In this paper we address the approximation of the coupling problem for the wave equation and Maxwell's equations of electromagnetism in the time domain in terms of the electric field, by means of a nodal linear finite-element discretization in space, combined with a classical'explicit finite-difference scheme for the time discretization. Our study applies to the particular case where the dielectric permittivity has a constant value outside a sub-domain, whose closure does not intersect the boundary of the domain where the problem is defined. Inside this sub-domain Maxwell's equations hold. Outside this sub-domain the wave equation holds, which may correspond to the Maxwell's equations with a constant permittivity under certain conditions. We consider as a model the case of first order absorbing boundary conditions. Optimal error estimates that hold in natural norms under reasonable assumptions are given, among which lies a typical CFL condition for hyperbolic equations.

In this paper, experimental results about the performance of a Takagi-Sugeno Fuzzy Controller (TSFC) for an EV3 Ballbot Robotic System (EV3BRS) are reported. The physical configuration for the EV3BRS has the form of an inverted pendulum mounted on a ball. The EV3BRS is an underactuated robotic system with four outputs and two control torques. The Takagi-Sugeno Fuzzy Model (TSFM) design comes from linearization of the nonlinear model around two operation points near from the upright position of the EV3BRS's body. The Parallel Distributed Compensation (PDC) approach is used to the design of the TSFC. The Linear Matrix Inequalities (LMIs) approach is used to get the feedback gains for every local linear controller guaranteeing global asymptotically stability, via a more relaxed stability condition, of the overall fuzzy control system. Measurement and control data from and to the EV3BRS are transferred via telecontrol and telemetry.

This paper considers the direction of arrival (DOA) estimation problem of phase ambiguity for unfolded coprime linear array (UCLA). The existing most common stacking subarray-based method can tackle the phase ambiguity problem. However, the method is not always true. For a given DOA, it has its corresponding steering vector, but if there are two DOAs which have the same steering vectors with the given DOA for different subarrays, the phase ambiguity problem still arises. A modified method, which defines a decision variable and uses the classic beamforming technique to estimate the DOAs is proposed. However, this method needs additional algorithm to distinguish the true DOAs besides multiple signal classification (MUSIC) spectrum. And sometimes this method is not reliable if the decision variable is not chosen appropriately. Therefore, based on the UCLA, we reconstruct the array to design an improved UCLA called IUCLA. With moving the reference element, the linear relationship among the directional vectors can be broken. In this way, we can directly utilize the MUSIC algorithm to estimate with no additional algorithm. The proposed method can solve the phase ambiguity problem and it does not demand other technique to decrease the complexity. Moreover, the Cramer-Rao Bound (CRB), as the lower bound of the unbiased estimation, is provided and numerical simulations are given to demonstrate the effectiveness and superiority of the proposed method.

Municipal Solid Waste Management (MSWM) struggles with significant policy and operational challenges, particularly concerning recyclables collection routes and fleet composition. Within the European Union, phasing out traditional fuel-based vocational vehicles, like garbage trucks, in favor of zero-emission alternatives is mandatory to achieve sustainable development objectives. Integrating electric solid waste collection vehicles into municipal fleets presents challenges due to differences in range, capacity, and noise levels. The emission is even more crucial in the systems where recyclables are collected separately, which requires a greater number of trips to be performed. This study addresses MSWM’s strategic aspect by minimizing the total cost of replacing waste collection vehicles while meeting emission constraints. The Fleet Transition Problem (FTP) was formulated and solved using a MARKAL-based approach. The objective of the FTP and a mixed integer linear program used to solve it is minimizing the overall cost of fleet modernization throughout a multi-phase planning horizon so that the sustainable transition of the fleet can be assured. Computational experiments affirmed the model’s effectiveness in strategizing fleet transition. This research outlines a multi-period model for transitioning to a zero-emission fleet and demonstrates the FTP’s potential for strategic decision-making. Notably, the study observes a consistent reduction in permissible emissions across the planning horizon.

Given several nonnegative matrices with a single pattern of allocation among their zero/nonzero elements, the average matrix should have the same pattern, too. This is the first tenet of the pattern-multiplicative average (PMA) concept, while the second one suggests the multiplicative (or geometric) nature of averaging. The original concept of PMA was motivated by the practice of matrix population models as a tool to assess the population viability from long-term monitoring data. The task has reduced to searching for an approximate solution to an overdetermined system of polynomial equations for unknown elements of the average matrix (G), hence to a nonlinear constrained minimization problem for the matrix norm. Former practical solutions faced certain technical problems, which required sophisticated algorithms but returned acceptable estimates. Fresh idea to use the eigenvalue approximation ensues also from the basic equation of averaging, which determines the exact value of λ1(G), the dominant eigenvalue of matrix G, too, and the corre-sponding eigenvector. These are bound by the well-known linear equations, which reduce the task to a standard problem of linear programing (LP). The LP approach is realized for 13 fixed-pattern matrices gained in a case study of Androsace albana, an alpine short-lived perennial, monitored on permanent plots during 14 years. A standard software routine reveals the unique exact solution, rather than an approximate one, to the PMA problem, which turns the LP approach into ‘’the best of versatile optimization tools”. The exact solution turns out to be peculiar in reaching zero bounds for certain nonnegative entries of G, which deserves a modified problem formulation separating the lower bounds from zero.

The successful vaccination implies the induction of effective specific immune responses. We intend to find biomarkers among various immune cell subpopulations, cytokines and antibodies which could be used to predict the levels of specific antibody- and cell-mediated responses after measles-mumps-rubella vaccination. We measured 59 baseline immune status parameters (frequencies of 42 immune cell subsets, levels of 13 cytokines, immunoglobulins) before vaccination and 13 response variables (specific IgA and IgG, antigen-induced IFN-γ production, CD107a expression on CD8+ T lymphocytes, and cellular proliferation levels by CFSE dilution) 6 weeks after vaccination for 19 individuals. Statistically significant Spearman correlations between some baseline parameters and response variables were found for each response variable (p<0.05). Due to the low number of observations relative to the number of baseline parameters and missing data for some observations, we utilized three feature selection strategies to select potential predictors of the post-vaccination responses among baseline variables: (a) screening of the variables based on the correlation analysis, (b) supervised screening based on the information of changes of baseline variables at day 7, (c) implicit feature selection is performed using regularization-based sparse regression. We identified optimal multivariate liner regression models for predicting the effectiveness of vaccination against measles-mumps-rubella using the baseline immune status parameters. It turned out that the sufficient number of predictor variables ranges from one to five depending on the response variable of interest.

Fire regimes in mountain landscapes of southern Europe have been shifting from their baselines due to the accumulation of fuel fostered by long-standing rural abandonment and fire exclusion policies. Understanding the role of fire on biodiversity is paramount to implement adequate management to mitigate the impacts of altered fire regimes and land abandonment on biodiversity. Here, we explored to what extent the spatiotemporal variation in burn severity has affected bird abundance of a mountain abandoned landscape located in the Atlantic-Mediterranean transition (NW Iberia). We took advantage of: (1) satellite images of Sentinel 2 and Landsat missions to compute burn severity indicators from 2010 to 2020, and (2) standardized bird surveys carried out over 206 point-counts along the breeding season of 2021. Bird abundance models were built from burn severity metrics together with well-known fire regime attributes (% of burnt area and time since fire). Our results showed that the spatiotemporal variation of burn severity significantly correlated with the abundance of the 39% of the modeled species, supporting the role of pyro-diversity in driving bird populations in our region. The burnt area also explained abundance patterns for 28% of species. Time since fire only correlated with the abundance of 3 species. Our findings confirm the importance of incorporating burn severity indicators into the toolkit of decision makers to anticipate the response of birds to fire management.

This paper is a slightly modified, abridged version of a previous work ``Parametric Gevrey asymptotics in two complex time variables through truncated Laplace transforms'' motivated by our contribution in the conference ``Formal and Analytic Solutions of Diff. (differential, partial differential, difference, q-difference, q-difference-differential) Equations on the Internet'' (FASnet20). It aims to clarify and give further detail at some crucial points concerning the asymptotic behavior of the solutions of the problems studied in that work.

Genomic selection (GS) can accelerate variety improvement when training set (TS) size, and its relationship with the breeding set (BS) are optimized for prediction accuracies (PA) of genomic prediction (GP) models. Sixteen GP algorithms were run on phenotypic best linear unbiased predictors (BLUPs) and estimators (BLUEs) of resistance to both fall armyworm (FAW) and maize weevil (MW) in a tropical maize panel. For MW resistance, 37% of the panel was the TS, and BS was the remainder whilst for FAW, random-based training sets (RBTS) and pedigree-based training sets (PBTS) were designed. PAs achieved with BLUPs varied from 0.66 to 0.82 for MW resistance traits, and, for FAW resistance, 0.694 to 0.714 for RBTS of 37%, and 0.843 to 0.844 for RBTS of 85%, and, these were at least two-fold those from BLUEs. For PBTS, FAW resistance PAs were generally higher than those for RBTS, except for one dataset. GP models generally showed similar PAs across individual traits whilst the TS designation was determinant since a positive correlation (R=0.92***) between TS size and PAs was observed for RBTS and, for the PBTS, it was negative (R=0.44**). This study pioneers the use of GS for maize resistance to insect pests in sub-Saharan Africa.

This paper is a slightly modified, abridged version of a previous work "Parametric Gevrey asymptotics in two complex time variables through truncated Laplace transforms'' motivated by our contribution in the conference "Formal and Analytic Solutions of Diff. (differential, partial differential, difference, q-difference, q-difference-differential) Equations on the Internet'' (FASnet20). It aims to clarify and give further detail at some crucial points concerning the asymptotic behavior of the solutions of the problems studied in that work.

