Two-dimensional heat diffusion problem with heat source which is quasilinear parabolic problem is examined analytically and numerically. Periodic boundary conditions are used as a boundary conditions. Since the problem is not linear, Picard’s successive approximation theorem is used. Under certain conditions of natural regularity and consistency imposed on the input data, establish the existence, uniqueness and constant dependence of the solution on the data using the generalized Fourier method. As a numerical solution, implicit finite difference scheme is used. The results ob-tained from analytical and the numerical solutions are so close to each other.

We discuss the neutron skins of 48Ca and 208Pb. We review and critically examine modern predictions and empirical constraints, with special attention to the dierent interpretations of the ndings from the PREX-II experiment and the recently reported value of the neutron skin in 48Ca extracted from the CREX experiment. We argue that, in the spirit of the ab initio philosophy, the path to understanding the behavior of dense neutron-rich matter must not circumvent fundamental nuclear forces. Based only on that argument, a thick neutron skin in 208Pb is highly unlikely.

We propose a new theory beyond the standard model of elementary-particle physics. Employing the concept of a quantized spacetime, our theory demonstrates that the zero-point energy of the vacuum alone is sufficient to create all the fields, including gravity, the static electromagnetic field, and the weak and strong interactions. No serious undetermined parameters are assumed. Furthermore, the relations between the forces at the quantum-mechanics level is made clear. Using these relations, we quantize Einstein’s gravitational equation: Beginning with the zero-point energy of the vacuum, and after quantizing Newtonian gravity equation, we combine the energies of a static electromagnetic field and gravity in a quantum spacetime. Applying these results to the Einstein gravity equation, we substitute the energy density derived from the zero-point energy in addition to redefining differentials in a quantized spacetime. This is how we derive the quantized Einstein gravitational equation without assuming the existence of macroscopic masses. For the weak interaction, by considering plane-wave electron and the zero-point energy, we obtain a wavefunction that represents a β collapse. In this process, from a different point of view than Weinberg-Salam theory, we derive the masses of the W and Z bosons and the neutrino, and we calculate the radius and lifetime of the neutron. For the strong interaction, we previously reported an analytical theory for calculating the mass of a proton by providing a specific linear attractive potential obtained from the zero-point energy, which agrees well with the measurements. In the present study, we further calculate the strong interaction between two nucleons, i.e., the mass of the pi-meson. The resulting calculated quantities agree with the measurements, which verifies our proposed theory.

This feature study attempts on setting a granules involving mesoscopic matter-aggregation context as a problem of passing locally by the matter-aggregating system from classical stochastic (mesoscopic limit) to a quantum description (nanoscale quantum-size effect limit). A d-dimensional entropy-production aggregation of the granules-involving matter is considered in terms of a (sub)diffusive realization. It turns out that when taking a full d-dimensional pathway of the aggregation toward the nanoscale, one is capable of disclosing a Heisenberg type (diffusional) relation, setting up an upper uncertainty bound for the (sub)diffusive very slow granules-including environment that matches the quantum limit of h/2pm (m– average mass of a granule; h – the Planck’s constant) for the diffusion coefficient of the aggregation, likely first proposed by Fürth in 1933, and qualitatively foreseen by Schrödinger some years before, both in the context of a diffusing particle cluster. The classical-quantum passage uncovered here, also termed insightfully the quantum-size effect (as borrowed from the quantum dots’ parlance), works properly for the three-dimensional (d=3) case, making use of a substantial physical fact that the (nano)granules interact readily via their surfaces with the also granular surroundings in which they are immersed. This natural observation is embodied in the basic averaging construction of the diffusion coefficient of the aggregation of interest. Certain, possibly biomedical, applications of the model can also be viewed by prospective inspection of tiny inhomogeneities in nanofibrillar and/or lamellar matter for which certain numerical realizations are plausible to prepare based on thorough nanoscale experiments.

In this study, a new empirical equation was established to predict the sedimentation volume resulting from the construction of a multipurpose weir or low-head dam. The study employed a one-dimensional numerical model (STAFF) to investigate the key parameters affecting sedimentation volume. Short-term predictions were conducted through laboratory experiments with movable bed, and the results indicated that dimensionless unit stream power and the Shields parameter exhibited the most significant correlation with dimensionless deposition volume. Using a multiple regression approach, an empirical equation was formulated and validated for predicting sedimentation in the upstream reservoir of the weir.

This article investigates on the radial and non-radial geodesic structures of the generalized K-essence Vaidya spacetime. Within the framework of K-essence geometry, it is important to note that the metric does not possess conformal equivalence to the conventional gravitational metric. This study employs a non-canonical action of the Dirac-Born-Infeld kind. In this work, we categorize the generalized K-essence Vaidya mass function into two distinct forms. Both the forms of the mass functions have been extensively utilized to analyze the radial and non-radial time-like or null geodesics in great details inside the comoving plane. Indications of the existence of wormhole can be noted during the extreme phases of spacetime, particularly in relation to black holes and white holes, which resemble the Einstein-Rosen bridge. In addition, we have also detected the distinctive indication of the quantum tunneling phenomenon around the central singularity.

Even with significant developments in nanoscience, fairly little is known about the interactions of nanocrystal semiconducting materials with bio-macromolecules. These interactions can influence the properties of both nanocrystals and bio-macromolecules. Understanding this interface is a condition to apply both nanoparticles and biomolecules for bioengineering. To investigate the interfacial phenomena of cadmium selenide quantum dots (CdSe QDs) nanocrystals with proteins extracted from Moringa oleifera seeds, different concentrations of cadmium selenide quantum dots-Moringa oleifera seed protein (CdSe—MSP) complexes were prepared. Respective CdSe QDs with hexagonal phase and crystalline size in the range of 4—7 nm were synthesized and labelled with the purified mesoporous MSP having a surface area of 8.4 m2/g. The interaction mechanism between CdSe QDs and MSP was studied using the UV-Vis absorption spectroscopy, fluorescence emission spectroscopy and Fourier Transform Infrared spectroscopy. The UV-Vis absorption spectrum showed an absorption band of CdSe-MSP complexes at 546.5 nm. The lowest absorbance intensity was observed for the complex with the highest concentration of M. oleifera seed proteins. The fluorescence (FL) spectroscopy of the complex was excited at 280 nm wavelength and emission was monitored at 598 nm. FL intensity of CdSe QDs was found to decrease with an increasing concentration of MSP. Using Stern-Volmer analysis, the binding constants (Kb), quenching constants (Kq) and the number of binding sites (n) were determined. The thermodynamic potentials ∆Hθ(—321.3 kJmol—1);\ ∆Sθ( 156.0 JK—1mol—1) and ∆Gθ(—46.6 kJmol—1) were also calculated. The complexes could be classified as the dynamic quenching mechanism. In the previous studies, the standard quenchers, viz. acrylamide, iodide and nitrate were used to quench the fluorescence of the MSP whereas in this study the protein has acted as a quencher of QDs fluorescence. The stability of the complex is strongly influenced by the CdSe QDs adsorbed into MSP through electrostatics interaction and surface-bound complexation equilibrium attraction. This information can help to elucidate the surface characteristics of MSP and its potential interactions with other molecules or nanoparticles.

The studies of laminar unsteady boundary layer flows is crucial for understanding laminar-turbulence transition and origins of turbulence. However, the task of finding its solutions poses a significant challenge. In this paper, we propose a novel approach by introducing a similar transformation to convert the 2D unsteady laminar boundary layer equations into a single partial differential equation. By applying this transformation, we are able to obtain the "exact" similarity solutions for the 2D unsteady laminar boundary layer equations, specifically for the case of flat plate boundary flow. Notably, this is the first time that such an exact solution has been obtained. Application of this exact solution is being used to solve Stokes' first problem in 2D boundary layer. Perspectives on the transition fron Rayleigh solution to Blasius solution is provided.

We introduce a special vector field ω on a Riemannian manifold (N^m, g), such that the Lie derivative of the metric g with respect to ω is equal to ρRic, where Ric is the Ricci curvature of (N^m, g) and ρ is a smooth function on N^{m} and call this vector field a ρ-Ricci vector field. We use ρ-Ricci vector field on a Riemannian manifold (N^m, g) and find two characterizations of m-sphere S^m(α). In first result, we show that an m-dimensional compact and connected Riemannian manifold (N^m, g) with nonzero scalar curvature admits a ρ-Ricci vector field ω such that ρ is nonconstant function and the integral of Ric(ω,ω) has a suitable lower bound is necessary and sufficient for (N^m, g) to be isometric to m-sphere S^m(α). In second result, we show that an m-dimensional complete and simply connected Riemannian manifold (N^m, g) of positive scalar curvature admits a ρ-Ricci vector field ω such that ρ is a nontrivial solution of Fischer-Marsden equation and the squared length of the covariant derivative of ω has an appropriate upper bound, if and only if, (N^m, g) to be isometric to m-sphere S^m(α).

The discovery of solitonlike coherent structure (SCS) in boundary layer flows is crucial for understanding turbulence origins and in particular for laminar-turbulence transition. However, the task of finding solutions for solitonlike coherent structure from the Navier-Stokes equations poses a significant challenge. In this paper, based on the author's previous work [B.H. Sun, Exact similarity solutions of unsteady laminar boundary layer flows, Preprints 2023, 2023092117], we are able to study convergent flow boundary layers, whose solution encompasses both shock wave and solitary wave solutions, and their superposition gives rise to solitary-like waves, namely solitonlike coherent structure. It is found that the solitonlike coherent structure can only be obtained by combining the Navier-Stokes equations and mass conservation, since the combined equations will have the third order derivatives respect to coordinate $x$, in other words, without the mass conservation condition, the Navier-Stokes equations does not contain solitonlike coherent structure by itself. Finally proved solitonlike coherent structure is a universal motion form of viscous fluid.

We study different aspects of an exactly solvable master equation (ME). Its simplicity allows one direct access to the details of its workings, highlighting significant features and peculiarities. The existence of phase transitions is unveiled.

In the mean-field approximation, the well-known effect of the critical quantum collapse in a 3D gas of particles pulled to the center by potential U(r) = -U_0/(2r^2) is suppressed by repulsive interparticle interactions, which create the otherwise non-existing s-wave ground state. Here, we address excited bound states carrying the angular momentum, with the orbital and magnetic quantum numbers, l and m. They exist above a threshold value of the potential's strength, U_0 > l(l+1). The sectoral, tesseral, and zonal modes, which correspond to m = l, 0 < m < l, and m = 0, respectively, are found in an approximate analytical form for relatively small values of U_0 - l(l + 1). Explicit results are produced for the p- and d-wave states, with l = 1 and 2, respectively. In the general form, the bound states are obtained numerically, confirming the accuracy of the analytical approximation.

