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This research was funded by the following projects: (ECODIGICOLOR), grant number TED2021‑132023B‑I00, supported MCIN/AEI /http://dx.doi.org/10.13039/501100011033 and Unión Europea NextGenerationEU/ PRTR (Proyectos estratégicos orientados a la transición ecológica y digital) and project “Aplicación avanzada de las algas procedentes de la Alhambra y el Generalife en técnicas artísticas y de conservación‑restauración, (FICOARTE2), grant number P18‑FR‑4477, supported by Consejería de Universidad, Investigacion e Innovación, Junta de Andalucía, Programa FEDER, “Andalucía se mueve con Europa”, Grant PID2020‑113022GB‑I00 funded by MCIN/AEI/10.13039/501100011033 and by “ERDF A way of making Europe”, by the “European Union”., The archaeological heritage at Cerrillo Blanco (Porcuna, Spain) is made up of 27 sculptural ensembles and hundreds of fragments dated between the seventh and second centuries BC. They represent a fundamental milestone in Iberian art and culture. Despite their relevance, no scientific studies have been carried out to date in order to fully understand the materials, intentions and techniques that led to their creation. This is a study carried out on original pieces from the Archaeological Museum of Jaen using stereoscopic optical microscopy (SOM), polarised optical microscopy (POM), X-ray diffraction analysis (XRD), Fourier-transform infrared spectroscopy (FTIR), field emission scanning electron microscopy with energy dispersive x-ray analysis (FESEM-EDX) and spectrophotometry (SF). The results obtained provide new information on the material composition of this important legacy of the Iberian civilization as well as its main alteration factors., MCIN/AEI TED2021-132023B-I00, PID2020-113022GB-I00, Unión Europea NextGenerationEU/ PRTR TED2021-132023B-I00, Junta de Andalucía, FEDER, "Andalucía se mueve con Europa" P18-FR-4477, "ERDF A way of making Europe" Unión Europea PID2020-113022GB-I00

This article investigates nonlocal, quasilinear generalizations of the classical biharmonic operator (- Δ) 2. These fractional p -biharmonic operators appear naturally in the variational characterization of the optimal fractional Poincaré constants in Bessel potential spaces. We study the following basic questions for anisotropic fractional p -biharmonic systems: existence and uniqueness of weak solutions to the associated interior source and exterior value problems, unique continuation properties, monotonicity relations, and inverse problems for the exterior Dirichlet-to-Neumann maps. Furthermore, we show the UCP for the fractional Laplacian in all Bessel potential spaces Ht,p for any t∈ R, 1 ≤ p< ∞ and s∈ R+\ N: If u∈ Ht,p(Rn) satisfies (- Δ) su= u= 0 in a nonempty open set V, then u≡ 0 in Rn. This property of the fractional Laplacian is then used to obtain a UCP for the fractional p -biharmonic systems and plays a central role in the analysis of the associated inverse problems. Our proofs use variational methods and the Caffarelli–Silvestre extension., Calculus of Variations and Partial Differential Equations, 62 (4), ISSN:0944-2669, ISSN:1432-0835

Recently a spectral Favard theorem for bounded banded lower Hessenberg matrices that admit a positive bidiagonal factorization was presented. These type of matrices are oscillatory. In this paper the Lima-Loureiro hypergeometric multiple orthogonal polynomials and the Jacobi-Pi\~neiro multiple orthogonal polynomials are discussed at the light of this bidiagonal factorization for tetradiagonal matrices. The Darboux transformations of tetradiagonal Hessenberg matrices is studied and Christoffel formulas for the elements of the bidiagonal factorization are given, i.e., the bidiagonal factorization is given in terms of the recursion polynomials evaluated at the origin., Comment: This is the third part of the splitting of the paper arXiv:2203.13578 into three. 15 pages and 1 figure

The Lamb dipole is a traveling wave solution to the two-dimensional Euler equations introduced by S. A. Chaplygin (1903) and H. Lamb (1906) at the early 20th century. We prove orbital stability of this solution based on a vorticity method initiated by V. I. Arnold. Our method is a minimization of a penalized energy with multiple constraints that deduces existence and orbital stability for a family of traveling waves. As a typical case, orbital stability of the Lamb dipole is deduced by characterizing a set of minimizers as an orbit of the dipole by a uniqueness theorem in the variational setting., Comment: 41 pages

