المؤلفون: Merkh, Thomas, Montúfar, Guido

مصطلحات موضوعية: keyword:multi-information, keyword:mutual information, keyword:divergence maximization, keyword:marginal specification problem, keyword:transportation polytope, msc:62B10, msc:94A17

وصف الملف: application/pdf

Relation: mr:MR4187782; reference:[1] Alemi, A., Fischer, I., Dillon, J., Murphy, K.: Deep variational information bottleneck.In: ICLR, 2017.; reference:[2] Ay, N.: An information-geometric approach to a theory of pragmatic structuring.Ann. Probab. 30 (2002), 1, 416-436. Zbl 1010.62007, MR 1894113, 10.1214/aop/1020107773; reference:[3] Ay, N.: Locality of global stochastic interaction in directed acyclic networks.Neural Comput. 14 (2002), 12, 2959-2980. Zbl 1079.68582, 10.1162/089976602760805368; reference:[4] Ay, N., Bertschinger, N., Der, R., Güttler, F., Olbrich, E.: Predictive information and explorative behavior of autonomous robots.Europ. Phys. J. B 63 (2008), 3, 329-339. MR 2421556, 10.1140/epjb/e2008-00175-0; reference:[5] Ay, N., Knauf, A.: Maximizing multi-information.Kybernetika 42 (2006), 5, 517-538. Zbl 1249.82011, MR 2283503; reference:[6] Baldassarre, G., Mirolli, M.: Intrinsically motivated learning systems: an overview.In: Intrinsically motivated learning in natural and artificial systems, Springer 2013, pp. 1-14. 10.1007/978-3-642-32375-1_1; reference:[7] Baudot, P., Tapia, M., Bennequin, D., Goaillard, J.-M.: Topological information data analysis.Entropy 21 (2019), 9, 869. MR 4016406, 10.3390/e21090869; reference:[8] Bekkerman, R., Sahami, M., Learned-Miller, E.: Combinatorial markov random fields.In: European Conference on Machine Learning, Springer 2006, pp. 30-41. MR 2336649, 10.1007/11871842_8; reference:[9] Belghazi, M. I., Baratin, A., Rajeshwar, S., Ozair, S., Bengio, Y., Courville, A., Hjelm, D.: Mutual information neural estimation.In: Proc. 35th International Conference on Machine Learning (J. Dy and A. Krause, eds.), Vol. 80 of Proceedings of Machine Learning Research, pp. 531-540, Stockholm 2018. PMLR.; reference:[10] Bertschinger, N., Rauh, J., Olbrich, E., Jost, J., Ay, N.: Quantifying unique information.Entropy 16 (2014), 4, 2161-2183. MR 3195286, 10.3390/e16042161; reference:[11] Bialek, W., Nemenman, I., Tishby, N.: Predictability, complexity, and learning.Neural Comput. 13 (2001), 11, 2409-2463. 10.1162/089976601753195969; reference:[12] Burda, Y., Edwards, H., Pathak, D., Storkey, A., Darrell, T., Efros, A. A.: Large-scale study of curiosity-driven learning.In: ICLR, 2019.; reference:[13] Buzzi, J., Zambotti, L.: Approximate maximizers of intricacy functionals.Probab. Theory Related Fields 153 (2012), 3-4, 421-440. MR 2948682, 10.1007/s00440-011-0350-y; reference:[14] Chentanez, N., Barto, A. G., Singh, S. P.: Intrinsically motivated reinforcement learning.In: Adv. Neural Inform. Process. Systems 2005, pp. 1281-1288. 10.21236/ada440280; reference:[15] Crutchfield, J. P., Feldman, D. P.: Synchronizing to the environment: Information-theoretic constraints on agent learning.Adv. Complex Systems 4 (2001), 02n03, 251-264. MR 1873760, 10.1142/s021952590100019x; reference:[16] Loera, J. de: Transportation polytopes.; reference:[17] Friedman, N., Mosenzon, O., Slonim, N., Tishby, N.: Multivariate information bottleneck.In: Proc. Seventeenth conference on Uncertainty in Artificial Intelligence, Morgan Kaufmann Publishers Inc., 2001, pp. 152-161.; reference:[18] Gabrié, M., Manoel, A., Luneau, C., Barbier, j., Macris, N., Krzakala, F., Zdeborová, L.: Entropy and mutual information in models of deep neural networks.In: Advances in Neural Information Processing Systems 31 (S. Bengio, H. Wallach, H. Larochelle, K. Grauman, N. Cesa-Bianchi, and R. Garnett, eds.), Curran Associates, Inc. 2018, pp. 1821-1831. MR 3841726; reference:[19] Gao, S., Steeg, G. Ver, Galstyan, A.: Efficient estimation of mutual information for strongly dependent variables.In: Artificial Intelligence and Statistics 2015, pp. 277-286.; reference:[20] Hjelm, R. D., Fedorov, A., Lavoie-Marchildon, S., Grewal, K., Bachman, P., Trischler, A., Y. Bengio.: Learning deep representations by mutual information.Representations, maximization. In International Conference on Learning. 2019.; reference:[21] Hosten, S., Sullivant, S.: Gröbner bases and polyhedral geometry of reducible and cyclic models.J. Comb. Theory Ser. A 100 (2002), 2, 277-301. MR 1940337, 10.1006/jcta.2002.3301; reference:[22] Jakulin, A., Bratko, I.: Quantifying and visualizing attribute interactions: An approach based on entropy.2003.; reference:[23] Klyubin, A. S., Polani, D., Nehaniv, C. L.: Empowerment: A universal agent-centric measure of control.In: 2005 IEEE Congress on Evolutionary Computation, Vol. 1, IEEE 2005, pp. 128-135.; reference:[24] Kraskov, A., Stögbauer, H./, Grassberger, P.: Estimating mutual information.Phys. Rev. E 69 (2004), 6, 066138. MR 2096503, 10.1103/physreve.69.066138; reference:[25] Matúš, F.: Maximization of information divergences from binary i.i.d. sequences.In: Proc. IPMU 2004 2 (2004), pp. 1303-1306.; reference:[26] Matúš, F.: Divergence from factorizable distributions and matroid representations by partitions.IEEE Trans. Inf. Theor. 55 (2009), 12, 5375-5381. MR 2597169, 10.1109/tit.2009.2032806; reference:[27] Matúš, F., Ay, N.: On maximization of the information divergence from an exponential family.In: Proc. 6th Workshop on Uncertainty Processing: Oeconomica 2003, Hejnice 2003, pp. 199-204.; reference:[28] Matúš, F., Rauh, J.: Maximization of the information divergence from an exponential family and criticality.In: 2011 IEEE International Symposium on Information Theory Proceedings 2011, pp. 903-907. MR 2817016, 10.1109/isit.2011.6034269; reference:[29] McGill, W.: Multivariate information transmission.Trans. IRE Profess. Group Inform. Theory 4 (1054), 4, 93-111. MR 0088155, 10.1109/tit.1954.1057469; reference:[30] Mohamed, S., Rezende, D. J.: Variational information maximisation for intrinsically motivated reinforcement learning.In: Advances in Neural Information Processing Systems 2015, 2125-2133, 2015.; reference:[31] Montúfar, G.: Universal approximation depth and errors of narrow belief networks with discrete units.Neural Comput. 26 (2014), 7, 1386-1407. MR 3222078, 10.1162/neco\_a\_00601; reference:[32] Montúfar, G., Ghazi-Zahedi, K., Ay, N.: A theory of cheap control in embodied systems.PLOS Comput. Biology 11 (2015), 9, 1-22. 10.1371/journal.pcbi.1004427; reference:[33] Montúfar, G., Ghazi-Zahedi, K., Ay, N.: Information theoretically aided reinforcement learning for embodied agents.arXiv preprint arXiv:1605.09735, 2016.; reference:[34] Montúfar, G., Rauh, J., Ay, N.: Expressive power and approximation errors of restricted Boltzmann machines.In: Advances in Neural Information Processing Systems 2011, pp. 415-423.; reference:[35] Montúfar, G., Rauh, J., Ay, N.: Maximal information divergence from statistical models defined by neural networks.In: Geometric Science of Information GSI 2013 (F. Nielsen and F. Barbaresco, eds.), Lecture Notes in Computer Science 3085 Springer 2013, pp. 759-766. MR 3126126, 10.1007/978-3-642-40020-9_85; reference:[36] Rauh, J.: Finding the maximizers of the information divergence from an exponential family.IEEE Trans. Inform. Theory 57 (2011), 6, 3236-3247. MR 2817016, 10.1109/tit.2011.2136230; reference:[37] Rauh, J.: Finding the Maximizers of the Information Divergence from an Exponential Family.PhD. Thesis, Universität Leipzig 2011. MR 2817016; reference:[38] Ince, R. A. A., Quantities, S. Panzeri, Schultz, S. R.: Summary of Information Theoretic.New York, pages 1-6, Springer, 2013.; reference:[39] Roulston, M. S.: Estimating the errors on measured entropy and mutual information.Physica D: Nonlinear Phenomena 125 (1999), 3-4, 285-294. 10.1016/s0167-2789(98)00269-3; reference:[40] Schossau, J., Adami, C., Hintze, A.: Information-theoretic neuro-correlates boost evolution of cognitive systems.Entropy 18 (2015), 1, 6. 10.3390/e18010006; reference:[41] Slonim, N., Atwal, G. S., Tkacik, G., Bialek, W.: Estimating mutual information and multi-information in large networks.arXiv preprint cs/0502017, 2005.; reference:[42] Slonim, N., Friedman, N., Tishby, N.: Multivariate information bottleneck.Neural Comput. 18 (2006), 8, 1739-1789. MR 2230853, 10.1162/neco.2006.18.8.1739; reference:[43] Still, S., Precup, D.: An information-theoretic approach to curiosity-driven reinforcement learning.Theory Biosci. 131 (2012), 3, 139-148. 10.1007/s12064-011-0142-z; reference:[44] Developers, The Sage: SageMath, the Sage Mathematics Software System (Version 8.7), 2019.https://www.sagemath.org.; reference:[45] Tishby, N., Pereira, F. C., Bialek, W.: The information bottleneck method.In: Proc. 37th Annual Allerton Conference on Communication, Control and Computing 1999, pp. 368-377.; reference:[46] Vergara, J. R., Estévez, P. A.: A review of feature selection methods based on mutual information.Neural Comput. Appl. 24 (2014), 1, 175-186. 10.1007/s00521-013-1368-0; reference:[47] Watanabe, S.: Information theoretical analysis of multivariate correlation.IBM J. Res. Develop. 4 (1960), 1, 66-82. MR 0109755, 10.1147/rd.41.0066; reference:[48] Witsenhausen, H. S., Wyner, A. D.: A conditional entropy bound for a pair of discrete random variables.IEEE Trans. Inform. Theory 21 (1075), 5, 493-501. MR 0381861, 10.1109/tit.1975.1055437; reference:[49] Yemelichev, V., Kovalev, M., Kravtsov, M.: Polytopes, Graphs and Optimisation.Cambridge University Press, 1984. MR 0744197; reference:[50] Zahedi, K., Ay, N., Der, R.: Higher coordination with less control: A result of information maximization in the sensorimotor loop.Adaptive Behavior 18 (2010), 3-4, 338-355. 10.1177/1059712310375314; reference:[51] Zahedi, K., Martius, G., Ay, N.: Linear combination of one-step predictive information with an external reward in an episodic policy gradient setting: a critical analysis.Front. Psychol. (2013), 4, 801. 10.3389/fpsyg.2013.00801

