Bessel beams (BBs) have gained prominence thanks to their diffraction-free propagation and self-healing properties. These are conventionally generated using different approaches, namely by transforming a narrow circular beam with lens, axicons or holographic beam-shaping techniques. methods involve space-consuming optics. To overcome this limitation, in the past, efforts been made create BBs di...

We study the mechanics of Hayward's trapping horizons, taking isolated horizons as equilibrium states. Zeroth and second laws of dynamic horizon mechanics come from the isolated and trapping horizon formalisms, respectively. We derive a dynamical first law by introducing a new perturbative formulation for dynamic horizons in which "slowly evolving" trapping horizons may be viewed as perturbativ...

We consider uniformly elliptic and parabolic second-order equations with bounded zeroth-order and bounded VMO leading coefficients and possibly growing first-order coefficients. We look for solutions which are summable to the p-th power with respect to the usual Lebesgue measure along with their first and second-order derivatives with respect to the spatial variable.

Developing foundational notions in the theory of Riemann surfaces, we prove the Riemann-Roch Theorem and Abel’s Theorem. These notions include sheaf cohomology, with particular focus on the zeroth and first cohomology groups, exact cohomology sequences induced by short exact sequences of sheaves, divisors, the Jacobian variety, and the Abel-Jacobi map. The general method of proof involves basic...

In this communication, we present a theoretical analysis, design, and fabrication of limited-diffractive planar Bessel beam launcher, that exhibits zeroth-order profile in the transverse electric field component with respect to z-propagation axis. The launcher is designed by synthesizing finite zeroth-order, first kind Hankel aperture distribution, polarized along fixed polarization unit vector...

Relying on a recurrence relation for the hypersums of powers of integers put forward recently, we develop an iterative procedure which allows us to express a hypersum of arbitrary order in terms of ordinary (zeroth order) power sums. Then, we derive the coefficients of the hypersum polynomial as a function of the Bernoulli numbers and the Stirling numbers of the first kind.

We formulate, under general conditions, the problem of maximisation of the total entropy of the system, assumed to be in a composable form, for fixed total value of the constrained quantity. We derive the general form of the composability function and also point out the criterion which leads to a violation of the zeroth law of thermodynamics. ∗e-mail: [email protected]