In this paper we introduce a new species of evolution algebras that we call Cayley evolution algebras. We show that if a field $k$ contains sufficiently many elements (for example if $k$ is infinite) then every finite group $G$ is isomorphic to $Aut(X)$ where $X$ is a finite-dimensional absolutely simple Cayley evolution $k$-algebra., Comment: This version of the article has been accepted for publication, after peer review but is not the Version of Record and does not reflect post-acceptance improvements, or any corrections. The Version of Record is published under the Creative Commons Attribution license and can be freely dowloaded it from https://doi.org/10.1007/s13398-023-01414-w

This paper is a continuation of the previous work (Pusateri, in: Forum of mathematics, Cambridge University Press) by the first two authors. We focus on 1-dimensional quadratic Klein–Gordon equations with a potential, under some assumptions that are less general than (Pusateri, in: Forum of mathematics, Cambridge University Press), but that allow us to present some simplifications in the proof of the global existence with decay for small solutions. In particular, we can propagate a stronger control on a basic L2-weighted-type norm while providing some shorter and less technical proofs for some of the arguments.

Archive for rational mechanics and analysis 247(3), 35 (2023). doi:10.1007/s00205-023-01864-x, Published by Springer, Berlin ; Heidelberg

We establish a Rademacher type theorem involving Hamiltonians H(x, p) under very weak conditions in both of Euclidean and Carnot-Carathéodory spaces. In particular, H(x, p) is assumed to be only measurable in the variable x, and to be quasiconvex and lower-semicontinuous in the variable p. Without the lower-semicontinuity in the variable p, we provide a counter example showing the failure of such a Rademacher type theorem. Moreover, by applying such a Rademacher type theorem we build up an existence result of absolute minimizers for the corresponding $$L^\infty $$ L ∞ -functional. These improve or extend several known results in the literature.

We consider a smooth, complete and non-compact Riemannian manifold (M, g) of dimension d≥ 3 , and we look for solutions to the semilinear elliptic equation -Δgw+V(σ)w=α(σ)f(w)+λwinM.The potential V: M→ R is a continuous function which is coercive in a suitable sense, while the nonlinearity f has a subcritical growth in the sense of Sobolev embeddings. By means of ∇ -theorems introduced by Marino and Saccon, we prove that at least three non-trivial solutions exist as soon as the parameter λ is sufficiently close to an eigenvalue of the operator - Δg.

We look for travelling wave fields $$\begin{aligned} E(x,y,z,t)&= U(x,y) \cos (kz+\omega t)+ {\widetilde{U}}(x,y)\sin (kz+\omega t),\\&\quad (x,y,z)\in \mathbb {R}^3,\, t\in \mathbb {R} \end{aligned}$$ E ( x , y , z , t ) = U ( x , y ) cos ( k z + ω t ) + U ~ ( x , y ) sin ( k z + ω t ) , ( x , y , z ) ∈ R 3 , t ∈ R satisfying Maxwell’s equations in a nonlinear medium which is not necessarily cylindrically symmetric. The nonlinearity of the medium enters Maxwell’s equations by postulating a nonlinear material law $$D=\varepsilon E+\chi (x,y, \langle |E|^2\rangle )E$$ D = ε E + χ ( x , y , ⟨ | E | 2 ⟩ ) E between the electric field E, its time averaged intensity $$\langle |E|^2\rangle $$ ⟨ | E | 2 ⟩ and the electric displacement field D. We derive a new semilinear elliptic problem for the profiles $$U,{\widetilde{U}}:\mathbb {R}^2\rightarrow \mathbb {R}^3$$ U , U ~ : R 2 → R 3 $$\begin{aligned} Lu-V(x,y)u=f(x,y,u)\quad \hbox {with }u=\begin{pmatrix} U \\ {\widetilde{U}} \end{pmatrix}, \hbox { for }(x,y)\in \mathbb {R}^2, \end{aligned}$$ L u - V ( x , y ) u = f ( x , y , u ) with u = U U ~ , for ( x , y ) ∈ R 2 , where $$f(x,y,u)=\omega ^2\chi (x,y, |u|^2)u$$ f ( x , y , u ) = ω 2 χ ( x , y , | u | 2 ) u . Solving this equation we can obtain exact travelling wave solutions of the underlying nonlinear Maxwell equations. We are able to deal with super quadratic and subcritical focusing effects, e.g. in the Kerr-like materials with the nonlinear susceptibility of the form $$\chi (x,y,\langle |E^2|\rangle E) = \chi ^{(3)}(x,y)\langle |E|^2\rangle E$$ χ ( x , y , ⟨ | E 2 | ⟩ E ) = χ ( 3 ) ( x , y ) ⟨ | E | 2 ⟩ E . A variational approach is presented for the semilinear problem. The energy functional associated with the equation is strongly indefinite, since L contains an infinite dimensional kernel. The methods developed in this paper may be applicable to other strongly indefinite elliptic problems and other nonlinear phenomena.

