bluuebunny/crossref_metadata_2025_split huggingface dataset:
Asymptotics of the circulation around a three‐dimensional thin wing
Authors: Hinder Rainer , Nazarov Sergueï A. 
Published: December 2024

We are interested in finding the velocity distribution at the wings of an aeroplane. Within the scope of a three‐dimensional linear theory we analyse a model which is formulated as a mixed screen boundary value problem for the Helmholtz equation $(\Delta + k^{ 2}) \varPhi =0$ in $\mathbb{R}^{ 3}\backslash \overline{S}$ , where $\varPhi $ denotes the perturbation velocity potential, induced by the presence of the wings and $\overline{S} := \overline{L} \cup \overline{W}$ with the projection $L$ of the wings onto the $(y_{ 1},y_{ 2})$ ‐plane and the wake $W$ . Not all Cauchy data are given explicitly on $L$ , respectively $W$ . These missing Cauchy data depend on the wing circulation $\varGamma $ . $\varGamma $ has to be fixed by the Kutta–Joukovskii condition: $\nabla \varPhi $ should be finite near the trailing edge $x_{\rm t}$ of $L$ . We reduce here this screen problem to an equivalent mixed boundary value problem in $\mathbb{R}^{ 3}_{ +}$ . The main problem is in both cases the calculation of $\varGamma $ . In order to find $\varPhi $ we use the method of matched asymptotics for some small geometrical parameter $\varepsilon$ and the ansatz $\varGamma = \varGamma _{ 0} + \varepsilon \varGamma _{ 1} + \cdots $ which makes it possible to split the problem into a sequence of problems for $\varGamma _{ 0},\varGamma _{ 1}, \ldots\,$ . Concretely, we calculate $\varGamma _{ 0}$ and $\varGamma _{ 1}$ explicitly by the demand of vanishing intensity factors of the solutions of the corresponding mixed problems at the borderline between $L$ and $W$ . Especially, we point out that $\varGamma _{ 0}$ can be obtained by solving a two‐dimensional problem for every cross‐section of $L$ while $\varGamma _{ 1}$ indicates the interaction of these cross‐sections.
$H^0$‐convergence for the linearized elasticity system
Authors: El Hajji Mohamed , Donato Patrizia 
Published: December 2024

In Nonlinear Partial Differential Equations and Their Applications, Vol. 13 (to appear), Briane, Damlamian and Donato extend to the case of perforated domains the $H$ ‐covergence introduced by Murat and Tartar (Sém. Anal. Fonct. Numér., 1977/1978; Topics in the Mathematical Modelling of Composite Materials, 1997) for the diffusion equation. In this paper, we define in the same spirit a notion of $H^0$ ‐convergence for the linearized elasticity system in perforated domains. This definition allows to obtain compactness, locality and corrector results.
Uniqueness of solutions of the Cauchy problem for parabolic equations degenerating at infinity
Authors: Eidelman S. , Kamin S. , Porper F. 
Published: December 2024

This paper is devoted to the investigation of classes of uniqueness for classical solutions of the Cauchy problem [Formula: see text] We study how the behaviour of the function $\rho(t,x)$ as $\vert x\vert \to \infty$ influences the classes of uniqueness of the Cauchy problem. In particular the dependence of such classes on the number of the space coordinates is clarified. We also discuss the sharpness of the obtained results.
An upper bound for the temperature for some combustion equations in the limit of large activation energy
Authors: Langlois A. , Marion M. 
Published: December 2024

This paper is concerned with the thermal diffusional model borrowed from the theory of combustion. The analytic methods currently used to investigate this model require a near‐equidiffusion condition, the inverse of the activation energy being the small parameter. The first step in these methods consists in assuming a suitable bound on the temperature. The aim of this paper is to derive rigorously such a bound. We show that the temperature is bounded independently of the activation energy β uniformly in time, at least for sufficiently large values of β. The proof relies on the use of a Lyapunov function first introduced by Barabanova [1] and energy type estimates.
Estimates on periodic and Dirichlet eigenvalues for the Zakharov–Shabat system
Authors: Grébert B. , Kappeler T. 
Published: December 2024