الاتاحة: http://hdl.handle.net/10338.dmlcz/148493

المؤلفون: Kobza, Vladimír

مصطلحات موضوعية: keyword:fuzzy set, keyword:divergence measure, keyword:scalar cardinality, keyword:fuzzy cardinality, msc:03B52, msc:03E75

وصف الملف: application/pdf

Relation: mr:MR3684678; zbl:Zbl 06819616; reference:[1] Ashraf, S., Rashid, T.: Fuzzy similarity measures.LAP LAMBERT Academic Publishing, 2010.; reference:[2] Casasnovas, J., Torrens, J.: An axiomatic approach to fuzzy cardinalities of finite fuzzy sets.Fuzzy Sets and Systems 133 (2003), 193-209. MR 1949022, 10.1016/s0165-0114(02)00345-7; reference:[3] Baets, B. De, Meyer, H. De, Naessens, H.: A class of rational cardinality-based similarity measures.J. Comput. Appl. Math. 132 (2001), 51-69. MR 1834802, 10.1016/s0377-0427(00)00596-3; reference:[4] Baets, B. De, Janssens, S., Meyer, H. De: On the transitivity of a parametric family of cardinality-based similarity measures.In. J. Approx. Reasoning 50 (2009), 104-116. Zbl 1191.68706, MR 2519040, 10.1016/j.ijar.2008.03.006; reference:[5] Deschrijver, G., Král', P.: On the cardinalities of interval-valued fuzzy sets.Fuzzy Sets and Systems 158 (2007), 1728-1750. MR 2341334, 10.1016/j.fss.2007.01.005; reference:[6] Klement, E. P., Mesiar, R., Pap, E.: Triangular Norms.Kluwer Academic Publishers, London 2000. Zbl 1087.20041, MR 1790096, 10.1007/978-94-015-9540-7; reference:[7] Kobza, V., Janiš, V., Montes, S.: Generalizated local divergence measures between fuzzy subsets.J. Intelligent and Fuzzy Systems (2017), accepted, in press. MR 3684678; reference:[8] Montes, I.: Comparison of Alternatives under Uncertainty and Imprecision.PhD Thesis, University of Oviedo 2013.; reference:[9] Montes, S., Couso, I., Gil, P., Bertoluzza, C.: Divergence measure between fuzzy sets.Int. J. Approx. Reasoning 30 (2002), 91-105. MR 1906630, 10.1016/s0888-613x(02)00063-4; reference:[10] Montes, S., Gil, P.: Some classes of divergence measures between fuzzy subsets and between fuzzy partitions.Mathware and Soft Computing 5 (1998), 253-265. MR 1704068; reference:[11] Ralescu, D.: Cardinality, quantifiers and the aggregation of fuzzy criteria.Fuzzy Sets and Systems 69 (1995), 355-365. MR 1319236, 10.1016/0165-0114(94)00177-9; reference:[12] Shang, G., Zhang, Z., Cao, C.: Multiplication operation on fuzzy numbers.J. Software 4 (2009), 331-338. 10.4304/jsw.4.4.331-338; reference:[13] Wygralak, M.: Cardinalities of Fuzzy Sets.Springer, Berlin, Heidelberg, New York 2003. 10.1007/978-3-540-36382-8; reference:[14] Wygralak, M.: Fuzzy sets with triangular norms and their cardinality theory.Fuzzy Sets and Systems 124 (2001), 1-24. MR 1859773, 10.1016/s0165-0114(00)00108-1; reference:[15] Wygralak, M.: Questions of cardinality of finite fuzzy sets.Fuzzy Sets and Systems 102 (1999), 185-210. MR 1674931, 10.1016/s0165-0114(97)00097-3; reference:[16] Zadeh, L.: Fuzzy sets and systems.System Theory, Brooklyn, Polytechnic Press (1965), 29-39. MR 0256772; reference:[17] Zadeh, L.: Fuzzy logic and its application to approximate reasoning.Inform. Process. 74 (1974), 591-594. MR 0408358

الاتاحة: http://hdl.handle.net/10338.dmlcz/146935

المؤلفون: Oswald, Peter

مصطلحات موضوعية: keyword:nonconforming P1 element, keyword:lowest order Raviart-Thomas element, keyword:discrete energy norm estimate, keyword:divergence of finite element method, keyword:maximum angle condition, keyword:distorted triangulation, msc:65N12, msc:65N15, msc:65N30

