Operational Properties of Two Integral Transforms of Fourier Type and their Convolutions

In this paper we present the operational properties of two integral transforms of Fourier type, provide the formulation of convolutions, and obtain eight new convolutions for those transforms. Moreover, we consider applications such as the construction of normed ring structures on L₁(\mathbbR)L_{1}({\mathbb{R}}), further applications to linear partial differential equations and an integral equation with a mixed Toeplitz-Hankel kernel.     

Impurity-induced anisotropic semiconductor-semimetal transition in monolayer biased black phosphorus

Taking into account the electron-impurity interaction within the continuum approximation of tight-binding model, the Born approximation, and the Green's function method, the main features of anisotropic electronic phase transition are investigated in monolayer biased black phosphorus (BP). To this end, we concentrated on the disordered electronic density of states (DOS), which gives useful information for electro-optical devices. Increasing the impurity concentration in both unbiased and biased impurity-infected single-layer BP, in addition to the decrease of the band gap, independent of the direction, leads to the midgap states and an extra Van Hove singularity inside and outside of the band gap, respectively. Furthermore, strong impurity scattering potentials lead to a semiconductor-semimetal transition and one more Van Hove singularity in x-direction of unbiased BP and surprisingly, this transition does not occur in biased BP. We found that there is no phase transition in y-direction. Since real applications require structures with modulated band gaps, we have studied the influence of different bias voltages on the disordered DOS in both directions, resulting in the increase of the band gap.     

Combined effect of the perpendicular magnetic field and dilute charged impurity on the electronic phase of bilayer AA-stacked hydrogenated graphene

We address the electronic phase engineering in the impurity-infected functionalized bilayer graphene with hydrogen atoms (H-BLG) subjected to a uniform Zeeman magnetic field, employing the tight-binding model, the Green's function technique, and the Born approximation. In particular, the key point of the present work is focused on the electronic density of states (DOS) in the vicinity of the Fermi energy. By exploiting the perturbative picture, we figure out that how the interaction and/or competition between host electrons, guest electrons, and the magnetic field potential can lead to the phase transition in H-BLG. Furthermore, different configurations of hydrogenation, namely reduced table-like and reduced chair-like, are also considered when impurities are the same and/or different. A comprehensive information on the various configurations provides the semimetallic and gapless semiconducting behaviors for unfunctionalized bilayer graphene and H-BLGs, respectively. Further numerical calculations propose a semimetal-to-metal and gapless semiconductor-to-semimetal phase transition, respectively, when only turning on the magnetic field. Interestingly, the results indicate that the impurity doping alone affects the systems as well, leading to semimetal-to-metal and no phase transition in the pristine system and hydrogenated ones, respectively. However, the combined effect of charged impurity and magnetic field shows that the pristine bilayer graphene is not influenced much as the functionalized ones and phase back transitions appear. Tuning of the electronic phase of H-BLG by using both types of electronic and magnetic perturbations play a decisive role in optical responses.     

Electrochemical synthesis of a thiophene-containing cyclo[9]pyrrole

A new member of the cyclo[n]pyrrole class of expanded porphyrins could be prepared from the corresponding thiophene-containing terpyrrole precursor through use of a mild electrochemical oxidative procedure. The isolated macrocycle, featuring nine heterocyclic subunits directly connected through their α,α'-positions, is the largest cyclo[n]pyrrole derivative reported to date (see figure).     

On the Nonlinear Schrödinger Equation on the Half Line with Homogeneous Robin Boundary Conditions

Boundary value problems for the nonlinear Schrödinger equations on the half line with homogeneous Robin boundary conditions are revisited using Bäcklund transformations. In particular: relations are obtained among the norming constants associated with symmetric eigenvalues; a linearizing transformation is derived for the Bäcklund transformation; the reflection‐induced soliton position shift is evaluated and the solution behavior is discussed. The results are illustrated by discussing several exact soliton solutions, which describe the soliton reflection at the boundary with or without the presence of self‐symmetric eigenvalues.     

