Let  be a non-trivial simple graph. A dominating set in a graph is a set of vertices such that every vertex not in the set is adjacent to at least one vertex in the set. A subset  is a minimum neighborhood dominating set if  is a dominating set and if for every  holds. The minimum cardinality of the minimum neighborhood dominating set of a graph  is called as minimum neighborhood dominating number and it is denoted by  . A minimum neighborhood dominating set is a dominating set where the intersection of the neighborhoods of all vertices in the set is as small as possible, (i.e., ). The minimum neighborhood dominating number, denoted by , is the minimum cardinality of a minimum neighborhood dominating set. In other words, it is the

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The best proximity point is a generalization of a fixed point that is beneficial when the contraction map is not a self-map. On other hand, best approximation theorems offer an approximate solution to the fixed point equation . It is used to solve the problem in order to come up with a good approximation. This paper's main purpose is to introduce new types of proximal contraction for nonself mappings in fuzzy normed space and then proved the best proximity point theorem for these mappings. At first, the definition of fuzzy normed space is given. Then the notions of the best proximity point and - proximal admissible in the context of fuzzy normed space are presented. The notion of α ̃–ψ ̃- proximal contractive mapping is introduced.

Every era characterizes with its thought and life philosophy , where Muslims left behind them educational and intellectual heritage we should proud of it because it reflects the image of past and lights the way of present and future path where we should make use of it to fit with our statuesque and contemporary issues because we don’t know about it but little as result of ignorance or imitation of the western culture.

      It’s wrong to regard heritage from the past but aphasia of Islamic and Arab genies that its roots tracing back to past and extending to future .

      Islamic Arab educational thought regards one of the ric

Based on Lyapunov exponent criterion, the aircraft lateral-directional stability during critical flight cases is presented. A periodic motion or limit cycle oscillation isdisplayed. A candidate mechanism for the wing rock limit cycle is the inertia coupling between an unstable lateral-directional (Dutch roll) mode with stable longitudinal (short period) mode. The coupling mechanism is provided by the nonlinear interaction of motion related terms in the complete set equations of motion. To analyze the state variables of the system, the complete set of nonlinear equations of motion at different high angles of attack are solved. A novel analysis including the variation of roll angle as a function of angle of attack is proposed. Furthermore

التعددية الثقافية هي مفهوم يتعلق بالمجتمعات التي تضم ثقافات عده، أو العالم الذي يتضمن ثقافات متنوعة؛ فالتعددية هي التنوع الثقافي والفكري؛ وبالتالي هي عنصر إثراء للإنسانية وأساس لوجودها؛ فالتعددية الثقافية تتضمن القبول بالثقافات والافكار الانسانية كلها، وإفساح المجال أمامها للمشاركة في بنا ء الثقافة والفكر العالمي؛ وهكذا فإنها تتمثل في التسامح مع الثقافات والافكار المختلفة الاعتراف بالهويات والخصوصيات

In this study lattice parameters, band structure, and optical characteristics of pure and V-doped ZnO are examined by employing (USP) and (GGA) with the assistance of First-principles calculation (FPC) derived from (DFT). The measurements are performed in the supercell geometry that were optimized. GGA+U, the geometrical structures of all models, are utilized to compute the amount of energy after optimizing all parameters in the models. The volume of the doped system grows as the content of the dopant V is increased. Pure and V-doped ZnO are investigated for band structure and energy bandgaps using the Monkhorst–Pack scheme's k-point sampling techniques in the Brillouin zone (G-A-H-K-G-M-L-H). In the presence of high V content, the ban

Potential health and environmental effects of nanoparticles need to be thoroughly assessed before their widespread commercialization. The present investigation was planned with the aims to determine the effects of gold nanoparticles (GNPs) on blast (BI) and mitotic (MI) indices of cultured lymphocytes. The results revealed that BI (50.3±2.3, 30.2±1.9, 10.5±0.7 and 0.0%, respectively) and MI (70.1±2.9, 20.4±1.1, 5.3±0.1 and 0.0%, respectively) showed a gradual decreased percentage as the concentration of GNPs was increased from 0.085 to 0.66 µg/mL, and the difference was significant compared to control culture (81.6±2.5 and 90.2±3.7%, respectively). A maximum inhibition of BI and MI was occurred at the concentration 0.66 µg/mL. In

The expression is a prominent feature of the Arabic language, but it is one of the characteristics that are inseparable from it. The expressive aspects of each other.
The issue of Arab differences and their impact on the divergence of meaning is one of the issues that have preoccupied the minds of the Arabic language owners and their views went to various doctrines. Introduction: (Whenever I finished a question concluded with a verse related to any download, and followed by the need for expressing, interpretation and interpretation) I found him in some of the Aarabip more than the face of some of the vocabulary raised and erected and a jar, when the verses of the Koran, resulting in a research lies between Grammar and the Koran under