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The objective of this study, is characterization of partially purified beta-glucosidase (BGS) extracted from apricot defatted seeds powder. The enzyme was extracted using sodium phosphate solution (0.2M, pH 7) containing 2% sodium chloride with mixing ratio of (1:5 solid: liquid) for extraction period of 3 hours at 4C. The crude extract was precipitated by ammonium sulfate at 20-70% saturation, dialyzed then concentrated. The specific activity of the enzyme, folds of purification and the enzymatic yield were 5.45 units/mg, 7.8 fold and 84.5%, respectively. The results showed that the optimum conditions for the enzyme activity were at pH 5.5 and 6.5, the optimum temperature for the enzyme’s activity was 40°C and 55°C, while the thermal stability of the enzyme was between 25-45°C when the enzyme retained more than 90% of its activity over 30 minutes incubation at the optimum pH for activity, and retained 88% of its activity at 50° C. The results also revealed the inhibitory and activator effects of minerals and chemical compounds on the BGS activity.

The pantograph equation is a basic model in the field of delay differential equations. This paper deals with an extended version of the pantograph delay equation by incorporating a variable coefficient of exponential order. At specific values of the involved parameters, the exact solution is obtained by applying the regular Maclaurin series expansion (MSE). A second approach is also applied on the current model based on a hybrid method combining the Laplace transform (LT) and the Adomian decomposition method (ADM) denoted as (LTADM). Although the MSE derives the exact solution in a straightforward manner, the LTADM determines the solution in a closed series form which is theoretically proved for convergence. Further, the accuracy of such a closed-form solution is examined through various comparisons with the exact solution. For validation, the residual errors are calculated and displayed in graphs. The results show that the solution obtained utilizing the LTADM is in full agreement with the exact solution using only a few terms of the closed-form series solution. Moreover, it is found that the residual errors tend to zero, which reflects the effectiveness of the LTADM. The present approach may merit further extension by including other types of linear delay differential equations with variable coefficients.

The projectile motion (PP) in a vacuum is re-examined in this paper, taking into account the relativistic mass in special relativity (SR). In the literature, the mass of the projectile was considered as a constant during motion. However, the mass of a projectile varies with velocity according to Einstein’s famous equation m=m01−v2/c2, where m0 is the rest mass of the projectile and c is the speed of light. The governing system consists of two-coupled nonlinear ordinary differential equations (NODEs) with prescribed initial conditions. An analytical approach is suggested to treat the current model. Explicit formulas are determined for the main characteristics of the relativistic projectile (RP) such as time of flight, time of maximum height, range, maximum height, and the trajectory. The relativistic results reduce to the corresponding ones of the non-relativistic projectile (NRP) in Newtonian mechanics, when the initial velocity is not comparable to c. It is revealed that the mass of the RP varies during the motion and an analytic formula for the instantaneous mass in terms of time is derived. Also, it is declared that the angle of maximum range of the RP depends on the launching velocity, i.e., unlike the NRP in which the angle of maximum range is always π/4. In addition, this angle lies in a certain interval [π/4,π/6) for any given initial velocity (

Time dilation (TD) is a principal concept in the special theory of relativity (STR). The Einstein TD formula is the relation between the proper time t0 measured in a moving frame of reference with velocity v and the dilated time t measured by a stationary observer. In this paper, an integral approach is firstly presented to rededuce the Einstein TD formula. Then, the concept of TD is introduced and examined in view of the fractional calculus (FC) by means of the Caputo fractional derivative definition (CFD). In contrast to the explicit standard TD formula, it is found that the fractional TD (FTD) is governed by a transcendental equation in terms of the hyperbolic function and the fractional-order α. For small v compared with the speed of light c (i.e., v≪c), our results tend to Newtonian mechanics, i.e., t→t0. For v comparable to c such as v=0.9994c, our numerical results are compared with the experimental ones for the TD of the muon particles μ+. Moreover, the influence of the arbitrary-order α on the FTD is analyzed. It is also declared that at a specific α, there is an agreement between the present theoretical results and the corresponding experimental ones for the muon particles μ+.

