bluuebunny/crossref_metadata_2025 huggingface dataset:
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.
Existence and continuity of uniform exponential attractors for a singular perturbation of a generalized Cahn–Hilliard equation
Authors: Bonfoh Ahmed
Published: December 2024

We consider a singular perturbation of a generalized Cahn–Hilliard equation based on constitutive equations derived by M. Gurtin. Compared to the classical Cahn–Hilliard equation, these models take into account the work of internal microforces and the anisotropy of the material. We prove the existence of exponential attractors and their convergence with respect to the parameter of perturbation ε when it goes to zero.
An existence result for Leray–Lions type operators with discontinuous coefficients
Authors: Gwiazda Piotr , Zatorska-Goldstein Anna
Published: December 2024

This note is concerned with an existence result for Leray–Lions quasilinear elliptic operator with discontinuous coefficients. The idea of the proof is based on compactness results for sequences of solutions to regularized problems obtained via compensated compactness, Young measures, and set-valued analysis tools.
Reduced equations for models of laminated materials in thin domains. II
Authors: DeVille R.E. Lee
Published: December 2024

In a companion paper, we considered a scalar wave equation on a thin, laminated, three‐dimensional plate. We showed that if the plate was sufficiently thin, then there exists a hierarchy of two‐dimensional equations whose dynamics model the dynamics of the full plate, each of which successively lengthens the time interval over which the approximation is valid. In certain cases, these approximating equations may formally be ill‐posed. In this paper, we consider modifications of the approximating equations which are themselves well‐posed, and which qualitatively afford the same approximation. We also present an algorithm to compute the coefficients in the approximating equations in closed form, and show numerical evidence that the estimates on the efficacy of the approximating equations are sharp.
Stable invariant manifolds for coupled Navier–Stokes and second-order wave systems
Authors: Leung Anthony W.
Published: December 2024

This article considers the dynamics of a coupled system of incompressible Navier–Stokes equations with second-order wave equations. The system may be used to approximate the interaction of ionized plasma particles with an electromagnetic field. Under appropriate assumptions and provided that the viscosity is sufficiently large, we prove the existence of an invariant manifold. Moreover, the manifold is attractive as t→+∞ for all close neighboring solutions.
Existence theorem for nonlinear difference equations
Authors: Immink G.K.
Published: December 2024

We prove an asymptotic existence theorem for locally analytic, nonlinear difference equations possessing a formal power series solution at ∞. The proof is based on a well-known contraction argument applied to Banach spaces of holomorphic functions on suitable unbounded domains of $\[$\mathbb{C}$$ . The main difficulty lies in the definition of appropriate domains for the case that the equation possesses a level “1+” in combination with lower levels.
A nonlocal energy functional in pseudo-plasticity
Authors: Licht C. , Michaille G.
Published: December 2024

We obtain a nonlocal functional as the variational limit of an integral functional associated with the strain energy of a pseudo-plastic material reinforced by a ε-periodic distribution of pseudo plastic fibers. We begin by studying separately the variational limit behavior, when ε goes to zero, of the structure made of the soft material without fibers, and of the structure constituted by the distribution of the small fibers. We show that the complete structure is, in the sense of the Γ-convergence, equivalent to a new homogeneous structure whose functional energy is the epigraphical sum of the limit integral functionals energies modeling each two previous structures.
Mixed amplitude solutions of semilinear systems of 3-dimensional wave equations
Authors: Takamura Hiroyuki
Published: December 2024

In this paper we study a global in time existence of classical solutions of semilinear systems of 3-dimensional wave equations. We see that one component of the global in time solution can be arbitrarily large if another component is small enough according to some balance of each amplitude. Also its sharpness is discussed. This is a specific nature of strongly coupled systems.
Asymptotic behavior of solutions to nonlinear parabolic equations with nonlocal terms
Authors: Zheng Songmu , Chipot Michel
Published: December 2024

In this paper the asymptotic behavior of the solutions, as time goes to infinity, to nonlinear parabolic equations with two classes of nonlocal terms is investigated. One of important features of our problems is that equilibria may be a continuum which is diffeomorphic to a piece of curve in R2.
On the homogenization of conservation laws with resonant oscillatory source
Authors: Amadori Debora
Published: December 2024

