Research Article | Open Access
Utilization of a Green Brominating Agent for the Spectrophotometric Determination of Pipazethate HCl in Pure Form and Pharmaceutical Preparations
Five simple, accurate, and sensitive spectrophotometric methods (A–E) have been described for the indirect assay of pipazethate HCl (PZT) either in pure form or in pharmaceutical preparations. The proposed methods are based on the bromination of pipazethate HCl with a solution of excess bromate-bromide mixture in hydrochloric acid medium and subsequent estimation of the residual bromine by different reaction schemes. In the first three methods (A–C), the determination of the residual bromine is based on its ability to bleach the color of methyl orange, indigo carmine, or thymol blue dyes and measuring the absorbance at 520, 610, and 550 nm for methods A, B, and C, respectively. Methods D and E involves treating the unreacted bromine with a measured excess of iron(II), and the remaining iron(II) is complexed with 1,10-phenanthroline, and the increase in absorbance is measured at 510 nm for method D and the resulting iron(III) is complexed with thiocyanate and the absorbance is measured at 480 nm for method E. The different experimental parameters affecting the development and stability of the color are carefully studied and optimized. Regression analysis of the Beer-Lambert plots showed good correlation in the concentration ranges of 0.5–8.0 μg . The apparent molar absorptivity, Sandell's sensitivity, detection and quantitation limits were evaluated. The proposed methods have been applied and validated successfully for the analysis of the drug in its pure form and pharmaceutical formulations with mean recoveries of 99.94%–100.15% and relative standard deviation ≤1.53. No interference was observed from a common pharmaceutical adjuvant. Statistical comparison of the results with the reference method shows excellent agreement and indicates no significant difference in accuracy and precision.
Pipazethate HCl is 2-(2-piperidinoethoxy)ethyl 10H-pyrido [3,2-b] [1,4]benzothiadiazine-10-carboxylate hydrochloride (PZT) , (Figure 1). PZT is a nonnarcotic antitussive drug that acts by suppressing irritable and spasmodic cough by inhibiting the excitability of the cough centre and of peripheral neural receptors in the respiratory passage [2, 3]. The response to the drug takes about 10–20 min and lasts for 4–6 h.
Several methods have been reported for the determination of PZT in both pure and pharmaceutical preparations, include high-performance liquid chromatographic (HPLC) [4–6], thin-layer chromatography (TLC) , gas chromatography (GC) , electrochemical methods [9, 10], UV-spectrophotometry , and visible spectrophotometry [11–19]. However, many of the reported spectrophotometric methods suffered from one or other disadvantage like poor sensitivity, heating or extraction step, use of organic solvents, use of expensive chemical, and/or complicated experimental setup as can be seen from Table 1.
|: wavelength of maximum absorption; : molar absorptivity; LOD: limit of detection.|
The aim of the present work was to develop five new sensitive, cost effective spectrophotometric methods for the determination of PZT in pure drug as well as in pharmaceutical preparations based on bromination of PZT by a green brominating agent (i.e., bromine-generated in situ). The proposed methods utilize bromate-bromide mixture in HCl acid medium as the ecofriendly and green brominating agent, and by employing three dyes, methyl orange, indigo carmine or thymol blue and the remaining iron(II) with 1,10-phenanthroline or iron (III), and thiocyanate as auxiliary regents. The reaction conditions were thoroughly studied, and, under optimum conditions, the procedures provide highly sensitive and selective assays for PZT in commercial dosage forms for industrial quality control. The proposed methods are economical compared to the previously reported chromatographic techniques. Moreover, these methods are sensitive, and simple, does not involve heating or extraction step, and are free from usage of hazardous chemicals. Since inexpensive and easily available chemicals are used, the developed methods evidence low cost per analysis.
All the absorption spectral measurements were made using Kontron 930 (UV-visible) spectrophotometer (German) with scanning speed 200 nm/min and band width 1.0 nm equipped with 10 mm matched quartz cells. All chemicals used were of analytical reagent grade and distilled water was used to prepare all solutions.
