In this work, two different structures are proposed which is fuzzy real normed space (FRNS) and fuzzy real Pre-Hilbert space (FRPHS). The basic concept of fuzzy norm on a real linear space is first presented to construct space, which is a FRNS with some modification of the definition introduced by G. Rano and T. Bag. The structure of fuzzy real Pre-Hilbert space (FRPHS) is then presented which is based on the structure of FRNS. Then, some of the properties and related concepts for the suggested space FRN such as -neighborhood, closure of the set named , the necessary condition for separable, fuzzy linear manifold (FLM) are discussed. The definition for a fuzzy seminorm on is also introduced with the prove that a fuzzy seminorm on is FRNS. The relationship between the -convergent sequence, -Cauchy sequence and -completeness is then investigated in this work. The structure of FRPHS with some important properties concerning on this space are introduced and proved. In addition, the property of orthogonality with some important properties for these spaces is included, for example the annihilator of the set . The relation between FRPHS and FRNS is investigated in the present work. Finally, after introducing the structure of FRPHS, it leads naturally to the definition of the most important class of FRPHS, namely the fuzzy real Hilbert space (FRHS).
This paper is concerned with introducing and studying the o-space by using out degree system (resp. i-space by using in degree system) which are the core concept in this paper. In addition, the m-lower approximations, the m-upper approximations and ospace and i-space. Furthermore, we introduce near supraopen (near supraclosed) d. g.'s. Finally, the supra-lower approximation, supraupper approximation, supra-accuracy are defined and some of its properties are investigated.
Abstract
This study aims to identify the repercussions of the Corona pandemic (Covid 19) and its impact on the educational and psychological functions of the Omani family from the point of view of a number of fathers and mothers. Drive for a group of fathers and mothers, some of whom work in the government sector and others are mothers enrolled in graduate studies programs at the university, their ages range between (30-50 years) totally (28) mothers and fathers: 22 mothers and 6 fathers. The results showed that the repercussions of the transformation of e-learning, home quarantine, social distancing, and the challenges associated with them were among the most frequent responses that posed a real challenge to the
... Show MoreWe aimed to examine the effect of amoxicillin and azithromycin suspensions on the microhardness of sliver-reinforced glass ionomer and nano-resin modified glass ionomer (GI). Method: Thirty discs (2mm height x 4mm diameter) of each type of GI were prepared, which were randomly assigned to amoxicillin, azithromycin, and artificial saliva groups. Microhardness was evaluated by Vickers hardness test before and after three immersion cycles. Results: The overall model (P < 0.001), before/after intervention (P < 0.001), intervention group (type of antibiotic) (P=0.013), and type of glass ionomer (P < 0.001) showed significant differences among study groups (P < 0.001). Post hoc test showed only non-significant before/after difference for Azithrom
... Show MoreAn experiment was conducted at botanical garden of Department of Biology ,College of Education (Ibn-AL –Haitham ,University of Baghdad during winter season of 2010 -2011.The aim of prsent study is to investigate the effect of Garlic (Allium sativum) extract and root extract of Ginger(Ziniber officinale)in two concentration of both extracts (20% and 30%)on growth and yield of (Cicer arietinum).The result showed that both extracts increased plant hight ,Chlorophyl content ,relative growth rate (RGR).Absolute growth rate (AGR),seeds yield .seed weight average ,biological yield ,carbohydrate and protein percentages in seeds,in comparsim with control plants .
Concrete structures is affected by a deleterious reaction, which is known as Alkali Aggregate Reaction (AAR). AAR can be defined as a chemical reaction between the alkali content in the pore water solution of the cement paste and reactive forms of silica hold in the aggregate. This internal reaction produces expansion and cracking in concrete, which can lead to loss of strength and stiffness. Carbon fiber-reinforced polymer (CFRP) is one of the methods used to suppress further AAR expansion and rehabilitate and support damaged concrete structures. In this research, thirty-six cylindrical specimens were fabricated from non-reactive and reactive concrete, which contained fused silica as