We consider the scalar conservation law with oscillatory, periodic source term [Formula: see text] and with initial data [Formula: see text] For possibly resonant initial data, we prove a corrector-type result for this problem, extending a previous one by E and Serre [Asymptotic Anal. 5 (1992), 311–316]: an asymptotic representation $\[$U(x,t,\tfrac{x}{\varepsilon})$$ is identified for the sequence uε(x,t), and the strong convergence of the asymptotic expansion is shown.
On internal and boundary layers with unbounded energy in thin shell theory. Hyperbolic characteristic and non-characteristic cases
Authors: Caillerie D. , Raoult A. , Sanchez-Palencia E.
Published: December 2024

We consider the system of equations of Koiter shell theory in a slightly simplified form, in the case when the limit (for small thickness) problem is hyperbolic, i.e., the principal curvatures of the middle surface are everywhere of opposite signs. Under loadings not belonging to the dual of the energy space of the limit problem, the energy of the solutions grows without limit as the thickness tends to zero and concentrates on internal or boundary layers. Two cases are considered, when the singular loadings are applied either along a non-characteristic or a characteristic curve. In both cases we define and prove the convergence to the leading order in the layers.
Global behavior of solutions of a reaction–diffusion equation with gradient absorption in unbounded domains
Authors: Bartier Jean-Philippe
Published: December 2024

We study the equation ∂tu−Δu=up−μ |∇u|qur in a general domain (bounded or not). Many results have been established in the case r=0, and we will generalize some properties. If q≥1 and q+r≥p, we will show that there is a strong connection between the finiteness of the inradius of Ω (or the Poincaré inequality) and the global existence of the solutions. More precisely if the inradius of Ω is finite, then the solutions u are global and if moreover μ is large enough, the solutions decay exponentially to zero. Conversely, if it is infinite, there always exists unbounded solution. Other qualitative results are also obtained.
Controllability results for some nonlinear coupled parabolic systems by one control force
Authors: González-Burgos Manuel , Pérez-García Rosario
Published: December 2024

In this paper, we present new controllability results for some nonlinear coupled parabolic systems considered in a bounded domain Ω of $\[$\mathbb{R}$$ N (with N≥1 being arbitrary) when the control force acts on a unique equation of the system through an arbitrarily small open set ω⊂Ω. As a model example, we consider a nonlinear phase field system with certain superlinear nonlinearities and prove the null controllability, the exact controllability to the trajectories and the approximate controllability of the model. The crucial point in this paper is the new strategy developed to deal with the null controllability of linear coupled parabolic systems by a unique control force. Global Carleman estimates and the parabolic regularizing effect of the problem are used.
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.
Semiclassical limit for nonlinear Schrödinger equation with potential. II
Authors: Keraani Sahbi
Published: December 2024

This paper is dedicated to the semiclassical limit of the nonlinear focusing Schrödinger equation (NLS) with a potential with initial data in the form $Q(\frac{x-x_{0}}{\varepsilon })\,\mathrm{e}^{\mathrm{i}\frac{x\cdot\xi_{0}}{\varepsilon }}$ , where Q is the ground state of the associated unscaled elliptic problem. Using a refined version of the method introduced by Bronski and Jerrard [Math. Res. Lett. 7(2–3) (2000), 329–342], we prove that, up to a time-dependent phase shift, the initial shape is conserved with parameters that are transported by the classical flow.
Internal null-controllability for a structurally damped beam equation
Authors: Edward Julian , Tebou Louis
Published: December 2024

In this paper we study the null-controllability of a beam equation with hinged ends and structural damping, the damping depending on a positive parameter. We prove that this system is exactly null controllable in arbitrarily small time. This result is proven using a combination of Ingham-type inequalities, adapted for complex frequencies, and exponential decay on various frequency bands. We then let the damping parameter tend to zero and we recover an earlier null-controllability result for the undamped beam equation.
Modelization of a split in a ferromagnetic body by an equivalent boundary condition: Part II
Authors: Santugini-Repiquet Kévin
Published: December 2024

We continue the study of equivalent boundary conditions in ferromagnetic domains crossed by a thin split. In this second part, we add nonhomogeneous boundary conditions arising from interactions such as surface anisotropy and super-exchange. We expand the problem up to the first order and establish equivalent boundary conditions in presence of surface anisotropy and super-exchange. In particular, the well-posedness of the expansion problem with equivalent boundary condition and the convergence in some meaning of the expansion are proven.
Asymptotic modeling of thin curved martensitic films
Authors: Le Dret Hervé , Zorgati Hamdi
Published: December 2024

