J. Phys. A, Math. Gen. 34 (2001), 1581-1594. Zbl 1001.17002, MR 1818753, 10.1088/0305-4470/34/8/305; reference:[2] Basalaev, A., Hertling, C.: 3-dimensional $F$-manifolds.Lett. Math. Phys. 111 (2021), Article ID 90, 50 pages. Zbl 1471.32040, MR 4282746, 10.1007/s11005-021-01432-y; reference:[3] Hassine, A. Ben, Chtioui, T., Maalaoui, M. A., Mabrouk, S.: On Hom-$F$-manifold algebras and quantization.Available at https://arxiv.org/abs/2102.05595Test (2021), 23 pages. MR 4456933; reference:[4] Morales, J. A. Cruz, Gutierrez, J. A., Torres-Gomez, A.: $F$-algebra-Rinehart pairs and super $F$-algebroids.Available at https://arxiv.org/abs/1904.04724v2Test (2019), 14 pages. MR 4515932; reference:[5] Chari, V., Pressley, A.: A Guide to Quantum Groups.Cambridge University Press, Cambridge (1994). Zbl 0839.17010, MR 1300632; reference:[6] Ding, M., Chen, Z., Li, J.: $F$-manifold color algebras.Available at https://arxiv.org/abs/2101.00959v2Test (2021), 13 pages.; reference:[7] Dotsenko, V.: Algebraic structures of $F$-manifolds via pre-Lie algebras.Ann. Mat. Pura Appl. (4) 198 (2019), 517-527. Zbl 07041963, MR 3927168, 10.1007/s10231-018-0787-z; reference:[8] Dubrovin, B.: Geometry of 2D topological field theories.Integrable Systems and Quantum Groups Lecture Notes in Mathematics 1620. Springer, Berlin (1996), 120-348. Zbl 0841.58065, MR 1397274, 10.1007/BFb0094793; reference:[9] Fulton, W., Harris, J.: Representation Theory: A First Course.Graduate Texts in Mathematics 129. Springer, New York (1991). Zbl 0744.22001, MR 1153249, 10.1007/978-1-4612-0979-9; reference:[10] Hertling, C.: Frobenius Manifolds and Moduli Spaces for Singularities.Cambridge Tracts in Mathematics 151. Cambridge University Press, Cambridge (2002). Zbl 1023.14018, MR 1924259, 10.1017/CBO9780511543104; reference:[11] Hertling, C., Manin, Y.: Weak Frobenius manifolds.Int. Math. Res. Not. 1999 (1999), 277-286. Zbl 0960.58003, MR 1680372, 10.1155/S1073792899000148; reference:[12] Liu, J., Bai, C., Sheng, Y.: Noncommutative Poisson bialgebras.J. Algebra 556 (2020), 35-66. Zbl 1475.17038, MR 4082054, 10.1016/j.jalgebra.2020.03.009; reference:[13] Liu, J., Sheng, Y., Bai, C.: $F$-manifold algebras and deformation quantization via pre-Lie algebras.J. Algebra 559 (2020), 467-495. Zbl 1442.17003, MR 4097911, 10.1016/j.jalgebra.2020.04.029; reference:[14] Ni, X., Bai, C.: Poisson bialgebras.J. Math. Phys. 54 (2013), Article ID 023515, 14 pages. Zbl 1290.17019, MR 3076642, 10.1063/1.4792668; reference:[15] Patera, J., Sharp, R. T., Winternitz, P., Zassenhaus, H.: Invariants of real low dimension Lie algebras.J. Math. Phys. 17 (1976), 986-994. Zbl 0357.17004, MR 0404362, 10.1063/1.522992; reference:[16] Šnobl, L., Winternitz, P.: Classification and Identification of Lie Algebras.CRM Monograph Series 33. AMS, Providence (2014). Zbl 1331.17001, MR 3184730, 10.1090/crmm/033; reference:[17] Uchino, K.: Quantum analogy of Poisson geometry, related dendriform algebras and Rota-Baxter operators.Lett. Math. Phys. 85 (2008), 91-109. Zbl 1243.17002, MR 2443932, 10.1007/s11005-008-0259-2