In the paper, we develop some numerical schemes including finite difference scheme and finite volume scheme for the fractional Laplacian operator, and apply the resulted numerical schemes to solve some fractional diffusion equations. First, the fractional Laplacian operator can be characterized as the weak singular integral by a integral operator with zero boundary condition. Second, because of the solution of fractional diffusion equation is usually singular near the boundary, we apply finite difference scheme to discrete fractional Laplacian operator and fractional diffusion equation by fractional interpolation function. Moreover, it is find that the differential matrix of the above scheme is symmetric matrix, and strictly row-wise diagonally dominant in special fractional interpolation function. Third, we show finite volume scheme to discrete fractional diffusion equation by fractional interpolation function, and analyze the properties of differential matrix. Finally, the numerical experiments are given, and verify the correctness of theoretical results and the efficiency of the schemes.

Randomized block Kaczmarz Method and randomized extended block Kaczmarz Method are proposed for solving matrix equation AXB=C, where the matrix A and B may be full rank or rank deficient. These methods are iterative methods without matrix multiplication, and are especially suitable for solving large-scale matrix equations. It is theoretically proved these methods converge to the solution or least square solution of the matrix equation. The numerical results show that these methods are more efficient than the existing algorithms for high-dimensional matrix equations.

The differential-equation of second order for space-time oscillation in flat tangential-spacetime of Minkowski-type can be written as an energy-equation. For this energy-equation the analogon of damping energy in two coupled Minkoswki-spacetimes with ftl can be calculated and formulated over Lamberts W-function or via Euler-equation.

To study the heat and mass transfer characteristics of an evaporative cooler for cooling high-temperature working fluids such as supercritical carbon dioxide, an experimental device of the evaporative cooler was built, and a corresponding test system was constructed. Then, the experimental study was carried out based on the orthogonal test method, and the law and extent of the influence of water flow in the tube, spray water flow rate, inlet water temperature in the tube, and air flow rate on heat dissipation, cooling efficiency, and heat and mass transfer coefficients have been obtained. The correlation equations of the heat and mass transfer coefficients were obtained by fitting the orthogonal experimental data, and the validity of the correlation equations was confirmed by the verification experiment.

People have long had a problem: the equations of motion that reflect the laws of physics are invariance under time inversion, while there always are irreversible processes for gases compose of microscopic particles. This article solves this problem. The point is that we should distinguish between the concepts of the equation of motion and motion. We also need to distinguish between the concepts of time-inverse motion and reverse motion. The former is anticlockwise, which is a frictional motion, while the latter is clockwise. For the single-particle motions in classical mechanics and in quantum mechanics, we present mathematical expressions for time-inversion motion and reverse motion, respectively. We demonstrate that single-particle motion is irreversible. The definition of the reversibility of two-particle collisions is given. According to the definition, the two-particle collision as a microscopic motion processes is irreversible. Consequently, for a gas consisting of a large number of particles colliding with each other, its movement should be irreversible, unless the condition of detailed balance is met. We give a physical explanation for the detailed balance, which does not concern the meaning of microscopic reversibility. The detailed balance means that after a pair of reciprocal collisions occur, the distribution function of the particles remains unchanged. Therefore, microscopic two-particle collision events are irreversible, but the statistical average of a large number of collision events makes it possible for the macroscopic process of a gas to be reversible. Conclusively, we clarify the microscopic mechanism of the irreversible process of gases.

This research paper is about to obtain new soliton solutions to the M-fractional (1+1)-dimensional nonlinear Westervelt model by utilizing $\exp_a$ function and modified simplest equation techniques. The gained solutions involving dark, bright, periodic, dark-bright and other solitons. These results have many applications in wave propagation of sound waves, high amplitude in medical imaging and therapy. Achieved results are verified by Mathematica tool and the effect of M-fractional derivative on the solutions is explained through 2-Dimensional, 3-Dimensional and contour plots. At the end, these techniques are simple, fruitful and effective to deal with nonlinear FPDEs.

The rationalization and modeling of an electric discharge in a fluid require the knowledge of electron swarm parameters. In this work, transport coefficients of alcohols, including methanol, ethanol, propanol, and butanol are reported. The electron energy distribution function, mean energy, reduced mobility, and diffusion coefficient, are calculated using the two-term expansion of the electron Boltzmann equation in the frame of BOLSIG+ and the Monte Carlo collision code METHES. For such, experimental and theoretical values of the electron-alcohol collision cross-section, covering a range of electron impact energy from 1 eV to 1000 eV, are employed. A temperature of 300K, reduced fields E/N between $1-10^4$ Td (1Td = $10^{-21}~\rm Vm^2$), and Plasma density of $10^{19}~\rm m^{-3}$ were used in simulations. The calculated coefficients are compared with data available from previous studies.

Water resource pollution, particularly in river channels, presents a grave environmental challenge that necessitates a comprehensive and systematic approach encompassing assessment, forecasting, and effective management. This article provides a comprehensive exploration of the methodology and modeling tools employed to scrutinize the process of river channel pollution due to silting, rooted in the fundamental principles of hydrodynamics and pollutant transport dynamics. The study's methodology seamlessly integrates numerical simulations with state-of-the-art neural network techniques, with a specific focus on the Physics-informed neural networks (PINN) method. This innovative approach represents a groundbreaking fusion of artificial neural networks (ANN) and physical equations, offering a more efficient and precise means of modeling a wide array of complex processes and phenomena. The proposed mathematical model, grounded in the Euler equation, has been meticulously implemented using the Ansys Fluent software package, ensuring accuracy and reliability in the computations. In a pivotal phase of the research, a thorough comparative analysis was conducted between the results derived from the PINN method and those obtained through conventional numerical approaches using the Ansys Fluent software package. The outcomes of this analysis revealed the superior performance of the PINN method, characterized by the generation of smoother pressure fluctuation profiles and significantly reduced computation time, underscoring its potential as a transformative modeling tool. The calculated data originating from this study assumes paramount significance in the ongoing battle against river sedimentation. Beyond this immediate application, these findings also serve as a valuable resource for creating predictive materials pertaining to river channel silting, thereby empowering decision-makers and environmental stakeholders with essential information. The utilization of modeling techniques to address pollution concerns in river channels holds the potential to revolutionize risk management and safeguard the integrity of our vital water resources. However, it is imperative to underscore that the effectiveness of such models hinges on ongoing monitoring and frequent data updates, ensuring that they remain aligned with real-world conditions. This research not only contributes to the enhanced understanding and proactive management of river channel pollution due to silting but also underscores the pivotal role of advanced modeling methodologies in the preservation of our invaluable water resources for present and future generations.

The oscillation of an elastically mounted rigid cylinder excited by steady fluid flow is investigated. Regarding the nonlinearity of real practical structures like marine risers and the stay cable of a long-span bridge, the dynamic behavior of the circular cylinder is described by double Duffing equations and the aerodynamic force performance of the wake flow is expressed by wake oscillator equation. Unlike previous studies, in the present investigation, attention is focused on coupling the wake oscillator equations, taking into account quadratic terms. Following this approach, the cylinder's combined cross-flow and in-line Vortex-Induced Vibrations (VIV) are modeled more accurately. Empirical coefficients are adjusted through comparison with previous credible experimental studies and the effects of changing coefficients of the quadratic terms on major VIV parameters are investigated. The oscillating amplitude calculated by the present model is close to that of the experiment. The relative error of results obtained by the present coupled model is lower than the previous model. Moreover, the present model successfully predicts the moving trajectories of a circular cylinder under VIV in a figure-of-eight shape.

We analyse recent contradictory results and conclusions about the spectrum of the screened Coulomb potential $V(r)=-r^{-1}e^{-C/r}$. The well known Hellmann-Feynman theorem shows that all the bound states of the Coulomb potential ($C=0$) remain bounded as $C$ increases. We derive a simple approximate analytical expression for the eigenvalues for sufficiently small values of the screening parameter $C$ and an approximate asymptotic expression for the asymptotic behaviour of the s-state eigenvalues when $C\rightarrow \infty $. Present results are expected to resolve the discrepancy about the spectrum of the quantum-mechanical model just mentioned.

Having as objective to reach a circular economy, it is important to maximize the Physical Asset’s Life Cycle. The evaluation of Physical Assets Life Cycle may have several approaches which may provide different results. These differences may not be very significant, but must be taken into consideration, because they have consequences in the manager decision. This permits to have a wider time interval to decide when to withdrawal the Physical Asset or to renewal it, and or if this ought to continue functioning because the profits are higher than the expenses, what allows to diminish waste and increase sustainability. These are some aspects that are discussed in this paper, which presents several models to evaluate the Physical Assets Life Cycle, considering the market value, devaluations methods and a more generalized way of Fisher’s Equation, which can include the Risk tax, among others. The results are discussed supported in data for simulation, which are used for each Econometric Model aiming to evaluate the differences among them. In all Models they are considered not only the expenses, namely of Investment and Functioning, but also the Profits, which permit to evaluate the Physical Asset Life Cycle in a holistic way. The models are very versatile, allowing to evaluate quantitatively the changing in the maintenance policies, the energy prices variations, the risk evaluation, the variation of profits according to the real market, and so on. The results demonstrated the robustness of the approach described and that maximize the Physical Assets Life Cycle allowing to minimize the consumption of world resources and, by consequence, it contributes for a more sustainable world.

In this paper, new types of M-fractional wave solutions of mathematical physics model named as truncated M-fractional (1+1)-dimensional non-linear simplified Modified Camassa-Holm model are achieved by applying the modified simplest equation (MSE), Sardar sub-equation and generalized Kudryashov techniques. The gained solutions containing dark, bright, periodic and mixed wave solitons. Effect of fractional order derivative is also discussed. Achieved wave solitons are verified by Mathematica tool. Few of the gained wave solitons are also described through 2-dimensional, 3-dimensional and contour graphs through Mathematica tool. The gained solutions are helpful for the further development of concerned model. Finally, these techniques are simple, fruitful and effective to deal with non-linear FPDEs.

In this paper, we analyze the convergence of a finite difference method with the implicit forward time central space (FTCS) scheme for solving the three-dimensional advection-diffusion-reaction equation (ADRE). It is proved that the method is unconditionally convergent. We apply the scheme to obtain numerical solutions for the transport of pollutants in street tunnel problems with various reaction coefficients and various rates of change of concentrations of sources or sinks of pollution.

In this research, a computation algorithm is established for a fractional order 2D fuzzy heat equation. In this study, Elzaki transform and HPM fusion is produced. Computing the desired outcome in series yields a fast convergence on an appropriate response. Examples are provided to support the conclusions, which are then compared with a particular approach to show the effectiveness and potential of the suggested approach. Two crisp equations—one for the lower bound solution and one for the upper bound solution are constructed from the input fuzzy fractional heat equation. The contour and surface representations of the approximate and exact results are offered for the lower and upper-bound solutions. The l∞-error norm is used in this study to validate the numerical convergence aspect. Together with the absolute inaccuracy, the approximate and exact solutions are matched. It has been demonstrated that the proposed regime will make it feasible to work with fuzzy fractional partial differential equations in a wide range of dimensions.