We consider a thin curved film made of a martensitic material. The behavior of the film is governed by a free energy composed of a bulk energy term and an interfacial energy term. We show that the minimizers of the free energy converge to the minimizers of an energy depending on a two-dimensional deformation and one Cosserat vector field when the thickness of the curved film goes to zero using $\varGamma$ -convergence arguments.
Liouville–Green asymptotics for almost-diagonal second-order matrix differential equations
Authors: Spigler Renato , Vianello Marco
Published: December 2024

A WKB (or Liouville–Green) asymptotic approximation theory is developed for the class of linear second-order matrix differential equations Y″=(D(t)+G(t))Y, on [a,+∞), where D(t) is a nonsingular diagonal matrix. A basis for the right-module of its solutions can be represented explicitly, and precise computable bounds for the error terms involved are given. The double asymptotic nature with respect to both, t and some parameters that might affect the matrix coefficient, is shown. Examples and applications are given.
Two-scale asymptotics for non-local effects in composites with highly anisotropic fibres
Authors: Cherednichenko Kirill D.
Published: December 2024

The problem of periodic homogenisation for a conducting two-phase composite exhibiting non-locality in the overall behaviour is considered. The matrix is isotropic and its conductivity is constant, while the fibre-shaped inclusions are assumed to be anisotropic, with high contrast between conductivities along the fibres and in the transverse directions. The contrast is set to correspond to the so-called double-porosity scaling, which is of special interest. A full two-scale asymptotic expansion for the solution is constructed and rigorously justified via appropriate error estimates. An example of the non-local homogenised operator in the case of fibres with circular cross-sections is given.
Entropy boundary layers
Authors: Sueur Franck
Published: December 2024

We consider the Euler system of compressible and entropic gaz dynamics in a bounded open domain of $\mathbb {R}$ d with wall boundary condition. We prove the existence and the stability of families of solutions which correspond to a ground state plus a large entropy boundary layer. The ground state is a solution of the Euler system which satisfies some explicit additional conditions on the boundary. These conditions are used in a reduction of the system. We construct BKW expansions at all order. The profile problems are linear thanks to a transparency property. We prove the stability of these expansions by proving ε-conormal estimates for a characteristic boundary value problem.
On the exponential decay of solutions in one-dimensional generalized porous-thermo-elasticity
Authors: Magaña A. , Quintanilla R.
Published: December 2024

In this paper we investigate the asymptotic behavior of the solutions of the one-dimensional generalized porous-thermo-elasticity problem. First, we prove that when only thermal damping is present the decay of solutions is slow (generically). Second, we show that if the porous dissipation is also present the decay of the solutions is controlled by an exponential.
Sensitivity analysis with respect to a local perturbation of the material property
Authors: Amstutz Samuel
Published: December 2024

In the present work, the notion of topological sensitivity is extended to the case of a local perturbation of the properties of the material constitutive of the domain. As a model example, we consider the problem −div(αεA∇uε)+βεuε=Fε in two and three dimensions, where A is a symmetric positive definite matrix and αε,βε,Fε are functions whose values inside a small subdomain ωε are different from those of the background medium. An adjoint method is used to determine an asymptotic expansion of a given criterion when the diameter of ωε goes to zero.
A rigorous asymptotic expansion for a control problem in a thin domain
Authors: Casado-Díaz J. , Couce-Calvo J. , Martín-Gómez J.D.
Published: December 2024

We study the asymptotic behavior of a control problem for a quadratic cost functional and a linear elliptic equation in a thin domain of wide ε. For each n∈N, we obtain an asymptotic expansion of the control, the direct state, and the adjoint state, giving an approximation of order εn+1. Since this is a singular perturbation problem, one of the main difficulties is the existence of boundary layers, and then the appearance of boundary terms in the asymptotic expansions. We show how this type of problems can be solved by an iterative scheme, which reduces the question to obtain an approximation of order ε. To carry out this procedure, the problem needs to be reformulated in such a way that its structure does not change with the iterates.
Stability of abstract linear semigroups arising from heat conduction with memory
Authors: Chepyzhov Vladimir V. , Mainini Edoardo , Pata Vittorino
Published: December 2024