  4. 4
    دورية أكاديمية

    المؤلفون: Kostić, Marko

    وصف الملف: application/pdf

    العلاقة: mr:MR4221838; zbl:07286017; reference:[1] Bayart, F., Grivaux, S.: Frequently hypercyclic operators.Trans. Am. Math. Soc. 358 (2006), 5083-5117. Zbl 1115.47005, MR 2231886, 10.1090/S0002-9947-06-04019-0; reference:[2] Bayart, F., Matheron, É.: Dynamics of Linear Operators.Cambridge Tracts in Mathematics 179. Cambridge University Press, Cambridge (2009). Zbl 1187.47001, MR 2533318, 10.1017/CBO9780511581113; reference:[3] Bès, J., Menet, Q., Peris, A., Puig, Y.: Strong transitivity properties for operators.Available at http://arxiv.org/pdf/arxiv:1703.03724Test. MR 3906215; reference:[4] Bondy, J. A., Murty, U. S. R.: Graph Theory with Applications.American Elsevier Publishing, New York (1976). Zbl 1226.05083, MR 0411988, 10.1007/978-1-349-03521-2; reference:[5] Bonilla, A., Grosse-Erdmann, K.-G.: Frequently hypercyclic operators and vectors.Ergodic Theory Dyn. Syst. 27 (2007), 383-404 erratum ibid. 29 2009 1993-1994. Zbl 1119.47011, MR 2308137, 10.1017/S014338570600085X; reference:[6] Bonilla, A., Grosse-Erdmann, K.-G.: Upper frequent hypercyclicity and related notions.Rev. Mat. Complut. 31 (2018), 673-711. Zbl 06946767, MR 3847081, 10.1007/s13163-018-0260-y; reference:[7] Chartrand, G., Lesniak, L.: Graphs and Digraphs.The Wadsworth & Brooks/Cole Mathematics Series. Wadsworth & Brooks/Cole Advanced Brooks & Software. VIII, Monterey (1986). Zbl 0666.05001, MR 0834583; reference:[8] Chen, C.-C., Conejero, J. A., Kostić, M., Murillo-Arcila, M.: Dynamics of multivalued linear operators.Open Math. 15 (2017), 948-958. Zbl 06751707, MR 3674105, 10.1515/math-2017-0082; reference:[9] Chen, C.-C., Conejero, J. A., Kostić, M., Murillo-Arcila, M.: Dynamics on binary relations over topological spaces.Symmetry 10 (2018), 12 pages. 10.3390/sym10060211; reference:[10] Cvetković, D., Doobs, M., Sachs, H.: Spectra of Graphs: Theory and Applications.VEB Deutscher Verlag der Wissenschaften, Berlin (1980). Zbl 0458.05042, MR 0572262; reference:[11] Cvetković, D., Rowlinson, P., Simić, S.: Eigenspaces of Graphs.Encyclopedia of Mathematics and Its Applications 66. Cambrige University Press, Cambridge (1997). Zbl 0878.05057, MR 1440854, 10.1017/CBO9781139086547; reference:[12] Fürstenberg, H.: Recurrence in Ergodic Theory and Combinatorial Number Theory.M. B. Porter Lectures, Rice University, Department of Mathematics, 1978. Princeton University Press, Princeton (1981). Zbl 0459.28023, MR 0603625; reference:[13] Grosse-Erdmann, K.-G., Manguillot, A. Peris: Linear Chaos.Universitext. Springer, Berlin (2011). Zbl 1246.47004, MR 2919812, 10.1007/978-1-4471-2170-1; reference:[14] Kostić, M.: ${\mathcal F}$-hypercyclic linear operators on Fréchet spaces. 10.13140/RG.2.2.26696.42245; reference:[15] Kostić, M.: $\mathcal{F}$-hypercyclic extensions and disjoint ${\mathcal F}$-hypercyclic extensions of binary relations over topological spaces.Funct. Anal. Approx. Comput. 10 (2018), 41-52. Zbl 06902499, MR 3804275; reference:[16] Mart'ı{n}ez-Avendaño, R. A.: Hypercyclicity of shifts on weighted {$L^p$} spaces of directed trees.J. Math. Anal. Appl. 446 (2017), 823-842. Zbl 1346.05032, MR 3554758, 10.1016/j.jmaa.2016.08.066; reference:[17] Menet, Q.: Linear chaos and frequent hypercyclicity.Trans. Am. Math. Soc. 369 (2017), 4977-4994. Zbl 06705106, MR 3632557, 10.1090/tran/6808; reference:[18] Moon, J. W.: Topics on Tournaments.Holt, Rinehart and Winston, New York (1968). Zbl 0191.22701, MR 0256919; reference:[19] Moon, J. W., Pullman, N. J.: On the powers of tournament matrices.J. Comb. Theory 3 (1967), 1-9. Zbl 0166.00901, MR 0213264, 10.1016/S0021-9800(67)80009-7; reference:[20] Namayanja, P.: Chaotic dynamics in a transport equation on a network.Discrete Contin. Dyn. Syst., Ser. B 23 (2018), 3415-3426. Zbl 06996836, MR 3848206, 10.3934/dcdsb.2018283; reference:[21] Petrović, V.: Graph Theory.University of Novi Sad, Novi Sad (1998), Serbian.

