A stochastic scale conjugate neural network procedure for the SIRC epidemic delay differential system.

In this study, a stochastic computing structure is provided for the numerical solutions of the SIRC epidemic delay differential model, i.e. SIRC-EDDM using the dynamics of the COVID-19. The design of the scale conjugate gradient (CG) neural networks (SCGNNs) is presented for the numerical treatment of SIRC-EDDM. The mathematical model is divided into susceptible S(ρ), recovered R(ρ), infected I(ρ), and cross-immune C(ρ), while the numerical performances have been provided into three different cases. The exactitude of the SCGNNs is perceived through the comparison of the accomplished and reference outcomes (Runge-Kutta scheme) and the negligible absolute error (AE) that are performed around 10-06 to 10-08 for each case of the SIRC-EDDM. The obtained results have been presented to reduce the mean square error (MSE) using the performances of train, validation, and test data. The neuron analysis is also performed that shows the AE by taking 14 neurons provide more accurateness as compared to 4 numbers of neurons. To check the proficiency of SCGNNs, the comprehensive studies are accessible using the error histograms (EHs) investigations, state transitions (STs) values, MSE performances, regression measures, and correlation.

A novel generalized Weibull Poisson G class of continuous probabilistic distributions with some copulas, properties and applications to real-life datasets.

The current study introduces and examines copula-coupled probability distributions. It explains their mathematical features and shows how they work with real datasets. Researchers, statisticians, and practitioners can use this study's findings to build models that capture complex multivariate data interactions for informed decision-making. The versatility of compound G families of continuous probability models allows them to mimic a wide range of events. These incidents can range from system failure duration to transaction losses to annual accident rates. Due to their versatility, compound families of continuous probability distributions are advantageous. They can simulate many events, even some not well represented by other probability distributions. Additionally, these compound families are easy to use. These compound families can also show random variable interdependencies. This work focuses on the construction and analysis of the novel generalized Weibull Poisson-G family. Combining the zero-truncated-Poisson G family and the generalized Weibull G family creates the compound G family. This family's statistics are mathematically analysed. This study uses Clayton, Archimedean-Ali-Mikhail-Haq, Renyi's entropy, Farlie, Gumbel, Morgenstern, and their modified variations spanning four minor types to design new bivariate type G families. The single-parameter Lomax model is highlighted. Two practical examples demonstrate the importance of the new family.

Coupling of physical extraction and mathematical filtration in spectrophotometric analysis of natural therapy essential for prophylaxis and treatment of COVID-19 infection - Comparative study along with greenness evaluation.

Diosmin (DIO) and hesperidin (HSP) are important classes of flavonoid glycoside effectively used to prevent comorbid diseases that are commonly associated with COVID-19. An innovative, green, ccurate, effective, cost, and timeless spectrophotometric strategy was established to analyze such challengeable mixture in a co-formulated tablet namely Diosed C® tablets that comprises DIO, HSP and vitamin C (VIT. C) in the ratio of (450 mg: 50 mg: 100 mg) necessary for prevention and treatment of COVID-19. Vitamin C was resolved through physical extraction using de-ionized water while DIO and HSP were extracted via spectrophotometric methods using two different solvents [0.1 M NaOH or solvent blend consisting of DMSO and methanol (1:1)]. Mathematical filtration technique is successfully applied to recover the parent spectra of both DIO and HSP via three methods which are absorbance resolution (AR), Induced absorbance resolution (IAR) and ratio extraction (RE). VIT. C was successfully analyzed in de-ionized water using its maxima at 266.0 nm in a linearity range 2.0-20.0 µg/mL, DIO was effectively determined in 0.1 M NaOH at 372.0 nm in a linearity range of 7.0-70.0 µg/mL as well as in solvent blend at 344.0 nm in linearity range of 5.0-55.0 µg/mL while HSP was accurately analyzed in 0.1 M NaOH at 240.0 nm in linearity range of 3.5-50.0 µg/mL as well as in solvent blend at 285.0 nm in linearity range of 4.0-50.0 µg/mL. Satisfactory results were accomplished when conducting ICH guidelines for assuring the methods validation. Comparative study was introduced in the analysis of such critical combination and was prosperously devoted for the effective analysis of pharmaceutical dosage form. The proposed extraction pathways undergo the guidelines of green analytical chemistry using Analytical Eco-Scale (AES), AGREE and GAPI greenness assessment tools which confirmed their eco-friendly nature with priority to 0.1 M NaOH. The obtained results of the suggested methods were set side by side with those of official/reported methods statistically and show satisfactory implications. The presented methods were simple, affordable, smoothly applicable and their results were acceptable that enhances their usage and application in the quality control laboratories.