Modern development of high-intensity and high-resolution X-ray technology allows detailed studies of the multiphoton absorption and scattering of X-ray photons by deep and subvalent shells of molecular systems on a wide energy range. The interpretation of experimental data requires the improvement of computational methods for obtaining excited and ionized electron states of molecular systems with one or several vacancies. The specificity of solving these problems requires the use of molecular orbitals obtained in one-center representation. Slow convergence of one-center expansions is a significant disadvantage of this approach; it affects the accuracy of the calculation of spectroscopic quantities. We offer a method of including higher harmonics in one-center expansion of a molecular orbital with the use of wave functions of electrons of deep shells of a ligand (off-center atom of a molecule). The method allows one to take into account correctly electron density of a linear molecule near the ligand when describing vacancies created in a molecular core leading to radial relaxation of electron density. The analysis of the parameters of one-center expansion of the ligand functions depending on ligand’s charge is performed. The criteria for the inclusion of higher harmonics of one-center decomposition of the ligand functions in the molecular orbital are determined. The efficiency of the method is demonstrated by the example of diatomic molecules HF, LiF, and BF by estimating energy characteristics of their ground and ionized states.

Exponential increase in mobile video delivery will continue with the demand for higher resolution, multi-view and large-scale multicast video services. Novel fifth generation (5G) 3GPP New Radio (NR) standard will bring a number of new opportunities for optimizing video delivery across both 5G core and radio access network. One of the promising approaches for video quality adaptation, throughput enhancement and erasure protection is the use of packet-level random linear network coding (RLNC). In this work, we discuss the integration of RLNC into the 5G NR standard, building upon the ideas and opportunities identified in 4G LTE. We explicitly identify and discuss in detail novel 5G NR features that provide support for RLNC-based video delivery in 5G, thus pointing out to the promising avenues for future research.

This article develops algorithms for the characterization and the visualization of micro-scale features by using a small number of sample points, and with a goal to mitigate for the measurement shortcomings which are often destructive or time consuming. We implement the algorithms to rapidly examine the microscopic features of a Microelectromechanical System (MEMS) surface. Such images are highly dense; therefore, traditional image processing techniques might be computationally expensive. The contribution of this research include first, we develop local and global algorithm based on modified Thin Plate Spline (TPS) model to reconstruct high resolution images of the micro-surface’s topography, and its derivatives by using low resolution images. Second, we obtain a bending energy algorithm from our modified TPS model, and use it to filter out image defects. Finally, we develop a computationally efficient Windowing technique, which combines TPS and Linear Sequential Estimation (LSE), to enhance the visualization of images. The Windowing technique allows rapid image reconstruction based on the reduction of inverse problem.

Hybrid power plants have recently emerged as reliable and flexible electricity generation stations by combining multiple renewable energy sources, energy storage systems (ESS), and fossil-based output. However, the effective operation of the hybrid power plants to ensure continuous energy dispatch under challenging conditions is a complex task. This paper proposes a dispatch engine (DE) based on mixed-integer linear programming (MILP) for the planning and management of hybrid power plants. To maintain the committed electricity output, the dispatch engine will provide schedules for operation over extended time periods as well as monitor and reschedule the operation in real-time. Through precise prediction of the PV and wind power output, the proposed approach guarantees optimum scheduling. The precise prediction of the PV and wind power are achieved by employing a predictor of Feed-Forward Neural Network (FFNN) type. With such a dispatch engine, the operational cost of the hybrid power plants, and the use of diesel generators (DGs) are both minimized. A case study is carried out to assess the proposed dispatch engine feasibility. A real-time measurement data pertaining to load, wind, and PV power outputs is obtained from different locations in the Sultanate of Oman. The real-time data is utilized to predict the future output power from PV and the Wind farm over 24 hours. The predicted powers are then used in combination with a PV-Wind-DG-ESS-Grid hybrid plant to evaluate the performance of the proposed dispatch engine. The proposed approach is implemented and simulated using MATLAB. The results of the simulation reveal the proposed Feed-Forward Neural Network’s (FFNN) powerful forecasting abilities. In addition, the results demonstrate that adopting the proposed DE can minimize the use of DG units and reduce plant running expenses.

Silver eel were sampled in 1981 and 1983 in River Brede, Denmark, with outlet to the North Sea. Yellow eel in River Køge-Lellinge, Denmark, with outlet to the Baltic Sea were sampled 1965-1968. Silver eel were aged by burning the otoliths. Silver male ages varied from 4 to 25 years, lengths 30.8 to 45.3 cm, and female silver eel varied from 7 to 25 years, lengths 42.3 to 77.3 cm. von Bertalanffy trajectories of length-at-age of male and female yellow eel were calculated in both rivers. Younger yellow eel had significantly higher annual growth rate compared to older age groups, and females grew significantly faster than males. Two models for natural mortality M were used to estimate number of glass eel needed to produce number of silver eel for each sex and silver age group. Annual silver eel production from River Brede Å was 49.2 kg ha-1, demanding 2,894 glass eel ha-1 and in River Køge-Lellinge, the silver eel production was 48.5 kg ha-1, demanding 5,570 glass eel ha-1. It was calculated that one (0.29 g) thousand glass eel contribute to 8.8 kg silver eel in River Køge-Lellinge, and 17.0 kg silver eel in River Brede. To fulfill the Danish EMP in rivers requires annual stocking of 33 tons or 9.4 million reared on-grown eel (3.5 g) to compensate for 183 tons lost silver eel.

Remote sensing technologies are critical for analyzing the escalating impacts of global climate change and increasing urbanization, providing vital insights into land surface temperature (LST), land use and cover (LULC) changes, and the identification of urban heat island (UHI) and surface urban heat island (SUHI) phenomena. This research focuses on the nexus between LULC alterations and variations in LST and air temperature (Tair), with a specific emphasis on the intensified SUHI effect in Kharkiv, Ukraine. Employing an integrated approach, the study analyzes time-series data from Landsat and MODIS satellites, alongside Tair climate records, utilizing machine learning techniques and linear regression analysis. Key findings indicate a statistically significant upward trend in Tair and LST during summer months from 1984 to 2023, with a notable positive correlation between Tair and LST across both datasets. MODIS data exhibit a stronger correlation R² = 0.879, compared to Landsat R² = 0.663. The application of supervised classification through Random Forest algorithms and vegetation indices on LULC data reveals significant alterations, manifested as a 70.3% increase in urban land, concurrently with a decrement in vegetative cover, especially 15.5% reduction in dense vegetation and a 62.9% decrease in sparse vegetation. Change detection analysis elucidates a 24.6% conversion of sparse vegetation into urban land, underscoring a pronounced trajectory towards urbanization. Temporal and seasonal LST variations across different LULC classes were analyzed using kernel density estimation (KDE) and boxplot analysis. Urban areas and sparse vegetation had the smallest average LST fluctuations, at 2.09°C and 2.16°C, respectively, but recorded the most extreme LST values. Water and dense vegetation classes exhibited slightly larger fluctuations of 2.30°C and 2.24°C, with the bare land class showing the highest fluctuation 2.46°C, but fewer extremes. Quantitative analysis with the application of Kolmogorov-Smirnov tests across various LULC classes substantiated the normality of LST distributions p > 0.05 for both monthly and annual data sets. Conversely, the Shapiro-Wilk test validated the normal distribution hypothesis exclusively for monthly data, indicating deviations from normality in the annual data. Thresholded LST classifies urban and bare lands as warmest classes with 39.51°C, 38.20°C and water by 35.96°C and dense vegetation 35.52°C, sparse vegetation 37.71°C as coldest, a trend consistent annually and monthly. The analysis of SUHI effects demonstrates an increasing trend in UHI intensity, with statistical trends indicating a growth in average SUHI values over time. This comprehensive study underscores the critical role of remote sensing in understanding and addressing the impacts of climate change and urbanization on local and global climates, emphasizing the need for sustainable urban planning and green infrastructure to mitigate UHI effects.

Different types of resonators are used to create acoustic metameterials and metasurfaces. Recent studies focused on the use of multiple resonators of dipole, quadrupole, octupole and even hexadecapole types. This paper considers the theory of an acoustic metasurface, which is a flat surface with a periodic arrangement of multiple resonators. The sound field reflected by the metasurface is determined. If the distance between the resonators is less than a half the wavelength of the incident plane wave, the far field can be described by a reflection coefficient that depends on the angle of incidence. This allows to characterize the acoustic properties of the metasurface by a homogenized boundary condition, which is a high order tangential impedance boundary condition. The tangential impedance depending on the multiple order of the resonators is introduced. In addition, we analyze sound absorption properties of these metasurfaces, which are a critical factor in determining their performance. The paper presents a theoretical model that accounts for the multiple orders of resonators and their impact on sound absorption. The maximum absorption coefficient for a diffuse sound field, as well as the optimal value for the homogenized impedance, are calculated for arbitrary multipole orders.

Non-Linear Simulation by Harmonic Balance Techniques of Load Modulated Power Amplifier Driven by Random Modulated Signals. Comparison with measured results.

: Low-temperature growth of diamond films by chemical vapor deposition (CVD) method is not so widely reported and especially its initial periods of nucleation and growth phenomenon are of particular interest to the researchers. Four sets of substrates were selected for growing diamond films by linear antenna microwave plasma enhanced CVD (LA-MPCVD). Among them, silicon and sapphire substrates were pre-treated with detonation nanodiamond (DND) seeds before diamond growth for enhancement of its nucleation. On the other hand, carbon nanotube (CNT) films on Si substrates were also used as another template for LA-MPCVD diamond growth. In order to enhance the diamond nucleation during CVD growth, some of the CNT films were again pre-treated by electrophoretic deposition (EPD) of diamond nanoparticles. All these substrates were then put inside the LA-MPCVD chamber for growing diamond films under variable processing conditions. Microwave input powers (1100 – 2800 W), input power modes (pulse or continuous), antenna to stage distances (5 - 6.5 cm), process gas recipes (with or without CO2), methane gas percentages (3 - 5%), deposition times (11 – 120 minutes) were altered to investigate their effect on the growth of diamond film on the pre-treated substrates. The substrate temperatures were found to vary from as low as 170oC to a maximum of 307oC during the alteration of the different processing parameters. Contrary to the conventional MPCVD, it was observed that during the first hour of LA-MPCVD diamond growth, DND seeds or the nucleating structures, do not coalesce together to make a continuous film. Deposition time was the most critical factor in fully covering the substrate surfaces with diamond film, since the substrate temperature could not become stable during the first hour of LA-MPCVD. CNT was found to be oxidised rapidly under LA-MPCVD plasma conditions; therefore, a CO2-free process gas recipe was used to reduce CNT burning. Moreover, EPD-coated CNT was found to be less oxidised by the LACVD plasma during diamond growth.