We analyze travelling wave (TW) solutions for nonlinear systems consisting of an ODE coupled to a degenerate PDE with a diffusion coefficient that vanishes as the solution tends to zero and blows up as it approaches its maximum value. Stable TW solutions for such systems have previously been observed numerically as well as in biological experiments on the growth of cellulolytic biofilms. In this work, we provide an analytical justification for these observations and prove existence and stability results for TW solutions of such models. Using the TW ansatz and a first integral, the system is reduced to an autonomous dynamical system with two unknowns. Analysing the system in the corresponding phase-plane, the existence of a unique TW is shown, which possesses a sharp front and a diffusive tail, and is moving with a constant speed. The linear stability of the TW in two space dimensions is proven under suitable assumptions on the initial data. Finally, numerical simulations are presented that affirm the theoretical predictions on the existence, stability, and parametric dependence of the travelling waves. K. Mitra and S. Sonner would like to thank the Nederlandse Organisatie voor Wetenschappelijk Onderzoek (NWO) for their support through the Grant OCENW.KLEIN.358. K. Mitra is further supported by Fonds voor Wetenschappelijk Onderzoek (FWO) through the Junior Postodoctoral Fellowship. J. Hughes is supported by the Natural Sciences and Engineering Research Council (NSERC) of Canada. H. Eberl acknowledges the financial support received from the Natural Sciences and Engineering Research Council of Canada (NSERC) through a Discovery Grant (RGPIN-2019-05003) and a Research Tools and Infrastructure Grant (RTI-2019-00317). We also thank C.J. van Duijn for fruitful discussions on stability, and the referees for their careful reading of the manuscript and valuable comments.

We present a numerical approach for computing attractive-repulsive power law equilibrium measures in arbitrary dimension. We prove new recurrence relationships for radial Jacobi polynomials on $d$-dimensional ball domains, providing a substantial generalization of the work based on recurrence relationships of Riesz potentials on arbitrary dimensional balls. Among the attractive features of the numerical method are good efficiency due to recursively generated banded and approximately banded Riesz potential operators and computational complexity independent of the dimension $d$, in stark contrast to the widely used particle swarm simulation approaches for these problems which scale catastrophically with the dimension. We present several numerical experiments to showcase the accuracy and applicability of the method and discuss how our method compares with alternative numerical approaches and conjectured analytical solutions which exist for certain special cases. Finally, we discuss how our method can be used to explore the analytically poorly understood gap formation boundary to spherical shell support., Comment: 40 pages, 14 figures

In this paper we compute the logarithmic energy of points in the unit interval [-1,1] chosen from different Gegenbauer Determinantal Point Processes. We check that all the different families of Gegenbauer polynomials yield the same asymptotic result to third order, we compute exactly the value for Chebyshev polynomials and we give a closed expression for the minimal possible logarithmic energy. The comparison suggests that DPPs cannot match the value of the minimum beyond the third asymptotic term., CRUE-CSIC agreement, Springer Nature

The Lyapunov approach is one of the most effective and efficient methods for the inves tigation of the stability of stochastic systems. Several authors analyzed the stability and stabilization of stochastic differential equations via Lyapunov techniques. Nevertheless, few results are concerned with the stability of stochastic systems based on the knowledge of the solution of the system explicitly. The originality of our work is to investigate the problem of stabilization of stochastic perturbed control–bilinear systems based on the explicit solution of the system by using the integral inequalities of the Gronwall type in particular Gami dov’s inequality. Namely, under some restrictions on the perturbed term, and based on the method of integral inequalities, we prove that the stochastic system can be stabilized by constant feedback. Further, we study the problem of stabilization of stochastic perturbed control affine systems based on the use of bilinear approximation. Different examples are provided to verify the effectiveness of the proposed results.