This study investigates the critical success factors (CSFs) of Lean Six Sigma (LSS) implementation and their impact on organizational growth in Nigerian enterprises. The objectives were to identify crucial CSFs for successful LSS deployment and assess their significance in achieving organizational growth. A mixed-method approach was used, including literature analysis, expert judgments, and a survey of 130 participants from various industries. The survey questionnaire employed a 5-point Likert scale to collect data on LSS CSFs and implementation success metrics. Structural equation modeling (SEM) with SmartPLS 4.0 analyzed the data, revealing that LSS CSFs significantly contribute (up to 39.2 percent) to the success of LSS implementations. The study identified 12 critical LSS CSFs, categorized into workers, business, and management, each influencing LSS implementation. Recommendations include creating a supportive environment, providing comprehensive training, and prioritizing continuous improvement efforts for successful LSS deployment. Future research possibilities include longitudinal studies, sector-specific analyses, and qualitative investigations to deepen understanding and enhance LSS implementation outcomes. In conclusion, successful LSS implementation empowers Nigerian organizations with improved productivity, waste reduction, and sustainable production systems, leading to overall growth and success.

We investigate the production of an isolated attosecond pulse (IAP) via the phase-matching gating of high-harmonic generation by intense laser pulses. Our study is based on the integration of the propagation equation for the fundamental and generated fields with nonlinear polarisation found via the numerical solution of the time-dependent Schr\"odinger equation. We study the XUV energy as a function of the propagation distance (or the medium density) and find that the onset of the IAP production corresponds to the change from linear to quadratic dependence of this energy on the propagation distance (or density). Finally, we show that the upper limit of the fundamental pulse duration for which the IAP generation is feasible is defined by the temporal spreading of the fundamental pulse during the propagation. This nonlinear spreading is defined by the difference of the group velocities for the neutral and photoionised medium.

The main object of this work is to establish the existence and uniqueness of a solution to the 3D Navier-Stokes (NS) system for an incompressible fluid with viscosity. The nonlinearity of the NS system, as well as the need to estimate velocity and pressure for every value of the viscosity parameter [1] make them challenging to solve. In this regard, in the present work, we study the Navier-Stokes system, which describe the flow of a viscous incompressible fluid and the solution was obtained for velocity and pressure in an analytical form. In addition, the found pressure distribution law, which is described by a Poisson type equation and plays a fundamental role in the theory of Navier-Stokes systems in constructing analytic smooth (conditionally smooth) solutions.

There are strong indications that the built environment intertwines consistently with the advent of Covid-19 and the need for post-disaster recovery. The advent of the Covid-19 pandemic has exerted adverse effects on both human and global developments; while the efforts to combat this menace call for an integrated human social capital index. This research seeks to adequately enhance the comprehension of how the built environment can be enhanced through resilience in the backdrop of the Covid-19 pandemic. The study's goal is to investigate the impact of a resilient built environment on increasing resilience in the aftermath of the Covid-19 pandemic in Nigeria. Overall, the quantitative study test the impact of four built environments resilience indices (Built Environment capitals; Disaster management indices, Awareness of the Covid-19 Pandemic, and Built Environment adaptive strategies) on Human social capital and Covid-19 pandemic Indices. This study reveals the role of human social capital in achieving a resilient built environment in the wake of Covid 19 pandemic in Nigeria. Also, built environment capitals, disaster management indices, and awareness on the Covid-19 have indirect effects on Covid-19 pandemic indices through the human social capital. The implication of the study is useful for Post-Covid 19 recovery; which is important for future planning of the built environment in Nigeria.

Unidirectional flow of a fluid with pressure-dependent viscosity through a porous structure is considered when the viscosity-pressure relationship is an exponential function of a pressure power function in order to investigate effects of the viscosity-pressure relation on the flow characteristics. The flow is governed by the generalized Brinkman’s equation with constant permeability, and a model flow domain of flow down an inclined porous channel is chosen for the sake of studying flow behaviour. Although the current work considers flow in a constant permeability porous structure, it does represent a first step in studying the more general, flow through a variable permeability porous channel. The arising governing equations are solved numerically using MATLAB and the flow is simulated to illustrate the effects of fluid properties as well as flow and medium parameters on the velocity profiles and shear stress.

We carry out in a thin heterogeneous porous layer, the multiscale analysis of Smoluchowski's discrete diffusion-coagulation equations describing the evolution density of diffusing particles that are subject to coagulate in pairs. Assuming that the thin heterogeneous layer is made of microstructures that are uniformly distributed inside, we obtain in the limit an upscaled model in lower space dimension. We also prove a corrector-type result very useful in numerical computations. In view of the thin structure of the domain, we appeal to a concept of two-scale convergence adapted to thin heterogeneous media to achieve our goal.

The main aim of this study is to examine the effects of Total Quality Management (TQM) practices (leadership of management, decision making, continuous improvement, customer focus, employee involvement, process management and relations with suppliers) on the financial and operational performance of hospitals in service industry. The data of the study were collected by the questionnaire prepared in the light of published studies and the suggestions of medical and administrative staff. Medical and administrative staff were chosen as target participants that reflect perspectives of hospitals. 1069 questionnaires were answered in 6 private and 26 public hospitals in the Marmara region in Turkey. The results claim that “customer focus” affects both operational performance as well as the financial performance of hospitals more than other TQM practices. While “process management” and “customer focus” explain the variance of financial performance significantly. “Process management” does not explain variance of operational performance.

We discuss the optimal control formulation for enhancement and denoising of satellite multiband images and propose to take it in the form of an L1-control problem for quasi-linear parabolic equation with non-local p[u]-Laplacian and with a cost functional of a tracking type. The main characteristic feature of the considered class of parabolic problems is the fact that the variable exponent p(t,x) and the anisotropic diffusion tensor D(t,x) are not well predefined a priori, but instead these characteristic non-locally depend on a solution of this problem, i.e., pu=p(t,x,u) and Du=D(t,x,u). We prove the existence of optimal pairs with sparse L1-controls using for that the indirect approach and a special family of approximation problems.

The study presented here, through the use of GIS and physical variables, generate a new meth-odology for the calculation of erosivity (Factor R) for the qualitative evaluation of soil loss po-tential (laminar erosion) in the Northwest margin of the municipality of São Francisco, mostly located in the Pardo-MG river basin. The results obtained were statistically correct when com-pared to the traditional R calculation and the laminar erosion methodology. It is worth noting that the new proposal presented here indicated sites of qualitative loss of soil in the same places where there are closed-loop satellite signals of degraded Cerrado, something not identified in the traditional model. As conclusion it can be said that the obtained results were extremely sat-isfactory, being advised more studies to verify this new method proposed here in more places beyond the study area elaborated here

Two clear-air over-the-horizon propagation mechanisms affecting Automatic Identification System (AIS) detection range are considered. Comparison results are presented between the path loss due to tropospheric ducting and path loss due to tropospheric scattering (troposcatter) for the AIS frequencies. The calculations are based on the well-known parabolic equation approximation to the wave equation, in which a simple troposcatter formula is incorporated. In most studied cases the ducting assures significantly greater reduction of path loss than troposcatter even when the AIS frequencies are not well trapped in the duct. Emphasis is placed on elevated trapping layers and some features that may make ducting propagation less favorable in terms of increasing the AIS detection range are discussed.

The paradigm of molecular communications is applied to the concrete case for delivering electrically charged nanoparticles to tumor. Once them have been injecetd in blood it is expecetd an optimal outcome as to reduce toxicity and minimal dispersion of drugs in the blood stream. With a fraction of nanoparticles arrives to surface of tumor, the scattered part of injected ones can minimize the success of scheme of drug delivery. In this paper is presented a theory based at the sequence electrodynamics-diffusion-Bayes theorem. The resulting probability of Bayes at the end of sequence, might be telling us that dynamical processes based in the injection of electrically charged nanoparticles might be dictated by stochastic formalism more that biochemical approaches by which makes impossible to know the success or fail of drug delivery dynamics. Illustrations demonstrating the transition of a linear to nonlinear scenario are presented

The paper examines rational Darboux-Crum transforms (RDCTs) of the Jacobi-reference (JRef) potential on the line, with an emphasis on the transformations using only normalizable seed solutions. The Cooper-Ginocchio-Khare (CGK) potential constitutes the simplest example of this rich family of exactly solvable one-dimensional (1D) potentials. It was explicitly confirmed that that an arbitrary Darboux-Crum transformation (DCT) of the given Sturm-Liouville equation (SLE) can be represented as a chain of sequential Darboux deformations of the associated Liouville potentials. If the rational SLE (RSLE) under consideration is exactly solvable and the transformation function (TF) used at each step is nodeless then each RSLE constructed in such a way was proven being exactly solvable itself. The exact solvability of RDCTs of the JRef canonical SLE (CSLE) was also confirmed for the DCTs using pairs of juxtaposed eigenfunctions (an extension of the renowned Adler theorem to the RCSLEs of our interest). By re-expressing the reference polynomial fraction (RefPF) of the transformed CSLE in terms of the Krein determinant (KD), instead of Crum Wronskian (CW), it was shown that the eigenfunctions under consideration are expressible in terms of polynomial solutions of a generalized Heun equation with positions of the most poles dependent on the exponent parameters. The outlined technique was extended to two isospectral SUSY partners of the JRef potential (as well as to its third sibling with the inserted new lowest-energy level) which, by analogy with the CGK potential, are quantized by polynomial solutions of the 2-Heun equation with all four poles at some fixed positions on the real axis.

Evaporating liquid sessile drop deposited on horizontal surface is an important object of applications (printing technologies, electronics, sensorics, medical diagnostics, hydrophobic coatings, etc.) and theoretical investigations (microfluidics, self-assembly of nanoparticle, crystallization of the solute, etc.). The arsenal of formulas for calculating the slow evaporation of an axisymmetric drop of capillary dimensions deposited on a flat solid surface is reviewed. Such characteristics as vapor density, evaporation flux density, total evaporation rate are considered. Exact solutions obtained in the framework of the Maxwellian model, in which the evaporation process of the drop is limited by vapor diffusion from the drop surface to the surrounding air, are presented. The summary covers both well-known results obtained during the last decades and new results published by us in the last few years, but practically unknown to the wide scientific community. The newest formulas, not yet published in refereed publications, concerning exact solutions for a number of specific contact angles are also presented. In addition, new approximate solutions are presented for the first time (total evaporation rate and mass loss per unit surface area per unit time in the whole range of contact angles ), which can be used in modeling without requiring significant computational resources.

