bluuebunny/crossref_metadata_2025 huggingface dataset:
Constant‐sign solutions of a system of integral equations: The semipositone and singular case
Authors: Agarwal Ravi P. , O'Regan Donal , Wong Patricia J.Y.
Published: December 2024

We consider the following system of integral equations ui(t)=μ∫01gi(t,s)f(s,u1(s),u2(s),…,un(s)) ds, t∈[0,1], 1≤i≤n, where μ>0, the function f may take negative values and f(·,u1,u2,…,un) may be singular at uj=0, j∈{1,2,…,n}. Our aim is to establish criteria such that the above system has a constant‐sign solution. To illustrate the generality of the results obtained, application to a well known boundary value problem is included. We also extend the above problem to that on the half‐line [0,∞) ui(t)=μ∫0∞gi(t,s)f(s,u1(s),u2(s),…,un(s)) ds, t∈[0,∞), 1≤i≤n.
On the Ruelle–Perron–Frobenius theorem
Authors: Stoyanov Luchezar
Published: December 2024

A comprehensive version of the Ruelle–Perron–Frobenius theorem is considered with explicit estimates of the spectral radius of the Ruelle transfer operator and various other quantities related to spectral properties of this operator.
The total variation flow with nonlinear boundary conditions
Authors: Andreu F. , Mazón J.M. , Moll J.S.
Published: December 2024

We study existence, uniqueness and the asymptotic behaviour of the entropy solutions for the Total Variation Flow with nonlinear boundary conditions. To prove the existence we use the nonlinear semigroup theory and for the uniqueness we apply Kruzhkov's method of doubling variables both in space and in time. We show that when the initial data are in L2, the entropy solutions are strong solutions. Respect to the asymptotic behaviour, we show that entropy solutions stabilize as t→∞ by converging to a constant function.
From Navier–Stokes equations to shallow waters with viscosity by asymptotic analysis
Authors: Rodríguez José M. , Taboada-Vázquez Raquel
Published: December 2024

In this paper, we study the Navier–Stokes equations in a domain with small depth. With this aim, we introduce a small adimensional parameter ε related to the depth. First we make a change of variable to a domain independent of ε and then we use asymptotic analysis to study what happens when ε becomes small. In this way we obtain a model for ε small that, after coming back to the original domain and without making a priori assumptions about velocity or pressure behavior, gives us a shallow water model including a new diffusion term.
Some existence's results for noncoercive “1-Laplacian” operator
Authors: Demengel Françoise
Published: December 2024

In this paper we study necessary and sufficient conditions on f and the first eigenfunctions for the 1-Laplacian, for equations of the form [Formula: see text] when q≤N/(N−1) and λ≥λ1, λ1 is the first eigenvalue for the 1-Laplacian.
Two-scale homogenization of a hydrodynamic Elrod–Adams model
Authors: Bayada G. , Martin S. , Vázquez C.
Published: December 2024

The present paper deals with the homogenization of a lubrication problem, via two-scale convergence and periodic unfolding techniques. We study in particular the Elrod–Adams problem with highly oscillating roughness effects.
Attractors for reaction–diffusion equations in $\[$\mathbb{R}^{N}$$ with continuous nonlinearity
Authors: Morillas Francisco , Valero José
Published: December 2024

In this paper we prove the existence of a compact global attractor for a reaction–diffusion equation on $\[$\mathbb{R}^{N}$$ . We do not assume that the nonlinear term is differentiable (just continuous) and, also, we do not guarantee the uniqueness of solutions of the Cauchy problem. Besides, the growth and dissipative conditions are different from the ones used in previous papers on the topic. An application is given to the Fitz–Hugh–Nagumo system, which models the transmission of signals across axons.
Singular optimal control: A linear 1-D parabolic–hyperbolic example
Authors: Coron J.-M. , Guerrero S.
Published: December 2024

We consider the problem of the null controllability of a family of 1-D linear control parabolic equations depending on two parameters, namely the viscosity and the coefficient of the transport term. We study the dependence, with respect to these parameters and the time of controllability, of the norm of the optimal controls. In particular we give estimates on the optimal control as the viscosity tends to 0.
Asymptotics for the travelling waves in the Gross–Pitaevskii equation
Authors: Gravejat Philippe
Published: December 2024

We investigate the asymptotic behaviour of the subsonic travelling waves of finite energy in the Gross–Pitaevskii equation in dimension larger than two. In particular, we give their first-order asymptotics in the case they are axisymmetric, and link it to their energy and momentum.
On a nonlinear coupled system for the beam equations with memory in noncylindrical domains
Authors: Santos M.L. , Rocha M.P.C. , Ferreira J.
Published: December 2024

We prove the exponential decay in the case n>2 as time goes to infinity of regular solutions for the nonlinear coupled system of beam equations with memory and weak damping

utt+Δ2u−Δu+∫t0g1(t−s)Δu(s) ds+αut+h(u−v)=0  in $\[$\widehat{Q}$$ ,

vtt+Δ2v−Δv+∫t0g2(t−s)Δv(s) ds+αvt−h(u−v)=0  in $\[$\widehat{Q}$$

in a noncylindrical domains of $\[$\mathbb{R}^{n+1}$$ (n≥1) under suitable hypothesis on the scalar functions g1, g2 and h where α is a positive constant. Observe that the coupled is nonlinear and we worked directly in the noncylindrical domain that presents some technical difficulties turning the interesting problem. We establish existence and uniqueness of regular solutions for any n≥1.
Compensated compactness for homogenization and reduction of dimension: The case of elastic laminates
Authors: Gustafsson Björn , Mossino Jacqueline
Published: December 2024

