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NORMALITY CRITERIA FOR A FAMILY OF MEROMORPHIC FUNCTIONS WITH MULTIPLE ZEROS
Datt, Gopal,Li, Yuntong,Rani, Poonam Korean Mathematical Society 2018 대한수학회논문집 Vol.33 No.3
In this article, we prove some normality criteria for a family of meromorphic functions having zeros with some multiplicity. Our main result involves sharing of a holomorphic function by certain differential polynomials. Our results generalize some of the results of Fang and Zalcman [4] and Chen et al. [2] to a great extent.
Mahesh Datt Bhatt,Colm O’Dwyer 한국물리학회 2014 Current Applied Physics Vol.14 No.3
The density functional theory (DFT) calculations have been performed to investigate the interaction of Liþ with various organic solvents widely used as Li ion rechargeable battery electrolytes such as ethylene carbonate (EC), propylene carbonate (PC), dimethyl carbonate (DMC), diethyl carbonate (DEC), ethyl methyl carbonate (EMC); and their EC-based binary mixtures at the level of B3LYP/6-31G (d). The interaction of Liþ with these solvents has been calculated in terms of electronic structures of clusters of the mixtures of organic solvents including a lithium ion. The main objective of our investigation is to help in understanding a stable and enhancing ionic transfer at graphite/electrolyte interface assisted by the mixtures of the solvents. The calculated results favor the stability of EC-based binary mixtures and high EC-content binary mixture systems. In infrared (IR) vibrational spectra, the IR active modes of the solvent show significant changes due to the cation-solvent interaction.
A STUDY OF SLANT WEIGHTED TOEPLITZ OPERATORS IN CALKIN ALGEBRA
Gopal Datt,NEELIMA OHRI 장전수학회 2018 Proceedings of the Jangjeon mathematical society Vol.21 No.1
We describe some structural properties of a kth-order slant weighted Toeplitz operator Uβκ,Φ(k≥ 2) on L²(β) with Φ∈ L∞(β). The study of this operator and its counterpart on H²(β) is also extended in reference to the Calkin algebra.
Effect of doping on metal doped semiconductor
Bhatt Mahesh Datt,Shugo Suzuki,Takeaki Sakurai,Katsuhiro Akimoto 한국물리학회 2011 Current Applied Physics Vol.11 No.2
The effect of doping on position of interface states for metal doped bathocuproine (BCP) was studied with density functional theory (DFT). The doping of Ca atoms with BCP induces the formation of interface states with shift in their relative positions from Fermi level and approximately no shift in HOMO position of BCP molecule. The shift in the position of interface states towards higher binding energy was believed to be due to the presence of doping excess electrons from Ca at the interface. The analysis of modification in intensity of LUMO or EF or interface states, suggests the formation of multiply charged anions in heavily doped film. It clearly gives the direct evidence for the origin of the doping interface states in organic molecules. The effects of Ca doping on electrical properties were discussed.
COINCIDENCE AND COMMON FIXED POINT THEOREMS FOR SINGLE-VALUED AND SET-VALUED MAPPINGS
Pant, Badri Datt,Samet, Bessem,Chauhan, Sunny Korean Mathematical Society 2012 대한수학회논문집 Vol.27 No.4
In the present paper, we prove common fixed point theorems for single-valued and set-valued occasionally weakly compatible mappings in Menger spaces. Our results improve and extend the results of Chen and Chang [Chi-Ming Chen and Tong-Huei Chang, Common fixed point theorems in Menger spaces, Int. J. Math. Math. Sci. 2006 (2006), Article ID 75931, Pages 1-15].
Bhatt Mahesh Datt,Akahasi Baba,Takeaki Sakurai,Katsuhiro Akimoto 한국물리학회 2011 Current Applied Physics Vol.11 No.3
We used ultraviolet photoelectron spectroscopy (UPS) to study the electronic structure at the interface between organic semiconductor (CBP) and metals (Mg, Ag, and Au). Controlling the injection of charges at the interface requires a better understanding of the basic mechanism of the formation of interface states. In this context, photoelectron spectroscopy and density functional theory calculations were used to investigate the interaction of CBP with metal (111) surfaces. The position of HOMO relative to the Fermi level and the magnitude of the interface dipole were measured for each interface by UPS measurement. For CBP on Au, interface state (continuous state) was observed near the Fermi level by density functional theory calculations. However, no interface state was observed for CBP on Mg and Ag. It is suggested that the interface state plays an important role in charge transport at the interface. It was analyzed by density functional theory calculations that the interface state is formed due to interaction of CBP with metals and the position of the Fermi level varies strongly with the metal work function. The mechanism of formation of interface states and electrical properties were discussed.
