The unsafe behavior of frontline workers at construction sites is the most important cause of construction accidents. This study proposed a comprehensive model of frontline workers' unsafe behaviors based on a systems perspective and used structural equation modeling (SEM) to explore the influence mechanisms between Objective Conditions (e.g., work environment, work climate, task complexity), Safety Management (e.g., safety education and training, safety reward and punishment regulations, safety inspection, safety technology disclosure, safety warning signs), Group Influence (propagation of unsafe behaviors among workers), Personal Perception (subjective judgment of operators on their safety knowledge and skills), and Unsafe Behaviors. Data from 460 frontline workers were collected through questionnaires and the correlation hypotheses were tested using SPSS 26.0 and Amos 26.0 software. The following conclusions were obtained: (1) Objective Conditions directly positively influence Safety Management, Group Influence, and Personal Perception, but indirectly negatively influence Unsafe Behavior; (2) Safety Management not only directly positively affects Personal Perception but also directly negatively affects Unsafe Behavior. However, the direct effect of Safety Management on Group Influence is not significant; (3) Group Influence has a direct positive effect on Unsafe Behavior, but the direct effect on Personal Perception is not significant; (4) The direct effect of Personal Perception on Unsafe Behavior is insignificant. These findings can be used as preliminary data to guide decision-makers or managers in construction companies to develop reasonable management plans to curb unsafe behaviors of frontline workers.

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.

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 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.

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.

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.

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.

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.

The present paper investigates the 'soft' determinants of social environmental sustainability of the country. A three-dimensional research approach, covering the education system and educational culture; socio-economic integration; and the legal system and the importance of public administration and citizenship, was utilized. A cross-sectional survey of 1,021 respondents and a structural equation modelling were selected as main research tools. Lithuania served as an empirical basis for the research. It was revealed that the most important factors in shaping the modernisation of the country through the lens of social environmental sustainability are the participation of citizens in social communities and social activities. Factors that need improvement are public participation and tolerance for the disabled.

We present a new family of Bessel solutions of the paraxial equation. Such solutions keep their form during propagation due to a quadratic phase factor that makes them scaled propagation invariant fields. The Bessel beams we introduce have the particularity that the topological phase is twice the order of the Bessel function and the argument varies quadratically with the radius

The application of evolutionary optimization algorithms in problem solving is currently gaining wide popularity. Use of Differential Evolution (DE) algorithm in obtaining analytically approximate solution of unstable second order initial value Ordinary Differential Equation (ODE) is presented in this work. The methodology involves solving an associated problem of optimization with con-strains to get an analytically approximate solution for the ODE under consider-ation. Three test cases were used to demonstrate the efficiency of our method. In comparison with other methods discussed in the literature, our method gave significant improvement on the accuracy of the obtained results.

Although there is a common physiological notion that the origin of the membrane potential is attributed to transmembrane ion transport, it is theoretically possible to explain its generation by the mechanism of ion adsorption. It was previously suggested that the ion adsorption mechanism led even to the potential formulas which are even identical to either the famous Nernst equation or Goldman-Hodgkin-Katz equation. Our further analysis shown in this paper indicates that the potential formula based on the ion adsorption mechanism leads to one equation which is the function of material surface charge density and the material surface potential. Furthermore, we confirmed that the equation holds in all the different experimental systems we studied. Although we have not succeeded in elucidating why such an equation is established, the equation appears to be the key equation governing the characteristics of the membrane potential regardless of the systems in question.

The description of stellar interiors remains as a big challenge for the nuclear astrophysics community. The consolidated knowledge is restricted to density regions around the saturation of hadronic matter $\rho _{0} = 2.8\times 10^{14} {\rm\ g\ cm^{-3}}$, regimes where our nuclear models are successfully applied. As one moves towards higher densities and extreme conditions up to five to twenty times $\rho_{0}$, little can be said about the microphysics of such obejects. Here, we employ an MCMC strategy in order to access the variability of polytropic three-pircewised models for neutron star equation of states. With a fixed description of the hadronic matter we explore a variety of models for the high density regimes leading to stellar masses up to 2.5 $M_{\odot}$. In addition, we also discuss the use of a Bayesian power regression model with heteroscedastic error. The set of EoS from LIGO was used as inputs and treated as data set for testing case.

We enhance Frobenius' method for solving linear ordinary differential equations about regular singular points. Key to Frobenius' approach is the exploration of the derivative with respect to a single parameter; this parameter is introduced through the powers of generalized power series. Extending this approach, we discover that tandem recurrence relations can be derived. These relations render coefficients for series occurring in logarithmic solutions. The method applies to the, practically important, exceptional cases in which the roots of the indicial equation are equal, or differ by a non-zero integer. We demonstrate the method on Bessel's equation and derive previously unknown tandem recurrence relations for coefficients of solutions of the second kind, for Bessel equations of all integer and half-integer order.

Poor households are more likely less resilient under climate change, risks of productive assets, social-related shocks, and decline of land productivity. The ability to deal with household resilience against poverty under the uncertain condition of risk is limited in the highlands of Ethiopia. The study aims to identify determinants of household resilience to livelihood insecurity under the crop-livestock mixed farming systems in Goncha district, Northwest highlands of Ethiopia. Primary data were collected by conducting face-to-face interviews among 280 households using structured questionnaire. Descriptive statistics, Kruskal-Wallis test and structural equation modeling were used to analyse the data. The results disclosed that sustainable management of the farming systems, cultivation of more fertile farmland, saving performance, diversification of income-earning activities, intensification of livestock husbandry practices, access to irrigation, and familiarity with practical technologies were found to be significant determinants at p<0.001 to household resilience of smallholder farmers. Social network development and tree plantation were explained household resilience to livelihood insecurity at P<0.01 and P<0.1 significant levels, respectively. The study concluded that scaling up sustainable management of the farming system and practical technologies, enhancing saving behavior, promoting income diversification, and intensifying agroforestry are significant for household resilience to livelihood insecurity of smallholders across agro-ecologies.