2.2. Materials and Reagents
All reagents and chemicals used were of analytical or pharmaceutical grade, and all solutions were prepared fresh daily.(i)Standard PZT: pharmaceutical grade PZT was provided by the Egyptian International Pharmaceutical Industries Company (EIPICO, 10th of Ramadan, Egypt), which was used as received. Its purity was found to be 100.60 ± 0.61 . Pharmaceutical dosage forms, Selgon drops that are claimed to contain 40 mg PZT per 1.0 mL and Selgon tablets that are claimed to contain 20 mg per tablet were purchased from the local markets. All dosage forms were manufactured by the Egyptian International Pharmaceutical Industries Co. (EIPICO), Egypt.(ii)Stock standard solution of PZT: a stock standard solution containing (50 μg mL−1) of PZT.HCL was prepared by dissolving accurately weighed 5.0 mg of pure drug in bidistilled water and diluting to the mark in a 100 mL calibrated flask. (iii)Bromate-bromide mixture: a bromate-bromide solution equivalent to 100 μg mL−1 KBrO3 and 10-fold excess of KBr were prepared by dissolving accurately weighed 10 mg of KBrO3 and 100 mg of KBr in bidistilled water and diluting to the mark in a 100 mL calibrated flask. (iv)Hydrochloric acid: a 5.0 mol L−1 of HCl was prepared by diluting 43 mL of concentrated acid (Merck, Darmstadt, Germany, sp. gr. 1.18, 37%) to 100 mL with bidistilled water and further appropriately diluted to get 2.0 mol L−1 acid.(v)Methyl orange: a 5.0 × 10−4 mol L−1 of methyl orange (Sigma-Aldrich, assay 85%) was first prepared by dissolving accurately weighed 13.9 mg of dye in bidistilled water and diluting to 100 mL in a calibrated flask and filtered using glass wool.(vi)Indigo carmine: a 5.0 × 10−4 mol L−1 of indigo carmine (Sigma-Aldrich, assay 99%) was prepared by dissolving 23.31 mg of dye in bidistilled water and diluting to 100 mL in a calibrated flask.(vii)Thymol blue: a 1.0 × 10−3 mol L−1 of thymol blue (Sigma-Aldrich, assay 100%) was prepared by dissolving 46.67 mg of dye in bidistilled water and diluting to 100 mL in a calibrated flask.(viii)Ferrous ammonium sulphate (FAS): a stock solution of 5.0 × 10−3 mol L−1 FAS was freshly prepared by dissolving 0.1961 g from (NH4)2Fe(SO4)2·6H2O of the salt (Merck) in 20 mL water containing 1.0 mL of 1.0 mol L−1 H2SO4 and diluted to 100 mL with distilled water.(ix)1,10-Phenanthroline: a 0.2% of 1,10-phenanthroline monohydrate (Sigma Chemical Company, St. Louis, USA) solution was made up by dissolving the solid in 1.0 mL of 2.0 mol L−1 HCl and diluted to 100 mL with water.(x)Ammonium thiocyanate: a 1.0 mol L−1 ammonium thiocyanate was prepared by dissolving 7.67 g of the chemical (Merck) in 100 mL water.(xi)Ammonia solution: a 1 : 1 ammonia solution was prepared by diluting 50 mL of strong ammonia with 50 mL of water.
2.3. Recommended Analytical Procedures
2.3.1. Methods (A–C)
Accurately measured volumes equivalent to (0.1–1.6 mL) of PZT standard solution (50 μg mL−1) were transferred into a series of 10 mL calibrated flasks by means of a microburette. To each flask, 1.0 mL of 2.0 mol L−1 HCl for methods (A or C) or 5.0 mol L−1 HCl for method B was added. Then, 1.5 mL of bromate-bromide (100 μg mL−1 in KBrO3) was added. The flasks were stoppered, content mixed and let stand for 10 min with occasional shaking. Finally, 1.5 and 2.0 mL of 5.0 × 10−4 mol L−1 methyl orange and indigo carmine, respectively or 1.0 mL of 1.0 × 10−3 mol L−1 thymol blue were added, and the contents were diluted to the mark with distilled water and mixed well. The absorbance of each solution was measured at 510, 610, and 550 nm against a reagent blank after 5.0 min for methyl orange, indigo carmine, and thymol blue, respectively.
