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The Adomian Decomposition Method for Solving Nonlinear Partial Differential Equation Using Maple

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Advances in Pure Mathematics 2021年第6期11卷 595-603页

作者： dalal adnan maturi Honaida Mohammed Malaikah Department of Mathematics Faculty of Science King Abdulaziz University Jeddah Saudi Arabia

The nonlinear partial differential equation is solved using the Adomian decomposition method (ADM) in this article. A number of examples have been provided to illustrate the numerical results, which is the comparison of the exact and numerical solutions, and it has been discovered through the tables that the amount of error between the exact and numerical solutions is very small and almost non-existent, and the graph also shows how the exact solution of absolutely applies to the numerical solution. This demonstrates the precision of the Adomian decomposition method (ADM) for solving the nonlinear partial differential equation with Maple18. And that in terms of obtaining numerical results, this approach is characterized by ease, speed, and high accuracy.

关键词： Nonlinear Partial Differential Equation Adomian Decomposition Method Maple18

Higher Order Implicit Scheme for Nonlinear Time-Dependent Convection-Diffusion- Reaction Equation

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American Journal of Computational Mathematics 2022年第2期12卷 232-248页

作者： Uzair Ahmed Daoud Suleiman Mashat dalal adnan maturi Department of Mathematics King Abdulaziz University Jeddah Saudi Arabia

A mathematical model comprising of nonlinear reaction, diffusion, and convection mechanisms seen in natural and anthropogenic processes is numerically investigated here. It is proposed that a higher order numerical scheme of finite difference method be used in conjunction with an iterative approach in order to solve the nonlinear one dimensional convection-diffusion-reaction equation. To account for the wide variety of physical characteristics and boundary conditions, an iterative approach is presented that yields a reliable and precise solution every time. We examined the accuracy and operational efficiency of two distinct finite difference approaches. The efficiency of the system is determined by comparing the estimated results to the appropriate analytical solution by adhering to established norms. Coherence and convergence were analyzed for each approach. The simulation results demonstrate the efficacy and accuracy of these methods in solving nonlinear convection- diffusion-reaction equations. Convection-diffusion-reaction equation modeling is critical for employing the offered results in heat and mass transport processes.

关键词： Finite Difference Method (FDM) Crank-Nicholson (CN) Fourth Order Implicit (FOI) Convection-Diffusion-Reaction (CDR)

Finite Difference Approximation for Solving Transient Heat Conduction Equation of Copper

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Advances in Pure Mathematics 2020年第5期10卷 350-358页

作者： dalal adnan maturi Nujud Makhdhur Alsulami Eman Salem Alaidarous Department of Mathematics Faculty of Science King Abdulaziz University Jeddah Saudi Arabia

In this paper, a numerical technique is proposed to obtain the solution for transient heat conduction equation of Copper. The copper element is characterized by many characteristics;the most important of which is its high ability to conduct heat and electrical conductivity, in addition to being a flexible and malleable metal that is easy to form without being broken, making it one of the basic minerals that humans have benefited from for thousands of years, it is one of the first minerals. That has been discovered and extracted, and still plays a major role in the development of societies. The obtained solutions are compared with the available exact solutions and the obtained solutions using the finite difference method. The results indicate that the finite difference method is a highly effective method for obtaining approximate solutions for the thermal conductivity equation for copper. It is also clear from the numerical results from copper in the high conductivity of heat and electricity.

关键词： Finite Difference Approximation Transient Heat Conduction Equation Copper Matlab

Non-static plane symmetric perfect fluid solutions and Killing symmetries in f(R,T)gravity

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Communications in Theoretical Physics 2024年第2期76卷 145-150页

作者： Preeti dalal Karanjeet Singh Sachin Kumar Department of Mathematics and Statistics Central University of PunjabBathinda151401PunjabIndia Department of Mathematics Jaypee University of Information TechnologySolan173234Himachal PradeshIndia

In this paper,the non-static solutions for perfect fluid distribution with plane symmetry in f(R,T)gravitational theory are ***,using the Lie symmetries,symmetry reductions are performed for considered vector fields to reduce the number of independent ***,corresponding to each reduction,exact solutions are *** vectors lead to different conserved ***,we figure out the Killing vector fields corresponding to all derived *** derived solutions are further studied and it is observed that all of the obtained spacetimes,at least admit to the minimal symmetry group which consists of δ_(y),δ_(z) and -zδ_(y)+yδ_(z).The obtained metrics,admit to 3,4,6,and 10,Killing vector *** of linear momentum in the direction of y and z,and angular momentum along the x axis is provided by all derived solutions.

