Economic Freedom: The Top, the Bottom, and the Reality. I. 1997–2007

We recall the historically admitted prerequisites of Economic Freedom (EF). We have examined 908 data points for the Economic Freedom of the World (EFW) index and 1884 points for the Index of Economic Freedom (IEF); the studied periods are 2000–2006 and 1997–2007, respectively, thereby following the Berlin wall collapse, and including 11 September 2001. After discussing EFW index and IEF, in order to compare the indices, one needs to study their overlap in time and space. That leaves 138 countries to be examined over a period extending from 2000 to 2006, thus 2 sets of 862 data points. The data analysis pertains to the rank-size law technique. It is examined whether the distributions obey an exponential or a power law. A correlation with the country’s Gross Domestic Product (GDP), an admittedly major determinant of EF, follows, distinguishing regional aspects, i.e., defining 6 continents. Semi-log plots show that the EFW-rank relationship is exponential for countries of high rank (≥20); overall the log–log plots point to a behaviour close to a power law. In contrast, for the IEF, the overall ranking has an exponential behaviour; but the log–log plots point to the existence of a transitional point between two different power laws, i.e., near rank 10. Moreover, log–log plots of the EFW index relationship to country GDP are characterised by a power law, with a rather stable exponent (γ≃0.674) as a function of time. In contrast, log–log plots of the IEF relationship with the country’s gross domestic product point to a downward evolutive power law as a function of time. Markedly the two studied indices provide different aspects of EF.

A review of high ideality factor in gallium nitride-based light-emitting diode

Theory concerning the high ideality factor of gallium nitride (GaN) based light- emitting diode (LED) has been reviewed. The presence of a high ideality factor indicates a large forward voltage that results in efficiency reduction. The paper suggests that tunneling is the main reason defining the exponential behaviour of current-voltage measurements, which leads to a high ideality factor. However, there is also a paper that suggests that the design of current geometry in the LED chip defines the value of ideality factor. An effective current spreading geometry in the LED chip will minimize the ideality factor and make it fall between the ideal range of 1 to 2. Besides, how the ideality factor is calculated will also play a major role in defining its value. By calculating the ideality factor based solely on the radiative recombination current formula, the value of ideality factor can result in an ideal ideality factor of 1.08.

Mathematical modelling of the agglomeration in a reactive porous medium with variable permeability

При переработке низкосортных твердых топлив, таких как отходы и биомасса, часто возникают проблемы, связанные с агломерацией. В работе предложен один из вариантов модели спекания, в которой локальная проницаемость изменяется при нагреве из-за физико-химического процесса (плавления), а центры агломерации (частицы плавящегося материала) случайным образом распределяются в двумерной пористой среде. Относительно простая модель позволяет исследовать развитие термогидродинамических неоднородностей в участке пористой среды и оценивать его гидравлическое сопротивление при разной доле расплавленного материала. Thermal processing of waste is usually carried out in fixed-bed reactors. Complex thermochemical behavior of individual components can lead to a decrease in technical and environmental efficiency. One of the problems is the bed agglomeration and formation of zones with decreasing permeability. The paper proposes a method of numerical simulation of porous media with physicochemical processes, which change permeability. Initial formulation proposes this process to be considered as melting of distributed particles in a stochastic media. The melting rate is controlled by heating of the selected element, and its local permeability changes during a phase transition. To solve this problem, numerical algorithm is developed on the basis of splitting methods. This algorithm was used to find a solution for system of non-stationary partial differential equations in two-dimensional case. The data on multiple calculations for different configurations are averaged to compare modelling results. The simulation results show that increasing the fraction of particles of the melting component leads to the significant change of the dynamic and stationary filtration regimes. The reduction in stationary flow rate is exponential function of the fraction of the melting particles. The dynamics of gas flow is also sensitive to the melting particles fraction, within the range of 510 there is a rather sharp transition from a gradual (almost linear) decrease of flow in time to a sharp one, which is close to exponential behaviour. The resulting calculations for the critical fraction are compared with the measured data published for the case of combustion of mixtures with sintering fuel particles (polymers). Further work will address the modification of the model to describe waste incineration, namely, taking into account the pyrolysis and oxidation processes, three-dimensional formulation, etc.

COVID-19 Epidemic Analysis using Machine Learning and Deep Learning Algorithms

The catastrophic outbreak of Severe Acute Respiratory Syndrome - Coronavirus (SARS-CoV-2) also known as COVID-2019 has brought the worldwide threat to the living society. The whole world is putting incredible efforts to fight against the spread of this deadly disease in terms of infrastructure, finance, data sources, protective gears, life-risk treatments and several other resources. The artificial intelligence researchers are focusing their expertise knowledge to develop mathematical models for analyzing this epidemic situation using nationwide shared data. To contribute towards the well-being of living society, this article proposes to utilize the machine learning and deep learning models with the aim for understanding its everyday exponential behaviour along with the prediction of future reachability of the COVID-2019 across the nations by utilizing the real-time information from the Johns Hopkins dashboard.