The Pantograph equation is a fundamental mathematical model in the field of delay differential equations. A special case of the Pantograph equation is well known as the Ambartsumian delay equation which has a particular application in Astrophysics. In this paper, the Laplace transform is successfully applied to solve the Pantograph delay equation. The solution is obtained in a closed series form in terms of exponential functions. This closed form reduces to the corresponding solution in the relevant literature for the Ambartsumian delay equation as a special case. In addition, the convergence of the obtained series is proved theoretically and validated graphically. Furthermore, the accuracy of the numerical results are estimated through several computations of the residual errors. It is shown that such residuals tend to zero, even in a huge domain. The obtained results reveal that the Laplace transform is a powerful approach to solve linear delay differential equations, including the Pantograph model.

The delay differential equations are of great importance in real-life phenomena. A special type of these equations is the Pantograph delay differential equation. Generally, solving a delay differential equation is a challenge, especially when the complexity of the delay terms increases. In this paper, the homotopy perturbation method is proposed to solve the Pantograph delay differential equation via two different canonical forms; thus, two types of closed-form solutions are determined. The first gives the standard power series solution while the second introduces the exponential function solution. It is declared that the current solution agrees with the corresponding ones in the literature in special cases. In addition, the properties of the solution are provided. Furthermore, the results are numerically validated through performing several comparisons with the available exact solutions. Moreover, the calculated residuals tend to zero, even in a huge domain, which reflects the high accuracy of the current analysis. The obtained results reveal the effectiveness and efficiency of the current analysis which can be further extended to other types of delay equations.

In this paper, the existence and uniqueness of the Fredholm–Volterra integro-differential equation with the nonlocal condition will be studied. Also, we study the continuous dependence of the initial data. The numerical solution of the problem will be studied using the central difference approximations and trapezoidal rule to transform the Volterra–Fredholm integro-differential equation into a system of algebraic equations which can be solved together to get the solution. Finally, we solve some examples numerically to show the accuracy of the proposed method.

This paper considers a class of non-homogeneous fractional systems with harmonic terms by means of the Riemann–Liouville definition. Two different approaches are applied to obtain the dual solution of the studied class. The first approach uses the Laplace transform (LT) and the solution is given in terms of the Mittag-Leffler functions. The second approach avoids the LT and expresses the solution in terms of exponential and periodic functions which is analytic in the whole domain. The current methods determine the solution directly and efficiently. The results are applicable for other problems of higher order.

Many real-world problems have been modeled via delay differential equations. The pantograph delay differential equation y′(t)=ay(t)+byct belongs to such a set of delay differential equations. To the authors’ knowledge, there are no standard methods to solve the delay differential equations, i.e., unlike the ordinary differential equations, for which numerous and standard methods are well-known. In this paper, the Adomian decomposition method is suggested to analyze the pantograph delay differential equation utilizing two different canonical forms. A power series solution is obtained through the first canonical form, while the second canonical form leads to the exponential function solution. The obtained power series solution coincides with the corresponding ones in the literature for special cases. Moreover, several exact solutions are derived from the present power series solution at a specific restriction of the proportional delay parameter c in terms of the parameters a and b. The exponential function solution is successfully obtained in a closed form and then compared with the available exact solutions (derived from the power series solution). The obtained results reveal that the present analysis is efficient and effective in dealing with pantograph delay differential equations.

