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Jha, P.
- On Generalized Useful Entropy for Incomplete Probability Distribution
Abstract Views :395 |
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Authors
Affiliations
1 Dept. of Maths, Govt. Chhattisgarh P.G. College, Raipur (Chhattisgarh)., IN
1 Dept. of Maths, Govt. Chhattisgarh P.G. College, Raipur (Chhattisgarh)., IN
Source
Global Journal of Mathematical Science:Theory and Practical, Vol 5, No 1 (2013), Pagination: 47-52Abstract
In 2005 Khan, Bhat and S. Pirzada proved a noiseless coding theorem by considering useful entropy and useful mean codeword length. In this communication we consider a generalization of the useful mean codeword length and derived lower and upper bounds for it in terms of useful entropy for incomplete probability distribution.Keywords
Useful Entropy, Useful Mean Code Word Length, Coding Theorem
References
- M.Belis and S.Guiasu, A qualitative-quantitative measure of information in Cyberna-tics Systems, IEEE Trans. Information Theory, IT-14(1968), 593-594.
- P.K.Bhatia, On generalized useful inaccuracy for incomplete probability distribution, Soochow J. Math., 25(2) (1999), 131-135.
- AFeinstein, Foundation of Information Theory, McGraw HILL, New York,(1958).
- S. Guiasu and C.F.Picard, Born infericutre de la Longuerur utile de certain codes, C.R Acad. Sci. Paris, 273A (1971), 248-251.
- Gurdial and F.Pessoa, On useful information of ordera, J. Comb. Information and syst. Sci., 2(1977), 158-162.
- AB.Khan and RAutar, On useful information of order a and f3, Soochow lMath., 5(1979),93-99.
- AB.Khan, B.ABhat and S,Pirzada,"Some result on a generalized useful information mea-sure",J. Ineq. Pure and Appl.Math., 6(4) Art. 117, (2005).
- G.Longo, A noiseless coding theorem for sources having utilities, SIAM l Appl. Math., 30(4) (1979), 739-748.
- L.K.Roy, Comparison of Renyi entropies of power distribution, AMM,56(1976),217-218.
- C.E.Shannon, A Mathematical theory of Communication, Bell Sysstem, Tech. r. 27(1948), 394-423, 623-656.
- O.Shisha, Inequalities, Academic Press, New York (1967).
- U-Compactness and Gδ-Continuity
Abstract Views :436 |
PDF Views:0
Authors
Affiliations
1 Govt . J. Y . Chhattisgarh College , Raipur (C.G.), IN
2 Govt. Nagarjun Science College , Raipur(C.G.), IN
3 3B. R .S. M . College of Agricultural Engineering and Technology, Raipur (C.G.), IN
1 Govt . J. Y . Chhattisgarh College , Raipur (C.G.), IN
2 Govt. Nagarjun Science College , Raipur(C.G.), IN
3 3B. R .S. M . College of Agricultural Engineering and Technology, Raipur (C.G.), IN
Source
International Journal of Mathematics Research, Vol 5, No 1 (2013), Pagination: 183-187Abstract
Velleman proved that a mapping from R to R is continuous if and only if the images of compact sets are compact sets . Arenas and Puertas generalized this characterization of cont--inuity between two topological spaces . G. Nordo and Pasinkov generalized the Arenas and Puertas result to some different classes of spaces, by generalizing the definition of set of mappings characterized by images of sets . In the present paper , we prove results based on Gδ-continuity and U-compact spaces.We prove that the U-compactness of the space is preserved under Gδ-continuous mapping and also prove that Gδ- continuous image of product of two U-compact spaces , is again U-compact.Keywords
U-compact spaces , Gδ-continuity.References
- Velleman , D. J., 1997 , “Characterizing Continuity “ , American Math. Monthly 104 (4) , 318-322.
- Nordo , G. and Pasynkov ,B. A. , “Characterizing Continuity in Topological Spaces “ , monograph 1-6 . Giorgio Nordo Department di matematica di Messina, Contrada Papardo Salita sperone 31 98166 sant’ Agata Massina (ITALY) E-mail : nordo©dipmat.unime. it Boris A. Pasinkov Chair of General Topology and Geometry, Mechanics and Mathematics Faculty, Moscow State University,Moscow 119899 (RUSSIA) E-mail: pasinkov©mech.math.msu.su.6
- Munkers , J. R . , 1992 , ” Topology A First Course” , Prentice-Hall of India,Private Limited , .
