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This paper focuses on the unconditionally optimal error estimates of a linearized second-order scheme for a nonlocal nonlinear parabolic problem. The first step of the scheme is based on Crank–Nicholson method while the second step is the second-order BDF method.

A rigorous error analysis is done, and optimal L² error estimates are derived using the error splitting technique. Some numerical simulations are presented to confirm the study’s theoretical analysis.

Optimal L² error estimates and energy norm.

The goal of this research article is to present and establish the unconditionally optimal error estimates of a linearized second-order BDF finite element scheme for the reaction-diffusion problem. An optimal error estimate for the proposed methods is derived by using the temporal-spatial error splitting techniques, which split the error between the exact solution and the numerical solution into two parts, that is, the temporal error and the spatial error. Since the spatial error is not dependent on the time step, the boundedness of the numerical solution in L∞-norm follows an inverse inequality immediately without any restriction on the grid mesh.

The purpose of this paper is to analyze numerically the blowup in finite time of the solutions to a one-dimensional, bidirectional, nonlinear wave model equation for the propagation of small-amplitude waves in shallow water, as a function of the relaxation time, linear and nonlinear drift, power of the nonlinear advection flux, viscosity coefficient, viscous attenuation, and amplitude, smoothness and width of three types of initial conditions.

An implicit, first-order accurate in time, finite difference method valid for semipositive relaxation times has been used to solve the equation in a truncated domain for three different initial conditions, a first-order time derivative initially equal to zero and several constant wave speeds.

The numerical experiments show a very rapid transient from the initial conditions to the formation of a leading propagating wave, whose duration depends strongly on the shape, amplitude and width of the initial data as well as on the coefficients of the bidirectional equation. The blowup times for the triangular conditions have been found to be larger than those for the Gaussian ones, and the latter are larger than those for rectangular conditions, thus indicating that the blowup time decreases as the smoothness of the initial conditions decreases. The blowup time has also been found to decrease as the relaxation time, degree of nonlinearity, linear drift coefficient and amplitude of the initial conditions are increased, and as the width of the initial condition is decreased, but it increases as the viscosity coefficient is increased. No blowup has been observed for relaxation times smaller than one-hundredth, viscosity coefficients larger than ten-thousandths, quadratic and cubic nonlinearities, and initial Gaussian, triangular and rectangular conditions of unity amplitude.

The blowup of a one-dimensional, bidirectional equation that is a model for the propagation of waves in shallow water, longitudinal displacement in homogeneous viscoelastic bars, nerve conduction, nonlinear acoustics and heat transfer in very small devices and/or at very high transfer rates has been determined numerically as a function of the linear and nonlinear drift coefficients, power of the nonlinear drift, viscosity coefficient, viscous attenuation, and amplitude, smoothness and width of the initial conditions for nonzero relaxation times.

The main purpose of this paper is to introduce the gradient discretisation method (GDM) to a system of reaction diffusion equations subject to non-homogeneous Dirichlet boundary conditions. Then, the authors show that the GDM provides a comprehensive convergence analysis of several numerical methods for the considered model. The convergence is established without non-physical regularity assumptions on the solutions.

In this paper, the authors use the GDM to discretise a system of reaction diffusion equations with non-homogeneous Dirichlet boundary conditions.

The authors provide a generic convergence analysis of a system of reaction diffusion equations. The authors introduce a specific example of numerical scheme that fits in the gradient discretisation method. The authors conduct a numerical test to measure the efficiency of the proposed method.

This work provides a unified convergence analysis of several numerical methods for a system of reaction diffusion equations. The generic convergence is proved under the classical assumptions on the solutions.

The purpose of this research study was to explore the relationship between adaptive performance and work-related indicators of psychological well-being among ‘The Episcopal Church bishops.’

Hierarchical regression models were used in this research study to explore the relationship between adaptive performance and work-related psychological health.

There was a positive correlation between adaptive performance and work-related psychological health. Demographic factors did not correlate to adaptive performance. However, a negative correlation was observed between the years ordained as a bishop and the interpersonal adaptability dimension of adaptive performance.

Managing work stress has been revealed as an integral part of adaptive performance and satisfaction in ministry. Interpersonal adaptability and reactivity could be understood, then, as useful vehicles for increasing the capacity of bishops to manage work stress. In this research, the authors applied the Scale for Individual Adaptive Performance and the two scales Scale of Satisfaction in Ministry and Scale of Emotional Exhaustion in Ministry .

