The main purpose of this paper, is to introduce a topological space , which is induced by reflexive graph and tolerance graph , such that  may be infinite. Furthermore, we offered some properties of  such as connectedness, compactness, Lindelöf and separate properties. We also study the concept of approximation spaces and get the sufficient and necessary condition that topological space is approximation spaces.

This paper proposes feedback linearization control (FBLC) based on function approximation technique (FAT) to regulate the vibrational motion of a smart thin plate considering the effect of axial stretching. The FBLC includes designing a nonlinear control law for the stabilization of the target dynamic system while the closed-loop dynamics are linear with ensured stability. The objective of the FAT is to estimate the cubic nonlinear restoring force vector using the linear parameterization of weighting and orthogonal basis function matrices. Orthogonal Chebyshev polynomials are used as strong approximators for adaptive schemes. The proposed control architecture is applied to a thin plate with a large deflection that stimulates the axial loadi

Ab – initio restricted Hartree - Fock method within the framework of large unit cell (LUC) formalism is used to investigate the electronic structure of Si and Ge nanocrystals. The surface and core properties are investigated. A large unit cell of 8 atoms is used in the present analysis. Cohesive energy, energy gap, conduction and valence band widths are obtained from the electronic structure calculations. The results are compared with available experimental data and theoretical results of other investigators. The calculated lattice constant is found to be slightly larger than the corresponding experimental value because we use only 8 atoms and we compared the results with that of the bulk crystals, nanoclusters are expected to have str

The decoration structure in calligraphy painting is one of the variables that characterized the structure of the calligraphic composition due to the artistic, aesthetic and expressive properties of the letters of the Arabic calligraphy, which are represented by flexibility, compliance and the ability to form. Therefore, the researcher defined his problem by asking the following question: What is the decorative structure in the calligraphic painting? The study aimed to reveal the structure of the ornamentation in the calligraphy painting, while the researcher dealt with in the second chapter three sections, the first (the ornamental concept and meaning) and the second topic (the structural characteristics of the Arabic letter in the calli

  The current research discussed biophysics data as a theoretical and applied knowledge base linking industrial design with the natural sciences at the level of applied strategies through which we can enrich the knowledge base of industrial design. The research focused on two main aspects of the scientific references for biophysics, namely: electromagnetism, and biomechanics. According to the performance and functional applications in designing the functions of industrial products at the electromagnetic level, it was found that remote sensing applications: such as fire sensors that were adopted from the insect (Black Beetle) and that their metaphors enable them to hear fire, and collision sensors, which were adopted from the insect

The conditional style represents a form of structures built on associative relationships within the sentence sometimes, which also coincides with textual relationships at other times. It is based on the principle of semantic interrelation between the conditional verb and its response with a tool, as well as the textual context in which it is woven, which leads to the production of different meanings according to the stylistic structure of the condition and its context. Rhetoricians looked for those relationships and their semantic production especially with Al-Skaki and the rhetoricians after him, as they studied the harmony built on restriction and attachment in the conditional structure and what it carries of structural and semantic featu

      The Umm Er Radhuma unconfined aquifer Hydrogeochemistry in the Saudi – Iraq border desert was studied to identify the main hydrogeochemical processes and rock-water interaction. The measurements were done using standard APHA procedures. The results indicated that Na⁺ and Cl^- are the dominant ions in the groundwater. The average contribution of cations in the aquifer is Na⁺ + K⁺ ( 26 %), Ca²⁺ (14 %), and Mg²⁺ (10%) ; whereas anions contribution is Cl^- (24 %) , SO₄^2- (20 %), and HCO₃^- (6 %).  The results reflect that the examined water is hard water of neutral to slightly alkaline, slightly brackish, with m

problem of the research is the decline of the role of urban space with time as an influential system in societal relations. The research aims to define indicators for achieving social interaction in the city, and to determine indicators for achieving integration in the urban space, and to study the relationship between the integration of urban space and community interaction over time. the research assumed that by distinguishing the social interaction space from the urban space and developing urban spaces in order to be truly interactive spaces, this will help us achieve social interaction and build a positive relationship between them, which enables us to achieve integration within the urban spaces leading to social interaction. Because

The influence and hazard of fire flame are one of the most important parameters that affecting the durability and strength of structural members. This research studied the influence of fire flame on the behavior of reinforced concrete beams affected by repeated load. Nine self- compacted reinforced concrete beams were castellated, all have the same geometric layout (0.15x0.15x1.00) m, reinforcement details and compressive strength (50 Mpa). To estimate the effect of fire flame disaster, four temperatures were adopted (200, 300, 400 and 500) oC and two method of cooling were used (graduated and sudden). In the first cooling method, graduated, the tested beams were leaved to cool in air while in the second method, sudden, water splash was use

This paper is devoted to investigate experimentally and theoretically the structural behavior of reinforced concrete hollow beams which have internal transverse ribs under effect of shear. The number of the internal ribs is the major variable adopted in this research, while, the other variables are kept constant for all tested specimens. The experimental part includes poured and test of four (200x300x1200mm) beam specimens, three of these specimens were hollow with different locations of internal ribs and one of them was solid. The experimental results indicated that the shear strength are increased (33%) to (60%) for beams containing internal ribs in comparison with reference beam. Also, the change of beam state from ho