وصف الملف: application/pdf

Relation: mr:MR3722898; zbl:Zbl 06819515; reference:[1] Acosta, G., Durán, R. G.: The maximum angle condition for mixed and nonconforming elements: Application to the Stokes equations.SIAM J. Numer. Anal. 37 (1999), 18-36. Zbl 0948.65115, MR 1721268, 10.1137/S0036142997331293; reference:[2] Babuška, I., Aziz, A. K.: On the angle condition in the finite element method.SIAM J. Numer. Anal. 13 (1976), 214-226. Zbl 0324.65046, MR 0455462, 10.1137/0713021; reference:[3] Braess, D.: Finite Elements. Theory, Fast Solvers and Applications in Solid Mechanics.Cambridge University Press, Cambridge (2007). Zbl 1118.65117, MR 2322235, 10.1017/CBO9780511618635; reference:[4] Braess, D.: An a posteriori error estimate and a comparison theorem for the nonconforming $P_1$ element.Calcolo 46 (2009), 149-155. Zbl 1192.65142, MR 2520373, 10.1007/s10092-009-0003-z; reference:[5] Brenner, S. C.: Poincaré-Friedrichs inequalities for piecewise $H^1$ functions.SIAM J. Numer. Anal. 41 (2003), 306-324. Zbl 1045.65100, MR 1974504, 10.1137/S0036142902401311; reference:[6] Brenner, S. C., Scott, L. R.: The Mathematical Theory of Finite Element Methods.Texts in Applied Mathematics 15, Springer, New York (2008). Zbl 0804.65101, MR 2373954, 10.1007/978-0-387-75934-0; reference:[7] Carstensen, C., Gedicke, J., Rim, D.: Explicit error estimates for Courant, Crouzeix-Raviart and Raviart-Thomas finite element methods.J. Comput. Math. 30 (2012), 337-353. Zbl 1274.65290, MR 2965987, 10.4208/jcm.1108-m3677; reference:[8] Carstensen, C., Peterseim, D., Schedensack, M.: Comparison results of finite element methods for the Poisson model problem.SIAM J. Numer. Anal. 50 (2012), 2803-2823. Zbl 1261.65115, MR 3022243, 10.1137/110845707; reference:[9] Crouzeix, M., Raviart, P.-A.: Conforming and nonconforming finite element methods for solving the stationary Stokes equations I.Rev. Franc. Automat. Inform. Rech. Operat. 7 (1973), 33-76. Zbl 0302.65087, MR 0343661, 10.1051/m2an/197307R300331; reference:[10] Hannukainen, A., Korotov, S., Křížek, M.: The maximum angle condition is not necessary for convergence of the finite element method.Numer. Math. 120 (2012), 79-88. Zbl 1255.65196, MR 2885598, 10.1007/s00211-011-0403-2; reference:[11] Jamet, P.: Estimations d'erreur pour des éléments finis droits presque dégénérés.Rev. Franc. Automat. Inform. Rech. Operat. 10, Analyse Numer. 10 (1976), 43-60. Zbl 0346.65052, MR 0455282, 10.1051/m2an/197610r100431; reference:[12] Kučera, V.: On necessary and sufficient conditions for finite element convergence.arXiv:1601.02942 (2016). MR 3700195; reference:[13] Marini, L. D.: An inexpensive method for the evaluation of the solution of the lowest order Raviart-Thomas mixed method.SIAM J. Numer. Anal. 22 (1985), 493-496. Zbl 0573.65082, MR 0787572, 10.1137/0722029; reference:[14] Oswald, P.: Divergence of FEM: Babuška-Aziz triangulatiuons revisited.Appl. Math., Praha 60 (2015), 473-484. Zbl 1363.65202, MR 3396476, 10.1007/s10492-015-0107-5; reference:[15] Raviart, P.-A., Thomas, J. M.: A mixed finite element method for 2nd order elliptic problems.Mathematical Aspects of Finite Element Method I. Galligani, E. Magenes Proc. Conf., Rome, 1975, Lect. Notes Math. 606, Springer, New York (1977), 292-315. Zbl 0362.65089, MR 0483555, 10.1007/bfb0064470; reference:[16] Schwarz, H. A.: Sur une définition erroneé de l'aire d'une surface courbe.Gesammelte Mathematische Abhandlungen 2 Springer, Berlin (1890), 309-311, 369-370.; reference:[17] Vohralík, M.: On the discrete Poincaré-Friedrichs inequalities for nonconforming approximations of the Sobolev space $H^1$.Numer. Funct. Anal. Optimization 26 (2005), 925-952. Zbl 1089.65124, MR 2192029, 10.1080/01630560500444533

الاتاحة: http://hdl.handle.net/10338.dmlcz/146914

المؤلفون: Oswald, Peter

مصطلحات موضوعية: keyword:finite elements, keyword:error bounds, keyword:divergence, keyword:maximum angle condition, keyword:triangulation, msc:65N12, msc:65N15, msc:65N30

وصف الملف: application/pdf

Relation: mr:MR3396476; zbl:Zbl 06486921; reference:[1] Apel, T.: Anisotropic Finite Elements: Local Estimates and Applications.Advances in Numerical Mathematics Teubner, Leipzig; Technische Univ., Chemnitz (1999). Zbl 0934.65121, MR 1716824; reference:[2] Babuška, I., Aziz, A. K.: On the angle condition in the finite element method.SIAM J. Numer. Anal. 13 (1976), 214-226. Zbl 0324.65046, MR 0455462, 10.1137/0713021; reference:[3] Bank, R. E., Yserentant, H.: A note on interpolation, best approximation, and the saturation property.Numer. Math. (2014), doi:10.1007/s00211-014-0687-0. MR 3383332, 10.1007/s00211-014-0687-0; reference:[4] Hannukainen, A., Juntunen, M., Huhtala, A.: Finite Element Methods I, course notes A.Mat-1.3650, Univ. Helsinki, 2015.; reference:[5] Hannukainen, A., Korotov, S., Křížek, M.: The maximum angle condition is not necessary for convergence of the finite element method.Numer. Math. 120 (2012), 79-88. Zbl 1255.65196, MR 2885598, 10.1007/s00211-011-0403-2; reference:[6] Jamet, P.: Estimations d'erreur pour des éléments finis droits presque dégénérés.Rev. Franc. Automat. Inform. Rech. Operat. {\it 10}, Analyse numer., R-1 (1976), 43-60. MR 0455282; reference:[7] Kobayashi, K., Tsuchiya, T.: A Babuška-Aziz type proof of the circumradius condition.Japan J. Ind. Appl. Math. 31 (2014), 193-210. Zbl 1295.65011, MR 3167084, 10.1007/s13160-013-0128-y; reference:[8] Křížek, M.: On semiregular families of triangulations and linear interpolation.Appl. Math., Praha 36 (1991), 223-232. Zbl 0728.41003, MR 1109126; reference:[9] Ludwig, L.: A discussion on the maximum angle condition/counterexample for the convergence of the FEM.Manuscript, TU Dresden, 2011.; reference:[10] Schwarz, H. A.: Sur une définition erroneé de l'aire d'une surface courbe.Gesammelte Mathematische Abhandlungen, vol. 2 Springer, Berlin (1890), 309-311, 369-370.

الاتاحة: http://hdl.handle.net/10338.dmlcz/144387

المؤلفون: Das, Pratulananda, Bhunia, Santanu

مصطلحات موضوعية: keyword:double sequences, keyword:$\mu $-statistical convergence, keyword:divergence and Cauchy criteria, keyword:convergence, keyword:divergence and Cauchy criteria in $\mu $-density, keyword:condition (APO$_2)$, msc:40A05, msc:40A30, msc:40B05

وصف الملف: application/pdf

Relation: mr:MR2563584; zbl:Zbl 1224.40009; reference:[1] Balcerzak, M., Dems, K.: Some types of convergence and related Baire systems.Real Anal. Exchange 30 (2004), 267-276. MR 2127531, 10.14321/realanalexch.30.1.0267; reference:[2] Connor, J.: Two valued measure and summability.Analysis 10 (1990), 373-385. MR 1085803, 10.1524/anly.1990.10.4.373; reference:[3] Connor, J.: $R$-type summability methods, Cauchy criterion, $P$-sets and statistical convergence.Proc. Amer. Math. Soc. 115 (1992), 319-327. MR 1095221; reference:[4] Connor, J., Fridy, J. A., Orhan, C.: Core equality results for sequences.J. Math. Anal. Appl. 321 (2006), 515-523. Zbl 1092.40001, MR 2241135, 10.1016/j.jmaa.2005.07.067; reference:[5] Das, P., Malik, P.: On the statistical and $I$ variation of double sequences.Real Anal. Exchange 33 (2008), 351-364. MR 2458252, 10.14321/realanalexch.33.2.0351; reference:[6] Das, P., Kostyrko, P., Wilczyński, W., Malik, P.: $I$ and $I^{*}$-convergence of double sequences.Math. Slovaca 58 (2008), 605-620. Zbl 1199.40026, MR 2434680, 10.2478/s12175-008-0096-x; reference:[7] Dems, K.: On $I$-Cauchy sequences.Real Anal. Exchange 30 (2004), 123-128. MR 2126799; reference:[8] Fast, H.: Sur la convergence statistique.Colloq. Math. 2 (1951), 241-244. Zbl 0044.33605, MR 0048548, 10.4064/cm-2-3-4-241-244; reference:[9] Fridy, J. A.: On statistical convergence.Analysis 5 (1985), 301-313. Zbl 0588.40001, MR 0816582, 10.1524/anly.1985.5.4.301; reference:[10] Kostyrko, P., Šalát, T., Wilczyński, W.: $I$-Convergence.Real Anal. Exchange 26 (2000/2001), 669-686. MR 1844385; reference:[11] Móricz, F.: Statistical convergence of multiple sequences.Arch. Math. 81 (2003), 82-89. MR 2002719, 10.1007/s00013-003-0506-9; reference:[12] Muresaleen, Edely, Osama H. H.: Statistical convergence of double sequences.J. Math. Anal. Appl. 288 (2003), 223-231. MR 2019757, 10.1016/j.jmaa.2003.08.004; reference:[13] Nuray, F., Ruckle, W. H.: Generalized statistical convergence and convergence free spaces.J. Math. Anal. Appl. 245 (2000), 513-527. Zbl 0955.40001, MR 1758553, 10.1006/jmaa.2000.6778; reference:[14] Pringsheim, A.: Zur Theorie der zweifach unendlichen Zahlenfolgen.Math. Ann. 53 (1900), 289-321. MR 1511092, 10.1007/BF01448977; reference:[15] Savas, E., Muresaleen: {On statistically convergent double sequences of fuzzy numbers}.Information Sciences 162 (2004), 183-192. MR 2076238, 10.1016/j.ins.2003.09.005; reference:[16] Šalát, T.: On statistically convergent sequences of real numbers.Math. Slovaca 30 (1980), 139-150. MR 0587239; reference:[17] Schoenberg, I. J.: The integrability of certain functions and related summability methods.Amer. Math. Monthly. 66 (1959), 361-375. Zbl 0089.04002, MR 0104946, 10.2307/2308747

