The planar polynomial vector fields with a center at the origin can be written as an scalar differential equation, for example Abel equation. If the coefficients of an Abel equation satisfy the composition condition, then the Abel equation has a center at the origin. Also the composition condition is sufficient for vanishing the first order moments of the coefficients. The composition conjectur...

This paper concerns with numerical approximations of solutions of fully nonlinear second order partial differential equations (PDEs). A new notion of weak solutions, called moment solutions, is introduced for fully nonlinear second order PDEs. Unlike viscosity solutions, moment solutions are defined by a constructive method, called the vanishing moment method, and hence, they can be readily com...

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In this paper, we derive a simplified formula of electric dipole moments (EDMs) fermion. the Standard Model, it is well-known that non-trivial cancellations between some rainbow-type diagrams induced by $W$ boson exchanges occur in calculation neutron EDM at two-loop level due to gauge symmetry. The fermion self-energy and vertex correction are related through Ward-Takahashi identity, relation ...

Time scale dependence on the working nature of wavelet analysis makes it a valuable tool for Hurst parameter estimation. Similar to other wavelet-based signal processing applications, the selection of a particular wavelet type and vanishing moment in wavelet based Hurst estimation is a challenging problem. In this paper, we investigate the best Daubechies wavelet in wavelet based Hurst estimati...

I show that the electric dipole moment of the W-boson dW vanishes to two loop order in the standard Kobayashi-Maskawa Model of CP violation. The argument is a simple generalization of that used to show the vanishing of the quark electric dipole moment. As a consequence, the electron electric dipole moment vanishes to three loop order. Including QCD corrections may give a non-vanishing result; I...