In this paper, a new approach is developed to solve a class of first-order fractional initial value problems. The present class is of practical interest in engineering science. The results are based on the Riemann–Liouville fractional derivative. It is shown that the dual solution can be determined for the considered class. The first solution is obtained by means of the Laplace transform and expressed in terms of the Mittag–Leffler functions. The second solution was determined through a newly developed approach and given in terms of exponential and trigonometric functions. Moreover, the results reduce to the ordinary version as the fractional-order tends to unity. Characteristics of the dual solution are discussed in detail. Furthermore, the advantages of the second solution over the first one is declared. It is revealed that the second solution is real at certain values of the fractional-order. Such values are derived theoretically and accordingly, and the behavior of the real solution is shown through several plots. The present analysis may be introduced for obtaining the solution in a straightforward manner for the first time. The developed approach can be further extended to include higher-order fractional initial value problems of oscillatory types.

This paper re-investigates the mathematical transport model of chlorine used as a water treatment model, when a variable order partial derivative is incorporated for describing the chlorine transport system. This model was introduced in the literature and governed by a fractional partial differential equation (FPDE) with prescribed boundary conditions. The obtained solution in the literature was based on implementing the Laplace transform (LT) combined with the method of residues and expressed in terms of regular exponential functions. However, the present analysis avoids such a method of residues, and thus a new analytical solution is introduced in this paper via Mittag-Leffler functions. Therefore, an effective approach is developed in this paper to solve the chlorine transport model with non-integer order derivative. In addition, our results are compared with several studies in the literature in case of integer-order derivative and the differences in results are explained.

The present paper analyzes a class of first-order fractional Fredholm integro differential equations in terms of Caputo fractional derivative. In the literature, such kind of fractional integro-differential equations have been solved using several numerical methods, while the exact solutions were not obtained. However, the exact solutions are obtained in this paper for various linear and nonlinear examples. It is shown that the exact solution of the linear problems is unique, while multiple exact solutions exist for the nonlinear ones. Moreover, the obtained results reduce to the classical ones in the relevant literature as the fractional order becomes unity. The obtained exact solutions can be further invested by other researchers to validate their numerical/approximation methods.

Background. Nipah belongs to the genus Henipavirus and the Paramyxoviridae family. It is an endemic most commonly found at South Asia and has first emerged in Malaysia in 1998. Bats are found to be the main reservoir for this virus, causing disease in both humans and animals. The last outbreak has occurred in May 2018 in Kerala. It is characterized by high pathogenicity and fatality rates which varies from 40% to 70% depending on the severity of the disease and on the availability of adequate healthcare facilities. Currently, there are no antiviral drugs available for NiV disease and the treatment is just supportive. Clinical presentations for this virus range from asymptomatic infection to fatal encephalitis. Objective. This study is aimed at predicting an effective epitope-based vaccine against glycoprotein G of Nipah henipavirus, using immunoinformatics approaches. Methods and Materials. Glycoprotein G of the Nipah virus sequence was retrieved from NCBI. Different prediction tools were used to analyze the epitopes, namely, BepiPred-2.0: Sequential B Cell Epitope Predictor for B cell and T cell MHC classes II and I. Then, the proposed peptides were docked using Autodock 4.0 software program. Results and Conclusions. The two peptides TVYHCSAVY and FLIDRINWI have showed a very strong binding affinity to MHC class I and MHC class II alleles. Furthermore, considering the conservancy, the affinity, and the population coverage, the peptide FLIDRINWIT is highly suitable to be utilized to formulate a new vaccine against glycoprotein G of Nipah henipavirus. An in vivo study for the proposed peptides is also highly recommended.

Inflammatory myofibroblastic tumor (IMT) is a benign lesion that occurs most frequently in the soft tissues and viscera. In the head and neck region, the tumor has been reported to occur in the orbit, tongue, nasopharynx, larynx, and paranasal sinuses and the central nervous system. Despite being a benign lesion, it exhibits infiltrative and destructive behaviours, making histopathological examination necessary to confirm the diagnosis. We report the case of a 38-year-old female presented with a right nasolabial fold mass, which was confirmed histologically to be an IMT. Surgical excision of the mass was achieved through a sublabial approach with an uneventful postoperative period. To the best of our knowledge, this is the first reported case of an IMT in the nasolabial fold.