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    وصف الملف: application/pdf

    العلاقة: 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

  6. 6
    دورية أكاديمية

    المؤلفون: Zhao, Yan, Liu, Ximin

    وصف الملف: application/pdf

    العلاقة: mr:MR4039608; zbl:07144863; reference:[1] Balmuş, A., Montaldo, S., Oniciuc, C.: Classification results for biharmonic submanifolds in spheres.Isr. J. Math. 168 (2008), 201-220. Zbl 1172.58004, MR 2448058, 10.1007/s11856-008-1064-4; reference:[2] Bayle, V.: Propriétés de concavité du profil isopérimétrique et applications.These de Doctorat, Université Joseph-Fourier, Grenoble French (2003).; reference:[3] Caddeo, R., Montaldo, S., Oniciuc, C.: Biharmonic submanifolds of $\mathbb S^{3}$.Int. J. Math. 12 (2001), 867-876. Zbl 1111.53302, MR 1863283, 10.1142/S0129167X01001027; reference:[4] Caddeo, R., Montaldo, S., Oniciuc, C.: Biharmonic submanifolds in spheres.Isr. J. Math. 130 (2002), 109-123. Zbl 1038.58011, MR 1919374, 10.1007/BF02764073; reference:[5] Chen, B.-Y.: Some open problems and conjectures on submanifolds of finite type.Soochow J. Math. 17 (1991), 169-188. Zbl 0749.53037, MR 1143504; reference:[6] Chen, B.-Y., Ishikawa, S.: Biharmonic pseudo-Riemannian submanifolds in pseudo-Euclidean spaces.Kyushu J. Math. 52 (1998), 167-185. Zbl 0892.53012, MR 1609044, 10.2206/kyushujm.52.167; reference:[7] Cheng, X., Mejia, T., Zhou, D.: Eigenvalue estimate and compactness for closed $f$-minimal surfaces.Pac. J. Math. 271 (2014), 347-367. Zbl 1322.58020, MR 3267533, 10.2140/pjm.2014.271.347; reference:[8] Cheng, X., Mejia, T., Zhou, D.: Stability and compactness for complete $f$-minimal surfaces.Trans. Am. Math. Soc. 367 (2015), 4041-4059. Zbl 1318.53061, MR 3324919, 10.1090/S0002-9947-2015-06207-2; reference:[9] Dimitrić, I.: Submanifolds of $E^{m}$ with harmonic mean curvature vector.Bull. Inst. Math., Acad. Sin. 20 (1992), 53-65. Zbl 0778.53046, MR 1166218; reference:[10] J. Eells, Jr., J. H. Sampson: Harmonic mappings of Riemannian manifolds.Am. J. Math. 86 (1964), 109-160. Zbl 0122.40102, MR 0164306, 10.2307/2373037; reference:[11] Fetcu, D., Oniciuc, C., Rosenberg, H.: Biharmonic submanifolds with parallel mean curvature in $\mathbb S^{n}\times \mathbb R$.J. Geom. Anal. 23 (2013), 2158-2176. Zbl 1281.58008, MR 3107694, 10.1007/s12220-012-9323-3; reference:[12] Hasanis, T., Vlachos, T.: Hypersurfaces in $E^{4}$ with harmonic mean curvature vector field.Math. Nachr. 172 (1995), 145-169. Zbl 0839.53007, MR 1330627, 10.1002/mana.19951720112; reference:[13] Jiang, G.: 2-harmonic maps and their first and second variational formulas.Chin. Ann. Math., Ser. A 7 (1986), 389-402 Chinese. Zbl 0628.58008, MR 0886529, 10.1285/i15900932v28n1supplp209; reference:[14] Jiang, G.: Some nonexistence theorems on 2-harmonic and isometric immersions in Euclidean space.Chin. Ann. Math., Ser. A 8 (1987), 377-383 Chinese. Zbl 0637.53071, MR 0924896; reference:[15] Li, X. X., Li, J. T.: The rigidity and stability of complete $f$-minimal hypersurfaces in $\mathbb{R}\times\mathbb{S}^{1}(a)$.(to appear) in Proc. Am. Math. Soc. MR 3600797; reference:[16] Liu, G.: Stable weighted minimal surfaces in manifolds with non-negative Bakry-Emery Ricci tensor.Commun. Anal. Geom. 21 (2013), 1061-1079. Zbl 1301.53057, MR 3152972, 10.4310/CAG.2013.v21.n5.a7; reference:[17] Lu, W. J.: On $f$-bi-harmonic maps and bi-$f$-harmonic maps between Riemannian manifolds.Sci. China, Math. 58 (2015), 1483-1498. Zbl 1334.53063, MR 3353985, 10.1007/s11425-015-4997-1; reference:[18] Ou, Y.-L., Wang, Z.-P.: Constant mean curvature and totally umbilical biharmonic surfaces in 3-dimensional geometries.J. Geom. Phys. 61 (2011), 1845-1853. Zbl 1227.58004, MR 2822453, 10.1016/j.geomphys.2011.04.008; reference:[19] Ouakkas, S., Nasri, R., Djaa, M.: On the $f$-harmonic and $f$-biharmonic maps.JP J. Geom. Topol. 10 (2010), 11-27. Zbl 1209.58014, MR 2677559

