In this paper, a sufficient condition for stability of a system of nonlinear multi-fractional order differential equations on a finite time interval with an illustrative example, has been presented to demonstrate our result. Also, an idea to extend our result on such system on an infinite time interval is suggested.
Experimental results for the density of states of hydrogenated amorphous silicon due to Jackson et al near the valence and conduction band edges were analyzed using Levenberg-Marquardt nonlinear fitting method. It is found that the density of states of the valence band and the conduction band can be fitted to a simple power law, with a power index 0.60 near the valence band edge, and 0.55 near the conduction band edge. These results indicate a modest but noticeable deviation from the square root law (power index=0.5) which is found in crystalline semiconductors. Analysis of Jackson et al density of states integral J(E) data over about (1.4 eV) of photon energy range, showed a significant fit to a simple power law with a power index of 2.11
... Show MoreThis research includes the use of an artificial intelligence algorithm, which is one of the algorithms of biological systems which is the algorithm of genetic regulatory networks (GRNs), which is a dynamic system for a group of variables representing space within time. To construct this biological system, we use (ODEs) and to analyze the stationarity of the model we use Euler's method. And through the factors that affect the process of gene expression in terms of inhibition and activation of the transcription process on DNA, we will use TF transcription factors. The current research aims to use the latest methods of the artificial intelligence algorithm. To apply Gene Regulation Networks (GRNs), we used a progr
... Show MoreIn this research a theoretical study has been carried out on the behavior and strength of simply supported composite beams strengthened by steel cover plate taking into consideration partial interaction of shear connectors and nonlinear behavior of the materials and shear connectors. Following the procedure that already has been adopted by Johnson (1975), the basic differential equations of equilibrium and compatibility were reduced to single differential equation in terms of interface slip between concrete slab and steel beam. Furthermore, in order to consider the nonlinear behavior of steel, concrete and shear connectors, the basic equation was rearranged so that all terms related to materials are isol
... Show MoreIn this paper, the dynamics of scavenger species predation of both susceptible and infected prey at different rates with prey refuge is mathematically proposed and studied. It is supposed that the disease was spread by direct contact between susceptible prey with infected prey described by Holling type-II infection function. The existence, uniqueness, and boundedness of the solution are investigated. The stability constraints of all equilibrium points are determined. In addition to establishing some sufficient conditions for global stability of them by using suitable Lyapunov functions. Finally, these theoretical results are shown and verified with numerical simulations.
This study involves the synthesis of a new class of silicon polymers, designated as P1-P7, derived from dichlorodimethylsilane (DCDMS) in combination with various organic compounds (Schiff bases prepared from different amines and appropriate aldehydes or ketones) [I-V] through condensation polymerization. The structures of all monomers and polymers were characterization by FTIR and 1HNMR spectroscopy (for some polymers). The results of thermogravimetric analysis (TGA) and differential scanning calorimetry DSC test show stable thermal behaviour. Polymers with a higher concentration of aromatic rings in their repeating structural units exhibited a higher temperature for weight loss, indicating increased thermal stability. Thermal meas
... Show MoreThis research discloses the synthesis of various polyester resins, the polyesters containing homoring aromatic and others heterocyclic were synthesized by the condensation polymerization of suitable monomers (which are containing variety function groups in different structures) with phthalic anhydride. The main objective is synthesis of new polyester with keeping a reasonable electrical insulating behavior. The structural of polymer was characterized by Fourier Transform infra-red spectroscopy FTIR and HNMR. The dielectric constant (real ε' and imaginary parts ε") and AC conductivity (σAC) for all the polyester samples are studied by varying the frequency (30, 50, 70, 90, 120, 300, 500Hz and 1KHZ) at 25⁰ C. Indeed, study of the electri
... Show MoreThe rheological and fusion behavior of polyvinyl chloride (PVC) compounds plays a dominant role in
the processing operations and in the development of physical properties in the processed material. A
comprehensive study was made in this work to evaluate the effect of shear and thermal history on stability, mechanical and rheological properties of rigid PVC compounds. Different samples of Rigid Poly vinyl chloride including dry blend powder, granules, and bottles molded from both were examined. A study was also made on recycled RPVC where 25% of reclaimed material was continuously blended with fresh dry blend and processed for 15 cycles. Results showed that compaction of the PVC material took place in the brabender plastograph at co
Stuck pipe is a prevalent and costly issue in drilling operations, with the potential to cost the petroleum industry billions of dollars annually. To reduce the likelihood of this issue, efforts have been made to identify the causes of stuck pipes. The main mechanisms that cause stuck pipes include drill cutting of the formation, inappropriate hole-cleaning, wellbore instability, and differential sticking forces, particularly in highly deviated wellbores. The significant consequences of a stuck pipe include an increase in well costs and Non-Productive Time (NPT), and in the worst-case scenario, the loss of a wellbore section and down-hole equipment, or the need to sidetrack, plug, or abandon the well. This paper provides a comprehensive
... Show MoreWe demonstrate a behavior of laser pulse grows through fiber laser inside and output cavity with a soliton fiber laser based on the multi-wall carbon nanotube saturable absorber (SA), we investigate the effects of a saturable absorber parameter on the mode-locking of a realistic Erbium fiber ring laser. Generalized nonlinear Schrodinger equation including the nonlinear effects as gain dispersion, second anomalous group velocity dispersion (GVD), self phase modulation (SPM), and two photon absorption used to describe pulse evolution. An analytical method has been used to understand and to quantify the role of the SA parameter on the propagation dynamics of pulse laser. We compute the chirp, power, width and phase of the soliton for range
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