关键词： Einstein field equations perfect fluid solutions f(R T)gravity killing symmetries

Co-seismic surface displacement of the June 21, 2022 M_(W)6 Khōst,Afghanistan earthquake from InSAR observations

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Geodesy and Geodynamics 2024年第3期15卷 201-208页

作者： Prohelika dalal Batakrushna Senapati Bhaskar Kundu Department of Earth and Atmospheric Sciences National Institute of TechnologyRourkelaOdisha 769008India

A robust estimation of the earthquake location, seismic moment, and fault geometry is essential for objective seismic hazard assessment. Seismic events in a remote location, specifically in the absence of seismic and GNSS networks, can be investigated effectively using the In SAR-based technique. This study adopts the Differential Interferometric SAR(DIn SAR) technique to quantify the co-seismic surface displacement caused by the June 21, 2022, Khōst M_(W)6 earthquake that occurred along the western plate boundary between the Indian and Eurasian plate. The interferograms show that the maximum surface deformation occurred on the northwest and southwest of the fault line. From coherence, the Line of Sight(LOS) displacement, and the co-seismic surface displacement analysis, it has been observed that surface deformation was most pronounced in the southwest region of the fault line, and the surface has moved to the opposite direction along the fault line, which indicates a sinistral slightly oblique strike-slip movement. This In SAR-based observation appears consistent with the seismic waveforms derived from co-seismic surface displacements. Further, it has been argued that the slip deficit accumulated during the period of the last about 48 years along the frontal region of the northward extension of the Suleiman range and associated fault zone is qualitatively estimated at about 1.5 m, which is consistent with the seismic waveforms derived finite slip model.

关键词： Seismic hazard Khōst earthquake DInSAR Slip deficit LOS displacement Finite slip model

On the Enhanced Power Graph of a Semigroup

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Algebra Colloquium 2024年第1期31卷 83-96页

作者： Sandeep dalal Jitender Kumart Siddharth Singh Department of Mathematics Birla Institute of Technology and Science Pilani PilaniIndia

The enhanced power graph P_(E)(S)of a semigroup S is a simple graph whose vertex set is S and two vertices a,y∈S are adjacent if and only if c,y∈(z)for some z∈S,where(z)is the subsemigroup generated by *** this paper,we first describe the structure of P_(E)(S)for an arbitrary semigroup S,and then discuss the connectedness of P_(E)(S).Further,we characterize the semigroup S in the cases when P_(E)(S)is separately a complete,bipartite,regular,tree and null *** planarity,together with the minimum degree and independence number,of P_(E)(S)is also *** chromatic number of a spanning subgraph,i.e.,the cyclic graph,of P_(E)(S)is proved to be *** the final part of this paper,we construct an example of a semigroup S such that the chromatic number of P_(E)(S)need not be countable.

关键词： monogenic semigroup completely regular semigroup planar graph enhanced powergraph

Deciphering the Hidden Secrets between the Early Skin Wrinkling & the Metabolic (X) Syndrome with the Possible Reversal of This Process at the Molecular Level

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Journal of Cosmetics, Dermatological Sciences and Applications 2024年第1期14卷 45-68页

作者： dalal Alsaadoun Dermatology Department King Faisal University Hofuf Kingdom of Saudi Arabia

The aging process is a group of degenerative changes that physiologically occur in most of the people in the elderly. This affects one or more of the human body systems. The treatment of diseases related to the aging process has a huge impact on the economy of all nations. Aging of the skin comes on the top and despite that, the results of the already present lines of treatment are not always satisfactory. This acts as a stimulus for us to dig deeper to discover the root causes of the premature aging of the skin. This was simply caused by the accumulation of repeated minute damage to the internal structure skin. In other words, if the degree of minute damage is more than the capacity of the skin to repair, the repeated micro-damage is presented in the long run as a skin wrinkling. Moreover, the skin acts as a mirror that reflects the internal structures of the human body. Thus, the more degenerative changes in the human body systems, the more the skin could become wrinkled. Our strategy to prevent or at least slow down the aging process of the skin depends on 2 main steps;the 1st is to reduce the micro-damage as can as possible, and the 2nd is to enhance the capacity of tissue regeneration to be able to reverse the already present damaged skin. As the 2 processes are synchronized with each other, this strategy would be considered the ideal for prevention of skin wrinkling especially premature ones. This not only reverses premature skin wrinkling but also protects it from future wrinklings. This review sharply pointed out the role of the functional collagen of the dermal layer of the skin in the prevention of skin wrinklings. Therefore, it would be the target to study how collagen works in the complex machinery of the dermal layer of the skin. This concept deeply believes that the recovery of dermal collagen has a much better effect than simply ingesting collagen or receiving a topical collagen booster. .