A low-order finite element method is constructed and analysed for an incompressible non-Newtonian flow problem with power-law rheology. The method is based on a continuous piecewise linear approximation of the velocity field and piecewise constant approximation of the pressure. Stabilisation, in the form of pressure jumps, is added to the formulation to compensate for the failure of the inf-sup condition, and using an appropriate lifting of the pressure jumps a divergence-free approximation to the velocity field is built and included in the discretisation of the convection term. This construction allows us to prove the convergence of the resulting finite element method for the entire range $r>\frac{2 d}{d+2}$ of the power-law index $r$ for which weak solutions to the model are known to exist in $d$ space dimensions, $d \in \{2,3\}$., 23 pages, 1 figure

We construct the propagator of the massless Dirac operator $W$ on a closed Riemannian 3-manifold as the sum of two invariantly defined oscillatory integrals, global in space and in time, with distinguished complex-valued phase functions. The two oscillatory integrals -- the positive and the negative propagators -- correspond to positive and negative eigenvalues of $W$, respectively. This enables us to provide a global invariant definition of the full symbols of the propagators (scalar matrix-functions on the cotangent bundle), a closed formula for the principal symbols and an algorithm for the explicit calculation of all their homogeneous components. Furthermore, we obtain small time expansions for principal and subprincipal symbols of the propagators in terms of geometric invariants. Lastly, we use our results to compute the third local Weyl coefficients in the asymptotic expansion of the eigenvalue counting functions of $W$., Final version, to appear in Integral Equations and Operator Theory

Inspired by the recent theory of Entropy-Transport problems and by the $\mathbf{D}$-distance of Sturm on normalised metric measure spaces, we define a new class of complete and separable distances between metric measure spaces of possibly different total mass. We provide several explicit examples of such distances, where a prominent role is played by a geodesic metric based on the Hellinger-Kantorovich distance. Moreover, we discuss some limiting cases of the theory, recovering the "pure transport" $\mathbf{D}$-distance and introducing a new class of "pure entropic" distances. We also study in detail the topology induced by such Entropy-Transport metrics, showing some compactness and stability results for metric measure spaces satisfying Ricci curvature lower bounds in a synthetic sense., Comment: 39 pages. Added a section with a comparison with the conic Gromov-Wasserstein distance. Some other minor improvements. Final version, to appear on "Probability Theory and Related Fields"

We analyze the relativistic Euler equations of conservation laws of baryon number and momentum with a general pressure law. The existence of global-in-time bounded entropy solutions for the system is established by developing a compensated compactness framework. The proof relies on a careful analysis of the entropy and entropy-flux functions, which are represented by the fundamental solutions of the entropy and entropy-flux equations for the relativistic Euler equations. Based on a careful entropy analysis, we establish the compactness framework for sequences of both exact solutions and approximate solutions of the relativistic Euler equations. Then we construct approximate solutions via the vanishing viscosity method and employ our compactness framework to deduce the global-in-time existence of entropy solutions. The compactness of the solution operator is also established. Finally, we apply our techniques to establish the convergence of the Newtonian limit from the entropy solutions of the relativistic Euler equations to the classical Euler equations.

In this paper we discuss and prove an analogy of the Carleson–Hunt theorem with respect to Vilenkin systems. In particular, we use the theory of martingales and give a new and shorter proof of the almost everywhere convergence of Vilenkin–Fourier series of$$f\in L_p(G_m)$$f∈Lp(Gm)for$$p>1$$p>1in case the Vilenkin system is bounded. Moreover, we also prove sharpness by stating an analogy of the Kolmogorov theorem for$$p=1$$p=1and construct a function$$f\in L_1(G_m)$$f∈L1(Gm)such that the partial sums with respect to Vilenkin systems diverge everywhere.