In light of Liu \emph{at el.}'s original works, this paper revisits the solution of Burgers's nonlinear equation $u_t=a(u_x)^2+bu_{xx} $. The study found two exact and explicit solutions for groups $G_4$ and $G_6$, as well as a general solution. A numerical simulation is carried out. In the appendix a Maple code is provided

We present a plausible solution to the now forty seven year old paleoclimatology riddle of the so-called Faint Young Sun Paradox via the combined hypothesis of the conservation of the state of radiation balance between the Earth and Sun and that of an expanding Earth, where, in the face of a changing (increasing) Solar luminosity, the Earth would maintain steady temperatures by re-adjusting the height of its atmosphere. That is to say, depending on whether or not the radius of the solid Earth is changing, this re-adjustment of the height of the Earth’s atmosphere would mean two things — i.e.: (1) either the height increases — in which event the Earth accretes matter from its immediate surroundings (i.e., the obvious pool formed by the Solar wind) thereby increasing the mass of the Earth’s atmosphere, or: (2) the height decreases — in which event the Earth naturally expels matter from its atmosphere, thereby decreasing the effective mass of the Earth. We demonstrate that if –- as the current state of the art ITRF observations seem to indicate, namely that — the Earth’s landmass is steadily expanding globally at a paltry rate of ∼+0.45±0.05mm·yr−1, and, that the Earth’s atmosphere is to have a present radial vertical height of about one third of the Earth’s radius (∼2860km) from the Earth’s surface, then, one can (might) with relative ease, explain not only the presence of liquid water on the Earth’s surface some ∼3.20±0.70Gyr ago during the Archaean eon when the Sun was about 75% of its current luminosity, but also the present radial expansion rate of the Earth. When all is said and done, the Earth system is herein cast as an auto-self-regulating incubator where the auto-self-regulating mechanism is as a result of the Earth’s atmosphere responding by automatically re-adjusting its height.

The information entropy for Smoluchowski coagulation equation is proposed based on statistical mechanics. And the normalized particle size distribution is a lognormal function at equilibrium from the principle of maximum entropy and moment constraint. The geometric mean volume and standard deviation in the distribution function are determined as simple constant. The results reveal that the assumption that algebraic mean volume be unit in self-preserving hypothesis is reasonable in some sense. Based on the present definition of information entropy, the Cercignani’s conjecture holds naturally for Smoluchowski coagulation equation. Together with the proof that the conjecture is also true for Boltzmann equation, Cercignani’s conjecture will holds for any two-body collision systems, which will benefit the understanding of Brownian motion and molecule kinematic theory, such as the stability of the dissipative system, and the mathematical theory of convergence to thermodynamic equilibrium.

The non-inertial effects on spin-0 scalar particle that interacts with scalar potentials of Cornell-type in cylindrical system and Coulomb-type in the magnetic cosmic string space-time using Kaluza-Klein theory is analyzed. We show that the energy eigenvalue and eigenfunction depend on the global parameters characterizing the space-time, and the gravitational analogue of the Aharonov-Bohm effect for bound states is observed.

We present a class of efficient parametric closure models for 1D stochastic Burgers equations. Casting it as statistical learning of the flow map, we derive the parametric form by representing the unresolved high wavenumber Fourier modes as functionals of the resolved variables’ trajectory. The reduced models are nonlinear autoregression (NAR) time series models, with coefficients estimated from data by least squares. The NAR models can accurately reproduce the energy spectrum, the invariant densities, and the autocorrelations. Taking advantage of the simplicity of the NAR models, we investigate maximal and optimal space-time reduction. Reduction in space dimension is unlimited, and NAR models with two Fourier modes can perform well. The NAR model’s stability limits time reduction, with a maximal time step smaller than that of the K-mode Galerkin system. We report a potential criterion for optimal space-time reduction: the NAR models achieve minimal relative error in the energy spectrum at the time step where the K-mode Galerkin system’s mean CFL number agrees with the full model’s.

In this work, meshless methods are applied for the solution of two-dimensional steady-state heat conduction problems with nonlocal multi-point boundary conditions (NMBC). These meshless procedures are based on multiquadric radial basis function (MQ RBF) and its modified version (i.e. integrated MQ RBF). The proposed meshless methods which were recently published in \cite{Reutskiy2016} is compared with standard collocation method (i.e. Kansa's method). Three different sorts of solution domain are considered in which Dirichlet boundary condition is specified on some part of the boundary and is related to the unknown function values at a discrete set of interior points. The influence of NMBC on the accuracy and condition number of the system matrix associated to the proposed methods is investigated. The sensitivity of the shape parameter is also analyzed in the proposed methods. Performance of the proposed approaches in terms of accuracy and efficiency is confirmed on the benchmark problems.

4-component relativistic atomic and molecular calculations are typically performed within the no-pair approximation where negative-energy solutions are discarded, hence the symmetry between electronic and positronic solutions is not considered. These states are however needed in QED calculations, where furthermore charge conjugation symmetry becomes an issue. In this work we shall discuss the realization of charge conjugation symmetry of the Dirac equation in a central field within the finite basis approximation. Three schemes for basis set construction are considered: restricted, inverse and dual kinetic balance. We find that charge conjugation symmetry can be realized within the restricted and inverse kinetic balance prescriptions, but only with a special form of basis functions that does not obey the right boundary conditions of the radial wavefunctions. The dual kinetic balance prescription is on the other hand compatible with charge conjugation symmetry without restricting the form of the radial basis functions. However, since charge conjugation relates solutions of opposite value of the quantum number κ, this requires the use of basis sets chosen according to total angular momentum j rather than orbital angular momentum ` . As a special case, we consider the free-particle Dirac equation, where the solutions of opposite sign of energy are related by charge conjugation symmetry. We note that there is additional symmetry in those solutions of the same value of κ come in pairs of opposite energy.

One of the typical forms of linear matrix expressions (linear matrix-valued functions) is given by $A + B_1X_1C_1 + \cdots + B_kX_kC_k$, where $X_1, \ldots, X_k$ are independent variable matrices of appropriate sizes, which include almost all matrices with unknown entries as its special cases. The domain of the matrix expression is defined to be all possible values of the matrix expressions with respect to $X_1, \ldots, X_k$. I this article, we approach some problems on the relationships between the domains of two linear matrix expressions by means of the block matrix method (BMM), the matrix rank method (MRM), and the matrix equation method (MEM). As application, we discuss some topics on the relationships among general solutions of some linear matrix equations and their reduced equations.

A second order rational difference equation $$x_{n+1}=px_{n}+\frac{q}{x_{n-1}^2}$$ with the parameters $p$ and $q$ which lies in $(0,1)$, is studied. The dynamics of the equilibrium is characterized through the trichotomy of the parameter $p<\frac{1}{2}$, $p=\frac{1}{2}$ and $p>\frac{1}{2}$. It is found that there is no periodic solution of period $2$ and $3$ but there exists periodic solutions with only periodic solution $5$ and $10$ are achieved computationally.

It is well known that the Continuous Galerkin Finite Element (CGFE) method is globally consistent with respect to the first law of thermodynamics. This means that, for any mesh, all obtained discrete solutions will conserve total energy. One might expect, that the method is, also, globally consistent with respect to the second law of thermodynamics. In this paper, we formally study if such conjecture is true. The heat conduction equation is used as the physical model for this analysis. In the present study it is proved that the conjecture is false: at least, for standard piecewise linear (1D and 2D) elements, the CGFE method is not always globally consistent with respect to the second law of thermodynamics. In other words, some obtained discrete solutions can violate the global postulate of the second law, which asserts that total entropy can never decrease.

