Analysis of Exact Solutions to Some Systems of Difference Equations

Some nonlinear difference equations can be sometimes solved analytically using manual iteration which begins with some given initial conditions. Obtaining next iterations always depends on the previous ones. Through this paper, we utilize the manual iteration in investigating the exact solutions of the following recursive sequences   $x_{n+1}=\frac{y_{n-5}x_{n-8}}{y_{n-2}(-1-y_{n-5}x_{n-8})},\ \ \ \ \ y_{n+1}=\frac{x_{n-5}y_{n-8}}{x_{n-2}\left( \pm1\pm x_{n-5}y_{n-8}\right) },$   where the initial conditions $x_{\delta},\ y_{\delta},\ \delta\in \{0,1,...,8\}$ are non-zero real numbers. Some numerical solutions are also presented in some figures to show the behaviour of the solutions. &nbsp

The what and where of adding channel noise to the Hodgkin-Huxley equations

One of the most celebrated successes in computational biology is the Hodgkin-Huxley framework for modeling electrically active cells. This framework, expressed through a set of differential equations, synthesizes the impact of ionic currents on a cell's voltage -- and the highly nonlinear impact of that voltage back on the currents themselves -- into the rapid push and pull of the action potential. Latter studies confirmed that these cellular dynamics are orchestrated by individual ion channels, whose conformational changes regulate the conductance of each ionic current. Thus, kinetic equations familiar from physical chemistry are the natural setting for describing conductances; for small-to-moderate numbers of channels, these will predict fluctuations in conductances and stochasticity in the resulting action potentials. At first glance, the kinetic equations provide a far more complex (and higher-dimensional) description than the original Hodgkin-Huxley equations. This has prompted more than a decade of efforts to capture channel fluctuations with noise terms added to the Hodgkin-Huxley equations. Many of these approaches, while intuitively appealing, produce quantitative errors when compared to kinetic equations; others, as only very recently demonstrated, are both accurate and relatively simple. We review what works, what doesn't, and why, seeking to build a bridge to well-established results for the deterministic Hodgkin-Huxley equations. As such, we hope that this review will speed emerging studies of how channel noise modulates electrophysiological dynamics and function. We supply user-friendly Matlab simulation code of these stochastic versions of the Hodgkin-Huxley equations on the ModelDB website (accession number 138950) and http://www.amath.washington.edu/~etsb/tutorials.html.Comment: 14 pages, 3 figures, review articl

The Effect of Continuous Suspension Constraint on the Free Vibration and Buckling of a Beam

In this paper, the free vibration and the buckling of a continuously suspended simply-supported beam are analyzed. A semi-analytical approach is used to calculate the natural circular frequencies and the critical forces of the beam. The length of the suspension is used as a parameter, and the natural circular frequencies and the critical forces are presented in a frequency map or a buckling map. The maps are analyzed in view of the trivial solutions, and the frequency map is compared to the map of discrete cable-stayed beams. Finally, for the validation of the results a numerical, finite element analysis is performed

Development of a Programmable Logic Controller Based Control System for a Water Plant

     The primary objective of this study is to use programmable logic techniques to control the operation of water sucking pumps to supply Bait Elmal plant from the S stream. Basically the proposed system works as follows: the raw water sucking pumps controlled by level sensors inside the water reservoir. The sand filter washing process is automatically initiated by level sensors installed inside the filter basin. Some are used to measure water flow rate and turbidity for adjusting the addition of chemicals    Practically the reservoir has been controlled by using two sensors connected to the raw water pumps through a Programmable Logic Controller (PLC). The filter washing  process valves are open and closed automatically by a signal coming from a control unit. The readings of flow rate, pH, and turbidity devices are used as inputs to the PLC with the aid of a program designed for automatically adjusting the addition of chemical materials      Finally, a complete control system has been successfully tested, where the sucking pumps are installed to supply Bait Elmal water plant from the river Nile. The result obtained prove the reliability and applicability or the system with more advantages at Bait Elmal plant or any similar drinking water plant

COMPREHENSIVE APPROACH FOR SWELLING SOILS REMEDIES

ABSTRACT: The effect of drying and remolding on undisturbed expansive soil samples were investigated at different periods. The results showed that the swelling potentials for remolded samples were higher than those for undisturbed samples for different periods of testing. The results also showed that final swells and swell pressures increased as the initial moisture contents decrease for both remolded and undisturbed samples. The swelling potential increased as the initial dry density increases for both remolded and undisturbed expansive soil samples, and vice versa The cement dust used as a new additive material to decrease the swelling potential of the expansive soil. The results showed that the plasticity index, linear shrinkage, and clay minerals decreased with increasing cement dust percentage, where 50% of the montmorillonite disappeared after treatment the soil with 5% cement dust. The effect of cement dust columns on the swelling potential of the soil also studied extensively. The cement dust columns were embedded in the middle of the expansive soils using CBR mould .The results showed that the swelling potential decreased with increasing number of cement dust columns and when increasing the diameter of the cement dust columns ,a distinctive decrease in the swelling potentials were recorded. When decreasing the densities and increasing the diameters of cement dust columns resulted in decreasing the swelling potentials of the expansive soil. The swelling of the expansive soil been decreased when increasing the number of reinforced and non-reinforced cement dust columns. The swelling potentials showed distinctive decrease when the lengths of the reinforced cement dust columns increased

