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We present an approach for pricing American put options with a regime-switching volatility. Our method reveals that the option price can be expressed as the sum of two components: the price of a European put option and the premium associated with the early exercise privilege. Our analysis demonstrates that, under these conditions, the perpetual put option consistently commands a higher price during periods of high volatility compared to those of low volatility. Moreover, we establish that the optimal exercise boundary is lower in high-volatility regimes than in low-volatility regimes. Additionally, we develop an analytical framework to describe American puts with an Erlang-distributed random-time horizon, which allows us to propose a numerical technique for approximating the value of American puts with finite expiry. We also show that a combined approach involving randomization and Richardson extrapolation can be a robust numerical algorithm for estimating American put prices with finite expiry.

This study aims to propose and numerically assess different ways of discretising a very weak formulation of the Poisson problem.

We use integration by parts twice to shift smoothness requirements to the test functions, thereby allowing low-regularity data and solutions.

Various conforming discretisations are presented and tested, with numerical results indicating good accuracy and stability in different types of problems.

This is one of the first articles to propose and test concrete discretisations for very weak variational formulations in primal form. The numerical results, which include a problem based on real MRI data, indicate the potential of very weak finite element methods for tackling problems with low regularity.

A novel type of heat transfer fluid known as hybrid nanofluids is used to improve the efficiency of heat exchangers. It is observed from literature evidence that hybrid nanofluids outperform single nanofluids in terms of thermal performance. This study aims to address the stagnation point flow induced by Williamson hybrid nanofluids across a vertical plate. This fluid is drenched under the influence of mixed convection in a Darcy–Forchheimer porous medium with heat source/sink and entropy generation.

By applying the proper similarity transformation, the partial differential equations that represent the leading model of the flow problem are reduced to ordinary differential equations. For the boundary value problem of the fourth-order code (bvp4c), a built-in MATLAB finite difference code is used to tackle the flow problem and carry out the dual numerical solutions.

The shear stress decreases, but the rate of heat transfer increases because of their greater influence on the permeability parameter and Weissenberg number for both solutions. The ability of hybrid nanofluids to strengthen heat transfer with the incorporation of a porous medium is demonstrated in this study.

The findings may be highly beneficial in raising the energy efficiency of thermal systems.

The originality of the research lies in the investigation of the Darcy–Forchheimer stagnation point flow of a Williamson hybrid nanofluid across a vertical plate, considering buoyancy forces, which introduces another layer of complexity to the flow problem. This aspect has not been extensively studied before. The results are verified and offer a very favorable balance with the acknowledged papers.

A novel method for modelling permanent magnets is investigated based on numerical approximations with rational functions. This study aims to introduce the AAA algorithm and other recently developed, cutting-edge mathematical tools, which provide outstandingly fast and accurate numerical computation of potentials and vector fields.

First, the AAA algorithm is briefly introduced along with its main variants and other advanced mathematical tools involved in the modelling. Then, the analysis of a circular Halbach array with a one-pole pair is carried out by means of the AAA-least squares method, focusing on vector potential and flux density in the bore and validating results by means of classic finite element software. Finally, the investigation is completed by a finite difference analysis.

AAA methods for field analysis prove to be strikingly fast and accurate. Results are in excellent agreement with those provided by the finite element model, and the very good agreement with those from finite differences suggests future improvements. They are also easy programming; the MATLAB code is less than 200 lines. This indicates they can provide an effective tool for rapid analysis.

AAA methods in magnetostatics are novel, but their extension to analogous physical problems seems straightforward. Being a meshless method, it is unlikely that local non-linearities can be considered. An aspect of particular interest, left for future research, is the capability of handling inhomogeneous domains, i.e. solving general interface problems.

The authors use cutting-edge mathematical tools for the modelling of complex physical objects in magnetostatics.

This paper addresses a significant research gap in the study of Rayleigh surface wave propagation within a piezoelectric medium characterized by piezoelectric properties, thermal effects and voids. Previous research has often overlooked the crucial aspects related to voids. This study aims to provide analytical solutions for Rayleigh waves propagating through a medium consisting of a nonlocal piezo-thermo-elastic material with voids under the Moore–Gibson–Thompson thermo-elasticity theory with memory dependencies.

The analytical solutions are derived using a wave-mode method, and roots are computed from the characteristic equation using the Durand–Kerner method. These roots are then filtered based on the decay condition of surface waves. The analysis pertains to a medium subjected to stress-free and isothermal boundary conditions.

Computational simulations are performed to determine the attenuation coefficient and phase velocity of Rayleigh waves. This investigation goes beyond mere calculations and examines particle motion to gain deeper insights into Rayleigh wave propagation. Furthermore, this investigates how kernel function and nonlocal parameters influence these wave phenomena.