The aim of this paper is to extend, to the linear elasticity system, the asymptotic analysis by compensated compactness previously developed by the authors for the linear diffusion equation. For simplicity, we restrict ourselves to stratified media. In the case of sole homogenization we recover the classical result of W.H. Mc Connel, deriving explicitly the effective elasticity tensor for stratified media. Here we give a new proof of his result, based on compensated compactness and on a technique of decomposing matrices. As for the case of simultaneous homogenization and reduction of dimension, we perform the asymptotic analysis, as the thickness tends to zero, of a three-dimensional laminated thin plate having an anisotropic, rapidly oscillating elasticity tensor. The limit problem is presented in three different ways, the final formulation being a fourth-order problem on the two-dimensional plate, with explicitly given elasticity tensors and effective source terms.
Nonintegrable perturbations of scalar viscous shock profiles
Authors: Engelberg Shlomo , Schochet Steven
Published: December 2024

Solutions of scalar viscous conservation laws whose initial data are bounded and tend at x=±∞ to values that may be connected by a shock profile are shown to converge in L∞ to a time-dependent translation of that profile. Unlike the standard theory, the initial data is not restricted to be an L1 perturbation of the shock profile, and the translation may not be linear in time. Estimates for the translation are obtained.
Asymptotics of a non-planar rod in non-linear elasticity
Authors: Pideri C. , Seppecher P.
Published: December 2024

We study the asymptotic behavior of a non-linear elastic material lying in a thin neighborhood of a non-planar line when the diameter of the section tends to zero. We first estimate the rigidity constant in such a domain then we prove the convergence of the three-dimensional model to a one-dimensional model. This convergence is established in the framework of $\varGamma $ -convergence. The resulting model is the one classically used in mechanics. It corresponds to a non-extensional line subjected to flexion and torsion. The torsion is an internal parameter which can eventually by eliminated but this elimination leads to a non-local energy. Indeed the non-planar geometry of the line couples the flexion and torsion terms.
Sums of zeros of Van Vleck polynomials
Authors: Bourget Alain
Published: December 2024

In this paper we show that the zeros of Van Vleck polynomials satisfy the strong law of large numbers and the central limit theorem as their degrees get arbitrary large.
Small coherence length limit for a two-dimensional quantum transport model
Authors: Negulescu Claudia
Published: December 2024

In a previous work [N. Ben Abdallah and C. Negulescu, A one-dimensional transport model with small coherence lengths, Transp. Theory and Stat. Phys. 31(4–6) (2002), 559–578] a one-dimensional transport model accounting for both, quantum phenomena and smallness of coherence lengths, has been analyzed. In the limit of infinitely small coherence lengths, this model leads to the classical Vlasov equation. In this paper the two-dimensional situation is considered by adding to the one-dimensional transport direction a transversal confined one. The transport direction is splitted into several regions of a size comparable to the coherence length. A quantum model, based on the 2D Schrödinger equation, describes the electron transport within each cell, while on larger distances, statistics defined on the interfaces of the cells, determine the electron motion. Reflection and transmission coefficients, deduced from the wavefunctions, solutions of the Schrödinger equation, relate neighboring statistics with one another. In the limit of small coherence lengths, we obtain a collisionless subband model, which is classical in the transport direction and keeps quantum features in the confined one.
Asymptotic expansion of the solution of an interface problem in a polygonal domain with thin layer
Authors: Caloz Gabriel , Costabel Martin , Dauge Monique , Vial Grégory
Published: December 2024

We consider the solution of an interface problem posed in a bounded domain coated with a layer of thickness ε and with external boundary conditions of Dirichlet or Neumann type. Our aim is to build a multi-scale expansion as ε goes to 0 for that solution.

After presenting a complete multi-scale expansion in a smooth coated domain, we focus on the case of a corner domain. Singularities appear, obstructing the construction of the expansion terms in the same way as in the smooth case. In order to take these singularities into account, we construct profiles in an infinite coated sectorial domain.