  7. 7
    دورية أكاديمية

    وصف الملف: application/pdf

    العلاقة: mr:MR3964438; zbl:Zbl 07088762; reference:[1] Audin, M.: Symplectic geometry in Frobenius manifolds and quantum cohomology.J. Geom. Phys. 25 (1–2) (1998), 183–204. MR 1611969, 10.1016/S0393-0440(97)00026-0; reference:[2] Crainic, M., Fernandes, R.L.: Lectures integrability Lie brackets.Geom. Topol. Monogr. 17 (2011), 1–107. MR 2795150; reference:[3] David, L., Strachan, I.A.B.: Dubrovin’s duality for F-manifolds with eventual identities.Adv. Math. 226 (4) (2011), 4031–4060. MR 2770440, 10.1016/j.aim.2010.11.006; reference:[4] Dotsenko, V.: Algebraic structures of F-manifolds via pre-Lie algebras.Ann. Mat. Pura Appl. (4) 198 (2019), 517–527. MR 3927168, 10.1007/s10231-018-0787-z; reference:[5] Dubrovin, B.: Geometry of 2D topological field theories.Lecture Notes in Math., vol. 1620, Springer, 1996. Zbl 0841.58065, MR 1397274; reference:[6] Dubrovin, B.: On almost duality for Frobenius manifolds.Amer. Math. Soc. Transl. 212 (2004), 75–132. MR 2070050; reference:[7] Dubrovin, B.: WDVV Equations and Frobenius Manifolds.Encyclopedia of Mathematical Physics, vol. 1, Elsevier, 2006, pp. 438–447.; reference:[8] Dufour, J.P., Zung, N.T.: Poisson Structures and Their Normal Forms.Birkhauser, 2000. MR 2178041; reference:[9] Fernandes, R.L.: Lie algebroids, holonomy and characteristic classes.Adv. Math. 170 (1) (2002), 119–179. MR 1929305, 10.1006/aima.2001.2070; reference:[10] Hertling, C.: Frobenius manifolds and moduli spaces for singularities.Cambridge University Press, 2004. MR 1924259; reference:[11] Hertling, C., Manin, Y.: Weak Frobenius manifolds.Internat. Math. Res. Notices 6 (1999), 277–286. Zbl 0960.58003, MR 1680372, 10.1155/S1073792899000148; reference:[12] Hitchin, N.: Frobenius manifolds.Gauge Theory and Symplectic Geometry, Springer, 1997. MR 1461570; reference:[13] Kodaira, K.: Complex Manifolds and Deformation of Complex Structures.Springer, 2005. MR 2109686; reference:[14] Mackenzie, K.C.H.: General Theory of Lie Groupoids and Lie Algebroids.Cambridge University Press, 2005. Zbl 1078.58011, MR 2157566; reference:[15] Manetti, M.: Lectures on deformation of complex manifolds.Rendiconti di Matematica 24 (2004), 1–183. MR 2130146; reference:[16] Manin, Y.: Mirrors, functoriality, and derived geometry.arXiv:1708.02849.; reference:[17] Manin, Y.: Frobenius Manifolds, Quantum Cohomology, and Moduli Spaces.Amer. Math. Soc. Colloq. Publ. 47 (1999), xiv+303 pp. Zbl 0952.14032, MR 1702284; reference:[18] Manin, Y.: F-manifolds with flat structure and Dubrovin’s duality.Adv. Math. 198 (1) (2005), 5–26. MR 2183247, 10.1016/j.aim.2004.12.003; reference:[19] Manin, Y.: Grothendieck-Verdier duality patterns in quantum algebra.Izv. Ross. Akad. Nauk Ser. Mat. 81 (4) (2017), 158–166. MR 3682786; reference:[20] Weinstein, A.: Linearization problems Lie algebroids and Lie groupoids.Lett. Math. Phys. 52 (2000), 93–102. MR 1800493, 10.1023/A:1007657920231