The oxidation kinetics of depleted uranium and its low-alloy molybdenum alloys in moist air

The oxidation kinetics of depleted uranium and its low-alloy molybdenum alloys (U-2wt.%Mo, U-5wt.%Mo) were measured in a moist air (75% relative humidity) at 60 and 75 ° C. Coefficients of reaction rate equations were determined for linear oxidation kinetics. In the oxidation of depleted uranium at 75 ° C, a change in reaction kinetics from linear to exponential behaviour was observed after about 2500 hours.

Lyapunov regularity and stability of linear non-instantaneous impulsive differential systems

In this paper, we discuss Lyapunov regularity and stability for linear non-instantaneous impulsive differential systems. In particular, we give sufficient conditions to guarantee any non-trivial solution has a finite Lyapunov exponent and we prove an impulsive system is stable using the Lyapunov exponent for the solution. A new version of Perron’s theorem is given by introducing the associated adjoint impulsive system and some criteria for the existence of non-uniform exponential behaviour are given. In addition, we present a stability result for a small perturbed nonlinear impulsive system when the linear impulsive system admits a non-uniform exponential contraction. Finally, we give a bound for the regularity coefficient.

Complete homotopy invariants for translation invariant symmetric quantum walks on a chain

We provide a classification of translation invariant one-dimensional quantum walks with respect to continuous deformations preserving unitarity, locality, translation invariance, a gap condition, and some symmetry of the tenfold way. The classification largely matches the one recently obtained (arXiv:1611.04439) for a similar setting leaving out translation invariance. However, the translation invariant case has some finer distinctions, because some walks may be connected only by breaking translation invariance along the way, retaining only invariance by an even number of sites. Similarly, if walks are considered equivalent when they differ only by adding a trivial walk, i.e., one that allows no jumps between cells, then the classification collapses also to the general one. The indices of the general classification can be computed in practice only for walks closely related to some translation invariant ones. We prove a completed collection of simple formulas in terms of winding numbers of band structures covering all symmetry types. Furthermore, we determine the strength of the locality conditions, and show that the continuity of the band structure, which is a minimal requirement for topological classifications in terms of winding numbers to make sense, implies the compactness of the commutator of the walk with a half-space projection, a condition which was also the basis of the general theory. In order to apply the theory to the joining of large but finite bulk pieces, one needs to determine the asymptotic behaviour of a stationary Schrödinger equation. We show exponential behaviour, and give a practical method for computing the decay constants.

Recent LHC/TOTEM data challenging the standard Regge pole theory

We analyse the recently discovered phenomena in elastic protonproton scattering at the LHC: the low-|t| “break” (departure from the exponential behaviour of the diffraction cone), the accelerating rise with energy of the forward slope B(s), the absence of secondary dips and bumps on the cone and the role of the odderon in the forward phase of the amplitude, ρ(13 TeV) = 0:09 ± 0:01, especially its contribution at the dip region, measured recently by TOTEM. The dip at 13 TeV seems to become more shallow with respect to lower energies, and we attribute this important new phenomena to the odderon contribution. These findings call for a revision of the standeard Regge-pole theory.

LOWER BOUNDS ALONG STABLE MANIFOLDS

It is well known that along any stable manifold the dynamics travels with an exponential rate. Moreover, this rate is close to the slowest exponential rate along the stable direction of the linearization, provided that the nonlinear part is sufficiently small. In this note, we show that whenever there is also a fastest finite exponential rate along the stable direction of the linearization, similarly we can establish a lower bound for the speed of the nonlinear dynamics along the stable manifold. We consider both cases of discrete and continuous time, as well as a nonuniform exponential behaviour.

Simulated climate change affects how biocrusts modulate infiltration and desiccation dynamics

Soil surface communities dominated by mosses, lichens and cyanobacteria (biocrusts) cover most of the soil surface between vegetation patches in drylands worldwide, and are known to affect soil wetting and drying after rainfall events. While ongoing climate change is already warming and changing rainfall patterns of drylands in many regions, little is known on how these changes may affect the hydrological behaviour of biocrust-covered soils. We used eight years of continuous soil moisture and rainfall data from a climate change experiment in central Spain to explore how biocrusts modify soil water gains and losses after rainfall events under simulated changes in temperature (2.5ºC warming) and rainfall (33% reduction). Both rainfall amount and biocrust cover increased soil water gains after rainfall events, whereas experimental warming, rainfall intensity and initial soil moisture decreased them. Initial moisture, maximum temperature and biocrust cover, by means of enhancing potential evapotranspiration or soil darkening, increased the drying rates and enhanced the exponential behaviour of the drying events. Meanwhile, the warming treatment reduced the exponential behaviour of these events. The effects of climate change treatments on soil water gains and losses changed through time, with important differences between the first two years of the experiment and after five years since its setup. These effects were mainly driven by the important reductions in biocrust cover and diversity observed under warming. Our results highlight the importance of long term studies to understand soil moisture responses to ongoing climate change in drylands.