We consider two–phase metrics of the form φ(x, ξ) := αχBα(x) |ξ|+βχBα(x) |ξ|, where α,β are fixed positive constants, and Bα, Bβ are disjoint Borel sets whose union is R , and we prove that they are dense in the class of symmetric Finsler metrics φ satisfying α|ξ| ≤ φ(x, ξ) ≤ β|ξ| on R × R . Then we study the closure Cl(M θ ) of the class M α,β θ of two–phase periodic metrics with prescribed vo...

The aim of this paper is to introduce $(L,M)$-fuzzy closurestructure where $L$ and $M$ are strictly two-sided, commutativequantales. Firstly, we define $(L,M)$-fuzzy closure spaces and getsome relations between $(L,M)$-double fuzzy topological spaces and$(L,M)$-fuzzy closure spaces. Then, we introduce initial$(L,M)$-fuzzy closure structures and we prove that the category$(L,M)$-{bf FC} of $(L,M...

The variation of refrigerant mass in the cylinder of refrigerator compressor has a great influence on the compressor’s thermodynamic process. In this paper, the m-θ diagram, which represents the variation of refrigerant mass in compressor cylinder (m) and the crank angle (θ), is proposed to investigate the thermodynamic process of the refrigerator compressor. Comparing with the traditional pres...

the aim of this paper is to introduce $(l,m)$-fuzzy closurestructure where $l$ and $m$ are strictly two-sided, commutativequantales. firstly, we define $(l,m)$-fuzzy closure spaces and getsome relations between $(l,m)$-double fuzzy topological spaces and$(l,m)$-fuzzy closure spaces. then, we introduce initial$(l,m)$-fuzzy closure structures and we prove that the category$(l,m)$-{bf fc} of $(l,m...

We consider involutory antimorphisms θ of a free monoid A∗ and their fixed points, called θ-palindromes or pseudopalindromes. A θ-palindrome reduces to a usual palindrome when θ is the reversal operator. For any word w ∈ A∗ the right (resp. left) θ-palindrome closure of w is the shortest θ-palindrome having w as a prefix (resp. suffix). We prove some results relating θ-palindrome closure operat...

We study some new classes of generalized closed sets (in the sense of N. Levine) in a topological space via the associated δ-closure and θ-closure. The relationships among these new classes and existing classes of generalized closed sets are investigated. In the last section we provide an extensive and more or less complete survey on separation axioms characterized via singletons. 2000 AMS Clas...

In this paper, we characterize the intuitionistic fuzzy δ-continuous, intuitionistic fuzzy weakly δ-continuous, intuitionistic fuzzy almost continuous, and intuitionistic fuzzy almost strongly θ-continuous functions in terms of intuitionistic fuzzy δ-closure and interior or θ-closure and interior.

♣ Rings . A ring is a non-empty set R with two binary operations ( + , · ) , called addition and multiplication, respectively satisfying : Axiom 1. Closure ( + ) : ∀x, y ∈ R , x + y ∈ R . Axiom 2. Commutative ( + ) : For every x, y ∈ R , x + y = y + x . Axiom 3. Associative ( + ) : ∀x, y, z ∈ R , x + (y + z) = (x + y) + z . Axiom 4. Neutral ( + ) : ∃ θ ∈ R , such that ∀x ∈ R, x + θ = θ + x = x ...

Let M be a separable compact Hausdorff space with dim M ≤ 2 and θ : M → M be a homeomorphism with prime period p (p ≥ 2). Set Mθ = {x ∈ M | θ(x) = x} 6= ∅ and M0 = M\Mθ. Suppose that M0 is dense in M and H(M0/θ,Z) ∼= 0, H(χ(M0/θ),Z) ∼= 0. Let M ′ be another separable compact Hausdorff space with dim M ′ ≤ 2 and θ′ be the self–homeomorphism of M ′ with prime period p. Suppose that M ′ 0 = M ′\M ...

In this paper we solve some open problems related to (pseudo)palindrome closure operators and to the infinite words generated by their iteration, that is, standard episturmian and pseudostandard words. We show that if θ is an involutory antimorphism of A, then both θ-palindromic closures of any factor of a θ-standard word are also factors of some θ-standard word. We also introduce the class of ...