Optical “fingerprints” are widely used in chemometrics-assited recognition of samples of different nature. An emerging trend in this area is the transition from obtaining "static" spectral data to reactions occurring over time. The indicator reactions are usually carried out in aqueous solutions; in this study we have developed the reactions that occur in an organic solvent, which makes it possible to recognize fat-soluble samples. In this capacity, we used 5W40, 10W40 and 5W30 motor oils of 4 manufacturers, totally 6 samples. The procedure involved mixing of the dye, sample, and reagents (HNO3, HCl, or t-butyl hydroperoxide) in ethanolic solution in a 96-well plate and measuring absorbance or near-IR fluorescence intensity every several minutes during 20–55 min. The obtained photographic images were processed by linear discriminant analysis (LDA) and k-nearest neighbors algorithm (kNN). The discrimination accuracy was evaluated by using the validation procedure. Reaction of oxidation of a dye with nitric acid allowed to recognize all 6 samples with 100% accuracy by LDA. Merging data of 4 reactions that did not provide complete discrimination ensured an accuracy of 93% by kNN technique. The developed indicator systems have good prospects for the discrimination of other fat-soluble samples. Overall, the results confirm the viability of the kinetic-based discrimination strategy.

This article analyzes 6 probability distributions from the Generalized Pareto family, with 3, 4 and 5 parameters, with main purpose to identify other distributions from this family with applicability in flood frequency analysis compared to the distribution already used in the literature from this family such as Generalized Pareto Type II and Wakeby. This analysis is part of a larger and more complex research carried out in the Faculty of Hydrotechnics regarding the elaboration of a norm for flood frequency analysis using the linear moments method. In Romania, the standard method of parameter estimation is the method of ordinary moments, thus the transition from this method to the method of linear moments is desired. All the necessary elements for the distributions use are presented like, the probability density functions, the complementary cumulative distribution functions, the quantile functions, the exact and approximate relations for estimating parameters, for both methods of parameters estimation. All these elements are necessary for a proper transition between the two methods, especially since the use of the method of ordinary moments is done by choosing the skewness of the observed data depending on the origin of the maximum flows. A flood frequency analysis case study, using annual maximum and annual exceedance series, was carried out for the Prigor river, to numerically present the analyzed distributions. The performance of this distributions is evaluated using relative mean error, relative absolute error and linear moments diagram.

Indirect imaging methods involve at least two steps, namely optical recording, and computational reconstruction. The optical recording process uses an optical modulator that transforms the light from the object into a typical intensity distribution. This distribution is numerically processed to reconstruct the object’s image corresponding to different spatial and spectral dimensions. There have been numerous optical modulation functions and reconstruction methods developed in the past years for different applications. In most cases, a compatible pair of optical modulation function and reconstruction method gives optimal performance. A new reconstruction method termed non-linear reconstruction (NLR) was developed in 2017 to reconstruct the object image in the case of optical scattering modulators. During the years, it was revealed that the NLR could reconstruct an object’s image modulated by an axicons, bifocal lenses and even exotic spiral diffractive elements, which generate deterministic optical fields. Apparently, NLR seems to be a universal reconstruction method for indirect imaging. In this review, the performance of NLR has been investigated for many deterministic and stochastic optical fields. Simulation and experimental results for different cases are presented and discussed.

In recent years, there have been frequent reports on the adverse effects of synthetic cannabinoid (SC) abuse. SCs cause psychoactive effects, similar to those caused by marijuana, by binding and activating cannabinoid receptor 1 (CB1R) in the central nervous system. The aim of this study was to establish a reliable quantitative structure-activity relationship (QSAR) model to correlate the structures and physicochemical properties of various SCs with their CB1R-binding affinities. We prepared 15 SCs and their derivatives (tetrahydrocannabinol [THC], naphthoylindoles, and cyclohexylphenols) and determined their binding affinity to CB1R, which is known as a dependence-related target. We calculated the molecular descriptors for dataset compounds using an R/CDK (R package integrated with CDK, version 3.5.0) toolkit to build QSAR regression models. These models were established and statistical evaluations were performed using the mlr and plsr packages in R software. The most reliable QSAR model was obtained from the partial least squares regression method via external validation. This model can be applied in vivo to predict the addictive properties of illicit new SCs. Using a limited number of dataset compounds and our own experimental activity data, we built a QSAR model for SCs with good predictability. This QSAR modeling approach provides a novel strategy for establishing an efficient tool to predict the abuse potential of various SCs and to control their illicit use.

We construct a family of two-step optimal fourth order iterative methods for finding single root of non-linear equations. We generalize these methods to simultaneous iterative methods for determining all the distinct as well as multiple roots of single variable non-linear equations. Convergence analysis is present for both cases to show that the order of convergence is four in case of single root finding method and is twelve for simultaneous determination of all roots of non-linear equation. The computational cost, Basin of attraction, efficiency, log of residual and numerical test examples shows, the newly constructed methods are more efficient as compared to the existing methods in literature.

Environmental pollution indicated by the presence of PM2.5 particulate matter varies based on prevailing atmospheric conditions described by certain meteorological variables. Consequently, it is important to understand atmospheric behavior in areas such as the Aburrá Valley, which experiences recurrent pollution events twice a year. This study examines the behavior of specific meteorological variables and PM2.5 particulate matter in the Aburrá Valley. By using statistical analysis tools such as correlation coefficients, principal component analysis (PCA), and multiple linear regression models, the research identifies relationships between PM2.5 and daily cycles of temperature, rainfall, radiation, and wind speed and direction. Data sets were analyzed considering periods before and after the COVID-19 lockdown (pre-pandemic and pandemic, respectively), and specific pollution events were also analyzed. Furthermore, this work considers the relationships between PM2.5 and meteorological variables, contrasting the pre-pandemic and pandemic periods. This study characterizes diurnal cycles of meteorological variables and their relationship with PM2.5. There are consistent patterns among temperature, atmospheric boundary layer (ABL) height, and solar radiation, whereas precipitation and relative humidity show opposite behavior. PM2.5 exhibits similar relative frequency functions during both daytime and nighttime, regardless of rainfall. An inverse relationship is noted between PM2.5 levels and ABL height at different times of the day. Moreover, the PCA results show that the first principal component explains around 60% of the total variance of the hydrometeorological data. The second PC explains 10%, and the rest of the variance is distributed among the other three to eight PCs. In this sense, there is no significant difference between the two PCA analyses with hydrometeorological data from a pre-pandemic period and a COVID-19 pandemic. Multiple regression analysis indicates a significant and consistent dependence of PM2.5 on temperature and solar radiation across both analyzed periods. This work presents new insights that enhance the diagnosis, understanding, and modeling of environmental pollution, thereby supporting informed decision-making and strengthening management efforts.

A system of two nonlinear difference equations under stochastic perturbations is considered. Nonlinearity of the exponential type in each equation of the system under consideration depends on all variables of the system. The stability in probability of a positive equilibrium of the system is studied via the general method of Lyapunov functionals construction and the method of linear matrix inequalities (LMIs). The obtained results are illustrated via examples and figures with numerical simulations of solutions of a considered system of stochastic difference equations. The proposed way of investigation can be applied to nonlinear systems of higher dimension and with other types of nonlinearity, for both difference equations and for delay differential equations.

The dynamic development of robotics is affecting people's lives. Flying robots replace pilots and crews in performing dangerous tasks. There are various designs of the above-mentioned robots such as multi-rotors, fixed-wing aircraft, helicopters, among which wing-in-ground (WIG) units can also be distinguished. WIG vehicles, which utilize ground effect to enhance efficiency and stability, share similarities with UAVs in their control and aerodynamic challenges. The article presented the results of the autopilot test for the NeoX UAV, which have the potential to be utilized in WIG UAVs. The NeoX was developed at the Air Force Institute of Technology as a reconnaissance flying robot and is a tailless mini UAV. It has a characteristic feature which is the flying wing with a small fuselage. The electric engine with the pusher propeller ensures thrust. The tailless airplane has a greater drag-to-lift ratio than a conventional airplane, but this airplane configuration needs a control system that ensures a stable flight. The structure of auto-pilot for the horizontal flight phase (a cruise phase), the climbing, and the descending phase were presented. The authors concentrated on the longitudinal channel of autopilot and showed the recorded results from the flight tests. The research focused on developing autopilot system that could be adapted for use in WIG craft, which operate with similar aerodynamic principles but require unique control adaptations due to their proximity to the water or ground. The findings from the NeoX UAV tests are instru-mental in enhancing the stability and performance of these specialized crafts, ensuring safer and more efficient operation in their respective environments.

As a vital component of the terrestrial ecosystem, grassland accounts for one-third of the global vegetation system. Grassland degradation has been exacerbated due to extreme overgrazing in China's Inner Mongolia Autonomous Region (IMAR). While conservation was carried out as the Ecological Subsidy and Award Program (ESAP) to mitigate grassland degradation, little is known about its effectiveness in improving the biophysical conditions of grassland. This paper integrates the conceptual frameworks of total socio-environmental systems to assess how ecological systems respond to ESAP, investigate spatial heterogeneity of ESAP, and explore the meddling effects of socio-environmental interactions on ESAP. We integrate ecological, climate, and socioeconomic data and developed several hierarchical linear mixed models (HLMM) to investigate how these factors interact with ESAP in IMAR. Our findings prove that the above-ground biomass between 2011 and 2015 responds significantly to variations in socioeconomic conditions and ecological communities. Available land resources, hospital and medical facilities, and net farmer and herdsman income are the most critical factors contributing to grassland productivity. Primary industries like mining, total consumer retail value, farming, forestry, animal husbandry, fishery productions, and GDP are the most damaging factors affecting biomass. Our study recommends a regionally or locally tailored ecological recovery policy, instead of a generalized one, in the future effort to conserve grassland.