This paper investigates the ion-acoustic wave structures in fluid ions for the Benjamin-Bona-Mahony-Peregrine-Burgers (BBMPB) equation. The various types of wave structures, are extracted including the three-wave hypothesis, breather wave, lump periodic, mixed-type wave, periodic cross-kink, cross-kink rational wave, M-shaped rational wave, M-shaped rational wave solution with one kink wave and M-shaped rational wave with two kink wave solutions. The Hirota bilinear transformation is a powerful tool that allows us to accurately solutions and predict the behavior of these wave structures. Through our analysis, we gain a better understanding of the complex dynamics of ion-acoustic waves and their potential applications in various fields. Moreover, our findings contribute to the ongoing research in plasma physics that utilize ion-acoustic wave phenomena. To show the physical behavior of the solutions, some 3D plots have been performed and their respective contour level, choosing different values of the parameters.

We propose a description of the electromagnetic field in the form of a four-component complex spinor, from which a vector of electromagnetic potential with two degrees of freedom, calibrated by two conditions - zero length and zero component along the y-axis - is obtained by using Pauli matrices. A similar approach is applied to the field of a fermion, in particular, the electron. It is known that the quantum field of the electron and the electron itself is a four-component complex spinor, so, existing in the Minkowski vector space, we cannot observe it directly. But with the help of Pauli matrices a vector is formed from the electron spinor, which is known to us as an electric current vector, and this current vector describes exactly a single particle. As a vector, it is available to us for observation in our vector space. Similarly, the electromagnetic field and its photon particle is also a four-component spinor, from which the universal formula using Pauli matrices produces a vector, it is known to us as the electromagnetic potential vector, and it too describes even a single photon. All the differences in the properties of the current vector and the electromagnetic potential vector, and hence the electron and the electromagnetic field, are due only to a slight difference in the structures of their four-component spinors and inextricable linked to them momentum spinors and coordinate spinors. Expressions for the electric and magnetic fields of a photon during its interaction with an electron.Thus, a unified way to describe bosons and fermions in spinor space is proposed. Each spinor using the same formula corresponds to a vector, in the case of a fermion it is a current vector, in the case of a boson it is a vector, for example, of the electromagnetic potential. Each spinor of a field is matched with a spinor of coordinates and a spinor of momentum, which are transformed by the same Lorentz transformations and which have the same structure as their corresponding field spinor, that is, the momentum and coordinates of boson have a bosonic spinor structure, while momentum and coordinates of fermion are a spinor with a fermionic structure. Field, coordinates and momentum vectors of boson automatically have a zero length, while in the case of fermion they all have a nonzero length, so the fermion, in contrast to the boson, has a nonzero mass, nonzero charge and moves with a sub light speed.While quantum mechanics treats probability as a real number, quantum field theory deals with probability as a four-dimensional real vector. The place of the probability amplitude, which in quantum mechanics is a complex number, in quantum field theory is taken by a complex spinor.In the same way as in quantum mechanics the processes of propagation and interaction are described at the level of complex probability amplitudes, and the final result is translated into a real probability value, so in quantum field theory all processes should be described in terms of complex spinor space, and the result is translated into the form of a real vector in Minkowski space.The presented approach, at its proper development, makes it possible to carry out calculations of the interaction of particles in two-dimensional spinor space, and to interpret in terms of the Minkowski vector space only the final results.

In a previous paper, we solved the partial differential equation of Mullins problem in the case of the evaporation-condensation in electronic devices and gave an exact solution relative to the geometric profile of the grain boundary grooving when materials are submitted to thermal and mechanical solicitation and fatigue effect. In this new research, new modelling of the grain groove profile was proposed and new analytical expressions of the groove profile, the derivative and the groove depth were obtained in the case of diffusion in thin polycrystalline films by the resolution of the fourth differential equation formulated by Mullins that supposed 〖y'〗^2≪1. The obtained analytical solution gave more accurate information on the geometric characteristics of the groove that were necessary to study the depth and the width of the groove. These new findings will open a new way to study with more accuracy the problem of the evaporation-condensation combined to the diffusion phenomenon on the material surfaces with the help of the analytical solutions.

Energy transition is a major structural change in the whole social system, and the energy system must be changed globally to replace fossil fuels. Hydropower is one of the largest renewable energy in the world. However the involuntary resettlees due to the construction of hydropower projects are suffering from being far away from their native land, losing the land cultivated for generations and the houses they live in, and losing the social relationship network based on geography and blood ties. Based on the system evaluation theory of reservoir resettlement and referring to relevant research findings, this paper constructs a comprehensive evaluation index framework for assessing the implementation effect of the PostRelocation Support (PReS) policy. The research region is located in Zhijin County, Bijie City, Guizhou Province, China. Accordingly, a combined method of a structural equation model and a fuzzy comprehensive evaluationary model is used in this paper to analyze the implementation of the PReS policy. The results show that the total score of implementing effects of the PReS policy is 4.4, with dramatic significance. The subindex scores of the resettlers’ family income, living conditions, and production conditions; the local economy; and social stability are 4.3, 4.6, 4.4, 4.6, and 4.3, respectively, with dramatic significance. This paper has analyzed and summarized the successful practices of implementing the PReS policy for reservoir resettlers in three dimensions: poverty alleviation, beautiful home construction and accelerating rural revitalization. Research shows that China's rural reservoir resettlers' PReS policy has been more effective in restoring the livelihoods of reservoir resettlers.

Louis de Broglie in the beginning 20th century voices his theory of a double solution, according to which a pilot wave accompanies a particle, simulated as a point singularity, along the most optimal path from its creation on a source up to the detection. The pilot wave is a real hidden wave, which is similar to the wave function resulting from the solution of the Schrödinger equation. This theory is in agreement with de Broglie’s postulate about the matter waves. In this article we are based on the Helmholtz decomposition theorem according to which any velocity may be represented as a sum of two velocities – irrotational and solenoidal ones. The first velocity stems from the gradient of the scalar field. The second occurs from a pseudo-vector field. We proclaim that the gradients of the scalar field define guiding paths of the pilot wave. While the pseudo-vector field defines a particle solenoidal filling. We give mathematical models of the irrotational and solenoidal flows simulating the position of a particle in a guiding wave. Modified Navier-Stokes equation in pair with the continuity equation resulting in the Schrödinger equation gives such solutions consisting of superposition of the irrotational and solenoidal flow. It is declared that the guiding wave forms from the irrotational flows. In turn, the solenoidal flows underlie forming particles that travel along optimal paths slave by the guiding wave. There are described mathematical solutions of the spherical particle washed by the superfluid representing the guiding wave along which it travels.

The invariant mass of free particles is used to derive a bound-state equation for several particle atomic systems at rest. This relativistic-kinematic bound-state equation is applied to the hydrogen and helium atoms. The derived equation has the well-known solutions for the single-electron bound states of the hydrogen atom, and the two-electron states of the helium atom. For the hydrogen atom, existence of the two-particle bound states, for which the electron and the proton kinetic energies are of the same order of magnitude, is predicted. The three-particle bound states with the same feature of the kinetic energies can exist in the helium atom. Radiative operators for processes involving the hydrogen two-particle bound states, are obtained. It is discussed that these new two- and three-particle bound states should be optically inactive.

TThis paper delves into the extension and characterization of radial positive definite functions into non-integer dimensions. We provide a thorough investigation by employing the Riemann-Liouville fractional integral and fractional Caputo derivatives, enabling a comprehensive understanding of these functions. Additionally, we introduce a secondary characterization based on the Bernstein characterization of completely monotone functions. The practical significance of our study is showcased through an examination of the positivity of the fundamental solution of the space-fractional Bessel diffusion equation, highlighting the real-world applicability of the developed concepts. Through this work, we contribute to the broader understanding of radial positive definite functions and their utility in diverse mathematical and applied contexts.

This study uses machine learning to predict the convergence results of the Duffing equation with and without damping. The Duffing equation represents a nonlinear second-order differential equation with interesting behavior in undamped free vibration and forced vibration with damping. Convergence alternates randomly between 1 and -1 in undamped free vibration, depending on initial conditions. For forced vibration with damping, multiple factors influence vibration patterns. We utilize the fourth-order Runge-Kutta method to collect convergence results for both conditions. Machine learning techniques, specifically the long short term memory (LSTM) and LSTM-Neural Network (LSTM-NN) method, are employed to predict these convergence values. The LSTM-NN model is a hybrid approach that combines the LSTM method with the addition of hidden layers of neurons. Both the LSTM and LSTM-NN models are thoroughly explored and analyzed in this research. The research process involves three stages: data preprocessing, training, and verification. The results show that the LSTM-NN model becomes more adept at predicting binary datasets, boasting an impressive accuracy of up to 98%. However, when it comes to predicting multiple solutions, the traditional LSTM method outperforms the LSTM-NN approach.

The elastic wave equation with the seismic tensorial force is solved in a homogeneous and isotropic medium (the Earth). Spherical-shell waves are obtained, which are associated to the primary P and S seismic waves. It is shown that these waves produce secondary waves with sources on the plane surface of a half-space, which have the form of abrupt walls with a long tail, propagating in the interior and on the surface of the half-space. These secondary waves are associated to the seismic mainshock. The results, previously reported, are re-derived by using Fourier transformations and specific regularization procedures. The relevance of this seismic motion for the ground motion, the seismographs' recordings and the effect of the inhomogeneities in the medium are discussed.

In this research, the application of the Physics-Informed Neural Network (PINN) model is explored to solve transport equation-based Partial Differential Equations (PDEs). The primary objective is to analyze the impact of different activation functions incorporated within the PINN model on its predictive performance, specifically assessing the Mean Squared Error (MSE) and Mean Absolute Error (MAE). The dataset used in the study consists of a varied set of input parameters related to strut diameter, unit cell size, and the corresponding yield stress values. Through this investigation, the aim is to understand the effectiveness of the PINN model and the significance of choosing appropriate activation functions for solving complex PDEs in real-world applications. The outcomes suggest that the choice of activation function may have minimal influence on the model's predictive accuracy for this particular problem. The PINN model showcases exceptional generalization capabilities, indicating its capacity to avoid overfitting with the provided dataset. The research underscores the importance of striking a balance between performance and computational efficiency while selecting an activation function for specific real-world applications. These valuable findings contribute to advancing the understanding and potential adoption of PINN as an effective tool for solving challenging PDEs in diverse scientific and engineering domains.