  8. 8
    دورية أكاديمية

    المؤلفون: Donnelly, John

    وصف الملف: application/pdf

    العلاقة: mr:MR3939061; zbl:Zbl 07088755; reference:[1] Brin, M., Squier, C.: Groups of piecewise linearhomeomorphisms of the real line.Invent. Math. 79 (3) (1985), 485–498. MR 0782231, 10.1007/BF01388519; reference:[2] Cannon, J.W., Floyd, W.J., Parry, W.R.: Introductory notes on Richard Thompson’s groups.Enseign. Math. 42 3–4) (1996), 215–256. MR 1426438; reference:[3] Frey, A.H.: Studies on Amenable Semigroups.Ph.D. thesis, University of Washington, 1960. MR 2613109

  9. 9
    دورية أكاديمية

    المؤلفون: Sharma, Rajendra K., Mittal, Gaurav

    وصف الملف: application/pdf

    العلاقة: mr:MR4387464; zbl:Zbl 07547237; reference:[1] Creedon, L., Gildea, J.: The structure of the unit group of the group algebra $F_{2^k}D_8$.Can. Math. Bull. 54 (2011), 237-243. Zbl 1242.16033, MR 2884238, 10.4153/CMB-2010-098-5; reference:[2] Ferraz, R. A.: Simple components of the center of $FG/J(FG)$.Commun. Algebra 36 (2008), 3191-3199. Zbl 1156.16019, MR 2441107, 10.1080/00927870802103503; reference:[3] Gildea, J.: The structure of the unit group of the group algebra $F_{2^k}A_4$.Czech. Math. J. 61 (2011), 531-539. Zbl 1237.16035, MR 2905421, 10.1007/s10587-011-0071-5; reference:[4] Gildea, J., Monaghan, F.: Units of some group algebras of groups of order 12 over any finite field of characteristic 3.Algebra Discrete Math. 11 (2011), 46-58. Zbl 1256.16023, MR 2868359; reference:[5] Hurley, T.: Group rings and rings of matrices.Int. J. Pure Appl. Math. 31 (2006), 319-335. Zbl 1136.20004, MR 2266951; reference:[6] Hurley, T.: Convolutional codes from units in matrix and group rings.Int. J. Pure Appl. Math. 50 (2009), 431-463. Zbl 1173.94452, MR 2490664; reference:[7] Lidl, R., Niederreiter, H.: Introduction to Finite Fields and Their Applications.Cambridge University Press, Cambridge (1994). Zbl 0820.11072, MR 1294139, 10.1017/CBO9781139172769; reference:[8] Maheshwari, S., Sharma, R. K.: The unit group of group algebra $F_qSL(2;Z_3)$.J. Algebra Comb. Discrete Struct. Appl. 3 (2016), 1-6. Zbl 1429.16027, MR 3450932, 10.13069/jacodesmath.83854; reference:[9] Makhijani, N., Sharma, R. K., Srivastava, J. B.: A note on units of $F_{p^m}[D_{2p^m}]$.Acta Math. Acad. Paedagog. Nyházi. (N.S.) 