On the finite embeddability property for residuated ordered groupoids

The finite embeddability property (FEP) for integral, commutative residuated ordered monoids was established by W. J. Blok and C. J. van Alten in 2002. Using Higman's finite basis theorem for divisibility orders we prove that the assumptions of commutativity and associativity are not required: the classes of integral residuated ordered monoids and integral residuated ordered groupoids have the FEP as well. The same holds for their respective subclasses of (bounded) (semi-)lattice ordered structures. The assumption of integrality cannot be dropped in general--the class of commutative, residuated, lattice ordered monoids does not have the FEP--but the class of -potent commutative residuated lattice ordered monoids does have the FEP, for any .

     

The finite embeddability property for residuated lattices, pocrims and BCK-algebras

A class of algebras has the finite embeddability property (FEP) if every finite partial subalgebra of an algebra in the class can be embedded into a finite algebra in the class. We investigate the relationship of the FEP with the finite model property (FMP) and strong finite model property (SFMP).? For quasivarieties the FEP and the SFMP are equivalent, and for quasivarieties with equationally definable principal relative congruences the three notions FEP, FMP and SFMP are equivalent. The variety of intuitionistic linear algebras –which is known to have the FMP–fails to have the FEP, and hence the SFMP as well. The variety of integral intuitionistic linear algebras (also known as the variety of residuated lattices) does possess the FEP, and hence also the SFMP. Similarly contrasting statements hold for various subreduct classes. In particular, the quasivarieties of pocrims and of BCK-algebras possess the FEP. As a consequence, the universal theories of the classes of residuated lattices, pocrims and BCK-algebras are decidable. Received February 16, 2001; accepted in final form November 2, 2001. RID="h1" ID="h1"The second author was supported by a postdoctoral research fellowship of the National Research Foundation of South Africa, hosted by the University of Illinois at Chicago.     

The finite model property for semilinear substructural logics

In this paper, we show that the finite model property fails for certain non‐integral semilinear substructural logics including Metcalfe and Montagna's uninorm logic and involutive uninorm logic, and a suitable extension of Metcalfe, Olivetti and Gabbay's pseudo‐uninorm logic. Algebraically, the results show that certain classes of bounded residuated lattices that are generated as varieties by their linearly ordered members are not generated as varieties by their finite members.     

A mapping finite difference model for infinite elastic media

A simple mapping finite difference model is presented for the solution of boundary-value problems in the theory of time-harmonic elastic vibrations. The finite problem domain is condensed by mapping into a smaller finite domain using a suitable coordinate transformation. The field equations and the boundary conditions are also appropriately transformed. The radiation condition at infinity is satisfied through a change of the dependent variable. Finite difference forms of the transformed equations are then solved in the mapped domain, subject to the transformed boundary conditions.     

Representable idempotent commutative residuated lattices

It is proved that the variety of representable idempotent commutative residuated lattices is locally finite. The -generated subdirectly irreducible algebras in this variety are shown to have at most elements each. A constructive characterization of the subdirectly irreducible algebras is provided, with some applications. The main result implies that every finitely based extension of positive relevance logic containing the mingle and Gödel-Dummett axioms has a solvable deducibility problem.

     

A secondary semantics for Second Order Intuitionistic Propositional Logic

In this paper we propose a Kripke‐style semantics for second order intuitionistic propositional logic and we provide a semantical proof of the disjunction and the explicit definability property. Moreover, we provide a tableau calculus which is sound and complete with respect to such a semantics. (© 2004 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)     

The Rohlin property for shifts of finite type

We show that an automorphism of a unital AF C^*-algebra with a certain approximate Rohlin property has the Rohlin property. This generalizes a result of Kishimoto. Using this we show that the shift automorphism on the bilateral C^*-algebra associated with an aperiodic irreducible shift of finite type has the Rohlin property.     

A constrained optimization based method for acoustic finite element model updating of cavities using pressure response

A method based on constrained optimization for updating of an acoustic finite element model using pressure response is proposed in this paper. The constrained optimization problem is solved using sequential quadratic programming algorithm. Updating parameters related to the properties of the sound absorbers and the measurement errors are considered. Effectiveness of the method is demonstrated by numerical studies on a 2D rectangular cavity and a car cavity. It is shown that the constrained formulation, that includes lower and upper bounds on the updating parameters in the form of inequality constraints, is important for obtaining a correct updated model. It is seen that the proposed updating method is not only able to effectively update the model to obtain a close match between the finite element model pressure response and the reference pressure response, but is also able to identify the correction factors to the parameters in error with reasonable accuracy.     

Tunneling of the hard‐core model on finite triangular lattices

We consider the hard‐core model on finite triangular lattices with Metropolis dynamics. Under suitable conditions on the triangular lattice sizes, this interacting particle system has 3 maximum‐occupancy configurations and we investigate its high‐fugacity behavior by studying tunneling times, that is, the first hitting times between these maximum‐occupancy configurations, and the mixing time. The proof method relies on the analysis of the corresponding state space using geometrical and combinatorial properties of the hard‐core configurations on finite triangular lattices, in combination with known results for first hitting times of Metropolis Markov chains in the equivalent zero‐temperature limit. In particular, we show how the order of magnitude of the expected tunneling times depends on the triangular lattice sizes in the low‐temperature regime and prove the asymptotic exponentiality of the rescaled tunneling time leveraging the intrinsic symmetry of the state space.     