Spectral technique with convergence analysis for solving one and two-dimensional mixed Volterra-Fredholm integral equation.

A numerical approach based on shifted Jacobi-Gauss collocation method for solving mixed Volterra-Fredholm integral equations is introduced. The novel technique with shifted Jacobi-Gauss nodes is applied to reduce the mixed Volterra-Fredholm integral equations to a system of algebraic equations that has an easy solved. The present algorithm is extended to solve the one and two-dimensional mixed Volterra-Fredholm integral equations. Convergence analysis for the present method is discussed and confirmed the exponential convergence of the spectral algorithm. Various numerical examples are approached to demonstrate the powerful and accuracy of the technique.

Exploiting the power of UPLC in separation and simultaneous determination of pholcodine, guaiacol along with three specified guaiacol impurities.

Pholcodine and guaiacol are widely used together in pharmaceutical syrups for cough treatment. On the other hand, the Ultra Performance Liquid Chromatographic technique is characterized by having the power of increasing chromatographic efficiency and decreasing run time compared to the traditional High Performance Liquid Chromatographic one. In this work, this power was exploited for the simultaneous determination of pholcodine, guaiacol along with three guaiacol impurities, namely; guaiacol impurity A, guaiacol impurity B, and guaiacol impurity E. Good separation was achieved by employing Agilent Zorbax C8 column (50 × 2.1 mm) as the stationary phase, and acetonitrile: phosphate buffer pH 3.5 (40: 60, by volume) as a mobile phase. The proposed method was validated as per International Council for Harmonisation guidelines. Linear relationships, at ranges of 50-1000 µg mL-1 for pholcodine and 5-100 µg mL-1 for guaiacol and the three related impurities, were established. Finally, the proposed method was applied for pholcodine and guaiacol determination in Coughpent® syrup and compared favorably to the reported one.

Green and Cost-Effective Extraction Techniques of Quercetin from Mixture of Nutraceuticals with Yield Analysis via Spectrophotometry and High-Performance Liquid Chromatography Methods.

BACKGROUND: Extraction is the leading critical stage in the analysis of nutraceuticals. Ginkgo biloba (GB) has gained interest because of its therapeutic usages. OBJECTIVES: The aim was to develop four cost-effective extraction techniques for the extraction of quercetin from GB in a sachet containing a mixture of nutraceuticals. These techniques are solid-phase extraction (SPE), liquid-liquid extraction, inverted dispersive liquid-liquid microextraction, and the QuEChERS (quick, easy, cheap, effective, rugged, and safe) method. METHOD: Direct spectrophotometry was used to monitor the recovery of the standard quercetin throughout the optimization steps. The HPLC-UV method of analysis was optimized to quantify the yields from the extracts present in the complicated contents of the sachets. The present study was assessed by analytical Eco-Scale assessment (ESA) and the National Environmental Method Index (NEMI) for greenness in comparison with the literature. RESULTS: SPE showed the best cleanup outcomes. ESA and NEMI showed an adequate greenness of the proposed extraction protocol. CONCLUSIONS: Quercetin (marker for GB) extraction from market nutraceutical sachets is considered an exemplar for analysis in the QC of nutraceuticals. Regarding the greenness results, the proposed method of extraction is better even with adequate greenness as the extraction was a one-step process, in comparison with multistep processes of previously published protocols. Accordingly, it is recommended for use in routine extraction and analysis of such nutraceuticals. HIGHLIGHTS: Four extraction protocols have been developed. For GB ternary-mixture sachets, proper recovery was obtained using C18 SPE. The assessment of greenness of the proposed protocol guaranteed the superiority of the presented method. Safer sorbents and chemicals are favored for use in routine extraction of nutraceuticals.

Numerical investigations of the nonlinear smoke model using the Gudermannian neural networks.

