Archimedeisation of Some Ordered Geometric Structures Which are Related to Kinematic Spaces

In view of the aim to “archimedeise ordered kinematic spaces” we compile here the following preliminary work: Connections between order notions like linear order, betweenness, separation and orientation ( = cyclic order) and between ordered, betweenness, separated and oriented groups; archimedeisation of separated groups; complete discussion of the archimedeisation of three types of separated groups derived from unitary associative algebras (A,K) of degree 2 over non archimedean ordered fields (K,+,·,≤).     

The Reflection Structures of Generalized Co-Minkowski Spaces Leading to K-Loops

We extend the notion co- Minkowski plane to “unitary co- Minkowski space” (P, G, ～) and discuss the problem whether there are subsets Q of P which can be turned into a geometric K- loop.     

Elliptic Reflection Spaces

This paper considers the Jensen type cubic fuzzy set-valued functional equation and the n-dimensional cubic fuzzy set-valued functional equation. We establish the Hyers–Ulam stability of these two types of cubic fuzzy set-valued functional equations by using the fixed point method. Our results can be regarded as two extensions of stability results corresponding to single-valued functional equations and set-valued functional equations, respectively.     

Fractals Corresponding to Subsets of Sequence Spaces

Recursion can generate a fractal limit set from a sequence of finite families of functions, even if every possible sequence does not converge to a limit point. Conditions, which make limit sets compact, are discussed. A construction giving an unbounded fractal is presented, together with an open question and an application of recursive compositions of contractions to sums of present values.     

Uniformity Structures on L-Fuzzy Spaces

We extend the notion of a uniform space in a natural way by defining a uniform spaces in L-fuzzy spaces.Although these spaces seem quite similar to ordinary case,we show that the category of this uniform spaces is a good extension of the category of ordinary uniform spaces and the category of L-uniform spaces.Moreover,we introduce the concept of uniform topological spaces in the framework of uniform spaces in L-fuzzy spaces.Furthermore,the relation between proximity and uniform spaces in L-fuzzy spaces will...     

Reflection Spaces, Partial K-Loops and K-Loops

Starting from a paper by Sperner (Archiv der Mathematik 5:458?C468, 1954) we introduce the notion reflection space and inside this concept, transitive elliptic and non-elliptic reflection spaces. On a transitive and non-elliptic reflection space we can apply the so called K-loop derivation and obtain a K-loop with fibration. In order to achieve similar results for elliptic reflection spaces we have to claim further conditions (the existence of a so called midpoint domain) and to extend the notion K-loop to partial K-loop with fibration.     

Homogeneous Poisson Structures on Symmetric Spaces

We calculate, in a relatively explicit way, the Hamiltoniansystems that arise from the Evens–Lu construction of homogeneousPoisson structures on both compact- and noncompact-type symmetricspaces. A corollary is that the Hamiltonian system arising inthe noncompact case is isomorphic to the generic Hamiltoniansystem arising in the compact case. In the group case, thesesystems are also isomorphic to those arising from the Bruhat–Poissonstructure on the flag space, and hence, by results of Lu, canbe completely factored.     

Generalized Tensor Structures of Kawaguchi Spaces

We prove that, in a generalized Kawaguchi space, there exist intrinsic almost product and almost complex structures associated to a metric of this space. We derive conditions for the integrability of these structures and find compatible affine connections.     

Statistical Structures on Metric Path Spaces

The authors extend the notion of statistical structure from Riemannian geometry to the general framework of path spaces endowed with a nonlinear connection and a generalized metric. Two particular cases of statistical data are defined. The existence and uniqueness of a nonlinear connection corresponding to these classes is proved. Two Koszul tensors are introduced in accordance with the Riemannian approach. As applications, the authors treat the Finslerian (α, β)-metrics and the Beil metrics used in relativity and field theories while the support Riemannian metric is the Fisher-Rao metric of a statistical model.     

The Eigenspaces of the Bose-Mesner-Algebras of the Association Schemes Corresponding to Projective Spaces and Polar Spaces

In an earlier paper 7, some properties of the eigenspaces of the Bose-Mesner-algebras of association schemes are figured out, leaving open the problem of determining the eigenspaces. In the present paper, these eigenspaces and the eigenvalues are determined for projective spaces and for polar spaces. This allows characterizations of certain sets of subspaces of these geometries.     

Uniform Structures of Metric Spaces and Open Manifolds

For the set of noncompact proper metric spaces we define series of uniform structures of Gromov-Hausdorff or Lipschitz type, respectively, and characterize the (arc) components. These are the first steps to an effective classification approach for metric L₂-Poincare complexes and complete manifolds.     

The Stochastic Reflection Problem in Hilbert Spaces

We construct a Markov process X associated with the stochastic reflection problem on a closed convex subset with non empty interior and smooth boundary in a Hilbert space, as a solution to a random convex control problem. The transition semigroup corresponding to X is exactly that defined by the Kolmogorov equation with Neumann homogeneous boundary conditions (see [3 Barbu , V. , Da Prato , G. , Tubaro , L. ( 2011 ). Kolmogorov equation associated to the stochastic reflection problem on a smooth convex set of a Hilbert space II . Ann. Inst. H. Poincaré 4 : 699 – 724 .[Crossref] , [Google Scholar]]).     

Geometric Structures over Four-Dimensional Generalized Symmetric Spaces

We classify Walker structures, self-dual and anti-self-dual metrics among the invariant metrics of four-dimensional generalized symmetric spaces.     

KM伪度量空间中的模糊化收敛结构

分别提供了由KM伪度量到模糊化收敛结构和由模糊伪度量链到模糊化收敛结构的转化方法,并且证明了由KM伪度量诱导的模糊化拓扑进而诱导的模糊化收敛结构和KM伪度量直接诱导的模糊化收敛结构相同.而且,还证明了由KM伪度量诱导的模糊伪度量链进而诱导的模糊化收敛结构和由KM伪度量直接诱导的模糊化收敛结构相同.     

On Priestley Spaces of Lattice-Ordered Algebraic Structures

The laws defining many important varieties of lattice-ordered algebras, such as linear Heyting algebras, MV-algebras and l-groups, can be cast in a form which allows dual representations to be derived in a very direct, and semi-automatic, way. This is achieved by developing a new duality theory for implicative lattices, which encompass all the varieries above. The approach focuses on distinguished subsets of the prime lattice filters of an implicative lattice, ordered as usual by inclusion. A decomposition theorem is proved, and the extent to which the order on the prime lattice filters determines the implicative structure is thereby revealed.