الاتاحة: http://hdl.handle.net/10338.dmlcz/140543

المؤلفون: Broniatowski, Michel

مصطلحات موضوعية: keyword:divergence, keyword:parametric estimation, keyword:robustness, msc:62B10, msc:62F10, msc:62F35

وصف الملف: application/pdf

Relation: mr:MR3013393; reference:[1] D. F. Andrews, P. J. Bickel, F. R. Hampel, P. J. Huber, W. H. Rogers, J. W. Tukey: Robust Estimates of Location.Princeton University Press, Princeton N. J. 1972. Zbl 0254.62001, MR 0331595; reference:[2] A. Basu, I. R. Harris, N. L. Hjort, M. C. Jones: Robust and efficient estimation by minimizing a density power divergence.Biometrika 85 (1998), 3, 549-559. MR 1665873, 10.1093/biomet/85.3.549; reference:[3] M. Broniatowski, A. Keziou: Minimization of $\phi$-divergences on sets of signed measures.Studia Sci. Math. Hungar. 43 (2006), 403-442. Zbl 1121.28004, MR 2273419; reference:[4] M. Broniatowski, A. Keziou: Parametric estimation and tests through divergences and the duality technique.J. Multivariate Anal. 100 (2009), 1, 16-31. Zbl 1151.62023, MR 2460474, 10.1016/j.jmva.2008.03.011; reference:[5] M. Broniatowski, A. Toma, I. Vajda: Decomposable pseudodistances and applications in statistical estimation.J. Statist. Plann. Inference. 142 (2012), 9, 2574-2585 MR 2922007, 10.1016/j.jspi.2012.03.019; reference:[6] M. Broniatowski, I. Vajda: Several applications of divergence criteria in continuous families.arXiv:0911.0937v1, 2009.; reference:[7] F. R. Hampel, E. M. Ronchetti, P. J. Rousseuw, W. A. Stahel: Robust Statistics: The approach Based on Influence Functions.Willey, New York 1986. MR 0829458; reference:[8] F. Liese, I. Vajda: Convex Statistical Distances.Teubner, Leipzig 1987. Zbl 0656.62004, MR 0926905; reference:[9] F. Liese, I. Vajda: On divergences and informations in statistics and information theory.IEEE Trans. Inform. Theory 52 (2006), 10, 4394-4412. MR 2300826, 10.1109/TIT.2006.881731; reference:[10] C. Miescke, F. Liese: Statistical Decision Theory.Springer, Berlin 2008. Zbl 1154.62008, MR 2421720; reference:[11] M. R. C. Read, N. A. C. Cressie: Goodness-of-Fit Statistics for Discrete Multivariate Data.Springer, Berlin 1988. Zbl 0663.62065, MR 0955054; reference:[12] A. Rényi: On measures of entropy and information.In: Proc. 4th Berkeley Symp. on Probability and Statistics, Vol. 1, University of California Press, Berkeley 1961, pp. 547-561. Zbl 0106.33001, MR 0132570; reference:[13] A. Toma, M. Broniatowski: Minimum divergence estimators and tests: Robustness results.J. Multivariate Anal. 102 (2011), 1, 20-36. MR 2729417, 10.1016/j.jmva.2010.07.010; reference:[14] I. Vajda: Minimum divergence principle in statistical estimation.Statist. Decisions (1984), Suppl. Issue No. 1, 239-261. Zbl 0558.62004, MR 0785211; reference:[15] I. Vajda: Efficiency and robustness control via distorted maximum likelihood estimation.Kybernetika 22 (1986), 47-67. Zbl 0603.62039, MR 0839344; reference:[16] I. Vajda: Comparison of asymptotic variances for several estimators of location.Probl. Control Inform. Theory 18 (1989), 2, 79-89. Zbl 0678.62035, MR 0991547; reference:[17] I. Vajda: Estimators asymptotically minimax in wide sense.Biometr. J. 31 (1989), 7, 803-810. MR 1054736, 10.1002/bimj.4710310706; reference:[18] I. Vajda: Modifications od Divergence Criteria for Applications in Continuous Families.Research Report No. 2230, Institute of Information Theory and Automation, Prague 2008.; reference:[19] A. W. van der Vaart: Asymptotic Statistics.Cambridge University Press, Cambridge 1998. Zbl 0910.62001, MR 1652247; reference:[20] A. W. van der Vaart, J. A. Wellner: Weak Convergence and Empirical Processes.Springer, Berlin 1996. Zbl 0862.60002, MR 1385671

الاتاحة: http://hdl.handle.net/10338.dmlcz/143054

المؤلفون: Atmania, R., Mazouzi, S.

مصطلحات موضوعية: keyword:impulsive condition, keyword:delayed parabolic equation, keyword:oscillation, keyword:divergence theorem, keyword:impulsive differential inequality, msc:35B05, msc:35K61, msc:35R12

وصف الملف: application/pdf

Relation: mr:MR2852382; zbl:Zbl 1249.35333; reference:[1] Bainov, D., Minchev, E.: Trends in theory of impulsive partial differential equations.Nonlinear World 3 (3) (1996), 357–384. MR 1411360; reference:[2] Bainov, D., Minchev, E.: Forced oscillations of solutions of impulsive nonlinear parabolic differential-difference equations.J. Korean Math. Soc. 35 (4) (1998), 881–890. Zbl 0922.35183, MR 1666462; reference:[3] Cui, B., Deng, F. Q., Li, W. N., Liu, Y. Q.: Oscillation problems for delay parabolic systems with impulses.Dyn. Contin. Discrete Impuls Syst. Ser. A Math. Anal. 12 (2005), 67–76. MR 2099905; reference:[4] Fu, X., Liu, X.: Oscillation criteria for impulsive hyperbolic systems.Dynam. Contin. Discrete Impuls. Systems 3 (2) (1997), 225–244. Zbl 0927.34008, MR 1448781; reference:[5] Fu, X., Liu, X., Sivaloganathan, S.: Oscillation criteria for impulsive parabolic differential equations with delay.J. Math. Anal. Appl. 268 (2002), 647–664. Zbl 1160.35429, MR 1896220, 10.1006/jmaa.2001.7840; reference:[6] Liu, A., Xiao, L., Liu, T.: Oscillation of nonlinear impulsive hyperbolic equations with several delays.Electron. J. Differential Equations 2004 (24) (2004), 1–6. Zbl 1060.35153, MR 2036208

الاتاحة: http://hdl.handle.net/10338.dmlcz/141708

المؤلفون: Lukáčová-Medviďová, Mária, Saibertová, Jitka, Warnecke, Gerald, Zahaykah, Yousef

مصطلحات موضوعية: keyword:hyperbolic systems, keyword:wave equation, keyword:evolution Galerkin schemes, keyword:Maxwell equations, keyword:linearized Euler equations, keyword:divergence-free, keyword:vorticity, keyword:dispersion, msc:35A35, msc:35Q35, msc:35Q60, msc:65M60, msc:76B99, msc:76M10, msc:78M10

