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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.
Party Organizations in Multiethnic and Homogenous Societies: Comparing India and Japan
Banerjee, Vasabjit World Association for Triple Helix and Future Stra 2014 Journal of Contemporary Eastern Asia Vol.13 No.2
How do party organizations respond to newly evolving social groups? Research on Indian party organizations reveals that in multiethnic societies with uneven modernization between social groups, internally competitive parties respond better to newly evolving groups. Moreover, it is claimed: the same dynamic works vis-$\grave{a}$-vis homogenous societies with cleavages based on economic differences; and, the pattern holds regardless of differences in electoral institutions. This study examines these claims by testing whether factional competition correlated with recruitment into Japan's Liberal Democratic Party in 1972 and 1983. Japan had a single-nontransferable-vote system with multi-member districts, while the research on India assumes a first-past-the-post system with single-member districts. This study conducts a difference of means test on the population of new and old politicians in the LDP in 1972 and 1983 with a pooled variance adjustment to account for differences in populations' size. The findings show that intra-party competition and recruitment are not correlated in Japan, thus tentatively rejecting both claims.
Microstructural engineering of dual phase steel to aid in bake hardening
Banerjee, M.K. Techno-Press 2015 Advances in materials research Vol.4 No.1
Low carbon steel of composition 0.05C - 0.18 Mn - 0.012 Si is intercritically annealed at temperatures $750^{\circ}C$, $775^{\circ}C$ and $800^{\circ}C$. The equilibrated alloys of different amounts of austenite with varying carbon contents are quenched in iced water. The same alloys are subcritically annealed at $675^{\circ}C$ and $700^{\circ}C$ for varying periods of times; the subcritically annealed alloy samples are quenched in iced water. Optical, scanning electron and transmission electron microscopy are carried out for all the samples. The dislocation structure, its distribution and density present in the above prepared duplex ferrite martensite steels are studied. The martensites are found to be highly dislocated due to lattice invariant deformation. At the same time ferrite adjoining the martensite areas also exhibits quite a high dislocation density. The high dislocation density is favorable for strain ageing and hence bakes hardenability. EDS analyses were carried out for both martensite and ferrite phases; it is found that the degree of supersaturation in ferrite together with carbon content in martensite varies with the process parameters. The microhardness test results show that the hardness values of different phases differ appreciably with process parameters. The microstructures and the corresponding microanalyses reveal that differently processed steels contain phases of varying compositions and different distribution.
Banerjee, Ipsita A,Muniz, Germaine,Lee, Sang-Yup,Matsui, Hiroshi American Scientific Publishers 2007 Journal of nanoscience and nanotechnology Vol.7 No.7
<P>While various mineralizing peptides have been applied to grow metal nanoparticles on bionanotube templates, the semiconductor nanoparticle growth on nanotubes has not extensively been explored yet. In this paper, various semiconductor nanocrystals were grown on the bionanotubes surfaces with controlled sizes. When three synthetic peptides, which recognize and selectively bind Ge, Ti, and Cu ions, respectively, were incorporated on template bionanotube surfaces, highly crystalline and monodisperse Ge, TiO2, and Cu2S nanocrystals were grown on the tube surfaces. The sizes of these nanocrystals could be tuned as a function of pH, and larger semiconductor nanocrystals were grown as the pH of growth solutions was increased. All of these nanocrystals from smaller sizes to larger sizes had the same crystallinity. This peptide-controlled nanocrystal growth technique will be very useful to prepare semiconductor nanowires as building blocks for future microelectronics, whose band gaps can be tuned by the sizes of coated semiconductor nanoparticles via their quantum confinement effect. The novelty of this approach in the electronic device fabrication is that the semiconductor nanocrystal size control can be achieved by controlling peptide configurations via pH change, and this control may tune electronic structures and band gaps of the resulting semiconductor nanowires.</P>
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.
On numerical equivalence for algebraic cobordism
Banerjee, A.,Park, J. North-Holland Pub. Co 2016 Journal of pure and applied algebra Vol.220 No.1
<P>We define and study the notion of numerical equivalence on algebraic cobordism cycles. We prove that algebraic cobordism modulo numerical equivalence is a finitely generated module over the Lazard ring, and it reproduces the Chow group modulo numerical equivalence. We show this theory defines an oriented Borel-Moore homology theory on schemes and oriented cohomology theory on smooth varieties. We compare it with homological equivalence and smash-equivalence for cobordism cycles. For the former, we show that homological equivalence on algebraic cobordism is strictly finer than numerical equivalence, answering negatively the integral cobordism analogue of the standard conjecture (D). For the latter, using Kimura finiteness on cobordism motives, we partially resolve the cobordism analogue of a conjecture by Voevodsky on rational smash-equivalence and numerical equivalence. (C) 2015 Elsevier B.V. All rights reserved.</P>