30 (2014), 17-25. Zbl 1324.16035, MR 3285078; reference:[10] Makhijani, N., Sharma, R. K., Srivastava, J. B.: The unit group of algebra of circulant matrices.Int. J. Group Theory 3 (2014), 13-16. Zbl 1335.16028, MR 3181770, 10.1142/S0219498813500904; reference:[11] Makhijani, N., Sharma, R. K., Srivastava, J. B.: The unit group of $F_q[D_{30}]$.Serdica Math. J. 41 (2015), 185-198. MR 3363601; reference:[12] Makhijani, N., Sharma, R. K., Srivastava, J. B.: A note on the structure of $F_{p^k}A_5/J(F_{p^k}A_5)$.Acta Sci. Math. 82 (2016), 29-43. Zbl 1399.16065, MR 3526335, 10.14232/actasm-014-311-2; reference:[13] Makhijani, N., Sharma, R. K., Srivastava, J. B.: The unit group of some special semi-simple group algebras.Quaest. Math. 39 (2016), 9-28. Zbl 1445.16023, MR 3483353, 10.2989/16073606.2015.1024410; reference:[14] Makhijani, N., Sharma, R. K., Srivastava, J. B.: Units in finite dihedral and quaternion group algebras.J. Egypt. Math. Soc. 24 (2016), 5-7. Zbl 1336.16042, MR 3456857, 10.1016/j.joems.2014.08.001; reference:[15] Mittal, G., Sharma, R.: On unit group of finite semisimple group algebras of nonmetabelian groups upto order 72.Math. Bohem. 146 (2021), 429-455. MR 4336549, 10.21136/MB.2021.0116-19; reference:[16] Perlis, S., Walker, G. L.: Abelian group algebras of finite order.Trans. Am. Math. Soc. 68 (1950), 420-426. Zbl 0038.17301, MR 0034758, 10.1090/S0002-9947-1950-0034758-3; reference:[17] Milies, C. Polcino, Sehgal, S. K., Sudarshan, S.: An Introduction to Group Rings.Algebras and Applications 1. Kluwer Academic Publishers, Dordrecht (2002). Zbl 0997.20003, MR 1896125, 10.1007/978-94-010-0405-3; reference:[18] Sharma, R. K., Srivastava, J. B., Khan, M.: The unit group of $FA_4$.Publ. Math. 71 (2007), 21-26. Zbl 1135.16033, MR 2340031; reference:[19] Sharma, R. K., Srivastava, J. B., Khan, M.: The unit group of $FS_3$.Acta Math. Acad. Paedagog. Nyházi. (N.S.) 23 (2007), 129-142. Zbl 1135.16034, MR 2368934; reference:[20] Sharma, R. K., Yadav, P.: Unit group of algebra of circulant matrices.Int. J. Group Theory 2 (2013), 1-6. Zbl 1306.16037, MR 3053357; reference:[21] Tang, G., Wei, Y., Li, Y.: Unit groups of group algebras of some small groups.Czech. Math. J. 64 (2014), 149-157. Zbl 1340.16040, MR 3247451, 10.1007/s10587-014-0090-0

