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Abstract:

This paper introduce and study four concepts of R0 supra fuzzy topological spaces. We have shown that all these four concepts are ‘good extension’ of the corresponding concepts of R0 topological spaces and established relations among them. It has been proved that all the definitions are hereditary, productive and projective. Further some other properties of these concepts are studied

Keywords:

fuzzy set, ,topological spaces,, supra fuzzy topological spaces,

Refference:

I. Abd EL –Monsef, M. E, and Ramadan, A. E.: On fuzzy supra topological spaces; Indian J. Pure and Appl.Math. 18 (4), 322-329, 1987.

II. Ali, D. M.: A note on T0 and R0 fuzzy topological spaces; Pro. Math. Soc. B. H. U. Vol. 3, 165-167, 1987.

III. Azad, K. K: On Fuzzy semi- continuity, Fuzzy almost continuity and Fuzzy weakly continuity; J. Math. Anal . Appl. 82(1), 14-32, 1981.

IV. Chang, C. L.: Fuzzy topological spaces; J. Math. Anal Appl. 24, 182-192, 1968.

V. Hossain, M. S. and Ali, D. M.: On R0 and R1 fuzzy topological spaces; R U Studies Part-B J Sc. 33, 51-63, 2005.

VI.Lowen, R.: Fuzzy topological spaces and fuzzy compactness; J. Math. Anal. Appl. 56, 621-633, 1976.

VII. Mashhour, A. S., Allam, A. A., Mahmoud, F. S. and Khedr, F. H.: On fuzzy supra topological spaces; Indian J. Pure and Appl. Math. 14 (4), 502-510, 1983.

VIII. Ming, P. P., Ming. L. Y.: Fuzzy topology II. Product and Quotient Spaces; J. Math. Anal. Appl. 77, 20-37, 1980.

IX.Wong, C. K: Fuzzy points and local properties of Fuzzy topology; J. Math. Anal . Appl. 46, 316-328, 1974.

X. Zadeh, L. A.: Fuzzy sets. Information and control, 8, 338-353, 1965.

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Abstract:

In this paper we compare the maximum term of composition of two entire func-tions with their corresponding left and right factors.

Keywords:

entire function, ,complex plane, ,composite entire functions,

Refference:

I. J. Clunie: The composition of entire and meromorphic functions, Mathematical Essays dedicated to A. J. Macintyre, Ohio University Press (1970), pp. 75-92.

II. S.K. Datta and T. Biswas: On the definition of a meromorphic function of order zero, Int. Math. Forum, Vol.4, No. 37(2009) pp.1851-1861.

III. Q. Lin and C. Dai: On a conjecture of Shah concerning small functions, Kexue Tong bao (English Ed.), Vol. 31, No.4 (1986), pp.220-224.

IV. I. Lahiri: Growth of composite integral functions, Indian J. Pure Appl. Math. Vol.20, No. 9(1989), pp.899-907.

V. I. Lahiri and S. K. Datta: On the growth properties of composite entire and mero-morphic functions, Bull. Allahabad Math. Soc., Vol. 18(2003), pp.15-34.

VI. L. Liao and C. C. Yang: On the growth of composite entire functions, Yokohama Math. J., Vol. 46(1999), pp. 97-107.

VII. S. M. Shah: On proximate order of integral functions, Bull Amer. Math. Soc., Vol.52 (1946), pp. 326-328.

VIII. A. P. Singh: On maximum term of composition of entire functions, Proc. Nat. Acad. Sci. India, Vol. 59(A), Part I (1989), pp. 103-115.

IX. A.P. Singh and M. S. Baloria : On maximum modulus and maximum term of composition of entire functions, Indian J. Pure Appl. Math., Vol.22, No.12(1991),pp. 1019-1026.