We establish some decay properties of the semigroup generated by a linear integro-differential equation in a Hilbert space, which is an abstract version of the equation ut(t)−βΔu(t)−∫0∞k(s)Δu(t−s) ds=0 describing hereditary heat conduction.
Spectral shift function for the Stark operator in the large coupling constant limit
Authors: Pushnitski A. , Sloushch V.
Published: December 2024

Let H be the Stark operator in $\mathbb{R}^{3}$ and let V=V(x) be a non-negative potential which decays at infinity as |x|−l for a sufficiently large l>0. The spectral shift function for the pair of operators H+tV, H is studied in the asymptotic regime t→∞. The leading term of the asymptotics is obtained; the result is in agreement with the phase space volume considerations.
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.
Global attractor for the 1-D thin film equation
Authors: Wu Hao , Zheng Songmu
Published: December 2024

This paper is concerned with a fourth-order degenerate parabolic equation, namely the thin film equation, in one space dimension which describes the dewetting phenomenon of a thin film under the long-range attractive force and the short-range stabilizing effect of Born repulsion. The existence of global attractor is proved.
Time evolution of quantum resonance states
Authors: Klein M. , Rama J. , Wüst R.
Published: December 2024

Let H0 be self-adjoint with E0 a possibly degenerate eigenvalue embedded in the continuous spectrum σc(H0) and ψ0 a normalized eigenfunction. For a certain class of perturbations W and H=H0+W we investigate the asymptotics of the (naive) resonance state e−itHψ0 in the limit W→0. This amplifies previous results of Merkli and Sigal.
Deduction by scaling: A unified approach to classic plate and rod theories
Authors: Miara B. , Podio-Guidugli P.
Published: December 2024

A method of formal scaling is presented that allows for a unified deduction from three-dimensional linear elasticity of the equations of structural mechanics, such as Reissner–Mindlin's equations for shearable plates and Timoshenko's equations for shearable rods. This method is based on the requirement that a scaled energy functional that may include second-gradient terms stay bounded in the limit of vanishing thickness.
On the long-time stability of the implicit Euler scheme for the 2D space-periodic Navier–Stokes equations
Authors: Tone Florentina
Published: December 2024

In this article we discretize the two-dimensional space-periodic Navier–Stokes equations in time using the implicit Euler scheme and, with the aid of the discrete Gronwall lemma and the uniform discrete lemma, we prove that the scheme is H2-uniformly stable in time. Moreover, in a final remark, we describe how the above result can be extended to show that the implicit Euler scheme is uniformly stable with respect to the H3-norm, for all time.
Total versus single point blow-up in heat equations with coupled localized sources
Authors: Zheng Sining , Wang Jinhuan
Published: December 2024

This paper considers heat equations with local and coupled localized sources subject to null Dirichlet boundary conditions. The behavior of solutions depends on the interactions among the local and localized sources as well as the diffusions with the null boundary conditions in the model. The aim of the paper is to distinguish total and single point blow-up for the non-global solutions. In addition, simultaneous versus non-simultaneous blow-up of solutions under different dominations are determined also with four possible simultaneous blow-up rates.
Stabilisation d'ondes électromagnétiques dans un domaine extérieur 2D
Authors: Moulahi Ammar
Published: December 2024

On étudie le problème de stabilisation des équations de Maxwell à l'extérieur d'un obstacle borné en dimension deux. On développe certains résultats concernant l'équation des ondes amorties de type Neumann et sous la condition de contrôle géométrique extérieur, on obtient le comportement des solutions pour des systèmes de Maxwell en grand temps.
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.
The quasineutral limit in the quantum drift-diffusion equations
Authors: Jüngel Ansgar , Violet Ingrid
Published: December 2024

The quasineutral limit in the transient quantum drift-diffusion equations in one space dimension is rigorously proved. The model consists of a fourth-order parabolic equation for the electron density, including the quantum Bohm potential, coupled to the Poisson equation for the electrostatic potential. The equations are supplemented with Dirichlet–Neumann boundary conditions. For the proof uniform a priori bounds for the solutions of the semi-discretized equations are derived from so-called entropy functionals. The drift term involving the electrostatic potential is estimated by proving a new bound for the electric energy. Since the electrostatic potential is not an admissible test function, an auxiliary test function has been carefully constructed.
On the asymptotic behavior of solutions to nonlinear ordinary differential equations
Authors: Agarwal Ravi P. , Djebali Smail , Moussaoui Toufik , Mustafa Octavian G. , Rogovchenko Yuri V.
Published: December 2024