关键词： Collagen Skin Wrinkling Glycation Hyper-Insulinemia Hidden Obesity Vis-ceral Fat Inflammatory Cytokines

Paradiplomacy for Non-recognized States:Case of Palestine

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International Relations and Diplomacy 2024年第1期12卷 34-39页

作者： dalal Iriqat Arab American University of Palestine RamallahPalestine

This paper endeavours to elucidate the intricacies of Palestinian Paradiplomacy,focusing in the political impetus pioneered by its principle actors,namely the Palestine Liberation Organisation(PLO)and subsequently,the establishment of the Palestinian National Authority(PNA).Additionally,attention will be directed towards the creation of the Palestinian Ministry of Foreign Affairs(PMOFA)and its subsidiary,the Palestinian International Cooperation Agency(PICA),albeit briefly *** inspiration from Alexander ***’s seminal work“Theory and Practice of Paradiplomacy:Subnational Governments in International Affairs”(2015),this paper tries to scrutinize the trajectory of Palestinian paradiplomacy and its evolutionary course over *** it comes to activity and growth,Palestinian paradiplomacy has a unique *** way in which topics pertaining to nations are not yet recognized has a great deal of bearing on current discussions and academic research about urgent political concerns like the right to self-determination and human *** analysis of de facto states via the prism of paradiplomacy naturally arises from the dominant state recognition procedures in international politics.

关键词： PLO nationalism non-state actors self-determination paradiplomacy Palestine foreign affairs

Gas Chromatographic Method for Identification and Quantification of Commonly Used Residual Solvents in Pharmaceuticals Products

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American Journal of Analytical Chemistry 2024年第8期15卷 241-252页

作者： Sreekanta Nath dalal Pranab Kumar Das Department of Applied Chemistry & Chemical Engineering Faculty of Engineering & Technology University of Dhaka Dhaka Bangladesh Department of Applied Chemistry & Chemical Engineering Faculty of Engineering University of Rajshahi Rajshahi Bangladesh

Background: Impurities are not expected in the final pharmaceutical products. All impurities should be regulated in both drug substances and drug products in accordance with pharmacopeias and ICH guidelines. Three different types of impurities are generally available in the pharmaceutical’s product specification: organic impurities, inorganic impurities, and residual solvents. Residual solvents are organic volatile chemicals used or generated during the manufacturing of drug substances or drug products. Purpose: The aim of this study is to develop a cost-effective gas chromatographic method for the identification and quantification of some commonly used solvents—methanol, acetone, isopropyl alcohol (IPA), methylene chloride, ethyl acetate, tetrahydrofuran (THF), benzene, toluene, and pyridine—in pharmaceutical product manufacturing. This method will be able to identify and quantify the multiple solvents within a single gas chromatographic procedure. Method: A gas chromatography (GC) equipped with a headspace sampler and a flame ionization detector, and a column DB 624, 30-meter-long × 0.32-millimeter internal diameter, 1,8 μm-thick, Brand-Agilent was used to develop this method. The initial GC oven temperature was 40°C and held for 5 minutes. It was then increase to 80˚C at a rate of 2˚C per minute, followed by a further increase to 225˚C at a rate of 30˚C per minute, with a final hold at 225˚C for 10 minutes. Nitrogen was used as a carrier gas at a flow rate of 1.20 mL per minute. Dimethyl sulfoxide (DMSO) was selected as sample solvent. Results: The developed method is precise and specific. The percent RSD for the areas of six replicate injections of this gas chromatographic method was within 10.0 and the recovery result found within 80.0% to 120.0%.

关键词： Method Development Gas Chromatography Compendial Method GDP Specificity Recovery