Testing an inflationary era in curvature–matter coupling gravity

In this paper, we investigate the cosmological inflation in the context of a minimal matter–geometry coupling, which is based on the [Formula: see text] gravity theory, where [Formula: see text] is a generic function of the curvature scalar [Formula: see text] and the trace [Formula: see text] of the energy–momentum tensor. Assuming that the slow-roll inflation conditions hold true in [Formula: see text] gravity, we obtain the various inflation-related observables such as the tensor-to-scalar ratio [Formula: see text], the scalar spectral index [Formula: see text], the running [Formula: see text] of the spectral index and the tensor spectral [Formula: see text] for two specific [Formula: see text] models from the Hubble slow-roll parameters. To observe the viability of these models, a numerical analysis of such parameters has been done. The results showed that, by using the various values of free parameters, it is possible to obtain a viable compatible with the observational data.

Testing an inflationary era in curvature–matter coupling gravity

In this paper, we investigate the cosmological inflation in the context of a minimal matter–geometry coupling, which is based on the [Formula: see text] gravity theory, where [Formula: see text] is a generic function of the curvature scalar [Formula: see text] and the trace [Formula: see text] of the energy–momentum tensor. Assuming that the slow-roll inflation conditions hold true in [Formula: see text] gravity, we obtain the various inflation-related observables such as the tensor-to-scalar ratio [Formula: see text], the scalar spectral index [Formula: see text], the running [Formula: see text] of the spectral index and the tensor spectral [Formula: see text] for two specific [Formula: see text] models from the Hubble slow-roll parameters. To observe the viability of these models, a numerical analysis of such parameters has been done. The results showed that, by using the various values of free parameters, it is possible to obtain a viable compatible with the observational data.

Complete integrability of the Benjamin–Ono equation on the multi-soliton manifolds

This paper is dedicated to proving the complete integrability of the Benjamin–Ono (BO) equation on the line when restricted to every N-soliton manifold, denoted by $$\mathcal {U}_N$$ U N . We construct generalized action–angle coordinates which establish a real analytic symplectomorphism from $$\mathcal {U}_N$$ U N onto some open convex subset of $${\mathbb {R}}^{2N}$$ R 2 N and allow to solve the equation by quadrature for any such initial datum. As a consequence, $$\mathcal {U}_N$$ U N is the universal covering of the manifold of N-gap potentials for the BO equation on the torus as described by Gérard–Kappeler (Commun Pure Appl Math, 2020. 10.1002/cpa.21896. arXiv:1905.01849). The global well-posedness of the BO equation on $$\mathcal {U}_N$$ U N is given by a polynomial characterization and a spectral characterization of the manifold $$\mathcal {U}_N$$ U N . Besides the spectral analysis of the Lax operator of the BO equation and the shift semigroup acting on some Hardy spaces, the construction of such coordinates also relies on the use of a generating functional, which encodes the entire BO hierarchy. The inverse spectral formula of an N-soliton provides a spectral connection between the Lax operator and the infinitesimal generator of the very shift semigroup.

PHOTONS GENERATED BY PLASMA FLUCTUATIONS

The totally ionized charged collisionless plasma at finite temperature is considered. Using the statistical and Schwinger field methods we derive the production of photons from the plasma by the Cerenkov mechanism. We derive the spectral formula of emitted photons by the plasma fluctuations. The calculation can be extended to the photon propagator involving radiative corrections.

AN IMPLICIT SPECTRAL FORMULA FOR GENERALIZED LINEAR SCHRÖDINGER EQUATIONS

We generalize the semiclassical Bohr–Sommerfeld quantization rule to an exact, implicit spectral formula for linear, generalized Schrödinger equations admitting a discrete spectrum. Special cases include the position-dependent mass Schrödinger equation or the Schrödinger equation for weighted energy. Requiring knowledge of the potential and the solution associated with the lowest spectral value, our formula predicts the complete spectrum in its exact form.

ON THE SURFACE GYROMAGNETIC PLASMONS IN A METAL SPHERE

It is argued that in the long wavelength limit of electromagnetic, far infrared, field optical response of an ultrafine metal particle threaded by uniform magnetic field can be properly modeled by equations of semiclassical electron theory in terms of the surface inertial-wave-like oscillations of free electrons driven by Lorentz restoring force. The detailed calculation of the frequency of size-independent gyromagnetic plasmon resonances computed as a function of multipole degree of electron cyclotron oscillations is presented. This spectrum is derived in juxtaposition with the canonical Mie's spectral formula for the surface plasmon resonances caused by the Coulomb-force-driven plasma oscillations of conduction electrons.

Application of the Generic Spectral Formula to Fetch-Limited Seas

A deep-water spectral formula, based on the Weibull probability distribution of wave periods, is modified to satisfy fetch-limited conditions for wind-generated seas Results of this generic spectral formula are compared with those obtained using the specific JONSWAP formula, in which the empirical parameters resulting from specific wind and fetch conditions are used. The comparisons are shown to be excellent for three of the five cases studied. For the last two cases, the generic formula is shown to be somewhat nonconservative near the spectral peak. In addition to the comparisons with the specific JONSWAP formula results, the generic formula results are compared with those obtained from the standard JONSWAP expression, where the Pierson-Moskowitz parametric values and averaged peak-enhancement values are used. Except for the greatest fetch length (37 km), the standard JONSWAP formula is shown to significantly under-predict the peak spectra values. The generic spectral formula is found to well-predict the spectra for fetch lengths of 11 km and greater.

Hilbert-Asai Eisenstein series, regularized products, and heat kernels

In a famous paper, Asai indicated how to develop a theory of Eisenstein series for arbitrary number fields, using hyperbolic 3-space to take care of the complex places. Unfortunately he limited himself to class number 1. The present paper gives a detailed exposition of the general case, to be used for many applications. First, it is shown that the Eisenstein series satisfy the authors’ definition of regularized products satisfying the generalized Lerch formula, and the basic axioms which allow the systematic development of the authors’ theory, including the Cramér theorem. It is indicated how previous results of Efrat and Zograf for the strict Hilbert modular case extend to arbitrary number fields, for instance a spectral decomposition of the heat kernel periodized with respect to SL2 of the integers of the number field. This gives rise to a theta inversion formula, to which the authors’ Gauss transform can be applied. In addition, the Eisenstein series can be twisted with the heat kernel, thus encoding an infinite amount of spectral information in one item coming from heat Eisenstein series. The main expected spectral formula is stated, but a complete exposition would require a substantial amount of space, and is currently under consideration.