Over the past decade and a half, dynamic functional imaging has revolutionized the neuroimaging field. Since 2009, it has revealed low dimensional brain connectivity measures, has identified potential common human spatial connectivity states, has tracked the transition patterns of these states, and has demonstrated meaningful alterations in these transition and spatial patterns in neurological disorders, psychiatric disorders, and over the course of development. Recently, researchers have begun to analyze this data from the perspective of dynamic system and information theory in the hopes of understanding how these dynamics support less easily quantified processes, such as information processing, cortical hierarchy, and consciousness. Consciousness, in particular, appears to be strongly linked to entropy production in the brain. Little attention has been paid to the effects of psychiatric disease on entropy production in the human brain, however. Even disorders characterized by substantial changes in conscious experience have not been widely analyzed from this perspective. We begin to rectify this by examining the complexity of subject trajectories in state space through the lens of information theory. Specifically, we identify a basis for the dynamic functional connectivity state space and track subject trajectories through this space over the course of the scan. The dynamic complexity of these trajectories is assessed along each dimension of the proposed basis space. Using these estimates, we demonstrate that schizophrenia patients display substantially simpler trajectories than demographically matched healthy controls, and that this drop in complexity concentrates along specific dimensions. We also demonstrate that entropy generation in at least one of these dimensions is linked to cognitive performance. Overall, results suggest great value in applying dynamic systems theory to problems of neuroimaging and reveal a substantial drop in the complexity of schizophrenia patients’ brain function.

Soccer is the leading cause of all sports-related ocular injuries in Europe and Israel and leads to blindness at a disproportionately high rate, especially among children (Thompson et al., 2019). With soccer being the most popular sport in the world, it is surprising the only solution to ocular injuries are sports glasses which can cause direct damage to the eye and impair peripheral vision by 15%, calling for an alternative (Smith & Jones, 2020). This work, based on an imported facial model, focuses on both the qualitative and quantitative aspects of building a personalized, low-cost (through optimizing material needed), superior apparatus to conventional sports glasses. The quantitative side examines a modified and model-validated (through a SRS of thirty unique extrapolated points) multivariate linear regression equation, based on horizontal and vertical rotation angles (n=60) trained with residual and computer simulation data, that can accurately extrapolate and quantify ocular impact from all horizontal and vertical rotation angles and a modified Hertzian Contact Stress Equation to determine the thickness of the apparatus using the elasticity modulus, impact force, and geometrical facial and soccer-ball features. The qualitative side examines where firstly, ocular impact is most prevalent, and secondly, where most impact is seen from rotating the ball horizontally and vertically through analysis of Pearson’s Correlation Coefficient at the supraorbital, medial canthus, infraorbital, and lateral canthus regions from both regression equations as well as a cost-benefit analysis for comparison with conventional sports glasses. The findings discovered in this work lay the groundwork for future research to build a customized low-cost ocular injury prevention device which can simultaneously ensure complete ocular safety while enhancing athletic performance for over 250,000,000 players (Johnson & Garcia, 2022).

In physics, thought experiments are impressive heuristic tools. They are valuable instruments to help scientists find new results and to teach students the known ones. However, as we shall show, they should always be received with prudence, even when they are a shortcut to 'prove' well-established results. Here, we show that the most widely known thought experiments devised to derive the gravitational frequency shift from energy conservation are, in fact, problematic. When properly set and correctly read, those thought experiments reveal that the existence of the gravitational frequency shift is, in fact, at odds with energy conservation. We also propose two new simple thought experiments, one using the conservation of energy and the other the conservation of linear momentum, that corroborate that conclusion, showing that those conservation principles do not imply the gravitational frequency shift. We think that our results may be of some epistemological interest and could serve as a warning sign on how thought experiments should be received and trusted.

The precise molecular basis of anti-tumor immunity is not yet fully understood, although commensal Bifidobacterium (c-BIF) is expected to be one of the key players in cancer control via antigenic mimicry. We investigated the sequence similarity between c-BIF and cytotoxic T lymphocyte (CTL) epitope peptides against human tumor-associated antigens to better understand the molecular basis of antigenic mimicry. We used two different similarity analyses for this purpose, a linear sequence analysis and a similarity analysis of T cell receptor (TCR)-mediated recognition of CTL epitope peptides on antigen-presenting cells. The linear sequence analysis revealed 3,900 positive numbers of similarity sites between them with 126 mean per peptide and 107 median per peptide, while the TCR-mediated recognition analysis revealed 5,018 positive numbers with a mean of 162 and median of 132 per peptide. These results demonstrated the existence of durable and abundant sequence similarities between c-BIF and CTL epitope peptides, suggesting that the former play a pivotal in inducing cellular and humoral immunity against the latter in the absence of cancer cells via antigenic mimicry.

The Yellow River Basin (YRB) is a crucial ecological zone and an environmentally vulnerable re-gion in China. Understanding the temporal and spatial trends of terraced-field areas (TRAs) and the factors underlying them in the YRB is essential for improving land use, conserving water re-sources, promoting biodiversity, and preserving cultural heritage. In this study, we employed ma-chine learning on the Google Earth Engine (GEE) platform to obtain spatial distribution images of TRAs from 1990 to 2020 using Landsat 5 (1990－2010) and Landsat 8 (2015－2020) remote sens-ing data. The GeoDa software platform was used for spatial autocorrelation analysis, revealing distinct spatial clustering patterns. Mixed linear and random forest models were constructed to identify the driving force factors behind TRA changes. The research findings reveal that TRAs were primarily concentrated in the upper and middle reaches of the YRB, encompassing provinc-es such as Shaanxi, Shanxi, Qinghai, and Gansu, with areas exceeding 40,000 km2, whereas other provinces had TRAs of less than 30,000 km2 in total. The TRAs exhibited a relatively stable trend, with provinces such as Gansu, Qinghai, and Shaanxi showing an overall upward trajectory. Conversely, Shanxi and Inner Mongolia demonstrated an overall declining trend. When com-pared with other provinces, the variations in TRAs in Ningxia, Shandong, Sichuan, and Henan appeared to be more stable. The linear mixed model (LMM) revealed that farmland, shrubs, and grassland had significant positive effects on the TRA, explaining 41.6% of the variance. The ran-dom forest model also indicated positive effects for these factors, with high R² values of 0.983 and 0.86 for the training and testing sets, respectively, thus outperforming the LMM. The findings of this study can contribute to the restoration of the YRB's ecosystem and support sustainable devel-opment. The insights gained will be valuable for policymaking and decision support in soil and water conservation, agricultural planning, and environmental protection in the region.

Keywords: Baseband, GeoSurf Constellation, Interference, Linear Distortions, Passband, Time Delay, Rain attenuation, Synthetic Storm Technique, ultra–wideband.

The article presents a new scalable iterative method for linear programming called the “apex method”. The key feature of this method is constructing a path close to optimal on the surface of the feasible region from a certain starting point to the exact solution of linear programming problem. The optimal path refers to a path of minimum length according to the Euclidean metric. The apex method is based on the predictor-corrector framework and proceeds in two stages: quest (predictor) and target (corrector). The quest stage calculates a rough initial approximation of linear programming problem. The target stage refines the initial approximation with a given precision. The main operation used in the apex method is an operation that calculates the pseudoprojection, which is a generalization of the metric projection to a convex closed set. This operation is used both in the quest stage and in the target stage. A parallel algorithm using a Fejér mapping to compute the pseudoprojection is presented. An analytical estimation of the parallelism degree of this algorithm is obtained. Also, an algorithm implementing the target stage is given. The convergence of this algorithm is proven. An experimental study of the scalability of the apex method on a cluster computing system is described. The results of applying the apex method to solve problems from the Netlib-LP repository are presented.

We define degree of dependence of two events A and B in a probability space by using Boltzmann-Shannon entropy function of an appropriate probability distribution produced by these events and depending on one parameter (the probability of intersection of A and B) varying within a closed interval I. The entropy function attains its global maximum when the events A and B are independent. The important particular case of discrete uniform probability space motivates this definition in the following way. The entropy function has a minimum at the left endpoint of I exactly when one of the events and the complement of the other are connected with the relation of inclusion (maximal negative dependence). It has a minimum at the right endpoint of I exactly when one of these events is included in the other (maximal positive dependence). Moreover, the deviation of the entropy from its maximum is equal to average information that carries one of the binary trials defined by A and B with respect to the other. As a consequence, the degree of dependence of A and B can be expressed in terms of information theory and is invariant with respect to the choice of unit of information. Using this formalism, we describe completely the screening tests and their reliability, measure efficacy of a vaccination, the impact of some events from the financial markets to other events, etc. A link is available for downloading an Excel program which calculates the degree of dependence of two events in a sample space with equally likely outcomes.

The remaining capacity can only be measured with offline method. This brings great challenge for the online prediction of Li-ion battery’s RUL. A novel online prediction method for Li-ion battery’s RUL was proposed, which is based on multiple health indicators (HIs) and can be derived from the batteries’ historical operation data. Firstly, four indirect HIs were built according to the battery’s operation current, voltage and temperature data respectively. On that basis, a generalized regression neural network (GRNN) was developed to estimate the battery’s remaining capacity, and the non-linear autoregressive approach (NAR) was utilized to predict the battery’s RUL based on the estimated capacity value. Furthermore, to reduce the interference, twice wavelet denoising were performed with different thresholds. A case study is conducted with a NASA battery dataset to demonstrate the effectiveness of the method. The result shows that the proposed method can obtain Li-ion batteries’ RUL effectively.