Manufacturing is a significant sector of the economy in many nations and is frequently regarded as an engine of economic expansion, particularly in developing nations. Despite its importance, the metal sector is seen as unsafe due to frequent and high accident rates as well as worker health issues. Therefore, the primary goal of this research is to create a safety model with the goal of development in occupational safety and health in order to reduce workplace injuries, diseases, and deaths in the Akaki Basic Metal Industry. The hypothesized model was developed and tested on a sample 215 respondents who worked for production businesses. The Statistical Package for the Social Sciences (SPSS) version 23.0 was used to enter and analyze the acquired data, and the Analysis Moment of Structure (AMOS) version 21 software was used to build the model. Through the use of structural equation modeling (SEM) and confirmatory factor analysis (CFA), research models were examined and confirmed. A good-fit structural model (PCLOSE=0.001, Goodness of Fit Index=0.971, Root Mean Square Error of Approximation=0.121, Comparative Fit Index=0.986 and TLI =0.906) indicated that Safety culture, safety police and safety climate constructs direct influence on firm productivity. The new structural model can be used to provide better understanding of the links between firm productivity indicators and contributing components, and make stronger recommendations for effective intervention in construction projects

Mangroves play an important role as a carbon sink and in mitigation of climate change. This study aimed to assess the anthropogenic activities, water and soil quality, mangrove diversity, and carbon sequestration potential of mangrove trees in the Kaingen River, Kawit, Cavite. The sampling period was conducted from November 2022 to March 2023 with the established three sampling sites. The DENR Administrative Order (DAO)- 2016-08 was used as a standard for water quality parameters, except for phosphates which used DAO-2021-19. The soil parameters were identified using the soil test kit from the Bureau of Soil and Water Management (BSWM) and at the BSWM laboratory. Mangrove species were identified using The Field Guide for Philippine Mangroves and were verified by experts. The carbon sequestration potential was obtained using an allometric equation for Southeast Asian mangroves. There are three mangrove species found in Kaingen Riverine such as Rhizophora mucronata, Avicennia alba, and Xylocarpus granatum. Based on species importance value Rhizophora mucronata is the dominant mangrove species. The result for carbon sequestration of each mangrove species showed that Rhizophora mucronata yielded the highest carbon stored (35.16 tC/ha) and carbon sequestered (128.92 tCO₂/ha). Among all the sampling sites, site 3 yielded the highest carbon stored (30.76 tC/ha) and carbon sequestered (112.81 tCO₂/ha) in Kaingen River. Overall, the results of the study showed that Kaingen River can potentially store carbon at 71.89 tC/ha and CO2 sequestered at 263.62 tCO₂/ha. This urges to practice conservation and protection measures for the mangroves forest of Kaingen River.

The nonlocality (superdiffusion) of turbulence is expressed in the empiric Richardson t3 scaling law for the mean square of the mutual separation of a pair of particles in a fluid or gaseous medium. The development of the theory of nonlocality of various processes in physics and other sciences based on the concept of Lévy flights resulted in the idea of Shlesinger and colleagues about the possibility of describing the nonlocality of turbulence using a linear integro-differential equation with a slowly falling kernel. The close approach developed by us made it possible to establish the closeness of the superdiffusion parameter of plasma density fluctuations moving across a strong magnetic field in a tokamak to the Richardson law. In this paper, we show the possibility of a universal description of the characteristics of nonlocality of transfer in a stochastic medium (including turbulence of gases and fluids) using the Biberman-Holstein approach to the transfer of excitation of a medium by photons, generalized to take into account the finiteness of the velocity of excitation carriers. This approach enables us to propose a scaling that generalizes Richardson's t3 scaling law to the combined regime of Lévy flights and Lévy walks.

Currently, two-component integrable nonlinear equations from the hierarchies of the vector nonlinear Schrodinger equation and the vector derivative nonlinear Schrödinger equation are being actively investigated. Usually, such two-component integrable nonlinear evolutionary equations are considered, the form of which does not depend on the replacement of one component with another. In this paper, we propose for consideration and usage a new hierarchy of two-component integrable nonlinear equations, which have an important difference from the already known equations. Among the hierarchy equations there are analogues of the two-component nonlinear Schrödinger equation (second equation from hierarchy) and the two-component modified Korteweg-de Vries equation (fourth equation from hierarchy). The third equation of the hierarchy is a combination of the nonlinear Schrödinger equation for one component and the modified Korteweg-de Vries equation for the second component. The equations for the individual components are very different from each other, even if they have the same order. Let us note that even hierarchy equations can be reduced to well-known variants of the scalar derivative nonlinear Schrödinger equations, and odd equations can’t be reduced. To construct the hierarchy equations, we use the monodromy matrix method, first proposed by B.A. Dubrovin. Knowledge of the monodromy matrix makes it possible to construct spectral curves of multiphase solutions, as well as to find stationary equations that these solutions satisfy. The last section presents the simplest solutions in the form of solitons and periodic one-phase waves, as well as spectral curves corresponding to these solutions.

In this paper, we succeed to discover the new exact wave solutions to the truncated M-fractional complex three coupled Maccari’s system by utilizing the Sardar sub-equation scheme. The obtained solutions are in the form of trigonometric and hyperbolic forms. These solutions have many applications in nonlinear optics, fiber optics, deep water-waves, plasma physics, mathematical physics, fluid mechanics, hydrodynamics and engineering where the propagation of nonlinear waves is important. Achieved solutions are verified with the use of Mathematica software. Some of the achieved solutions are also described graphically by 2-dimensional, 3-dimensional and contour plots with the help of Maple software. The gained solutions are helpful for the further development of concerned model. Finally, this technique is simple, fruitful and reliable to handle the nonlinear FPDEs.

This paper discusses the mathematical modelling of exothermic explosions in a slab. This model is based on a nonlinear equation containing a nonlinear term related to Arrhenius, bimolecular, and sensitised laws of reaction kinetics. The absolute temperature can be obtained by solving the nonlinear equation using Akbari-Ganji’s method. The influence of the parameters Frank-Kamenetskii, activation energy and numerical exponent on temperature is discussed. The analytical results are compared with previous available analytical and numerical results ( Matlab). A satisfactory agreement is noted.

Despite a growing concern over sustainability in tourism, research on this domain regarding, specifically, lake destinations, is still scarce. Although perceptions on lake destinations have been studied, no study is known that analyses the impact of visitors’ perceptions on satisfaction and behavioral intentions. Thus, this paper aims to develop and test a model to analyse the effect of lake visitors’ perceptions of destination’s sustainability on both satisfaction and loyalty towards lake destinations. A questionnaire survey was conducted in the Shchuchinsk-Burabay resort area, an important lake destination in northern Kazakhstan. The results support the proposed lake destination loyalty model, tested using partial least squares structural equation modelling (PLS-SEM). Sustainability proved to be decisively influential, with water quality being the dimension with the highest impact on satisfaction with the lakes, along with a positive key impact of the absence of congestion. In addition, both water quality and lack of congestion had a significant indirect impact on satisfaction with the lake destination, and on loyalty. Based on the research findings, theoretical conclusions and practical implications are drawn.

The mass of the nucleons is calculated from first principles by defining the quark as a non-gravitational particle, subject to Dirac’s equation with non-canonical gamma matrices. Unlike the canonical electron-type, this Dirac particle has two real dipole moments, which allows a structural modelling of hadrons. It is shown how such modelling reveals striking correspondences and differences between dually related particles and properties like electrons and quarks, photons and gluons, pions and nucleons, spin and isospin and protons and neutrons. It is a stepping stone to the actual calculation, which competes in precision with lattice QCD. The appendix contains a Lorentz covariance proof of hadrons composed by such particular Dirac-type quarks.

This study investigates via Lie symmetry analysis the Hunter-Saxton equation, an equation relevant to the theoretical analysis of nematic liquid crystals. We employ the multiplier method to obtain conservation laws of the equation derived from first-order multipliers. Conservation laws of the Hunter-Saxton equation, in combination with the Lie point symmetries of the equation, enable us to perform symmetry reductions through employment of the double reduction method. The method exploits the relationship between Lie point symmetries and conservation laws to effectively reduce both the number of variables and the order of the equation. Five nontrivial conservation laws of the Hunter-Saxton equation are derived, four of which are found to have associated Lie point symmetries. Applying the double reduction method to the Hunter-Saxton equation results in a set of first-order ordinary differential equations, the solutions of which represent invariant solutions for the equation.

This paper delves into the dynamics of asset pricing within Bachelier’s market model (BMM), elucidating the representation of risky asset price dynamics and the definition of riskless assets. It highlights the fundamental differences between BMM and the Black-Scholes-Merton market model (BSMMM), including the extension of BMM to handle assets yielding a simple dividend. Our investigation further explores Bachelier’s term structure of interest rates (BTSIR), introducing a novel version of Bachelier’s Heath-Jarrow-Morton model and adapting the Hull-White interest rate model to fit BMM. The study concludes by examining the applicability of BMM in real-world scenarios, such as those involving environmental, social, and governance (ESG)-adjusted stock prices and commodity spreads.

In this investigation, we explore the existence and intriguing features of matter wave positons in a nonautonomous one-dimensional Bose-Einstein condensate (BEC) system with attractive interatomic interactions. We focus on the Gross-Pitaevskii (GP) equation/nonlinear Schrödinger (NLS)-type equation with time-modulated nonlinearity and trap potential, governing nonlinear wave propagation in the BEC. Our approach involves constructing second- and third-order matter wave positons using a similarity transformation technique. We also identify the constraints on the time-modulated system parameters that give rise to these nonlinear localized profiles. The study considers three distinct forms of modulated nonlinearities: (i) kink-like, (ii) localized or -like, and (iii) periodic. By varying the parameters associated with the nonlinearity strengths, we observe a rich variety of evolution behaviors in the matter wave positon profiles. These behaviors include stretching, curving, oscillating, breathing, collapsing, amplification, and suppression. Our comprehensive studies shed light on the intricate dynamics of matter wave positons in BECs, providing valuable insights into their behavior and characteristics in the presence of time-modulated nonlinearity and trap potential effects.

We establish certain modular equations of degree three based on some results of Ramanujan's theta functions.

A family of singularly perturbed q-difference-differential equations under the action of a small complex perturbation parameter is studied. The action of the formal monodromy around the origin is present in the equation, which suggests the construction of holomorphic solutions holding logarithmic terms in both, the formal and the analytic level. We provide both solutions and describe the asymptotic behavior relating them by means of q-gevrey asymptotic expansions of some positive order, with respect to the perturbation parameter. On the way, the development of a space product of Banach spaces in the Borel plane is needed to provide a fixed point for a coupled system of equations.

E-commerce platforms created to meet the needs of digital consumers, who are the leading actors of digital-oriented consumption, are increasing rapidly. Revolutionizing our daily lives by offering the digital equivalent of real-world experiences, e-commerce now offers a comfortable shopping experience that transcends the limitations of time and space. This phenomenon has been embraced by individuals spanning all age groups, from young children to the elderly. Structural equation modeling was used in this study, in which the factors affecting online shopping addiction were determined. In this direction, the causal and correlational relationships between the variables of fear of missing out (FoMO), cognitive load, personality types, some socio-demographic characteristics (gender and monthly shopping amount) and online shopping addiction in online shopping were revealed structurally. Since the purposive sampling was used, the study was carried out on 488 people. The goodness-of-fit indices included in the created model were found at an “acceptable” level (χ2/df= 2.248, p=0.000; RMSEA=0.051; GFI=0.878; AGFI=0.856; CFI=0.950; NFI=0.914). These results show that the final version of the model meets the necessary criteria for a good fit, its validity and accuracy. The study revealed the causal and correlational relationship between online shopping addiction and cognitive load, personality types, FoMO, gender, and monthly online shopping amount.