X. G. Valiron: Lectures on the general theory of integral functions, Chelsea Publish-ing Company (1949).

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Abstract:

By applying Parikh-Wilczek’s semi-classical tunneling method we obtain the emission rate of massless uncharged particle at the event horizon of non-accelerating and rotating blackhole with electric and magnetic charges. We consider the spacetime background dynamical and incorporate the self-gravitation effect of the emitted particles when energy conservation and angular momentum conservation are taken into account. We find that the emission rate at the event horizon is equal to the difference of Bekenstein-Hawking entropy before and after emission. We also find the Hawking temperature

Keywords:

uncharged particle,emission rate ,self-gravitation effect ,Bekenstein-Hawking entropy,Hawking temperature ,

Refference:

I. S.W. Hawking; Nature (London)248,30 (1974). Commun. Math. Phys. 43, 199(1975).

II. S. W. Hawking; Phys. Rev. D14,2460(1976); 72,084013(2005).

III. Qing-Quan Jiang, Shuang-Qing Wu, Xu- Cai; “ Hawking radiation as tunneling from Kerr and Kerr-Newman blackholes” . hep-th/0512351.

IV. J. B. Hartle and S. W. Hawking; Phys. Rev. D13, 2188(1976).

V. P. Krause and F. Wilczek; Nucl. Phys. B 433(1995) 403, gr-qc/9406042.

VI. M. K. Parikh and F. Wilczek; Phys. Rev. Lett.85,5042(2000) hep-th/9907001.

VII. M. K. Parikh; Phys. Lett. B 546,189(2002) ; hep-th/0204107.

VIII.M. K. Parikh; hep-th/ 0402166.

IX. M. K. Parikh; Int. J. Mod. Phys. D 13,2351(2004).[ Gen. Rel. Grav. 36, 2419(2004), hep-th/0405160]

X. J. Zhang, Zheng Zhao; Phys. Lett. B 618(2005)14

XI. W.Liu; Chinese Journal of physics, Vol.45, No.1(2007) February.

XII. S. Sarkar, D.Kothawala; gr-qc/07094448

XIII. J. Zhang, Zheng Zhao; gr-qc/0512153.

XIV. Qing-Quan Jiang, Shuang-Qing Wu, Xu- Cai; hep-th/0512351(2006)

XV. R, Kerner, R,B. Mann; hep-th/08032246.

XVI. Xiao-Xiong Zeng, Hang-Song Hou and Shu-Zheng Yang; PRAMANA, Journal of Physics, Vol. 70, No.3, March(2008).

XVII. Ya-Peng Hu, Jing-Yi Zhang, Zheng Zhao; gr-qc/09012680.

XVIII.R. Kerner, R.B. Mann ; gr-qc/0603019.

