Strictly and asymptotically scale-invariant probabilistic models of NN correlated binary random variables having {\em q}--Gaussians as N→∞N\to \infty limiting distributions

In order to physically enlighten the relationship between {\it $q$--independence} and {\it scale-invariance}, we introduce three types of asymptotically scale-invariant probabilistic models with binary random variables, namely (i) a family, characterized by an index $\nu=1,2,3,...$, unifying the Leibnitz triangle ($\nu=1$) and the case of independent variables ($\nu\to\infty$); (ii) two slightly different discretizations of $q$--Gaussians; (iii) a special family, characterized by the parameter $\chi$, which generalizes the usual case of independent variables (recovered for $\chi=1/2$). Models (i) and (iii) are in fact strictly scale-invariant. For models (i), we analytically show that the $N \to\infty$ probability distribution is a $q$--Gaussian with $q=(\nu -2)/(\nu-1)$. Models (ii) approach $q$--Gaussians by construction, and we numerically show that they do so with asymptotic scale-invariance. Models (iii), like two other strictly scale-invariant models recently discussed by Hilhorst and Schehr (2007), approach instead limiting distributions which are {\it not} $q$--Gaussians. The scenario which emerges is that asymptotic (or even strict) scale-invariance is not sufficient but it might be necessary for having strict (or asymptotic) $q$--independence, which, in turn, mandates $q$--Gaussian attractors.Comment: The present version is accepted for publication in JSTA

Piezophotoresistive Qualities Of р-TlInSe2 Monocrystals

The effect of uniaxial unalloyed deformation, temperature and optical lighting on tenzoresistive properties of p- TllnSe2 monocrystals is investigated. It is shown that with temperature increase sensitivity to TllnSe2 of unalloyed crystals toward deformation increases considerably, coefficient of tenzosensetivity at the same time increases linearly with temperature

A note on q-Gaussians and non-Gaussians in statistical mechanics

The sum of $N$ sufficiently strongly correlated random variables will not in general be Gaussian distributed in the limit N\to\infty. We revisit examples of sums x that have recently been put forward as instances of variables obeying a q-Gaussian law, that is, one of type (cst)\times[1-(1-q)x^2]^{1/(1-q)}. We show by explicit calculation that the probability distributions in the examples are actually analytically different from q-Gaussians, in spite of numerically resembling them very closely. Although q-Gaussians exhibit many interesting properties, the examples investigated do not support the idea that they play a special role as limit distributions of correlated sums.Comment: 17 pages including 3 figures. Introduction and references expande

On q-Gaussians and Exchangeability

The q-Gaussians are discussed from the point of view of variance mixtures of normals and exchangeability. For each q< 3, there is a q-Gaussian distribution that maximizes the Tsallis entropy under suitable constraints. This paper shows that q-Gaussian random variables can be represented as variance mixtures of normals. These variance mixtures of normals are the attractors in central limit theorems for sequences of exchangeable random variables; thereby, providing a possible model that has been extensively studied in probability theory. The formulation provided has the additional advantage of yielding process versions which are naturally q-Brownian motions. Explicit mixing distributions for q-Gaussians should facilitate applications to areas such as option pricing. The model might provide insight into the study of superstatistics.Comment: 14 page

Functional-differential equations for FqF_q%-transforms of qq-Gaussians

In the paper the question - Is the q-Fourier transform of a q-Gaussian a q'-Gaussian (with some q') up to a constant factor? - is studied for the whole range of $q\in (-\infty, 3)$. This question is connected with applicability of the q-Fourier transform in the study of limit processes in nonextensive statistical mechanics. We prove that the answer is affirmative if and only if q > 1, excluding two particular cases of q<1, namely, q = 1/2 and q = 2/3, which are also out of the theory valid for q \ge 1. We also discuss some applications of the q-Fourier transform to nonlinear partial differential equations such as the porous medium equation.Comment: 14 pages A new section on a related solution of the porous medium equation in comparison with the previous version has been introduc

On the Diagnostic Role of Morphological Signs of Wild Rose (Rosa L.)

