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Kumar Datta, Sanjib
- Growth Properties of Solutions of Complex Linear Differential-difference Equations with Coefficients having the Same Logarithmic Order in the Unit Disc
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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 disc
References
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- 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.
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- Gowers U3 Norm of Cubic MMF Bent-Negabent Functions Constructed by using Feistel Functions
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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.
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- 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
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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
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- 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.
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- 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.