In the paper, a fully discrete compact difference scheme with $O(\tau^{2}+h^{4})$ precision is established by considering the numerical approximation of the one-dimensional Allen-Cahn equation. The numerical solutions satisfy discrete maximum principle under reasonable step ratio and time step constraint is proved. And the energy stability for the fully discrete scheme is investigated. An example is finally presented to show the effectiveness of scheme.

We explore the use of inverse multiquadratic (IMQ) functions as basis functions when solving the vibrational Schrödinger equation with the rectangular collocation method. The quality of the vibrational spectrum of formaldehyde (in six dimensions) is compared to that obtained using Gaussian basis functions when using different numbers of width-optimized IMQ functions. The effects of the ratio of the number of collocation points to the number of basis functions and of the choice of the IMQ exponent are studied. We show that the IMQ basis can be used with parameters where the IMQ function is not integrable. We find that the quality of the spectrum with IMQ basis functions is somewhat lower that that with a Gaussian basis when the basis size is large and for a range of IMQ exponents. The IMQ functions are, however, advantageous when a small number of functions is used or with a small number of collocation points e.g. when using square collocation.

The generalized Kuramoto–Sivashinsky equation is investigated using the modified Kudrayshov method for the exact analytical solution. The modified Kudrayshov method converts the nonlinear partial differential equation to algebraic equations, as a result of various steps, which on solving the so obtained equation systems yields the analytical solution. By this way various exact solutions including complex structures are found and drawn their behaviour in complex plane by Maple to compare the uniqueness of solutions.

In order to understand the hot deformation behavior of novel Cu/Al laminated composites, isothermal hot compression tests were conducted by Gleeble-1500D thermo-mechanical simulator. And the effect of bonding interface, deformation temperature and strain rate on the deformation behavior was analyzed. Results show that under the interface constraint effect, soft Al layer trends to flow synchronously with hard Cu layer. And further microstructure examinations indicate the cooperative deformation capability of Cu/Al composites increases with increasing stain rate and decreasing deformation temperature. Strain hardening exponent, calculated based on the true stress-true strain data, also proves the effect of deformation temperature and strain rate on the cooperative deformation behavior. Meanwhile, unique composites structure allows the Al matrix to exhibit the characteristic of dynamic recrystallization during the hot deformation process. Lastly, strain compensated Arrhenius-type constitutive equation was employed to describe the coupling effect of temperature, strain rate and strain on the flow stress.

Identification of costs drivers and their influence level on building development costs play a key role in the development of construction models and improve the efficiency and effectiveness of any project. Forty-five indicators influencing building development costs in New Zealand are explored by literature review and pilot interviews. These indicators are grouped into seven categories. The determination and ranking of the cost drivers are carried out by a questionnaire survey distributed to key professionals working in New Zealand’s construction industry. Structural equation modeling (SEM) software was employed for analysis of the collected data. One of the key advantages of this powerful software is to provide the p-value according to the structure of the research model. Findings of this study indicate that the property market and construction industry factor, statutory and regulatory factor, and socio-economic factor are major factors affecting building development costs in New Zealand.

In the note, the authors find several simple and explicit forms for a family of inhomogeneous linear ordinary differential equations studied in "D. Lim, Differential equations for Daehee polynomials and their applications, J. Nonlinear Sci. Appl. 10 (2017), no. 4, 1303-1315; Available online at http://dx.doi.org/10.22436/jnsa.010.04.02".

In the present work the problem of the attenuation of longitudinal sound oscillations in a conducting medium are considered. The proposed approach is based on the dynamic interaction of electron gas with the lattice vibrations. This interaction is manifested in the modification of kinetic equation for electrons. The process is accompanied by generation of an electric field.

Recently, there has been a growing interest in the production of electricity from renewable energy sources (RES). The RES investment is characterized by uncertainty, which is long-term, costly, depend on feed-in-tariff and support schemes. In this paper, we address the real option valuation (ROV) of a solar power plant investment. The real option framework is investigated. This framework considers the renewable certificate price, furthermore the cost of delay between establishing and operating the solar power plant. The optimal time of launching the project and assess the value of deferred option are discussed. The new three stage numerical methods are constructed, the Lobatto3C-Milstein (L3CM) methods. The numerical methods are integrated with concept of Black-Scholes option pricing theory, and applied in option valuation for solar energy investment with uncertainty. The numerical results of L3CM, finite difference and Monte Carlo methods are compared to show the efficiency of our methods. Our data set refers to the Arab Republic of Egypt.

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 Polynomial coefficient function, from the complex hyperspace Cⁿ in itself, is the function Fⁿ that provides the coefficients of the polynomial (x - a₁)(x - a₂)... (x-a_n). A proof of the fundamental theorem of algebra is given where the surjectivity of this function is obtained from a Recurrent Coefficient Equation.

An atomic matter stores its motion information which is contained in velocity-induced shifts in the atomic energy levels. For redshifts less than or of the order of $\frac{1}{137}$, the velocity-dependent shifts of the energy levels of hydrogen atoms are calculated analytically. These velocity-dependent energy shifts lead to the changes of radiative transition wavelengths and doublet splittings of the quasar spectral lines. These spectral variations can be described by the effective value of the fine structure constant depended on the radiative source velocities. In the expanding Universe, these velocities are variable in time and space. It leads to the change of the effective value of the fine structure constant with the cosmological epochs, whereas the fundamental value of the fine structure constant does not.

Newton's kinetic energy equation delineates the laws of motion for objects travelling at speeds much less than the speed of light, an equation extensively validated at these lower velocities. Any new, more complete formulation of kinetic energy must approximate Newton's kinetic energy equation under these conditions. Einstein's special relativity, utilizing the Lorentz factor, introduces a new perspective on spacetime, adhering to the requirement that the Newtonian kinetic energy equation serves as an approximation at low velocities. In this paper, we identify all factor expressions satisfying the condition that their approximate solutions at low velocities align with Newton's kinetic energy equation. We introduce the Yuyunrui factor, incorporating two real number hyperparameters, $\alpha$ and $\beta$, encompassing all potentially correct factors, with the Lorentz factor as a specific instance where $(\alpha=0$, $\beta=1)$. We classify all potentially correct $(\alpha, \beta)$ combinations into six categories based on their distinct scaling effects and present the corresponding scaling effects. The combinations of $(\alpha, \beta)$ values applicable in the real world are necessarily included within these candidates, with the precise values requiring rigorous experimental validation. This work aims to refine our understanding of special relativity beyond the Lorentz factor.

