It is possible to obtain a quality assurance (QA) of the dosimetry within a short time by using the new mathematical tools for a water phantom where dose measurements were made at two points only for a few square field sizes of the linear accelerator beam. The human body is not homogeneous. Water phantom makes it possible to create inhomogeneous phantoms by introducing blocks within it at suita...

We develop singular value techniques in the context of time inhomogeneous finite Markov chains with the goal of obtaining quantitative results concerning the asymptotic behavior of such chains. We introduce the notion of c-stability which can be viewed as a generalization of the case when a time inhomogeneous chain admits an invariant measure. We describe a number of examples where these techni...

In reality, colloidal particles often possess an arbitrary inhomogeneity profile. We present a first-principles approach to dielectrophoresis of such an inhomogeneous colloidal particle under an inhomogeneous field of an oscillating electric dipole moment. For numerical simulations, we treat the inhomogeneous particle as a specific graded one with a physically motivated dielectric model and con...

In this paper, the Schwarz boundary value problem (BVP) for the inhomogeneous Cauchy-Riemann equation in a triangle is investigated explicitly. Firstly, by the technique of parquetingreflection and the Cauchy-Pompeiu representation formula a modified Cauchy-Schwarz representation formula is obtained. Then, the solution of the Schwarz BVP is explicitly solved. In particular, the boundary behavio...