This paper is concerned with introducing an explicit expression for orthogonal Boubaker polynomial functions with some important properties. Taking advantage of the interesting properties of Boubaker polynomials, the definition of Boubaker wavelets on interval [0,1) is achieved. These basic functions are orthonormal and have compact support. Wavelets have many advantages and applications in the theoretical and applied fields, and they are applied with the orthogonal polynomials to propose a new method for treating several problems in sciences, and engineering that is wavelet method, which is computationally more attractive in the various fields. A novel property of Boubaker wavelet function derivative in terms of Boubaker wavelet themselves is also obtained. This Boubaker wavelet is utilized along with a collocation method to obtain an approximate numerical solution of singular linear type of Lane-Emden equations. Lane-Emden equations describe several important phenomena in mathematical science and astrophysics such as thermal explosions and stellar structure. It is one of the cases of singular initial value problem in the form of second order nonlinear ordinary differential equation. The suggested method converts Lane-Emden equation into a system of linear differential equations, which can be performed easily on computer. Consequently, the numerical solution concurs with the exact solution even with a small number of Boubaker wavelets used in estimation. An estimation of error bound for the present method is also proved in this work. Three examples of Lane-Emden type equations are included to demonstrate the applicability of the proposed method. The exact known solutions against the obtained approximate results are illustrated in figures for comparison
Atenolol was used with ammonium molybdate to prove the efficiency, reliability and repeatability of the long distance chasing photometer (NAG-ADF-300-2) using continuous flow injection analysis. The method is based on reaction between atenolol and ammonium molybdate in an aqueous medium to obtain a dark brown precipitate. Optimum parameters was studied to increase the sensitivity for developed method. A linear range for calibration graph was 0.1-3.5 mmol/L for cell A and 0.3-3.5 mmol/L for cell B, and LOD 133.1680 ng/100 µL and 532.6720 ng/100 µL for cell A and cell B respectively with correlation coefficient (r) 0.9910 for cell A and 0.9901 for cell B, RSD% was lower than 1%, (n=8) for the determination of ate
... Show MoreSignature verification involves vague situations in which a signature could resemble many reference samples or might differ because of handwriting variances. By presenting the features and similarity score of signatures from the matching algorithm as fuzzy sets and capturing the degrees of membership, non-membership, and indeterminacy, a neutrosophic engine can significantly contribute to signature verification by addressing the inherent uncertainties and ambiguities present in signatures. But type-1 neutrosophic logic gives these membership functions fixed values, which could not adequately capture the various degrees of uncertainty in the characteristics of signatures. Type-1 neutrosophic representation is also unable to adjust to various
... Show MoreTwitter is becoming an increasingly popular platform used by financial analysts to monitor and forecast financial markets. In this paper we investigate the impact of the sentiments expressed in Twitter on the subsequent market movement, specifically the bitcoin exchange rate. This study is divided into two phases, the first phase is sentiment analysis, and the second phase is correlation and regression. We analyzed tweets associated with the Bitcoin in order to determine if the user’s sentiment contained within those tweets reflects the exchange rate of the currency. The sentiment of users over a 2-month period is classified as having a positive or negative sentiment of the digital currency using the proposed CNN-LSTM
... Show MoreThe research dealt with a comparative study between some semi-parametric estimation methods to the Partial linear Single Index Model using simulation. There are two approaches to model estimation two-stage procedure and MADE to estimate this model. Simulations were used to study the finite sample performance of estimating methods based on different Single Index models, error variances, and different sample sizes , and the mean average squared errors were used as a comparison criterion between the methods were used. The results showed a preference for the two-stage procedure depending on all the cases that were used
In this work, studying the effect of ethylenediamine as a corrosion inhibitor was investigated for carbon steel in aerated HCl solution in range of 0.1-1N under dynamic conditions, i.e., rotational velocity of 400–1200 rpm in the temperature range 35 – 65 ºC. Weight loss method was employed in absence and presence of the inhibitor as an adsorption type in concentration range 1000 – 5000 ppm using rotating cylinder specimens. The experimental results showed that corrosion rate in absence and presence of inhibitor is increased with increasing temperature, rotational velocity and concentration of acid. It is decreased with increasing inhibitor concentration for the whole range of temperature, rotational velocity and concentrati
... Show MoreIn this research, salbutamol sulphate (SAS) has been determined by a simple, rapid and sensitive spectrophotometric method. Salbutamol sulphate in this method is based on the coupling of SAS with diazotized ρ- bromoaniline reagent in alkaline medium of Triton X-100 (Tx) to form an orange azo dye which is stable and water-soluble. The azo dye is exhibiting maximum absorption at 441 nm. A 10 - 800 µg of SAS is obeyed of Beer's law in a final volume of 20 ml, i.e., 0.5- 40 ppm with ε, the molar absorptivity of 48558 L.mol-1.cm-1 and Sandell's sensitivity index of 0.01188 µg.cm-2. This new method does not need solvent extraction or temperature control which is well applied to determine SAS in d
... Show MoreThe AlAdhaim Dam is located 133 kilometers northeast of Baghdad. It is a multipurpose dam and joints the Iraqi dam system in 2000. It has a storage capacity of 1.5 billion m3. The dam has an ogee spillway with a length of 562 m, a crest level of 131.5 m.a.m.s.l. and a maximum discharge capacity of 1150 m3/s at its maximum storage height of 143 m.a.m.s.l. This research aimed to investigate the hydrodynamics performance of the spillway and the stilling basin of AlAdhiam Dam by using numerical simulation models under gated situations. It was suggested to modify the dam capacity by increasing the dam's storage capacity by installing gates on the crest of the dam spillway. The FLUENT program was used to
... Show MoreThe limitations of wireless sensor nodes are power, computational capabilities, and memory. This paper suggests a method to reduce the power consumption by a sensor node. This work is based on the analogy of the routing problem to distribute an electrical field in a physical media with a given density of charges. From this analogy a set of partial differential equations (Poisson's equation) is obtained. A finite difference method is utilized to solve this set numerically. Then a parallel implementation is presented. The parallel implementation is based on domain decomposition, where the original calculation domain is decomposed into several blocks, each of which given to a processing element. All nodes then execute computations in parall
... Show MoreRecently, the financial mathematics has been emerged to interpret and predict the underlying mechanism that generates an incident of concern. A system of differential equations can reveal a dynamical development of financial mechanism across time. Multivariate wiener process represents the stochastic term in a system of stochastic differential equations (SDE). The standard wiener process follows a Markov chain, and hence it is a martingale (kind of Markov chain), which is a good integrator. Though, the fractional Wiener process does not follow a Markov chain, hence it is not a good integrator. This problem will produce an Arbitrage (non-equilibrium in the market) in the predicted series. It is undesired property that leads to erroneous conc
... Show MoreThis study depicts the removal of Manganese ions (Mn2+) from simulated wastewater by combined electrocoagulation/ electroflotation technologies. The effects of initial Mn concentration, current density (C.D.), electrolysis time, and different mesh numbers of stainless steel screen electrodes were investigated in a batch cell by adopting Taguchi experimental design to explore the optimum conditions for maximum removal efficiency of Mn. The results of multiple regression and signal to noise ratio (S/N) showed that the optimum conditions were Mn initial concentration of 100 ppm, C.D. of 4 mA/cm2, time of 120 min, and mesh no. of 30 (wire/inch). Also, the relative significance of each factor was attained by the analysis
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