{We present a statistical simulation replicating the correlation observed in EPR coincidence experiments without needing non-local connectivity. We define spin coherence as a spin attribute that complements polarization by being anti-symmetric and generating helicity. Point particle spin becomes structured with two orthogonal magnetic moments, each with a spin of $\frac{1}{2}$—these moments couple in free flight to create a spin-1 boson. Depending on its orientation in the field, when it encounters a filter, it either decouples into two independent fermion spins of $\frac{1}{2}$, or it remains a boson and precesses without decoupling. The only variable in this study is the angle that orients a spin on the Bloch sphere, first identified in the 1920s. There are no hidden variables. The new features introduced in this work result from changing the spin symmetry from SU(2) to the quaternion group, $Q_8$, which complexifies the Dirac field. The transition from a free-flight boson to a measured fermion is the reason for the observed violation of Bell's Inequalities and resolves the EPR paradox.

Image restoration plays a vital role in image processing and pattern recognition in producing better recognition accuracy. It was observed that, most of the traditional restoration algorithms were meant for removing a single type of noise and efforts have been made towards the use of partial differential equation model (PDE), to restore different types of images such as super-resolution, bleeding through and deblurring. This research work deployed hybridized shock filter, shock diffusion of higher order PDE to remove degraded images that have been affected by atmospheric turbulence and water smear images. Degraded images of different types were acquired from various sources. The degraded images were subjected to shock filter algorithm, shock diffusion of higher order PDE. The shock filter was combined with PDE, likewise the shock diffusion was also combined with PDE, and the three algorithms were also combined to test the efficiency of the hybridized method on different degraded images. The result was validated using Mean Square Error, Structural Similarity Index Measure (SSIM), Peak-to-Noise-Signal -Ratio (PNSR) and universal quality index (UQI). From the result, it was observed that the combination of many image restoration algorithms does not give better results whereas, the combination of two of the algorithms has really proved effective.

The present study discusses how adopting cryptos affects financial inclusion in developing economies. Primary constructs like Financial Inclusion (FI), Perceived Economic Empowerment (PEE), Trust in Financial Institutions (TFI), User Satisfaction (US), and Cryptocurrency Adoption (CA) were tested through Structural Equation Modeling (SEM). The results indicated that CA significantly and positively influenced FI, US, TFI, and PEE. These relationships extend to the interaction effects: US, TFI, and PEE all positively related to FI. It is a reflection of cryptocurrencies as an opportunity to redress most of the afflictions characteristic of traditional finance systems and to promote financial inclusion and economic empowerment in developing countries. Future research should also investigate whether digital literacy and regulatory environments support cryptocurrency access.

Good Boussinesq equations will be considered in this work. First we apply three combined compact schemes to approximate spatial derivatives of good Boussinesq equations. Then three fully discrete schemes are developed based on symplectic scheme in time direction, which are sympletic-structure preserving.Meanwhile, the convergence and conservation of the fully discrete schemes are analyzed. Finally, we present numerical experiments to confirm our theoretical analysis. Both our analysis and numerical test indicate that the fully discrete schemes are efficient in solving the spatial derivative mixed equation.

Under the quaternion group, $Q_8$, spin helicity emerges as an element of reality, and complementary to spin polarization. Here we show that the correlation in EPR coincidence experiments is conserved upon separation from a singlet, being divided between polarization and coherence. Including helicity accounts for the violation of Bell's Inequalities without non-locality.

We present an analysis of the Dirac equation when the spin symmetry is changed from SU(2) to the quaternion group, $Q_8$, afforded by multiplying one of the $\gamma$-matrices by the imaginary number. The reason for doing this is to introduce a bivector into the spin algebra. This complexifies the Dirac field which separates into two distinct and complementary spaces: one describing polarization and the other coherence. The former describes a 2D structured spin and the latter its helicity, generated by a unit quaternion.

Plantation-based farmer cooperatives play an important role in promoting agricultural modernization and increasing farmer income, and the management of business risks of such cooperatives not only influences the development of the cooperatives themselves, but also concerns the interests of farmers. Based on the survey data of 226 sample cooperatives from Guizhou province, this article uses factor analysis to measure business risks of plantation-based farmer cooperatives and carries out empirical tests on influence factors of business risks through structural equation model. According to the research results, the ordering of business risks of plantation-based farmer cooperative based on their significance is as follows: market risk > policy risk > natural risk > technical risk > management risk. Influence factors including policy environment, economic environment, social service environment, technical environment, resource endowment of the cooperative and manager characteristics have significant positive influence on the cooperative, with economic environment and manager characteristics generating relatively stronger influence and social service environment generating relatively weaker influence. Through this research, several policy implications on driving high-quality development of plantation-based farmer cooperative are made, including specifying supportive policies of plantation-based farmer cooperative, improving economic environment of agricultural market, upgrading agricultural infrastructure, depending reform of land transfer system, and enhancing internal management of the cooperative.

Reconstructing a 3D model of a scene from a set of multiple views poses a significant challenge in the field of computer vision. The advent of NeRF has marked a major breakthrough in this domain. However, there is a need to extend the capabilities of the NeRF model to enable editing tasks such as relighting and deformation, as well as to enhance its training efficiency. Neural reflectance fields introduce the concept of the reflectance equation into the NeRF framework to achieve relighting of the NeRF model. We leverage the TensoRF approach, which incorporates tensor decomposition and employs multiple tensors to store features, to expedite the training process of the NeRF model. Our novel method, called StensorR, combines the reflectance equation and tensor decomposition within the radiation field model framework. Differing from previous approaches, we employ a single tensor to store scene features and render the surface color of our scene using a simplified reflectance equation. This approach accelerates model convergence and enables relighting of the NeRF model. Experimental results demonstrate that our method achieves a 50% faster convergence rate compared to existing relighting radiation field models, while successfully enabling relighting and improving the quality of synthesized images from new viewpoints.

In this paper, a class of nonlinear ordinary differential equations with impulses at variable times is considered. The existence and uniqueness of solution are given. At the same time, modifying the classical definitions of continuous dependence and Ga^teaux differentiability, some results on continuous dependence and Ga^teaux differentiable of solution relative to the initial value also are presented in new topology sense. For the autonomous impulsive system, the periodicity of solution is given. As an application, properties of solution for a type of controlled nonlinear ordinary differential equation with impulses at variable times is obtained. These results are foundation to study optimal control problems of systems governed by the differential equations with impulses at variable times.

In this article, we review some of the key results concerning the stress-energy-momentum tensor in general theory of relativty. First, we derive Einstein's field equation using analytic approach. Then, we discuss different properties of stress-energy-momentum tensor for physical and scalar fields.

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).

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.

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.

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.

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.

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.

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.

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.

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.

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.