وصف الملف: application/pdf

Relation: mr:MR2086087; zbl:Zbl 1099.65088; reference:[1] C. A. Balanis: Advance Engineering Electromagnetics.John Wiley & Sons, New York-Chichester-Brisbane-Toronto-Singapore, 1989.; reference:[2] D. K. Cheng: Field and Wave Electromagnetics.Addison-Wesley Publishing Company, second edition, 1989.; reference:[3] J. D. Jackson: Classical Electrodynamics.John Wiley & Sons, third edition, New York, 1999. Zbl 0920.00012, MR 0436782; reference:[4] M. Lukáčová-Medviďová, K. W. Morton, and G. Warnecke: Finite volume evolution, Galerkin metods for Euler equations of gas dynamics.Internat. J. Numer. Methods Fluids 40 (2002), 425–434. MR 1932992, 10.1002/fld.297; reference:[5] M. Lukáčová-Medviďová, K. W. Morton, and G. Warnecke: Evolution Galerkin methods for hyperbolic systems in two space dimensions.Math. Comp. 69 (2000), 1355–1348. MR 1709154, 10.1090/S0025-5718-00-01228-X; reference:[6] M. Lukáčová-Medviďová, J. Saibertová, and G. Warnecke: Finite volume evolution Galerkin methods for nonlinear hyperbolic systems.J. Comput. Phys. 183 (2002), 533–562. MR 1947781, 10.1006/jcph.2002.7207; reference:[7] M. Lukáčová-Medviďová, G. Warnecke, and Y. Zahaykah: On the boundary conditions for EG-methods applied to the two-dimensional wave equation system.Z. Angew. Math. Mech. 84 (2004), 237–251. MR 2045490, 10.1002/zamm.200310103; reference:[8] M. Lukáčová-Medviďová, G. Warnecke, and Y. Zahaykah: Third order finite volume evolution Galerkin (FVEG) methods for two-dimensional wave equation system.J. Numer. Math. 11 (2003), 235–251. MR 2018817; reference:[9] S. Ostkamp: Multidimensional characteristic Galerkin schemes and evolution operators for hyperbolic systems.Math. Methods Appl. Sci. 20 (1997), 1111–1125. MR 1465396, 10.1002/(SICI)1099-1476(19970910)20:133.0.CO;2-1; reference:[10] G. Strang: On the construction and comparison of difference schemes.SIAM J. Numer. Anal. 5 (1968), 506–517. MR 0235754, 10.1137/0705041; reference:[11] Y. Zahaykah: Evolution Galerkin schemes and discrete boundary condition for multidimensional first order systems.PhD. thesis, Magdeburg, 2002.

الاتاحة: http://hdl.handle.net/10338.dmlcz/134577

المؤلفون: Štěpánek, František

مصطلحات موضوعية: keyword:Fourier series, keyword:divergence, keyword:convergence, msc:01A60, msc:42A20, msc:42A24

وصف الملف: application/pdf

Relation: zbl:Zbl 1265.01011; reference:[33] Choquet, G.: Spojité, diskrétní a . všechno ostatní.48 (2003), 158–168.; reference:[34] Katětov, M.: N. N. Luzin a teorie reálných funkcí.20 (1975) 137–145.; reference:[35] Kuratowski, K.: A half century of Polish mathematics.PWN, Warszawa and Pergamon Press, Oxford 1980. Zbl 0438.01006, MR 0565253; reference:[36] Luzin, N. N.: Integral i trigonometričeskij rjad.Gos. izdatělstvo tech.-teor. litěratury, Moskva-Leningrad 1951. MR 0048364; reference:[37] Uljanov, P. L.: A. N. Kolmogorov i raschodjaščijesja rjady Furje.Uspěchi matem. nauk 38 (1983), 51–90. MR 0710114; reference:[38] Edwards, R. E.: Fourier series, Vol. I + Vol. II.Holt, Rinehart and Winston, New York 1967.; reference:[39] Lasser, R.: Introduction to Fourier series.Marcel Dekker, New York 1996. Zbl 0848.42001, MR 1379801; reference:[40] Zygmund, A.: Trigonometrical series.Monografje matematyczne Tom V, Warszawa–Lwów 1935. (Citace podle ruského překladu: Trigonometričeskije rjady. Izdatělstvo MIR, Moskva 1965.) Zbl 0011.01703; reference:[41] Jorsboe, O. G., Mejlboro, L.: The Carleson-Hunt theorem on Fourier series.Lecture Notes in Math. 911, Springer-Verlag, Berlin 1982. MR 0653477; reference:[42] Štěpánek, F.: Teorie aproximací I. (Základy teorie limitovacích metod).SPN, Praha 1979.; reference:[43] Kahane, J.-P.: Sur la divergence presque sûre presque partout de certaines séries de Fourier aléatoires.Annales Universitatis Scientiarum Budapestinensis, Sectio Mathematica, 3–4 (1960–1961), 101–108. MR 0132961; reference:[44] Konyagin, S. V.: On everywhere divergence of trigonometric Fourier series.Sborník: Mathematics 191 (2000), 97–120. Zbl 0967.42004, MR 1753494; reference:[45] Körner, T. W.: Sets of divergence for Fourier series.Bull. London Math. Soc. 3 (1971), 152–154. MR 0290022, 10.1112/blms/3.2.152; reference:[46] Körner, T. W.: Everywhere divergent Fourier series.Colloq. Math. 45 (1981), 103–118. MR 0652607; reference:[47] Lusin, N. N.: Sur la convergence des séries trigonométriques de Fourier.Comptes Rendus Acad. Sci. Paris 156 (1913), 1655–1658.; reference:[48] Prestini, E.: On the two proofs of pointwise convergence of Fourier series.Amer. J. Math. 104 (1982), 127–139. Zbl 0499.42003, MR 0648483, 10.2307/2374070; reference:[49] Zygmund, A.: On certain lemmas of Marcinkiewicz and Carleson.J. Approx. Theory 2 (1969), 249–257. Zbl 0175.35303, MR 0261408

الاتاحة: http://hdl.handle.net/10338.dmlcz/140852

المؤلفون: Dragomir, S. S.

مصطلحات موضوعية: keyword:$f$-divergence, keyword:divergence measures in information theory, keyword:Jensen’s inequality, keyword:Hellinger and triangular discrimination, msc:26D15, msc:94A17

وصف الملف: application/pdf

Relation: mr:MR1980368; zbl:Zbl 1099.94015; reference:[1] I. Csiszár: Information measures: A critical survey.Trans. 7th Prague Conf. on Info. Th., Statist. Decis. Funct., Random Processes and 8th European Meeting of Statist., Volume B, Academia Prague, 1978, pp. 73–86. MR 0519465; reference:[2] I. Csiszár: Information-type measures of difference of probability functions and indirect observations.Studia Sci. Math. Hungar. 2 (1967), 299–318. MR 0219345; reference:[3] I. Csiszár, J. Körner: Information Theory: Coding Theorem for Discrete Memory-less Systems.Academic Press, New York, 1981. MR 0666545; reference:[4] : Maximum Entropy and Bayesian Methods in Applied Statistics.J. H. Justice (ed.), Cambridge University Press, Cambridge, 1986. Zbl 0597.00025, MR 0892126; reference:[5] J. N. Kapur: On the roles of maximum entropy and minimum discrimination information principles in Statistics.Technical Address of the 38th Annual Conference of the Indian Society of Agricultural Statistics, 1984, pp. 1–44. MR 0786009; reference:[6] I. Burbea, C. R. Rao: On the convexity of some divergence measures based on entropy functions.IEEE Transactions on Information Theory 28 (1982), 489–495. MR 0672884, 10.1109/TIT.1982.1056497; reference:[7] R. G. Gallager: Information Theory and Reliable Communications.J. Wiley, New York, 1968.; reference:[8] C. E. Shannon: A mathematical theory of communication.Bull. Sept. Tech. J. 27 (1948), 370–423 and 623–656. Zbl 1154.94303, MR 0026286; reference:[9] B. R. Frieden: Image enhancement and restoration.Picture Processing and Digital Filtering, T. S. Huang (ed.), Springer-Verlag, Berlin, 1975.; reference:[10] R. M. Leahy, C. E. Goutis: An optimal technique for constraint-based image restoration and mensuration.IEEE Trans. on Acoustics, Speech and Signal Processing 34 (1986), 1629–1642. 10.1109/TASSP.1986.1165001; reference:[11] S. Kullback: Information Theory and Statistics.J. Wiley, New York, 1959. Zbl 0088.10406, MR 0103557; reference:[12] S. Kullback, R. A. Leibler: On information and sufficiency.Ann. Math. Statistics 22 (1951), 79–86. MR 0039968, 10.1214/aoms/1177729694; reference:[13] R. Beran: Minimum Hellinger distance estimates for parametric models.Ann. Statist. 5 (1977), 445–463. Zbl 0381.62028, MR 0448700, 10.1214/aos/1176343842; reference:[14] A. Renyi: On measures of entropy and information.Proc. Fourth Berkeley Symp. Math. Statist. Prob., Vol. 1, University of California Press, Berkeley, 1961. Zbl 0106.33001, MR 0132570; reference:[15] S. S. Dragomir, N. M. Ionescu: Some converse of Jensen’s inequality and applications.Anal. Numer. Theor. Approx. 23 (1994), 71–78. MR 1325895; reference:[16] S. S. Dragomir, C. J. Goh: A counterpart of Jensen’s discrete inequality for differentiable convex mappings and applications in information theory.Math. Comput. Modelling 24 (1996), 1–11. MR 1403525, 10.1016/0895-7177(96)00085-4; reference:[17] S. S. Dragomir, C. J. Goh: Some counterpart inequalities in for a functional associated with Jensen’s inequality.J. Inequal. Appl. 1 (1997), 311–325. MR 1732628; reference:[18] S. S. Dragomir, C. J. Goh: Some bounds on entropy measures in information theory.Appl. Math. Lett. 10 (1997), 23–28. MR 1457634, 10.1016/S0893-9659(97)00028-1; reference:[19] S. S. Dragomir, C. J. Goh: A counterpart of Jensen’s continuous inequality and applications in information theory.RGMIA Preprint.http://matilda.vu.edu.au/~rgmia/InfTheory/Continuse.dvi. MR 1977385; reference:[20] M. Matić: Jensen’s inequality and applications in information theory.Ph.D. Thesis, Univ. of Zagreb, 1999. (Croatian); reference:[21] S. S. Dragomir, J. Unde and M. Scholz: Some upper bounds for relative entropy and applications.Comput. Math. Appl. 39 (2000), 257–266. MR 1753564, 10.1016/S0898-1221(00)00089-4; reference:[22] J. N. Kapur: A comparative assessment of various measures of directed divergence.Advances Manag. Stud. 3 (1984), 1–16.; reference:[23] D. S. Mitrinović, J. E. Pečarić and A. M. Fink: Classical and New Inequalities in Analysis.Kluwer Academic Publishers, , 1993. MR 1220224; reference:[24] F. Topsoe: Some inequalities for information divergence and related measures of discrimination.Res. Rep. Coll. RGMIA 2 (1999), 85–98. MR 1768575; reference:[25] D. Dacunha-Castelle: Vitesse de convergence pour certains problemes statistiques.In: Ecole d’été de Probabilités de Saint-Flour, VII (Saint-Flour, 1977). Lecture Notes in Math. Vol. 678, Springer, Berlin, 1978, pp. 1–172. Zbl 0387.62015, MR 0518733; reference:[26] H. Jeffreys: An invariant form for the prior probability in estimation problems.Proc. Roy. Soc. London Ser. A 186 (1946), 453–461. Zbl 0063.03050, MR 0017504, 10.1098/rspa.1946.0056; reference:[27] A. Bhattacharyya: On a measure of divergence between two statistical populations defined by their probability distributions.Bull. Calcutta Math. Soc. 35 (1943), 99–109. Zbl 0063.00364, MR 0010358; reference:[28] S. S. Dragomir: Some inequalities for the Csiszár $\Phi $-divergence.Submitted.; reference:[29] S. S. Dragomir: A converse inequality for the Csiszár $\Phi $-divergence.Submitted. Zbl 1066.94007; reference:[30] S. S. Dragomir: Some inequalities for $(m,M)$-convex mappings and applications for the Csiszár $\Phi $-divergence in information theory.Math. J. Ibaraki Univ. (Japan) 33 (2001), 35–50. Zbl 0996.26019, MR 1883258; reference:[31] F. Liese, I. Vajda: Convex Statistical Distances.Teubner Verlag, Leipzig, 1987. MR 0926905; reference:[32] I. Vajda: Theory of Statistical Inference and Information.Kluwer, Boston, 1989. Zbl 0711.62002

