In this paper, we show that the category of directed complete posets with bottom elements (cpos) endowed with an action of a monoid M on them forms a monoidal category. It is also proved that this category is symmetric closed.

We consider a category C enriched over the segment [0; 1] whose hom-objects are real numbers from [0; 1]. For a suitably defined function ^v assigning to each formula ' some object of C, the hom-object C(^v('); ^v( )) represents the degree of derivability ofψ from φ. We reformulate completeness result for intuitionistic propositional logic, as well as H ajek's completeness results concerning the product, G odel and Lukasiewicz fuzzy logic in the context of enriched category theory.

Background and Aim: Different surgical techniques have been proposed for crown exposure among patients under orthodontic treatment. The aim of this study was to investigate periodontal indices in closed flap operation technique used for impacted teeth crown exposure.Materials and Methods: In this descriptive study (2001-2003) 20 patients (15 females and 5 males), age ranging from 15 to 20 years, were participated. Following the performance of closed flap operation technique, in 12 patients impacted canine and central incisors were exposed and treated orthodontically. Periodontal parameters including sulcular depth, width of keratinized gingiva and attachment loss were recorded. Results: The mean of gingival sulcus depth was 1.50±0.43, the means of keratinized gingival in central incisors and canines were 3.07±0.53 and 2.30±0.42, respectively. In one patient, attachment loss was reported.Conclusion: Considering the optimal sulcular depth and keratinized gingiva, the closed flap operation technique seems suitable.

In this paper first we define the morphism between geometric spaces in two different types. We construct two categories of U-GESP and L-GESP from geometric spaces then investigate some properties of the two categories, for instance U-GESP is topological. The relation between hypergroups and geometric spaces is studied. By constructing the category SNS-Hv of Hv-groups we answer the question that which construction of hyperstructures on the category of sets has free object in the sense of universal property. At the end we define the category of geometric Hypergroups and we study its relation with the category of hypergroup.

A category C is called Cartesian closed provided that it has  nite products and for each C-object A the functor (A  􀀀 ): A! A has a right adjoint. It is well known that the category TopFuzz of all topological fuzzes is both complete and cocomplete, but it is not Cartesian closed. In this paper, we introduce some Cartesian closed subcategories of this category.

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For many centuries the linguists have almost always studied morphology. But with the advent of Transformational Grammar , syntactic studies and the structure of sentences have earned maximum importance, therefore Sentence was the focus of study until 70s , and from then on , little by little linguists have begun to study the structure of NP, and they have found many similarities between NPs , VPs and sentences . The idea of this similarity has led to many comparative studies. The Empty category is one of the arguments discussed in sentence structure and pro /PRO is one of these empty categories. This article intends to indicate the existence of pro/PRO in NPs . Comparing Persian and Italian languages we find the same control properties in sentences.

The aim of this paper is to introduce an abstract notion of determinant which we call quantum determinant, verifying the properties of the classical one. We introduce R−, basis and R−, solution on rigid objects of a monoidal 𝐴, 𝑏, −, category, for a compatibility relation R, such that we require the notion of duality introduced by Joyal and Street, the notion given by Yetter and Freyd and the classical one, then we show that R−, solutions over a semisimple ribbon 𝐴, 𝑏, −, category form as well a semisimple ribbon 𝐴, 𝑏, −, category. This allows us to define a concept of so-called quantum determinant in ribbon category. Moreover, we establish relations between these and the classical determinants. Some properties of the quantum determinants are exhibited.