This article reports on the comparative study of the hot deformation behaviour of virgin (steel A) and rejuvenated heat treatment creep-exhausted (steel B) P91 steels. Hot uniaxial compression tests were conducted on the two steels at the deformation temperature range of 900°C-1050°C and a strain rate range of 0.01-10s-1 to 0.6 strain using Gleeble® 3500 equipment. The results showed that the flow stress largely depends on the deformation conditions. The flow stress for the two steels increased with an increase in strain rate at a given deformation temperature and vice versa. The flow stress-strain curves exhibited a dynamic recovery as the softening mechanism. The material constants determined using Arrhenius constitutive equations were: stress exponent was: steel A (5.76) and steel B (6.67), and the apparent activation energy was: steel A (473.1 kJ mol-1) and steel B (564.5 kJmol-1). From these results, steel A exhibited better workability than steel B. Statistical parameters analyses showed that the flow stress for the two steels had a good correlation between the experimental and predicted data. Pearson’s correlation coefficient (R) was: steel A (0.97) and steel B (0.98). The Average Absolute Relative Error (AARE) values were: 7.62% (steel A) and 6.54% (steel B). The study shows that the Arrhenius equations can effectively describe the flow stress behaviour of P91 steel, and this method is applicable to the industrial metalworking process.

We studies the initial value problem for the fractional Navier-Stokes-Coriolis equations, which obtained by replacing the Laplacian operator in the Navier-Stokes-Coriolis equation by the more general operator $(-\Delta)^\alpha$ with $\alpha>0$. We introduce function spaces of the Besove type characterized by the time evolution semigroup associated with the general linear Stokes-Coriolis operator. Next, we establish the unique existence of global in time mild solutions for small initial data belonging to our function spaces characterized by semigroups in both the scaling subcritical and critical settings.

We simulate the effects of diagenesis, cementation and compaction on the elastic properties of shales and sandstones with four different petro-elastical theories and a basin-evolution model, based on constant heating and sedimentation rates. We consider shales composed of clay minerals, mainly smectite and illite, depending on the burial depth, and the pore space is assumed to be saturated with water at hydrostatic conditions. Diagenesis in shale (smectite/illite transformation here) as a function of depth is described by a 5th-order kinetic equation, based on an Arrhenius reaction rate. On the other hand, quartz cementation in sandstones is based on a model that estimates the volume of precipitated quartz cement and the resulting porosity loss from the temperature history, using an equation relating the precipitation rate to temperature. Effective pressure effects (additional compaction) are accounted for by using Athy equation and the Hertz-Mindlin model. The petro-elastic models yield similar seismic velocities, despite the different level of complexity and physics approaches, with increasing density and seismic velocities as a function of depth. The methodology provides a simple procedure to obtain the velocity of shales and sandstones versus temperature and pressure due to the diagenesis-cementation-compaction process.

The brittle shear failure of reinforced concrete beams is complexed and unfavorable. For decades, research on the mechanical properties and durability of recycled coarse aggregate (RCA) to make recycled aggregate concrete (RAC) has been widely investigated. However, test results on the shear strength of reinforced recycled aggregate concrete beams are still limited and contradictory. This paper reports the shear strength of reinforced recycled aggregate concrete beams without stirrups. Eight RAC beams and two controlled beams with natural coarse aggregate (NCA) were tested under the four-point flexural test with the shear span-to-effective depth ratio (a/d) of 3.10. Parameters in this study were the replacement percentage of RCA (0%, 25%, 50%, 75%, and 100%) and longitudinal reinforcement ratio (w) of 1.16% and 1.80%. It was found that the normalized shear stresses of RAC beams with w = 1.80% at all levels of replacement percentage were quite similar to that of the NAC counterparts. Normalized shear stress of the beam with 100% RCA and w = 1.16% was lower than that of the NAC beam by 5%. Database of 128 RAC beams without shear reinforcement from literature was analyzed to evaluate the ability of the most recent ACI 318-19 shear provisions in shear strength prediction. A reduction factor of 0.75 is proposed to the current ACI code provision to account for the physical variations of RCA such as replacement percentage, RCA source and quality, density, amount of residual mortar, and physical irregularity.

The methods for constructing solutions to integro-differential equations of the Volterra type are considered. The equations are related to fractional conformable derivatives. Explicit solutions of homogeneous and inhomogeneous equations are constructed and a Cauchy-type problem is studied. It should be noted that the considered method is based on the construction of normalized systems of functions with respect to a differential operator of fractional order.

A new kind of quantum gates, higher braiding gates, as matrix solutions of the polyadic braid equations (different from the generalized Yang-Baxter equations) is introduced. Such gates lead to another special multiqubit entanglement which can speed up key distribution and accelerate algorithms. Ternary braiding gates acting on three qubit states are studied in details. We also consider exotic noninvertible gates which can be related with qubit loss, and define partial identities (which can be orthogonal), partial unitarity, and partially bounded operators (which can be noninvertible). We define two classes of matrices, star and circle ones, such that the magic matrices (connected with the Cartan decomposition) belong to the star class. The general algebraic structure of the introduced classes is described in terms of semigroups, ternary and $5$-ary groups and modules. The higher braid group and its representation by the higher braid operators are given. Finally, we show, that for each multiqubit state there exist higher braiding gates which are not entangling, and the concrete conditions to be non-entangling are given for the obtained binary and ternary gates.

Here we are concerning with two problems of a coupled system of random and stochastic nonlinear differential equations with two coupled systems of nonlinear nonlocal random and stochastic integral conditions. The existence of solutions will be studied. The sufficient condition for the uniqueness of the solution will be given. The continuous dependence of the unique solution on the nonlocal conditions will be proved.

In this paper, we present some new models for anisotropic compact stars within the framework of 5-dimensional Einstein-Gauss-Bonnet (EGB) gravity with a linear and nonlinear equation of state considering a metric potential proposed for Thirukkanesh and Ragel (2012) and generalized for Malaver (2014). The new obtained models satisfy all physical requirements of a physically reasonable stellar object. Variables as energy density, radial pressure and the anisotropy are dependent of the values of the Gauss-Bonnet coupling constant

The Vacuum Energy Parameter (VEP) of standard cosmology denotes the fraction of the critical density attributed to the accelerated expansion of the Universe. Astrophysical evidence sets the numerical range of VEP at 0.692 +, - 0.012, yet the root cause of these values is currently unknown. Drawing from the stochastic interpretation of early-Universe cosmology, we develop here a derivation of the VEP based on classical diffusion theory and the Langevin equation. Predictions are shown to be in reasonable agreement with observations.

We present set-theoretical solutions of the Yang-Baxter equation in BCK–algebras. Some solutions in BCK−algebras are not solutions in other structures (such as MV −algebras). Related to our investigations we also consider some new structures: Boolean coalgebras and a unified braid condition – quantum Yang-Baxter equation. Finally, we will see how poetry has accompanied the development / history of the Yang–Baxter equation.

This work focuses on the bifurcation behavior before chaos phenomenon happens. Traditional numerical method is unable to solve the unstable limit cycle of nonlinear system. One algorithm is introduced to solve the unstable one, which is based one of the continuation method is called DEPAR approach. Combined with analytic and numerical method, the two stable and symmetrical equilibrium solutions exist through Fork bifurcation and the unstable and symmetrical limit cycles exist through Hopf bifurcation of Lorenz system. With the continuation algorithm, the bifurcation behavior and its phase diagram is solved. The results demonstrate the unstable periodical solution is around the equilibrium solution, besides the trajectory into the unstable area cannot escape but only converge to the equilibrium solution.