الاتاحة: http://hdl.handle.net/10338.dmlcz/134528

المؤلفون: Franchi, Bruno, Serapioni, Raul, Cassano, Francesco Serra

مصطلحات موضوعية: keyword:Carnot groups, keyword:perimeter, keyword:rectifiability, keyword:divergence theorem, msc:22E30, msc:49Q15

وصف الملف: application/pdf

Relation: mr:MR1981527; zbl:Zbl 1018.49029; reference:[1] L. Ambrosio: Some fine properties of sets of finite perimeter in Ahlfors regular metric measure spaces.Adv. Math. 159 (2001), 51–67. Zbl 1002.28004, MR 1823840, 10.1006/aima.2000.1963; reference:[2] E. De Giorgi: Su una teoria generale della misura $(r-1)$-dimensionale in uno spazio ad $r$ dimensioni.Ann. Mat. Pura Appl. 36 (1954), 191–213. Zbl 0055.28504, MR 0062214, 10.1007/BF02412838; reference:[3] E. De Giorgi: Nuovi teoremi relativi alle misure $(r-1)$-dimensionali in uno spazio ad $r$ dimensioni.Ricerche Mat. 4 (1955), 95–113. Zbl 0066.29903, MR 0074499; reference:[4] H. Federer: Geometric Measure Theory.Springer, 1969. Zbl 0176.00801, MR 0257325; reference:[5] G. B.Folland, E. M. Stein: Hardy Spaces on Homogeneous Groups.Princeton University Press, 1982. Zbl 0508.42025, MR 0657581; reference:[6] B. Franchi, R. Serapioni, F. Serra Cassano: Meyers-Serrin type theorems and relaxation of variational integrals depending on vector fields.Houston J. Math. 22 (1996), 859–889. MR 1437714; reference:[7] B. Franchi, R. Serapioni, F. Serra Cassano: Rectifiability and perimeter in the Heisenberg group.Math. Ann. 321 (2001), 479–531. MR 1871966, 10.1007/s002080100228; reference:[8] B. Franchi, R. Serapioni, F. Serra Cassano: Regular hypersurfaces, intrinsic perimeter and implicit function theorem in Carnot groups.Preprint (2001). MR 2032504; reference:[9] B. Franchi, R. Serapioni, F. Serra Cassano: On the structure of finite perimeter sets in step 2 Carnot groups.Preprint (2001). MR 1984849; reference:[10] N. Garofalo, D. M. Nhieu: Isoperimetric and Sobolev inequalities for Carnot-Carathéodory spaces and the existence of minimal surfaces.Comm. Pure Appl. Math. 49 (1996), 1081–1144. MR 1404326, 10.1002/(SICI)1097-0312(199610)49:103.0.CO;2-A; reference:[11] M. Gromov: Metric Structures for Riemannian and non Riemannian Spaces.vol. 152, Progress in Mathematics, Birkhauser, Boston, 1999. Zbl 0953.53002, MR 1699320; reference:[12] J. Heinonen: Calculus on Carnot groups.Ber., Univ. Jyväskylä 68 (1995), 1–31. Zbl 0863.22009, MR 1351042; reference:[13] A. Korányi, H. M. Reimann: Foundation for the theory of quasiconformal mappings on the Heisenberg group.Adv. Math. 111 (1995), 1–87. 10.1006/aima.1995.1017; reference:[14] J. Mitchell: On Carnot-Carathéodory metrics.J. Differ. Geom. 21 (1985), 35–45. Zbl 0554.53023, MR 0806700, 10.4310/jdg/1214439462; reference:[15] R. Monti, F. Serra Cassano: Surface measures in Carnot-Carathéodory spaces.Calc. Var. Partial Differ. Equ (to appear). MR 1865002; reference:[16] P. Pansu: Métriques de Carnot-Carathéodory et quasiisométries des espaces symétriques de rang un.Ann. Math. 129 (1989), 1–60. Zbl 0678.53042, MR 0979599, 10.2307/1971484; reference:[17] E. Sawyer, R. L. Wheeden: Weighted inequalities for fractional integrals on Euclidean and homogeneous spaces.Amer. J. Math. 114 (1992), 813–874. MR 1175693, 10.2307/2374799

الاتاحة: http://hdl.handle.net/10338.dmlcz/134175

المؤلفون: Menéndez, M., Morales, D., Pardo, L., Vajda, I.

مصطلحات موضوعية: keyword:divergence, keyword:disparity, keyword:minimum disparity estimators, keyword:robustness, keyword:asymptotic efficiency, msc:62B10, msc:62E20