2.3.2. Methods (D and E)
Into a series of 10 mL volumetric flasks, different aliquots (0.1–0.8 mL) of PZT standard solution (50 μg mL−1) were transferred by means of a microburette. The solution was acidified by adding 1.0 mL of 2.0 and 5.0 mol L−1 HCl for methods D and E, respectively. Then, 1.0 mL of bromate-bromide (100 μg mL−1 in KBrO3) solution was then added to each flask. The flasks were kept a side for 10 and 5.0 min, for methods D and E, respectively with occasional shaking. Then, 0.8 and 1.5 mL of 5.0 × 10−3 mol L−1 of FAS were added for methods D and E, respectively, and mixed well. After 5.0 min, 1.0 mL of 0.2% of 1,10-phenanthroine and 1.0 mL of 1 : 1 ammonia solution were added to each flask for method D. After 10 min, 2.0 mL of 1.0 mol L−1 ammonium thiocyanate solution was added to each flask for method E. The solutions in the calibrated flasks were made up to 10 mL with bidistilled water. The absorbance of the colored product of oxidation was measured at 510 and 480 nm against the reagent blank treated similarly, after 10 and 5.0 min for methods D and E, respectively.
In all spectrophotometric methods, the calibration graph was prepared by plotting the absorbance versus the concentration of drug (methods A–D) and by plotting the absorbance of thiocyanate complex against water blank (method E). The concentration of the unknown drug in each sample was calculated or computed either from the calibration graph or the regression equation derived using Beer’s law data.
2.3.3. Procedures for Pharmaceutical Preparations
(1) Procedure for Tablets. Twenty tablets of the drug (Skelegon tablets, 20 mg PZT per tablet) were accurately weighed, finely powdered, and the average weight of tablet was calculated. A portion of the powder equivalent to 20 mg of the PZT was dissolved in bidistilled water. The solution was shaken well and filtered through a Whatman filter paper no. 42, and the filtrate was made up to 100 mL with distilled water. An aliquot of the diluted drug solution was then treated as described above in procedures A–E.
(2) Procedure for Drops. The contents of five bottles (Selgon drops, 40 mg PZT per mL) were mixed well. An aliquot volume of the solution equivalent to 20 mg PZT was quantitatively transferred to 100 mL calibrated flask and made up to the mark with bidistilled water. The above-stated procedures described were applied to determine drug concentrations.
3. Results and Discussion
3.1. Methods (A–C) Using Three Dyes
The acidified solution of bromate and bromide behaves as an equivalent solution of bromine and has been widely used for the determination of many organic and inorganic substances. The proposed spectrophotometric methods are indirect and are based on the determination of the residual bromine (in situ generated) after allowing the reaction between PZT and a measured amount of bromine to be complete. The bromine was determined by reacting it with a fixed amount of methyl orange, indigo carmine, or thymol blue dye. The methods make use of the oxidizing/brominating ability, and bleaching action of in situ generated bromine on the dyes is used, the discoloration being caused by the oxidative destruction of the dyes and measuring the absorbance at 520, 610, and 550 nm using methyl orange, indigo carmine, and thymol blue, respectively (Figure 2).
In this work, the development of the reaction occurs in two steps:(i)oxidation of PZT by bromine, in situ generated by the action of acid on a bromate-bromide mixture,(ii)determination of unreacted bromine by reacting it with a fixed amount of methyl orange (method A), indigocarmine (method B), or thymol blue (method C).
3.2. Optimum of Experimental Conditions
In order to establish the experimental conditions in methods A, B, and C, PZT was allowed to react with in the presence of dyes and HCl. The effect of reagent concentrations ( and dyes), temperature, time, and order of addition of reagents were studied by means of control experiments.
3.2.1. Selection of Acid Type and Acid Concentration
The reactions were tested in HCl, H2SO4, HNO3, and CH3COOH solutions. The results indicate that the reaction is suitable in hydrochloric acid medium. A 5.0 mol L−1 and 2.0 mol L−1 of hydrochloric acid for methods (A or C) and B, respectively, was found to be adequate for the oxidation reaction of the drug. The variation in HCl concentration indicated that constant absorbance was obtained with 0.25–3.0 mL of HCl with optimum concentrations; subsequent studies were performed with 1.0 mL of 2.0, and 5.0 mol L−1 HCl for methods (A or C) and B, respectively, was maintained for the bleaching step.
3.2.2. The Effect of Bromate Concentration
The effect of bromate concentration has been optimized, and the influence of KBr concentrations on the sensitivity were investigated. The results showed that in the absence of bromide the sensitivity was a little poor. The oxidation of PZT by bromate was accelerated when bromide is present. Therefore, in this work, the mixed reagent solution that contains a relatively large amount of bromide was used.