带有限反馈下层的二层规划问题的部分合作模型

对下层最优反馈为离散有限多个的二层规划问题的部分合作模型进行探讨. 当下层的合作程度依赖于上层的决策变量时, 给出一个确定合作系数函数的一般方法, 进而得到一个新的部分合作模型. 在适当地假设下, 可保证所给的部分合作模型一定可以找到比悲观解要好的解, 并结合新的部分合作模型对原不适定问题进行分析, 得到了一些有益的结论. 最后以实际算例说明了所给部分合作模型的可行性.     

Finite problems and the logic of the weak law of excluded middle

A new characteristic of propositional formulas as operations on finite problems, the cardinality of a sufficient solution set, is defined. It is proved that if a formula is deducible in the logic of the weak law of excluded middle, then the cardinality of a sufficient solution set is bounded by a constant depending only on the number of variables; otherwise, the accessible cardinality of a sufficient solution set is close to (greater than the nth root of) its trivial upper bound. This statement is an analog of the authors result about the algorithmic complexity of sets obtained as values of propositional formulas, which was published previously. Also, we introduce the notion of Kolmogorov complexity of finite problems and obtain similar results.Translated from Matematicheskie Zametki, vol. 77, no. 2, 2005, pp. 291–302.Original Russian Text Copyright © 2005 by A. V. Chernov.This revised version was published online in April 2005 with a corrected issue number.     

A nonconforming mixed finite element for second-order elliptic problems

In a recent work, Hiptmair [Mathematisches Institut, M9404, 1994] has constructed and analyzed a family of nonconforming mixed finite elements for second-order elliptic problems. However, his analysis does not work on the lowest order elements. In this article, we show that it is possible to construct a nonconforming mixed finite element for the lowest order case. We prove the convergence and give estimates of optimal order for this finite element. Our proof is based on the use of the properties of the so-called nonconforming bubble function to control the consistency terms introduced by the nonconforming approximation. We further establish an equivalence between this mixed finite element and the nonconforming piecewise quadratic finite element of Fortin and Soulie [J. Numer. Methods Eng., 19, 505–520, 1983]. © 1997 John Wiley & Sons, Inc. Numer Methods Partial Differential Eq 13: 445–457, 1997     

A criterion for finite lattice coverings

For a centrally symmetric convex and a covering lattice L for K, a lattice polygon P is called a covering polygon, if . We prove that P is a covering polygon, if and only if its boundary bd(P) is covered by (L ∩ P) + K. Further we show that this characterization is false for non-symmetric planar convex bodies and in Euclidean d–space, d ≥ 3, even for the unit ball K = B ^d. This revised version was published online in June 2006 with corrections to the Cover Date.     

Iterated function systems of finite type and the weak separation property

We prove that any iterated function system of finite type possesses the weak separation property.

     

Superconvergence of nonconforming finite element method for the Stokes equations

This article derives a general superconvergence result for nonconforming finite element approximations of the Stokes problem by using a least‐squares surface fitting method proposed and analyzed recently by Wang for the standard Galerkin method. The superconvergence result is based on some regularity assumption for the Stokes problem and is applicable to any nonconforming stable finite elements with regular but nonuniform partitions. © 2002 Wiley Periodicals, Inc. Numer Methods Partial Differential Eq 18: 143–154, 2002; DOI 10.1002/num.1036     

A new stabilized finite element method for optimal control for a Ladyzhenskaya model for unsteady flows

This article considers the time‐dependent optimal control problem of tracking the velocity for the viscous incompressible flows which is governed by a Ladyzhenskaya equations with distributed control. The existence of the optimal solution is shown and the first‐order optimality condition is established. The semidiscrete‐in‐time approximation of the optimal control problem is also given. The spatial discretization of the optimal control problem is accomplished by using a new stabilized finite element method which does not need a stabilization parameter or calculation of high order derivatives. Finally a gradient algorithm for the fully discrete optimal control problem is effectively proposed and implemented with some numerical examples. © 2010 Wiley Periodicals, Inc. Numer Methods Partial Differential Eq 28: 263–287, 2012     

A monotone finite element scheme for convection-diffusion equations

A simple technique is given in this paper for the construction and analysis of a class of finite element discretizations for convection-diffusion problems in any spatial dimension by properly averaging the PDE coefficients on element edges. The resulting finite element stiffness matrix is an -matrix under some mild assumption for the underlying (generally unstructured) finite element grids. As a consequence the proposed edge-averaged finite element scheme is particularly interesting for the discretization of convection dominated problems. This scheme admits a simple variational formulation, it is easy to analyze, and it is also suitable for problems with a relatively smooth flux variable. Some simple numerical examples are given to demonstrate its effectiveness for convection dominated problems.

     

The property O n for finite seminormal functors

We give a finite combinatorial test for finite seminormal functors to possess the property O _n and use it in establishing that in some cases this property leads to some well-known functors. For example, if some functor F possesses the property O ₂ then F ₂ coincides with either exp₂ or the squaring functor. Hence we conclude that if F(D ^ω ₁) and D ^ω ₁ are homeomorphic then F ₂ is either exp₂ or (·)².     

Mesh-centered finite differences from nodal finite elements for elliptic problems

After it is shown that the classical five-point mesh-centered finite difference scheme can be derived from a low-order nodal finite element scheme by using nonstandard quadrature formulae, higher-order block mesh-centered finite difference schemes for second-order elliptic problems are derived from higher-order nodal finite elements with nonstandard quadrature formulae as before, combined to a procedure known as “transverse integration.” Numerical experiments with uniform and nonuniform meshes and different types of boundary conditions confirm the theoretical predictions, in discrete as well as continuous norms. © 1998 John Wiley & Sons, Inc. Numer Methods Partial Differential Eq 14: 439–465, 1998