وصف الملف: application/pdf

Relation: mr:MR1865516; zbl:Zbl 1059.62001; reference:[1] A. Basu, S. Sarkar: Minimum disparity estimation in the errors-in-variables model.Statist. Probab. Lett. 20 (1994), 69–73. MR 1294806, 10.1016/0167-7152(94)90236-4; reference:[2] A. Basu, S. Sarkar: The trade-off between robustness and efficiency and the effect of model smoothing.J. Statist. Comput. Simulation 50 (1994), 173–185. 10.1080/00949659408811609; reference:[3] M. W. Birch: A new proof of the Pearson-Fisher theorem.Ann. Math. Statist. 35 (1964), 817–824. Zbl 0259.62017, MR 0169324, 10.1214/aoms/1177703581; reference:[4] E. Bofinger: Goodness-of-fit using sample quantiles.J. Roy. Statist. Soc. Ser. B 35 (1973), 277–284. MR 0336896; reference:[5] H. Cramér: Mathematical Methods of Statistics.Princeton University Press, Princeton, 1946. MR 0016588; reference:[6] N. A. C. Cressie, R. C. Read: Multinomial goodness-of-fit tests.J. Roy. Statist. Soc. Ser. B 46 (1984), 440–464. MR 0790631; reference:[7] R. A. Fisher: Statistical Methods for Research Workers (8th edition).London, 1941.; reference:[8] F. Liese, I. Vajda: Convex Statistical Distances.Teubner, Leipzig, 1987. MR 0926905; reference:[9] B. G. Lindsay: Efficiency versus robutness: The case for minimum Hellinger distance and other methods.Ann. Statist. 22 (1994), 1081–1114. MR 1292557, 10.1214/aos/1176325512; reference:[10] M. L. Menéndez, D. Morales, L. Pardo and I. Vajda: Two approaches to grouping of data and related disparity statistics.Comm. Statist. Theory Methods 27 (1998), 609–633. MR 1619038, 10.1080/03610929808832117; reference:[11] M. L. Menéndez, D. Morales, L. Pardo and I. Vajda: Minimum divergence estimators based on grouped data.Ann. Inst. Statist. Math. 53 (2001), 277–288. MR 1841136, 10.1023/A:1012466605316; reference:[12] D. Morales, L. Pardo and I. Vajda: Asymptotic divergence of estimates of discrete distributions.J. Statist. Plann. Inference 48 (1995), 347–369. MR 1368984, 10.1016/0378-3758(95)00013-Y; reference:[13] J. Neyman: Contribution to the theory of the $\chi ^2$ test.In: Proc. Berkeley Symp. Math. Statist. Probab., Berkeley, CA, Berkeley University Press, Berkeley, 1949, pp. 239–273. MR 0028003; reference:[14] Ch. Park, A. Basu and S. Basu: Robust minimum distance inference based on combined distances.Comm. Statist. Simulation Comput. 24 (1995), 653–673. 10.1080/03610919508813265; reference:[15] C. R. Rao: Asymptotic efficiency and limiting information.In: Proc. 4th Berkeley Symp. Math. Stat. Probab., Berkeley, CA, Berkeley University Press, Berkeley, 1961, pp. 531–545. Zbl 0156.39802, MR 0133192; reference:[16] C. R. Rao: Linear Statistical Inference and its Applications (2nd edition).Wiley, New York, 1973. MR 0346957; reference:[17] R. C. Read, N. A. C. Cressie: Goodness-of-fit Statistics for Discrete Multivariate Data.Springer-Verlag, New York, 1988. MR 0955054; reference:[18] C. A. Robertson: On minimum discrepancy estimators.Sankhyä Ser. A 34 (1972), 133–144. Zbl 0266.62021, MR 0331606; reference:[19] I. Vajda: $\chi ^2$-divergence and generalized Fisher information.In: Transactions of the Sixth Prague Conference on Information Theory, Statistical Decision Functions and Random Processes, Academia, Prague, 1973, pp. 223–234. Zbl 0297.62003, MR 0356302; reference:[20] I. Vajda: Theory of Statistical Inference and Information.Kluwer Academic Publishers, Boston, 1989. Zbl 0711.62002; reference:[21] B. L. van der Waarden: Mathematische Statistik.Springer-Verlag, Berlin, 1957.; reference:[22] K. Pearson: On the criterion that a given system of deviations from the probable in the case of correlated system of variables is such that it can be reasonably supposed to have arisen from random sampling.Philosophical Magazine 50 (1990), 157–172.; reference:[23] I. Csiszár: Eine Informationstheoretische Ungleichung und ihre Anwendung auf den Beweis der Ergodizität von Markoffschen Ketten.Publications of the Mathematical Institute of the Hungarian Academy of Sciences, Series A 8 (1963), 85–108. MR 0164374; reference:[24] M. S. Ali, S. D. Silvey: A general class of coefficients of divergence of one distribution from another.J. Roy. Statist. Soc. Ser. B 28 (1966), 131–140. MR 0196777; reference:[25] A. Rényi: On measures of entropy and information.In: Proceedings of the 4th Berkeley Symposium on Probability Theory and Mathematical Statistics, Vol. 1, University of California Press, Berkeley, 1961, pp. 531–546. MR 0132570; reference:[26] A. W. Marshall, I. Olkin: Inequalities: Theory of Majorization and its Applications.Academic Press, New York, 1979. MR 0552278

الاتاحة: http://hdl.handle.net/10338.dmlcz/134477

المؤلفون: Korotov, Sergey

مصطلحات موضوعية: keyword:divergence-free functions, keyword:finite elements, keyword:internal approximation, keyword:stream function, keyword:Fourier transform, msc:65N30, msc:74S05, msc:76M10

وصف الملف: application/pdf

Relation: mr:MR1441632; zbl:Zbl 0902.65055; reference:[1] V. Girault, P. A. Raviart: Finite Element Approximation of the Navier-Stokes Equations.Springer-Verlag, Berlin, 1979. MR 0548867; reference:[2] I. Hlaváček, M. Křížek: Internal finite element approximations in the dual variational methods for second order elliptic problems with curved boundaries.Apl. Mat. 29 (1984), 52–69. MR 0729953; reference:[3] M. Křížek, P. Neittaanmäki: Internal FE approximation of spaces of divergence-free functions in 3-dimensional domains.Internat. J. Numer. Methods Fluids 6 (1986), 811–817. MR 0865678, 10.1002/fld.1650061104; reference:[4] M. Křížek, P. Neittaanmäki: Finite Element Approximation of Variational Problems and Applications.Longman Scientific & Technical, Harlow, 1990. MR 1066462; reference:[5] J. C. Nedelec: Eléments finis mixtes incompressibles pour l’equation de Stokes dans $^3$.Numer. Math. 39 (1982), 97–112. MR 0664539, 10.1007/BF01399314; reference:[6] R. Temam: Navier-Stokes Equations.North-Holland, Amsterdam, 1979. Zbl 0454.35073, MR 0603444; reference:[7] V. S. Vladimirov: Equations of Mathematical Physics.Marcel Dekker, New York, 1971. Zbl 0231.35002, MR 0268497

الاتاحة: http://hdl.handle.net/10338.dmlcz/134355

المؤلفون: Král, Josef

مصطلحات موضوعية: keyword:perimeter, keyword:divergence theorem, keyword:the divergence theorem of Gauss-Ostrogradski, msc:01A70, msc:28-03, msc:28A75, msc:28B20

وصف الملف: application/pdf

Relation: mr:MR1428138; zbl:Zbl 0879.28011; reference:[1] M. Chlebík: Tricomi Potentials.Thesis presented in the Mathematical Institute of the Czechoslovak Academy of Sciences in 1988. (In Slovak.); reference:[2] E. De Giorgi: Su una teoria generale della misura (r-1)-dimensionale in uno spazio ad r dimensioni.Annali di Matematica (IV) 36 (1954), 191-213. Zbl 0055.28504, MR 0062214, 10.1007/BF02412838; reference:[3] E. De Giorgi: Nuovi teoremi relativi alle misure (r-1)-dimensionali in uno spazio ad r dimensioni.Ricerche di Matematica IV (1955), 94-113. Zbl 0066.29903; reference:[4] H. Federer: Geometric measure theory.Springer-Verlag, Berlin 1969. Zbl 0176.00801, MR 0257325; reference:[5] K. Krickegerg: Distributionen, Funktionen beschränkter Variation und Lebesgueschei Inhalt nichtparametrischer Flächen.Annali di Matematica pura ed applicada (IV) XLIV (1957), 105-134. MR 0095922; reference:[6] J. Mařík: The surface integral.Časopis Pěst. Mat. 81 (1956), 79-82. (In Czech.) MR 0089891; reference:[7] J. Mařík: The surface integral.Czechoslovak Math. J. 6(81) (1956), 522-558. MR 0089891; reference:[8] J. Mařík: A note to the length of a Jordan curve.Časopis Pěst. Mat. 83 (1958), 91-96. (In Czech.) MR 0095243; reference:[9] A. I. Voľpert: BV spaces and quasilinear equations.Matem. sbornik 73 (115) (1967), No. 2, 255-302. (In Russian.) MR 0216338

الاتاحة: http://hdl.handle.net/10338.dmlcz/126043

المؤلفون: Hao, Wenge, Leonardi, Salvatore, Steinhauer, Mark

مصطلحات موضوعية: keyword:divergence-free solutions, keyword:elliptic systems, keyword:systems of Stokes-type, keyword:regularity, msc:35B65, msc:35C05, msc:35D10, msc:35J15, msc:35J45, msc:35Q30