Below T_CO=157 K the quasi-one-dimensional charge-transfer salt (TMTTF)_2SbF_6 undergoes a pronounced phase transition to a charge-ordered ground state. We have explored the non-linear and photoconductive behavior as a function of applied voltage, laser pulse energy and temperature. Besides a decay of the photoconductive signal in a double exponential fashion in the millisecond range, we discover current oscillations in the kHz range induced by the application of short laser pulses. While the resonance frequencies do not depend on voltage or laser intensity and vary only slightly with temperature, the amplitude changes linearly with the laser intensity and voltage. The findings are discussed and compared to comparable phenomena in other low-dimensional electron systems.

The various methods used to choose the profile shift coefficients, primarily the so-called equalizations, were based on assumed advantages without physical evidence proving them. In this paper a new calculation method is presented for determining profile shift coefficient. The procedure gives the pair of values ​​of the profile shift coefficients, in which case, under the given load, the resulting bending stress will be of the lowest possible value.

Carbon footprint mitigation actions have become a key issue for companies involved in urban freight transport. The electrification of the delivery fleets is one of the crucial sustainable actions carried out. To this end, it is necessary to explore several fleet renewal strategies over a finite planning horizon evaluating different types of electric powertrains for light commercial vehicles. The primary goal of this purpose-built analysis is to assist and boost the fleet managers' decisions when transitioning to alternative-fuelled vans, intending to maximize cost savings and reduce greenhouse gas emissions inventory. The model presented in this work is a Multi-Objective Linear Programming hybrid analysis taking into account the vehicle and energy supply infrastructure costs and the emissions reported in each inventory scope following the Greenhouse Gas Protocol sustainability guidelines. From this perspective, the conducted research offers a novel approximation to fleet management problems enabling a break-down cost analysis and an evaluation of the annual emissions company report. The comprehensive numerical simulations carried out over different study scenarios in Spain demonstrate that the optimization approach does not only show effective fleet renewal strategies but also identifies critical factors that impact the fleet's competitiveness, offering valuable insights for fleet managers and policymakers to meet carbon footprint reductions in a cost-effectively way.

TThe following three objectives were tested in this study: (1) investigate the utility of low-altitude remote sensing using UAS technology to compare the effects of different N application systems in rice production; (2) use spatial extrapolation to scale up plot-level generated to farmer field rice yield data based on crop spectral signatures, and (3) predict and map out rice productivity as a function of N placement systems. Images were captured on a UAV platform at midseason of the rice crop. Orthomosaics were developed for selected fields in rice-producing zones. Grain yields were assessed from low, medium, and high crop health plots delineated based on NDVI values. On the plot scale, UDP outyielded non-UDP by 0.84%. Individual plot yield data were scaled up to the farmer field level through Jenks natural breaks classification and es-tablishing an empirical relationship between OSAVI and plot yields. Assessment of the scaled-up field levelfield-level data also confirmed the superiority of UDP N man-agement over the non-UDP systems in promoting rice yields. Scaling up plot scale da-ta to whole field levels also facilitated generating and mapping expected yield maps for individual farmer fields in the three zones studied. This study has established a tangible simple but tangible protocol protocol for predicting and mapping rice yields in small-scale farmer fields using UAS data.

We consider a family of nonlinear singularly perturbed PDEs whose coefficients involve a logarithmic dependence in time with confluent Fuchsian singularities that unfold an irregular singularity at the origin and rely on a single perturbation parameter. We exhibit two distinguished finite sets of holomorphic solutions, so-called outer and inner solutions, by means of a Laplace transform with special kernel and Fourier integral. We analyze the asymptotic expansions of these solutions relatively to the perturbation parameter and show that they are (at most) of Gevrey order 1 for the first set of solutions and of some Gevrey order that hinges on the unfolding of the irregular singularity for the second.

The present article addresses the long-standing problem of the polymer brush bilayers under stationary shear flow at non-linear response regime where the system gets a non-Newtonian fluid. The main idea behind this research would be the fact that the immense lubricity of the polymer brush bilayers originates from a global restructuring that takes place at large shear rates. It is shown here that physical quantities like, stress tensor, viscosity tensor, the friction coefficient and the chain extensions could become dependent on the shear rate at non-Newtonian regime. Apparently, the sub-linear scaling of the physical quantities at large shear rates is solely due to the fact that the chains stretch in the shear direction.

Ultra-wideband wavelength division multiplexed networks enable operators to use more effectively the bandwidth offered by a single fiber pair and thus make significant savings, both in operational and capital expenditures. The main objective of this study is to minimize optical node resources, such as transponders, multiplexers and wavelength selective switches, needed to provide and maintain high quality of network services, in ultra-wideband wavelength division multiplexed networks, at low cost. A model based on integer programming is proposed, which includes a detailed description of optical network nodal resources. The developed optimization tools are used to study the ultra-wideband wavelength division multiplexed network performance when compared with the traditional C-band wavelength division multiplexed networks. The analysis is carried out for realistic networks of different dimensions and traffic demand sets.

The energy transition towards renewable and more decentral power production triggers the need for grid and storage expansion on all voltage levels. Today's power system planning focuses on certain voltage levels or spatial resolutions. In this work we present an open source software tool eGo which is able to optimize grid and storage expansion throughout all voltage levels in a developed top-down approach. System costs are minimized by applying a linear optimal power flow considering the grid infrastructure of the extra-high and high-voltage (380 to 110 kV) level. Hence, the common differentiation of transmission and distribution grid is partly dissolved, integrating the high-voltage level into the optimization problem. Consecutively, optimized curtailment and storage units are allocated in the medium voltage grid in order to lower medium and low voltage grid expansion needs, that are consequently determined. Here, heuristic optimization methods using the non-linear power flow were developed. Applying the tool on future scenarios we derived cost-efficient grid and storage expansion for all voltage levels in Germany. Due to the integrated approach storage expansion and curtailment can significantly lower grid expansion costs in medium and low voltage grids and at the same time serve the optimal functioning of the overall system. Nevertheless, the cost-reducing effect for the whole of Germany was marginal. Instead, the consideration of realistic, spatially differentiated time series lead to substantial overall savings.

In this article, the linear non-equilibrium thermodynamic approach is used to analyze the energy regularities of the interior permanent magnet synchronous motor (IPMSM) taking into account iron losses. The IPMSM is considered a linear power converter (PC) that is multiple linearized at operating points with given angular velocity and load torque. A universal description of such a PC by a system of dimensionless parameters and characteristics made it possible to analyze the perfection of energy conversion in the object. For IPMSM, taking into account iron losses, a mathematical model of the corresponding PC has been built, and an algorithm and research program have been developed, which is valid in a wide range of machine speed regulations. This allows you to obtain the efficiency maps for IPMSM and choose the optimal points of PC operation according to the maximum efficiency criteria. The results of the studies demonstrate the effectiveness of the proposed method for determining the optimal reference of the components d and q of the armature current for both the MTPA strategy at motor speed adjusting below the nominal value and for the FW strategy at its adjusting above the nominal value.

This article compares the predictive capabilities of six models namely the Linear Discriminant Analysis (LDA), Logistic Regression (LR), Support Vector Machine (SVM), XGBoost, Random Forest (RF) and Deep Neural Network (DNN) to predict the default behaviour of credit card holders in Taiwan using data from the UCI machine learning database. Python programming language was used for data analysis. Statistical methods were compared with machine learning algorithms using the confusion matrix measured in metric terms of prediction accuracy, sensitivity, specificity, precision, G-mean, F1 score, ROC and AUC. The dataset contains 30,000 credit card user’s information with 6636 default observations and 23,364 non-default cases. The study results found that modern machine learning methods outperformed traditional statistical methods in terms of predictive performance measured by F1 score, G-mean and AUC. Traditional methods like logistic regression were marginally better than linear discriminant analysis and support vector machines in terms of predictive performance measured by area under the receiver operating characteristic curve. In the modern machine learning methods, deep neural networks were better in most of the predictive performance metrics than XGBoost and Random Forest methods.

High-frequency circuit performance is significantly impacted by impedance variations, particularly within the low-resistance regime. Traditional Ohm’s Law based modeling approaches often fail to accurately predict circuit behavior in these conditions, leading to design inaccuracies and potential system failures. The Standard Ohm’s Law based model’s prediction of infinite current as resistance approaches zero is physically unrealistic and hinders its application in practical scenarios. Despite the recognition of these limitations, existing models have not comprehensively addressed the complex impedance behavior observed in high-frequency circuits. To overcome these challenges, this paper introduces a modified version of the Ohm’s Law incorporating an exponential correction term. The Modified Ohm’s Law’s accuracy was evaluated through simulated experiments across a wide frequency range (1kHz to 1GHz) using various electronic components. The findings demonstrate the superior performance of the modified model in predicting currents under low-resistance and high-current conditions compared to the Standard Ohm’s Law model. By providing finite and accurate current values, the proposed model effectively mitigates the unrealistic infinite current predictions of the standard approach. The enhanced predictive capabilities of the Modified Ohm’s Law hold significant implications for high-frequency circuit design and analysis. Its application can lead to improved performance and reliability in power electronics, telecommunications, and other high-frequency systems. By incorporating non-linear impedance behavior, the model offers a more accurate representation of real-world circuit conditions. Future research should focus on refining the exponential term’s parameters to optimize the model's accuracy across a broader range of applications. Additionally, real-time implementation and hardware validation are essential to assess the model's practical utility in complex circuit environments.

This paper presents two control design strategies for voltage regulation in a single inductor dual output (SIDO) DC-DC Buck converter system. Based on a nominal multiple input multiple output (MIMO) plant model and performance requirements, both an LQR and a decoupled PI control laws are designed to control the power converter system, under parametric uncertainties such as voltage source variation, CPL power variation, and load resistance variation. Therefore, the SIDO converter can cascade operating, which may cause the undesired effects of voltage oscillation and reduce the system's stability margin. The control performance was assessed under both uncertainties resistive loading and power variation of a constant power load (CPL). A SIDO DC-DC Buck converter board has been developed for experimental tests. The experimental results show that the LQR strategy, compared to the PI strategy, presented a robust performance in the presence of parametric uncertainties in the resistive loads being, however, sensitive to uncertainties due to the presence of CPL loads.

