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ON UNIQUENESS OF MEROMORPHIC FUNCTIONS WHEN TWO DIFFERENTIAL MONOMIALS SHARE ONE VALUE
Banerjee, Abhijit Korean Mathematical Society 2007 대한수학회보 Vol.44 No.4
We prove four theorems on the uniqueness of non linear differential polynomials sharing one value which improve a result of Yang and Hua, and supplements some results of Lahiri, Xu and Qiu and Banerjee.
MEROMORPHIC FUNCTION PARTIALLY SHARES SMALL FUNCTIONS OR VALUES WITH ITS LINEAR c-SHIFT OPERATOR
Banerjee, Abhijit,Maity, Sayantan Korean Mathematical Society 2021 대한수학회보 Vol.58 No.5
In this paper, we have studied on the uniqueness problems of meromorphic functions with its linear c-shift operator in the light of partial sharing. Our two results improve and generalize two very recent results of Noulorvang-Pham [Bull. Korean Math. Soc. 57 (2020), no. 5, 1083-1094] in some sense. In addition, our other results have improved and generalized a series of results due to Lü-Lü [Comput. Methods Funct. Theo. 17 (2017), no. 3, 395-403], Zhen [J. Contemp. Math. Anal. 54 (2019), no. 5, 296-301] and Banerjee-Bhattacharyya [Adv. Differ. Equ. 509 (2019), 1-23]. We have exhibited a number of examples to show that some conditions used in our results are essential.
Abhijit Banerjee,Arpita Kundu 대한수학회 2023 대한수학회논문집 Vol.38 No.2
In the paper, we have exhaustively studied about the uniqueness of meromorphic function sharing two small functions with its $k$-th derivative as these types of results have never been studied earlier. We have obtained a series of results which will improve and extend some recent results of Banerjee-Maity \cite{Ban-Maity_Contemp.}.
Phototrophic Bacteria as Fish Feed Supplement
Banerjee, S.,Azad, S.A.,Vikineswary, S.,Selvaraj, O.S.,Mukherjee, T.K. Asian Australasian Association of Animal Productio 2000 Animal Bioscience Vol.13 No.7
Single cell of an indigenous phototrophic bacterium, Rhodovulum sulfidophilum, was incorporated in commercial fish feed for Oreochromis niloticus. The bacterial cell was analyzed for nutritional value and tested for toxicity and acceptability as an aquaculture feed supplement. The results showed higher survival rate and significantly higher growth rate (p<0.001) in O. niloticus fed with the bacteria incorporated fish feed. It is suggested that R sulfidophilum can be utilized as an aquaculture feed supplement.
Banerjee, A.N.,Hamnabard, N.,Joo, S.W. Ceramurgica ; Elsevier Science Ltd 2016 Ceramics international Vol.42 No.10
Pd-doped anatase TiO<SUB>2</SUB> nanoparticles were synthesized by a modified sol-gel deposition technique. The synthetic strategy is applicable to other transition and post-transition metals to obtain phase-pure anatase titania nanoparticles. This is important in the sense that anatase titania forms the most hydroxyl radicals (compared to other polymorphs like rutile, brookite, etc.) for better photocatalytic performance. XRD and Raman data confirm the phase-pure anatase formation. Doping of Pd<SUP>2+</SUP> into Ti<SUP>4+</SUP> sites (for substitutional doping) or interstitial sites (for interstitial doping) creates strain within the nanoparticles and is reflected in the XRD peak broadening and Raman peak shifts. This is because of the ionic radii difference between Ti<SUP>4+</SUP>(~68pm) and Pd<SUP>2+</SUP>(~86pm). XPS data confirm the formation of high surface titanol groups at the nanoparticle surface and a large number of loosely bound Ti<SUP>3+</SUP>-O bonds, both of which considerably enhance the photocatalytic activity of the doped nanoparticles. A comparative study with other metal doping (Ga) shows that TiO<SUB>2</SUB>: Pd nanoparticles have more Ti<SUP>3+</SUP>-O bonds, which enhance the charge transfer rate and hence improve the photocatalytic activity compared to other transition and post-transition metal-doped titania nanostructures.
Banerjee, Ujjal,Choudhuri, D.K. 한국곤충학회 1986 Korean journal of entomology Vol.16 No.1
Information about the toxic effects of nicotine on the biochemical components of the central nervous system is limited. A single sublethal dose of nicotine (54 $\mu\textrm{g}$/g body weight) was found to interfere with the enzyme acetylcholinesterase, acid phosphatase and nucleotidase. Acetylcho line is the familiar neurotransmitter in insects. But adenosine which acts as a putative neuro-transmitter during emergency period when acetylcholinesterase activity gets inhibited and transmission of nerve impulse becomes blocked is yet to be properly understood. The toxic stress produced due to nicotine treatment reduced the acetylcholinesterase activity and boosted up the activity of 5'-nucleotidase. The physiological significance of these findings have been discussed elaborately in this communication.
A New Furocoumarin from the Leaves of Camellia sinensis(L.) O. Kuntze
Banerjee, Jayashree,Ganguly, S.N. The Korean Society of Pharmacognosy 1997 Natural Product Sciences Vol.3 No.1
From the methanolic extract of defatted tender leaf of Camellia sinensis a new 4-hydroxy angular furocoumarin $C_{12}H_8O_5$, m.p. $212^{\circ}C$, was isolated using high-speed counter-current chromatographic technique. The structure of the compound was established as 4-hydroxy-2'-methoxy angular furocoumarin on the basis of physical methods viz. $^1H$ NMR, $^{13}C$ NMR and MS.
ON TRANSCENDENTAL MEROMORPHIC SOLUTIONS OF CERTAIN TYPES OF DIFFERENTIAL EQUATIONS
Banerjee, Abhijit,Biswas, Tania,Maity, Sayantan Korean Mathematical Society 2022 대한수학회보 Vol.59 No.5
In this paper, for a transcendental meromorphic function f and α ∈ ℂ, we have exhaustively studied the nature and form of solutions of a new type of non-linear differential equation of the following form which has never been investigated earlier: $$f^n+{\alpha}f^{n-2}f^{\prime}+P_d(z,f)={\sum\limits_{i=1}^{k}}{p_i(z)e^{{\alpha}_i(z)},$$ where P<sub>d</sub>(z, f) is a differential polynomial of f, p<sub>i</sub>'s and α<sub>i</sub>'s are non-vanishing rational functions and non-constant polynomials, respectively. When α = 0, we have pointed out a major lacuna in a recent result of Xue [17] and rectifying the result, presented the corrected form of the same equation at a large extent. In addition, our main result is also an improvement of a recent result of Chen-Lian [2] by rectifying a gap in the proof of the theorem of the same paper. The case α ≠ 0 has also been manipulated to determine the form of the solutions. We also illustrate a handful number of examples for showing the accuracy of our results.