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Datta, Sanjib Kumar
- Some Results on the Exponent of Convergence of Zeros of Entire Functions
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Authors
Affiliations
1 Department of Mathematics, University of Kalyani, Kalyani, Dist. - Nadia, Pin - 741235, West Bengal, IN
1 Department of Mathematics, University of Kalyani, Kalyani, Dist. - Nadia, Pin - 741235, West Bengal, IN
Source
International Journal: Mathematical Manuscripts, Vol 6, No 1 (2013), Pagination: 21-31Abstract
In the paper we establish some inequalities on the basis of the exponent of convergence of zeros of entire functions.Keywords
Entire Function, Exponent of Convergence of Zeros.
References
- Z. X. Chen and C. C. Yang: Some further results on the zeros and growths of entire solutions of second order linear differential equations, Kodai Math. J.,Vol. 22 (1999), pp. 273–285.
- W. K. Hayman: Meromorphic functions, The Clarendon Press, Oxford, 1964.
- G. Valiron: Lectures on the general theory of integral functions, Chelsea Publishing Company, 1949.
- On Relative Order and Relative Type Based Growth Properties of Differential Monomials
Abstract Views :231 |
PDF Views:2
Authors
Affiliations
1 Department of Mathematics, University of Kalyani, P.O.-Kalyani, Dist-Nadia, 741235, West Bengal, IN
2 Rajbari, Rabindrapalli, R. N. Tagore Road, P.O. Krishnagar, Dist-Nadia, 741101, West Bengal, IN
3 Jhorehat F. C. High School for Girls, P.O.- Jhorehat, Dist-Howrah, 711302, West Bengal, IN
1 Department of Mathematics, University of Kalyani, P.O.-Kalyani, Dist-Nadia, 741235, West Bengal, IN
2 Rajbari, Rabindrapalli, R. N. Tagore Road, P.O. Krishnagar, Dist-Nadia, 741101, West Bengal, IN
3 Jhorehat F. C. High School for Girls, P.O.- Jhorehat, Dist-Howrah, 711302, West Bengal, IN
Source
The Journal of the Indian Mathematical Society, Vol 82, No 3-4 (2015), Pagination: 39-52Abstract
In this paper some newly developed results based on the growth properties of relative order (relative lower order), relative type (relative lower type) and relative weak type of differential monomials generated by entire and meromorphic functions are investigated.Keywords
Entire Function, Meromorphic Function, Relative Order, Relative Type, Differential Monomial.- A Brief Study on Boolean Logic as a Dual Analogue of an Ideal
Abstract Views :368 |
PDF Views:5
Authors
Affiliations
1 UGC-JRF, Department of Philosophy , University of Kalyani, P.O.: Kalyani , Dist: Nadia , PIN: 741235, IN
2 Department of Philosophy, University of Kalyani, P.O.: Kalyani, Dist:Nadia, PIN:741235, IN
3 Department of Mathematics, University of Kalyani, P.O.: Kalyani, Dist:Nadia, PIN:741235., IN
1 UGC-JRF, Department of Philosophy , University of Kalyani, P.O.: Kalyani , Dist: Nadia , PIN: 741235, IN
2 Department of Philosophy, University of Kalyani, P.O.: Kalyani, Dist:Nadia, PIN:741235, IN
3 Department of Mathematics, University of Kalyani, P.O.: Kalyani, Dist:Nadia, PIN:741235., IN
Source
Indian Science Cruiser, Vol 32, No 6 (2018), Pagination: 32-35Abstract
In this paper we wish to establish a Structure termed as Quotient Boolean algebra from the view point of a filter as a dual analogue of an Ideal. Some related properties are also to be developed in this work.Keywords
Boolean Algebra , Principle of Duality, Ideal, Filter.References
- Boolean Algebra and its Application, John Eldon Whitesitt. Dover Publication.
- Logic and Boolean Algebra, Bradford Henry Arnold, Prentice-Hall, 1962, pp. 1-144
- The Laws of Thought, George Boole, Release Date: July 19, 2017
- G. Boole, An Investigation of the Laws of Thought , Dover Publication , New York , 1958.
- G. Boole, The Laws of Thought , facsimile of 1854 edition, 1854/2003.