The complexity of modern power grids, exacerbated by integrating diverse energy sources, espe-cially inverter-based resources (IBRs), presents a significant challenge to grid operation and plan-ning since linear models fail to capture the intricate IBR dynamics. This study employs the Sparse Identification of Nonlinear Dynamics (SINDy) method to bridge the gap between theoretical un-derstanding and practical implementation in power system analysis. It introduces the novel Volterra-based Nonlinearity Index (VNI) to examine system-level nonlinearity comprehensively. The distinction of dynamics into first-order linearizable terms, second-order nonlinear dynamics, and third-order noise elucidates the intricacy of power systems. The findings demonstrate a fundamental shift in system dynamics as power sources transit to IBRs, revealing system-level nonlinearity compared to module-level nonlinearity in conventional syn-chronous generators. The VNI quantifies nonlinear-to-linear relationships, enriching our comprehension of power system behavior and offering a versatile tool for distinguishing between different nonlinearities and visualizing their distinct patterns through the proposed VIN profile.

We introduce linear probing hashing schemes that construct a hash table of size $n$, with constant load factor $\alpha$, on which the worst-case unsuccessful search time is asymptotically almost surely $O(\log \log n)$. The schemes employ two linear probe sequences to find empty cells for the keys. Matching lower bounds on the maximum cluster size produced by any algorithm that uses two linear probe sequences are obtained as well.

Identifying macroeconomic events that are responsible for dramatic changes of economy is of particular relevance to understand the overall economic dynamics. We introduce an open-source available efficient Python implementation of a Bayesian multi-trend change point analysis which solves significant memory and computing time limitations to extract crisis information from a correlation metric. Therefore, we focus on the recently investigated S&P500 mean market correlation in a period of roughly 20 years that includes the dot-com bubble, the global financial crisis and the Euro crisis. The analysis is performed two-fold: first, in retrospect on the whole dataset and second, in an on-line adaptive manner in pre-crisis segments. The on-line sensitivity horizon is roughly determined to be 80 up to 100 trading days after a crisis onset. A detailed comparison to global economic events supports the interpretation of the mean market correlation as an informative macroeconomic measure by a rather good agreement of change point distributions and major crisis events. Furthermore, the results hint to the importance of the U.S. housing bubble as trigger of the global financial crisis, provide new evidence for the general reasoning of locally (meta)stable economic states and could work as a comparative impact rating of specific economic events.

The seasonal variation in fatty acids and minerals concentrations was investigated through the analysis of Pecorino Romano cheese samples collected in January, April, and June. A fraction of samples contained missing values in their fatty acid profile. Probabilistic Principal component analysis coupled with Linear Discriminant Analysis was employed to classify cheese samples on a production season basis while accounting for missing data and quantifying the missing Fatty acids concentration for the sample in which they were absent. The levels of rumenic acid, vac-cenic acid and omega-3 compounds were positively correlated with the spring season, while the length of the saturated fatty acids increased throughout the production seasons. Concerning the classification performances, the optimal number of principal components (i.e., 5) achieved an ac-curacy in cross-validation equal to 98 %. Then, when the model was tasked to impute the lacking Fatty acid concentration values, the optimal number of principal components resulted in an R2 value in cross-validation of 99.53%

We present a model of infection dynamics that might explain slower approaching the herd immunity during the covid-19 epidemy in Sweden than it was predicted by a variety of other models; see graphs Fig. \ref{GROWTH2}. The new model takes into account the hierarchic structure of social clusters in the human society. We apply the well developed theory of random walk on the energy landscapes represented mathematically with ultrametric spaces. This theory was created for applications to spin glasses and protein dynamics. To move from one social cluster (valley) to another, the virus should cross a social barrier between them. The magnitude of a barrier depends on the number of social hierarchy's levels composing this barrier. As the most appropriate for the recent situation in Sweden, we consider linearly increasing (with respect to hierarchy's levels) barriers. This structure of barriers matches with a rather soft regulations imposed in Sweden in March 2020. In this model, the infection spreads rather easily inside a social cluster (say working collective), but jumps to other clusters are constrained by social barriers. This model's feature matches with the real situation during the covid-19 epidemy, with its cluster spreading structure. Clusters need not be determined solely geographically, they are based on a number of hierarchically ordered social coordinates. The model differs crucially from the standard models of spread of disease, such as the SIR-model. Our model describes such a specialty of spread of covid-19 virus as the presence of ``super-infectors'' who by performing a kind of random walk on a hierarchic landscape of social clusters spreads infection. In future, this model will be completed by adding the SIR-type counterpart. But, the latter is not a specialty of covid-19 spreading.

Free volume is an extremely important intrinsic defect in polymers. Structurally, the free volume is the randomly distributed holes in the polymer molecular chain segments. From the perspective of molecular movement, it is also the space needed for the movement of molecular segments. In proton exchange membrane fuel cells, the free volume is also the space needed for the directional conduction of protons. Irradiation grafting sulfonated polyvinylidene fluoride (PVDF) is one of the methods to produce proton exchange membrane with good proton channel rate. Using the LYS-1 program, based on the linear absorption coefficient and backscatter coefficient models, the percentage of annihilated positrons in PVDF in the two-layer model and the three-layer model was studied, and comparing the two fitting results it is determined that the model closest to the positron annihilation percentage required by the PALS experiment is the two-layer model, which allows the percentage of positrons that are annihilated in PVDF films with a thickness of 100 μm to reach 46% using the high energy positron source ⁴⁴Ti without using the positron moderator. Using positron annihilation lifetime spectrum (PALS) analysis methods, based on Eldrup's classical model of free volume, the influence of absorbed doses of α particles on the free volume and crystallinity of PVDF was investigated, respectively. Based on the two test results the model of cross-linking and degradation of polyvinylidene fluoride irradiated by α particles was determined. Afterwards, X-ray diffraction (XRD) methods was used to study the change of PVDF crystal area before and after irradiation. The XRD results are consistent with the results measured by PALS.

This paper examines the correlation between numbers of computer cores in parallel genetic algorithms. The objective to determine the linear polynomial complementary equation in order represent the relation between number of parallel processing and optimum solutions. Model this relation as optimization function (f(x)) which able to produce many simulation results. F(x) performance is outperform genetic algorithms. Compression results between genetic algorithm and optimization function is done. Also the optimization function give model to speed up genetic algorithm. Optimization function is a complementary transformation which maps a TSP given to linear without changing the roots of the polynomials.

For a linear ordinary differential equation (ODE in short) of the third order, results are presented that supplement the theory of conjugate points and extremal solutions by W. Leighton, Z. Nehari, M. Hanan. It is especially noted the sensitivity of solutions to the initial data, which makes their numerical study difficult. Similar results were obtained for the third-order nonlinear equations of the Emden-Fowler type.

H-adaptivity is an effective tool to introduce local mesh refinement in FEM-based numerical simulation of crack propagation. The implementation of h-adaptivity could benefit the numerical simulation of fatigue or accidental load scenarios involving large structures such as ship hulls. In engineering applications, the element deletion method is frequently used to represent cracks. However, the element deletion method has some drawbacks such as strong mesh dependency and loss of mass or energy. In order to mitigate this problem, the element splitting method could be applied. In this study, a numerical method called ‘h-adaptive element splitting’ (h-AES) is introduced. The h-AES method is applied in FEM programs by combining h-adaptivity with the element splitting method. Two examples using the h-AES method to simulate cracks in large structures under linear-elastic fracture mechanics scenario are presented. The numerical results are verified against analytical solutions. Based on the examples, the h-AES method is proven to be able to introduce mesh refinement in large-scale numerical models that consist of structured coarse meshes. By employing the mesh refinement introduced in this paper, very small cracks are well represented in large structures.

In this paper, mean-field type games between two players with backward stochastic dynamics are defined and studied. They make up a class of non-zero-sum differential games where the players' state dynamics solve backward stochastic differential equations (BSDEs) that depend on the marginal distributions of player states. Players try to minimize their individual cost functionals, also depending on the marginal state distributions. Under some regularity conditions, we derive necessary and sufficient conditions for existence of Nash equilibria. Player behavior is illustrated by numerical examples, and is compared to a centrally planned solution where the social cost, the sum of player costs, is minimized. The inefficiency of a Nash equilibrium, compared to socially optimal behavior, is quantified by the so-called price of anarchy. Numerical simulations of the price of anarchy indicate how the improvement in social cost achievable by a central planner depends on problem parameters.

Electrical energy demand increase does evolve rapidly due to several socioeconomic factors such as industrialization, population growth, urbanization and of course the evolution of modern technologies in this 4th industrial revolution era. Such rapid increase in energy demand introduces a huge challenge in power system. Such has paved way for network operators to seek for alternative energy resources other than the conventional fossil fuel system. Hence, the penetration of renewable energy into the electricity supply mix has evolved rapidly in the past three decades. However, the grid system has to be well planned ahead to accommodate such increase in energy demand in the long run. Transmission Network Expansion Planning (TNEP) is a well ordered and profitable expansion of power facilities that meets the expected electric energy demand with an allowable degree of reliability. This paper proposes a TNEP model that minimises the network reinforcements, operational costs and costs of renewable energy penetrations, while satisfying the increase in demand. The problem is formulated as a mixed integer linear programming (MILP) problem. The developed model has been tested in several IEEE test systems in multi-period scenarios. The paper also carried out a detailed derivation of the new non-negative variables in terms of the power flow magnitudes, the bus voltage phase angles and the lines’ phase angles for proper mixed integer variables’ decomposition techniques. Moreover, this paper tends to provide additional recommendation in terms of which particular year (within 20 years of planning period) can the network operators install new line(s), new corridor(s) and/or additional generation capacity to the respective existing power networks. Such is achieved by running incremental periods simulations from base year through the planning horizon. The results show the efficacy of the developed model in solving the TNEP problem with a reduced and acceptable computation time even for large power grid system.

