Nonlinear differential equation stability is a very important feature of applied mathematics, as it has a wide variety of applications in both practical and physical life problems. The major object of the manuscript is to discuss and apply several techniques using modify the Krasovskii's method and the modify variable gradient method which are used to check the stability for some kinds of linear or nonlinear differential equations. Lyapunov function is constructed using the variable gradient method and Krasovskii’s method to estimate the stability of nonlinear systems. If the function of Lyapunov is positive, it implies that the nonlinear system is asymptotically stable. For the nonlinear systems, stability is still difficult even though the Lyapunov methods are applied. There has to find a positive definite Lyapunov function, and its derivative function has to be negative definite. A new approach had been tested in several …
Background: Hyperfunction of the muscles of the upper lip is considered as the most common cause of excessive gingival display (EGD). The aim of this study was to demonstrate the effectiveness of botulinum toxin (BT) injection as a conservative treatment for EGD due to muscular hyperfunction and to compare the outcome of 2 injection methods. Material and methods: This study included 40 participants who were randomly assigned into 2 groups of 20 each, The first group received 2.5IU BT injection at 1 point per side (2-points group), while the second group received a total of 5 IU of BT at 2 points per side (4-points group). The outcome variables were the reduction in the central and lateral gingival display expressed as the difference between
... Show MoreA roundabout is a highway engineering concept meant to calm traffic, increase safety, reduce stop-and-go travel, reduce accidents and congestion, and decrease traffic delays. It is circular and facilitates one-way traffic flow around a central point. The first part of this study evaluated the principles and methods used to compare the capacity methods of roundabouts with different traffic conditions and geometric configurations. These methods include gap acceptance, empirical, and simulation software methods. Previous studies mentioned in this research used various methods and other new models developed by several researchers. However, this paper's main aim is to compare different roundabout capacity models for acceptabl
... Show MoreAmong several separation processes, the air flotation distinguish as remarkably high potential separation process related to its high separation efficiency and throughput, energy-efficient, simple process, cost-effective, applicable to a wide range of oily wastewater and no by-products. The current study aimed to investigate the effect of the type and concentration of surfactant on the stability of oil-water emulsion and efficiency of the separation process. For this purpose, three types of surfactant where used (anionic SDS, mixed nonionic Span 85/Tween 80, and cationic CTAB). The results demonstrated that the Span 85/Tween 80 surfactant has the best stability, and it increases with the surfactant concentration augmentation. The removal ef
... Show MoreIn this paper we prove the boundedness of the solutions and their derivatives of the second order ordinary differential equation x ?+f(x) x ?+g(x)=u(t), under certain conditions on f,g and u. Our results are generalization of those given in [1].
Purpose: This study aimed to compare the stability and marginal bone loss of implants inserted with flapped and flapless approaches 8 weeks after surgery and 3 months after loading. Material and Methods: Thirty SLActive implants were inserted in 11 patients and early loaded with final restoration 8 weeks after healing period. The stability values determined by Osstell and the marginal bone loss measured by CBCT at the initial time (1st) and 8 weeks of the healing period (2nd) and 3 months after loading (3rd). Results: The overall survival rate was 100%. A significant increase in the 3rd implant stability value in the age of ˂ 40. A significant decrease in the 2nd implant stability value in both gender and traumatic zone with a flapless app
... Show MoreBackground: Understanding the challenges facing nurses toward providing care to patients with cerebrovascular accidents is the initial step in developing strategies to address these challenges, thereby ensuring high-quality care. Aim: The study aimed to assess the challenges experienced by nurses in delivering care to patients with CVAs in neurological wards. Results: Of the 80 questionnaire participants in the qualitative part, (MS = 0.66) reported a "moderate" rating as an overall assessment. These challenges are divided into workload (MS = 0.53) at a moderate rate, the psychological burden (MS = 0.85) at a high rate, the supporting materials (MS = 0.85) at a high rate, the sense of responsibility (MS = 0.77) at a high rate, and the role
... Show MoreThe current research aims at finding out how to properly and correctly manage waste and solid waste and reduce the difficulties faced by all countries. However, it is becoming increasingly acute in developed cities because their economies are growing rapidly. It is necessary to identify the modern methods used in developed countries in managing wastes. The use of modern waste management techniques is a coordinated effort by international agencies within the borders responsible for them. The problem of the study can be identified in the lack of clarity of environmental management procedures in place. The importance of the research contributes to providing greater capacity to the administrative and technical leadership in the municipality
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