XIX. U. A. Gillani, M. Rehman and K. Saifullah; hep-th/11020029.

XX. M. Bilal and K.Saifullah; gr-qc/10105575.

XXI. M. Rehman and K. Saifullah; hep-th/10115129.

XXII. Huei-Chan Lin and Chopin Soo; gr-qc/0905-3244.

XXIII. M. Arzano, A. J. M. Medved, Elias C. Vagenas; hep-th/0505266

XXIV. M. Angheben, M. Nadalini , L. vanzo and S. Zerbini; hep-th/0503081.

XXV. Yang-Geng Miao, Zhao Xue and Shao-Jun Zhang; hep-th/10122426.

XXVI. T. Jian, Chan-Bing-Bing; ACTA PHYSICA POLONICA B Vol.40(2009) No.2

XXVII. B.R.Majhi; hep-th/08091508.

XXVIII. K. Matsuno and K. Umetsu; hep-th/11012091.

XXIX. M. H.Ali; gr-qc/ 07063890.

XXX. M. H.Ali; gr-qc/ 07071079

XXXI. W. liu; New coordinates of BTZ Black Hole and Hawking radiation via tunneling.

XXXII.A.J.M. Medved; hep-th/0110289

XXXIII. Shuang-Qing Wu, Qing-Quan Jiang; hep-th/0602033

XXXIV. J. B. Grifiths and J. Podolsky; Class Quantum Grav.22(2005)3467.

XXXV. J. B. Grifiths and J. Podolsky; Phys. Rev. D 73(2006)044018.

XXXVI. J. F. Plebnski and M. Demianski; Am. Phys. NY 98(1970)98

XXXVII. Usman A. Gillani, Mudassar Rehman and K. Saifullah; hep-th/11020029.

XXXVIII. Painleve , P. (1921); Comptes Rendus de l’ Academic des Sciences, Serie I ( Mathematique) 173,677.

XXXIX. L. D. Landau, E. M. Lifshitz, the classical theory of field, Pergaman, London(1975).

XL. H. Zhang, Z Zhao, J. Beijing Normal Univ.(Natural Sci.) 37(2001)471(in Chinese).

XLI. (10)Jingyi Zhang, Zheng Zhao; Phys. Lett. B 618(2005)14-22.

XLII. J. M. Bardeen, B. Carter, S. W. Hawking, Commun. Math. Phys. 31(1973)161.

XLIII. J. Zhang and Zheng Zhao; JHEP 10(2005)055.

XLIV. J. Makela and P. Repo; Phys. Rev.D 57, 1899(1998).

XLV. N. Dadhich and Z. Ya. Turakulov; Class Quantum Grav. 19(2002) 2765

XLVI. Li Hui-Ling, YANG Shu-Zheng and QI De-Jiang; commun. Theor. Phys. (Beijing China) 46(2006) PP.991-994.

XLVII. J. B. Griffiths and J. Podolosky; gr-qc/0507021.

XLVIII. LEI Jie-Hong, LIU Zhi-Xiang and YANG Shu-Zheng; Commun. Theor. Phys. (Beijing, China)49 (2008) pp. 133-136 , Vol.49 No.1January 15,2008.

XLIX. P. Krause and E.Keski Vakkuri; Nucl. Phys. B491(1977)219. R. Parentani Nucl. Phys. B 575(2000) 333.

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Abstract:

In this paper it is shown that a vector cone metric space as introduced by us bears a metric like topology. Cantor’s intersection like Theorem is proved and as an application of the same a useful fixed point Theorem is obtained.

Keywords:

vector cone,metric space, topology,fixed point Theorem,

Refference:

I.Dejan Ilic, Vladimir Rakocevic, Common fixed points for maps on cone metric space, J. Math. Anal. Appl. 341 (2008), 876-882.

II.Huang Long-Guang, Zhang Xian, Cone metric spaces and fixed point theorem of contractive mappings, J. Math. Anal. Appl. 332 (2007), 1468-1476.

III.M. Abbas, G. Jungck, Common fixed point results for non commuting mappings without continuity in cone metric spaces, J. Math. Anal. Appl, 341 (2008), 416-420.

IV.P. Velro, Common fixed points in cone metric spaces, Rendieonti del Circolo Mathematico di Palermo, Vol. 56 no. 3 (2007), pp. 464-468.

V.Sh. Rezapour, R. Hamlbarani, Some notes on the paper, Cone metric spaces and fixed point theorems of contractive mappings, J. Math. Anal. Appl. 345 (2008), 719-724.

VI.Sreenivasan, T. K., Some properties of distance functions, Jour. Indian Math. Soc. 11 (1947)

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Abstract:

n this paper the authors have introduced the notion of modular elements in a nearlattice. We have included several characterizations of modular and strongly distributive elements with examples. We have also proved that an element in a nearlattice is standard if and only if it is both modular and strongly distributive.

Keywords:

modular elements,nearlattice,strongly distributive elements,

Refference:

I.W. H. Cornosh and A. S. A. Noor; Standard elements in a nearlattice, Bull. Austral. Math .Soc. 26(2), (1982); 185-213.

II.G. Gratzer and E.T. Schmidt, Standrad ideals in lattices, Acta. Math. Acad. Sci. Hung. 12(1961); 17-86.

III.A. S. A Noor and A. K. M. S. Islam, Relative annihilators in nearlattices, The Rajshahi University Studies (part-B) 25(1997); 117-120.

IV.M. R. Talukder and A. S. A. Noor, Modular ideals of a join semilattice Directed below, SEA Bull. Math 22(1998); 215-218.

V.M. B. Rahman, A study on distributive nearlattices, Ph.D Thesis, Rajshahi University, Bangladesh, (1994)

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Abstract:

In this paper we have developed a new technique to determine optimal solution to box pushing problem by two robots . Non-Dominated sorting genetic algorithm and Biogeography-based optimization algorithm are combined to obtain optimal solution. A modified algorithm is developed to obtain better energy and time optimization to the box pushing problem.

