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On the solutions of xκ =g in a finite group
Sunil Kumar Prajapati,Ritumoni Sarma 대한수학회 2013 대한수학회보 Vol.50 No.2
The function g →ζ k G(g) which counts the number of solu- tions of xk = g in a finite group G, is not necessarily a character of G. We study this function for the case of dihedral groups and generalized quaternion groups.
ON THE SOLUTIONS OF x<sup>κ</sup> = g IN A FINITE GROUP
Prajapati, Sunil Kumar,Sarma, Ritumoni Korean Mathematical Society 2013 대한수학회보 Vol.50 No.2
The function $g{\mapsto}{\zeta}^k_G(g)$ which counts the number of solutions of $x^k=g$ in a finite group G, is not necessarily a character of G. We study this function for the case of dihedral groups and generalized quaternion groups.
Mohd. Zahid Ansari,Shashank Kumar,Sunil Kumar Prajapati,조종두 성균관대학교(자연과학캠퍼스) 성균나노과학기술원 2018 NANO Vol.13 No.5
The biaxial and planar characteristics of surface stress produce a parabolic differential stress distribution inside the sensing zone of microcantilever biosensors, which can be used to design novel biosensors. The present work studies and compares the effect of parabolic and conventional rectangular-shaped piezoresistor placed inside this sensing zone on sensitivity of the biosensors. Two different cantilevers made of silicon and silicon dioxide with doped silicon as piezoresistor are used in five design variations. The cantilevers are characterized for their deflections, von Mises stresses, resonant frequencies and self-heating temperatures produced using ANSYS. Analytical models for predicting deflections in the cantilevers is presented and compared with numerical results obtained. Results show good compatibility between analytical and numerical values for deflection with a 4–5% average deviation and that parabolic designs have higher sensitivity.