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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.
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.
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.}.
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.
Inhibition of Proliferation of Cervical and Leukemic Cancer Cells by Penicillin G
Banerjee, Aditya,Dahiya, Meetu,Anand, M.T.,Kumar, Sudhir Asian Pacific Journal of Cancer Prevention 2013 Asian Pacific journal of cancer prevention Vol.14 No.3
Cancer, despite all the efforts, still causes one in five deaths worldwide. Surgery, chemotherapy and radiotherapy provide inadequate protection and instead affect normal cells along with cancer cells. The search for cancer cures from natural products (plants and animals) has been practice for over a decade and the use of purified chemical to treat cancer still continues. Several studies have been undertaken during last three decades to find the anti-cancerous property of various plant extract and toxins secreted by animals and micro-organism. These lead to the discovery of several promising molecule having anticancer activity, some of which are in clinical trial and may emerged to be a potential future drug in cancer therapy. In this study we have used penicillin to evaluate its anti-cancer activity. It shown significant effects at cellular and molecular levels against growth of HeLa and K562 cell lines.
Language Modeling Approaches to Information Retrieval
Banerjee, Protima,Han, Hyo-Il Korean Institute of Information Scientists and Eng 2009 Journal of Computing Science and Engineering Vol.3 No.3
This article surveys recent research in the area of language modeling (sometimes called statistical language modeling) approaches to information retrieval. Language modeling is a formal probabilistic retrieval framework with roots in speech recognition and natural language processing. The underlying assumption of language modeling is that human language generation is a random process; the goal is to model that process via a generative statistical model. In this article, we discuss current research in the application of language modeling to information retrieval, the role of semantics in the language modeling framework, cluster-based language models, use of language modeling for XML retrieval and future trends.
Structural characterization of telechelic polyisobutylene diol
Banerjee, Sanjib,Shah, Priyank N.,Jeong, Youncheol,Chang, Taihyun,Seethamraju, Kasyap,Faust, Rudolf Elsevier 2015 Journal of chromatography Vol.1376 No.-
<P><B>Abstract</B></P> <P>The chemical homogeneity of telechelic polyisobutylene diol (PIB-diol), prepared by hydroboration-oxidation of allyl telechelic PIB obtained by reacting living PIB with allyltrimethylsilane, was investigated by liquid chromatography at critical conditions (LCCC) and HPLC coupled with matrix-assisted laser desorption/ionization time-of-flight mass spectrometry (MALDI-TOF MS). A normal phase gradient HPLC method was developed that was able to separate the as-synthesized PIB-diol into three components; PIB-diol, PIB-monool and PIB without any OH functionality. These were analyzed by MALDI-TOF MS, which suggested that the reaction of living PIB with allyltrimethylsilane was incomplete. LCCC using refractive index (RI) detector as a concentration detector allowed separation and quantification of PIB species according to their chemical heterogeneity (PIB-diol=95.3%, PIB-monool=3.3%, non-functional PIB=1.4%). The calculated number average functionality (<I>F</I> <SUB>n</SUB>) of PIB-diol=1.94 suggests high quality of PIB-diol suitable for high molecular weight polyurethane synthesis.</P> <P><B>Highlights</B></P> <P> <UL> <LI> Development of liquid chromatography at critical conditions using RI detector. </LI> <LI> Investigation of chemical homogeneity of polyisobutylene diol (PIB-diol). </LI> <LI> Separation and identification of species using gradient HPLC and MALDI-TOF MS. </LI> <LI> Determination of the number average hydroxyl functionality (<I>F</I> <SUB>n</SUB>) of PIB-diol. </LI> </UL> </P>
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.