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Stanley's Tree Isomorphism Conjecture posits that the chromatic symmetric function can distinguish non-isomorphic trees. While already established for caterpillars and other subclasses of trees, we prove the conjecture's validity for a new class of trees that generalize proper caterpillars, thus confirming the conjecture for a broader class of trees., Comment: 11 pages

The transportation industry is transitioning from conventional Internal Combustion Engine Vehicles (ICVs) to Electric Vehicles (EVs) due to the depletion of fossil fuels and the rise in non-traditional energy sources. EVs are emerging as the new leaders in the industry. Some essential requirements necessary for the widespread adoption of EVs include sufficient charging stations with numerous chargers, less to no wait time before charging, quick charging, and better range. To enable a quicker transition from ICVs to EVs, commercial organizations and governments would have to put in a mammoth effort, given the low number of installed chargers in developing nations such as India. One solution to lower the waiting time is to have multiple vehicles charging simultaneously, which might involve charging two- and four-wheelers simultaneously, even though their battery voltage ratings differ. This paper begins by providing the details of the power sources for EV charging, the charging levels and connector types, along with the specifications of some of the commercial chargers. The necessity of AC-DC converters in EV charging systems is addressed along with the power quality concerns due to the increased penetration of EVs. Next, a review of the existing research and technology of isolated DC-DC converters for simultaneous charging of EV batteries is provided. Further, several potential isolated DC-DC converter topologies for simultaneous charging are described with their design and loss estimation. A summary of the existing products and projects with simultaneous charging features is provided. Finally, insight is given into the future of simultaneous charging.

The proposed research explores Multi-Walled Carbon Nanotube’s (MWCNT’s) effect on the mechanical buckling behavior of glass fiber-enhanced thermosetting composites using UTM and the load vs displacement curve is plotted. Using the inflection point method, the critical buckling load is obtained from the load vs displacement curve for beams with three different volume fractions of MWCNT. The nonlinear finite element method is used to numerically obtain the load vs deflection curve and the numerical results are compared with the experimental results, and a close match is found with the experimental results. It is observed that the nonlinearity associated with the structure can significantly reduce the critical buckling load. The critical buckling load is found to increase and reported a 27.4% increase in buckling load with 0.3 wt.% of MWCNT which could be accounted for the increase in flexural modulus of the material.