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Characterizations of the associated spaces and second associated spaces of the Hardy space on $\mathbb{R}^n$ are given. Some results on the associated spaces of the $\textrm{BMO}(\mathbb{R}^n)$ space are proved also.

Nonlinear plasmonic effects in perspective 2D materials containing low-dimensional quantum emitters can be a basis of a novel technological platform for the fabrication of fast all-plasmonic triggers, transistors, and sensors. This article considers the conditions for achieving a strong plasmon-exciton coupling in the system with quantum nanowire (NW) placed in proximity to the nanostructured graphene sheets. In the condition of strong coupling, nonlinear interaction between two surface plasmon-polariton (SPP) modes propagating along the graphene waveguide integrated with a stub nanoresonator loaded with a core-shell semiconductor NWs is investigated. Using the 2D full-wave electromagnetic simulation, we studied the different transmittance regimes of the stub with NW for both the strong pump SPP and weak signal SPP tuned to interband and intraband transition in NW, respectively. We found such a regime of NW-SPP interaction that corresponds to the destructive interference with the signal SPP transmittance through the stub less than 7% in the case for pump SPP to be turned off. In contrast, the turning on the pump SPP leads to a transition to constructive interference in the stub and enhancement of signal SPP transmittance to 93%. In our model, the effect of plasmonic switching occurs with a rate of 50 GHz at wavelength 8 um for signal SPP localized inside 20 nm graphene stub loaded with core-shell InAs/ZnS NW., Comment: 19 pages, 13 figures

We study weigted altered Ces\`aro space Ch$_{\infty,w}(I)$, which is non-ideal enlargement of the usual Ces\`aro space. We prove the connection of the space with one weighted Sobolev space of first order on real line and give characterization of associate spaces for the space.

The features of polarization control of multiple multiresonances for quasi-trapped modes excited by synchronization of bianisotropic dipole responses in MoS$_2$ disks with a hole are considered. Using the numerical calculations with analytical multipole analysis, we showed that the presence of a strong optical anisotropy of MoS$_2$ nanoparticles provides an additional degree of freedom and allows to observe several resonances of electric and magnetic dipoles at once in a narrow spectral range. Based on the simulation results, we obtained the frequency dependences for the dipole polarizabilities of the MoS$_2$ disk with a hole, which allow one to distinguish the contributions of the nonlocal and bianisotropic dipole responses and possessing several features in the near infrared range. Using the polarizability spectra of single nanoparticles and applying the tuning strategy, the design of the MoS$_2$ metasurface supporting three resonances of quasi-trapped modes at once in a narrow spectral range was developed. One of these resonances corresponds to the telecom wavelength of 1550 nm. The spectrum of light reflection for MoS$_2$ metasurface is characterized by three narrowband dips corresponding to the wavelengths of the quasi-trapped modes. It was shown that a change in the polarization of a wave normally incident on the metasurface to orthogonal one leads to a change in the type of bianisotropic response excited in each MoS$_2$ disk and to the excitation of three other features in the reflection spectra of the metasurface at wavelengths close to the initial values., Comment: 8 pages, 5 figures

The RELEC scientific instrumentation onboard the Vernov spacecraft launched on July 8, 2014, included the DRGE gamma-ray and electron spectrometer. This instrument incorporates a set of scintillation phoswich detectors, including four identical X-ray and gamma-ray detectors in the energy range from 10 keV to 3 MeV with a total area of $\sim$500 $cm^{2}$ directed toward the nadir, and an electron spectrometer containing three mutually orthogonal detector units with a geometry factor of $\sim$2 $cm^{2} sr$, which is also sensitive to X-rays and gamma-rays. The goal of the space experiment with the DRGE instrument was to investigate phenomena with fast temporal variability, in particular, terrestrial gamma-ray flashes (TGFs) and magnetospheric electron precipitations. However, the detectors of the DRGE instrument could record cosmic gamma-ray bursts (GRBs) and allowed one not only to perform a detailed analysis of the gamma-ray variability but also to compare the time profiles with the measurements made by other instruments of the RELEC scientific instrumentation (the detectors of optical and ultraviolet flashes, the radio-frequency and low-frequency analyzers of electromagnetic field parameters). We present the results of our observations of cosmic GRB 141011A and GRB 141104A, compare the parameters obtained in the GBM/Fermi and KONUSWind experiments, and estimate the redshifts and Eiso for the sources of these GRBs. The detectability of GRBs and good agreement between the independent estimates of their parameters obtained in various experiments are an important factor of the successful operation of similar detectors onboard the Lomonosov spacecraft., Comment: 19 pages, 8 figures

We study weighted altered Ces\`aro and Copson spaces, which is non-ideal enlargement of the usual spaces. We give full characterization of dual spaces for the spaces.