We discuss a number of issues important for the asymptotic integration of ordinary differential equations. After developing the tools required for application of the fixed point theory in the investigation, we present some general results about the long-time behavior of solutions of n-th order nonlinear differential equations with an emphasis on the existence of polynomial-like solutions, the asymptotic representation for the derivatives and the effect of perturbations upon the asymptotic behavior of solutions.
On the perfect superconducting solution for a generalized Ginzburg–Landau equation
Authors: Kachmar Ayman
Published: December 2024

We study a generalized Ginzburg–Landau equation that models a sample formed of a superconducting/normal junction and which is not submitted to an applied magnetic field. We prove the existence of a unique positive (and bounded) solution of this equation. In the particular case when the domain is the entire plane, we determine the explicit expression of the solution (and we find that it satisfies a Robin (de Gennes) boundary condition on the boundary of the superconducting side). Using the result of the entire plane, we determine for the case of general domains, the asymptotic behavior of the solution for large values of the Ginzburg–Landau parameter. The main tools are Hopf's Lemma, the Strong Maximum Principle, elliptic estimates and Agmon type estimates.
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).
Large time behavior of the a priori bounds for the solutions to the spatially homogeneous Boltzmann equations with soft potentials
Authors: Desvillettes Laurent , Mouhot Clément
Published: December 2024

We consider the spatially homogeneous Boltzmann equation for regularized soft potentials and Grad's angular cutoff. We prove that uniform (in time) bounds in L1((1+|v|s) dv) and Hk norms, s, k≥0 hold for its solution. The proof is based on the mixture of estimates of polynomial growth in time of those norms together with the quantitative results of relaxation to equilibrium in L1 obtained by the so-called “entropy–entropy production” method in the context of dissipative systems with slowly growing a priori bounds (G. Toscani and C. Villani, J. Statist. Phys. 98 (2000), 1279–1309).
Semi-classical trace formula, isochronous case. Application to conservative systems
Authors: Cassanas Roch
Published: December 2024

Under conditions of clean flow we compute the leading term in the STF when the set of periods of the energy surface is discrete. Comparing to the case of non-degenerate periodic orbits, we obtain a supplementary term which is given in terms of the linearized flow. As particular cases, we give a STF for quadratic Hamiltonians and we obtain the Berry–Tabor formula for integrable systems. For conservative systems (i.e. systems with several first integrals), we give practical conditions to get a clean flow and interpret the leading term of the STF for a compact symmetry. We give several examples to illustrate our computation.
On the stability of normal states for a generalized Ginzburg–Landau model
Authors: Kachmar Ayman
Published: December 2024

We formulate a spectral problem related to the onset of superconductivity for a generalized Ginzburg–Landau model, where the order parameter and the magnetic potential are defined in the whole space. This model is devoted to the ‘proximity effect’ for a superconducting sample surrounded by a normal material. In the regime when the Ginzburg–Landau parameter (of the superconducting material) is large, we estimate the critical applied magnetic field for which the normal state will lose its stability, a result that has some roots in the physical literature. In some asymptotic situations, we recover results related to the ‘standard’ Ginzburg–Landau model, where we mention in particular the two-term expansion for the upper critical field obtained by Helffer–Pan.
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.
Motion of interfaces by an Allen–Cahn type equation with multiple-well potentials
Authors: Ohtsuka Takeshi
Published: December 2024

We consider the singular limit of an Allen–Cahn type equation with a periodic nonlinear term. In this case we can find a multi-step internal transition layer when the interface thickness parameter tends to zero. We give a rigorous proof of the convergence of internal transition layers to interfaces which move under a mean curvature flow with a driving force, even if no traveling wave solutions connecting two nonadjacent stable equilibria exist.
Word Problem in Distributive Magmas
Authors: Pallo Jean Marcel
Published: December 2024

This paper shows that among the transformations which have words formed with three operators and four variables correspond to words formed with two operators and three variables, distributivity clone verifies some remarkable properties. Indeed, it is a confluent and noetherian relation which satisfies an inductive comparison theorem. One can deduce a computer – programmable algorithm which makes it possible to solve the word problem in a set of variables with two associative operators one of which is distributive on the right with respect to the other, i.e. to decide whether or not two words composed of variables and operators can be proved equal as a consequence of the identities of associativity and distributivity satisfied by these operators.
The PMA and Relativizing Minimal Change for Action Update
Authors: Doherty Patrick , Łukaszewicz Witold , Madalińska-Bugaj Ewa
Published: December 2024

