We present a technique to recover f ∈ Q(ζp) where ζp is a primitive pth root of unity for a prime p, given its norm g = f ∗ f̄ in the totally real field Q(ζp + ζ −1 p ). The classical method of solving this problem involves finding generators of principal ideals by enumerating the whole class group associated with Q(ζp), but this approach quickly becomes infeasible as p increases. The apparent h...

In addition to optimal conditions, invariant laws of Lorentz, parity and time reversal are imposed to find the relation between observables (spin rotation parameters) and bilinear combination of helicity amplitudes in pion-proton elastic scattering at 6.0 GeV/c. By normalizing the differential cross-section to unity, the magnitudes of helicity amplitudes and the angle between them are dete...

duns scouts the famous theologian of thirteen century under the influence of avecina’s doctorine of “nature” on the basis of hierarchy of the unity presents a hypothesis and describes the unconditioned nature as minor unity and individual entities as numerical unity. as an celeberating hypothesis of“distinct forms” it accounts with the haeccity as the criterion of individuality of external enti...

Based on the canonical quantization of d > 2-dimensional general relativity (GR) via Dirac constraint formalism (also termed as ‘constraint quantization’), we propose loss covariance a fundamental property theory. This breakdown occurs for first-order Einstein–Hilbert action, whereby diffeomorphism invariance, besides first-class constraints, second-class constraints also exist leading to no...

Surface plasmon polaritons carrying orbital angular momentum are of great fundamental and applied interest. However, common approaches for their generation restricted to having a weak dependence on the properties plasmon-generating illumination, providing limited degree control over amount delivered momentum. Here we experimentally show that by tailoring local global geometries vortex generator...

We give deterministic polynomial-time algorithms that, given an order, compute the primitive idempotents and determine a set of generators for the group of roots of unity in the order. Also, we show that the discrete logarithm problem in the group of roots of unity can be solved in polynomial time. As an auxiliary result, we solve the discrete logarithm problem for certain unit groups in finite...