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).
To assess the biochemical, mechanical and structural characteristics of retained dentin after applying three novel bromelain‑contained chemomechanical caries removal (CMCR) formulations in comparison to the conventional excavation methods (hand and rotary) and a commercial papain‑contained gel (Brix 3000). Seventy‑two extracted permanent molars with natural occlusal carious lesions (score > 4 following the International Caries Detection and Assessment System (ICDAS‑II)) were randomly allocated into six groups (n = 12) according to the excavation methods: hand excavation, rotary excavation, Brix 3000, bromelain‑contained gel (F1), bromelain‑chloramine‑T (F2), and bromelain chlorhexidine gel (F3). The superficial and deepe
... Show MoreThis research investigates manganese (Mn) extraction from Electric Arc Furnace Steel Slag (EAFS) by using the Liquid-liquid extraction (LLE) method. The chemical analysis was done on the slag using X-ray fluorescence, X-ray diffraction, and atomic absorption spectroscopy. This work consisted of two parts: the first was an extensive study of the effect of variables that can affect the leaching process rate for Mn element from slag (reaction time, nitric acid concentration, solid to liquid ratio, and stirring speed), and the second part evaluates the extraction of Mn element from leached solution. The results showed the possibility of leaching 83.5 % of Mn element from the slag at a temperature of 25°C, nitric acid co
... Show MoreCommercial banks represent the main pivot in financing national economic activity and its development. The capital represents safety margin to depositors and represents a defense line that protects bank work from dangers. Basel committee requirements represent protection and comprehensive supervision to bank activities for depositors, debtors and the bank. It provides trust in bank dealings and tackles activities of high dangers. The most prominent of these requirements are capital adequacy that concerns bank management and supervision and auditing bodies such as the central bank and protecting banks that suffer weakness in its vital important borrowing activity that reflects weakness in implementing borrowing policy .The purpose
... Show MoreBackground: Melanin pigmentation of the gingiva appears in all ethnicities. Excessive pigmentation is an esthetic concern that has increased awareness about depigmentation procedures. This epidemiological study aims to find the correlation between skin color and gingival pigmentation in Sulaimani Governorate, Kurdistan/Iraq.
Subjects and Methods: A total of 820 apparently healthy and non-smokers, including 338 males and 482 females with healthy gingiva, aged between (18-40 years old) were enrolled in this study. Clinical examination on the participants’ gingivae was performed to assess color, and the distribution of pigmentations. Afterward the of participants skin color were
... Show MoreThe printing designer's creative thinking is a deliberate mental process based on specific skills that stimulate the motivation of the student to learn and call for new information for the investigation and research to discover the problems and attitudes and through reformulating the experience in new patterns depending on the active imagination and the flexible scientific thinking through providing the largest number possible of various unfamiliar printing design models, and testing their suitability and then readjusting the results with the availability of suitable educational, learning and academic atmosphere.
The designer's creative thinking depends on main skills. Fluency skill is to put t
... Show MoreBackground: This study was designed to measure the displacement pattern of posterior palatal seal (pps) area in different forms of the palate and with different impression techniques. Materials and method: This study was used to measure the displacement pattern of (pps)in different palatal shapes by using different impression materials Korrecta wax No.4,Green compound and design of House for pps for each palatal forms by using a 3D Scanner of CAD/CAM and measuring the distance between 2 points in pps area by using Caural Threw. Result: The results show highly significant differences between these techniques and the control group (impression with light body) Conclusion: The physiological impression technique of pps with Korecta wax no.4
... Show MoreA simple straightforward mathematical method has been developed to cluster grid nodes on a boundary segment of an arbitrary geometry that can be fitted by a relevant polynomial. The method of solution is accomplished in two steps. At the first step, the length of the boundary segment is evaluated by using the mean value theorem, then grids are clustered as desired, using relevant linear clustering functions. At the second step, as the coordinates cell nodes have been computed and the incremental distance between each two nodes has been evaluated, the original coordinate of each node is then computed utilizing the same fitted polynomial with the mean value theorem but reversibly.
The method is utilized to predict
... Show MoreThe study deals with the issue of multi-choice linear mathematical programming. The right side of the constraints will be multi-choice. However, the issue of multi-purpose mathematical programming can not be solved directly through linear or nonlinear techniques. The idea is to transform this matter into a normal linear problem and solve it In this research, a simple technique is introduced that enables us to deal with this issue as regular linear programming. The idea is to introduce a number of binary variables And its use to create a linear combination gives one parameter was used multiple. As well as the options of linear programming model to maximize profits to the General Company for Plastic Industries product irrigation sy
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