These investigations are to find the numerical solutions of the nonlinear smoke model to exploit a stochastic framework called gudermannian neural works (GNNs) along with the optimization procedures of global/local search terminologies based genetic algorithm (GA) and interior-point algorithm (IPA), i.e., GNNs-GA-IPA. The nonlinear smoke system depends upon four groups, temporary smokers, potential smokers, permanent smokers and smokers. In order to solve the model, the design of fitness function is presented based on the differential system and the initial conditions of the nonlinear smoke system. To check the correctness of the GNNs-GA-IPA, the obtained results are compared with the Runge-Kutta method. The plots of the weight vectors, absolute error and comparison of the results are provided for each group of the nonlinear smoke model. Furthermore, statistical performances are provided using the single and multiple trial to authenticate the stability and reliability of the GNNs-GA-IPA for solving the nonlinear smoke system.

Solid Phase Extraction and Simultaneous Chromatographic Quantification of some Non-steroidal Anti-inflammatory Drug Residues; an Application in Pharmaceutical Industrial Wastewater Effluent

Abstract Two sensitive and selective methods were developed for the simultaneous determination of four commonly used non-steroidal anti-inflammatory drugs (NSAIDs), namely; paracetamol (PCM), diclofenac sodium (DCF), ibuprofen (IBP), and indomethacin (IND) in wastewater effluents. The first method used HPLC for the determination of the studied drugs using a mobile phase consisting of phosphate buffer (pH 3.0) and acetonitrile at a flow rate of 1 mL/min. in gradient elution mode and detection at 220 nm. The separation process was performed on BDS Hypersil Cyano column (250 x 4.6 mm, 5 µm). The second method was a TLC-densitometric one which was performed using n-Hexane: ethyl acetate: acetic acid in the ratio (6:3.5:0.5) as a developing system. The proposed chromatographic methods were successfully applied for the selective determination of the four studied drugs in simulated and real pharmaceutical wastewater samples after their solid-phase extraction

An efficient numerical algorithm for solving fractional SIRC model with salmonella bacterial infection.

This paper revisits the study of numerical approaches for fractional SIRC model with Salmonella bacterial infection (FSIRC-MSBI). This model is investigated by the aid of fully shifted Jacobi's collocation method for temporal discretization. It is concluded that the method of the current paper is far more efficient and reliable for the considered model. Numerical results illustrate the performance efficiency of the algorithm. The results also point out that the scheme can lead to spectral accuracy of the studied model.

Development and Validation of Two Robust Stability-Indicating Chromatographic Methods for Determination of Metolazone in Drug Substance and Pharmaceutical Dosage Form in the Presence of Its Degradation Products and Characterization of Main Degradation Products Based on LC-MS.

Two robust and selective stability-indicating chromatographic methods were developed and validated for the determination of metolazone in drug substance and pharmaceutical dosage form in the presence of its degradation products. The HPLC method employed a Kromasil C18 (250 × 4.6,5 µm) column and a mobile phase of acetonitrile: 0.2% orthophosphoric acid (32:68 v/v) at a flow rate 2 mL/min and detection at 238 nm. The separation was performed in HPLC isocratic mode. The robustness of the suggested method was assessed using the Plackett-Burman design, parameters affecting system suitability were established and non-significant intervals for the significant parameters were considered. The HPTLC method employed Nano-SIL-20 UV254 HPTLC plates as adsorbent, ethyl acetate: toluene: acetic acid solution (4:4:0.5, v/v/v), as a developing solvent system and densitometric detection at 238 nm. Metolazone was exposed to different stress conditions, including acid and alkaline hydrolysis and oxidative and photolytic degradation. The main degradation products obtained have been characterized and interpreted based on LC-MS. The linearity of the suggested methods was proved in the concentration range of 20-75 µg/mL for the HPLC method and 100-900 ng/spot for the HPTLC method. The suggested methods were validated according to international conference on harmonization guidelines. These methods were successfully dedicated for the estimation of metolazone in drug substance and pharmaceutical dosage form in the presence of its degradation products. The results of the suggested methods were evaluated and compared statistically with results obtained by an official method without finding any significant difference.

Quantitative Determination of Synthesized Genotoxic Impurities in Nifuroxazide Capsules by Validated Chromatographic Methods.