Various collective motions of camphor boats have been studied. Camphor boats are self-driven particles that interact with each other through the change of surface tension on water surface by camphor molecules. Consequently, even in a one-dimensional circuit, a congested state or jamming can be observed (Suematsu et al. in Phys Rev E 81:056210, 2010). In this phenomenon, the unidirectional motion of each particle is considered a traveling wave, and the concentration of camphor molecules forms a pulse shape. Hence, each pair of particles interacts with each other like a pulse–pulse interaction. Thus, we expect that the center manifold theories proposed in Ei (J Dyn Differ Equ 14:85–137, 2002) and Ei et al. (Physica D 165:176–198 2002) are applicable for the analysis of the collective motion of camphor boats. However, spatial discontinuity in our model, in particular the existence of Dirac delta functions in a linearized operator, does not fulfill the requirement in the reduction process because the authors developed their theories in $$L^2$$ -framework and for smooth nonlinearity in Ei (2002) and Ei et al. (2002). In this article, we extend the results obtained in Ei (2002) and Ei et al. (2002) and establish a new center manifold approach in $$(H^1)^*$$ -framework. Finally, we succeed to rigorously reduce a mathematical model (Nagayama et al. in Physica D: Nonlinear Phenom 194:151–165, 2004) coupled with a Newtonian equation and a reaction–diffusion equation including delta functions to an ordinary differential system that represents the motions of camphor boats.

We prove that in arbitrary Carnot groups$\mathbb {G}$Gof step 2, with a splitting$\mathbb {G}=\mathbb {W}\cdot \mathbb {L}$G=W⋅Lwith$\mathbb {L}$Lone-dimensional, the intrinsic graph of a continuous function$\varphi \colon U\subseteq \mathbb {W}\to \mathbb {L}$φ:U⊆W→Lis$C^{1}_{\mathrm {H}}$CH1-regular precisely whenφsatisfies, in the distributional sense, a Burgers’ type systemDφφ=ω, with a continuousω. We stress that this equivalence does not hold already in the easiest step-3 Carnot group, namely the Engel group. We notice that our results generalize previous works by Ambrosio-Serra Cassano-Vittone and Bigolin-Serra Cassano in the setting of Heisenberg groups. As a tool for the proof we show that a continuous distributional solutionφto a Burgers’ type systemDφφ=ω, withωcontinuous, is actually a broad solution toDφφ=ω. As a by-product of independent interest we obtain that all the continuous distributional solutions toDφφ=ω, withωcontinuous, enjoy 1/2-little Hölder regularity along vertical directions.

ispartof: CONSTRUCTIVE APPROXIMATION vol:55 issue:3 pages:775-827 status: published

This paper examines the impact of process accountability on two biases causing myopic or short-sighted decision making. These biases are strong preferences for immediate and certain outcomes known as delay and risk aversion. We hypothe- size that accountability alone is insufficient to undo the biases, but if coupled with a cue on subjective discount rates, it will attenuate biases. To analyze our research question, we used a within- and between-subjects experimental design (two account- ability conditions compared with a non-accountability condition and with each other) with delay and probability discounting choice tasks involving 118 students of accounting, finance and management in an online experiment. In line with our hypotheses, we find that process accountability successfully reduces excessive delay and risk aversion only if it provides a cue about the subjective discount rate. We dis- cuss the implications of our findings for management control.

Jsou odvozeny podmínky zaručující, že obor hodnot spojitého zobrazení definovaného na kompaktní konvexní množině obsahuje předem danou množinu. Ve Fréchetových prostorech uvažujeme aproximace jedním zobrazením, jehož inverzní zobrazení má konvexní hodnoty nebo má spojitou selekci. Posléze v Banachových prostorech a prostorech konečné dimenze uvažujeme aproximace určené konvexní množinou spojitých lineárních operátorů. Ukazujeme, že tento přístup je velmi užitečný a umožňuje jednotný popis různých, ne nutně lokálních, vlastností otevřenosti pro obecně nehladká zobrazení. V prostorech konečné dimenze prezentujeme postačující podmínky pro směrovou otevřenost s lineárním řádem s omezeními, metrickou a silnou metrickou regularitu. Tyto podmínky pokrývají, sjednocují a zobecňují například Pourciauovu větu o otevřeném zobrazení, Clarkeovu větu o inverzní a implicitní funkci a jejich zobecnění odvozená V. Jeyakumarem a D.T. Lucem za použití konceptu shora polospojitého neomezeného pesudo-jakobiánu nebo A. Neumaierem za použití intervalového rozšíření derivace hladkého zobrazení. Na konec odvozujeme podmínky zaručující, že nelineární obraz kompaktní konvexní podmnožiny obsahuje předepsaný uspořádaný interval, což vede na aplikace v oblasti bezpečnosti elektrické přenosové soustavy, např. předcházení tzv. blackoutu. We derive conditions ensuring that the range of a given continuous mapping with a compact convex domain covers a prescribed set. In Fréchet spaces, we consider approximations by one single-valued mapping such that the inverse of it has either convex fibers or admits a continuous single-valued selection. Subsequently, in Banach and finite-dimensional spaces, we focus on approximations determined by a convex set of bounded linear mappings. We demonstrate that our approach is highly flexible and provides the unified treatment of various, in general non-local, covering properties of possibly non-smooth mappings. In finite-dimensional spaces, we present sufficient conditions for constrained directional semiregularity, metric regularity and strong metric regularity. These conditions cover, unify, and extend such well-known results as Pourciau’s open mapping theorem and Clarke’s inverse and implicit function theorems as well as their generalizations established by V. Jeyakumar and D.T. Luc by using upper semi-continuous unbounded pseudo-Jacobians or by A. Neumaier by considering various interval extensions of the derivative of a smooth mapping. Finally, we provide conditions guaranteeing that the non-linear image of a compact convex set contains a prescribed ordered interval which has direct applications in power network security management such as preventing the electricity blackout.