Recently, a great deal of progress has been made using nonmonotonic temporal logics to formalize reasoning about action and change. In particular, much focus has been placed on the proper representation of non-deterministic actions and the indirect effects of actions. For the latter the use of causal or fluent dependency rule approaches has been dominant. Although much recent effort has also been spent applying the belief revision/update (BR/U) approach to the action and change domain, there has been less progress in dealing with nondeterministic update and indirect effects represented as integrity constraints. We demonstrate that much is to be gained by cross-fertilization between the two paradigms and we show this in the following manner. We first propose a generalization of the PMA, called the modified MPMA which uses intuitions from the TL paradigm to permit representation of nondeterministic update and the use of integrity constraints interpreted as causal or fluent dependency rules. We provide several syntactic characterizations of MPMA, one of which is in terms of a simple temporal logic and provide a representation theorem showing equivalence between the two. In constructing the MPMA, we discovered a syntactic anomaly which we call the {\em redundant atom anomaly} that many TL approaches suffer from. We provide a method for avoiding the problem which is equally applicable across paradigms. We also describe a syntactic characterization of MPMA in terms of Dijkstra semantics. We set up a framework for future generalization of the BR/U approach and conclude with a formal comparison of related approaches.
Approximating a Shortest Watchman Route
Authors: Nilsson Bengt J.
Published: December 2024

We present a fast algorithm for computing a watchman route in a simple polygon that is at most a constant factor longer than the shortest watchman route. The algorithm runs in O(n log n) time as compared to the best known algorithm that computes a shortest watchman route which runs in O(n^6) time.
On Different Models for Packet Flow in Multistage Interconnection	Networks
Authors: Dietzfelbinger Martin , Gambin Anna , Lasota Sławomir
Published: December 2024

Multistage interconnection networks (MINs) have a number of applications in many areas, for example in parallel computing systems or high-speed communication networks. In the paper we define Markov chains describing several models of packet flow through the buffered MIN with a butterfly interconnection structure and 2×2 switching elements. We develop a notation together with a mathematical framework enabling to prove certain results relating the models. Moreover, we show that all considered Markov chains are ergodic and discuss relationships between stationary distributions. The important novelty is that our approach is compositional, which allows to keep the complexity of description of a very complicated network's behaviour on a reasonable and tractable level. Considerations are mostly independent of specific network topology and routing protocol, hence we expect our method to be applicable also in other contexts for stochastic models of massively parallel systems.
Computability in Type-2 Objects with Well-Behaved Type-1 Oracles	is p-Normal
Authors: Tourlakis George
Published: December 2024

We show that computability in a type-2 object is p-normal if type-1 partial inputs are computed by ``well-behaved oracles''.
Non-Clausal Reasoning with Definite Theories
Authors: Stachniak Zbigniew
Published: December 2024

In this paper we propose a general-purpose first-order automated reasoning framework based on the notion of a definite formula and on a non-clausal variant of SLD-resolution. This framework provides a universal Horn clause-like representation of knowledge for classical as well as a range of non-classical first-order logics. It provides a resolution-style method for automated reasoning with theories of definite formulas.
The Topological Structures of Membrane Computing
Authors: Giavitto Jean-Louis , Michel Olivier
Published: December 2024

In its initial presentation, the P system formalism describes the topology of the membranes as a set of nested regions. In this paper, we present an algebraic structure developped in combinatorial topology that can be used to describe finer adjacency relationships between membranes. Using an appropriate abstract setting, this technical device enables us to reformulate also the computation within a membrane and proposes a unified view on several computational mechanisms initially inspired by biological processes. These theoretical tools are instantiated in MGS, an experimental programming language handling various types of membrane structures in a homogeneous and uniform syntax.
Completeness of Timed μCRL
Authors: Reniers Michel , Groote J.F , van der Zwaag M.B. , van Wamel J.
Published: December 2024