Two accurate, selective, and precise chromatographic methods, namely TLC-densitometric and reversed-phase (RP)-HPLC, were developed and validated for the simultaneous determination of nifuroxazide (NIF) and its four synthesized impurities, which are also reported to be its related substances in the range of 10-100 µg/band and 10-100 µg/mL for NIF in the TLC and RP-HPLC methods, respectively. The developed TLC-densitometric method depended on the separation and quantitation of the studied components on silica gel 60 F254 TLC plates. Ethyl acetate-acetone-methanol-ammonia (85 + 25 + 5 + 0.5, v/v/v/v) was used as the developing system, and the separated bands were UV-scanned at 230 nm. On the other hand, the developed RP-HPLC method depended on chromatographic separation using a C8 column at 25°C and an aqueous solution of 0.1% sodium lauryl sulfate-acetonitrile as the mobile phase delivered according to the gradient elution program. Factors affecting the developed methods were studied and optimized. Also, method validation was carried out according to International Conference on Harmonization guidelines. The proposed methods were successfully applied for the determination of the studied drug in its bulk powder and in its pharmaceutical formulation. The developed methods showed no significant difference when compared with the reported RP-HPLC one. Their advantage is being the first stability-indicating methods for NIF and its genotoxic impurities.

A space-time spectral collocation algorithm for the variable order fractional wave equation.

The variable order wave equation plays a major role in acoustics, electromagnetics, and fluid dynamics. In this paper, we consider the space-time variable order fractional wave equation with variable coefficients. We propose an effective numerical method for solving the aforementioned problem in a bounded domain. The shifted Jacobi polynomials are used as basis functions, and the variable-order fractional derivative is described in the Caputo sense. The proposed method is a combination of shifted Jacobi-Gauss-Lobatto collocation scheme for the spatial discretization and the shifted Jacobi-Gauss-Radau collocation scheme for temporal discretization. The aforementioned problem is then reduced to a problem consists of a system of easily solvable algebraic equations. Finally, numerical examples are presented to show the effectiveness of the proposed numerical method.

A comparative study of ICH validated novel spectrophotometric techniques for resolving completely overlapping spectra of quaternary mixtures.

A pharmaceutically marketed mixture of Yohimbine, Alpha-tocopheryl acetate, Niacin, and Caffeine co-formulated as a promising therapy for erectile dysfunction. Simultaneous determination of the aforementioned pharmaceutical formulation without prior separation steps was applied using mean centering of ratio spectra and triple divisor spectrophotometric methods. Mean centering of ratio spectra method depended on using the mean centered ratio spectra in three successive steps which eliminated the derivative steps and so the signal to noise ratio was improved. The absorption spectra of the prepared solutions were measured in the wavelength range of 215-300 nm in the concentration ranges of 1-15, 3-15, 1-20, and 3-15 µg mL(-1) for Yohimbine, Alpha-tocopheryl acetate, Niacin, and Caffeine, respectively. The amplitudes of the mean centered third ratio spectra were measured at 250 nm and 268 nm for Yohimbine and Alpha-tocopheryl acetate, respectively and at peak to peak 272-273 and 262-263 nm for Niacin and Caffeine, respectively. In triple divisor method each drug in the quaternary mixture was determined by dividing the spectrum of the quaternary mixture by a standard spectrum of a mixture containing equal concentrations of the other three drugs. First derivative of these ratio spectra was obtained where determination could be achieved without any interference from the other three drugs. Amplitudes of 1-15, 3-15, 1-15, and 3-15 µg mL(-1) were used for selective determination of Yohimbine, Alpha-tocopheryl acetate, Niacin, and Caffeine, respectively. Laboratory prepared mixtures were analyzed by the developed novel methods to investigate their selectivity also, Super Act® capsules were successfully analyzed to ensure absence of interference from additives. The developed methods were validated according to the ICH guidelines. The proposed methods were statistically compared with each other and with the reported methods; using student t-test, F-test, and one way ANOVA, where no significant difference was found with respect to accuracy and precision.

Validated RP-HPLC and TLC-Densitometric Methods for Analysis of Ternary Mixture of Cetylpyridinium Chloride, Chlorocresol and Lidocaine in Oral Antiseptic Formulation.

