Refine your search
Collections
Co-Authors
A B C D E F G H I J K L M N O P Q R S T U V W X Y Z All
Kumar Datta, Sanjib
- Growth Properties of Solutions of Complex Linear Differential-difference Equations with Coefficients having the Same Logarithmic Order in the Unit Disc
Abstract Views :398 |
PDF Views:0
Authors
Source
The Journal of the Indian Mathematical Society, Vol 88, No 3-4 (2021), Pagination: 237–249Abstract
In this paper, we investigate the relations between the growth of meromorphic coefficients and that of meromorphic solutions of complex linear differential-difference equations with meromorphic cofficients of finite logarithmic order in the unit disc. Our results can be viewed as the generalization for both the cases of complex linear differential equations and complex linear difference equations.Keywords
Nevanlinna's Theory, Linear differential-difference equation, Meromorphic solution, Logarithmic order, Unit discReferences
- N. Biswas and S. Tamang, Growth of solutions to linear differential equations with entire coefficients of [p; q]-order in the complex plane, Commun. Korean Math. Soc., 33 (4) 2018, 1217-1227.
- N. Biswas, S. K. Datta and S. Tamang, On growth properties of transcendental mero- morphic solutions of linear differential equations with entire coefficients of higher order, Commun. Korean Math. Soc., 34 (4) (2019), 1245-1259.
- T. Y. P. Chern, On meromorphic functions with finite logarithmic order, Trans. Am. Math. Soc., 358 (2) (2006), 473-489.
- S. K. Datta and N. Biswas, Growth properties of solutions of complex linear differential- difference equations with coefficients having the same 'φ-order, Bull. Cal. Math. Soc., 111(3) (2019), 253-266.
- A. Goldberg and I. Ostrovskii, Value Distribution of Meromorphic Functions, Transl. Math. Monogr., 236, Amer. Math. Soc. Providence RI, 2008.
- G. G. Gundersen, Finite order solutions of second order linear differential equations, Trans. Amer. Math. Soc., 305 (1) (1988), 415-429.
- W. K. Hayman, Meromorphic Functions, Clarendon press, Oxford, 1964.
- J. Heittokangas and Z.T. Wen, Functions of Finite logarithmic order in the unit disc, Part I, J. Math. Anal. Appl., 415 (2014), 435-461.
- J. Heittokangas and Z.T. Wen, Functions of Finite logarithmic order in the unit disc, Part II, Comput. Methods Funct. Theory, 15 (2015), 37-58.
- I. Laine, Nevanlinna Theory and Complex Differential Equations, Walter de Gruyter, Berlin, New York, 1993.
- I. Laine and C. C. Yang, Clunie theorems for difference and q-difference polynomials, J. Lond. Math. Soc., 76 (3) (2007), 556-566.
- H. Liu and Z. Mao, On the meromorphic solutions of some linear difference equations. Adv. Difference Equ., 133 (2013), 1-12.
- C. Pommerenke, On the mean growth of the solutions of complex linear di erential equationsin the disc, Complex Var. Ell. Equ., 1(1) (1982), 23-38.
- J. Tu and C. F. Yi, On the growth of solutions of a class of higher order linear differential equations with coecients having the same order, J. Math. Anal. Appl., 340 (1) (2008), 487-497.
- J. T. Wen, Finite logarithmic order solutions of linear q-difference equations, Bull. Korean Math. Soc., 51 (1) (2014), 83-98.
- Gowers U3 Norm of Cubic MMF Bent-Negabent Functions Constructed by using Feistel Functions
Abstract Views :161 |
PDF Views:0
Authors
Source
The Journal of the Indian Mathematical Society, Vol 89, No 3-4 (2022), Pagination: 293-303Abstract
We obtain the Gowers U3 norm of a class of cubic Maiorana-McFarland bent{negabent functions constructed by using Feis- tel functions.
Keywords
Boolean functions, Gowers uniformity norm, bent-negabent functions.References
- V. Y-W. Chen, The Gowers norm in the testing of Boolean functions, Ph.D. Thesis, Massachusetts Institute of Technology, June 2009.
- S. Gangopadhyay, B. Mandal and P. St˘anic˘a, Gowers U3 norm of some classes of bent Boolean functions, Designs, Codes and Cryptography, 86(5) (2018), 1131–1148.
- S. Gangopadhyay and B. Mandal, Second order nonlinearity bounds of cubic MMF Bent– negabent functions constructed by using Feistel functions, IPSI BgD Trans. Advanced Research, 11(1) (2015), 13–19.
- T. Gowers, A new proof of Szemerdis theorem, Geom. Funct. Anal., 11(3) (2001), 465588.
- S. Markovski and A. Mileva, Generating huge quasigroups from small non-linear bijections via extended Feistel function, Quasigroups related systems, 17 (2009), 91-106.