In [25] a straightforward extension of the process algebra μCRL was proposed to explicitly deal with time. The process algebra μCRL has been especially designed to deal with data in a process algebraic context. Using the features for data, only a minor extension of the language was needed to obtain a very expressive variant of time. But [25] contains syntax, operational semantics and axioms characterising timed μCRL. It did not contain an in depth analysis of theory of timed μCRL. This paper fills this gap, by providing soundness and completeness results. The main tool to establish these is a mapping of timed to untimed μCRL and employing the completeness results obtained for untimed μCRL.
Residual Finite State Automata
Authors: Denis François , Lemay Aurélien , Terlutte Alain
Published: December 2024

We define a new variety of Nondeterministic Finite Automata (NFA): a Residual Finite State Automaton (RFSA) is an NFA all the states of which define residual languages of the language L that it recognizes; a residual language according to a word u is the set of words v such that uv is in L. We prove that every regular language is recognized by a unique (canonical) RFSA which has a minimal number of states and a maximal number of transitions. Canonical RFSAs are based on the notion of prime residual languages, i.e. that are not the union of other residual languages. We provide an algorithmic construction of the canonical RFSA similar to the subset construction used to build the minimal DFA from a given NFA. We study the size of canonical RFSAs and the complexity of our constructions.
Comparing Refinements for Failure and Bisimulation Semantics
Authors: Eshuis Rik , Fokkinga Maarten M.
Published: December 2024

Refinement in bisimulation semantics is defined differently from refinement in failure semantics: in bisimulation semantics refinement is based on simulations between labelled transition systems, whereas in failure semantics refinement is based on inclusions between failure systems. There exist however pairs of refinements, for bisimulation and failure semantics respectively, that have almost the same properties. Furthermore, each refinement in bisimulation semantics implies its counterpart in failure semantics, and conversely each refinement in failure semantics implies its counterpart in bisimulation semantics defined on the canonical form of the compared processes.
Object Oriented Database with Authorization Policies
Authors: Bai Yun , Varadharajan Vijay
Published: December 2024

Authorization specification in object oriented databases is being increasingly investigated recently by many researchers [4,5,7,9,10]. However, most of the work todate suffers from a lack of formal logic semantics to characterize different types of inheritance properties of authorization policies among complex data objects. This paper is to address this issue from a formal logic point of view. In particular, we propose a logic language that has a clear and declarative semantics to specify the structural features of object oriented databases and authorizations associated with complex data objects in databases. Our formalization characterizes the model-theoretic semantics of object oriented databases and authorizations associated with them. A direct advantage of this approach is that we can formally specify and reason about authorizations on data objects without loosing inheritance and abstraction features of object oriented databases.
Making revision reversible: an approach based on polynomials
Authors: Benferhat Salem , Dubois Didier , Lagrue Sylvain , Papini Odile
Published: December 2024

This paper deals with iterated belief change and proposes a drastic revision rule that modifies a plausibility ordering of interpretations in such a way that any world where the input observation holds is more plausible that any world where it does not. This change rule makes sense in a dynamic context where observations are received, and the newer observations are considered more plausible than older ones. It is shown how to encode an epistemic state using polynomials equipped with the lexicographic ordering. This encoding makes it very easy to implement and iterate the revision rule using simple operations on these polynomials. Moreover, polynomials allow to keep track of the sequence of observations. Lastly, it is shown how to efficiently compute the revision rule at the syntactical level, when the epistemic state is concisely represented by a prioritized belief base. Our revision rule is the most drastic one can think of, in accordance with Darwiche and Pearl's principles, and thus contrasts with the minimal change rule called natural belief revision. The paper also shows how to obtain the reversibility of Boutilier's natural belief revision and possibilistic revision using polynomials.
Approximate Entropy Reducts
Authors: Ślezak Dominik
Published: December 2024

We use information entropy measure to extend the rough set based notion of a reduct. We introduce the Approximate Entropy Reduction Principle (AERP). It states that any simplification (reduction of attributes) in the decision model, which approximately preserves its conditional entropy (the measure of inconsistency of defining decision by conditional attributes) should be performed to decrease its prior entropy (the measure of the model's complexity). We show NP-hardness of optimization tasks concerning application of various modifications of AERP to data analysis.
Integrating Forms of Interaction in a Distributed Model
Authors: Bandini Stefania , Simone Carla
Published: December 2024