This work was concerned with development, optimization, application and validation of reversed phase high performance liquid chromatography (RP-HPLC) and thin layer chromatography (TLC)-densitometric methods for analysis of cetylpyridinium chloride, chlorocresol and lidocaine in Canyon(®) gel. The first developed RP-HPLC method depended on chromatographic separation on a ZORBAX Eclipse Plus C8 column, with elution with a mobile phase consisting of 0.05% phosphoric acid solution : acetonitrile : methanol (15 : 24 : 61, by volume), pumping the mobile phase at a flow rate of 1.00 mL min(-1), with ultraviolet detection at 220 nm. While in the subsequently developed method, the TLC-densitometric method, complete separation of the studied mixture was achieved using methanol : acetone : acetic acid (7 : 3 : 0.2, by volume) as a mobile phase, aluminum plates precoated with silica gel 60 F254 as a stationary phase and 215 nm as the scanning wavelength. Factors affecting the developed methods were studied and optimized; moreover, methods had been validated as per the International Conference of Harmonization guideline and the results indicated that the suggested methods were reproducible, reliable and applicable for rapid routine analysis. Statistical comparison of the two developed methods with the reported HPLC ones using F- and Student's t tests showed no significant difference.

Novel spectrophotometric determination of flumethasone pivalate and clioquinol in their binary mixture and pharmaceutical formulation.

This work is concerned with development and validation of three simple, specific, accurate and precise spectrophotometric methods for determination of flumethasone pivalate (FP) and clioquinol (CL) in their binary mixture and ear drops. Method A is a ratio subtraction spectrophotometric one (RSM). Method B is a ratio difference spectrophotometric one (RDSM), while method C is a mean center spectrophotometric one (MCR). The calibration curves are linear over the concentration range of 3-45 µg/mL for FP, and 2-25 µg/mL for CL. The specificity of the developed methods was assessed by analyzing different laboratory prepared mixtures of the FP and CL. The three methods were validated as per ICH guidelines; accuracy, precision and repeatability are found to be within the acceptable limits.

Validated chromatographic methods for simultaneous determination of tolfenamic acid and its major impurities.

Two accurate, selective and precise chromatographic methods, namely thin-layer chromatography (TLC)-densitometric method and reversed phase high-performance liquid chromatography (RP-HPLC) method, were developed and validated for the simultaneous determination of tolfenamic acid (TOL) and its two major impurities, 2-chlorobenzoic acid (CBA) and 3-chloro-2-methylaniline (CMA), which are also reported to be its related substances. The developed TLC-densitometric method depended on separation and quantitation of the studied drugs on silica gel 60F254 TLC plates. Hexane:chloroform:acetone:acetic acid (75:25:20:0.1, v/v/v/v) was used as a developing system and the separated bands were UV-scanned at 240 nm. Linear relationships were obtained in the range of 10-100 µg band(-1) for the drug and in the range of 0.1-1 µg band(-1) for the studied impurities. The developed RP-HPLC depended on chromatographic separation of the studied drugs on a C18 column using 0.05 M KH2PO4 buffer (pH 3):acetonitrile (45:55, v/v) as a mobile phase delivered at constant flow rate of 1 mL min(-1) with UV detection at 230 nm. Calibration curves for TOL and the two impurities were constructed over the concentration ranges of 10-100 µg mL(-1) for TOL and 0.01-0.1 µg mL(-1) for both CBA and CMA. Factors affecting the developed methods have been studied and optimized. Further, methods validation has been carried out according to International Conference on Harmonization guidelines. The proposed methods were successfully applied for determination of the studied drug in its bulk powder and in pharmaceutical formulation. The methods showed no significant difference when compared with the reported RP-HPLC one. The developed methods have advantages of being more sensitive and specific than the published methods.

Kinetic study and mechanism of Niclosamide degradation.

A spectrophotometric kinetic study of Niclosamide alkaline degradation as a function of drug concentration, alkaline concentration and temperature has been established utilizing double divisor-ratio spectra spectrophotometric method. The developed method allowed determination of Niclosamide in presence of its alkaline degradation products; namely; 2-chloro-4-nitro aniline (DEG I) and 5-chloro salicylic acid (DEG II) with characterization of its degradation mechanism. It was found that degradation kinetic of Niclosamide followed pseudo-first order under the established experimental conditions with a degradation rate constant (k) of 0.0829 mol/h and half life (t1/2) of 8.35 h. The overall degradation rate constant as a function of the temperature under the given conditions obeyed Arrhenius equation where the activation energy was calculated to be 3.41 kcal/mol.

