Polynomial-Exponential Bounds for Some Trigonometric and Hyperbolic Functions

Recent advances in mathematical inequalities suggest that bounds of polynomial-exponential-type are appropriate for evaluating key trigonometric functions. In this paper, we innovate in this sense by establishing new and sharp bounds of the form (1−αx2)eβx2 for the trigonometric sinc and cosine functions. Our main result for the sinc function is a double inequality holding on the interval (0, π), while our main result for the cosine function is a double inequality holding on the interval (0, π/2). Comparable sharp results for hyperbolic functions are also obtained. The proofs are based on series expansions, inequalities on the Bernoulli numbers, and the monotone form of the l’Hospital rule. Some comparable bounds of the literature are improved. Examples of application via integral techniques are given.

A Pretreatment Method of Volterra the External Boundary Value Problem of Integral Differential Equations

In the process of traditional methods, the error rate of external boundary value problem is always at a high level, which seriously affects the subsequent calculation and cannot meet the requirements of current Volterra products. To solve this problem, Volterra's preprocessing method for the external boundary value problem of Integro differential equations is studied in this paper. The Sinc function is used to deal with the external value problem of Volterra Integro differential equation, which reduces the error of the external value problem and reduces the error of the external value problem. In order to prove the existence of the solution of the differential equation, when the existence of the solution can be proved, the differential equation is transformed into a Volterra integral equation, the Taylor expansion equation is used, the symplectic function is used to deal with the external value problem of homogeneous boundary conditions, and the uniform effective numerical solution of the external value problem of the equation is obtained by homogeneous transformation according to the non-homogeneous boundary conditions.

Filtered orthogonal frequency division multiplexing for improved 5G systems

Wireless communications became an integrated part of the human life. Fifth generation (5G) is the modern communication which provides enhanced mobile broadband (eMBB), ultra reliable low latency communications (URLLC), and massive machine type communication (mMTC). Thus, 5G have to provide coverage to multi-numerology devices, therefore, modulation and access schemes are suggested in the literature such as cyclic prefix orthogonal frequency division multiplexing (CP-OFDM) and filtered OFDM (f-OFDM). CP-OFDM suffers from the high out of band emission which limited the multi-numerology applications. In f-OFDM, the out of band emission can be suppressed to an accepted extent such that different numerologies can be coexisting. On the other hand, f-OFDM can be more improved by using a proper filtering approach. In this paper three different filters are suggested based windowed-sinc function; Hanning, Hamming, and Blackman. Simulation results show that the proposed filters are promising for high spectral efficiency and out of band emission rejection. Furthermore, the bit error rate, error vector magnitude, and power spectral density are further improved with respect to CP-OFDM scheme but some trade-off is present. Overall, the suggested windowed-sinc filters are outperforming the traditional CP-OFDM. As a conclusion, the suggested windnowed-sinc filters have no limitations on the modulation order or the number of subcarriers utilized in the system.

Using GEDI Waveforms for Improved TanDEM-X Forest Height Mapping: A Combined SINC + Legendre Approach

In this paper, we consider a new method for forest canopy height estimation using TanDEM-X single-pass radar interferometry. We exploit available information from sample-based, space-borne LiDAR systems, such as the Global Ecosystem Dynamics Investigation (GEDI) sensor, which offers high-resolution vertical profiling of forest canopies. To respond to this, we have developed a new extended Fourier-Legendre series approach for fusing high-resolution (but sparsely spatially sampled) GEDI LiDAR waveforms with TanDEM-X radar interferometric data to improve wide-area and wall-to-wall estimation of forest canopy height. Our key methodological development is a fusion of the standard uniform assumption for the vertical structure function (the SINC function) with LiDAR vertical profiles using a Fourier-Legendre approach, which produces a convergent series of approximations of the LiDAR profiles matched to the interferometric baseline. Our results showed that in our test site, the Petawawa Research Forest, the SINC function is more accurate in areas with shorter canopy heights (<~27 m). In taller forests, the SINC approach underestimates forest canopy height, whereas the Legendre approach avails upon simulated GEDI forest structural vertical profiles to overcome SINC underestimation issues. Overall, the SINC + Legendre approach improved canopy height estimates (RMSE = 1.29 m) compared to the SINC approach (RMSE = 4.1 m).

