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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.}.
Uniqueness of Meromorphic Functions That Share Three Sets
Banerjee, Abhijit Department of Mathematics 2009 Kyungpook mathematical journal Vol.49 No.1
Dealing with a question of gross, we prove some uniqueness theorems concerning meromorphic functions with the notion of weighted sharing of sets. Our results will not only improve and supplement respectively two results of Lahiri-Banerjee [9] and Qiu and Fang [13] but also improve a very recent result of the present author [1].
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.
Adaptive Slicing with Curvature Considerations
Banerjee, Ashis Gopal,Kumar, Aloke,Tejavath, Shankar,Choudhury, Asimava Roy Society for Computational Design and Engineering 2003 International Journal of CAD/CAM Vol.3 No.1
In this paper, first order slice height calculation in Laminated Object Manufacturing (LOM) of free form surfaces is done with two different considerations: that a) the cutter trajectory is oriented in the direction of local absolute maximum more in number when compared to the case where the cutter trajectory is contained in the normal vertical section (NVS). However, it would help in achieving higher form accuracy of the final part because it would be a form of worst-case check. For the second proposed strategy, least number of slices results, thereby reducing overall build time drastically.
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.
"All This is Indeed Brahman" Rammohun Roy and a 'Global' History of the Rights-Bearing Self
Banerjee, Milinda The Asian Association of World Historians 2015 The Asian review of world histories Vol.3 No.1
This essay interrogates the category of the 'global' in the emerging domain of 'global intellectual history'. Through a case study of the Indian social-religious reformer Rammohun Roy (1772/4-1833), I argue that notions of global selfhood and rights-consciousness (which have been preoccupying concerns of recent debates in intellectual history) have multiple conceptual and practical points of origin. Thus in early colonial India a person like Rammohun Roy could invoke centuries-old Indic terms of globality (vishva, jagat, sarva, sarvabhuta, etc.), selfhood (atman/brahman), and notions of right (adhikara) to liberation/salvation (mukti/moksha) as well as late precolonial discourses on 'worldly' rights consciousness (to life, property, religious toleration) and models of participatory governance present in an Indo-Islamic society, and hybridize these with Western-origin notions of rights and liberties. Thereby Rammohun could challenge the racial and confessional assumptions of colonial authority and produce a more deterritorialized and non-sectarian idea of selfhood and governance. However, Rammohun's comparativist world-historical notions excluded other models of selfhood and globality, such as those produced by devotional Vaishnava, Shaiva, and Shakta-Tantric discourses under the influence of non-Brahmanical communities and women. Rammohun's puritan condemnation of non-Brahmanical sexual and gender relations created a homogenized and hierarchical model of globality, obscuring alternate subaltern-inflected notions of selfhood. Class, caste, and gender biases rendered Rammohun supportive of British colonial rule and distanced him from popular anti-colonial revolts and social mobility movements in India. This article argues that today's intellectual historians run the risk of repeating Rammohun's biases (or those of Hegel's Weltgeschichte) if they privilege the historicity and value of certain models of global selfhood and rights-consciousness (such as those derived from a constructed notion of the 'West' or from constructed notions of various 'elite' classicized 'cultures'), to the exclusion of models produced by disenfranchised actors across the world. Instead of operating through hierarchical assumptions about local/global polarity, intellectual historians should remain sensitive to and learn from the universalizable models of selfhood, rights, and justice produced by actors in different spatio-temporal locations and intersections.
Banerjee, Kaberi,Singla, Bhavana,Verma, Priyanka The Korean Society for Reproductive Medicine 2022 Clinical and Experimental Reproductive Medicine Vol.49 No.1
Objective: This study was conducted to assess the efficacy of subcutaneous granulocyte colony-stimulating factor (G-CSF) for treating thin endometrium. Methods: Data from 88 infertile women with thin endometrium (<7 mm) aged 23 to 40 years were evaluated retrospectively over a period of 1 year. In group 1, subcutaneous infusion of G-CSF (300 ㎍/mL) was administered to 44 women along with other supplemental treatments. If the lining did not exceed 7 mm within 72 hours, a second infusion was administered. In group 2, which also had 44 women, only estradiol valerate and sildenafil were administered, while subcutaneous G-CSF infusion was not. Embryo transfers were performed once the lining exceeded 7.5 mm. The efficacy of G-CSF was evaluated by assessing the thickness of the endometrium before embryo transfer, pregnancy rates, and clinical pregnancy rates. Results: There were no differences between the groups regarding demographic variables, egg reserves, sperm parameters, the number of embryos transferred, and embryo quality. The pregnancy rate was significantly higher in group 1 (60%, 24 of 40 cases) than in group 2 (31%, 9 of 29 cases) (p<0.001). The clinical pregnancy rate was also significantly higher in group 1 (55%) than in group 2 (24%) (p<0.001). Conclusion: Subcutaneous G-CSF infusion improved the thickness of the endometrium when it was thin. To the best of our knowledge, this is the first documented study to clearly demonstrate the benefits of subcutaneous G-CSF infusion for treating thin endometrium.