- A Study on A Different Formulation of Boolean Structure
Abstract Views :338 |
PDF Views:3
Authors
Affiliations
1 Department of Philosophy, University of Kalyani. P.O.: Kalyani, Dist.: Nadia, West Bengal, Pin: 741235, IN
2 Department of Philosophy, University of Kalyani, P.O. Kalyani, Dist. Nadia, West Bengal, Pin 741235, IN
3 epartment of Mathematics, University of Kalyani, P.O. Kalyani, Dist. Nadia, West Bengal, Pin 741235, IN
1 Department of Philosophy, University of Kalyani. P.O.: Kalyani, Dist.: Nadia, West Bengal, Pin: 741235, IN
2 Department of Philosophy, University of Kalyani, P.O. Kalyani, Dist. Nadia, West Bengal, Pin 741235, IN
3 epartment of Mathematics, University of Kalyani, P.O. Kalyani, Dist. Nadia, West Bengal, Pin 741235, IN
Source
Indian Science Cruiser, Vol 33, No 1 (2019), Pagination: 25-29Abstract
Logic is the main essence of human reasoning. English Scientist and Logician George Boole (1815-1864) initiated the idea of a structure which is based upon some reasoning of difference occurrence in the Universe. Professor Boole wrote a book entitled “The Laws of Thought” which was collection of his papers on such type of reasoning. In this book he formulated a structure upon the interrelationship of element. After his name the structure is known as Boolean Structure. In this paper we present a somewhat different formulation of a Boolean Structure. Further it has been shown in the paper that Associative Laws in a Boolean structure follow from the other axioms of the same i.e., in other words it may be stated that the axiom of Associative Laws in the definition of a Boolean algebra is redundant.Keywords
Boolean Structure, Another Formulation, Commutative Law, Associative Law.References
- G. Boole, The Release Date: July 19, 2017. ‘Laws of Thought’, [EBook #15114], URL: https://www.gutenberg.org/files/15114/15114-pdf.pdf. pp.1-344.
- F.M. Brown, Boolean Reasoning, ISBN 978-14757-2078-5.
- B.F. Arnold, 1962, Logic and Boolean Algebra, Prentice-Hall, pp. 1-144
- J.E Whitesitt, Boolean Algebra and its Application, Dover Publication.URL: http://store.doverpublications.com/0486477673.html
- Peirce, 1880. “ A Boolean algebra with one constant” , MS collected papers v.4, paragraphs 12-20 reprinted writings v.4, pp. 218-21.
- G. Boole, 1847. Mathematical analysis of logic (Cambridge and London); repr. In studies in logic and probabilities ed. R. Rhees (London 1952).
- G. Boole, 1854. The Laws of Thought ( London and Cambridge ); repr. as Collected Logical Works. Vol. 2 , ( Chicago and London ; Open Court, 1940).
- G Frege, 1882. Boole’s Logical Calculus and the Concept Script, in posthumous writing transl. P. Long and R . White 1969 , pp. 9-46
- A Mukherjee and K Biswas, 2018, ON BOOLEAN LOGIC: A MOTIVATION FROM A FEMALE LOGICIAN, Communicated.
- K Biswas, and A Mukherjee, 2018, An approach made by female logician to the deductive system in Boolean Logic, Communicated.
- A Mukherjee, and K Biswas, 2018, On Boolean Logic as an ordered pair of Boolean Structure and its Filter, Communicated.
- On Some Results in Quotient Boolean Algebra and Boolean Logic
Abstract Views :231 |
PDF Views:80
Authors
Affiliations
1 Department of Philosophy, University of Kalyani, P.O.: Kalyani, Dist:Nadia, PIN:741235, IN
2 Department of Mathematics, University of Kalyani, P.O.: Kalyani, Dist:Nadia, PIN:741235, IN
1 Department of Philosophy, University of Kalyani, P.O.: Kalyani, Dist:Nadia, PIN:741235, IN
2 Department of Mathematics, University of Kalyani, P.O.: Kalyani, Dist:Nadia, PIN:741235, IN
Source
Indian Science Cruiser, Vol 33, No 6 (2019), Pagination: 11-16Abstract
The aim of this paper is to derive some results in quotient Boolean algebra and as a consequence also in Boolean logic. The work carried out in the present paper is in fact an extension of Behara, Biswas and Datta {cf.[1]}.Full Text
References
- Rinku Behara, Kuheli Biswas and Sanjib Kumar Datta, A Brief Study on Boolean Logic as a Dual Analogue of an Ideal, Indian Science Cruiser, Vol. 32, No. 6, November 2018, pp. 32-35.
- Bradford Henry Arnold, Logic and Boolean Algebra, Prentice-Hall, 1962, pp. 1-144
- George Boole, The Laws of Thought, , Release Date: July 19, 2017
- George Boole, An Investigation of the Laws of Thought , Dover Publication , New York , 1958.
- George Boole, The Laws of Thought , facsimile of 1854 edition , 1854/2003.
- On Different Relative Growth Factors of Entire Functions
Abstract Views :295 |
PDF Views:1
Authors
Affiliations
1 Department of Mathematics, University of Kalyani, Kalyani, IN
2 Department of Mathematics, Darjeeling Government College, Darjeeling, IN
3 Department of Mathematics, Chakdaha College, Chakdaha, IN
1 Department of Mathematics, University of Kalyani, Kalyani, IN
2 Department of Mathematics, Darjeeling Government College, Darjeeling, IN
3 Department of Mathematics, Chakdaha College, Chakdaha, IN
Source
The Journal of the Indian Mathematical Society, Vol 87, No 1-2 (2020), Pagination: 37–55Abstract
In this paper we investigate some properties related to sum and product of different relative growth factors of an entire function with respect to another entire function in connection with a special type of non-decreasing, unbounded function ψ.Keywords
Entire function, Growth, Order (Lower Order), (p;q;t)L−ψ-order (p;q;t)L−ψ−Lower Order), Non-Decreasing, Unbounded Function.References
- R. P. Agarwal, S. K. Datta, T. Biswas and P. Sahoo, On the growth analysis of iterated entire functions, Advanced Studies in Contemporary Mathematics. 26(1) (2016) , 93-137.