  10. 10
    دورية أكاديمية

    وصف الملف: application/pdf

    العلاقة: mr:MR4303577; zbl:Zbl 07396218; reference:[1] Aledo J. A., Rubio R. M.: Stable minimal surfaces in Riemannian warped products.J. Geom. Anal. 27 (2017), no. 1, 65–78. MR 3606544, 10.1007/s12220-015-9673-8; reference:[2] Alexandrov A. D.: Uniqueness theorems for surfaces in the large I.Vestnik Leiningrad Univ. 11 (1956), no. 19, 5–17 (Russian). MR 0086338; reference:[3] Alexandrov A. D.: A characteristic property of spheres.Ann. Mat. Pura Appl. 58 (1962), no. 4, 303–315. MR 0143162, 10.1007/BF02413056; reference:[4] Alías L. J., Dajczer M., Ripoll J. R.: A Bernstein-type theorem for Riemannian manifolds with a Killing field.Ann. Global Anal. Geom. 31 (2007), no. 4, 363–373. MR 2325221, 10.1007/s10455-006-9045-5; reference:[5] Alías L. J., de Lira J. H. S., Malacarne J. M.: Constant higher-order mean curvature hypersurfaces in Riemannian spaces.J. Inst. Math. Jussieu 5 (2006), no. 4, 527–562. Zbl 1118.53038, MR 2261223, 10.1017/S1474748006000077; reference:[6] Bakry D., Émery M.: Diffusions hypercontractives.Séminaire de probabilités, XIX, 1983/84, Lecture Notes in Math., 1123, Springer, Berlin, 1985, pages 177–206 (French). MR 0889476; reference:[7] Barbosa J. L. M., do Carmo M., Eschenburg J.: Stability of hypersurfaces with constant mean curvature in Riemannian manifolds.Math. Z. 197 (1988), no. 1, 123–138. MR 0917854, 10.1007/BF01161634; reference:[8] Batista M., Cavalcante M. P., Pyo J.: Some isoperimetric inequalities and eigenvalue estimates in weighted manifolds.J. Math. Anal. Appl. 419 (2014), no. 1, 617–626. MR 3217170, 10.1016/j.jmaa.2014.04.074; reference:[9] Bernstein S.: Sur les surfaces définies au moyen de leur courboure moyenne ou totale.Ann. Sci. École Norm. Sup. 27 (1910), no. 3, 233–256 (French). MR 1509123, 10.24033/asens.621; reference:[10] Caminha A.: The geometry of closed conformal vector fields on Riemannian spaces.Bull. Braz. Math. Soc. (N.S.) 42 (2011), no. 2, 277–300. Zbl 1242.53068, MR 2833803, 10.1007/s00574-011-0015-6; reference:[11] Caminha A., de Lima H. F.: Complete vertical graphs with constant mean curvature in semi-Riemannian warped products.Bull. Belg. Math. Soc. Simon Stevin 16 (2009), no. 1, 91–105. MR 2498961, 10.36045/bbms/1235574194; reference:[12] Cañete A., Rosales C.: Compact stable hypersurfaces with free boundary in convex solid cones with homogeneous densities.Cal. Var. Partial Differential Equations 51 (2014), no. 3–4, 887–913. MR 3268875, 10.1007/s00526-013-0699-0; reference:[13] Castro K., Rosales C.: Free boundary stable hypersurfaces in manifolds with density and rigidity results.J. Geom. Phys. 79 (2014), 14–28. MR 3176286, 10.1016/j.geomphys.2014.01.013; reference:[14] Cavalcante M. P., de Lima H. F., Santos M. S.: On Bernstein-type properties of complete hypersurfaces in weighted warped products.Ann. Mat. Pura Appl. (4) 195 (2016), no. 2, 309–322. MR 3476675, 10.1007/s10231-014-0464-9; reference:[15] Dajczer M., de Lira J. H.: Conformal Killing graphs with prescribed mean curvature.J. Geom. Anal. 22 (2012), no. 3, 780–799. MR 2927678, 10.1007/s12220-011-9214-z; reference:[16] Dajczer M., Hinojosa P., de Lira J. H.: Killing graphs with prescribed mean curvature.Calc. Var. Partial Differential Equations 33 (2008), no. 2, 231–248. Zbl 1152.53046, MR 2413108, 10.1007/s00526-008-0163-8; reference:[17] de Lima H. F., de