Keywords:

box pushing, robots ,Non-Dominated sorting genetic algorithm,Biogeography-based algorithm ,

Refference:

I.J. Chakrabarty, A.Konar,A.nagar,S.das, “Rotation and translation selective Pareto optimal solution to the box-pushing problem by mobile robots using NSGA-II” IEEE CEC 2009

II.Biogeography-Based OptimizationDan Simon, Senior Member, IEEE

3)An analysis of the equilibrium of migration models for biogeography-based optimization,Department of Electrical Engineering, Shaoxing University, Shaoxing, Zhejiang 312000, China

IV.A Fast and Elitist Multiobjective Genetic Algorithm: NSGA-II Kalyanmoy Deb, Associate Member, IEEE, Amrit Pratap, Sameer Agarwal, and T. Meyarivan

V.F. C. Lin, and J. Y. -J. Hsu, “Cost-balanced Cooperation protocols in multi-agent robotic systems,” in International Conference on Parallel and Distributed Systems, pp.72, 1996.

VI.T. Langle, and H. worn, “Human-robot cooperation using multi-agent systems,” Journal of Intelligent and Robotic system, vol. 32, pp. 143- 160, 2001.

VII.B. Innocenti, B. Lopez, and J. Salvi, “A multi-agent architecture with cooperative fuzzy control for a mobile robot,” Robotics and

VIII. Autonomous Systems, vol. 55, pp 881-891, 2007.

IX.R. A. Brooks, “A robust layered control system for a mobile robot,” Journal of Robotics and Automation, pp. 14-23, 1986.

X.C. R. Kube, and H. Zhang, “The use of perceptual cues in multi-robot box pushing,” in IEEE International Conference on Robotics and Automation, 1996, vol. 3, pp. 2085-2090.

XI.Y. W. Leung, and Y. P. Wang, “Multiobjective programming using uniform design and Genetic Algorithm,” IEEE Transactions on Systems, Man, and Cybernetics-Part C: Applications and Reviews, 2000, vol. 3, pp. 293-304.

XII.C. M. Fonseca, and P. J. Flaming, “Genetic algorithm for multi-objective optimization: Formulation, discussion, and generalization,” in Proceedings of the 5th International Conference on Genetic Algorithms, 1993, pp. 416-423.

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Abstract:

In this paper we have developed some properties of nilpotent ideals and radical of Γ-rings. At last we have prove that an external direct sum of finitely many matrix gamma rings over division gamma rings is a semi-simple Γn-ring.

Keywords:

gamma rings,nilpotent ideals,radical of gamma rings ,

Refference:

I. S. A. Amitsur,“A general theory of radicals I” Amer . J. Math. 74(1952), 774 – 776.

II. W. E. Barnes , “On the gamma rings of Nobusawa”, Pacific J. Math. 18 (1966), 411 – 422.

III. G. L. Booth, “Radicals of matrix gamma rings”, Math. Japonica 33, No. 3, 325 – 334, (1988).

IV. W. E. Coppage and J. Luh, “Radicals of gamma rings”, J. Math. Soc. Japan, Vol. 23, No. 1 (1971), 40 – 52.

V. N. J. Divinsky, “Rings and radicals”, George Allen and Unwin, London, 1965.

VI. A. Kurosh, “Radicals of rings and algebra”, Math. Sb.33,13 – 26, (1953).

VII. N. Nobusawa, “On a generalization of the ring theory” Osaka J.Math.1 (1964), 81 – 89.

8) Hiram Paley and Paul M. Weichsel :“A First Course in Abstract Algebra”, Holt, Rinehart and Winston, Inc., 1966.

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Abstract:

In this paper, we introduce the notion of pairwise almost normality which is a generalization of almost normality.

Keywords:

bitopological space, pairwise normal,pairwise almost normal,

Refference:

I. M. K. Bose, A. Roy Choudhury and A. Mukharjee, On bitopological paracompactness, Mat.Vesnik 60 (2008), 255-259.

II. M. K. Bose and Ajoy Mukharjee, On bitopological full normality, Mat. Vesnik 60 (2008), 11-18.

III. M. C. Datta, Paracompactness in bitopological spaces and an application to quasi-metric spaces, Indian J. Pure Appl. Math. (6) 8 (1977), 685-690.

IV. P. Fletcher, H. B. Hoyle III and C. W. Patty, The comparison of topologies, Duke Math. J. 36 (1969), 325-331.

V. J. C. Kelly, Bitopological spaces, J. Lond. Math. Soc. (3) 13 (1963), 71-89.

VI.M. K. Singal and Asha Rani Singal, Some more separation axioms in bitopological spaces, Ann. Soc. Sci. Brux., 84 (1970), 207-230.

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