- L. Bernal, Orden relativ de crecimiento de funciones enteras, Collect Mth. 39(1988), 209-229.
- T. Biswas, Some results relating to sum and product theorems of relative (p,q, t)L-th order and relative (p,q, t)L-th type of entire functions, Korean J. Math. 26(2) (2018), 215-269.
- S. K. Datta, T. Biswas and C. Ghosh, On relative (p,q)-th order based growth measure of entire functions, Filomat. 30 (7) (2016) , 1723-1735.
- W. K. Hayman, Meromorphic functions, The Calendron Press, Oxford, 1964.
- O. P. Juneja, G. P. Kapoor, and S. K. Bajpai, On the (p,q)-order and lower (p,q)-order of an entire function, J. Reine Angew. Math. 282(1976) , 53-67.
- O. P. Juneja, G. P. Kapoor, and S. K. Bajpai, On the (p,q)-type and lower (p,q)-type of an entire function, J. Reine Angew. Math. 290(1977), 180-190.
- L. M. Sanchez Ruiz, S. K. Datta, T. Biswas, and G. K. Mandal, On the (p,q)th relative order and oriented growth properties of entire functions, Abstr. Appl. Anal. 2014, Article ID 826137, 8 pages, http://dx.doi.org/10.1155/2014/826137.
- D. Somasundaram, and R. Thamizharasi, A note on the entire functions of L-bounded index and L-type, Indian J. Pure. Appl. Math. 19 (3)(1988), 284-293.
- H. M. Srivastava, S. K. Datta, T. Biswas and D. Dutta, Sum and product theorems depending on the (p,q)-th order and (p,q)-th type of entire functions, Cogent Mathematics. 2015, 2 : 1107951, 1-22.
- T. Samten and N. Biswas, Some results on the integer translation of composite entire and meromorphic functions, Konuralp J. Math. 5(2) (2017), 1-11.
- G. Valiron, Lectures on the General Theory of Integral Functions, Chelsea Publishing Company, 1949.
- Linear Differential Equations with Solutions of Finite Iterated p-Φ Order
Abstract Views :137 |
PDF Views:2
Authors
Affiliations
1 Department of Mathematics, Kazi Nazrul University, Asansol-713340, IN
2 Department of Mathematics, University of Kalyani, Kalyani - 741235, IN
3 53, Gopalpur Primary School, Raninagar-I, Murshidabad -742304, IN
4 28, Dolua Dakshinpara Haridas Primary School, Beldanga, Murshidabad -742133, IN
1 Department of Mathematics, Kazi Nazrul University, Asansol-713340, IN
2 Department of Mathematics, University of Kalyani, Kalyani - 741235, IN
3 53, Gopalpur Primary School, Raninagar-I, Murshidabad -742304, IN
4 28, Dolua Dakshinpara Haridas Primary School, Beldanga, Murshidabad -742133, IN
Source
The Journal of the Indian Mathematical Society, Vol 90, No 1-2 (2023), Pagination: 23-36Abstract
In this article, we have studied complex linear homogeneous differential equations whose coefficients are entire functions having finite iterated p − Φ order and the growth of its nontrivial solutions.Keywords
Entire Function, Iterated p − Φ Order, Finiteness Degree.References
- L. G. Bernal, On growth k−order of solutions of a complex homogeneous linear differential equation, Proc. Amer. Math. Soc., 101 (2)(1987), 317–322.
- I. Chyzhykov, J. Heittokangas and J. R¨atty¨a, Finiteness of φ-order of solutions of linear differential equations in the unit disc, J. Anal. Math., 109 (2009), 163–198.
- W. K. Hayman, Meromorphic Functions. Oxford Mathematical Monographs Clarendon Press, Oxford, 1964.
- H. Herold, Differentialgleichungen im Komplexen, Vandenhoeck & Ruprecht, G¨ottingen, 1975.
- G. Jank and L. Volkman, Meromorphe Funktionen Und Differentialgleichungen, Birk¨auser, Basel-Boston, 1985.
- L. Kinnunen, Linear differential equations with solutions of finite iterated order, South-east Asian Bull. Math., 22 (4)(1998), 385–405.
- I. Laine, Nevanlinna Theory and Complex Differential Equations, Walter de Gruyter, Berlin, New Work, 1993.
- D. Sato, On the rate of growth of entire functions of fast growth, Bull. Amer. Math. Soc., 69 (1963), 411–414.
- M. N. Seremetao, On the connection between the growth of the maximum modulus of an entire function and the moduli of the coefficients of its power series expansion, Izv. Vyssh. Uchebn. Zaved. Mat., 2 (1967), 100–108.
- X. Shen, J. Tu and H. Y. Xu, Complex oscillation of a second-order linear differential equation with entire coefficients of [p, q] − φ order, Advances in Difference Equations 2014, 2014:200.