Small-Scale Spatial-Temporal Correlation Modeling for Reconfigurable Intelligent Surfaces

<div><div><div><p>The reconfigurable intelligent surface (RIS) is an emerging promising candidate technology for the sixth-generation wireless networks, where the element spacing is usually of sub-wavelength. Only limited knowledge, however, has been gained about the spatial-temporal correlation behavior among the elements in an RIS. In this paper, we investigate the spatial-temporal correlation models for an RIS in a wireless communication system. Joint small-scale spatial-temporal correlation functions are provided and analyzed for both ideal isotropic scattering and more practical non-isotropic scattering environments, where the latter is studied via employing an angular distribution derived from real-world millimeter-wave measurements. Furthermore, for the special case of spatial-only correlation under isotropic scattering, an analytical expression is proposed to characterize the spatial degrees of freedom (DoF) for RISs with finite element spacing and aperture sizes in practice. Analytical and numerical results demonstrate that the joint spatial-temporal correlation can be represented by a four-dimensional sinc function under isotropic scattering, while the correlation is generally stronger with more fluctuation and significantly fewer dominant eigenvalues hence smaller DoF for non-isotropic scattering.</p></div></div></div>

Small-Scale Spatial-Temporal Correlation Modeling for Reconfigurable Intelligent Surfaces

<div><div><div><p>The reconfigurable intelligent surface (RIS) is an emerging promising candidate technology for the sixth-generation wireless networks, where the element spacing is usually of sub-wavelength. Only limited knowledge, however, has been gained about the spatial-temporal correlation behavior among the elements in an RIS. In this paper, we investigate the spatial-temporal correlation models for an RIS in a wireless communication system. Joint small-scale spatial-temporal correlation functions are provided and analyzed for both ideal isotropic scattering and more practical non-isotropic scattering environments, where the latter is studied via employing an angular distribution derived from real-world millimeter-wave measurements. Furthermore, for the special case of spatial-only correlation under isotropic scattering, an analytical expression is proposed to characterize the spatial degrees of freedom (DoF) for RISs with finite element spacing and aperture sizes in practice. Analytical and numerical results demonstrate that the joint spatial-temporal correlation can be represented by a four-dimensional sinc function under isotropic scattering, while the correlation is generally stronger with more fluctuation and significantly fewer dominant eigenvalues hence smaller DoF for non-isotropic scattering.</p></div></div></div>

Spatiotemporal Correlations of Mesoscale Neocortical Activities in Patients with Focal Epilepsy

Brain function is reflected in both the action potentials of individual neurons and interactions through e.g. synaptic currents reflected in widespread, slow fluctuations of the local field potential (LFP). We analyzed microelectrode array data to determine state-dependent correlations between action potential and LFP during seizure events as well as interictally in patients with focal epilepsy. We also examined activity in two different cortical network territories: the seizure core and surrounding penumbra (Schevon et al., 2012). The cross-correlation of spiking activity in the core showed an association of the ictal action potentials with the global oscillatory aspect of the seizure activity and indicated local failure of inhibitory restraint surrounding the ictal spike. These patterns were not observed in the penumbra. Our analyses from clinical recordings and a model of a single ictal spike in the core revealed that both the temporal and spatial components of the network's cross-correlation can be approximated by a sine cardinal (sinc) function. The biological interpretation of these findings is that important functional differences across the neocortical network exist, with a critical role of the millimeter-range excitatory connections within the grey matter. Therefore, localized intervention that prevents escape of hyperactivity from the seizure core may be considered as a therapeutic strategy.

Studying and Analysis of a Novel RK-Sinc Scheme

In this paper, a novel high-order method, Runge-Kutta Sinc (RK-Sinc), is proposed. The RK-Sinc scheme employs the strong stability preserving Runge-Kutta (SSP-RK) algorithm to substitute time derivative and the Sinc function to replace spatial derivates. The computational efficiency, numerical dispersion and convergence of the RK-Sinc algorithm are addressed. The proposed method presents the better numerical dispersion and the faster convergence rate both in time and space domain. It is found that the computational memory of the RK-Sinc is more than two times of the FDTD for the same stencil size. Compared with the conventional FDTD, the new scheme provides more accuracy and great potential in computational electromagnetic field.