Combining expansions in the smooth case with splittings in regular and singular parts involving the profiles, we construct two families of multi-scale expansions for the solution in the coated domain with corner. We prove optimal estimates for the remainders of the multi-scale expansions.
Stabilization and Lp–Lq decay estimates
Authors: Matsuyama Tokio , Reissig Michael
Published: December 2024

The goal of the paper is to derive Strichartz estimates for solutions to wave equations with time-dependent coefficients belonging to Cr, 2≤r≤2n+1, and generating an anisotropic speed of propagation. A stabilization condition for the coefficients is introduced. This condition allows to show the Log-effect in Lp–Lq estimates and explains in this way the loss of decay.
Regularity results for the Primitive Equations of the ocean
Authors: Nodet Maëlle
Published: December 2024

We consider the linear Primitive Equations of the ocean in the three-dimensional space, with horizontal periodic and vertical Dirichlet boundary conditions. Thanks to Fourier transforms we are able to calculate explicitly the pressure term. We then state existence, unicity and regularity results for the linear time-depending Primitive Equations, with low-regularity right-hand side.
A criterion for H-convergence in elasticity
Authors: Gustafsson Björn , Mossino Jacqueline
Published: December 2024

We give a criterion for H-convergence of elasticity tensors in terms of ordinary weak convergence of the factors in certain quotient representations of the tensors.
Geometric and projective instability for the Gross–Pitaevski equation
Authors: Thomann Laurent
Published: December 2024

Using variational methods, we construct approximate solutions for the Gross–Pitaevski equation which concentrate on circles in $\mathbb{R}$ 3. These solutions will help to show that the L2 flow is unstable for the usual topology and for the projective distance.
On the dynamics of magneto-elastic interactions: existence of solutions and limit behaviors
Authors: Valente V. , Vergara Caffarelli G.
Published: December 2024

The dynamics of magneto-elastic materials is described by a nonlinear system which couples the equations of the magnetization and the displacements. We study the three-dimensional case and establish the existence of weak solutions. Our starting point is the Gilbert–Landau–Lifschitz equation introduced for describing the dynamics of micro-magnetic processes. Three terms of the total free energy are taken into account: the exchange energy, the elastic energy and the magneto-elastic energy usually adopted for cubic crystals, neglecting, in this approach, the contributions due to the anisotropy and the demagnetization effects. The existence theorem for the proposed differential system is proved combining the Faedo–Galerkin approximations and the penalty method (FGP method). The asymptotic behavior are deduced from compactness properties.
Uniform asymptotic formulae for Green's tensors in elastic singularly perturbed domains
Authors: Maz'ya V.G. , Movchan A.B. , Nieves M.J.
Published: December 2024

We present uniform asymptotic approximations of Green's kernels for boundary value problems of elasticity in singularly perturbed domains containing a small hole. We consider the cases of two and three dimensions, for an isotropic Lamé operator and the Dirichlet boundary conditions. The main feature of the asymptotic approximations mentioned is their uniformity with respect to the independent spatial variables. The formal asymptotic formulae are supplied with rigorous derivations and the remainder estimates.
Asymptotic behaviour for a semilinear nonlocal equation
Authors: Pazoto Ademir F. , Rossi Julio D.
Published: December 2024

We study the semilinear nonlocal equation ut=J*u−u−up in the whole ${\mathbb{R}}^{N}$ . First, we prove the global well-posedness for initial conditions $u(x,0)=u_{0}(x)\in L^{1}({\mathbb{R}}^{N})\cap L^{\infty}({\mathbb{R}}^{N})$ . Next, we obtain the long time behaviour of the solutions. We show that different behaviours are possible depending on the exponent p and the kernel J: finite time extinction for p<1, faster than exponential decay for the linear case p=1, a weakly nonlinear behaviour for p large enough and a decay governed by the nonlinear term when p is greater than one but not so large.
A distributed parabolic control with mixed boundary conditions
Authors: Menaldi Jose-Luis , Tarzia Domingo Alberto
Published: December 2024

We study the asymptotic behavior of an optimal distributed control problem where the state is given by the heat equation with mixed boundary conditions. The parameter α intervenes in the Robin boundary condition and it represents the heat transfer coefficient on a portion $\varGamma _{1}$ of the boundary of a given regular n-dimensional domain. For each α, the distributed parabolic control problem optimizes the internal energy g. It is proven that the optimal control $\hat{g}_{\alpha}$ with optimal state $u_{\hat{g}_{\alpha}\alpha}$ and optimal adjoint state $p_{\hat{g}_{\alpha}\alpha}$ are convergent as α→∞ (in norm of a suitable Sobolev parabolic space) to $\hat{g},$ $u_{\hat{g}}$ and $p_{\hat{g}},$ respectively, where the limit problem has Dirichlet (instead of Robin) boundary conditions on $\varGamma _{1}.$ The main techniques used are derived from the parabolic variational inequality theory.
Inviscid limit for the two-dimensional Navier–Stokes system in a critical Besov space
Authors: Hmidi Taoufik , Keraani Sahbi
Published: December 2024

In a recent paper (Arch. Rational Mech. Anal. 145(3) (1998), 197–214), Vishik proved the global well-posedness of the two-dimensional Euler equation in the critical Besov space B2,12. In the present paper we prove that the Navier–Stokes system is globally well-posed in B2,12, with uniform estimates on the viscosity. We prove also a global result of inviscid limit. The convergence rate in L2 is of order ν.
Asymptotic analysis of linearly viscoelastic shells – justification of Koiter's shell equations
Authors: Li Fushan
Published: December 2024

By asymptotic analysis, we prove that the displacement of linearly viscoelastic Koiter's shell equations converges to the solution of two-dimensional linearly viscoelastic membrane shell or flexural shell model problem.
Asymptotique à l'infini du spectre discret de l'opérateur de Dirac avec champ magnétique
Authors: Sourisse Arnaud , Wang Xue Ping
Published: December 2024