Combining Islamic Equity Portfolios and Digital Currencies: Evidence from Portfolio Diversification

Digital currencies are unregulated and potentially have a destabilizing effect coupled with increased concerns over capital gains and losses in a high volatility environment. When added to a portfolio, this currency may have certain driving factors in terms of return and risks in the case of portfolio diversification. In this study, from the Sharia angle, we follow the position of Monzer Kahf (Fatwa on Bitcoin (by Monzer Kahf). http://lightuponlight.com/blog/fatwa-on-bitcoin-by-monzer-kahf/. Accessed 03 Feb 2020, 2017) who explained that Bitcoin is considered “Like any other currency”. It should be used under the “same conditions of exchanging currencies”. Therefore, we explore the effects of adding digital currencies to an Islamic portfolio by relying on a mean-variance efficient frontier and comparing the risk-return of portfolios with and without digital currencies for different scenarios. The results show that by adding digital currencies to Shariah-compliant portfolios, its performance improves; but this depends more or less on the increase in returns than in the reduction of total risk. Specifically, digital currencies may have a big role in bringing high risks with speculative effect in portfolio diversification. Therefore, we provide some recommendations to investors and regulators to secure these currencies in Islamic capital markets

Glomerulogenesis and Histomorphometeric in Mus musculus Embryo

In mammals, the kidneys originate in an embryo from the mesoderm through three excretory organs, namely: Pronephros, Mesonephros, and Metanephros. After the formation of Metanephros is completed, the kidneys begin to form nephrogenesis through mesenchymal cells located at the tip of the ureteric bud, that contribute in the formation of glomerulus and Renal tubules. The stages of glomerulus formation in the embryo of albino mice at the age of 14 to 19 days of gestation were studied. It was obtained after the sacrifice of the expectant mother and the kidneys were excised from the embryos and fixed using Aqueous Bouin's solution, Microscopic slices with a thickness of 6 microns were then made in a paraffin method and were photographed by a camera for microscopic imaging. Histological measurements were performed on them using the program IMAGE J program and analyzed statistically using the SPSS program.  Results of the current study showed the presence of five stages of glomerulus formation, namely, the renal vesicle, which represents the first stage in the formation of the nephron and glomerulus. This is followed by the Comma shape stage, S-shaped stage, Capillary loop stage and finally the Mature glomerulus. This is surrounded by a capsule, known as Bowman’s capsule being part of the Malpighian or Renal corpuscle. The statistical analysis showed that there were significant differences between the average diameters of the glomerular development stages, and that the mature glomerulus was larger in diameter than the rest of the stages. The study aims to determine the stages of glomerulus formation and histologically measure its diameter in the embryo of a Mus musculus.

An efficient system for preprocessing confocal corneal images for subsequent analysis

A confocal microscope provides a sequence of images of the various corneal layers and structures at different depths from which medical clinicians can extract clinical information on the state of health of the patient's cornea. Preprocessing the confocal corneal images to make them suitable for analysis is very challenging due the nature of these images and the amount of the noise present in them. This paper presents an efficient preprocessing approach for confocal corneal images consisting of three main steps including enhancement, binarisation and refinement. Improved visualisation, cell counts and measurements of cell properties have been achieved through this system and an interactive graphical user interface has been developed

An introduction to programming Physics-Informed Neural Network-based computational solid mechanics

Physics-informed neural network (PINN) has recently gained increasing interest in computational mechanics. In this work, we present a detailed introduction to programming PINN-based computational solid mechanics. Besides, two prevailingly used physics-informed loss functions for PINN-based computational solid mechanics are summarised. Moreover, numerical examples ranging from 1D to 3D solid problems are presented to show the performance of PINN-based computational solid mechanics. The programs are built via Python coding language and TensorFlow library with step-by-step explanations. It is worth highlighting that PINN-based computational mechanics is easy to implement and can be extended for more challenging applications. This work aims to help the researchers who are interested in the PINN-based solid mechanics solver to have a clear insight into this emerging area. The programs for all the numerical examples presented in this work are available on https://github.com/JinshuaiBai/PINN_Comp_Mech.Comment: 32 pages, 20 figures are include in this manuscrip