Bhatt, Mahesh Datt,Cho, Maenghyo,Cho, Kyeongjae Canadian Science Publishing 2011 Canadian journal of chemistry Vol.89 No.12
<P> The interaction of lithium (Li<SUP>+</SUP>) cation and hexafluorophosphate (PF6<SUP>-</SUP>) anion with nonaqueous electrolytes is studied by using density functional theory at the B3LYP/6-311++G(d,p) level in the gas phase in terms of the coordination of Li<SUP>+</SUP> and PF6<SUP>-</SUP> with these solvents. Ethylene carbonate (EC) coordinates with Li<SUP>+</SUP> and PF6<SUP>-</SUP> most strongly and reaches the anode and cathode most easily because of its highest dielectric constant among all the solvent molecules, resulting in its preferential reduction on the anode and oxidation on the cathode. For cyclic carbonates EC and propylene carbonate (PC), the structure Li<SUP>+</SUP>(S)4 is found to be the most stable. However, for linear carbonates dimethyl carbonate (DMC), diethyl carbonate (DEC), and ethyl methyl carbonate (EMC), the formation of PF6<SUP>-</SUP>(S)n=1-3 is not favorable. Such analysis may be useful in applications for lithium ion batteries. </P>
Bhatt, Mahesh Datt,Lee, Geunsik,Lee, Jae Sung Pergamon Press 2017 Electrochimica Acta Vol. No.
<P><B>Abstract</B></P> <P>The density functional theory (DFT) calculations are performed to study the oxygen reduction reaction (ORR) on M-N<SUB>2</SUB>-G (M=Ti, Cu, Mo, Nb and Ru) electrocatalyst surfaces. In order to explain catalytic properties of M-N<SUB>2</SUB>-G (M=Ti, Cu, Mo, Nb and Ru) electrocatalysts, adsorption properties of all six intermediates O<SUB>2</SUB>, O, OOH, OH, H<SUB>2</SUB>O and H<SUB>2</SUB>O<SUB>2</SUB> are analyzed. We also calculate the adsorption property of ORR intermediates on Cu-N<SUB>2</SUB>-G (for example, an ideal catalyst) with the presence of H<SUB>3</SUB>O<SUP>+</SUP> ion (acid), OH<SUP>−</SUP> ion (base) and water molecule. After analysis, we can see clearly that the stable adsorption site for ORR intermediates in presence of acid, base and water is atop. Moreover, the adsorption properties of ORR intermediates in acid are quantitatively more stable than in base and water respectively. The catalytic activity of the ORR intermediates is found to be enhanced with the increase in the concentration of acid and base, but not of water. Our calculated results reveal that the ORR via a 4 electron transfer mechanism is energetically favorable on the M-N<SUB>2</SUB>-G (M=Ti, Mo, Nb and Ru) electrocatalyst surfaces to form two water molecules, while Cu-N<SUB>2</SUB>-G catalyst surface favors 2 electron transfer pathway to form unwanted hydrogen peroxide. Such types of electrocatalysts will be useful in the practical applications of polymer electrolyte fuel cells.</P>
FIXED POINTS OF OCCASIONALLY WEAKLY COMPATIBLE MAPPINGS USING IMPLICIT RELATION
Pant, Badri Datt,Chauhan, Sunny Korean Mathematical Society 2012 대한수학회논문집 Vol.27 No.3
In this paper, we prove common fixed point theorems for families of occasionally weakly compatible mappings in Menger spaces using implicit relation. Our results extend and generalize the results of Altun and Turkoglu [9] in the sense that the concept of occasionally weakly compatible maps is the most general among all the commutativity concepts. Also the completeness of the whole space, continuity of the involved maps and containment of ranges amongst involved maps are completely relaxed.