introduction:  stereotactic  radiosurgery  is  a  technique  for  the  treatment  of  intracranial  lesions  with  highly  collimated  x-ray  beam.  linac-based  radiosurgery  is  currently  performed  by  two  techniques:  couch or pedestal mounted. in the first technique, a device is required to affix patient's head to a couch  and  moreover  to  translate  it  accurately.  structure  of...

We have seen that the accuracy of methods for computing integrals or derivatives of a function f(x) depends on the spacing between points at which f is evaluated, and that the approximation tends to the exact value as this spacing tends to 0. Suppose that a uniform spacing h is used. We denote by F (h) the approximation computed using the spacing h, from which it follows that the exact value is...

Abstract— There are several works dedicated to the investigation of Volterra integro-differential equations. In addition, there are theoretical and practical representations of stable methods that have a high order of accuracy and extended stability regions; these representations were constructed using the minimum values of arithmetic operations. Here, hybrid methods are proposed for the constr...

The International Muon Ionization Cooling Experiment (MICE) is devoted to a study of a muon cooling channel capable of giving the desired performance for a Neutrino Factory. One of the goals is achieving an absolute accuracy of measurements of emittance reduction as high as ±0.1%. The paper describes results of a Monte Carlo study on allowed density variations of liquid hydrogen corresponding t...

The ability to prepare single-crystal faces has become central to developing and testing models for chemistry at interfaces, spectacularly demonstrated by heterogeneous catalysis and nanoscience. This ability has been hampered for hexagonal ice, Ih--a fundamental hydrogen-bonded surface--due to two characteristics of ice: ice does not readily cleave along a crystal lattice plane and properties ...

introduction we aimed to introduce a 6-universal-prismatic-spherical (ups) parallel mechanism for the human jaw motion and theoretically evaluate its kinematic problem. we proposed a strategy to provide a fast and accurate solution to the kinematic problem. the proposed strategy could accelerate the process of solution-finding for the direct kinematic problem by reducing the number of required ...

We prove that the ENO reconstruction and ENO interpolation procedures are stable in the sense that the jump of the reconstructed ENO point values at each cell interface has the same sign as the jump of the underlying cell averages across that interface. Moreover, we prove that the size of these jumps after reconstruction relative to the jump of the underlying cell averages is bounded. Similar s...

and Applied Analysis 3 exist and are bounded for a self-adjoint positive operator A. Here B 1 2 ( τA √ A 4 τ2A ) , K ( I 2τA 5 4 τA 2 )−1 . 2.2 Theorem 2.1. For any gk, 1 ≤ k ≤ N − 1, and fk,−N 1 ≤ k ≤ 0, the solution of problem 1.2 exists and the following formula holds: uk ( I − R2N )−1{[ R − R2N−k ] u0 [ RN−k − R k ][ Pu0 − τ 0 ∑ s −N 1 P N−1Gfs μ ] − [ RN−k − R k ] I τB 2I τB −1B−1 N−1 ∑ s ...

The initial-value problem for hyperbolic equation d2u(t)/dt2 +A(t)u(t) = f (t) (0 ≤ t ≤ T), u(0) = φ,u(0) = ψ in a Hilbert space H with the self-adjoint positive definite operators A(t) is considered. The second order of accuracy difference scheme for the approximately solving this initial-value problem is presented. The stability estimates for the solution of this difference scheme are establi...