In this paper, we propose a method for finding certain eigenvalues of a generalized eigenvalue problem that lie in a given domain of the complex plane. The proposed method projects the matrix pencil onto a subspace associated with the eigenvalues that are located in the domain via numerical integration. The projection produces a small pencil with Hankel matrices.

This study quantifies the dosimetric accuracy of a commercial treatment planning system as functions of treatment depth, air gap, and range shifter thickness for superficial pencil beam scanning proton therapy treatments. The RayStation 6 pencil beam and Monte Carlo dose engines were each used to calculate the dose distributions for a single treatment plan with varying range shifter air gaps. C...

This paper is devoted to the study of perturbations a matrix pencil, structured or unstructured, such that perturbed pencil will reproduce given deflating pair while maintaining invariance complementary pair. If latter unknown, it referred as no spillover updating. The specific structures considered in this include symmetric, Hermitian, ?-even, ?-odd and ?-skew-Hamiltonian/Hamiltonian pencils. ...

Reports of graphite pencil lead injuries to the eye are rare. Although graphite is considered to remain inert in the eye, it has been known to cause severe inflammation and damage to ocular structures. We report a case of a 12-year-old girl with intracorneal graphite foreign bodies following a graphite pencil injury.

PURPOSE To verify the clinical pencil beam dose calculation algorithm for passive scattering proton therapy using field with large range in tissue, i.e. in prostate cancer, using a Monte Carlo (MC) simulation system. METHODS Previously treated prostate cancer cases were randomly selected from our patient database. All patients received the same dose prescription of 50Gy (25 fractions) to plan...

In this study, we introduce a new type of surface curves called $D$-type curve. This curve is defined by the property that the unit Darboux vector $vec{W}_{0} $ of a surface curve $vec{r}(s)$ and unit surface normal $vec{n} $ along the curve $vec{r}(s)$ satisfy the condition $leftlangle vec{n} ,vec{W}_{0} rightrangle =text{constant}$. We point out that a $D$-type curve is a geodesic curve or an...