Abelian <Emphasis Type=Italic>ℓ</Emphasis>-Groups with Strong Unit and Perfect MV-Algebras

We investigate the class of abelian ℓ-groups with strong unit corresponding to perfect MV-algebras via the Γ functor, showing that this is a universal subclass of the class of all abelian ℓ-groups with strong unit and describing the formulas that axiomatize it. We further describe results for classes of abelian ℓ-groups with strong unit corresponding to local MV-algebras with finite rank.     

Categories of semigroups in quantum computational structures

We investigate a categorial duality between quasi MV-algebras (a variety of algebras arising from quantum computation and tightly connected with fuzzy logic) and a reflective subcategory of l-groups with strong units.      

Perfect MV-algebras and their Logic

In this paper, after recounting the basic properties of perfect MV-algebras, we explore the role of such algebras in localization issues. Further, we analyze some logics that are based on Łukasiewicz connectives and are complete with respect to linearly ordered perfect MV-algebras.      

Higher order Schwarzian derivatives and quasisymmetric homeomorphisms北大核心CSCD

We characterize two subclasses of quasisymmetric homeomorphisms of the unit circle in terms of higher order Schwarzian derivatives, which are the strongly symmetric homeomorphisms and the Weil-Petersson class. ©, 2015, Chinese Academy of Sciences. All right reserved.     

Embeddings of open manifolds

Let be the simplicial group of homeomorphisms of . The following theorems are proved.

Theorem A. Let be a topological manifold of dim 5 with a finite number of tame ends , . Let be the simplicial group of end preserving homeomorphisms of . Let be a periodic neighborhood of each end in , and let be manifold approximate fibrations. Then there exists a map such that the homotopy fiber of is equivalent to , the simplicial group of homeomorphisms of which have compact support.

Theorem B. Let be a compact topological manifold of dim 5, with connected boundary , and denote the interior of by . Let be the restriction map and let be the homotopy fiber of over . Then is isomorphic to for , where is the concordance space of .

Theorem C. Let be a manifold approximate fibration with dim 5. Then there exist maps and for , such that , where is a compact and connected manifold and is the infinite cyclic cover of .

     

Pavelka-style completeness in expansions of Łukasiewicz logic

An algebraic setting for the validity of Pavelka style completeness for some natural expansions of Łukasiewicz logic by new connectives and rational constants is given. This algebraic approach is based on the fact that the standard MV-algebra on the real segment [0, 1] is an injective MV-algebra. In particular the logics associated with MV-algebras with product and with divisible MV-algebras are considered. The author express his gratitude to Roberto Cignoli, for his advice during the preparation of this paper.     

Beurling-Ahlfors延拓与调和映照

研究BA延拓和调和映照的关系,首先,给出了BA延拓为双曲调和的一个必要条件,特别地,若边界对应h局部是C~2和奇的,则其BA延拓不是双曲调和的。其次,证明了若h是分段C~2的则其BA延拓不是π调和的,除非h(x)=ax b,x∈R.     

The fixed subgroups of homeomorphisms of Seifert manifolds

Let M be a compact connected orientable Seifert manifold with hyperbolic orbifold B M,and fπ : π1(M) →π1(M) be an automorphism induced by an orientation-reversing homeomorphism f of M. We give a bound on the rank of the fixed subgroup of fπ, namely, rank Fix(fπ) 2rankπ1(M),which is an analogue of inequalities on surface groups and hyperbolic 3-manifold groups.     

Piecewise-linear programming: The compact (CPLP) algorithm

A compact algorithm is presented for solving the convex piecewise-linear-programming problem, formulated by means of a separable convex piecewise-linear objective function (to be minimized) and a set of linear constraints. This algorithm consists of a finite sequence of cycles, derived from the simplex method, characteritic of linear programming, and the line search, characteristic of nonlinear programming. Both the required storage and amount of calculation are reduced with respect to the usual approach, based on a linear-programming formulation with an expanded tableau. The tableau dimensions arem×(n+1), wherem is the number of constraints andn the number of the (original) structural variables, and they do not increase with the number of breakpoints of the piecewise-linear terms constituting the objective function.     

The groups of quasiconformal homeomorphisms on Riemann surfaces

Suppose is a connected Riemann surface. Let denote the homeomorphism group of with the compact-open topology, and denote the subgroup of quasiconformal mappings of onto itself, and let and denote the identity components of and respectively. In this paper we show that the pair is an -manifold, and determine their topological types.