A bromate concentration of 100 μg mL−1 in the presence of a large excess of bromide was found to bleach the red, blue, and violet colors of methyl orange, indigocarmine, and thymol blue, respectively. Under the experimental conditions, the concentration range of was found to be 1.0–2.0 mL (100 μg mL−1 in KBrO3). Therefore, 1.5 mL of was adopted in the recommended procedure.
3.2.3. Sequence of Addition
The sequence of addition of bromate-bromide mixture, drug solution, and HCl was studied via the formation of the colored complexes. There was no appreciable change in the absorbance of oxidation product when the sequence of these reactants was altered.
3.2.4. The Effect of Dye Concentration
Preliminary experiments were performed to fix the upper concentrations of the dyes which could be spectrophotometrically determined in acid medium, and these were found to be 1.5 mL of 5.0 × 10−4 mol L−1 methyl orange, 2.0 mL of 5.0 × 10−4 mol L−1 indigo carmine, and 1.0 mL of 1.0 × 10−3 mol L−1 thymol blue.
3.2.5. The Effect of Time and Temperature
The reaction time between PZT and the bromine generated in situ was found to be ranged from 5.0 to 10 mins in the three methods at room temperature (25 ± 2°C) to give constant and reproducible absorbance values. After completion, the reaction between the drug and the bromine, the residual bromine would brominates the dyes, and this bromination process was found to be complete in 5.0 min for all three methods. The absorbance of the measured species was constant up to 12 hours even in the presence of the reaction products.
3.3. Method D and E
For method D, the colorimetric method based on the complexation reaction between iron(II) and 1,10-phenanthroline forming the red tris (o-phenanthroline) iron(II) chelate ion, called ferroin, continues to be the most sensitive and the most widely used procedure for the determination of iron in a variety of materials . The unreacted bromine is treated with a measured excess of iron(II), and remaining iron(II) is complexed with 1,10 phenanthroline and measured at 510 nm.
In method E, complex formation reaction involving iron(III) and thiocyanate is a well-known reaction that has been widely used for trace level determination of iron(III) . The present method is based on the oxidation-bromination of PZT with a solution of excess brominating mixture in hydrochloric acid medium. After bromination is completed, reduction of the residual oxidant by a fixed amount of iron(II) and subsequent formation of iron(III)-thiocyanate complex is measured at 480 nm. When a fixed concentration of bromate is reacted with increasing concentrations of PZT, there will be a proportional decrease in the concentration of the oxidant. The unreacted oxidant when treated with a fixed concentration of iron(II) accounts for a proportional decrease in the iron(III) concentration. This is observed as a proportional decrease in the absorbance of iron(III)-thiocyanate complex on increasing the concentration of PZT, as shown in (Figure 3), which formed the basis for the assay of drug.
3.3.1. Optimum of Experimental Conditions
The optimum reaction conditions for the quantitative determination of PZT were established through a number of preliminary experiments.
(1) The Effect of Acid Concentration. For method D, the formation of ferroin complex was slow at room temperature and at low pH and required longer time for completion. Hence, efforts were made to accelerate by carrying out the reaction at higher pH range (4.0–6.0). The pH of hydrochloric acidic medium employed for the redox reaction was raised by adding 1.0 mL of 1 : 1 ammonia solution which was found to be optimum. The volume of 1 : 1 ammonia was not critical, since the stability and sensitivity of ferroin are unaffected over a wide pH range. However, 1.0 mL of 1 : 1 ammonia was used to raise the pH to about 4.0 required for iron(II)-phenanthroline complex formation.
A 1.0 mL of 2.0 and 5.0 mol L−1 HCl for methods D and E, respectively, was used for the oxidation step which was complete in 10 and 5.0 min, for methods D and E, respectively, and the same acidic condition was used to reduce the residual bromine by iron(II); resulting iron(III).
(2) The Effect of Bromate Concentration. The results obtained show that at least 1.0 mL of (100 μg mL−1) bromate-bromide mixture is required for maximum color development.
(3) The Effect of Ferrous Ammonium Sulphate Concentration. The effect of FAS was studied by measuring the absorbance of solutions containing a fixed concentration of PZT and varied amounts of the reagent separately. It was observed that the maximum color intensity was obtained with 0.8 and 1.5 mL of 5.0 × 10−3 mol L−1 FAS for methods D and E, respectively, after which further increase in volume resulted in no change in the absorbance.