- Arya , S.P. , and Jha , P. , 1993 , “ U-Fuzzy Compactness and Fuzzy Supercompactness “, The Journal of Fuzzy Mathematics , 1(2) , Los Angeles .
- On Suitable Codes Corresponding to M- Probability Distributions
Abstract Views :255 |
PDF Views:0
Authors
Affiliations
1 Department of Mathematics, Govt. J.Y. Chhattisgarh College, Raipur: 492001, IN
1 Department of Mathematics, Govt. J.Y. Chhattisgarh College, Raipur: 492001, IN
Source
Global Journal of Theoretical and Applied Mathematics Sciences, Vol 2, No 2 (2012), Pagination: 129-135Abstract
In this chapter we have introduced the concept of information for Mprobability distributions and then we obtained the suitable codes corresponding to M- probability distributions.Keywords
Coding Theory, Suitable Codes, Uniquely Decipherable CodesReferences
- Campbell, L.L. (1965): “A coding theorem and Renyi entropy”; Information and Control, 8, 423-429.
- Kerridge, D.F. (1961): “Inaccuracy and Inferences”; J. Royal Stat. Soc. Series B, Vol.23, 184-194.
- Kraft’s, L.G. (1949): “A device for quantizing grouping and coding amplitude modulated pluses”; M.S. Thesis, Elect. Deptt. MIT.
- Renyi, A. (1961): “On Measure of Entropy & Information”; Proc. 4th Berkely Symp. Stat. 1, 546-561.
- Shannon, C.E. (1948): “The Mathematical Theory of Communication”; Bell. Sys. Tech. J. Vol.27, 377-427, 623-659.
- Modular Lattice Generated by Fuzzy Implicationl
Abstract Views :147 |
PDF Views:0
Authors
Affiliations
1 Department of Engineering ITM University, Raipur 493661, IN
1 Department of Engineering ITM University, Raipur 493661, IN
Source
Indian Journal of Science and Technology, Vol 9, No 36 (2016), Pagination:Abstract
Background Objective: Lattice has been used in mathematics in 18th century. Modular lattice is one of the most important types of lattice. In18 Michal and Drewniak define a lattice which is generated by fuzzy implication. Method: In this paper we use 9 most frequently used implication and all of the full-fill the condition I(0, 0) = I(0, 1) = I(1, 1) = 1, I(1, 0) = 0 and are monotonic in both variable so they belong to FI. Finding: In this paper we present modular lattice generated by fuzzy implication. We show that these lattice lead to various algebraic structure on the set of almost fuzzy implication. We consider these implications and generate some formula for fuzzy implications thorough. Application/Improvement: Our investigations were inspired by paper of Czogula, Leski and Baczynski Drewniak and this paper is generalization of Michal and Drewniak paper “Lattice generated by fuzzy implication”. 2010 AMS Classification: 03G10, 03B05, 06B10, 04A72Keywords
Fuzzy Implication, Fuzzy Implication Lattice, Lattice, Modular Lattice.Full Text
- Measures of Directed Divergence
Abstract Views :146 |
PDF Views:8
Authors
Affiliations
1 Dhote Bandhu Science College, Gondia, Maharashtra, IN
2 R. T. M. Nagpur University, IN
3 Gov. J.Y. Chhattisgarh College, Raipur (C.G.), IN
1 Dhote Bandhu Science College, Gondia, Maharashtra, IN
2 R. T. M. Nagpur University, IN
3 Gov. J.Y. Chhattisgarh College, Raipur (C.G.), IN
Source
International Journal of Innovative Research and Development, Vol 5, No 5 (2016), Pagination: 254-257Abstract
The measures of directed divergence of parametric entropy have been obtained which are generalizations of Shannon’s Kapur’s, Bose Einstein, Fermi-Dirac, and Havrda-Charvat’s measures of Entropy. We have also examined its concavity property and some special cases.
Keywords
Measure of Entropy.Full Text