Despite marked advancements, life expectancy (LE) growth in Saudi Arabia and the United Arab Emirates (UAE) has remained stagnant compared to other developed nations. This study aims to investigate the significant correlation between macroeconomic (ME), sociodemographic (SD), and health status-resources (HSR) factors and LE to formulate an explanatory model for Saudi Arabia and the UAE – a previously unexplored area. Utilizing an ecological, retrospective, time-series study design, we delved into secondary data on SD, ME, HSR, and LE of the UAE population spanning three decades (1980-2020). We employed the partial least squares-structural equation modeling for statistical analysis. Our analysis revealed significant direct impacts of HSR on LE for Saudi Arabia (Beta=0.958, p<0.001) and the UAE (Beta=0.716, p<0.001). Furthermore, we discerned a notable indirect influence of ME on LE, mediated through SD and HSR for Saudi Arabia (Beta=0.507, p<0.001) and UAE (Beta=0.509, p<0.001), along with a considerable indirect effect of SD on LE through HSR (Saudi Arabia: Beta=0.529, p<0.001; UAE: Beta=0.711, p<0.001). This study underscores the mediating role of a nexus of ME-SD-HSR factors on LE in Saudi Arabia and the UAE. Consequently, these findings signal an imperative need for holistically policy interventions addressing ME, SD, and HSR factors, aiming to alter health behaviors and improve LE projections for Saudi Arabia and the UAE in the long run.

At present paper, we aim to study the long-time behavior of a stochastic semi-linear degenerate parabolic equation on bounded or unbounded domain and driven by a nonlinear noise and defined. Since the theory of pathwise random dynamical systems can not be applied directly to the equation with nonlinear noise, first, we establish the existence of weak pullback mean random attractors for the equation by applying the theory of mean-square random dynamical systems; then, we prove the existence of (pathwise) pullback random attractors for the Wong-Zakai approximate system of the equation. In addition, we establish the upper semicontinuity of pullback random attractors for the Wong-Zakai approximate system of the equation under consideration driven by a linear multiplicative noise.

The Lagrangian formalism is developed for the population dynamics of interacting species that are described by several well-known models. The formalism is based on standard Lagrangians, which represent differences between the physical kinetic and potential energy-like terms. A method to derive these Lagrangians is presented and applied to selected theoretical models of the population dynamics. The role of the derived Lagrangians and the energy-like terms in the population dynamics is investigated, and it is shown that the obtained standard Lagrangians can be used to study oscillatory behavior of the models and the period of their oscillations, which may have ecological and environmental implications. These and other physical and biological insights gained from the derived standard Lagrangians are discussed.

In order to sustain the marine environment relationship between the environmental factors and marine biota must be investigated. This study aims to study such a correlation in the adjacent waters of Nan Wan Bay, Kenting, Taiwan, and to explore the covariance of environmental factors on marine life (whether they enhance or diminish it). To achieve these objectives, factor analysis was used to identify potential latent variables that could affect the water quality of the adjacent waters, including phytoplankton (quantity), zooplankton (quantity), and fish (quantity and species). These potential variables were named based on the results of past studies and related literature. Finally, a structural equation model (SEM) was constructed to establish a marine ecological model among the potential variables. The factor analysis results revealed that nutrients, upwelling, and primary productivity are the primary factors affecting the environmental changes in the adjacent waters of Nan Wan Bay. The comprehensive SEM showed that nutrients and primary productivity significantly impact plankton. Path analysis indicated that primary productivity has the highest direct effect on the phytoplankton cluster. However, the upwelling has a low significance in its effect on phytoplankton, zooplankton, and fish clusters. Compared to the results of past related studies, the SEM proposed in this study can reflect a considerable degree of change in the waters.

This paper applied the space-time generalized finite difference scheme for solving the nonlinear dispersive shallow water waves as the modified Camassa−Holm equation, modified Degasperis-Procesi equation, Fornberg-Whitham equation, and its modified form. The proposed meshless numerical scheme was composed of the space-time generalized finite difference method, the two-step Newton-Raphson method, and the time-marching method. The space-time approach can treat the temporal derivative as one of the spatial derivatives. This numerical technique enables all the partial derivatives in the governing equation can be discretized by a spatial discretization method, and the mixed derivative can efficiently deal with using the proposed meshless numerical scheme. The space-time generalized finite difference method is advanced from the Taylor series expansion and the moving-least square method. The numerical discretization process is only related to functional data and weighting coefficients on the central node and its nearby nodes. Thus, the matrix system composed of nonlinear algebraic equations will be a sparse matrix and can be efficiently solved by the two-step Newton-Raphson method. Furthermore, the time-marching method was utilized to proceed with the space-time domain along the time axis. In this paper, several numerical examples were tested to verify the capability of the proposed space-time generalized finite difference scheme.

The paper examines common elements between Lévai’s and Milson’s potentials obtained by Liouville transformations of two rational canonical Sturm-Liouville equations (RCSLEs) with even density functions which are exactly solvable via Jacobi polynomials in a real or accordingly imaginary argument. We refer to the polynomial numerators of the given rational density function as ‘tangent polynomial’ (TP) and thereby term the aforementioned potentials as ‘e-TP’ A special attention is given to the overlap between the two potentials along symmetric curves which represent two different forms of the Ginocchio potential exactly quantized via Gegenbauer and Masjed-Jamei polynomials respectively. Our analysis reveals that the actual interconnection between Lévai’s parameters for these two rational realizations of the Ginocchio potential is much more complicated than one could expect based on the striking resemblance between two quartic equations derived by Lévai for ‘averaged’ Jacobi indexes.

New analytical solutions of the heat conduction equation are presented in cylindrical and spherical coordinates. Then these solutions are reproduced with high accuracy by recent explicit and unconditionally stable finite difference methods. After this, real experimental data from the literature regarding a heated cylinder are reproduced by the explicit numerical methods as well as by Finite Element Methods (FEM) ANSYS workbench. Convection and nonlinear radiation are also considered on the boundary of the cylinder, and it is shown that the explicit methods are much more accurate than the commercial software.

This paper is concerned with variational methods for open quantum systems with Markovian dynamics governed by Hudson-Parthasarathy quantum stochastic differential equations. These QSDEs are driven by quantum Wiener processes of the external bosonic fields and are specified by the system Hamiltonian and system-field coupling operators. We consider the system response to perturbations in these operators and introduce a transverse Hamiltonian which encodes the propagation of the perturbations through the unitary system-field evolution. This approach provides an infinitesimal perturbation analysis tool which can be used for the development of optimality conditions in quantum control and filtering problems. Such settings employ, as performance criteria, quadratic (or more complicated) cost functionals of the system and field variables to be minimised over the energy and coupling parameters of system interconnections. We demonstrate an application of the transverse Hamiltonian variational approach to a mean square optimal coherent quantum filtering problem for a measurement-free field-mediated cascade connection of a quantum system with a quantum observer.

Polynomial recurrence bounds for a class of stochastic differential equations with a gradient type drift and an additive Wiener process are studied without Lyapunov functions.

In this paper, we introduce a way of representing a given mapping as the sum of odd and even mappings. Then, by using this representation, we investigate the stability of various forms for the general nonic functional equation.

This paper proposed a time two-mesh (TT-M) finite difference numerical scheme to improve the efficiency of solving the symmetric regularized long wave (SRLW) equation. The TT-M Crank-Nicolson discretization and finite difference method are employed in time and space approximation respectively. The scheme involves three main steps: firstly, the time interval is divided into coarse and fine time meshes, then the nonlinear system is solved on the coarse time mesh; secondly, coarse numerical solutions on the fine time mesh are computed using an interpolation formula based on the solutions derived in the step one; lastly, the TT-M finite difference numerical solutions can be obtained through constructing the linearized fine time mesh system using Taylor’s formula. Compared to the currently existing TT-M numerical methods, the novelty of this study is that the nonlinear term including derivatives is linearized by Taylor’s formula for a function with three variables, whose error analysis is more complex. Finally, some numerical examples, including computational time and accuracy, preservation of conservation laws, are given to verify the efficiency of the scheme. By comparing it with the standard nonlinear finite difference scheme, this method can reduce CPU time without sacrificing accuracy.

In this paper, we compile the fractional power series method and the Laplace transform to design a new algorithm for solving the fractional Volterra integro-differential equation. For that, we assume the Laplace power series (LPS) solution in terms of power q=1m,m∈Z+, where the fractional derivative of order α=qγ for which γ∈Z+. This assumption will help us to write the integral, the kernel, and the nonhomogeneous terms as a LPS with the same power. The recurrence relations for finding the series coefficients can be constructed using this form. To demonstrate the algorithm's accuracy, the residual error is defined and calculated for several values of the fractional derivative. Two strongly nonlinear examples are discussed to provide the efficiency of the algorithm. The algorithm gains powerful results for this kind of problem. Under Caputo meaning the obtained results are illustrated numerically, and graphically. Geometrically, the behavior of the solution declares that the changing of the fractional derivative parameter values' in their domain alters the style of the attained solution in a symmetrical meaning and fully coinciding to the ordinary derivative value'. From these simulations, the results report that the recommended novel algorithm is a straightforward, accurate, and superb tool to generate analytic-approximate solutions for Integral, and integro-differental equations of fractional order.

We firstly present two popular space discretization models of the Nonlinear Schrödinger Equation in dark solitons motion : the Direct-Discrete model and the Ablowitz-Ladik model. Applying the midpoint scheme to the space discretization models, we get two time-space discretization models: the Crank-Nicolson method and the New-Difference method. Secondly, we demonstrate that the solutions of the two space discretization models converge to the solution of the Nonlinear Schrödinger Equation. Also, we prove that the convergence order of the two time-space discretization models are O(h2+τ2) in discrete L2-norm error estimates. Finally, the numerical experiments agree well with the proven theoretical results.

The Macroscopic Mechanical Equilibrium Condition can be shown to be the physical origin of the Equation of State of any material system, then can describe all thermodynamic quasi-equilibrium processes caused by the change of the external temperature and/or mechanical environment. If it cannot be satisfied, the system would be broken.