Flaxseed oil is one of the best sources of n-3 fatty acids, thus its adulteration with refined oils can lead to a reduction in its nutritional value and overall quality. The purpose of this study was to use the differential scanning calorimetry (DSC) technique to detect adulterations of cold-pressed flaxseed oil with refined rapeseed oil (RP). Based on the melting phase transition curve, parameters such as peak temperature (T), peak height (h), and percentage of area (P) were determined for pure and adulterated flaxseed oils with a RP concentration of 5, 10, 20, 30, 50% (w/w). Significant linear correlations (p ≤ 0.05) between the RP concentration and all DSC parameters were observed, except for h1. In order to assess the usefulness of the DSC technique for detecting adulterations, three chemometric approaches were compared: 1) classification models (Linear Discriminant Analysis, LDA Adaptive Regression Splines, MARS, Support Vector Machine, SVM, Artificial Neural Networks, ANNs); 2) regression models (Multiple Linear Regression, MLR, MARS, SVM, ANNs, PLS) and 3) a combined model of Orthogonal Partial Least Squares Discriminant Analysis (OPLS-DA). With the LDA model, the highest accuracy of 99.5% in classifying the samples, followed by ANN> SVM > MARS was achieved. Among the regression models, the ANN model showed the highest correlation between observed and predicted values (R= 0.996), while other models showed goodness of fit as following MARS> SVM> MLR. Comparing OPLS-DA and PLS methods, higher values of R2X(cum) =0.986 and Q2 =0.973 were observed with the PLS model than OPLS-DA. These results demonstrate the usefulness of the DSC technique combined with chemometrics for predicting the adulteration of cold-pressed flaxseed oil with refined rapeseed oil.

The influence of linear and nonlinear modes of ADC driver on the operational amplifier (Op-Amp), which has different values of maximum output voltage slew rate, on the effective number of bits of ADC is considered. It is shown that the effective number of bits of ADC when op-amps on bipolar transistors with input signal amplitudes exceeding 50-100 mV is determined by the nonlinear modes of its input differential stage.

Various factors, such as uncertainty of component parameters and uncertainty of sensor meas-urement values, contribute to the difficulty of fault detection in the landing gear retrac-tion/extension hydraulic system. In this paper, we introduce linear fractional transformation technology and uncertainty analysis theory for the construction of the diagnostic bond graph of the landing gear retraction/extension hydraulic system. In this way, interval analytical redundancy relations and fault signature matrix can be derived. Using the fault signature matrix, existing faults of the system can be preliminarily detected and isolated. Additionally, interval analytical re-dundancy relations can be used to detect system faults in detail, and cases analysis can be carried out to determine if the actuator is externally or internally leaky, and if the landing gear selector valve is reversing stuck. Compared to the traditional analytical redundancy relations, this method takes into account the negative factors of uncertainty; and compared to the traditional absolute diagnostic threshold, the interval diagnostic threshold is more accurate and sensitive.

In real-life scenario, there are many mathematical tools to handle the incomplete and imprecise data. One of them is the fuzzy approach. This article aims to contribute to the literature of fuzzy multi-objective dynamic programming issues involving the fuzzy objective functions. The piecewise quadratic fuzzy numbers characterize these fuzzy parameters. Some basic notions in the problem under the α-pareto optimal solution concept is redefined and analyzed to study the stability of the problem. Furthermore, a technique, named as enhancing decomposition approach, is presented for achieving a subset for the parametric space that contains the sameα-pareto optimal solution. For a better understanding and comprehension of the suggested concept, a numerical example is provided.

Solving Linear equations with large number of variable contains many computations to be performed either iteratively or recursively. Thus it consumes more time when implemented in a sequential manner. There are many ways to solve the linear equations such as Gaussian elimination, Cholesky factorization, LU factorization, QR factorization. But even these methods when implemented on a sequential platform yield slower results as compared to a parallel platform where the time consumption is reduced considerably due to concurrent execution of instructions. The above mentioned linear equation solving methods can be implemented on the parallel platform using the direct approaches such as pipelining or 1D and 2D Partitioning approach. Vedic mathematics is a very ancient approach for solving mathematical problems. These Vedic mathematical approaches are well known for quicker and faster computation of mathematical problems. Vedic Mathematics provides a very different outlook towards the approach of solving linear Equation on parallel platform. It could be considered as a better approach for reducing space consumption and minimizing the number of algebraic operations involved in solving linear equation. In future Vedic Mathematics might serve as a viable solution for solving linear equation on parallel platform.

We present a new mathematical model of disease spread reflecting specialties of covid-19 epidemic by elevating the role social clustering of population. The model can be used to explain slower approaching herd immunity in Sweden, than it was predicted by a variety of other mathematical models; see graphs Fig. \ref{GROWTH2}. The hierarchic structure of social clusters is mathematically modeled with ultrametric spaces having treelike geometry. To simplify mathematics, we consider homogeneous trees with $p$-branches leaving each vertex. Such trees are endowed with algebraic structure, the $p$-adic number fields. We apply theory of the $p$-adic diffusion equation to describe coronavirus' spread in hierarchically clustered population. This equation has applications to statistical physics and microbiology for modeling {\it dynamics on energy landscapes.} To move from one social cluster (valley) to another, the virus (its carrier) should cross a social barrier between them. The magnitude of a barrier depends on the number of social hierarchy's levels composing this barrier. As the most appropriate for the recent situation in Sweden, we consider {\it linearly increasing barriers.} This structure matches with mild regulations in Sweden. The virus spreads rather easily inside a social cluster (say working collective), but jumps to other clusters are constrained by social barriers. This behavior matches with the covid-19 epidemic, with its cluster spreading structure. Our model differs crucially from the standard mathematical models of spread of disease, such as the SIR-model. We present socio-medical specialties of the covid-19 epidemic supporting our purely diffusional model.

In the paper, the authors present an explicit form for a family of inhomogeneous linear ordinary differential equations, find a more significant expression for all derivatives of a function related to the solution to the family of inhomogeneous linear ordinary differential equations in terms of the Lerch transcendent, establish an explicit formula for computing all derivatives of the solution to the family of inhomogeneous linear ordinary differential equations, acquire the absolute monotonicity, complete monotonicity, the Bernstein function property of several functions related to the solution to the family of inhomogeneous linear ordinary differential equations, discover a diagonal recurrence relation of the Stirling numbers of the first kind, and derive an inequality for bounding the logarithmic function.

Volatile organic compounds (VOCs) released from plants have been correlated with disease-status. Analysis of VOCs using GC-MS is time-consuming, laboratory-based, and requires specialist training. Electronic nose devices (E-nose) provide a portable alternative. Three different E-nose devices were compared to assess how accurately they could detect Mango Twig Tip Dieback and Panama disease in banana. The devices were initially trained on known volatiles, then pure cultures of Pantoea sp., Staphylococcus sp., and Fusarium odoratissimum, and finally, on infected and healthy mango leaves and field-collected, infected banana pseudo-stems. The experiments were repeated three times with six replicates for each host-pathogen pair. The variation between healthy and infected host materials was evaluated by principal component and linear discriminant analysis, cross-validation and chemometric data analysis. GC-MS analysis was conducted contemporaneously and identified an 80% similarity between healthy and infected plant material. The portable C 320 was 100% successful in discriminating known volatiles but had a low capability in differentiating healthy and infected plant substrates. The advanced devices (PEN 3 / MSEM 160) successfully detected healthy and diseased samples with a high variance. The results suggest that E-nose devices are more sensitive and accurate in detecting changes of VOCs between healthy and infected plants compared to headspace GC-MS.

Microarray gene expression-based detection and classification of medical conditions have been prominent in research studies over the past few decades. However, extracting relevant data from the high-volume microarray gene expression with inherent nonlinearity and inseparable noise components raises significant challenges during data classification and disease detection. So, this paper proposes a two-level strategy involving feature extraction and selection methods before the classification step. The feature extraction step utilizes Short Term Fourier Transform (STFT), and the feature selection step employs Particle Swarm Optimization (PSO) and Harmonic Search (HS) metaheuristic methods. The classifiers employed are Non-Linear Regression, Gaussian Mixture Model, Softmax Discriminant, Naive Bayes, SVM (Linear), SVM (Polynomial), and SVM (RBF). The two-level extracted relevant features are compared with raw data classification results, including Convolutional Neural Network (CNN) Methodology. Among the methods, STFT with PSO feature selection and SVM (RBF) classifier produced the highest accuracy of 94.47%.

This article presents six probability distributions from the Gamma family with three parameters, for the flood frequency analysis in hydrology. The choice of the Gamma family of statistical dis-tributions was driven by its frequent use in hydrology. In the Faculty of Hydrotechnics, the im-provement of the estimation of maximum flows and including the methodological bases for the realization of a regionalization study with the linear moments method with the corrected pa-rameters was researched, being an element of novelty. The linear moments method is better than MOM because it avoids the choice of skewness depending on the origin of the flows, practiced in Romania. The L-moments method conforms to the current trend for estimating the parameters of statistical distributions. Observed data from hydrometric stations are of relatively short length, so the statistical parameters that characterize them are of a sample that requires correction. The correction of the statistical parameters is proposed, using the method of least squares based on the inverse functions of the statistical distributions expressed with the frequency factor for L-moments. All the necessary elements for their use are presented like, quantile functions, the exact and ap-proximate relations for estimating parameters and frequency factors. A flood frequency analysis case study was carried out for the Ialomita river, to verify the proposed methodology. The per-formance of this distributions is evaluated using Kiling-Gupta and Nash-Sutcliff coefficients.