Nisin, an antibacterial compound produced by Lactococcus lactis strains, has been approved by the US Food and Drug Administration to be used as a safe food additive to control the growth of undesirable pathogenic bacteria. Nisin is commonly described as a pH-dependent primary metabolite, since its production depends on growth and culture pH evolution. However, the relationship between bacteriocin synthesis and the consumption of the limiting nutrient has not been described until now. Therefore, this study aimed to develop a competitive four-dimensional Lotka Volterra-like equation to describe the relationships between culture pH, limiting nutrient (total nitrogen: TN) consumption and production of biomass (X) and nisin (BT) in four series of batch fermentation with L. lactis CECT 539 in diluted whey (DW)-based media. The developed four-dimensional LV-like equation (with a unique set of parameters) could not be used to describe all cultures belonging to each fermentation series. However, the four-dimensional LV-like equation described accurately each individual culture, providing a good description of the relationships between pH, TN, X and BT, higher values for R2 and F-ratios, lower values (&lt; 10%) for the mean relative percentage deviation modulus, with bias and accuracy factor values approximately equal to one.

Low levels of physical activity (PA) and sedentarism are associated with the onset of different pathologies and health problems. Regular physical activity has been linked with being beneficial to the health of the general population. Within this framework of analysis, the aim of the present study is to analyse the existing association between the time spent doing physical activity and the expressed motives for doing so, from which the first innovative aspect of the paper emerges: the use of the time spent doing PA as a study variable of the phenomenon. The data analysed come from the latest special Eurobarometer survey about the sport and physical activity done in Europe. Using an exploratory factorial analysis and a structural equations model, we were able to find a six-dimensional factorial model that explains the reasons for doing PA, demonstrating that there is no relationship between the reasons for and time spent doing PA. Therefore, motivation is not a variable that explains the time spent doing PA and another type of variable must be used to explain the phenomenon if PA is to be incentivised.

General wisdom thinks that the central of blackholes are singular and featured by mass, charge and spin exclusively; the microstate reflected in the Bekenstein-Hawking entropy can be accounted for only in some quantum gravity. We challenge this wisdom with two exact solution families to the sourceful Einstein equation which describe dust ball with oscillatory inner structure and variety of mass profiles. We attribute the matter content's oscillation across the central point of the system to the forward scattering domination in high energy collisions induced by inter-gravitating acceleration and provide their Penrose-Carter diagram representation and quantum description briefly. Our solution family provides a very simple semi-classic picture for the micorstate definition of black holes.

The material derivative is important in continuum physics. This Letter shows that the expression $\frac{d }{dt}=\frac{\partial }{\partial t}+(\bm v\cdot \bm \nabla)$, used in most literature and textbooks, is incorrect. The correct expression $ \frac{d (:)}{dt}=\frac{\partial }{\partial t}(:)+\bm v\cdot [\bm \nabla (:)]$ is formulated. The solution existence condition of Navier-Stokes equation has been proposed from its form-solution, the conclusion is that "\emph{The Navier-Stokes equation has a solution if and only if the determinant of flow velocity gradient is not zero, namely $\det (\bm \nabla \bm v)\neq 0$.}"

In this paper the dynamics of spatially extended infected phytoplankton with the Holling type II functional response and logistically growing susceptible phytoplankton system is studied. The proposed model is an extension of temporal model available [6], in spatiotemporal domain. The reaction diffusion system exhibits spatiotemporal chaos in phytoplankton dynamics. This is particularly important for the spatially extended systems that are studied in this paper as they display a wide spectrum of ecologically relevant behavior, including chaos. In this system stability of the system is studied with respect to disease contact rate and the growth fraction of infected phytoplankton indirectly rejoin the susceptible phytoplankton population. The results of numerical experiments in one dimension and two dimensions in space as well as time series in temporal models are presented using MATLAB simulation. Moreover, the stability of the corresponding temporal model is studied analytically. Finally, the comparison of the three types of numerical experimentations are discussed in conclusion.

In this paper, we revisit the two theoretical approaches for the formulation of the tachyonic Dirac equation. The first approach works within the theory of restricted relativity, starting from a Lorentz invariant Lagrangian consistent with a spacelike four-momentum. The second approach uses the theory of relativity extended to superluminal motions and works directly on the ordinary Dirac equation through superluminal Lorentz transformations. The equations resulting from the two approaches show mostly different, if not opposite, properties. In particular, the first equation violates the invariance under the action of the parity and charge conjugation operations. Although it is a good mathematical tool to describe the dynamics of a space-like particle, it also shows that the mean particle velocity is subluminal. In contrast, the second equation is invariant under the action of parity and charge conjugation symmetries, but the particle it describes is consistent with the classical dynamics of a tachyon. This study shows that it is not possible with the currently available theories to formulate a covariant equation that coherently describes the neutrino in the framework of the physics of tachyons, and depending on the experiment, one equation rather than the other should be used.

A mathematical model is proposed for quantitative description of the outbreak of novel coronavirus COVID-19 Although the model is relatively simple, the comparison with the public data shows that an exact solution solution of the model (with the correctly-specified parameters) leads to the results, which are in good agreement with the measured data in China and Austria. Prediction of the total number of the COVID-19 cases is discussed and examples are presented using the measured data in Austria, France and Poland.

In this paper, we study the existence of the random -pullback attractor of a non-autonomous local modified stochastic Swift-Hohenberg equation with multiplicative noise in stratonovich sense. It is shown that a random -pullback attractor exists in when its external force has exponential growth. Due to the stochastic term, the estimate are delicate, we overcome this difficulty by using the Ornstein-Uhlenbeck(O-U) transformation and its properties.

Flour yield determined the profitability of flour mill, but the intrinsic variability of the grain makes it very complex to analysis and estimate wheat grain flour yield. Simulation for flour yield attributes offer considerable advantages in flour mill, if reliable predictions of flour yield can be provided, because the wheat grain characteristics can be tested before milling. If this is possible, the characteristics thus observed could be quantified more reliably and objectively by Structural Equation Modelling (SEM). SEM was used to look for the most important wheat grain characteristics on flour yield, and then these wheat grain characteristics were used to simulate flour yield. Furthermore, the regressive equation was verified by the field experiment. The coefficient of variation of grain characteristics was low and distributed rather closely. The results of SEM showed that test weight had the most significantly effects on flour yield, followed by the hardness index. Test weight and hardness index could excellently estimate flour yield by multiplicative effect of test weight and hardness index, and which could determine 68% of the variation in flour yield. The simulation result can not only predict flour yield, but also look for the important grain characteristics for the flour yield.