On étudie l'asymptotique des valeurs propres de l'opérateur de Dirac en dimension deux avec un champ magnétique variable qui tend vers l'infini. On utilise la structure supersymétique de cet opérateur pour se ramener à l'étude des valeurs propres de l'opérateur de Schrödinger avec un potentiel électrique égal au champ magnétique.
Homogenizing a critical binary structure of finite diffusivities
Authors: Gruais Isabelle , Poliševski Dan
Published: December 2024

We study the homogenization of a diffusion process which takes place in a binary structure formed by an ambient connected phase surrounding a suspension of very small spheres distributed in an ε-periodic network. We consider the critical radius case with finite diffusivities in both phases. The asymptotic distribution of the concentration is determined, as ε→0, assuming that the suspension has mass of unity order and vanishing volume. It appears that the ambient macroscopic concentration is satisfying a Volterra integro-differential equation and it is defining straightly the macroscopic concentration associated to the suspension.
Nonlinear reinforcement problems with right-hand side in L1
Authors: Mercaldo Anna , Mossino Jacqueline , Prignet Alain
Published: December 2024

We study the asymptotic behaviour, as ε goes to zero, of the entropy solution uε to a class of nonlinear elliptic problems whose prototype is

−div((δε)p−1|∇uε|p−2∇uε)=fε

in Ωε, uε=0 on ∂Ωε, where 1<p<N, $\varOmega^{\varepsilon}=\overline{\varOmega}\cup\Sigma^{\varepsilon}$ , Ω⊂RN is a bounded domain of class C1,1, surrounded along its boundary by a layer Σε of small thickness ε, δε=1 in Ω, δε=ε in Σε, and fε belongs to L1(Ωε). The solutions uε also satisfies natural transmission conditions on ∂Ω.
On the motion and collisions of rigid bodies in an ideal fluid
Authors: Houot Jean , Munnier Alexandre
Published: December 2024

In this paper we study a coupled system of partial differential equations and ordinary differential equations. This system is a model for the 3d interactive free motion of rigid bodies immersed in an ideal fluid. Applying the least action principle of Lagrangian mechanics we prove that the degrees of freedom of the solids solve a system of second-order nonlinear ordinary differential equations. Under suitable smoothness assumptions on the fluid's domain boundary we prove the existence and C∞ regularity of the solids motion, up to a collision between two solids or between a solid with the boundary of the fluid's domain. The case of an infinite cylinder surrounded by a fluid in a half space cavity is tackled. By a careful asymptotic analysis of a Neumann boundary value problem (solved by the fluid's potential) when the distance between the cylinder and the wall goes to zero we prove that collisions with non zero relative velocity can occur.
Boldface Recursion on Platek Spaces
Authors: Ivanov Lyubomir
Published: December 2024

The present work develops a boldface version of the theory of Platek spaces initiated by [2]. This is done by studying recursion on spaces with special elements which embody the so called transfer operation of [1], Chapter 14 affording full lambda-abstraction. Transfer is characteristic of the monotonic hierarchies of operative spaces, which hierarchies form models of a typed lambda-mu-calculus. The principal result here is a boldface version of the abstract Platek First Recursion Theorem of [2]; we prove appropriate boldface Enumeration and Second Recursion Theorems as well.
Conditional Concatenation
Authors: Dassow Jürgen , Martín-Vide Carlos , Păun Gheorghe , Rodríguez-Patón Alfonso
Published: December 2024

Inspired from biochemistry and DNA computing, we introduce several variants of controlled concatenation of strings and languages: a finite set of pairs of strings is given and two arbitrary strings are concatenated only when among their substrings (scattered substrings, of various forms) we can find a pair in this control set. Five types of non-iterated and iterated (like Kleene closure) conditional concatenations are considered. The closure properties of abstract families of languages (hence also of families in the Chomsky hierarchy) are settled. They are similar to the closure properties under usual concatenation and Kleene closure. A representation of regular languages in terms of these operations (and a coding) is also given. Then, we use the new concatenation operations as basic operations in Chomsky grammars: rewriting a nonterminal means concatenating a new string with the strings to the left and the right of that nonterminal, hence restricted concatenations can be used. Context-free grammars working in this restricted manner can generate non-context-free languages; in one case, characterizations of recursively enumerable or of context-sensitive languages are obtained, depending on using or not erasing rules. Some topics for further research are also suggested.
Iteration-free PDL with Intersection: a Complete	Axiomatization
Authors: Balbiani Philippe , Vakarelov Dimiter
Published: December 2024

This paper is devoted to the completeness issue of PDL_0^∩ – an iteration-free fragment of Propositional Dynamic Logic with intersection of programs. The trouble with PDL_0^∩ is that the operation of intersection is not modally definable. Using new techniques connected with rules for intersection and the notions of large and maximal programs, the paper demonstrates that the presented proof theory for PDL_0^∩ is complete for the standard Kripke semantics of PDL_0^∩.
Sup-Compact and Inf-Compact Representations of W-Operators
Authors: Barrera Junior , Hasimoto Ronaldo Fumio
Published: December 2024