Let $${\mathbb {D}}$$ D be the unit disc in $${\mathbb {C}}$$ C . If $$\mu $$ μ is a finite positive Borel measure on the interval [0, 1) and f is an analytic function in $${\mathbb {D}}$$ D , $$f(z)=\sum _{n=0}^\infty a_nz^n$$ f ( z ) = ∑ n = 0 ∞ a n z n ($$z\in {\mathbb {D}}$$ z ∈ D ), we define $$\begin{aligned} {\mathcal {C}}_\mu (f)(z)= \sum _{n=0}^\infty \mu _n\left( \sum _{k=0}^na_k\right) z^n,\quad z\in {\mathbb {D}}, \end{aligned}$$ C μ ( f ) ( z ) = ∑ n = 0 ∞ μ n ∑ k = 0 n a k z n , z ∈ D , where, for $$n\ge 0$$ n ≥ 0 , $$\mu _n$$ μ n denotes the n-th moment of the measure $$\mu $$ μ , that is, $$\mu _n=\int _{[0, 1)}t^nd\mu (t).$$ μ n = ∫ [ 0 , 1 ) t n d μ ( t ) . In this way, $${\mathcal {C}}_\mu $$ C μ becomes a linear operator defined on the space $${\mathrm{Hol}}({\mathbb {D}})$$ Hol ( D ) of all analytic functions in $${\mathbb {D}}$$ D . We study the action of the operators $${\mathcal {C}}_\mu $$ C μ on distinct spaces of analytic functions in $${\mathbb {D}}$$ D , such as the Hardy spaces $$H^p$$ H p , the weighted Bergman spaces $$A^p_\alpha $$ A α p , BMOA, and the Bloch space $${\mathcal {B}}$$ B .

In contemporary times, digital technologies are recognized as a vital tool in socio-economic development in many countries, as well as their prerequisite is recognized for many industries, including tourism. The growth of information and communication technologies, demand for digitalization in various economic sectors, challenges many destinations towards the introduction and development of digital technologies in the tourism sector. In this context, the objective of the present book chapter is to explore the current state of the digital technology application in the tourism industry and identify the limitations and problems associated with their implementation in the case of Kazakhstan, as an emerging and promising tourism destination. Using the gravity model, we examine the impact of information and communication technology on the tourism demand of Kazakhstan for the period of 2000–2018. The secondary data has been compiled and decomposed from international organizations, the ministries, national and regional authorities of Kazakhstan. The study updates traditional policy implications and provides remarkable recommendations for applications of digital technologies in the tourism development of the country.

We consider the standard symmetric elliptic integral $$R_F(x,y,z)$$ R F ( x , y , z ) for complex x, y, z. We derive convergent expansions of $$R_F(x,y,z)$$ R F ( x , y , z ) in terms of elementary functions that hold uniformly for one of the three variables x, y or z in closed subsets (possibly unbounded) of $$\mathbb {C}{\setminus }(-\infty ,0]$$ C \ ( - ∞ , 0 ] . The expansions are accompanied by error bounds. The accuracy of the expansions and their uniform features are illustrated by means of some numerical examples.