The main aim of this paper is to present the formal description of the Multilayered Reaction-Diffusion Machine (MRDM, an extension of a previously introduced RDM, Reaction-Diffusion Machine) which can be seen as a generalization of Cellular Automata since it relaxes some constraints on uniformity, locality and closure. The MRDM offers a formal and computational environment where to describe, represent and simulate coordination models which explicitly require spatial features to be considered and integrates different forms of interaction. The paper is divided into two main parts. In the first one, the formal description of the MRDM is presented. In the second part the MRDM is put in relation with deterministic Turing machines; moreover we show how the MRDM, under determined constraints, collapses on a traditional CA.
Asynchronous Circuits, Communicating Processes, and Muller	Automaton
Authors: Redziejowski Roman R.
Published: December 2024

A finite-state model of communicating processes is presented alongside with the Muller-Bartky model of asynchronous circuits. The purpose of such presentation is to expose a close similarity of these models, at a level of abstraction much lower than the Muller automaton.
Semirings in Operations Research and Computer Science: More	Algebra
Authors: Rudeanu Sergiu , Vaida Dragoş
Published: December 2024

We undertake an axiomatic study of certain semirings and related structures that occur in operations research and computer science. We focus on the properties A,I,U,G,Z,L that have been used in the algebraic study of path problems in graphs and prove that the only implications linking the above properties are essentially those already known. On the other hand we extend those implications to the framework of left and right variants of A,I,U,G,Z,L, and we also prove two embedding theorems. Further generalizations refer mainly to semiring-like algebras with a partially defined addition, which is needed in semantics. As suggested by idempotency (I) and absorption (A), we also examine in some detail the connections between semirings and distributive lattices, which yield new systems of axioms for the latter.
Located Actions in Process Algebra with Timing
Authors: Bergstra Jan A. , Middelburg Cornelis A.
Published: December 2024

We propose a process algebra obtained by adapting the process algebra with continuous relative timing from Baeten and Middelburg [Process Algebra with Timing, Springer, 2002, Chap. 4] to spatially located actions. This process algebra makes it possible to deal with the behaviour of systems with a known time-dependent spatial distribution, such as protocols transmitting data via a mobile intermediate station. It is a reformulation of the real space process algebra from Baeten and Bergstra [Formal Aspects of Computing, 5, 1993, 481–529] in a setting with urgent actions. This leads to many simplifications.
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.
Enhanced of Key Agreement Protocols Resistant to a	Denial-of-Service Attack
Authors: Hwang Min-Shiang , Lo Jung-Wen , Liu Chia-Hsin
Published: December 2024

The denial-of-service attack, a malicious client executes a key agreement protocol simultaneously many times to exhaust the server's memory or computing resource and to interfere the honest client connecting with the server. It is a serious problem in the key agreement protocol. A key agreement protocol which resists to the storage-exhaustion and the CPU-exhaustion attack was firstly proposed by Hiros-Matsuura. However, their protocol is not efficient enough during the weak key validation. Our proposed protocol modifies the weak key validation and avoids the unnecessary heavy computation to enhance the resistance of the denial-of-service attack. The most important contributions of our protocol are not only efficiently to resist CPU-exhaustion and memory-exhaustion attacks but also prevent bandwidth consumption.
A Timed Extension for ALTARICA
Authors: Cassez Franck , Pagetti Claire , Roux Olivier
Published: December 2024

In this paper we present a timed extension of the ALTARICA formalism. Following previous works, we first extend the semantics of ALTARICA with time and define timed components and timed nodes. Moreover we lift the priority features of ALTARICA to the timed case. We obtain a timed version of ALTARICA, called ALTARICA. Finally we give a translation of a ALTARICA specification into a usual timed automaton. These are the semantic foundations of a high-level hierarchical language for the specification of timed systems.
Approximation Algorithms for MAX-BISECTION on Low Degree Regular	Graphs
Authors: Karpinski Marek , Kowaluk Miroslaw , Lingas Andrzej
Published: December 2024

The max-bisection problem is to find a partition of the vertices of a graph into two equal size subsets that maximizes the number of edges with endpoints in both subsets. We obtain new improved approximation ratios for the max-bisection problem on the low degree k-regular graphs for 3≤k≤8, by deriving some improved transformations from a maximum cut into a maximum bisection. In the case of three regular graphs we obtain an approximation ratio of 0.854, and in the case of four and five regular graphs, approximation ratios of 0.805, and 0.812, respectively.