It is well known that any W-operator can be represented as the supremum (respectively, infimum) of sup-generating and (respectively, inf-generating) operators, that is, the families of sup-generating and inf-generating operators constitute the building blocks for representing W-operators. Here, we present two new families of building blocks to represent W-operators: compositions of sup-generating operators with dilations and compositions of inf-generating operators with erosions. The representations based on these new families of operators are called, respectively, sup-compact and inf-compact representations, since they may use less building blocks than the classical sup-generating and inf-generating representations. Considering the W-operators that are both anti-extensive and idempotent –in a strict sense–, we have also gotten a simplification of the sup-compact representation. We have also shown how the inf-compact representation can be simplified for any W-operator such that it is extensive and its dual operator is idempotent –in a strict sense–. Furthermore, if the W-operators are openings (respectively, closings), we have shown that this simplified sup-compact (respectively, inf-compact) representation reduces to a minimal realization of the classical Matheron's representations for translation invariant openings (respectively, closings).
Sensitivity Analysis for Selective Learning by Feedforward Neural	Networks
Authors: Engelbrecht Andries P.
Published: December 2024

Research on improving the performance of feedforward neural networks has concentrated mostly on the optimal setting of initial weights and learning parameters, sophisticated optimization techniques, architecture optimization, and adaptive activation functions. An alternative approach is presented in this paper where the neural network dynamically selects training patterns from a candidate training set during training, using the network's current attained knowledge about the target concept. Sensitivity analysis of the neural network output with respect to small input perturbations is used to quantify the informativeness of candidate patterns. Only the most informative patterns, which are those patterns closest to decision boundaries, are selected for training. Experimental results show a significant reduction in the training set size, without negatively influencing generalization performance and convergence characteristics. This approach to selective learning is then compared to an alternative where informativeness is measured as the magnitude in prediction error.
Sensitivity Analysis for Selective Learning by Feedforward Neural	Networks
Authors: Engelbrecht A.P.
Published: December 2024

Research on improving the performance of feedforward neural networks has concentrated mostly on the optimal setting of initial weights and learning parameters, sophisticated optimization techniques, architecture optimization, and adaptive activation functions. An alternative approach is presented in this paper where the neural network dynamically selects training patterns from a candidate training set during training, using the network's current attained knowledge about the target concept. Sensitivity analysis of the neural network output with respect to small input perturbations is used to quantify the informativeness of candidate patterns. Only the most informative patterns, which are those patterns closest to decision boundaries, are selected for training. Experimental results show a significant reduction in the training set size, without negatively influencing generalization performance and convergence characteristics. This approach to selective learning is then compared to an alternative where informativeness is measured as the magnitude in prediction error.
A Class of Composable and Preemptible High-level Petri Nets with	an Application to Multi-Tasking Systems
Authors: Klaudel Hanna , Pommereau Franck
Published: December 2024

This paper presents an extension of an algebra of high-level Petri nets with operations for suspension and abortion. These operations are sound with respect to the semantics of preemption, and can be applied to the modelling of the semantics of high-level parallel programming languages with preemption-related features. As an illustration, the paper gives an application to the modelling of a multi-tasking system in a parallel programming language, which is provided with a concurrent semantics based on Petri nets and for which implemented tools can be used.
Self-describing Turing machines
Authors: Margenstern Maurice , Rogozhin Yurii
Published: December 2024

After a sketchy historical account on the question of self-describeness and self-reproduction, and after discussing the definition of suitable encodings for self-describeness, we give the construction of several self-describing Turing machines, namely self-describing machines with, respectively, 350, 267, 224 and 206 instructions.
Another Example of Higher Order Randomness
Authors: Becher Verónica , Chaitin Gregory
Published: December 2024

We consider the notion of algorithmic randomness relative to an oracle. We prove that the probability β that a program for infinite computations (a program that never halts) outputs a cofinite set is random in the second jump of the halting problem. Indeed, we prove that β is exactly as random as the halting probability of a universal machine equipped with an oracle for the second jump of the halting problem, in spite of the fact that β is defined without considering oracles.
On Equations Including Strings
Authors: Kopeček Ivan , Novotný Miroslav
Published: December 2024

A system of equations is solved where the right side member of any equation is a known string and the left side member is formed by concatenation of some unknown strings. This problem appears in connection with the division of parts of speech into syllable segments.
Concept lattices and similarity in non-commutative fuzzy	logic
Authors: Georgescu George , Popescu Andrei
Published: December 2024

A classical (crisp) concept is given by its extent (a set of objects) and its intent (a set of properties). In commutative fuzzy logic, the generalization comes naturally, considering fuzzy sets of objects and properties. In both cases (the first being actually a particular case of the second), the situation is perfectly symmetrical: a concept is given by a pair (A,B), where A is the largest set of objects sharing the attributes from B and B is the largest set of attributes shared by the objects from A (with the necessary nuance when fuzziness is concerned). Because of this symmetry, working with objects is the same as working with properties, so there is no need to make any choice. In this paper, we define concepts in a "non-commutative fuzzy world", where conjunction of sentences is not necessarily commutative, which leads to the following non-symmetrical situation: a concept has one extent (because, at the end of the day, concepts are meant to embrace, using certain descriptions, diverse sets of objects), but two intents, given by the two residua (implications) of the non-commutative conjunction.
Process Algebra with Nonstandard Timing
Authors: Middelburg Kees A.
Published: December 2024

