A Multiparameter Hardy–Hilbert-Type Inequality Containing Partial Sums as the Terms of Series

In this study, a multiparameter Hardy–Hilbert-type inequality for double series is established, which contains partial sums as the terms of one of the series. Based on the obtained inequality, we discuss the equivalent statements of the best possible constant factor related to several parameters. Moreover, we illustrate how the inequality obtained can generate some new Hardy–Hilbert-type inequalities.

Tauberian theorems in the case of strong summability in degree $p$ of double series

We establish a Tauberian theorem in the case of strong summability in degree $p$ of double series by matrix methods, give its application to Abel methods.

Tauberian theorems in the case of absolute summability in degree $p$ of double series

We establish a Tauberian theorem in the case of absolute summability in degree $p$ of double series by matrix methods, give its application to Abel methods.

Generalizing the sampling theorem for a frequency-time domain to sample signals under the conditions of a priori uncertainty

The radio monitoring of radiation and interference with electronic means is characterized by the issue related to the structural-parametric a priori uncertainty about the type and parameters of the ensemble of signals by radio-emitting sources. Given this, it is a relevant task to devise a technique for the mathematical notation of signals in order to implement their processing, overcoming their a priori uncertainty in terms of form and parameters. A given problem has been solved by the method of generalization and proof for the finite signals of the Whittaker-Kotelnikov-Shannon sampling theorem (WKS) in the frequency-time domain. The result of proving it is a new discrete frequency-temporal description of an arbitrary finite signal in the form of expansion into a double series on the orthogonal functions such as sinx/x, or rectangular Woodward strobe functions, with an explicit form of the phase-frequency-temporal modulation function. The properties of the sampling theorem in the frequency-time domain have been substantiated. These properties establish that the basis of the frequency-time representation is orthogonal, the accuracy of approximation by the basic functions sinx/x and rectangular Woodward strobe functions are the same, and correspond to the accuracy of the UCS theorem approximation, while the number of reference points of an arbitrary, limited in the width of the spectrum and duration, signal, now taken by frequency and time, is determined by the signal base. The devised description of signals in the frequency-time domain has been experimentally investigated using the detection-recovery of continuous, simple pulse, and linear-frequency-modulated (LFM) radio signals. The constructive nature of the resulting description has been confirmed, which is important and useful when devising methods, procedures, and algorithms for processing signals under the conditions of structural-parametric a priori uncertainty.

Clitics in embryo

The chapter aims to provide a principled account of the emergence of clitic pronouns in the transition from Latin to early Romance. The discussion revolves around the hypothesis that a double series of pronouns (which in Late Latin were still homophonous) emerged from the reanalysis of a discourse-driven displacement. So-called weak pronouns in Latin are strong pronouns that are displaced to the Wackernagel Position, which is analysed as a Criterial Position in the sense of Rizzi (2006, 2007). Productive interpolation in medieval Portuguese and Spanish results from the same syntactic displacement, but the Romance languages, unlike Latin, have exhibited a double series of pronouns (clitic/strong) from the earliest attestations. The emergence of a second series of pronouns witnesses a change in the morphophonological status of pronouns, which is the prelude to another change which will yield the incorporation of clitics into verbal hosts.

The rise of adverbal clitics

Latin differs Romance in two main respects: first, it did not display a double series of pronouns of the kind we observe from the earliest Romance attestations (in the eighth–ninth century); second, in Latin pronouns were not incorporated into the verb, although they were frequently close to the verb when the latter was displaced in the left periphery of the clause. The emergence of a double series of pronouns resulted from the reanalysis of Wackernagel pronouns into prosodically deficient elements. Being stress-less, inherently topical pronouns began to undergo linguistic changes affecting unstressed vowels, which eventually led to the incorporation of unstressed pronominal forms into verbs. The chapter elaborates on the modelling of incorporation and wonders about the historical relationship between the rise of incorporation and the loss of scrambling (and interpolation).

Some hypergeometric summations formulas and series identities with applications

In the paper we present two incomplete Gaussian hypergeometric formulas in summation form by specific known formulas.We also developed each of these formulas and how they use to derive double series identities in general forms.

On the multipath effects due to wall reflections for wave reception in a corner

Multipath effects occur when receiving a wave near a corner, for example, the noise of an helicopter or an aircraft or a drone or other forms of urban air mobility near a building, or a telecommunications receiver antenna near an obstacle. The total signal received in a corner consists of four parts: (i) a direct signal from source to observer; (ii) a second signal reflected on the ground; (iii) a third signal reflected on the wall; (iv) a fourth signal reflected from both wall and ground. The problem is solved in two-dimensions to specify the total signal, whose ratio to the direct signal specifies the multipath factor. The amplitude and phase of the multipath factor are plotted as functions of the frequency over the audible range, for various relative positions of observer and source, and for several combinations of the reflection coefficients of the ground and wall. It is shown that the received signal consists of a double series of spectral bands, in other words: (i) the interference effects lead to spectral bands with peaks and zeros; (ii) the successive peaks also go through zeros and “peaks of the peaks”. The results apply not only to sound, but also to other waves, e.g., electromagnetic waves using the corresponding frequency band and reflection factors.

Approximate Asymptotic Expressions for the Electromagnetic Field and the Mutual Admittance of Slоts in a Conducting Convex Surface of Rotation in the Form of Series of Azimuthal Harmonics

In this paper, we obtain approximate asymptotic expressions for the electromagnetic field and the self and mutual admittances of "single-mode" slots in a smooth convex surface of rotation of large sizes in the form of a series of azimuthal harmonics. The coefficients of the series are expressed as integrals over the wave spectrum and can be calculated numerically or as a sum series of deductions (for mutual admittances). The expressions for the coefficients are uniformly valid in the boundary surface layer, except for the vicinity of the poles of the surface of rotation, and do not have discontinuities on the caustics of the surface rays. The resulting expressions can be directly used to calculate the fields and the self and mutual admittances of annular slots. In contrast to the eigenfunction method, asymptotic expressions allow us to cover the case of an arbitrary-shaped surface and avoid summing slowly converging double series. A comparison of the results of calculating the admittances of annular slots in a conducting spherical surface obtained by the proposed method and the method of eigenfunctions was executed, and their good agreement shown even for a small radius of the sphere equal to 3λ.