Consider the 2×2 first order system due to Zakharov–Shabat, $LY:={\rm i}\left(\matrix{1&0\cr 0&-1}\right)Y'+\left(\matrix{0&\psi_{1}\cr \psi _{2}&0}\right)Y=\lambda Y$ with ψ1,ψ2 being complex valued functions of period one in the weighted Sobolev space $H^{w}\equiv H^{w}_{\mathbb{C}}.$ Denote by spec(ψ1,ψ2) the set of periodic eigenvalues of L(ψ1,ψ2) with respect to the interval [0,2] and by specDir(ψ1,ψ2) the set of Dirichlet eigenvalues of L(ψ1,ψ2) when considered on the interval [0,1]. It is well known that spec(ψ1,ψ2) and specDir(ψ1,ψ2) are discrete. Theorem. Assume that w is a weight such that, for some δ>0, w−δ(k)=(1+|k|)−δw(k) is a weight as well. Then for any bounded subset ${\mathbb{B}}$ of 1‐periodic elements in Hw×Hw there exist N≥1 and M≥1 so that for any |k|≥N, and $(\psi_{1},\psi_{2})\in{\mathbb{B}} $ , the set $\mathit{spec}(\psi_{1},\psi_{2})\cap \{\lambda \in{\mathbb{C}} \mid |\lambda -k\pi | < \pi/2\}$ contains exactly one isolated pair of eigenvalues {λ+k,λ−k} and $\mathit{spec}_{\rm Dir}(\psi_{1},\psi_{2})\cap \{\lambda \in{\mathbb{C}} \mid |\lambda -k\pi |<{\pi}/{2}\}$ contains a single Dirichlet eigenvalue μk. These eigenvalues satisfy the following estimates (i) Σ|k|≥Nw(2k)2|λ+k−λ−k|2≤M; (ii) $\sum _{|k|\geq N}w(2k)^{2}|\frac{(\lambda ^{+}_{k}+\lambda ^{-}_{k})} {2}-\mu _{k}|^{2}\leq M.$ Furthermore spec(ψ1,ψ2)\{λ±k,|k|≥N} and $\mathit{spec}_{\rm Dir}(\psi_{1},\psi_{2})\backslash \{\mu _{k}\mid |k|\geq N\}$ are contained in $\{\lambda \in{\mathbb{C}} \mid |\lambda | < N\pi -\pi /2\}$ and its cardinality is 4N−2, respectively 2N−1. When $\psi_{2}=\overline{\psi } _{1}$ (respectively $\psi_{2}=-\overline{\psi } _{1}),L(\psi_{1},\psi_{2})$ is one of the operators in the Lax pair for the defocusing (resp. focusing) nonlinear Schrödinger equation.
Variational limit of a one dimensional discrete and statistically homogeneous system of material points
Authors: Iosifescu Oana , Licht Christian , Michaille Gérard 
Published: December 2024

We show that the energy of a discrete system of material points on a line and subjected to random nearest‐neighbour interactions, almost surely converges in a variational sense to a deterministic energy defined on spaces of functions with bounded variation. Résumé. Nous montrons que l'énergie discrète en dimension 1 d'un système de points matériels soumis à des intéractions aléatoires locales, converge presque surement, en un sens variationnel, vers une énergie déterministe définie dans les espaces BV ou SBV.
Ondes guidées dans une bande élastique et existence d'une onde de Rayleigh asymptotique
Authors: Bouhennache Tark 
Published: December 2024

Nous étudions le comportement asymptotique à haute fréquence des ondes guidées dans une bande élastique isotrope et hétérogène Ω={(x,y); y∈(0,L)} ⊂ R2, avec les conditions de surface libre en y=0 et de Dirichlet en y=L. Nous montrons en particulier l'existence d'une “onde de Rayleigh asymptotique”. Abstract. We study the asymptotic behavior at high frequency of the guided waves in an isotropic and heterogeneous elastic strip Ω={(x,y); y∈(0,L)} ⊂ R2, with the free surface condition on y=0 and Dirichlet condition on y=L. We prove, in particular, the existence of an “asymptotic Rayleigh wave”.
Quantitative homogenization of global attractors for reaction–diffusion systems with rapidly oscillating terms
Authors: Fiedler Bernold , Vishik Mark I. 
Published: December 2024

