The "extinction theorem" is used to prove that the fields of reflector antennas determined by integration of the current on the illuminated surface of the reflector are identical to the fields determined by aperture field integration with the Kottler-Franz formulas over any surface Sa that caps the reflector. As a corollary to this equivalence theorem, the fields predicted by integration of the...

For n≥2 and 1<p<∞ we prove an L p -version of the generalized Korn-type inequality for incompatible, p-integrable tensor fields P:Ω→ℝ n×n having Curl ̲ vanishing tangential trace Pτ l =0 on ∂Ω, denoting by {τ } l=1,...,n-1 a moving tangent frame more precisely have:

We model the supermassive dark object $M87^*$ as a Schwarzschild lens and study variations in tangential, radial, total (the product of tangential radial) magnifications images (primary, secondary, relativistic) against changes angular source position ratio lens-source to observer-source distance. Further, we behavior partial derivatives (with respect position) position. Finally, objects at cen...

We investigated the relative effectiveness of tangential versus normal displacements of skin for eliciting tactile sensations. Subjects adjusted the magnitude of slow tangential and oblique displacements of a cylindrical, flat-ended 1 mm diameter probe glued to the skin in order to match the perceived intensity of a reference displacement that indented the skin normal to the surface. At both th...

Abstract We consider the solvability of direct scattering problem an obliquely incident time-harmonic electromagnetic wave by a piecewise constant inhomogeneous, penetrable and infinitely long cylinder. The three-dimensional described Maxwell’s equations reduces to set two-dimensional Helmholtz equations, but with transmission conditions having also tangential derivatives fields. ellipticity is...

The present study quantified surface doses on several rectangular phantom setups and on curved surface phantoms for a 6 MV photon field using the Attix parallel-plate chamber and Gafchromic EBT2 film. For the rectangular phantom setups, the surface doses on a homogenous water equivalent phantom and a water equivalent phantom with 60 mm thick lung equivalent material were measured. The measureme...

We investigated the relative effectiveness of tangential versus normal displacements of skin for producing tactile sensations. Subjects adjusted the magnitude of slow tangential and oblique displacements of a flat-ended, cylindrical, 1 mm diameter probe glued to the skin in order to match the perceived intensity of a reference displacement that indented the skin normal to the surface. At both t...

We propose a new method of tangential redistribution of points by controlling the tangential motion in curvature driven flow of plane curves. The tangential velocity is designed by taking into account the shape of curves. It is based on combination of method of asymptotic uniform redistribution and the tangential velocity in crystalline curvature flow equations.

background: breast cancer is the most frequently diagnosed cancer and the leading global cause of cancer death among women worldwide. radiotherapy plays a significant role in treatment of breast cancer and reduces locoregional recurrence and eventually improves survival. the treatment fields applied for breast cancer treatment include: tangential, axillary, supraclavicular and internal mammary ...