The Caputo definition of fractional derivatives introduces solution to the difficulties appears in the numerical treatment of differential equations due its consistency in differentiating constant functions. In the same time the memory and hereditary behaviors of the time fractional order derivatives (TFODE) still common in all definitions of fractional derivatives. The use of properties of companion matrices appears in reformulating multilevel schemes as generalized two level schemes is employed with the Gerschgorin disc theorems to prove stability condition. Caputo fractional derivatives with finite difference representations is considered. Moreover the effect of using the inverse operator which transmit the memory and hereditary effects to other terms is examined. The theoretical results is applied to a numerical example. The calculated solution has a good agreement with the exact solution.
Cancer disease has a complicated pathophysiology and is one of the major causes of death and morbidity. Classical cancer therapies include chemotherapy, radiation therapy, and immunotherapy. A typical treatment is chemotherapy, which delivers cytotoxic medications to patients to suppress the uncontrolled growth of cancerous cells. Conventional oral medication has a number of drawbacks, including a lack of selectivity, cytotoxicity, and multi-drug resistance, all of which offer significant obstacles to effective cancer treatment. Multidrug resistance (MDR) remains a major challenge for effective cancer chemotherapeutic interventions. The advent of nanotechnology approach has developed the field of tumor diagnosis and treatment. Cancer nanote
... Show MoreBackground: The insertion torque (IT) values and implant stability quotient (ISQ) values are the measurements most used to assess primary implant stability. This study aimed to assess the relationship between ISQ values and IT. Materials and methods: This study included 24 patients with a mean (SD) age of 47.9 (13.64) years (range 25-75 years). The patients received 42 dental implants (DI), 33 in the mandible and 9 in the maxilla. The DI were installed using the motorized method with 35 Ncm torque, When DI could not be inserted to the requisite depth by the motorized method, a hand ratchet was used and the IT was recorded as ˃ 35 Ncm. Implant stability was measured utilizing Osstell® ISQ. The secondary stability was measured after 16
... Show MoreLanguage always conveys ideologies that represent an essential aspect of the world we live in. The beliefs and opinions of an individual or community can be organized, interacted with, and negotiated via the use of language. Recent researches have paid attention to bullying as a social issue. They have focused on the psychological aspect of bullying rather than the linguistic one. To bridge this gap, the current study is intended to investigate the ideology of bullying from a critical stylistic perspective. The researchers adopt Jeffries' (2010) critical stylistics model to analyze the data which is five extracts taken from Hunt’s Fish in a Tree (2015). The analysis demonstrates
... Show MoreIn every country in the world, there are a number of amputees who have been exposed to some accidents that led to the loss of their upper limbs. The aim of this study is to suggest a system for real-time classification of five classes of shoulder girdle motions for high-level upper limb amputees using a pattern recognition system. In the suggested system, the wavelet transform was utilized for feature extraction, and the extreme learning machine was used as a classifier. The system was tested on four intact-limbed subjects and one amputee, with eight channels involving five electromyography channels and three-axis accelerometer sensor. The study shows that the suggested pattern recognition system has the ability to classify the sho
... Show MoreThe present study deals with successive stages of productive
operations happened to produce a production within each stage befo re it moves to the next one. ll cou ld be deduced that this study is an extension to what bas been mentioned in (1 ) .ln (I), the optimum distribution of di!Terent jobs of workers and machines in the productive operations has been st ud ied whi le the study invol ves the optimum schedule for the succession of these operations presuming that thay have already been distributed on machines and workers (2).A mathematical form has been put for this study to define the "Object.ive Function "
... Show MoreDegenerate parabolic partial differential equations (PDEs) with vanishing or unbounded leading coefficient make the PDE non-uniformly parabolic, and new theories need to be developed in the context of practical applications of such rather unstudied mathematical models arising in porous media, population dynamics, financial mathematics, etc. With this new challenge in mind, this paper considers investigating newly formulated direct and inverse problems associated with non-uniform parabolic PDEs where the leading space- and time-dependent coefficient is allowed to vanish on a non-empty, but zero measure, kernel set. In the context of inverse analysis, we consider the linear but ill-pose
This paper considers a new Double Integral transform called Double Sumudu-Elzaki transform DSET. The combining of the DSET with a semi-analytical method, namely the variational iteration method DSETVIM, to arrive numerical solution of nonlinear PDEs of Fractional Order derivatives. The proposed dual method property decreases the number of calculations required, so combining these two methods leads to calculating the solution's speed. The suggested technique is tested on four problems. The results demonstrated that solving these types of equations using the DSETVIM was more advantageous and efficient