This paper is the continuation of the study on discrete harmonic analysis related to Jacobi expansions initiated in [1]. Considering the operator $\mathcal{J}^{(\alpha,\beta)}=J^{(\alpha,\beta)}-I$, where $J^{(\alpha,\beta)}$ is the three-term recurrence relation for the normalized Jacobi polynomials and $I$ is the identity operator, we focus on the study of weighted inequalities for the Riesz transform associated with it., Comment: 19 pages

The real estate sector is evolving and changing rapidly with the increase in housing demand, and new luxury housing projects appear every day. The reliability of housing market investments is largely dependent on accurate pricing.The aim of this study is to introduce a dynamic pricing procedure that estimates house prices using the most important characteristics of a house. For this purpose, a hybrid algorithm using linear regression, clustering analysis, nearest neighbor classification and Support Vector Regression (SVR) method is proposed. Our hybrid algorithm involves using the output of one method as the input of another method for home price prediction to deal with the heteroscedastic nature of the housing data. In other words, the aim of this study is to present a hybrid algorithm that will create different housing clusters from the available data set, classify the houses to which the cluster is unknown, and make price predictions by creating separate prediction models for each class. Housing data collected through manual web scraping of Kadikoy district in Istanbul were used for training and validation of the proposed algorithm. In addition to these data, we validated our algorithm on the KAGGLE house dataset, which covers a wide range of features. The results of the hybrid algorithm were compared using multiple linear regression, Lasso, ridge regression, Support Vector Regression (SVR), AdaBoost, decision tree, random forest and XGBoost regression. Experimental results show that the proposed hybrid model is superior in terms of both Residual Mean Square Error (RMSE), Mean Absolute Value Percent Error (MAPE) and adjusted Rsquare measures for both Kadikoy and KAGGLE housing dataset.

For a parameter dimension d∈ N, we consider the approximation of many-parametric maps u:[-1,1]d→R by deep ReLU neural networks. The input dimension d may possibly be large, and we assume quantitative control of the domain of holomorphy of u: i.e., u admits a holomorphic extension to a Bernstein polyellipse Eρ1×⋯×Eρd⊂Cd of semiaxis sums ρi> 1 containing [-1,1]d. We establish the exponential rate O(exp(-bN1/(d+1))) of expressive power in terms of the total NN size N and of the input dimension d of the ReLU NN in W1,∞([-1,1]d). The constant b> 0 depends on (ρj)j=1d which characterizes the coordinate-wise sizes of the Bernstein-ellipses for u. We also prove exponential convergence in stronger norms for the approximation by DNNs with more regular, so-called “rectified power unit” activations. Finally, we extend DNN expression rate bounds also to two classes of non-holomorphic functions, in particular to d-variate, Gevrey-regular functions, and, by composition, to certain multivariate probability distribution functions with Lipschitz marginals., Constructive Approximation, 55 (1), ISSN:0176-4276, ISSN:1432-0940

We characterize all pairs of entire functions $$(u,\psi )$$ ( u , ψ ) for which the induced weighted superposition operator $$S_{(u,\psi )}$$ S ( u , ψ ) transforms one Fock space into another Fock space. Further analytical structures like boundedness and Lipschitz continuity of $$S_{(u,\psi )}$$ S ( u , ψ ) are described. We, in particular, show the Fock spaces support no compact weighted superposition operator.

When observational studies are used to establish the causal effects of treatments, the estimated effect is affected by treatment selection bias. The inverse propensity score weight (IPSW) is often used to deal with such bias. However, IPSW requires strong assumptions whose misspecifications and strategies to correct the misspecifications were rarely studied. We present a bootstrap bias correction of IPSW (BC-IPSW) to improve the performance of propensity score in dealing with treatment selection bias in the presence of failure to the ignorability and overlap assumptions. The approach was motivated by a real observational study to explore the potential of anticoagulant treatment for reducing mortality in patients with end-stage renal disease. The benefit of the treatment to enhance survival was demonstrated; the suggested BC-IPSW method indicated a statistically significant reduction in mortality for patients receiving the treatment. Using extensive simulations, we show that BC-IPSW substantially reduced the bias due to the misspecification of the ignorability and overlap assumptions. Further, we showed that IPSW is still useful to account for the lack of treatment randomization, but its advantages are stringently linked to the satisfaction of ignorability, indicating that the existence of relevant though unmeasured or unused covariates can worsen the selection bias.