Validated stability indicating TLC-densitometric method for the determination of diacerein.

This work presents an accurate, sensitive and selective thin-layer chromatography-densitometry method for the simultaneous determination of diacerein in the presence of rhein, the active metabolite and hydrolytic degradation product of diacerein, and emodin, the diacerein impurity, in bulk powder and different pharmaceutical formulations. Chromatographic separation was performed on aluminum plates precoated with 60 F254 silica gel using hexane-ethyl acetate-acetic acid (60:40:0.8, by volume) as a developing system and with detection at 230 nm. The retention factor values of diacerein, rhein and emodin were 0.12, 0.44 and 0.6, respectively. The method was successfully applied for the determination of these compounds with high sensitivity; the linearity ranges were found to be 0.5-10 µg/band (for diacerein and rhein) and 0.5-7 µg/band (for emodin). The developed method was validated according to International Conference on Harmonization guidelines and was applied for the determination of diacerein in different pharmaceutical formulations. Moreover, a statistical comparison between the results of the developed method and those of the reported reversed-phase high-performance liquid chromatography method showed no significant differences. This method can be used for the routine analysis of diacerein, rhein and emodin in quality control laboratories.

Simultaneous HPTLC and RP-HPLC methods for determination of bumadizone in the presence of its alkaline-induced degradation product.

Accurate, selective, sensitive and precise HPTLC-densitometric and RP-HPLC methods were developed and validated for determination of bumadizone calcium semi-hydrate in the presence of its alkaline-induced degradation product and in pharmaceutical formulation. Method A uses HPTLC-densitometry, depending on separation and quantitation of bumadizone and its alkaline-induced degradation product on TLC silica gel 60 F(254) plates, using hexane-ethyl acetate-glacial acetic acid (8:2:0.2, v/v/v) as a mobile phase followed by densitometric measurement of the bands at 240 nm. Method B comprises RP-HPLC separation of bumadizone and its alkaline-induced degradation product using a mobile phase consisting of methanol-water-acetonitrile (20:30:50, v/v/v) on a Phenomenex C(18) column at a flow-rate of 2 mL/min and UV detection at 235 nm. The proposed methods were successfully applied to the analysis of bumadizone either in bulk powder or in pharmaceutical formulation without interference from other dosage form additives, and the results were statistically compared with the established method.

Validated chromatographic methods for determination of hydrochlorothiazide and spironolactone in pharmaceutical formulation in presence of impurities and degradants.

Two specific, sensitive, and precise stability indicating chromatographic methods have been developed, optimized, and validated for Hydrochlorothiazide (HCT) and Spironolactone (SPR) determination in their mixtures and in presence of their impurities and degradation products. The first method was based on thin layer chromatographic (TLC) combined with densitometric determination of the separated spots. The separation was achieved using silica gel 60 F(254) TLC plates and ethyl acetate-chloroform-formic acid-triethyl amine (7:3:0.1:0.1, by volume) as a developing system. Good correlations were obtained between the integrated peak area of the studied drugs and their corresponding concentrations in different ranges. The second method was based on the high-performance liquid chromatography with ultraviolet detection, by which the proposed components were separated on a reversed phase C(18) analytical column using gradient elution system with deionized water-acetonitrile (97:3, v/v) for 8 min. Then acetonitrile was successively increased to 35% in the next 2 min, and kept constant in the following 10 min, finally 3% acetonitrile was regained again to stabilize the chromatographic system. The flow rate was maintained at 2 mL/min and the detection wavelength was at 230 nm. Linear regressions were obtained in the range of 4.0-50 µg/mL and 5.0-50 µg/mL for both HCT and SPR, respectively. Different parameters affecting the suggested methods were optimized for maximum separation of the cited components. System suitability parameters of the two developed methods were also tested. The suggested methods were validated in compliance with the ICH guidelines and were successfully applied for determination of HCT and SPR in their commercial tablets. Both methods were also statistically compared to each other and to the reported method with no significant difference in performance.