The results provided insights into the behaviors necessary for adequate development of bishops in their role. The religious landscape was becoming more challenging from a revenue generation perspective. The resultant complexity and the financial strain would necessitate the need for development of different models of ministry for long-term sustainability. This could further necessitate a different set of knowledge creation related to a set of behavioral capacities like those of adaptive performance. Such insights would assist in the promotion and development of greater work-related psychological health in bishops while deepening their ability to deal with complex and uncertain environments. Furthermore, this would increase satisfaction in ministry through improved workplace management skills.

Presently, very few studies empirically established the developmental needs of bishops as they entered, learned and grew into their leadership roles. Such insights would allow the formation programs for new bishops to be grounded in empirical data. Furthermore, this research study examined a largely unexplored population. This would provide a basis for a larger research agenda related to adaptive performance in judicatory leaders and their work-related psychological health. Consequently, it is posited that improved psychological health would result in better workplace learning.

This paper aims to study Irreversible conversion processes, which examine the spread of a one way change of state (from state 0 to state 1) through a specified society (the spread of disease through populations, the spread of opinion through social networks, etc.) where the conversion rule is determined at the beginning of the study. These processes can be modeled into graph theoretical models where the vertex set V(G) represents the set of individuals on which the conversion is spreading.

The irreversible k-threshold conversion process on a graph G=(V,E) is an iterative process which starts by choosing a set S_0?V, and for each step t (t = 1, 2,…,), S_t is obtained from S_(t−1) by adjoining all vertices that have at least k neighbors in S_(t−1). S_0 is called the seed set of the k-threshold conversion process and is called an irreversible k-threshold conversion set (IkCS) of G if S_t = V(G) for some t = 0. The minimum cardinality of all the IkCSs of G is referred to as the irreversible k-threshold conversion number of G and is denoted by C_k (G).

In this paper the authors determine C_k (G) for generalized Jahangir graph J_(s,m) for 1 < k = m and s, m are arbitraries. The authors also determine C_k (G) for strong grids P_2? P_n when k = 4, 5. Finally, the authors determine C_2 (G) for P_n? P_n when n is arbitrary.

This work is 100% original and has important use in real life problems like Anti-Bioterrorism.

This study evaluates the moderating role of work-based social supports (i.e. supervisor support and co-worker support) in the relationship between job insecurity and job burnout among hospitality employees in Malaysia. Besides, the direct effect between job insecurity and job burnout is examined.

The cross-sectional data of this study were based on a total of 220 self-administered questionnaires that have been completed by hospitality employees from three different states in Malaysia. Respondents were recruited based on a snowball sampling approach. The data were collected during the COVID-19 pandemic, which was from October 2020 to January 2021.

Partial least square-structural equation modeling (PLS-SEM) was performed via SmartPLS software. The finding confirmed that job insecurity significantly intensifies employees' job burnout. Supervisor support and co-worker support were found to moderate the link between job insecurity and burnout. As anticipated, the relationship between job insecurity and job burnout increased when supervisor support is low. But high co-worker support was found to strengthen the impact of job insecurity on job burnout instead of the reverse.

This study supplements the existing literature by clarifying which sources of work-based social support (i.e. co-worker support or supervisor) is more salient in alleviating the adverse impact of job insecurity on job burnout during the COVID-19 pandemic among hospitality employees in Malaysia.

In fire resistance tests (FRTs) of building materials, a crucial criterion to pass the test procedure is to avoid the leakage of the hot flue gases caused by gaps and cracks occurring due to the thermal exposure. The present study's aim is to calculate the deformation of a steel door, which is embedded within a wall made of bricks, and qualitatively determine the flue gas leakage.

A computational fluid dynamics/finite element method (CFD/FEM) coupling was introduced representing an intermediate approach between a one-way and a full two-way coupling methodology, leading to a simplified two-way coupling (STWC). In contrast to a full two way-coupling, the heat transfer through the steel door was simulated based on a one-way approach. Subsequently, the predicted temperatures at the door from the one-way simulation were used in the following CFD/FEM simulation, where the fluid flow inside and outside the furnace as well as the deformation of the door were calculated simultaneously.

