in this paper we will prove that if $l$ is a continuous symmetric n-linear form on a hilbert spaceand $widehat{l}$ is the associated continuous n-homogeneous polynomial, then $||l||=||widehat{l}||$.for the proof we are using a classical generalized  inequality due to s. bernstein for entire functions of exponential type. furthermore we study the case that if x is a banach space then we have tha...

In this paper we will prove that if $L$ is a continuous symmetric n-linear form on a Hilbert space and $widehat{L}$ is the associated continuous n-homogeneous polynomial, then $||L||=||widehat{L}||$. For the proof we are using a classical generalized  inequality due to S. Bernstein for entire functions of exponential type. Furthermore we study the case that if X is a Banach space then we have t...

The propagation environment of electromagnetic waves in mine tunnels is confined areas. The mine tunnel is regard as wave-guide which contains kinds of un-beneficial medium, the field formulas of different polarization waves were presented based on Marcatili method, and field prediction of horizontal and vertical polarization waves were simulated. The results showed that propagation effect of v...

We are interested in the global bifurcation structure of solutions for a nonlinear boundary value problem with nonlocal constraint (SLP) that appears cell polarization model mass conservation proposed by Y. Mori, A. Jilkine and L. Edelstein-Keshet. obtained primitive representation formulas all investigated surface $${\mathcal {S}}$$ consisting diagrams heights. However, we could not find any p...

Antenna measurement data is collected over a surface as a function of position relative to the antenna. The data collection coordinate system directly affects how data is mapped to the surface: planar, cylindrical, spherical or other types. Far-field measurements are usually mapped or converted to spherical surfaces from which directivity, polarization and patterns are calculated and projected....