Through this study, we established equations for estimating the standing tree carbon stock, based on 24 tree species in multiple size classes in a case study at the Ngao Demonstration Forest (NDF) in northern Thailand. Four hundred thirty-nine wood samples from trees in mixed deciduous forest (MDF), dry dipterocarp forest (DDF), and dry evergreen forest (DEF), were collected using non-destructive methods to estimate above-ground carbon equations through statistical regression. The equations were established based on four criteria: 1) the coefficient of determination (R2), 2) Standard error of estimate (SE), 3) F-value, and 4) Significant value (p-value, α ≤ 0.05). The above-ground carbon stock (C) equations for standing trees in the MDF was C = 0.0199DBH2.1887H0.5825, for DDF was C = 0.0145DBH2.1435 H0.748, for DEF was C = 0.0167DBH2.1423H0.7070, and the general equation for all species/wood density groups was C = 0.017543DBH2.1625H0.6614, where DBH is tree diameter at breast height and H is tree total height. The above-ground carbon stock in the DDF, MDF, and DEF was 142, 53.02, and, 12 tons/ha, respectively, and the estimated above-ground carbon stock in the Mae Huad sector at the NDF was 61 tons/ha.

In this paper, we exhibit new dynamical properties of the two-mode Caudrey-Dodd-Gibbon (TMCDG) equation. This model describes the motion of dual-waves in dispersive and nonlinear media, which mainly depends on the nonlinearity and dispersion parameters. The overlapping of such two-mode waves is affected by the phase-velocity parameter. The study takes a full advantages of the Kudryashov method and of the exponential-expansion method. For the first time, dual-wave solutions are obtained for arbitrary values of the nonlinearity and dispersive factors. The graphs of the novel solutions are also provided in order to depict the waves propagation, as well as to show the influence of the parameters.

We analyze different approaches to quantum gravity. It is stressed that nonperturbative methods to quantise gravity and the usage of diffeomorphism-invariant variables are very important. We pay attention on the Wheeler--DeWitt equation in the framework of canonical quantum gravity. The Wheeler--DeWitt equation is presented in the first order formalism with the hope that this form can solve some problems such as singularities and the ordering. Also, there is a problem of defining the time.

In this paper, we consider the fourth-order parabolic equations with integer and fractional order time derivatives with Neumann boundary conditions. The integer order time derivatives are approximated by backward Euler difference quotients, and the fractional order time derivatives are approximated by L1 interpolation. We propose the block-centered finite difference scheme for fourth-order parabolic equations of integer and fractional order time derivatives. We prove the stability of the block-centered finite difference scheme and the second-order convergence of the discrete L2 norms of the approximate solution and its derivatives of every order. Numerical examples are given to verify the effectiveness of the block-centered finite difference scheme.

The following system of equations {x_1 \cdot x_1=x_2, x_2 \cdot x_2=x_3, 2^{2^{x_1}}=x_3, x_4 \cdot x_5=x_2, x_6 \cdot x_7=x_2} has exactly one solution in ({\mathbb N}\{0,1})^7, namely (2,4,16,2,2,2,2). Hypothesis 1 states that if a system of equations S \subseteq {x_i \cdot x_j=x_k: i,j,k \in {1,...,7}} \cup {2^{2^{x_j}}=x_k: j,k \in {1,...,7}} has at most five equations and at most finitely many solutions in ({\mathbb N}\{0,1})^7, then each such solution (x_1,...,x_7) satisfies x_1,...,x_7 \leq 16. Hypothesis 1 implies that there are infinitely many composite numbers of the form 2^{2^{n}}+1. Hypotheses 2 and 3 are of similar kind. Hypothesis 2 implies that if the equation x!+1=y^2 has at most finitely many solutions in positive integers x and y, then each such solution (x,y) belongs to the set {(4,5),(5,11),(7,71)}. Hypothesis 3 implies that if the equation x(x+1)=y! has at most finitely many solutions in positive integers x and y, then each such solution (x,y) belongs to the set {(1,2),(2,3)}. We describe semi-algorithms sem_j (j=1,2,3) that never terminate. For every j \in {1,2,3}, if Hypothesis j is true, then sem_j endlessly prints consecutive positive integers starting from 1. For every j \in {1,2,3}, if Hypothesis j is false, then sem_j prints a finite number (including zero) of consecutive positive integers starting from 1.

We think of time as one of four dimensions appearing in the equations of motion of Newtonian and quantum physics, but participating independently of space. In these pages we explore the way the time variable affects how space is perceived. We show first that non-commutation may be interpreted as the difference between electron and photon cycling during radiation processes. For every electron cycle of a quantum oscillator there are two photon cycles. Secondly, the difference between relativistic and non-relativistic quantum mechanics is shown to be related to time evolution. Only relativistic models evolve continuously. The reasoning of Einstein is implicit to an understanding of both physical models. Previously obtained derivations of relativistic quantum mechanics are reaffirmed by following the ideas of Dirac.

The propagation of electromagnetic waves beyond the line of sight can be caused by atmospheric ducts, which are a significant concerns in the fields of radar and communication. This paper utilizes data from seven automatic stations and five radio-sounding stations to statistically analyze the characteristics of the atmospheric ducts in the northwest region of the South China Sea (SCS). After verifying the practicality of numerical analysis data from NCEP CFSv2 and ERA5 in studying atmospheric ducts using measured data, we analyzed the space-time distribution characteristics of the height of the regional evaporation duct and the bottom height of the elevated duct. Using the parabolic equation model, we simulated electromagnetic propagation loss under different frequencies and radiation elevation angles in both uniform and non-uniform duct environments within a typical atmospheric duct structure. The study found that the NCEP CFSv2 data accurately captures the evaporation duct height and duct occurrence rate in the study area, and the elevated duct bottom height obtained from the inversion of ERA5 and the measured data has a good consistency. The occurrence rate and height of evaporation duct in coastal stations in the northwest of the SCS vary significantly by month, demonstrating clear monthly distribution patterns. Conversely, changes in the Xisha station are minimal, indicating good temporal uniformity. For lower atmospheric ducts, the difference in occurrence rates between 00:00 and 12:00 (UTC) is negligible. The occurrence probability of elevated ducts in the Beibu Gulf area is relatively high, mainly concentrated from January to April, and the Xisha area is dominated by surface ducts without foundation layer, mainly concentrated from June to August. The monsoon plays a critical role in the generation and evolution of atmospheric ducts in the northwest of the SCS, with the height of the evaporation duct increasing and the bottom height of the elevated duct decreasing after the onset of the summer monsoon. Electromagnetic propagation simulations demonstrate that higher frequency and lower elevation angles of radiation sources in the trapping layer of the evaporation duct make it easier to be trapped. As the evaporation duct height decreases, the amplitude of the "sinusoidal fluctuation" of the propagation loss also decreases. Frequency changes of the radiation source in the surface duct environment have minimal impact on electromagnetic propagation loss, but the elevation angle of the radiation source is a critical factor. The frequency of the "sinusoidal fluctuation" in propagation loss is higher in a hybrid duct environment compared to a uniform surface duct. Additionally, the propagation loss increases faster with distance at the height of the evaporation duct, resulting in greater electromagnetic propagation loss.

This study presents the solution of the second type of a two-dimensional nonlinear integral equation in Banach space. Also, the existence and uniqueness of this equation’s solution are discussed. We utilize a numerical approach involving hybrid and block-pulse functions to obtain the approximate solution of a two-dimensional nonlinear integral equation. Nonlinear integral equation in two dimensions is reduced numerically to a system of nonlinear algebraic equations that can be solved using numerical methods. This study focuses on showing the convergence analysis for the numerical approach and obtaining an error estimate. Some numerical examples have been provided to demonstrate the approach’s viability and efficacy

We consider the propagation of electromagnetic waves in the Friedman – Lemaître – Robertson – Walker metric. The exact solutions for plane and spherical wave are written down. The corresponding redshift, amplitude change, and dispersion are discussed. We also speculate about the connection of the electromagnetic wave equation to the Klein–Gordon equation.

This article derives the closed form solution to finding the roots of a quadratic equation in SU3.

In this contribution to the Festschrift for Prof. Remo Ruffini, we investigated a formulation of quantum gravity based on the Wheeler-DeWitt (WDW) equation combined with the classical concepts of the branch-cut cosmology, which contemplates as a new scenario for the origin of the Universe, a smooth transition region between the contraction phase, prior to the primordial singularity, and the subsequent expansion phase. Through the introduction of an energy-dependent effective potential, which describes the space-time curvature associated with the embedding geometry and its coupling with the cosmological constant and matter fields, solutions of the WDW equation for the wave function of the Universe are obtained. The Lagrangian density is quantized through the standard procedure of raising the Hamiltonian, the helix-like complex scale factor of branched cosmology as well as the corresponding conjugate momentum to the category of quantum operators. As a novelty, ambiguities in the ordering of the quantum operators are overcome with the introduction of a set of ordering factors α, whose values are restricted to the integers α=[0,1,2], since non-integers have no physical meaning, allowing this way a broader class of solutions for the wave function of the Universe. As another novelty, additional energy-dependent parametrizations are considered, more specifically, in addition to a branched universe filled with underlying background vacuum energy, matter and radiation, in order to make contact with standard model calculations, we additionally supplement the formulation with baryon matter, dark matter and quintessence contributions. As an additional novelty, the boundary conditions for the wave function of the Universe are imposed by assuming the Bekenstein criterion. Our results indicate this way, as a novelty conclusion, the consistency of a topological quantum leap, or alternatively a quantum tunneling, for the transition region of the early universe in contrast to the classic branched cosmology view of a smooth transition.

Background The purpose of this study was to clarify the relationship structure of quality of life (QOL) in survivors of breast cancer, including difficulty in daily life and negative experience as health-related indicators. Methods Participants were survivors of breast cancer for more than 2 years after primary breast cancer surgery and belonged to self-help groups. The assessment used FACT-B (QOL), HADS (anxiety and depression), SOC (sense of coherence), WHODAS 2.0 (difficulties in daily life), and CAOD (negative experiences). Bayesian structural equation modeling (BSEM) was performed to analyze the hypothesized model. If the causal model was significant, multiplication of the path coefficient from anxiety and depression to QOL, and from SOC to anxiety and depression, was considered a direct effect on QOL, and from SOC to difficulty in daily life, from difficulty in daily life to negative experiences, and from negative experiences to anxiety and depression were considered indirect effects on QOL. Results Goodness of fit of the model in the BSEM was satisfactory. The direct effect was 0.274, and indirect effect was 0.163. Conclusions These direct and indirect approaches to difficulties in daily life are very significant because they can provide a basis for development of support strategies to increase QOL.

The paper's main goal is to introduce a novel type of interpolative convex contraction and build up some fresh findings for it using the interpolative convex contractions' progressive approach. We have established certain conclusions using orbitally S-complete and Suzuki type contractions in F-metric spaces. My research aims to examine the fixed point method's efficacy in solving fractional differential equation with boundary conditions.