Identification and systematics of species of wild rose (Rosa L.) are often associated with difficulties due to the diversity and variability of morphological features used in this process. They also arise in establishing genetic links between taxa of different ranks. Clarity in the diagnostic role of specific or group of characters is not only theoretical but also of practical importance. Such an attempt is made on the example of species of the genus Rosa from different sections and subsections (R. canina. R. danaiorum, R. ruprechtii, R. marschalliana, R. obtusifolia, R. svanetica, Rosa mollis, R. buschiana, R. pulverulenta, R pomifera, R. iberica, R. pimpinnefolia, etc.) of Chechnya and adjacent territories. The set of signs of the vegetative and generative sphere used in identifying species, subsections, sections has been considered. There was a lack of representativeness for the intraspecific diagnostics of such signs as: “free, immersed columns”, or “sessile stigmas in the hemispherical head above the fetal throat”, “occasionally solid sepals, with downward directed fruits” and others used in sectional diagnoses, because they are characteristic of species of different sections. The authors noted the heterogeneity of the authors’ approach to the characterization of section rank taxa, the inadmissibility of the universal, and the need for a differentiated approach in using the same characteristics when identifying taxa of different levels

An Integro-Differential Equation of the Fractional Form: Cauchy Problem and Solution

Producción CientíficaWe solve the Cauchy problem defined by the fractional partial differential equation [∂tt − κD]u = 0, with D the pseudo-differential Riesz operator of first order, and certain initial conditions. The solution of the Cauchy problem resulting from the substitution of the Gaussian pulse u(x, 0) by the Dirac delta distribution ϕ(x) = μδ(x) is obtained as corollary.MINECO grant MTM2014-57129-C2-1-P

Compacton matter waves in binary Bose gases under strong nonlinear management

The existence of compacton matter waves in binary mixtures of quasi one-dimensional Bose-Einstein condensates in deep optical lattices and in the presence of nonlinearity management, is first demonstrated. For this, we derive an averaged vector discrete nonlinear Schr\"odinger equation (DNLSE) and show that compacton solutions of different types can exist as stable excitations. Stability properties are studied by linear analysis and by direct numerical integrations of the DNLSE system and their dependence on the inter- and intra-species scattering lengths, investigated. We show that under proper management conditions, compactons can be very robust excitations that can emerge spontaneously from generic initial conditions. A possible experimental setting for compacton observation is also discussed.Comment: 11 pages, 11 figures, Physical Review A in pres

Note on a q-modified central limit theorem

A q-modified version of the central limit theorem due to Umarov et al. affirms that q-Gaussians are attractors under addition and rescaling of certain classes of strongly correlated random variables. The proof of this theorem rests on a nonlinear q-modified Fourier transform. By exhibiting an invariance property we show that this Fourier transform does not have an inverse. As a consequence, the theorem falls short of achieving its stated goal.Comment: 10 pages, no figure

Prospects of Development of the Metaverse: Empirical Evidence

The purpose of the research is to analyze the key features of the metaverse, the possibilities and advantages of its tools, security issues and the format of user participation in the metaverse virtual space. The relevance of the study is caused by the changes in the global economic order and the metaverse technologies awareness from both the expert community and ordinary users. The authors use methods of comparative analysis of Russian and foreign scientific sources, as well as statistical analysis and forecasting from leading consulting, rating and analytical agencies (Gartner, Statista, Emergenresearch, Moscow Innovation Agency, World Economic Forum, Tadviser). The scope of the achieved results is determined by the possibility of using the practical part of the study in building scenarios for the metaverse technologies application by various stakeholders. The authors draw conclusion that there is a wide range of use of the metaverse tools in various felds of human activity (professional, educational, social, entertainment, etc.), as well as about stimulating the development of the digital market using metaverse technologies. The prospects of non-interchangeable tokens, one of the innovative tools of the metaverse, are discussed and the audience growth rate of the metaverse innovative technologies potential consumers in the future is predicted