Long Range Dependence (LRD) in functional sequences is characterized in the spectral domain under suitable conditions. Particularly, multifractionally integrated functional autoregressive moving averages processes can be introduced in this framework. The convergence to zero in the Hilbert-Schmidt operator norm of the integrated bias of the periodogram operator is proved. Under a Gaussian scenario, a weak-consistent parametric estimator of the long-memory operator is then obtained by minimizing, in the norm of bounded linear operators, a divergence information functional loss. The results derived allow, in particular, to develop inference from the discrete sampling of the Gaussian solution to fractional and multifractional pseudodifferential models introduced in Anh et al. (Fract Calc Appl Anal 19(5):1161-1199, 2016; 19(6):1434– 1459, 2016) and Kelbert (Adv Appl Probab 37(1):1–25, 2005)., University of Granada (FEDER funds) MCIN / AEI / PGC2018-099549-B-I00 CEX2020-001105-M / AEI / 10.13039/ 501100011033

New rigidity results for complete non-compact spacelike submanifolds of arbitrary codimension in plane fronted waves are obtained. Under appropriate assumptions, we prove that a complete spacelike submanifold in these spacetimes is contained in a characteristic lightlike hypersurface. Moreover, for a complete codimension two extremal submanifold in a plane fronted wave we show sufficient conditions to guarantee that it is a (totally geodesic) wavefront., Spanish Government PID2020-118452GBI00 PID2020-116126GB-I00, ERDF project P20-01391, "Maria de Maeztu" Excellence Unit IMAG - MCIN-AEI CEX2020-001105-M

We establish the Krylov-Safonov Harnack inequalities and Holder estimates for fully nonlinear nonlocal operators of non-divergence form on Riemannian manifolds with nonnegative sectional curvatures. To this end, we first define the nonlocal Pucci operators on manifolds that give rise to the concept of non-divergence form operators. We then provide the uniform regularity estimates for these operators which recover the classical estimates for second order local operators as limits.

Under suitable conditions, we show that the Euler characteristic of a foliated Riemannian manifold can be computed only from curvature invariants which are transverse to the leaves. Our proof uses the hypoelliptic sub-Laplacian on forms recently introduced by two of the authors in Baudoin and Grong (Ann Glob Anal Geom 56(2):403–428, 2019).

In this paper, we focus on the construction of a hybrid scheme for the approximation of non-Maxwellian kinetic models with uncertainties. In the context of multiagent systems, the introduction of a kernel at the kinetic level is useful to avoid unphysical interactions. The methods here proposed, combine a direct simulation Monte Carlo (DSMC) in the phase space together with stochastic Galerkin (sG) methods in the random space. The developed schemes preserve the main physical properties of the solution together with accuracy in the random space. The consistency of the methods is tested with respect to surrogate Fokker-Planck models that can be obtained in the quasi-invariant regime of parameters. Several applications of the schemes to non-Maxwellian models of multiagent systems are reported., Comment: 28 pages, 8 figures

We prove that there exists a martingale $f\in H_{p} $ f ∈ H p such that the subsequence $\{L_{2^{n}}f \}$ { L 2 n f } of Nörlund logarithmic means with respect to the Walsh system are not bounded from the martingale Hardy spaces $H_{p}$ H p to the space $weak-L_{p} $ w e a k − L p for $0< p 0 < p < 1 . We also prove that for any $f\in L_{p}$ f ∈ L p , $p\geq 1 $ p ≥ 1 , $L_{2^{n}}f$ L 2 n f converge to f at any Lebesgue point x. Moreover, some new related inequalities are derived.

We prove a complex formulation of the real interpolation method, showing that the real and complex interpolation methods are not inherently real or complex. Using this complex formulation, we prove Stein interpolation for the real interpolation method. We apply this theorem to interpolate weighted $L^p$-spaces and the sectoriality of closed operators with the real interpolation method., 15 pages, slightly improved presentation

This work is a contribution to the ongoing search for algebraic structures within a nonlinear setting. Here, we shall focus on the study of lineability of subsets of continuous functions on the one hand and within the setting of Sobolev spaces on the other (which represents a novelty in the area of research).