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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.}.
ON I AND I<sup>*</sup>-CAUCHY CONDITIONS IN C<sup>*</sup>-ALGEBRA VALUED METRIC SPACES
Banerjee, Amar Kumar,Paul, Anirban The Kangwon-Kyungki Mathematical Society 2021 한국수학논문집 Vol.29 No.3
The idea of C<sup>*</sup>-algebra valued metric spaces was given by Ma, Jiang and Sun. In this paper we have studied the ideas of I-Cauchy and I<sup>*</sup>-Cauchy sequences and their properties in such spaces and also we give the idea of C<sup>*</sup>-algebra valued normed spaces.
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.
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.
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.
Nanotubular metal-insulator-metal capacitor arrays for energy storage
Banerjee, Parag,Perez, Israel,Henn-Lecordier, Laurent,Lee, Sang Bok,Rubloff, Gary W. Springer Science and Business Media LLC 2009 Nature nanotechnology Vol.4 No.5
<P>Nanostructured devices have the potential to serve as the basis for next-generation energy systems that make use of densely packed interfaces and thin films. One approach to making such devices is to build multilayer structures of large area inside the open volume of a nanostructured template. Here, we report the use of atomic layer deposition to fabricate arrays of metal-insulator-metal nanocapacitors in anodic aluminium oxide nanopores. These highly regular arrays have a capacitance per unit planar area of approximately 10 microF cm-2 for 1-microm-thick anodic aluminium oxide and approximately 100 microF cm-2 for 10-microm-thick anodic aluminium oxide, significantly exceeding previously reported values for metal-insulator-metal capacitors in porous templates. It should be possible to scale devices fabricated with this approach to make viable energy storage systems that provide both high energy density and high power density.</P>
Banerjee, Debapriya,Verma, Pramod Kumar,Pal, Samir Kumar Korean Society of Photoscience 2009 Photochemical & photobiological sciences Vol.8 No.10
The influence of ion dissolution in water is still controversial. The challenge posed to the existing concept of dissolved ions acting as water structure makers and structure breakers through recent studies calls for more experimental evidence. The temperature-dependent relaxation dynamics of water in bulk and in ionic salt solutions can give an idea about the hydrogen-bonded network and hence the perturbation induced in the tetrahedral structure of bulk water subsequent to ion dissolution. In our study, the temperature dependence of the observed relaxation dynamics in bulk water and guanidinium hydrochloride reveals the activation energy needed to convert water from hydrogen bonded to the free forms and hence the difference in the hydrogen-bonded network in the close vicinity of the probe molecule. The results might prove helpful to understand the interaction of hydrophobic amino acid residues with guanidinium hydrochloride during protein denaturation.