In this paper only one basic assumption has been made: if we try to describe black holes, their behavior should be understood in the same language as the one we use for particles; black holes should be treated just like atoms. They must be quantum forms of matter, moving in accordance with Schrödinger equations just like everything else. In particular, Rosen’s quantization approach to the gravitational collapse is applied in the simple case of a pressureless “star of dust” by finding the gravitational potential, the Schrödinger equation and the solution for the collapse’s energy levels. By applying the constraints for a Schwarzschild black hole (BH) and by using the concept of BH effective state, previously introduced by one of the authors (CC), the BH quantum gravitational potential, Schrödinger equation and the BH energy spectrum are found. Remarkably, such an energy spectrum is in agreement (in its absolute value) with the one which was conjectured by Bekenstein in 1974 and consistent with other ones in the literature. This approach also permits to find an interesting quantum representation of the Schwarzschild BH ground state at the Planck scale. Moreover, two fundamental issues about black hole quantum physics are addressed by this model: the area quantization and the singularity resolution. As regards the former, a result similar to the one obtained by Bekenstein, but with a different coefficient, has been found. About the latter, it is shown that the traditional classical singularity in the core of the Schwarzschild BH is replaced, in a full quantum treatment, by a two-particle system where the two components strongly interact with each other via a quantum gravitational potential. The two-particle system seems to be non-singular from the quantum point of view and is analogous to the hydrogen atom because it consists of a “nucleus” and an “electron”.

This article is devoted to Feller's diffusion equation which arises naturally in probabilities and physics (e.g. wave turbulence theory). If discretized naively, this equation may represent serious numerical difficulties since the diffusion coefficient is practically unbounded and most of its solutions are weakly divergent at the origin. In order to overcome these difficulties we reformulate this equation using some ideas from the Lagrangian fluid mechanics. This allows us to obtain a numerical scheme with a rather generous stability condition. Finally, the algorithm admits an elegant implementation and the corresponding Matlab code is provided with this article under an open source license.

Our goal in this paper is to study the relationship between the linear approximation of Einstein's equations to the Klein-Gordon’s equation. The part one presents what the Klein-Gordon’s equation and the integration of the theory of quantum information in it. The Part two deals with the Stress Energy tensor quantum, wherein the detail I linearized gravity of Einstein equation, and wherein I develop the tensor quantum energy pulse from the equivalence of equation einstein the linearized gravity and the Schrödinger equation relativistic described by Klein-Gordon’s equation.

In this paper, we introduce some basic idea of Variational iteration method for short (VIM) to solve the Volterra’s integro-differential equations. The VIM is used to solve effectively, easily, and accurately a large class of non-linear problems with approximations which converge rapidly to accurate solutions. For linear problems, it’s exact solution can be obtained by only one iteration step due to the fact that the Lagrange multiplier can be exactly identified. It is to be noted that the Lagrange multiplier reduces the iteration on integral operator and also minimizes the computational time. The method requires no transformation or linearization of any forms. Two numerical examples are presented to show the effectiveness and efficiency of the method. Also, we compare the result with the result from Homotopy perturbation method (HPM). Finally, we investigate the absolute difference between variational iteration method and homotopy perturbation method and draw the graph of difference function by using Mathematica.

We have recently solved the tumbling-snake model for concentrated polymer solutions and entangled melts in the presence of both steady-state and transient shear and uniaxial elongational flows, supplemented by a variable link tension coefficient. Here, we provide the transient and stationary solutions of the tumbling-snake model under biaxial elongation both analytically, for small and large elongation rates, and via Brownian dynamics simulations, for the case of planar elongational flow over a wide range of rates, times, and the model parameters. We show that both the steady-state and transient first planar viscosity predictions are similar to their uniaxial counterparts, in accord with recent experimental data. The second planar viscosity seems to behave in all aspects similarly to the shear viscosity, if shear rate is replaced by elongation rate.

Recently, the awareness of energy conservation, carbon emission reduction, and environmental protection in Taiwan has begun to gradually improve, and bicycles have become an important vehicle for residents. In 2009, Kaohsiung began promoting public bicycle sharing. The number of users in that year amounted to 140,000. By 2015, the accumulated number of users reached nine million. This study adopted the Theory of Planned Behavior (TPB) to explore the factors influencing the behavioral intentions of public bicycle users, including the three dimensions of attitude, subjective norm, and perceived behavioral control, and probed into the relationship between the factors influencing the behavioral intentions of public bicycle users in Kaohsiung City and the dimensions. This study used a questionnaire to collect data and SPSS & AMOS for statistical analysis. The empirical results demonstrated that the most prominent factors influencing the behavioral intentions of public bicycle users in Kaohsiung City included perceived behavioral control, attitude, and subjective norm, in order. Among the influencing factors in the three dimensions, personal interests, main groups, and self-competence had a positive and significant correlation. Administrators should provide more incentives related to the three influencing factors to encourage the public in Kaohsiung City to use public bicycles more frequently as their short-distance travel mode, so as to achieve the purposes of saving energy, reducing carbon emissions, and protecting the urban environment.

Current-quark masses are compared to the rest masses allowed by the Helmholtz equation in a polar model. Within the uncertainty of the current u quark mass determination, the current quark mass coincides with the rest mass allowed by the Helmholtz equation in the polar model in accordance with the second root of the zero Neumann function. Current d quark mass coincides with the rest mass calculated in accordance with the third root of the Bessel zero function. On the basis of a comparison of these results with the results obtained earlier for ordinary real particles u and d quarks stability is discussed.

The goal of the study was to assess the farmers’ acceptance of three sustainable production strategies, namely ‘Agro-forestry’, ‘Alternative protein source’ and ‘Prolonged maternal feeding’. Data on the acceptance of these strategies were collected by a survey of dairy farmers in six EU countries (AT, BE, DK, FI, IT, UK). An extended version of the Technology Acceptance Model (TAM) was applied by means of Structural Equation Modelling to testing various hypotheses on attitudes and intentions of dairy farmers towards these novel production strategies, as well as the influence of organic practices and collaborative behaviours along the supply chain. We found that the most preferred strategy - across all countries - was soy substitution by alternative protein sources. We also found that the intention to adopt a sustainable production strategy may derive from the influence of opinions (and behaviours) of relevant others, showing the role of interactions among farmers and other stakeholders in the adoption of innovations. Finally, the perceived usefulness of all investigated strategies is higher for organic farmers, while collaborative patterns reduce the impact of subjective norm on usefulness and overall acceptance. Our findings should encourage policy makers to consider the important role of supply chain management practices, including collaboration, to enhance the sustainability of dairy farming systems.