For rapidly spatially oscillating nonlinearities f and inhomogeneities g we compare solutions uε of reaction–diffusion systems ∂tuε=aΔuε−f(ε,x,x/ε,u)+g(ε,x,x/ε) with solutions u0 of the formally homogenized, spatially averaged system ∂tu0=aΔu0−f0(x,u0)+g0(x,u0). We consider a smooth bounded domain x∈Ω⊆ $\mathbb{R}^{n}$ , n≤3, with Dirichlet boundary conditions. We also impose sufficient regularity and dissipation conditions, such that solutions exist globally in time and, in fact, converge to their compact global attractors 𝒜ε and 𝒜0, respectively, in L2(Ω). Based on ε‐independent a priori estimates we prove ‖uε(·,t)−u0(·,t)‖L2(Ω)≤Cε eρt, uniformly for all t≥0 and 0<ε≤ε0. Here the solutions uε and u0 start at the same initial condition u=u0(x)∈H1(Ω) for t=0, and C=C(‖u0‖H1). Based on an ε‐independent H2‐bound on the global attractors 𝒜ε as well as an exponential attraction rate ν of the homogenized attractor 𝒜0 in L2(Ω), we also prove fractional order upper semicontinuity of the global attractors for $\varepsilon\searrow 0$ , distL2(Ω)(𝒜ε,𝒜0)≤Cεγ′ for γ′=(1+ρ/ν)−1. This result requires the homogenized nonlinearity f0(x,w) to be near a potential vector function f1(x,w)=∇wF(x,w) with scalar potential F. Both quantitative homogenization estimates are proved only for quasiperiodic dependence of f,g on the spatially rapidly oscillating variable x/ε. Moreover, the finitely many frequencies describing this quasiperiodic dependence are assumed to satisfy Diophantine conditions, as are familiar from small divisor problems in Kolmogorov–Arnold–Moser theory. Alternatively, the results hold if f, g admit a sufficiently regular divergence representation which describes their explicit spatial dependence. All results apply to, and are illustrated for, the case of FitzHugh–Nagumo systems with spatially rapidly oscillating quasiperiodic coefficients and inhomogeneities. For an earlier preprint version of the present paper see [6]. In the companion paper [7], based on analytic semigroup methods, similar results are obtained for the quantitative homogenization of solutions and invariant manifolds. Examples include homogenization of the Navier–Stokes system under periodic boundary conditions and for spatially rapidly oscillating quasiperiodic forces. For a recent extension to strongly continuous semigroups with an application to damped hyperbolic wave equations see [8].
Behaviour of the energy density associated to a Kelvin–Voight model in viscoelasticity
Authors: Petrini Milena 
Published: December 2024

We study an initial values problem related to a viscoelasticity model in a periodic medium, with oscillating data at t=0, looking for the homogenization limit of the associated energy density. This limit is determined in a specific case in which there is a constant proportionality between the elastic coefficient and the one in the viscosity part, where it follows an exponential decay in time of the energy density.
A new proof of the stability of renormalized solutions to elliptic equations with measure data
Authors: Malusa Annalisa 
Published: December 2024

One of the recent advances in the investigation on nonlinear elliptic equations with a measure as forcing term is a paper by G. Dal Maso, F. Murat, L. Orsina and A. Prignet in which it has been introduced the notion of renormalized solution to the problem [Formula: see text] Here Ω is a bounded open set of RN, N≥2, the operator is modelled on the p‐Laplacian, and μ is a Radon measure with bounded variation in Ω. The existence of a renormalized solution is obtained by approximation as a consequence of a stability result. We provide a new proof of this stability result, based on the properties of the truncations of the renormalized solutions. The approach, which does not need the strong convergence of the truncations of the solutions in the energy space, turns out to be easier and shorter than the original one.
Asymptotique des résonances pour une barrière de potentiel dégénérée
Authors: Baklouti Hamadi , Mnif Maher 
Published: December 2024

We study the resonances of semi-classical Schrödinger operator in the one-dimensional case. We consider potential with a degenerate maximum of quartic type. We first get a precise asymptotic expansion of the scattering matrix. Then we give the asymptotic expansion of resonances near the barrier maximum outside a ball of radius 𝒪(h4/3). Finally we describe the asymptotic expansion of resonances inside the ball. Résumé. Nous étudions les résonances de l'opérateur de Schrödinger semi-classique à une variable. Nous considérons le cas d'un potentiel présentant un maximum dégénéré de type quartique. Nous obtenons une asymptotique précise de la matrice de scattering. Nous donnons aussi l'asymptotique des résonances proche du sommet de la barrière mais restant en dehors d'un disque de rayon 𝒪(h4/3). Nous décrivons enfin le développement asymptotique des résonances à l'intérieur du disque.
Optimal decay rates of the energy of a hyperbolic–parabolic system coupled by an interface
Authors: Duyckaerts Thomas 
Published: December 2024