The possibility of two or more actions to be performed consecutively at the same point in time is not excluded in the process algebras from the framework of process algebras with timing presented by Baeten and Middelburg [Handbook of Process Algebra, Elsevier, 2001, Chapter 10]. This possibility is useful in practice when describing and analyzing systems in which actions occur that are entirely independent. However, it is an abstraction of reality to assume that actions can be performed consecutively at the same point in time. In this paper, we propose a process algebra with timing in which this possibility is excluded, but nonstandard non-negative real numbers are included in the time domain. It is shown that this new process algebra generalizes the process algebras with timing from the aforementioned framework in a smooth and natural way.
Complexity of the Unique Extension Problem in Default Logic
Authors: Zhao Xishun , Liberatore Paolo
Published: December 2024

In this paper we analyze the problem of checking whether a default theory has a single extension. This problem is important for at least three reasons. First, if a theory has a single extension, nonmonotonic inference can be reduced to entailment in propositional logic (which is computationally easier) using the set of consequences of the generating defaults. Second, a theory with many extensions is typically weak i.e., it has few consequences; this indicates that the theory is of little use, and that new information has to be added to it, either as new formulae, or as preferences over defaults. Third, some applications require as few extensions as possible (e.g. diagnosis). We study the complexity of checking whether a default theory has a single extension. We consider the combination of several restrictions of default logics: seminormal, normal, disjunction-free, unary, ordered. Complexity varies from the first to the third level of the polynomial hierarchy. The problem of checking whether a theory has a given number of extensions is also discussed.
Cryptanalysis of the Hwang-Shi Proxy Signature Scheme
Authors: Hwang Min-Shiang , Lee Cheng-Ch , Hwang Shin-Jia
Published: December 2024

Recently, Hwang and Shi proposed an efficient proxy signature scheme without using one-way hash functions. In their scheme, an original signer needn't send a proxy certificate to a proxy signer through secure channels. However, there are two public key substitution methods that can be used to attack their scheme. In this article, we show that their scheme is vulnerable to the public key substitution attacks.
Probabilistic Cluster Unfoldings
Authors: Haar Stefan
Published: December 2024

This article introduces probabilistic cluster branching processes, a probabilistic unfolding semantics for untimed Petri nets with no structural or safety assumptions. The unfolding is constructed by local choices on each cluster (conflict closed subnet), while the authorization for cluster actions is governed by a stochastic trace, the policy. The probabilistic model for this semantics yields probability measures for concurrent runs. We introduce and characterize stopping times for this model, and prove a strong Markov property. Particularly adequate probability measures for the choice of step in a cluster, as well as for the policy, are obtained by constructing Markov Fields from suitable marking-dependent Gibbs potentials.
Analytic Calculi for Monoidal T-norm Based Logic
Authors: Baaz Matthias , Ciabattoni Agata , Montagna Franco
Published: December 2024

Monoidal t-norm based logic MTL is the logic of left continuous t-norms. We introduce two analytic calculi for first-order MTL. These are obtained by lifting two sequent calculi for different fragments of this logic to the hypersequent level with subsequent addition of Avron's communication rule. Our calculi enable to prove the mid(hyper)sequent theorem. As corollaries follow Herbrand's theorem for first-order MTL, the decidability of its ∀∃-fragment and admissibility of Skolemization.
Leader Election in Rings with Nonunique Labels
Authors: Dobrev Stefan , Pelc Andrzej
Published: December 2024

We consider the leader election problem in a ring whose nodes have possibly nonunique labels. Every node knows a priori its own label and two integers, m and M, which are, respectively, a lower and an upper bound on the (unknown) size n of the ring. The aim is to decide whether leader election is possible and to perform it, if so. We consider both the synchronous and the asynchronous version of the problem and we are interested in message complexity in both cases. For the synchronous version we present an algorithm using O(n log n) messages and working in time O(M). Moreover, our algorithm uses O(n) messages when all identifiers are distinct. For the asynchronous version we show an Ω(nM) lower bound on message complexity for this problem, and present an algorithm for it using O(nM) messages.
Register Cellular Automata in the Hyperbolic Plane
Authors: Grigorieff Serge , Margenstern Maurice
Published: December 2024

In this paper, we consider cellular automata on special grids of the hyperbolic plane: the grids are constructed on infinigons, i.e. polygons with infinitely many sides. We show that the truth of arithmetical formulas can be decided in finite time with infinite initial recursive configurations. Next, we define a new kind of cellular automata, endowed with data and more powerful operations which we call register cellular automata. This time, starting from finite configurations, it is possible to decide the truth of arithmetic formulas in linear time with respect to the size of the formula.
A Note on 3-valued Rough Logic Accepting Decision Rules
Authors: Polkowski Lech
Published: December 2024