- A. Muratovi-Ribi and E. Pasalic, A note on complete polynomials over finite fields and their applications in cryptography, Finite Fields Appl., 25 (2014), 306-315.
- M. G. Parker and A. Pott, On Boolean functions which are bent and negabent, In: Proc. Int. Conf. Sequences, Subsequences, Consequences 2007, LNCS, Springer, Vol. 4893 (2007), 9-23.
- C. Riera and M. G. Parker, Generalized bent criteria for Boolean functions, IEEE Trans. Inform. Theory, 52 (9) (2006), 4142-4159.
- K.-U. Schmidt, M. G. Parker and A. Pott, Negabent functions in the MaioranaMcFarland class, In Proc. International Conference on Sequences and Their Applications 2008, LNCS, Springer, Vol. 5203 (2008), 390-402.
- P. Stnic, S. Gangopadhyay, A. Chaturvedi, A. K. Gangopadhyay and S. Maitra, Investigations on bent and negabent functions via the negaHadamard transform, IEEE Trans. Inform. Theory, 58 (6) (2012), 4064-4072.
- W. Su, A. Pott and X. Tang, Characterization of negabent functions and construction of bentnegabent functions with maximum algebraic degree, IEEE Trans. Inform. Theory, 59 (6) (2013), 3387-3395.
- On Topological Bihyperbolic Modules
Abstract Views :173 |
PDF Views:2
Authors
Affiliations
1 28, Dolua Dakshinpara Haridas Primary School Beldanga, Murshidabad Pin-742133, West Bengal, IN
2 Department of Mathematics, Kazi Nazrul University, Nazrul Road, P.O.- Kalla C.H. Asansol-713340, West Bengal, IN
3 Department of Mathematics University of Kalyani, P.O.-Kalyani, Dist-Nadia, PIN-741235, West Bengal
1 28, Dolua Dakshinpara Haridas Primary School Beldanga, Murshidabad Pin-742133, West Bengal, IN
2 Department of Mathematics, Kazi Nazrul University, Nazrul Road, P.O.- Kalla C.H. Asansol-713340, West Bengal, IN
3 Department of Mathematics University of Kalyani, P.O.-Kalyani, Dist-Nadia, PIN-741235, West Bengal
Source
The Journal of the Indian Mathematical Society, Vol 90, No 3-4 (2023), Pagination: 233–248Abstract
In this paper, we introduce topological modules over the ring of bihyperbolic numbers. We discuss bihyperbolic convexity, bihyperbolic-valued seminorms and bihyperbolic-valued Minkowski functionals in topological bihyperbolic modules. Finally we introduce locally bihyperbolic convex modules.Keywords
Bihyperbolic Modules, Topological Bihyperbolic Modules, Bihyperbolic Convexity, Bihyperbolic-Valued Seminorms, Bihyperbolic-Valued Minkowski Functionals, Locally Bihyperbolic Convex Modules.References
- M. Bilgin and S. Ersoy, Algebraic properties of bihyperbolic numbers, Advances in Applied Clifford Algebras, 30 (1):13(2020).
- J. Cockle, On certain functions resembling quaternions and on a new imaginary in algebra, Lond-Dublin-Edinb. Philos. Mag., 3 (33)(1848), 435-439.
- R. Kumar, R. Kumar and D. Rochon, The fundamental theorems in the framework of bicomplex topological modules, arXiv: 1109.3424v1(2011).
- R. Kumar and H. Saini, Topological bicomplex modules, Adv. Appl. Clifford Algebras, 26 (4)(2016), 1249-1270.
- R. Larsen, Functional Analysis: An Introduction, Marcel Dekker, New York 1973.
- M. E. Luna-Elizarraras, C. O. Perez-Regalado and M. Shapiro, On linear functionals and Hahn–Banach theorems for hyperbolic and bicomplex modules, Adv. Appl. Clifford Algebras, 24 (2014), 1105-1129.
- L. Narici and E. Beckenstein, Topological Vector Spaces, Marcel Dekker, New York 1985.
- S. Olariu, Complex Numbers in n-dimensions, North-Holland Mathematics Studies, Elsevier, Amsterdam, Boston, 190 (2002), 51-148.
- A. A. Pogorui, R. M. Rodriguez-Dagnino and R. D. Rodrigue-Said, On the set of zeros of bihyperbolic polynomials, Complex Var. Elliptic Equ. 53 (7)(2008), 685-690.
- W. Rudin, Functional Analysis, 2nd edn., McGraw Hill, New York 1991.
- C. Segre, Le rappresentazioni reali delle forme complesse e gli enti iperalgebrici (The real representation of complex elements and hyperalgebraic entities), Math. Ann., 40 (1892), 413-467.