In the present paper, the collective near-field effects in a two-graphene sheets plasmonic waveguide loaded with an array of Ag$_2$Se quantum dots excited by external radiation are theoretically studied. This research aims to develop a theoretical approach to realizing controllable excitation and the propagation of surface plasmon polaritons (SPPs) in planar graphene waveguides. The proposed model is based on the semiclassical description that implies the dispersion equation's solution for SPPs excited in two coupled graphene sheets and the embedded quantum dots' energy spectra analysis. Using the finite difference time domain method, the different near-field patterns realized in the waveguides depending on the quantum dots' ordering and an external voltage applied independently to each graphene sheet with additional gold electrodes are numerically investigated. The research shows that applying external voltages allows locally changing the graphene chemical potential, thereby leading to controllable excitation of SPPs in the space between the electrodes. Under these conditions, the propagation direction of the excited SPPs is determined by the geometrical configurations of the gold electrodes providing the required SPP routing. The investigated system offers new opportunities for near-field energy transport and concentration, which can be applied to develop ultra-compact photonic devices.

We investigate the resonant optical response of single material-anisotropic nanoparticles (NPs) of molybdenum disulfide (MoS$_2$) and their two-dimensional arrays (metasurfaces) irradiated by plane waves of the telecomunication optical range. Nanoparticles in the form of a disk with centered and shifted hole are considered. Using the recently experimental measured the MoS$_2$ dielectric permittivity and numerical calculations with analytical multipole analysis, we show that the material-anisotropy of NPs can lead to specific nonlocal contributions in their magnetic and electric dipole response and affect the effective dipole polarizabilities. Applying a special procedure we determine the period of the MoS$_2$ metasurfaces supporting the quasi-trapped mode (QTM) resonance around the tellecom wavelength of 1550 nm. It is shown that regardless extremely weak absorption of the single nanoparticles, the excitation of the QTM leads to effective narrowband absorption in the metasurfaces. Influences of the linear polarization direction of normally incident waves on the QTM implementation and the reflection and transmission spectra are studied. It is found and demonstrated, for the first time, that a metasurface, composed of the MoS$_2$ disks with their anisotropy perpendicularto the metasurface plane, has the properties of a continuous birefringent medium. Due to these properties, normally incident and linear-polarized waves can be transformed in the transmitted and reflected waves with changed polarizations.

We study theoretically a problem of nonlinear interaction between two surface plasmon-polariton (SPP) modes propagating along the graphene waveguide integrated with a stub nanoresonator loaded with a core-shell quantum dot (QD). The conditions of strong coupling and very narrowband resonance for Ladder-type SPP-QD interaction in nanoresonator leading to $\pi$-phase shift of signal SPP mode are established and discussed. Using the full-wave electromagnetic simulation we demonstrate that turning on the pump SPP leads to a transition from destructive to constructive interference in the stub nanoresonator and subsequent effect of switching from locking to transmitting the signal SPP through the waveguide. On the base of the obtained results we develop the model of all-plasmonic graphene transistor with optimized characteristics including the size about $25$ nm and the clock frequency about $100$ GHz functioning at the near-infrared wavelength range., Comment: 8 pages, 4 figures

The present paper theoretically investigates features of quantum dynamics for localized plasmons in three-particle or four-particle spaser systems consisting of metal nanoparticles and semiconductor quantum dots. In the framework of the mean field approximation, the conditions for the observation of stable stationary regimes for single-particle plasmons in spaser systems are revealed, and realization of these regimes is discussed. The strong dipole-dipole interaction between adjacent nanoparticles for the four-particle spaser system is investigated. We show that this interaction can lead to the decreasing of the autocorrelation function values for plasmons. The generation of entangled plasmons in a three-particle spaser system with nonlinear plasmon-exciton interaction is predicted. For the first time the use of an external magnetic field is proposed for control of the cross-correlation between plasmons in the three-particle spaser system., Comment: 16 pages, 10 figures

The formation of pulses of surface electromagnetic waves in a metal/dielectric interface is considered in the process of cooperative decay of excitons of quantum dots distributed near a metal surface in a dielectric layer. It is shown that the efficiency of exciton energy transfer to excited plasmons can be increased by selecting the dielectric material with specified values of the complex permittivity. It is found that in the mean field approximation the semiclassical model of formation of plasmon pulses in the system under study is reduced to the pendulum equation with the additional term of nonlinear losses., Comment: 12 pages, 6 figures

Weighted $L^p-L^r$ inequalities with arbitrary measurable non-negative weights for positive quasilinear integral operators with Oinarov's kernel on the semiaxis are characterized. Application to the boundedness of maximal operator in the Lorentz $\Gamma-$spaces is given.

In this work we discuss the problem of selecting suitable approximators from families of parameterized elementary functions that are known to be dense in a Hilbert space of functions. We consider and analyze published procedures, both randomized and deterministic, for selecting elements from these families that have been shown to ensure the rate of convergence in $L_2$ norm of order $O(1/N)$, where $N$ is the number of elements. We show that both randomized and deterministic procedures are successful if additional information about the families of functions to be approximated is provided. In the absence of such additional information one may observe exponential growth of the number of terms needed to approximate the function and/or extreme sensitivity of the outcome of the approximation to parameters. Implications of our analysis for applications of neural networks in modeling and control are illustrated with examples., Comment: arXiv admin note: text overlap with arXiv:0905.0677