The results of this study reveal several unique cases that significantly contribute to the understanding of Rayleigh wave propagation within this intricate material system, particularly in the presence of voids.

This investigation provides valuable insights into the synergistic dynamics among piezoelectric constituents, void structures and Rayleigh wave propagation, enabling advancements in sensor technology, augmented energy harvesting methodologies and pioneering seismic monitoring approaches.

This study formulates a novel governing equation for a nonlocal piezo-thermo-elastic medium with voids, highlighting the significance of Rayleigh waves and investigating the impact of memory.

The purpose of the paper is to showcase the significant achievements of Egypt's scientists in the 20th century across various fields of study such as medicine, physics, chemistry, biology, math, geology, astronomy and engineering. The paper highlights the struggles and successes of these scientists, as well as the cultural, social and political factors that influenced their lives and work. The aim is to inspire young people to pursue careers in science and make their own contributions to society by presenting these scientists as role models for hard work and dedication. Ultimately, the paper seeks to promote the importance of science and its impact on society.

The purpose of this review is to present the scientific biographies of Egypt's most distinguished scientists, primarily in the field of Natural Sciences, in a balanced and comprehensive manner. The work is objective, honest and abstract, avoiding any bias or exaggeration. The author provides a clear and concise methodology, including a brief introduction to the scientist and their field of study, an explanation of their major contributions, the impact of their work on society, any challenges or obstacles faced during their career and their lasting legacy. The aim is to showcase the important achievements of these scientists, their impact on their respective fields and to inspire future generations to pursue scientific careers.

The group of outstanding scientists in 20th century Egypt were shaped by various factors, including familial upbringing, education, society, political and cultural atmosphere and state support for scientific research. These scientists made significant contributions to various academic disciplines, including medicine, physics, chemistry, biology, mathematics and engineering. Their impact on their communities and cultures has received international acclaim, making them role models for future generations of scientists and researchers. The history of these scientists highlights the importance of educational investments and supporting scientific research to foster innovation and social progress. The encyclopedia serves as a useful tool for students, instructors and education professionals, preserving Egypt's scientific heritage and honouring the scientists' outstanding accomplishments.

The encyclopedia preserves Egypt's scientific heritage, which has been overlooked for political or other reasons. It is a useful tool for a variety of readers, including students, instructors and education professionals, and it offers insights into universally relevant scientific success factors as well as scientific research methodologies. The encyclopedia honours the outstanding scientific accomplishments of Egyptian researchers and their contributions to the world's scientific community.

The practical implications of this paper are several. First, it highlights the importance of education, family upbringing and societal support for scientific research in fostering innovation and social progress. Second, it underscores the need for continued funding and support for scientific research to maintain and build upon the accomplishments of past generations of scientists. Third, it encourages young people to pursue scientific careers and make their own contributions to society. Fourth, it preserves the scientific heritage of Egypt and honors the contributions of its outstanding scientists. Finally, it serves as a useful tool for students, instructors and education professionals seeking to understand the factors underlying scientific success and research methodologies.

The social implications of the paper include promoting national pride and cultural identity, raising awareness of the importance of education and scientific research in driving social progress, inspiring future generations of scientists and researchers, reducing socioeconomic disparities and emphasizing the role of society, politics and culture in shaping scientific researchers' personalities and interests.

The paper's originality/value lies in its comprehensive documentation of the scientific biographies of Egypt's most prominent scientists in the 20th century, providing unique insights into the factors that contributed to their development and their impact across various academic disciplines. It preserves Egypt's scientific heritage and inspires future generations of scientists and researchers through the promotion of educational investments and scientific research. The encyclopedia serves as a useful tool for education professionals seeking to understand scientific success factors and research methodologies, emphasizing the importance of supportive and inclusive environments for scientific development.

The purpose of this study is to solve two unique but difficult partial differential equations: the foam drainage equation and the nonlinear time-fractional fisher’s equation. Through our methods, we aim to provide accurate solutions and gain a deeper understanding of the intricate behaviors exhibited by these systems.

In this study, we use a dual technique that combines the Aboodh residual power series method and the Aboodh transform iteration method, both of which are combined with the Caputo operator.

We develop exact and efficient solutions by merging these unique methodologies. Our results, presented through illustrative figures and data, demonstrate the efficacy and versatility of the Aboodh methods in tackling such complex mathematical models.

Owing to their fractional derivatives and nonlinear behavior, these equations are crucial in modeling complex processes and confront analytical complications in various scientific and engineering contexts.

