1 Introduction In order to study arithmetic properties of a variety over an algebraic number field, it is desirable to have a model over the ring of integers. We are interested in the particular case of a Shimura variety (of PEL type), and ask for a model over O E , where E is the completion of the reflex field at a prime of residue characteristic p > 0. Since a Shimura variety of PEL type is a...

Background: Several high-precision stereotactic radiation therapy modalities are currently used in clinical settings. We aimed to evaluate whether the CyberKnife (CK) or TrueBeam (TB) radiation treatment systems were more appropriate for treating targets of various morphologies according to the physical properties of each device.  Materials and Methods: Spheres (diameter = 5–50 mm), as well as ...

We propose a simple version of chaotic inflation which leads to a division of the universe into infinitely many open universes with all possible values of Ω from 1 to 0. 1 E-mail: [email protected] Flatness of the universe (Ω = 1) for a long time has been considered as one of the most definite predictions of the inflationary theory. However, what will happen if ten years from now it wi...

Measurement and verification are one of the prime stages in the entire course of geometrical products in new generation of geometrical product specifications (GPS) standard. Like other kinds of form tolerances, flatness error is one of the important characteristics affecting the functionality and quality of machined components; sufficient efforts have long been made to determine the flatness er...

manufacturing of an optical lenses demand a specialized technology and thus needs sophisticated precision manufacturing process. pmma is one of the most used optical polymer for manufacturing of optical lenses, the shaping of which into the required precision and accuracy is a challenging task. the focus of the present paper is to understand the effect of machining parameters on the surface cha...

The acceleration statistics of sheared and rotating homogeneous turbulence are studied using direct numerical simulation results. The statistical properties of Lagrangian and Eulerian accelerations are considered together with the influence of the rotation to shear ratio, as well as the scale dependence of their statistics. The probability density functions (pdfs) of both Lagrangian and Euleria...

Shape is a key characteristic to determine the quality of outgoing flat-rolled products in the steel industry. It is greatly influenced by flatness, a feature to describe how the surface of a rolled product approaches a plane. Flatness is of the utmost importance in steelmaking, since it is used by most downstream processes and customers for the acceptance or rejection of rolled products. Flatn...

For a monoid S, a (left) S-act is a non-empty set B together with a mapping S × B → B sending (s, b) to sb such that s(tb) = (st)b and 1b = b for all s, t ∈ S and b ∈ B. Right S-acts A can also be defined, and a tensor product A⊗S B (a set) can be defined that has the customary universal property with respect to balanced maps from A×B into arbitrary sets. Over the past three decades, an extensi...

2 Equivalence and flatness 6 2.1 Control systems as infinite dimensional vector fields . . . . . . . 6 2.2 Equivalence of systems . . . . . . . . . . . . . . . . . . . . . . . . 9 2.3 Differential Flatness . . . . . . . . . . . . . . . . . . . . . . . . . 12 2.4 Application to motion planning . . . . . . . . . . . . . . . . . . . 13 2.5 Motion planning with singularities . . . . . . . . . . . ....

A Bézier curve segment is generally rendered by subdividing it into a series of disjoint curve subsegments, and then approximating each subsegment by joining its endpoints by a line segment (chord). The maximum transverse deviation of each curve subsegment from the corresponding chord (the achieved flatness) should be no greater than a minimum error value, , called the flatness. The standard te...