(4) The Effect of 1,10-Phenanthroline or Ammonium Thiocyanate Concentration. For method D, it was observed that the maximum color intensity was obtained with 0.8–1.2 mL of 0.2% 1,10-phenanthroine after which further increase in volume resulted in no change in the absorbance. Also, It was found that 1.8–2.2 mL of 1.0 mol L−1 of ammonium thiocyanate gave the maximum pronounced effect on the absorbance of iron(III)-thiocyanate complex for method E. Therefore, 1.0 mL of 0.2% 1,10-phenanthroine and 2.0 mL of 1.0 mol L−1 ammonium thiocyanate were employed in the investigation.
(5) The Effect of Time and Temperature. Developed color was stable for at least 6.0 and 4.0 h in the presence of reaction products for methods D and E, respectively. The influence of temperature was studied over the range of 25–100°C. The results show that the absorbance was decreased when the temperature was higher than 30°C. Therefore, the room temperature (25 ± 2°C) was adopted for further experiments.
Two blanks were prepared for method E. The reagent blank which contained optimum concentrations of all the reagents except PZT gave maximum absorbance. The other blank was prepared in the absence of bromate and drug to determine the contribution of other reagents to the absorbance of the system. Since the absorbance of the second blank was negligible; the absorbance measurement was made against water blank.
3.4. Validation of the Proposed Methods
3.4.1. Linearity, Detection, and Quantification Limit
The linearity of the calibration graphs is apparent from the correlation coefficient (), obtained by determining the best-fit line via linear least-squares treatment . A linear relation was found between absorbance and concentration in the concentration ranges given in Table 2. The correlation coefficient (), the slope (), and the intercept () of the regression equation ( = absorbance and = PZT concentration in mol L−1), the apparent molar absorptivity (), Sandell’s sensitivity, limit of detection (LOD), and limit of quantification (LOQ) are summarized in Table 2. Results listed in Table 2 indicate high sensitivity and low background effect of the methods. The percentage recoveries of the pure drug using the proposed methods compared with that given by the reported method are illustrated in Table 2. The proposed methods were evaluated by statistical analysis between the results achieved from the proposed methods and that of the reported method . Regarding the calculated Student’s -test and variance ratio -test (Table 2), there is no significant difference between the proposed and reported methods regarding accuracy and precision.
|, where is the concentration of PZT in g mL−1, is the absorbance units, is the intercept, and is the slope.|
bAverage of six determinations.
cThe theoretical values of and are 2.57 and 5.05, respectively, at confidence limit at 95% confidence level and five degrees of freedom ().
The Limits of detection (LOD) is defined as the minimum level at which the analyte can be reliably detected for PZT which was calculated using the following equation [22, 23] and listed in Table 2: where is the standard deviation of the absorbanceof replicate determination values under the same conditions as for the sample analysis in the absence of the analyte and is the sensitivity, namely, the slope of the calibration graph. In accordance with the formula, the detection limits were found to be 0.094, 0.086, 0.25, 0.072, and 0.102 μg mL−1 for methods A, B, C, D, and E, respectively.
The limits of quantization, LOQ, is defined as the lowest concentration that can be measured with acceptable accuracy and precision [22, 23]: According to this equation, the limit of quantization was found to be 0.31, 0.287, 0.83, 0.24, and 0.34 μg mL−1 for methods A, B, C, D, and E, respectively.
3.4.2. Accuracy and Precision
In order to evaluate the accuracy and precision of the proposed methods, four concentrations of pure PZT solution within the linearity range were chosen. Intraday precision was carried out by using the recommended volumes and concentrations of all the reagents through five independent analyses. The relative standard deviation (RSD%) was in the range of 0.76%–1.53%. In addition, the accuracy of the proposed methods was measured by calculating relative error (RE%), which was varied between −0.60% and 0.15%. The RSD% and RE% values which are less than 2.0% are indicative of good accuracy and precision of the methods (Table 3).
|Mean of five determination.|
bRSD%: percentage relative standard deviation; Er: percentage relative error.
cConfidence limit at 95% confidence level and four degree of freedom ().
