One of the holy grails in research and development focused on rechargeable magnesium batteries is development of "conventional" electrolyte solutions that are compatible with both anode and cathode and support highly reversible magnesium electrochemical activity. In the last couple of years, MgTFSI 2 , a "simple" salt, attracted considerable attention owing to its high solubility in a range of relevant solvents and apparent compatibility with magnesium anode and cathode materials. Nonetheless, questions were raised regarding the validity of the chemical and electrochemical inertness attributed to the TFSI anion, in particular when electrochemistry of magnesium is in the spotlight. Here, we demonstrate the impact of the TFSI anion on the intercalation kinetics of Mg ions into V 2 O 5 . The importance of this work is the fact that V 2 O 5 is considered to be the most attractive high-voltage/high-capacity cathode for secondary Mg batteries, while MgTFSI 2 is considered a very important electrolyte for the same systems.
The aim of the present paper is to introduce the notion of weak reciprocal continuity and obtain fixed point theorems by employing the new notion. The new notion is a proper generalization of reciprocal continuity and is applicable to compatible mappings as well as noncompatible mappings. Our results generalize several fixed point theorems.
The aim of this paper is to generalize celebrated results due to Boyd and
Wong [2] and Matkowski [9] and also to provide yet new solutions to the once
open problem on the existence of a contractive mapping which possesses a
fixed point but is not continuous at the fixed point. Besides continuous
mappings our results also apply to discontinuous mappings which include
threshold operations that are integral part of many a phenomena.
We present a well behaved class of Charge Analogue of Heintzmann (Z. Phys. 228:489, 1969) solution. This solution describes charge fluid balls with positively finite central pressure and positively finite central density ; their ratio is less than one and causality condition is obeyed at the centre. The outmarch of pressure, density, pressuredensity ratio and the adiabatic speed of sound is monotonically decreasing, however, the electric intensity is monotonically increasing in nature. The solution gives us wide range of constant K (1.25 ≤ K ≤ 15) for which the solution is well behaved and therefore, suitable for modeling of super dense star. For this solution the mass of a star is maximized with all degrees of suitability and by assuming the surface density ρ b = 2 × 10 14 g/cm 3 . Corresponding to K = 1.25 and X = 0.42, the maximum mass of the star comes out to be 3.64M with linear dimension 24.31 km and central redshift 1.5316.The charge analogue of Heint-solution has simple algebraic expressions. In order to study the behavior of physical parameters from centre to boundary we use the analytic method with the help of the developed theorem. However, the charge analogue of exact solutions, so far obtained, the numerical methods have been used to study the behavior of physical parameters from centre to boundary. N. Pant ( ) · R.N. Mehta
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