In this work, new nanoadsorbents consisting of polymer‐modified multi‐walled carbon nanotubes (MWCNTs) were used to remove toxic ionic dyes, of methylene blue (MB) and methyl orange (MO), effectively from aqueous solutions. The MWCNTs were coated with polymer brushes of poly(potassium 3‐sulfopropyl methacrylate) (PKSPMA) and poly(2‐methacryloyloxyethyltrimethylammonium chloride) (PMETAC) via surface‐initiated atom transfer‐radical polymerization. The PKSPMA@MWCNTs and PMETAC@MWCNTs delivered removal efficiencies of ~80% at pH 7. Maximum adsorption capacity (qmax) reached 411.62 mg/g for MB using PKSPMA@MWCNTs and 224.60 mg/g for MO using PMETAC@MWCNTs, showcasing the effectiveness of these novel nanoadsorbents. The experimental results were analyzed using adsorption isotherm models (Langmuir, Freundlich, and Temkin) and kinetic models (pseudo‐first‐order, pseudo‐second‐order, and intraparticle diffusion). The Freundlich model provided an excellent fit for MB adsorption on both adsorbents, whereas the Temkin model best described MO adsorption on PKSPMA@MWCNTs and the Langmuir model on PMETAC@MWCNTs. The fitting results showed that the pseudo‐second‐order kinetic model was the most accurate fit for MB and MO adsorption on both nanoadsorbents, suggesting that the removal mechanism was chemisorption. In conclusion, PKSPMA@MWCNTs and PMETAC@MWCNTs demonstrate significant potential as effective adsorbents for dye removal from water, providing a promising approach for water treatment and environmental remediation. [ABSTRACT FROM AUTHOR]

BACKGROUND/OBJECTIVES: Adequate protein intake is essential to retaining muscle and maintaining physical function, especially in the elderly, and L-Leucine has received attention as an essential amino acid (EAA) that enhances protein retention. The study's aim was to compare the efficacy of EAA mixtures on lean tissue mass (LTM) and functional performance (FP) in a healthy elderly population. SUBJECTS/METHODS: Thirty-six subjects (65-75 years) volunteered to receive capsules with EAAs (Groups A and B containing 20% and 40% L-Leucine, respectively) or placebo (lactose containing 0% L-Leucine, Group C) for 12 weeks. The daily amount ranged from 11 to 21 g (0.21 g/kg/day) and was taken in two equal dosages alongside food, morning and evening. Main outcomes measured before and after intervention were LTM and FP (30-s arm-curl test; 30-s chair-stand test (30-CST); 6-min walk test (6-WT); and handgrip strength). Secondary outcomes included dietary intakes and physical activity. RESULTS: Twenty-five subjects (11 male and 14 female) completed the study (Group A, n = 8; Group B, n = 8; Group C, n = 9). Gains associated with medium effect sizes were noted in LTM (Group B, 1.1 [+ or -] 1.1%, P = 0.003) and FP (Group A in 30-CST (11.0 [+ or -] 11.5%, P = 0.02) and 6-WT (8.8 [+ or -] 10.0%, P = 0.02); Group B in 6-WT (5.8 [+ or -] 6.6%, P =0.03) and a trend in 30-CST (13.2 [+ or -] 16.0, P = 0.06)). Significant differences between groups were not observed in secondary outcomes. CONCLUSIONS: Twice-daily supplementation of EAAs containing 20% or 40% L-Leucine improved aspects of functional status and at the higher level improved LTM. Further work to establish change in a larger sample and palatable supplemental format is now required. European Journal of Clinical Nutrition (2016) 70, 182-188; doi:10.1038/ejcn.2015.91; published online 17 June 2015, INTRODUCTION Sarcopenia is a complex and multifactorial syndrome associated with significant clinical, social and economic consequences. With an ageing population, age-related sarcopenia has increased, and estimated prevalence rates are 13% [...]