Recently, due to the miniaturization of electronic products, printed circuit boards (PCBs) have also become smaller. This trend has led to the need for high-precision electrical test equipment to check PCBs for disconnections and short circuits. The purpose of this study is to improve the position repeatability of the platform unit up to ±2.5 μm in a linear stage type test equipment. For this purpose, the causes of position errors of the platform unit are analyzed. The platform unit holding the PCB is driven by a single-axis linear ball screw drive system offset from its geometric center due to design constraints. The yaw rotation of the platform is found to have a dominant effect on position repeatability. To address this problem, the methods of adding balancing weights to the platform unit and adjusting the stiffness of LM Guides are proposed. This reduces the yaw rotation by moving the centers of mass and stiffness closer to the linear ball screw actuator. In the verification tests, the position repeatability was decreased to less than ±1.0 μm.

Assuming a two component, positive and negative mass, superfluid/supersolid for space (the Winterberg model), we model the Higgs field as a condensate made up of a positive and a negative mass, planckion pair. The connection is shown to be consistent (compatible) with the underlying field equations for each field, and the continuity equation is satisfied for both species of planckions, as well as for the Higgs field. An inherent length scale for space (the vacuum) emerges, which we estimate from previous work to be of the order of,

A typical halogen-free flame-retardant (HFFR) formulation for electric cables may contain polymers, various additives, and fire-retardant fillers. In this study, composites are prepared by mixing natural magnesium hydroxide (n-MDH) with linear low-density polyethylene (LLDPE) and a few types of ethylene-octene copolymers (C₈-POE). Depending on the content of LLDPE and C₈-POE, we obtained composites with different crystallinity that affected the final mechanical properties. The nucleation effect of the n-MDH and the variations in crystallinity caused by the blending of C₈-POE/LLDPE/n-MDH were investigated. In the C₈-POE/LLDPE blend, we found a decrease in the crystallization temperature of LLPDE compared to pure LLDPE and an increase in the crystallization temperature of C₈-POE compared to pure C₈-POE. On the contrary, the addition of n-MDH led to an increase in the crystallization temperature of LLDPE. As expected, the increase in the crystallinity of the polyolefin matrix of composites led to higher elastic modulus, higher tensile strength, and lower elongation at break. Overall, these results show how to obtain the required mechanical features for halogen-free flame-retardant compounds for electric cable applications depending on the quantities of the two miscible components in the final blend.

This paper introduces an innovative nanotechnology-based approach that provides a pathway to enhance the energy release efficiency of nanoenergetic materials (nEMs) by harnessing self-synchronized collective atomic vibrations and phonon wave resonance within the transition domains between nanocomponents, without altering the material composition. The key innovation involves incorporating finely-tuned 2D-ordered linear-chain carbon-based multilayer nano-enhanced interfaces as programmable nanodevices into the transition domains using advanced multistage processing and assembly techniques. These programmable nanodevices enable precise control over self-synchronized collective atomic vibrations and phonon wave propagation, leading to synergistic effects. To activate and optimize these effects, a combination of various methods is employed, including energy-driven initiation of allotropic phase transformations, surface acoustic wave-assisted micro/nano-manipulation, heteroatom doping, directed self-assembly using high-frequency electromagnetic fields, and data-driven inverse design approaches. By leveraging a data-driven inverse design strategy and uncovering hidden structure-property relationships, we maximize energy release efficiency using the carbon nano-materials genome approach derived from multifactorial neural network-based predictive models. This approach not only unlocks new functionalities in nEMs but also improves environmental performance and safety levels. By pioneering transformative pathways for nEMs through harnessing phonon wave resonance in low-dimensional nanocarbon transition interfaces, this research brings significant advancements in the field.

Power sources that can consistently deliver high levels of energy over extended periods are crucial for various space applications. Among the many methods of energy generation, direct heat-to-electricity conversion without intermediate steps or moving components shows particular promise but also presents significant challenges. The aim of this research is to address these challenges by enhancing the energy efficiency of thermionic conversion, which transforms thermal energy into electrical energy, through the development and utilization of a novel class of emission nanomaterials known as multilayer carbyne-enriched 3D-shaped nano-interfaces. By manipulating the topological, physicochemical, and functional characteristics of these interfaces, we seek to optimize their thermionic conversion capabilities. Building on the recent discovery of collective atomic vibrations called phonon waves within transition domains of multilayer nanostructures, we have devised a new approach to enhance the efficiency of thermionic energy converters. This involves unlocking the predictive functionality of 2D-ordered linear-chain carbon-based multilayer emitters through the excitation and fine-tuning of collective atomic vibrations and nanoarchitecture. To achieve this, we propose employing a combination of techniques that leverage interface effects, enable phonon wave propagation, facilitate energy exchange, and capitalize on synergistic effects offered by the multilayer nano-enhanced interfaces. The resulting devices for thermionic energy conversion have the potential to significantly surpass the efficiency of existing plasma thermionic converters by several orders of magnitude. Moreover, these electricity-generating sources based on thermionic conversion represent fundamental options for the advancement of Lunar and Martian research missions, opening up possibilities for sustainable energy production in extraterrestrial environments.

Low Power Wide Area Networks (LPWAN) enable a growing number of Internet-of-Things (IoT) applications with large geographical coverage, low bit-rate, and long lifetime requirements. LoRa (Long Range) is a well-known LPWAN technology that uses a proprietary Chirp Spread Spectrum (CSS) physical layer, while the upper layers are defined by an open standard - LoRaWAN. In this paper, we propose a simple yet effective method to improve the Quality-of-Service (QoS) of LoRa networks by fine-tuning specific radio parameters. Through a Mixed Integer Linear Programming (MILP) problem formulation, we find optimal settings for the Spreading Factor (SF) and Carrier Frequency (CF) radio parameters, considering the network traffic specifications as a whole, to improve the Data Extraction Rate (DER) and to reduce the packet collision rate and the energy consumption in LoRa networks. The effectiveness of the optimization procedure is demonstrated by simulations, using LoRaSim for different network scales. In relation to the traditional LoRa radio parameter assignment policies, our solution leads to an average increase of 6% in DER, and a number of collisions 13 times smaller. In comparison to networks with dynamic radio parameter assignment policies, there is an increase of 5%, 2.8%, and 2% of DER, and a number of collisions 11, 7.8 and 2.5 times smaller than equal-distribution, Tiurlikova's (SoTa), and random distribution, respectively. Regarding the network energy consumption metric, the proposed optimization obtained an average consumption similar to Tiurlikova's, and 2.8 times lower than the equal-distribution and random dynamic allocation policies. Furthermore, we approach the practical aspects of how to implement and integrate the optimization mechanism proposed in LoRa, guaranteeing backward compatibility with the standard protocol.

This work is a physical review, with elements of additions and thinning, on the methods of theoretical studies of nonlinear electrophysical phenomena in crystals with ion-molecular chemical bonds (CIMB). Crystals of this class include ionic dielectrics (characterized by high ionic conductivity), layered crystals, a special case of which are hydrogen-bonded crystals (HBC), defined as proton semiconductors and dielectrics (PSD).A scientific review (comparative analysis and justification of various approximations) was carried out on the methods of constructing and solving a generalized quasi-classical kinetic equation describing the mechanism of nonlinear relaxation polarization and conductivity processes in dielectric materials with ion-molecular chemical bonds (a special case is hydrogen-bonded crystals (HBC)) in a wide temperature range (1-1550 K) and polarizing field strengths (0.1-1000 V/m) at alternating field frequencies of the order of 1 kHz - 1000 MHz. The most important variant of the equations of the kinetic theory of dielectric relaxation in this work is the generalized non-linear by polarizing field quasi-classical kinetic equation of ionic (in HBC, proton) relaxation, based on the particle number balance equation (conductivity ions) in potential wells and having (in these models) the meaning of the ion current continuity equation (in HBC, protons), solved by the method of successive approximations by decomposition into infinite power series by degrees of a small dimensionless comparison parameter. It was found that in the area of ​ ​ weak fields (0.1-1 MW/m) at temperatures T = 50 - 550 K, for a number of ionic dielectrics (including HBC and similar dielectric properties and lattice structure) the generalized quasi-classical kinetic equation transforms to the linearized Fokker – Planck equation and, in the region of low (50-100K) and higher temperatures (250-550 K) begin to manifest non-linear polarization effects due to respectively proton tunneling (in the case of HBC) and volume charge relaxation (in the case of the HBC and for a wider class of ionic dielectrics). At ultra-low (1-10 K) temperatures in the region of weak fields (0.1-1 MW/m) and ultra-high temperatures (550-1550 K) in the region of strong fields (10-1000 MW/m), the contribution of this kind of effects to polarization is significantly enhanced. The effect of nonlinearities on relaxation times for microscopic acts of proton transitions across a potential barrier (assumed to be parabolic) is investigated. Nonlinear effects at volume-charge polarization in the hydrogen-bonded crystals (HBC) in alternating electric field, in radio frequency range are investigated. From the solution of the system of nonlinear Fokker-Planck equations (macroscopic kinetic equation) and Poisson, with blocking electrodes, using Fourier series, a recurrent (convenient for use in any approximation of perturbation theory) expression is constructed for complex amplitudes of relaxation modes of volumetric charge. Complex dielectric permittivity (CDP) is calculated as a series decomposition over even frequency harmonics of a variable field. The effect of quantum proton transitions and polarizing field parameters (strength, frequency) on the nonlinear properties of proton semiconductors and dielectrics has been established.

Backward electromagnetic waves are extraordinary waves with contra-directed phase velocity and energy flux. Unusual properties of the coherent nonlinear optical coupling of the phase-matched ordinary and backward electromagnetic waves with contra-directed energy fluxes are described which enable greatly-enhanced frequency and propagation direction conversion, parametrical amplification, as well as control of shape of the light pulses. Extraordinary transient processes that emerge in such metamaterials in pulsed regimes are described. The results of the numerical simulation of particular plasmonic metamaterials with hyperbolic dispersion are presented, which prove the possibility to match phases of such coupled guided ordinary and backward electromagnetic waves. Particular properties of the outlined processes in the proposed metamaterial are demonstrated through numerical simulations. Potential applications include ultra-miniature amplifiers, frequency changing reflectors, modulators, pulse shapers, and remotely actuated sensors.