This work is dedicated to the study of a linear model arising in fluid-structure interaction and introduced by Rauch, Zhang and Zuazua. The system is formed of a heat and a wave equation, taking place in two distinct domains, and coupled by transmission conditions at the interface of the domains. Two different transmission conditions are considered. In both cases, when the interface geometrically controls the wave domain, we show the quick polynomial decay of the energy for solutions with smooth initial data, improving the rate of decay obtained by the previous authors. The polynomial stability is deduced from an optimal observability inequality conjectured in their work. The proof of this estimate mainly relies on a known generalized trace lemma for solutions of partial differential equations and the results of Bardos, Lebeau and Rauch on the control of the wave equation. Without the geometric condition, we show, using a Carleman inequality of Lebeau and Robbiano and an abstract theorem of N. Burq, a logarithmic decay for solution of the system with one of the two transmission conditions. This result improves the speed of decay obtained by Zhang and Zuazua, and is also optimal in some geometries.
An inverse inequality for some transport–diffusion equation. Application to the regional approximate controllability
Authors: Guerrero S. , Mercado A. , Osses A. 
Published: December 2024

In this paper we prove an inverse inequality for the parabolic equation [Formula: see text] in a bounded domain Ω⊂ $\mathbb{R}^{n}$ with Dirichlet boundary conditions. With the motivation of finding an estimate of g in terms on the trace of the solution in 𝒪×(0,T) for ε small, our approach consists in studying the convergence of the solutions of this equation to the solutions of some transport equation when ε→0, and then recover some inverse inequality from the properties of the last one. Under some conditions on the open sets ω, 𝒪 and the time T, we are able to prove that, in the particular case when g∈H01(ω) and it does not depend on time, we have: |g|L2(ω)≤C(|u|H1(0,T;L2(𝒪))+ε1/2|g|H1(ω)). On the other hand, we prove that this estimate implies a regional controllability result for the same equation but with a control acting in 𝒪×(0,T) through the right-hand side: for any fixed f∈L2(ω) , the L2-norm of the control needed to have |u(T)|ω−f|H−1(ω)≤γ remains bounded with respect to γ if ε≤Cγ2.
Discrete analogues of Laplace's approximation
Authors: Wang X.S. , Wong R. 
Published: December 2024

An asymptotic formula is derived for the sum In(1|q):=Σnk=0fn(k)qgn(k) as n→∞, where fn(k) and gn(k) are functions defined on nonnegative integers and 0<q<1. This formula is a discrete analogue of Laplace's approximation for integrals. Corresponding results are also provided for the more general sum In(z|q):=Σnk=0fn(k)qgn(k)zk which is typically an nth order polynomial. The results obtained are then used to give asymptotic formulas for the q−1-Hermite polynomial hn(x|q), the Stieltjes–Wigert polynomial Sn(x; q) and the q-Laguerre polynomial Lαn(x; q).
On inverse scattering in electromagnetic field in classical relativistic mechanics at high energies
Authors: Jollivet A. 
Published: December 2024

We consider the multidimensional Newton–Einstein equation in static electromagnetic field p·=F(x, x·), F(x, x·)=−∇V(x)+(1/c)B(x)x·, p=x·/\sqrt(1−|x·|2/c2)), p·=dp/dt, x·=dx/dt, x∈C1(R, Rd),  (*) where V∈C2(Rd, R), B(x) is the d×d real antisymmetric matrix with elements Bi,k(x)=∂/∂xi Ak(x)−∂/∂xk Ai(x), and |∂xjAi(x)|+|∂xjV(x)|≤β|j|(1+|x|)−(α+|j|) for x∈Rd, |j|≤2, i=1, …, d, and some α>1. We give estimates and asymptotics for scattering solutions and scattering data for the equation (*) for the case of small angle scattering. We show that at high energies the velocity valued component of the scattering operator uniquely determines the X-ray transforms P∇V and PBi,k for i, k=1, …, d, i≠k. Applying results on inversion of the X-ray transform P we obtain that for d≥2 the velocity valued component of the scattering operator at high energies uniquely determines (V, B). In addition we show that our high energy asymptotics found for the configuration valued component of the scattering operator doesn't determine uniquely V when d≥2 and B when d=2 but that it uniquely determines B when d≥3.
Consistency Conditions in Fuzzy Consumers Theory
Authors: Georgescu Irina 
Published: December 2024

This paper is concerned with consistency properties for fuzzy consumers. We introduce the consistency conditions Fα, Fβ, Fδ as fuzzy forms of Sen's properties alpha, beta and delta. Other consistency conditions are also studied: Fα2, Fβ(+), Fγ2 and FPI. The main results are: (1) A fuzzy consumer verifies Fα, Fβ if and only if the congruence axiom WFCA holds; (2) If h is a normal fuzzy consumer then Fδ holds if and only if the associated fuzzy preference relation R is quasi-transitive; (3) A fuzzy consumer is normal if and only if conditions Fα2, Fγ2 hold.
On Winning Conditions of High Borel Complexity in Pushdown	Games
Authors: Finkel Olivier 
Published: December 2024