Polymer-based thermal interface materials (TIMs) are having pump out problem and could be resolved for reliable application. Solid-based interface materials have been suggested and reported. The purpose of this paper is suggesting thin film-based TIM to sustain the light-emiting diode (LED) performance and electronic device miniaturization.

Consequently, ZnO thin film at various thicknesses was prepared by chemical vapour deposition (CVD) method and tested their thermal behaviour using thermal transient analysis as solid TIM for high-power LED.

Low value in total thermal resistance (R_th-tot) was observed for ZnO thin film boundary condition than bare Al boundary condition. The measured interface (ZnO thin film) resistance {(R_th-bhs) thermal resistance of the interface layer (thin film) placed between metal core printed circuit board (MCPCB) board and Al substrates} was nearly equal to Ag paste boundary condition and showed low values for ZnO film prepared at 30 min process time measured at 700 mA. The T_J value of LED mounted on ZnO thin film (prepared at 30 min.) coated Al substrates was measured to be 74.8°C. High value in junction temperature difference (ΔT_J) of about 4.7°C was noticed with 30 min processed ZnO thin film when compared with Al boundary condition. Low correlated colour temperature and high luminous flux values of tested LED were also observed with ZnO thin film boundary condition (processed at 30 min) compared with both Al substrate and Ag paste boundary condition.

Overall, 30 min CVD processed ZnO thin film would be an alternative for commercial TIM to achieve efficient thermal management. This will increase the life span of the LED as the proposed material decreases the T_J values.

The study aims to optimize truck routes by minimizing social and economic costs. It introduces a strategy involving diverse drones and their potential for reusing at DNs based on flight range. In HTDRP-DC, trucks can select and transport various drones to LDs to reduce deprivation time. This study estimates the nonlinear deprivation cost function using a linear two-piece-wise function, leading to MILP formulations. A heuristic-based Benders Decomposition approach is implemented to address medium and large instances. Valid inequalities and a heuristic method enhance convergence boundaries, ensuring an efficient solution methodology.

Research has yet to address critical factors in disaster logistics: minimizing the social and economic costs simultaneously and using drones in relief distribution; deprivation as a social cost measures the human suffering from a shortage of relief supplies. The proposed hybrid truck-drone routing problem minimizing deprivation cost (HTDRP-DC) involves distributing relief supplies to dispersed demand nodes with undamaged (LDs) or damaged (DNs) access roads, utilizing multiple trucks and diverse drones. A Benders Decomposition approach is enhanced by accelerating techniques.

Incorporating deprivation and economic costs results in selecting optimal routes, effectively reducing the time required to assist affected areas. Additionally, employing various drone types and their reuse in damaged nodes reduces deprivation time and associated deprivation costs. The study employs valid inequalities and the heuristic method to solve the master problem, substantially reducing computational time and iterations compared to GAMS and classical Benders Decomposition Algorithm. The proposed heuristic-based Benders Decomposition approach is applied to a disaster in Tehran, demonstrating efficient solutions for the HTDRP-DC regarding computational time and convergence rate.

Current research introduces an HTDRP-DC problem that addresses minimizing deprivation costs considering the vehicle’s arrival time as the deprivation time, offering a unique solution to optimize route selection in relief distribution. Furthermore, integrating heuristic methods and valid inequalities into the Benders Decomposition approach enhances its effectiveness in solving complex routing challenges in disaster scenarios.

This study aims to investigate how configurations of boundary objects (BOs) support innovation teams in developing innovative product concepts. Specifically, it explores the effectiveness of different artefact configurations in facilitating collaboration and bridging knowledge boundaries during the concept development process.

The research is based on data from ten undergraduate innovation teams working with an industry partner in a creative industry. Six categories of BOs are identified, which serve as tools for collaboration. The study applies fsQCA (fuzzy-set qualitative comparative analysis) to analyse the configurations employed by the teams to bridge knowledge boundaries and support the development of innovative product concepts.

The findings of the study reveal two distinct groups of configurations: product envisioning and product design. The configurations within the “product envisioning” group support the activities of visioning and pivoting, enabling teams to innovate the product concept by altering the product vision. On the other hand, the configurations within the “product design” group facilitate experimenting, modelling and prototyping, allowing teams to design the attributes of the innovative product concept while maintaining the product vision.

This research contributes to the field of innovation by providing insights into the role of BOs and their configurations in supporting innovation teams during concept development. The results suggest that configurations of “product envisioning” support bridging semantic knowledge boundaries, while configurations within “product design” bridge pragmatic knowledge boundaries. This understanding contributes to the broader field of knowledge integration and innovation in design contexts.