Based on the generalized multiparticle Mie theory, multiple scattering of an aggregate of uniaxial anisotropic spheres illuminated by a zero-order Bessel beam (ZOBB) with arbitrary propagation direction is investigated. The particle size and configuration are arbitrary. The arbitrary incident Bessel beam is expanded in terms of spherical vector wave functions (SVWFs). Utilizing the vector addit...

Abstract Let g be a primitive holomorphic or Maass newform for $\Gamma_0(D)$. In this paper, by studying the Bessel integrals associated with g, we prove an asymptotic δ-identity g. Among other applications, following hybrid subconvexity bound $$\begin{eqnarray*} L\left(1/2+it,g\otimes \chi\right)\ll_{g,\varepsilon} (q(1+|t|))^{\varepsilon}q^{3/8}(1+|t|)^{1/3} \end{eqnarray*}$$ any ε > 0...

A field theoretic approach that is based on the method of characteristics is outlined to prove the optimality of a synthesis of controlled trajectories that contains chattering arcs. Since the corresponding controls are not piecewise continuous they switch infinitely many times on finite intervals the classical argument by Boltyansky to prove differentiability of the associated value function i...