Rough sets carry, intuitively, a 3-valued logical structure related to the three regions into which any rough set x divides the universe., viz., the lower definable set i(x), the upper definable set c(x), and the boundary region c(x)\setminus i(x) witnessing the vagueness of associated knowledge. In spite of this intuition, the currently known way of relating rough sets and 3-valued logics is only via 3-valued Łukasiewicz algebras (Pagliani) that endow spaces of disjoint representations of rough sets with its structure. Here, we point to a 3-valued rough logic RL of unary predicates in which values of logical formulas are given as intensions over possible worlds that are definable sets in a model of rough set theory (RZF). This logic is closely related to the Łukasiewicz 3-valued logic, i.e., its theorems are theorems of the Łukasiewicz 3-valued logic and theorems of the Łukasiewicz 3-valued logic are in one-to-one correspondence with acceptable formulas of rough logic. The formulas of rough logic have denotations and are evaluated in any universe U in which a structure of RZF has been established. RZF is introduced in this note as a variant of set theory in which elementship is defined via containment, i.e., it acquires a mereological character (for this, see the cited exposition of Lesniewski's ideas). As an application of rough logic RL, decision rules and dependencies in information systems are characterized as acceptable formulas of this logic whereas functional dependencies turn out to be theorems of rough logic RL.
Scenery Image Segmentation Using Support Vector Machines
Authors: Yu Yuan-Hui , Chang Chin-Chen
Published: December 2024

This paper presents an effective and efficient method for solving scenery image segmentation by applying the SVMs methodology. Scenery image segmentation is regarded as a data classification problem, and is effectively answered by the proposed method in this paper. Using the model selection in our system architecture, our system is relatively simple compared to other conventional heuristic image segmentation approaches yet demonstrates promising classification results.
An Adaptive Steganographic Scheme for Color Images
Authors: Chang Chin-Chen , Tsai Piyu , Lin Min-Hui
Published: December 2024

In this paper, a new palette-based image steganography is proposed. Palette-based images such as GIF files have been widely used on the Internet and web pages such that all browsers can recognize them. Palette-based images can be used as good carriers for transmitting secret messages. In this scheme, the Least Significant Bits (LSBs) of the palette-based image are utilized in order to hide the secret message by using the computational information hiding technique. The adaptive hiding capacity can be computed according to different sizes of the embedding block. Experimental results also show that existing artifacts in the traditional LSB-based method are unnoticeable. The number of modification pixels in the embedding process is decreased, while good stego-image quality is maintained, and the cover image is left unblemished by camouflaged information. Furthermore, the feature of adaptive hiding capacity provides the possibility of protecting different sizes of embedded secret messages.
An ω-Power of a Finitary Language Which is a Borel Set of	Infinite Rank
Authors: Finkel Olivier
Published: December 2024

ω-powers of finitary languages are ω-languages in the form Vω, where V is a finitary language over a finite alphabet Sigma. Since the set Σω of infinite words over Σ can be equipped with the usual Cantor topology, the question of the topological complexity of ω-powers naturally arises and has been raised by Niwinski [13], by Simonnet [15], and by Staiger [18]. It has been proved in [14] that for each integer n≥1, there exist some ω-powers of context free languages which are Πn0-complete Borel sets, and in [5] that there exists a context free language L such that Lω is analytic but not Borel. But the question was still open whether there exists a finitary language V such that Vω is a Borel set of infinite rank. We answer this question in this paper, giving an example of a finitary language whose ω-power is Borel of infinite rank.
Optimal Unification of Infinite Sets of Types
Authors: Marciniec Jacek
Published: December 2024

In this paper we focus on the properties of infinite sets of types that have finite substitutional images. Since the number of such images may be infinite, we provide the way of its reduction. Having this done, we apply the new methods in the field of learnability of classical categorial grammars.
Knowledge Acquisition under Incomplete Knowledge using Methods	from Formal Concept Analysis: Part II
Authors: Holzer Richard
Published: December 2024

Attribute exploration is an interactive computer algorithm which helps the expert to get informations about the attribute implications of a formal context. In the part I of this paper (see [H04]) an algorithm for attribute exploration with incomplete knowledge was presented. In this part we prove the main results of the algorithm: At the end of the attribute exploration the expert gets maximal information with respect to his knowledge about the unknown universe: He gets a list of implications which are certainly valid, a list of implications which are possibly valid, a list of counterexamples against the implications which are certainly not valid and a list of fictitious counterexamples against the implications which he answered by "unknown". He only has to check the implications which he answered by "unknown" and if he can decide for each of these implications whether it is valid or not, he gets complete knowledge about the implications of the context.
ACTLS properties and Bounded Model Checking
Authors: Woźna Bożena
Published: December 2024

The main contribution of the paper consists in showing that the bounded model checking (BMC) method is feasible for ACTLS* (the universal fragment of CTLS*) which subsumes both ACTL and LTL. The extension to ACTLS^* is obtained by redefining the function returning the sufficient number of executions over which an ACTLS* formula is checked, and then combining the two known translations to SAT for ACTL and LTL formulas. The proposed translation of ACTLS* formulas is essentially different from the existing translations of both ACTL and LTL formulas. Moreover, the formal treatment is the basis for the implementation of the technique in the symbolic model checker √erics.
Embedding Invisible Watermarks into Digital Images Based on	Side-Match Vector Quantization
Authors: Wu Hsien-Chu , Chang Chin-Chen
Published: December 2024