In a recent paper [19, 20] Serre has presented some decidable winning conditions Ω _{A_1&rtri;&mldr;&rtri;A_n&rtri;A_{n+1}} of arbitrarily high finite Borel complexity for games on finite graphs or on pushdown graphs. We answer in this paper several questions which were raised by Serre in [19,20]. We study classes C _n (A), defined in [20], and show that these classes are included in the class of non-ambiguous context free ω-languages. Moreover from the study of a larger class C _n^&lambda; (A) we infer that the complements of languages in C _n (A) are also non-ambiguous context free ω-languages. We conclude the study of classes C _n (A) by showing that they are neither closed under union nor under intersection. We prove also that there exists pushdown games, equipped with winning conditions in the form Ω _{A_1&rtri;A_2} , where the winning sets are not deterministic context free languages, giving examples of winning sets which are non-deterministic non-ambiguous context free languages, inherently ambiguous context free languages, or even non context free languages.
A Genetic Hillclimbing Algorithm for the Optimal Linear	Arrangement Problem
Authors: Poranen Timo 
Published: December 2024

The optimal linear arrangement problem is defined as follows: given a graph G, find a linear ordering for the vertices of G on a line such that the sum of the edge lengths is minimized over all orderings. The problem is NP-complete and it has many applications in graph drawing and in VLSI circuit design. We introduce a genetic hillclimbing algorithm for the optimal linear arrangement problem. We compare the quality of the solutions and running times of our algorithm to those obtained by simulated annealing algorithms. To obtain comparable results, we use a benchmark graph suite for the problem. Our experiments show that there are graph classes for which the optimal linear arrangement problem can be efficiently approximated using our genetic hillclimbing algorithm but not using simulated annealing based algorithms. For hypercubes, binary trees and bipartite graphs, the solution quality is better and the running times are shorter than with simulated annealing algorithms. Also the average results are better. On the other hand, there also are graph classes for which simulated annealing algorithms work better.
Random Surfer with Back Step
Authors: Sydow Marcin 
Published: December 2024

The World Wide Web with its billions of hyperlinked documents is a huge and important resource of information. There is a necessity of filtering this information. Link analysis of the Web graph turned out to be a powerful tool for automatically identifying authoritative documents. One of the best examples is the PageRank algorithm used in Google [1] to rank search results. In this paper we extend the model underlying the PageRank algorithm by incorporating "back button" usage modeling in order to make the model less simplistic. We explain the existence and uniqueness of the ranking induced by the extended model. We also develop and implement an efficient approximation method for computing the novel ranking and present succesful experimental results made on 80- and 50- million page samples of the real Web.
Some Issues on Inner Structure of Information. A Definition of the	Decision Making Problem
Authors: Terlikowski Tomasz 
Published: December 2024

We continue the analysis of the notion of information in a two-stage decision process. In the previous work and in the present one, when examining specific concepts and types of information, we achieve a better understanding of mathematical contents of the notion. Only elementary set-theoretical tools are used. All the formalism previously introduced is largely used here; it is shortly recalled here. We try to formally approach several concepts: uncertainty, measurement and prediction, often applied in decision-making theory. Then, after introducing the notion of independent information, we attempt to formulate a precise definition of what we understand as decision making problem.
Characterizing DNA Bond Shapes Using Trajectories
Authors: Domaratzki Michael 
Published: December 2024

We consider the use of DNA trajectories to characterize DNA bond shapes. This is an extension of recent work on the bond-free properties of a language. Using a new definition of bondfreeness, we show that we can increase the types of DNA bond shapes which are expressible. This is motivated by the types of bond shapes frequently found in DNA computing. We examine the algebraic properties of sets of DNA trajectories. In particular, we consider rotation of trajectories and weakening of the bonding conditions expressed by a set of DNA trajectories. We also consider decidability results for bond-freeness with respect to our definition.
Effective Prediction of Web User Behaviour with User-Level	Models
Authors: Dembczyński Krzysztof , Kotłowski Wojciech , Sydow Marcin 
Published: December 2024

The paper concerns the problem of predicting behaviour of web users, based on real historical data which constitutes an important issue in web mining. The research reported here was conducted while the authors participated in the international ECML/ PKDD 2007 Discovery Challenge competition – Track 1. The results presented here ended up as the winning solution to the contest. We describe the contest tasks and the real industrial datasets concerning the recorded behaviour of sample of Polish Web users on which our experiments were performed. We present the whole extensive experimental process from the data preprocessing phase to exploratory analysis of the data to the experimental comparison and discussion of various prediction models which we examined. As we explain, our solution has low time and space complexity, scales well with large datasets and, at the same time, produces high-quality results.