The simulation showed large gaps and flue gas leakage above the door lock and at the upper edge of the door, which was in close accordance to the experiment. Furthermore, it was found that STWC predicted similar deformations compared to the one-way coupling.

Since two-way coupling approaches for fluid/structure interaction in fire research are computationally demanding, the number of studies is low. Only a few are dealing with the flue gas exit from rooms due to destruction of solid components. Thus, the present study is the first two-way approach dealing with flue gas leakage due to gap formation.

A stylized fact in finance literature is the belief in positive relationship between ex ante return and risk. Hence, a rational investor, by utility preference axiom can only consider committing fund in asset which promises commensurate higher return for higher risk. Questions have been asked as to whether this holds true across securities, sectors and markets. Empirical evidence appears less convincing, especially in developing markets. Accordingly, the author investigates the nature of reward for taking risk in the Nigerian Capital Market within the context of individual assets and markets.

The author employed ex post design to collect weekly stock prices of firms listed on the Premium Board of Nigerian Stock Exchange for period 2014–2022 to attempt to answer research questions. Data were analyzed using a unique M Vec TGarch-in-Mean model considered to be robust in handling many assets, and hence portfolio management.

The study found that idea of risk-expected return trade-off is perhaps more general than as depicted by traditional finance literature. The regression revealed that conditional variance and covariance risks reveal minimal or no differences in sign and sizes of coefficients. However, standard errors were also found to be large suggesting somewhat inconclusive evidence of existence of defined incentive structure for taking additional risk in the market.

In terms of choice of methodology and outcomes, this research adds substantial value to body of knowledge. The adapted multivariate model used in this paper is a rare approach especially for management of portfolios in developing markets. Remarkably, the research found empirical evidence that positive risk-expected return trade-off, as known in mainstream literature, is not supported especially using a typical developing country data.

The purpose of this paper is to illuminate the ethical concerns associated with the use of artificial intelligence (AI) in the medical sector and to provide solutions that allow deriving maximum benefits from this technology without compromising ethical principles.

This paper provides a comprehensive overview of AI in medicine, exploring its technical capabilities, practical applications, and ethical implications. Based on our expertise, we offer insights from both technical and practical perspectives.

The study identifies several advantages of AI in medicine, including its ability to improve diagnostic accuracy, enhance surgical outcomes, and optimize healthcare delivery. However, there are pending ethical issues such as algorithmic bias, lack of transparency, data privacy issues, and the potential for AI to deskill healthcare professionals and erode humanistic values in patient care. Therefore, it is important to address these issues as promptly as possible to make sure that we benefit from the AI’s implementation without causing any serious drawbacks.

This paper gains its value from the combined practical experience of Professor Elhassan gained through his practice at top hospitals worldwide, and the theoretical expertise of Dr. Arabi acquired from international institutes. The shared experiences of the authors provide valuable insights that are beneficial for raising awareness and guiding action in addressing the ethical concerns associated with the integration of artificial intelligence in medicine.

This study aims to develop an experimentally validated three-dimensional numerical model for predicting different flow patterns produced with a gas dynamic virtual nozzle (GDVN).

The physical model is posed in the mixture formulation and copes with the unsteady, incompressible, isothermal, Newtonian, low turbulent two-phase flow. The computational fluid dynamics numerical solution is based on the half-space finite volume discretisation. The geo-reconstruct volume-of-fluid scheme tracks the interphase boundary between the gas and the liquid. To ensure numerical stability in the transition regime and adequately account for turbulent behaviour, the k-ω shear stress transport turbulence model is used. The model is validated by comparison with the experimental measurements on a vertical, downward-positioned GDVN configuration. Three different combinations of air and water volumetric flow rates have been solved numerically in the range of Reynolds numbers for airflow 1,009–2,596 and water 61–133, respectively, at Weber numbers 1.2–6.2.

The half-space symmetry allows the numerical reconstruction of the dripping, jetting and indication of the whipping mode. The kinetic energy transfer from the gas to the liquid is analysed, and locations with locally increased gas kinetic energy are observed. The calculated jet shapes reasonably well match the experimentally obtained high-speed camera videos.

The model is used for the virtual studies of new GDVN nozzle designs and optimisation of their operation.

To the best of the authors’ knowledge, the developed model numerically reconstructs all three GDVN flow regimes for the first time.