     

On Topological Classification of Non-Archimedean Fréchet Spaces

We prove that any infinite-dimensional non-archimedean Fréchet space E is homeomorphic to where D is a discrete space with card(D) = dens(E). It follows that infinite-dimensional non-archimedean Fréchet spaces E and F are homeomorphic if and only if dens(E) = dens(F). In particular, any infinite-dimensional non-archimedean Fréchet space of countable type over a field is homeomorphic to the non-archimedean Fréchet space .     

Dichotomies between uniform hyperbolicity and zero Lyapunov exponents for SL(2, ℝ) cocycles

We consider the linear cocycle (T, A) induced by a measure preserving dynamical system T : X → X and a map A: X → SL(2, ℝ). We address the dependence of the upper Lyapunov exponent of (T, A) on the dynamics T when the map A is kept fixed. We introduce explicit conditions on the cocycle that allow to perturb the dynamics, in the weak and uniform topologies, to make the exponent drop arbitrarily close to zero. In the weak topology we deduce that if X is a compact connected manifold, then for a C^r (r ≥ 1) open and dense set of maps A, either (T, A) is uniformly hyperbolic for every T, or the Lyapunov exponents of (T, A) vanish for the generic measurable T. For the continuous case, we obtain that if X is of dimension greater than 2, then for a C^r (r ≥ 1) generic map A, there is a residual set of volume-preserving homeomorphisms T for which either (T, A) is uniformly hyperbolic or the Lyapunov exponents of (T, A) vanish. *Partially supported by CNPq-Profix and Franco-Brazilian cooperation program in Mathematics.     

Local product structure for expansive homeomorphisms

Let be an expansive homeomorphism with dense topologically hyperbolic periodic points, M a closed manifold. We prove that there is a local product structure in an open and dense subset of M. Moreover, if some topologically hyperbolic periodic point has codimension one, then this local product structure is uniform. In particular, we conclude that the homeomorphism is conjugated to a linear Anosov diffeomorphism of a torus.     

An analysis of the logic of Riesz spaces with strong unit

We study ?ukasiewicz logic enriched by a scalar multiplication with scalars in $[0,1]$. Its algebraic models, called Riesz MV-algebras, are, up to isomorphism, unit intervals of Riesz spaces with strong unit endowed with an appropriate structure. When only rational scalars are considered, one gets the class of DMV-algebras and a corresponding logical system. Our research follows two objectives. The first one is to deepen the connections between functional analysis and the logic of Riesz MV-algebras. The second one is to study the finitely presented MV-algebras, DMV-algebras and Riesz MV-algebras, connecting them from logical, algebraic and geometric perspective.     

Rotation numbers in Thompson–Stein groups and applications

We study the rationality properties of rotation numbers for some groups of piecewise linear homeomorphisms of the circle, the Thompson–Stein groups. We prove that for many Thompson–Stein groups the outer automorphism group has order 2. As another application, we construct Thompson–Stein groups which do not admit non trivial representations in Diff⁹(S ¹).      

On the infinite-valued Łukasiewicz logic that preserves degrees of truth

Łukasiewicz’s infinite-valued logic is commonly defined as the set of formulas that take the value 1 under all evaluations in the Łukasiewicz algebra on the unit real interval. In the literature a deductive system axiomatized in a Hilbert style was associated to it, and was later shown to be semantically defined from Łukasiewicz algebra by using a “truth-preserving” scheme. This deductive system is algebraizable, non-selfextensional and does not satisfy the deduction theorem. In addition, there exists no Gentzen calculus fully adequate for it. Another presentation of the same deductive system can be obtained from a substructural Gentzen calculus. In this paper we use the framework of abstract algebraic logic to study a different deductive system which uses the aforementioned algebra under a scheme of “preservation of degrees of truth”. We characterize the resulting deductive system in a natural way by using the lattice filters of Wajsberg algebras, and also by using a structural Gentzen calculus, which is shown to be fully adequate for it. This logic is an interesting example for the general theory: it is selfextensional, non-protoalgebraic, and satisfies a “graded” deduction theorem. Moreover, the Gentzen system is algebraizable. The first deductive system mentioned turns out to be the extension of the second by the rule of Modus Ponens.While writing this paper, the authors were partially supported by grants MTM2004-03101 and TIN2004-07933-C03-02 of the Spanish Ministry of Education and Science, including FEDER funds of the European Union.     

Solving stochastic differential equations on Homeo(S)

The Brownian motion with respect to the metric H^3/2 on Diff(S¹) has been constructed. It is realized on the group of homeomorphisms Homeo(S¹). In this work, we shall resolve the stochastic differential equations on Homeo(S¹) for a given drift Z.