Let q ≥ 1 be an integer, Sq be the unit sphere embedded in Rq+1, and μq be the volume element of Sq. For x0 ∈ Sq, and α ∈ (0, π), let Sα(x0) denote the cap {ξ ∈ Sq : x0 · ξ ≥ cosα}. We prove that for any integer m ≥ 1, there exists a positive constant c = c(q,m), independent of α, with the following property. Given an arbitrary set C of points in Sα(x0), satisftying the mesh norm condition max ...

In this paper we wish to present a new class of tight frames on the sphere. These frames have excellent pointwise localization and approximation properties. These properties are based on pointwise localization of kernels arising in the spectral calculus for certain self-adjoint operators, and on a positive-weight quadrature formula for the sphere that the authors have recently developed. Improv...

Within the framework of the composite surface scattering model, analytical formulas for Doppler shift and bandwidth of radar echoes backscattered from time-varying sea surface are derived in the forms of three-dimensional integrals. In our derivations, the influences of the tilt modulation (TM), the hydrodynamic modulation (HM), the shadow and the curvature of large-scale undulating waves are a...

We have shown that a reverse energy flow (negative projection of the Poynting vector onto optical axis) at sharp focus an vortex with topological charge 2 and left-hand circular polarization arises because axial spin has negative axis is greater in magnitude than positive orbital (canonical flow). Also, using Richards-Wolf formulas, it when focusing left-handed circularly polarized light, regio...

When observed by XMM–Newton in 2003, the type 1.5 quasi-stellar object 2MASS 0918+2117 was found to be in a low state, with an X-ray flux approximately four to five times fainter than during an earlier Chandra observation. The 2–6 keV spectrum was unusually hard (photon index ∼ 1.25), with evidence for a reflection-dominated continuum, while a soft excess visible below ∼1 keV prevented confirma...

Properties and different representations of the Uehling potential are investigated. Based on these properties by using our formulas for Fourier transform we have developed new analytical, logically closed physically transparent procedure which can be used to evaluate lowest-order vacuum polarization correction cross sections a number QED processes, including Mott electron scattering, bremsstrah...

Background: In several disease conditions, patients must inevitably be nourished by enteral feeding (EF). Though in many countries, commercial formulas are routinely used for EF, in Iran still home-made formulas are commonly employed as commercial formulas are not covered by insurance. This may pose patients to malnutrition and bring about further costs.  The aim of this study was to evalu...

Nonlinear Schrödinger (NLS) systems are important examples of physically-significant nonlinear evolution equations that can be solved by the inverse scattering transform (IST) method. In fact, the IST for discrete and continuous, as well as scalar and vector, NLS systems all fit into the same framework, which is reviewed here. The parallel presentation of the IST for each of these systems not o...