وصف الملف: application/pdf

Relation: mr:MR1364492; zbl:Zbl 0837.35041; reference:[1] Campanato S.: Sistemi ellittici in forma divergenza. Regolarita' all'interno.Quaderno Sc. Norm. Sup. Pisa Pisa (1980). Zbl 0453.35026, MR 0668196; reference:[2] De Giorgi E.: Un esempio di estremali discontinue per un problema variazionale di tipo ellittico.Boll. U.M.I. 4 (1968), 135-137. MR 0227827; reference:[3] Frehse J.: Una generalizzazione di un controesempio di De Giorgi nella teoria delle equazioni ellitiche.Boll. U.M.I. 6 (1970), 998-1002. MR 0276612; reference:[4] Galdi G.P.: An introduction to the mathematical theory of the Navier-Stokes equations, Volume I: Linearized steady problems.Springer tracts in natural philosophy vol.38, Springer-Verlag, New York Berlin Heidelberg et alii, 1994. MR 1284205; reference:[5] Giaquinta M.: Multiple integrals in the calculus of variations and nonlinear elliptic systems.Annals of Math. Studies, vol. 105 Princeton University Press Princeton (1983). Zbl 0516.49003, MR 0717034; reference:[6] Giaquinta M., Modica G.: Non linear systems of the type of the Navier-Stokes system.J. Reine Angewandte Math. 330 (1982), 173-214. MR 0641818; reference:[7] John O., Malý J., Stará J.: Nowhere continuous solutions to elliptic systems.Comment. Math. Univ. Carolinae 30 (1989), 33-43. MR 0995699; reference:[8] Koshelev A.I., Chelkak S.I.: Regularity of solutions of quasilinear elliptic systems.Teubner Leipzig (1985). Zbl 0581.35003, MR 0825485; reference:[9] Ladyzhenskaya O. A.: The mathematical theory of viscous incompressible flow.Gordon and Breach Science Publishers New York (1969). Zbl 0184.52603, MR 0254401; reference:[10] Leonardi S.: On constants of some regularity theorems. De Giorgi counterexamples.Preprint N.I.U (1993) [Thesis (1995-96)], to appear.; reference:[11] Munkres J.R.: Analysis on manifolds.Addison-Wesley Redwood City (1991). Zbl 0743.26006, MR 1079066; reference:[12] Nečas J.: Introduction to the theory of nonlinear elliptic equations.Teubner, Leipzig, 1983 or J. Wiley, Chichester (1986). MR 0731261; reference:[13] Nečas J.: Notes for a talk given at the Equadiff 8 in Bratislava 1993.(personal communication).; reference:[14] Souček J.: Singular solutions to linear elliptic systems,.Comment. Math. Univ. Carolinae 25 (1984), 273-281. MR 0768815; reference:[15] Steinhauer M.: Funktionenräume vom Campanato-Typ und Regularitätseigenschaften elliptischer Systeme zweiter Ordnung.Diplomarbeit Univ. Bonn (1993).

الاتاحة: http://hdl.handle.net/10338.dmlcz/118780

المؤلفون: Taneja, Inder Jeet, Pardo, L., Morales, D.

مصطلحات موضوعية: keyword:divergence measures, keyword:information radius, keyword:statistical experiment, keyword:sufficiency of experiments, keyword:Shannon's entropy, keyword:comparison of experiments, keyword:stochastic transformations, keyword:unified scalar parametric generalizations of Jensen difference divergence measure, msc:62B10, msc:62B15, msc:94A15, msc:94A17

وصف الملف: application/pdf

Relation: mr:MR1134921; zbl:Zbl 0748.62003; reference:[1] Blackwell D. (1951): Comparison of experiments.Proc. 2nd Berkeley Symp. Berkeley: University of California Press, 93-102. MR 0046002; reference:[2] Burbea J. (1984): The Bose-Einstein Entropy of degree a and its Jensen Difference.Utilitas Math. 25, 225-240. MR 0752861; reference:[3] Burbea J., Rao C . R. (1982): Entropy Differential Metric, Distance and Divergence Measures in Probability Spaces: A Unified Approach.J. Multi. Analy. 12, 575 - 596. MR 0680530, 10.1016/0047-259X(82)90065-3; reference:[4] Burbea J., Rao C. R. (1982): On the Convexity of some Divergence Measures based on Entropy Functions.IEEE Trans. on Inform. Theory IT-28, 489-495. MR 0672884; reference:[5] Capocelli R. M., Taneja I. J. (1984): Generalized Divergence Measures and Error Bounds.Proc. IEEE Internat. Conf. on Systems, man and Cybernetics, Oct. 9-12, Halifax, Canada, pp. 43 - 47.; reference:[6] Campbell L. L. (1986): An extended Čencov characterization of the Information Metric.Proc. Ann. Math. Soc., 98, 135-141. MR 0848890; reference:[7] Čencov N. N. (1982): Statistical Decisions Rules and Optimal Inference.Trans. of Math. Monographs, 53, Am. Math. Soc., Providence, R. L. MR 0645898; reference:[8] De Groot M. H. (1970): Optimal Statistical Decisions.McGraw-Hill. New York. MR 0356303; reference:[9] Ferentinos K., Papaioannou T. (1982): Information in experiments and sufficiency.J. Statist. Plann. Inference 6, 309-317. MR 0667911, 10.1016/0378-3758(82)90001-5; reference:[10] Goel P. K., De Groot (1979): Comparison of experiments and information measures.Ann. Statist. 7, 1066-1077. MR 0536509, 10.1214/aos/1176344790; reference:[11] Kullback S., Leibler A. (1951): On information and sufficiency.Ann. Math Stat. 27, 986-1005.; reference:[12] Lindley D. V. (1956): On a measure of information provided by an experiment.Ann. Math. Statis. 27, 986-1005. MR 0083936, 10.1214/aoms/1177728069; reference:[13] Marshall A. W., Olkin I. (1979): Inequalities: Theory of Majorization and its Applications.Academic Press. New York. MR 0552278; reference:[14] Morales D., Taneja I. J., Pardo L.: Comparison of Experiments based on $\phi$-Measures of Jensen Difference.Communicated.; reference:[15] Pardo L., Morales D., Taneja I. J.: $\lambda$-measures of hypoentropy and comparison of experiments: Bayesian approach.To appear in Statistica. Zbl 0782.62011, MR 1173196; reference:[16] Rao C. R. (1982): Diversity and Dissimilarity Coefficients: A Unified Approach.J. Theoret. Pop. Biology, 21, 24-43. MR 0662520, 10.1016/0040-5809(82)90004-1; reference:[17] Rao C. R., Nayak T. K. (1985): Cross Entropy, Dissimilarity Measures and characterization of Quadratic Entropy.IEEE Trans, on Inform. Theory, IT-31(5), 589-593. MR 0808230, 10.1109/TIT.1985.1057082; reference:[18] Sakaguchi M. (1964): Information Theory and Decision Making.Unpublished Lecture Notes, Statist. Dept., George Washington Univ., Washington DC.; reference:[19] Sanťanna A. P., Taneja I. J.: Trigonometric Entropies, Jensen Difference Divergence Measures and Error Bounds.Information Sciences 25, 145-156. MR 0794765; reference:[20] Shannon C. E. (1948): A Mathematical Theory of Communications.Bell. Syst. Tech. J. 27, 379-423. MR 0026286, 10.1002/j.1538-7305.1948.tb01338.x; reference:[21] Sibson R. (1969): Information Radius.Z. Wahrs. und verw. Geb. 14, 149-160. MR 0258198, 10.1007/BF00537520; reference:[22] Taneja I. J.: 1(983): On characterization of J-divergence and its generalizations.J. Combin. Inform. System Sci. 8, 206-212. MR 0783757; reference:[23] Taneja I. J. (1986): $\lambda$-measures of hypoentropy and their applications.Statistica, anno XLVI, n. 4, 465-478. MR 0887303; reference:[24] Taneja I. J. (1986): Unified Measure of Information applied to Markov Chains and Sufficiency.J. Comb. Inform. & Syst. Sci., 11, 99-109. MR 0966074; reference:[25] Taneja I. J. (1987): Statistical aspects of Divergence Measures.J. Statist. Plann. & Inferen., 16, 137-145. MR 0895754, 10.1016/0378-3758(87)90063-2; reference:[26] Taneja I. J. (1989): On Generalized Information Measures and their Applications.Adv. Elect. Phys. 76, 327 - 413. Academic Press.; reference:[27] Taneja I. J. (1990): Bounds on the Probability of Error in Terms of Generalized Information Radius.Information Sciences. 46.; reference:[28] Taneja I. J., Morales D., Pardo L. (1991): $\lambda$-measures of hypoentropy and comparison of experiments: Blackwell and Lehemann approach.Kybernetika, 27, 413 - 420. MR 1132603; reference:[29] Vajda I. (1968): Bounds on the Minimal Error Probability and checking a finite or countable number of Hypothesis.Inform. Trans. Problems 4, 9-17. MR 0267685; reference:[30] Vajda I. (1989): Theory of Statistical Inference and Information.Kluwer Academic Publishers, Dordrecht/Boston/London/.

الاتاحة: http://hdl.handle.net/10338.dmlcz/104481