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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, 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>
Is Higher Education A Potential Means of Promoting Labour Mobility?
Banerjee Minali,Singh Manju ASCONS 2018 INTERNATIONAL JOURNAL OF EMERGING MULTIDISCIPLINAR Vol.2 No.1
The Article supports the hypothesis that in the Globalised era, a country can develop by globalising its workforce. India is having the youngest population in the world and is continuously facing the challenge of educating its young population and preparing them to meet the Global competition. Its struggle to provide employment to its increasing workforce can be resolved by providing efficient education which will increase inter- regional and international student mobility and as a result will make the workforce more Globalised. Therefore the Article shows a strong positive relation between Education (preferably Higher Education), Student mobility and labour mobility and concludes that an increase in one of these factor results in an increase in the other two.
λ<sup>*</sup>-CLOSED SETS AND NEW SEPARATION AXIOMS IN ALEXANDROFF SPACES
Banerjee, Amar Kumar,Pal, Jagannath The Kangwon-Kyungki Mathematical Society 2018 한국수학논문집 Vol.26 No.4
Here we have studied the ideas of $g^*$-closed sets, $g{\bigwedge}_{{\tau}^-}$ sets and ${\lambda}^*$-closed sets and investigate some of their properties in the spaces of A. D. Alexandroff [1]. We have also studied some separation axioms like $T_{\frac{\omega}{4}}$, $T_{\frac{3\omega}{8}}$, $T_{\omega}$ in Alexandroff spaces and also have introduced a new separation axiom namely $T_{\frac{5\omega}{8}}$ axiom in this space.
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.