The study aims to investigate Gen Z's intentions to utilize the Waze mobile application as a solution for sustainable traffic management in Meto Manila. The extended Technology Acceptance Model (TAM) was used to define user behavior and technology usage to determine the factors influencing Filipino drivers' application acceptance of Waze. The study’s data results have revealed that the System Quality, Perceived Location Accuracy, Perceived Usefulness, and Perceived Ease of Use affect Filipinos' intentions to use traffic navigation applications, particularly Waze. The study utilized a survey and was given to 300 Filipino drivers traveling within the National Capital Region to accurately measure the factors and their connections to usage intention and actual use. The analytical approach used for this investigation was partial least squares structural equation modeling (PLS-SEM). The study's results can be applied as a theoretical framework for future researchers of Waze mobile applications, Waze route accuracy, and Waze overall application performance, as well as the features of the Waze application, to evaluate how the use of the Waze mobile application could help in the effective management of traffic situations in Metro Manila. The study was able to assess the effectiveness of the Waze navigation app as a platform for efficiently managing traffic situations in Metro Manila. Moreover, this study also highlighted the application performance of Waze and its acceptance by Filipino drivers in Metro Manila. Furthermore, the study implores a critical review of Waze's application performance. The study recommends that similar future studies must consider samples from a more diverse geographic background to obtain a more accurate representation of Filipinos traveling. Future researchers are also advised to adopt a qualitative research design to gain more detailed insights of Filipinos regarding their experience with the Waze application.

On the basis of the force and safety factor analysis of traditional retaining wall, a new analytical method of force and displacement of slope is suggested, the numerical theoretical solution of the stress distribution of the sliding body can be obtained under the conditions, which the stresses distribution are satisfied with the differential equilibrium equations, the boundary conditions, the compatibility equation and the macroscopic equilibrium equations. The interface stresses between the sliding body and the retaining wall are continuous, the theoretical solution of retaining wall stress distributions can be gotten, while the stress differential equilibrium equation, the compatibility equation, macroscopic force and moment balance equations are satisfied. The strain and displacement solutions can be obtained by using Duncan Chang and Hooke constitutive equations for the slope and the retaining wall respectively. The transfer station of landfill in the Guandukou Town of Badong County is taken as an example, the results of the sliding body and retaining wall analysis show: The stress and strain solutions of a slope and a retaining wall can be obtained by the proposed method, the forces between the retaining wall and the sliding body include shear stress and normal stress, and the stress distributions change with the deformation of the sliding body, the shape and material of retaining wall can be optimized according to the calculation results，it is feasible for the proposed analysis method of slope with retaining wall design to be run many years.

In this work, we propose a transition wave equation from quantum to classical regime in the framework of the von Neumann formalism for ensembles and then obtain an equivalent scaled equation. This leads us to develop a scaled statistical theory following the well-known Wigner-Moyal approach of quantum mechanics. This scaled nonequilibrium statistical mechanics has in it all the ingredients of the classical and quantum theory described in terms of a continuous parameter displaying all the dynamical regimes in-between the two extreme cases. Finally, a simple application of our scaled formalism consisting of reflection from a mirror by computing various quantities including probability density plots, scaled trajectories and arrival times are analyzed.

Background: The infant mortality rate (IMR) is an important reflection of the well-being of infants and the overall health of the population. This study aims to examine the macroeconomic (ME), sociodemographic (SD), and health status and resources (HSR) effects on IMR, as well as how they may interact with each other. Methods: A retrospective time-series study using yearly data for Oman from 1980 to 2022. Partial Least Squares-Structural Equation Modelling (PLS-SEM) was utilized to develop the exploratory model of the determinants of IMR. Results: The model indicates that HSR determinants directly but negatively affect IMR (= -0.617, p&lt;0.001). SD directly and positively affects IMR (= 0.447, p&lt;0.001). ME only indirectly affects IMR (=-0.854, p&lt;0.001). ME determinants also exert some direct influences on both HSR (= 0.722, p&lt;0.001) and SD (= -0.916, p&lt;0.001) determinants. Conclusions: These findings indicate that an integrated policy that addresses socioeconomic and health-related factors and the overall ME environment is necessary for the health and well-being of the children and the population overall in Oman.

The satisfaction of basic psychological needs leads students to engage in a sport modality on their own initiative. In the Spanish public educational system, mixed and heterogeneous, the gender and sport experience of students influence the teaching and motivation of invasion sports. This study investigated whether students' gender and sport experience, and method influence the psychological variables (basic psychological needs and sport adherence) when teaching school soccer and basketball. Furthermore, correlations were calculated between these psychological variables. The study involved 165 fifth and sixth grade students (age, 11.27 ± 0.68 years old) from several Spanish state schools in the same autonomous community. A non-random convenience sample was used. The needs for autonomy, perceived competence and social relationships were measured using the Basic Psychological Needs in Physical Exercise Scale. Sport adherence was measured using the Measure of Intentionality to be Physically Active. A Confirmatory Factor Analysis and Cronbach's alpha were used to analyze the psychometric properties of the scales. Descriptive and inferential analyses were performed with the Mann-Whitney U and Kruskal-Wallis H tests. There were significant differences in the needs for autonomy and perceived competence according to the students’ gender (boys &gt; girls). Attending to sport adherence, there were also significant differences according to the students’ gender (boys &gt; girls) and sport experience (experienced students &gt; inexperienced students). Likewise, a regression analysis (structural equation model) revealed that the autonomy need showed low association with sport adherence. Higher perceived competence (β = 0.52) and social relationships (β = 0.36) were associated with greater adherence to sport (R2 = 0.65). Increased sport adherence will have health benefits.

Pakistan relies mostly on fossil fuel for fulfilling its energy demand which is expensive as 11 well as not friendly for the environment. The need of the hour is to shift from fossil fuels to renew-12 able energy resources like geothermal, wind, solar etc. to cater for global warming issues. Pakistan 13 has a lot of potential geothermal sites because of several fault lines and hot springs. A sound 14 knowledge of ground temperature is essential to use geothermal energy, which is obtained by drill-15 ing boreholes and putting sensors making it an expensive procedure. Thus, to avoid huge cost for 16 drilling bore holes, particularly for ground temperature analysis, a numerical approach has been 17 considered for determining ground temperature. Furthermore, correlation charts between air and 18 ground temperatures have been developed as there were no proper studies on the ground temper-19 ature of Pakistan. Then, with the help of a boreholes drilled in National University of Sciences and 20 Technology Islamabad Pakistan, the actual ground and numerically calculated temperatures have 21 been compared which shows an error margin in the range between 0.27% for higher depths to 7.3% 22 near surface. Thus, it is shown that the proposed method is easy to implement and better than large 23 scale testing methods for the depths at which geothermal energy is extracted.

Artificial intelligence (AI) applications in different fields are developing rapidly, among which AI painting technology, as an emerging technology, has received wide attention from users for its creativity and efficiency. This study aimed to investigate the factors that influence user acceptance of the use of AIBPS by proposing an extended model that combines the Extended Technology Acceptance Model (ETAM) with the AI-based Painting System (AIBPS).A questionnaire was administered to 528 Chinese participants, using validated factor analysis data and Structural Equation Modeling (SEM) was used to test the hypotheses. The findings showed that hedonic motivation (HM) and perceived trust (PE) had a positive effect (+) on users' perceived usefulness (PU) and perceived ease of use (PEOU), while previous experience (PE) and technical features (TF) had no effect (-) on users' perceived usefulness (PU). This study provides an important contribution to the literature on AIBPS and the evaluation of systems of the same type, which helps to promote the sustainable development of AI in different domains and provides a possible space for further extension of TAM, thus helping to improve the user experience of AIBPS. The results of the study provide insights for system developers and enterprises to better motivate users to use AIBPS.

Two-dimensional (2D) of transition metal dichalcogenides (TMDCs) are potential candidates for thermoelectric (TE) applications due to their unique structural properties. In this paper, we constructed an 2D monolayer TMDCs semiconductor γ-PbSn2(X=S, Se, Te) and first-principles calculations and Boltzmann transport theory are used to study the thermoelectric performance. We found that γ-PbSnX2 had an ultra-high carrier mobility up to 4.04×103 cm2V−1s−1 leading to a metal-like electrical conductivity. Meanwhile, γ-PbSnX2 both have high Seebeck coefficients, resulting in high power-factors, and also shows intrinsic low lattice thermal conductivity of 6-8 W/mK at room temperature. The lower lattice thermal conductivity and high power-factors resulted in excellent thermoelectric performance. The high ZT values of γ-PbSnS2 and γ-PbSnSe2 were as high as 2.65 and 2.96 at 900 K, respectively. The result suggests that the monolayer γ-PbSnX2 are better candidates for excellent thermoelectric performance.

Exact sequential state estimation of orbiting objects in space can be found by predicting the state using Fokker Planck Kolmogorov Equation (FPKE) and measurement correction using Bayes’ conditional/posterior Probability Density Function (PDF). Posterior PDF can be expressed as Gaussian density expanded in terms of Hermite polynomials named as Gram Charlier Series (GCS). This research is an extension of an earlier work on second order linearized solution to nonlinear Bayesian filtering using Taylor series and third order GCS expansion of posterior PDF. In this new extension, Bayes’ posterior PDF is approximated by a mixture of GCS functions for which the parameters are propagated using linear propagation theory. The update of weights of different components of GCS mixture model uses the FPKE error as feedback to adapt for the amplitude of different GCS components while solving a quadratic programming problem earlier used for Gaussian Mixture Model (GMM) PDF. Proposed filtering method is applied on tracking of space debris. The simulation results for the filter shows performance is moderately better than single GCS filter, Extended Kalman Filter (EKF) and Gaussian Sum Filter (GSF) under space debris’ highly uncertain initial conditions and sparse measurement availability.

Many problems in the fields of finance and actuarial science can be transformed into the problem of solving backward stochastic differential equations (BSDE) and partial differential equations (PDE) with jumps, which are often difficult to solve in high-dimensional cases. To solve this problem, this paper applies the deep learning algorithm to solve a class of high-dimensional nonlinear partial differential equations with jump terms and their corresponding backward stochastic differential equations (BSDE) with jump terms. Using the nonlinear Feynman-Kac formula, the problem of solving this kind of PDE is transformed into the problem of solving the corresponding backward stochastic differential equations with jump terms, and the numerical solution problem is turned into a stochastic control problem. At the same time, the gradient and jump process of the unknown solution are separately regarded as the strategy function and they are approximated respectively by using two multilayer neural networks as function approximators. Thus, deep learning-based method is used to overcome the “curse of dimensionality” caused by high-dimensional PDE with jump, and the numerical solution is obtained. In addition, this paper proposes a new optimization algorithm based on the existing neural network random optimization algorithm, and compares the results with the traditional optimization algorithm, and achieves good results. Finally, the proposed method is applied to three practical high-dimensional problems: Hamilton-Jacobi-Bellman equation, bond pricing under the jump Vasicek model and high-dimensional option pricing model with default risk. The proposed numerical method has obtained satisfactory accuracy and efficiency. The method has important application value and practical significance in investment decision-making, option pricing, insurance and other fields.