Lima J. R., Velásquez M. A. L.: On the nullity of conformal Killing graphs in foliated Riemannian spaces.Aequationes Math. 87 (2014), no. 3, 285–299. MR 3266117; reference:[18] de Lima H. F., de Lima J. R., Velásquez M. A. L.: Entire conformal Killing graphs in foliated Riemannian spaces.J. Geom. Anal. 25 (2015), no. 1, 171–188. MR 3299274, 10.1007/s12220-013-9418-5; reference:[19] de Lima H. F., Oliveira A. M., Velásquez M. A. L.: On the uniqueness of complete two-sided hypersurfaces immersed in a class of weighted warped products.J. Geom. Anal. 27 (2017), no. 3, 2278–2301. MR 3667431, 10.1007/s12220-017-9761-z; reference:[20] Fang F., Li X.-D., Zhang Z.: Two generalizations of Cheeger–Gromoll splitting theorem via Bakry–Émery Ricci curvature.Ann. Inst. Fourier (Grenoble) 59 (2009), no. 2, 563–573. MR 2521428, 10.5802/aif.2440; reference:[21] Hieu D. T., Nam T. L.: Bernstein type theorem for entire weighted minimal graphs in $\mathbb{G}^n\times\mathbb{R}$.J. Geom. Phys. 81 (2014), 87–91. MR 3194217, 10.1016/j.geomphys.2014.03.011; reference:[22] Impera D., de Lira J. H., Pigola S., Setti A. G.: Height estimates for Killing graphs.J. Geom. Anal. 28 (2018), no. 3, 2857–2885. MR 3833821, 10.1007/s12220-017-9938-5; reference:[23] Impera D., Rimoldi M.: Stability properties and topology at infinity of $f$-minimal hypersurfaces.Geom. Dedicata 178 (2015), 21–47. MR 3397480, 10.1007/s10711-014-9999-6; reference:[24] Jellett J. J.: Sur la surface dont la courbure moyenne est constante.J. Math. Pures Appl. 18 (1853), 163–167 (French).; reference:[25] Lichnerowicz A.: Variétés Riemanniennes à tenseur C non négatif.C. R. Acad. Sci. Paris Sér. A-B 271 (1970), A650–A653 (French). MR 0268812; reference:[26] Lichnerowicz A.: Variétés Kählériennes à première classe de Chern non negative et variétés Riemanniennes à courbure de Ricci généralisée non negative.J. Differential Geometry 6 (1971/72), 47–94 (French). MR 0300228; reference:[27] Liebmann H.: Eine neue Eigenschaft der Kugel.Nachr. Kg. Ges. Wiss. Götingen, Math. Phys. Kl. (1899), 44–55 (German).; reference:[28] McGonagle M., Ross J.: The hyperplane is the only stable, smooth solution to the isoperimetric problem in Gaussian space.Geom. Dedicata 178 (2015), 277–296. MR 3397495, 10.1007/s10711-015-0057-9; reference:[29] Montiel S.: Unicity of constant mean curvature hypersurfaces in some Riemannian manifolds.Indiana Univ. Math. J. 48 (1999), no. 2, 711–748. MR 1722814, 10.1512/iumj.1999.48.1562; reference:[30] O'Neill B.: Semi-Riemannian Geometry.With Applications to Relativity, Pure and Applied Mathematics, 103, Academic Press, New York, 1983. MR 0719023; reference:[31] Pan T. K.: Conformal vector fields in compact Riemannian manifolds.Proc. Amer. Math. Soc. 14 (1963), 653–657. MR 0157324, 10.1090/S0002-9939-1963-0157324-2; reference:[32] Rosales C., Ca nete A., Bayle V., Morgan F.: On the isoperimetric problem in Euclidean space with density.Calc. Var. Partial Differential Equations 31 (2008), no. 1, 27–46. MR 2342613, 10.1007/s00526-007-0104-y; reference:[33] Wei G., Wylie W.: Comparison geometry for the Bakry–Émery Ricci tensor.J. Differential Geom. 83 (2009), no. 2, 377–405. MR 2577473; reference:[34] Yau S. T.: Some function-theoretic properties of complete Riemannian manifold and their applications to geometry.Indiana Univ. Math. J. 25 (1976), no. 7, 659–670. MR 0417452, 10.1512/iumj.1976.25.25051