This paper proposes an effective digital watermarking scheme to protect the intellectual property rights of digital images. This scheme embeds representative watermarks into images during the process of side-match vector quantization (SMVQ)@compresses and extracts the digital watermark effectively in order to determine the ownership of the image when a dispute over intellectual property rights occurs. The method proposed in this paper embeds a watermark based on the grouping of the codewords in a state codebook, and it stresses the fact that the SMVQ compressed image and the decompressed image both contain watermarks. In addition, the decompressed image has strong resistance against being damaged. Even under JPEG lossy compression, the watermark can still be restored effectively. The proposed method enables the watermark to be embedded directly into a compressed image that is much smaller than the original one. Once applied to the network, the method can save time in image transmission as well as storage space.
Algebraic Structures Related to Many Valued Logical Systems. Part	II: Equivalence Among some Widespread Structures
Authors: Cattaneo Gianpiero , Ciucci Davide , Giuntini Roberto , Konig Martin
Published: December 2024

Several algebraic structures (namely HW, BZMVdM, Stonean MV and MVΔ algebras) related to many valued logical systems are considered and their equivalence is proved. Four propositional calculi whose Lindenbaum–Tarski algebra corresponds to the four equivalent algebraic structures are axiomatized and their semantical completeness is given.
Applying term rewriting to partial algebra theory
Authors: Dojer Norbert
Published: December 2024

In our paper we apply term rewriting to decidability of equations in classes of partial algebras, as well as to embeddability of partial algebras into classes of total ones. We follow the approach to partial algebras introduced by H.J. Kreowski in [13], in which (classes of) partial algebras are described by means of (classes of) total ones.
Revealed Preference, Congruence and Rationality: A Fuzzy	Approach
Authors: Georgescu Irina
Published: December 2024

In a previous paper connections between the congruence axioms WFCA, SFCA and the revealed preference axioms WAFRP, SAFRP for fuzzy choice functions whose domain contains the characteristic functions of pairs and of triples of alternatives have been studied.

The first objective of this paper is to establish such connections for the case of arbitrary fuzzy choice functions. We introduce the new revealed preference axioms WAFRP ^o , SAFRP ^o , HAFRP and we prove two main theorems:

1. The axioms WFCA and WAFRP ^o are equivalent;

2. The axioms SFCA and HAFRP are equivalent.

Our second objective is to define G-rational, M-rational, G-normal and M-normal fuzzy choice functions and to investigate some of their properties.

The notions and the results are formulated in terms of the residuum of the Gödel t-norm and the proofs use the residuated lattice structure of the interval [0,1].
On countable RCC models
Authors: Li Sanjiang , Ying Mingsheng , Li Yongming
Published: December 2024

Region Connection Calculus (RCC) is the most widely studied formalism of Qualitative Spatial Reasoning. It has been known for some time that each connected regular topological space provides an RCC model. These 'standard' models are inevitable uncountable and regions there cannot be represented finitely. This paper, however, draws researchers' attention to RCC models that can be constructed from finite models hierarchically. Compared with those 'standard' models, these countable models have the nice property that regions where can be constructed in finite steps from basic ones. We first investigate properties of three countable models introduced by Düuntsch, Stell, Li and Ying, resp. In particular, we show that (i) the contact relation algebra of our minimal model is not atomic complete; and (ii) these three models are non-isomorphic. Second, for each n>0, we construct a countable RCC model that is a sub-model of the standard model over the Euclidean unit n-cube; and show that all these countable models are non-isomorphic. Third, we show that every finite model can be isomorphically embedded in any RCC model. This leads to a simple proof for the result that each consistent spatial network has a realization in any RCC model.
Generalized Interpolation in First Order Logic
Authors: Borzyszkowski Tomasz
Published: December 2024

We consider the Craig Interpolation Property for many sorted first-order logic. The Craig Interpolation Property explored in this paper is inspired by the institution independent generalization of this property presented in [21]. In [3] the author presents the interpolation result for the institution of many sorted first-order logic, with both morphisms in the pushout square being injective on sort names. The author also shows that the Craig Interpolation Property does not hold when both morphisms are certain morphisms which are noninjective on sort names. An open question in that paper was whether the interpolation property holds with only one morphism being injective on sort names.

In this paper we give answer to this question. Following the overall structure of the classical proof presented in [7] for single sorted first-order logic, but with new technicalities concerning the many sorted case, we show that many sorted first-order logic has the interpolation property when just one (left or right) morphism is injective on sort names.
First and Second Order Recursion on Abstract Data Types
Authors: Xu Jian , Zucker Jeffery
Published: December 2024

This paper compares two scheme-based models of computation on abstract many-sorted algebras A: Feferman's system ACP(A) of "abstract computational procedures" based on a least fixed point operator, and Tucker and Zucker's system μPR(A) based on primitive recursion on the naturals together with a least number operator. We prove a conjecture of Feferman that (assuming contains sorts for natural numbers and arrays of data) the two systems are equivalent. The main step in the proof is showing the equivalence of both systems to a system Rec(A) of computation by an imperative programming language with recursive calls. The result provides a confirmation for a Generalized Church-Turing Thesis for computation on abstract data types.