Measurements of anomalous dispersion in rayleigh scattering of characteristic X-ray fluorescence

Summary When using characteristic fluorescence X-rays or γ-rays of energy under 100 keV to study the Rayleigh scattering of photons from atoms the effect of anomalous dispersion is not in general negligible. On the contrary, it may cause the atomic cross-section values to vary with respect to the tabulated values—usually calculated in nonresonant approximation—of an order of magnitude in the most critical cases. In this work we present experimental results of Rayleigh scattering where this effect is well evident. We used as sources of excitation a radioisotope (²⁴¹Am,E _γ 59.6 keV) and a X-ray tube with a series of different secondary anodes and solid-state detectors to detect the scattered radiation. We reviewed the atomic form factor formalism which describes the phenomenon in a nonrelativistic treatment and we show its strict analogy with QEDS-matrix theory. We obtained numerical values for the cross-sections by using the tabulated values of the photoelectric cross-sections and we made a comparison with the experimental values. The error of the measurements (∼3%) derives from the superposition of the Rayleigh scattering with the characteristic X-ray fluorescence lines. Within the error limits the agreement with the values from the form factor approximation is very satisfactory.

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Riassunto Quando si utilizza la radiazione X di fluorescenza caratteristica o la radiazione γ di energia minore di 100 keV per studiare la diffusione elastica da parte degli atomi (diffusione di Rayleigh), l'effetto della diffusione anomala non è in generale trascurabile. Al contrario, essa può causare variazioni anche di un ordine di grandezza dei valori delle sezioni d'urto atomiche rispetto ai valori tabulati che sono usualmente calcolati nell'approssimazione non risonante. In questo lavoro si presentano i risultati sperimentali di alcune misure di diffusione di Rayleigh nei quali questo effetto è ben evidente. Come sorgenti di radiazione sono stati utilizzati un isotopo radioattivo (²⁴¹Am,E _γ=59.6 keV) e una serie di anodi secondari associati a un tubo X. Per la rivelazione della radiazione X sono stati utilizzati rivelatori a stato solido. Si è eseguita una revisione del formalismo dei fattori di forma atomici per la descrizione del fenomeno in una trattazione non relativistica e si mostra la stretta analogia con la teoria della matriceS dell'elettrodinamica quantistica. Si sono ottenuti i risultati numerici per le sezioni d'urto di diffusione elastica utilizzando i valori tabulati per le sezioni d'urto fotoelettriche e si sono confrontati con i valori ottenuti sperimentalmente. L'errore delle misure (∼3%) deriva dalla sovrapposizione della diffusione di Rayleigh con le righe di fluorescenza caratteristica. Entro questi limiti di errore l'accordo con i valori ricavati nell'approssimazione dei fattori di forma è molto soddisfacente.

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Резюме При использовании характеристической рентгеновской или γ-лучевой флуоресценции с энергией до 100 кэВ для исследования рэлеевского рассеяния фотонов на атомах, влияние аномальной дисперсии не является в общем случае пренебрежимо малым. Наоборот, эффект аномальной дисперсии может изменить значения атомных поперечных сечений по сравнению с табулированными значениями, обычно вычисляемыми в нерезонансном приближении, в наиболее критических случаях на порядок величины. В этой работе приводятся резулятаты для рэлеевского рассеяния, где эффект аномальной дисперсии является существенным. Мы используем в качестве источников возбуждения радиоизотоп (²⁴¹Am,E _γ=59.6 кэВ) и рентгеновскую трубку с различными вторичными анодами и твердотельные детекторы для регистрации рассеянного излучения. Мы используем формализм атомного форм-фактора, который описывает явление в нерелятивистском приближении. Мы отмечаем точную аналогию с теориейS-матрицы в квантовой электродинамике. Получаются численные значения для поперечных сечений, используя табулированные величины для фотоэлектрических поперечных сечений. Проводится сравнение полученных значений с экспериментальными данными. Погрешность измерений (∼3%) определяется из суперпозиции рэлеевского рассеяния с линиями характеристической рентгеновской Флуоресценции. В пределах погрешностей получается удовлетворительное согласие с результатами, полученными из приближения атомного форм-фактора.

     

The subgroups of the special linear group over a skew field that contain the group of diagonal matrices

For any (noncommutative) skew field T, the lattice of subgroups of the special linear group Λ=SL(n,T) that contain the subgroup Δ=SD(n,T) of diagonal matrices (with Dieudonné determinants equal to 1) is studied. It is established that for any subgroup H, Δ≤H≤Λ, there exists a uniquely determined unital net σ such that Λ(σ)≤H≤N(σ), where Λ(σ) is the net subgroup associated with the net σ and N(σ) is its normalizer in Λ. Bibliography: 11 titles. Published inZapiski Nauchnykh Seminarov POMI, Vol. 211, 1994, pp. 91–103. Translated by Bui Xuan Hai.