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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.}.
Banerjee, Shrabani,Choudhury, Binayak Samadder Korean Mathematical Society 2007 대한수학회보 Vol.44 No.3
In this paper weak and strong convergence theorems of modified Noor iterations to fixed points for asymptotically nonexpansive mappings in the intermediate sense in Banach spaces are established. In one theorem where we establish strong convergence we assume an additional property of the operator whereas in another theorem where we establish weak convergence assume an additional property of the space.
Banerjee, Mainak,Das, Sunirban,Yoon, Minyoung,Choi, Hee Jung,Hyun, Myung Ho,Park, Se Min,Seo, Gon,Kim, Kimoon American Chemical Society 2009 JOURNAL OF THE AMERICAN CHEMICAL SOCIETY - Vol.131 No.22
<P>The postsynthetic modification strategy is adopted to demonstrate for the first time the syntheses of catalytically active chiral MOPMs from a preassambled achiral framework, MIL-101, by attaching L-proline-derived chiral catalytic units to the open metal coordination sites of the host framework. Various characterization techniques (including PXRD, TGA, IR, and N(2) absorption measurements) indicated that the chiral units are successfully incorporated into MIL-101, keeping the parent framework intact. The new chiral MOPMs show remarkable catalytic activities in asymmetric aldol reactions (yield up to 90% and ee up to 80%). It is interesting to note that these heterogeneous catalysts show much higher enantioselectivity than the corresponding chiral catalytic units as homogeneous catalysts. This study demonstrates a simple and efficient route for the generation of catalytically active chiral MOPMs. A variety of chiral catalytic units can be, in principle, incorporated into chemically robust achiral MOPMs with large pores by postmodification and the resulting chiral MOPMs may find useful applications in catalytic asymmetric transformations.</P>
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>
Age of Information Games Between Power Constrained Schedulers and Adversaries
Banerjee, Subhankar,Ulukus, Sennur,Ephremides, Anthony 한국통신학회 2023 Journal of communications and networks Vol.25 No.5
We consider a time slotted communication network consisting of a base station (BS), an adversary, $N$ users and $N_{s}$ communication channels. In the first part of the paper, we consider the setting where $N_{s}$ communication channels $\mathcal{N}_{s}$ are heterogeneously divided among $N$ users. The BS transmits an update to the $i$th user on a subset of the communication channels $\mathcal{N}_{s,i}$ where $\mathcal{N}_{s,i}\cap \mathcal{N}_{s,j}$ is not necessarily an empty set. At each time slot, the BS transmits an update packet to a user through a communication channel and the adversary aims to block the update packet sent by the BS by blocking a communication channel. The BS has $n$ discrete transmission power levels to communicate with the users and the adversary has $m$ discrete blocking power levels to block the communication channels. The probability of successful transmission of an update packet depends on these power levels. The BS and the adversary have a transmission and blocking average power constraint, respectively. We provide a universal lower bound for the average age of information for this communication network. We prove that the uniform user choosing policy, the uniform communication channel choosing policy with any arbitrary feasible transmission power choosing policy is $4$ optimal; and the max-age user choosing policy, the uniform communication channel choosing policy with any arbitrary feasible transmission power choosing policy is $2$ optimal. In the second part of the paper, we consider the setting where the BS chooses a transmission policy and the adversary chooses a blocking policy from the set of randomized stationary policies and $\mathcal{N}_{s,i}=\mathcal{N}_{s}$ for all $i$, i.e., all users can receive updates on all channels. We show that a Nash equilibrium may or may not exist for this communication network, and identify special cases where a Nash equilibrium always exists.
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.
Banerjee, S.,Basak, S.,Adhikari, M.R. 충청수학회 2006 충청수학회지 Vol.19 No.4
The aim of this paper is to endow a monoid structure on the set S of all oriented knots(links) under the operation ${\biguplus}$, called addition of knots. Moreover, we prove that there exists a homomorphism of monoids between ($S_d,\;{\biguplus}$) to (N, +), where $S_d$ is a subset of S with an extra condition and N is the monoid of non negative integers under usual addition.