The percentage relative error calculated using the following equation:
For a better picture of reproducibility on a day to-day basis, a series was run in which standard drug solution at four levels was determined each day for 5.0 days, preparing all the solutions afresh. The day-to-day RSD% values were less than 3.0% and represent the best appraisal of the procedures in daily use. For additional confirmation of the accuracy and precision of the proposed methods, standard addition method was performed by adding a known amount of pure drug to the preanalyzed dosage forms. The results suggest that the excipients, which are commonly presented in pharmaceutical formulations, do not interfere with the proposed methods as shown in Table 4.
|Average of six determinations.|
3.4.3. Robustness and Ruggedness
Robustness was examined by evaluating the influence of a small variation of the method variables including the concentration of analytical reagents and reaction time on the performance of the proposed methods. In these experiments, one parameter was changed, whereas the others were kept unchanged, and the recovery percentage was calculated for each time (Table 5). It was found that small variations in these variables did not affect the method significantly. This was an indication of the reliability of the proposed methods during its routine application for analysis of the investigated drug, and so the proposed spectrophotometric methods are considered robust.
|Average of three determinations.|
bFollowing the general assay procedure conditions.
Method ruggedness was demonstrated by having the analysis done by three analysts, and also by a single analyst performing analysis on three different instruments in the same laboratory. The robustness and the ruggedness were checked at three different drug levels. The intermediate precision values expressed as (RSD%) which is a measure of robustness and ruggedness were in the range 0.45%–2.16% indicating acceptable ruggedness limits. The results are presented in Table 5.
3.4.4. Interference Studies
The effects of common excipients and fillers added in pharmaceutical preparations were tested for their possible interferences in the assay of PZT. It was observed that the talc, glucose, starch, lactose, dextrose, and magnesium stearate did not interfere in the determination at the levels found in dosage forms. This is clear from the results obtained for pharmaceutical formulations, which are presented in Table 4.
3.5. Analytical Applications
The proposed methods were successfully applied for the determination of PZT in pharmaceutical formulations. The performance of the proposed methods was judged by calculating the Student’s - and -values. At 95% confidence level, the calculated - and -values did not exceed the theoretical values as evident from Table 6. Hence, it was concluded that there is no significant difference between the proposed methods and the reported method . Moreover, the spectrophotometric methods for the determination of PZT in pharmaceutical formulations reported in this paper are simple, fast, inexpensive, precise, and accurate, and it may be suitable for routine analysis.
|Average ± SD of six determinations.|
bTheoretical value for - and F-values for five degrees of freedom and 95% confidence limits () are 2.57 and 5.05, respectively.
3.6. Comparison with Other Methods
The performance of the proposed methods is compared with those of other existing spectrophotometric methods. Table 1 reveals that the proposed methods are more sensitive than the other reported spectrophotometric methods due to its higher molar absorptivity and low range under the Beer law limit. The proposed methods are also easier to perform and use inexpensive reagent and readily available compared to many reported technique [12, 14–18] and do not require any expensive or toxic reagents or organic solvents [15, 16]. The comparative study of the molar absorptivity indicated good sensitivity of the proposed methods which follow the order of E > A > D > B > C. The proposed methods do not require any pretreatment of the drug and tedious extraction procedure prior to its analysis.
Five sensitive spectrophotometric methods for the determination of PZT have been developed and validated based on the current ICH guidelines . The present methods demonstrate that bromate-bromide mixture and three dyes, methyl orange, indigo carmine or thymol blue and the remaining iron(II) with 1,10-phenanthroline or iron (III), and thiocyanate as auxiliary regents can be used for the quantitative determination of PZT in bulk drug as well as pharmaceutical preparations. The proposed methods have the advantages of utilization of bromine generated in situ as a green brominating reagent, free from critical experimental conditions, and complicated procedures such as heating or extraction step. The reagents used in the proposed methods are cheap, readily available, and the procedures do not involve any tedious sample preparation. These advantages encourage the application of the proposed methods in routine quality control analysis of PZT in pharmaceutical preparations.
|:||Wavelength of maximum absorption|
|ICH:||The international Conference on Harmonization|
|LOD:||Limit of detection|
|LOQ:||Limit of quantification|
|RSD:||Relative standard deviation|
|Er:||Percentage relative error.|
Conflict of Interests
The author declares that he has no conflict of interests.
The author is thankful to Professor Dr. Ragaa El Sheikh for helping him in this work.
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