The authors undertook pilot studies to assess the accuracy of the reverse engineering process of worn nonstandard spur gears (non-standardized modulus value, unusual profile/pressure angle, high or low teeth), using conventional techniques and measuring instruments. Eight gears were tested, the module of which ranges from 1.020 to 4.98 mm and the number of teeth from 13 to 42. The key parameter, the basic pitch, was selected to estimate the accuracy of the process. The goal is to determine the value of the profile angle. Eleven models were proposed to estimate the nominal tolerance field, using various types of random data distribution. The tested gears were made in IT grade: 6, 7, 8 and 9 according to DIN 3961. Vernier disc micrometers with various measurement ranges were used for research. It has been shown that the nominal module does not have to be treated as a random variable in the population. EIG (Equation of Identity) was developed, allowing conversion of any gear with specific values of geometric parameters into an identical gear with alternative values of these parameters. The directions and degrees of shifts of the estimated tolerance fields relative to the nominal field were determined. The most effective estimating model was selected in the context of the percentage filling of the nominal tolerance field, taking into account the symmetric Student-Fisher distribution with a confidence level of 60%. Further directions of the research activities were described.

We provide representations for the generalized Drazin inverse of an anti-triangular matrix of the form $\left( \begin{array}{cc} a&b\\ 1&0 \end{array} \right)$ in a Banach algebra $\mathcal{A}$, under the condition that $ab=ba$. Specifically, we present the representation of Drazin inverse for these types of anti-triangular matrices in Banach algebras.

The microbial communities are closely related to the overall health and quality of soil, but studies on microbial ecology in apple-pear orchard soils are limited. In the current study, 28 soil samples were collected from three apple-pear orchards in northeastern China, and the composition and structure of fungal and bacterial communities were investigated by high-throughput sequencing. Molecular ecological network showed that the keystone taxa of bacterial communities were Actinobacteria, Proteobacteria, Gemmatimonadetes, Acidobacteria, Nitrospirae, and Chloroflexi, and the keystone taxa of fungal communities was Ascomycota. Mantel tests showed that soil texture and pH were important factors shaping soil bacterial and fungal communities, and soil water soluble organic carbon (WSOC) and nitrate nitrogen (NO3--N) were also closely related to soil bacterial communities. Canonical correspondence analysis (CCA) and variation partition analysis (VPA) analysis revealed that geographic distance, soil texture, pH, and other soil properties could explain 10.55%, 13.5%, and 19.03% of the overall variation of bacterial communities, and they explained 11.61%, 13.03%, and 20.26% of the overall variation of fungal communities, respectively. The key stone taxa of bacterial and fungal communities in apple-pear orchard soils and their strong correlation with soil properties could provide useful clues toward sustainable management of orchards.

Food security is the cornerstone of national security, and exploring the resilience of the grain industry chain is particularly important under the current complex and changing external environment. The study is to evaluate the grain industry chain resilience and identify its influencing factors. Based on the panel data of 30 provinces (cities) in China from 2011 to 2022, this paper adopted Partial Least Squares structural equation modeling method to carry out comprehensive evaluation, applied Dagum Gini coefficient to analyze spatial differences, and used geo-detectors to identify the influencing factors. The results showed that (1) from an overall perspective, the resilience of China's grain industry chain showed an overall upward trend, and each region had been greatly improved; (2) from the perspective of spatial differences, the overall spatial variability of China's grain industry chain is relatively small, and the gap mainly originates from inter-regional differences; (3) from the perspective of influencing factors, the level of grain foreign trade, regional market size and agricultural innovation level were important factors. In order to enhance the resilience of China's grain industry chain, based on the heterogeneous characteristics, the coordinated development of each region should be integrated, and the endogenous power should be given full play to enhance the resilience of the industry chain.

Reservoir routing has been a routine procedure in hydrology, hydraulics and water management. It is typically based on the mass balance (continuity equation) and a conceptual equation relating storage and outflow. If the latter is linear, then there exists an analytical solution of the resulting differential equation, which can directly be utilized to find the outflow from known inflow, and to obtain macroscopic characteristics of the process, such as response and residence times, and their distribution functions. Here we streamline the reservoir routing framework and extend it to find approximate solutions for nonlinear cases. The proposed framework can also be useful for climatic tasks, such as describing the mass balance of atmospheric carbon dioxide and determining characteristic residence times, which have been an issue of controversy. Application of the theoretical framework results in excellent agreement with real world data. In this manner, we easily quantify the atmospheric carbon exchanges, and obtain reliable and intuitive results, without the need to resort to complex climate models. The mean residence time of atmospheric carbon dioxide turns out to be no more than four years and the response time is smaller than that, thus opposing the much longer mainstream estimates.

Two distinct measures of information, connected respectively to the amplitude and phase of the wave function of a particle, are proposed. There are relations between the time derivatives of these two measures and their gradients on the configuration space, which are equivalent to the wave equation. The information related to the amplitude measures the strength of the potential coupling of the particle (which is itself aspatial) with each volume of its configuration space, i.e. its tendency to participate in an interaction localized in a region of ordinary physical space corresponding to that volume. The information connected to the phase is that required to obtain the time evolution of the particle as a persistent entity starting from a random succession of bits. It can be considered as the information provided by conservation principles. The meaning of the so-called "quantum potential" in this context is briefly discussed.

Let a,b,c be positive integers such that a²+b²=c², 2|b,gcd(a,b)=1. In 1956, Jesmanowicz conjectured that for any positive integer w, the only solution of (aw)^x+(bw)^y=(cw)^z in positive integers is (x, y, z) = (2, 2, 2). In this paper, based on Gaussian integer ring, we show that Je$\acute{s}$manowicz' conjecture is true for any positive integer

This article presents a detailed examination of the methodology and modeling tools utilized to analyze gas flow in pipelines, rooted in the fundamental principles of gas dynamics. The methodology integrates numerical simulations with modern neural network techniques, particularly focusing on the Physics-Informed Neural Network (PINN) method. This innovative approach combines artificial neural networks (ANNs) with physical equations, offering a more efficient and accurate way to model various complex processes and phenomena. The proposed mathematical model, based on the Euler equation, has been meticulously implemented using the Python language. Verification with analytical solutions ensures the accuracy and reliability of the computations. In the research, a comprehensive comparative analysis was conducted between results obtained using the PINN method and those from conventional Computational Fluid Dynamics (CFD) approaches. The analysis highlighted the advantages of the PINN method, which produced smoother pressure and velocity fluctuation profiles while reducing computation time, demonstrating its potential as a transformative modeling tool. The data derived from this study are of paramount importance for ensuring ongoing energy supply reliability and can also be used to create predictive models related to gas behavior in pipelines. The application of modeling techniques for gas flow simulation has the potential to revolutionize the integrity of our energy infrastructure and utilization of gas resources. However, it is crucial to emphasize that the effectiveness of such models relies on continuous monitoring and frequent updates to ensure alignment with real-world conditions. This research not only contributes to a deeper understanding of compressible gas flows but also underscores the crucial role of advanced modeling methodologies in the sustainable management of gas resources for both current and future generations.

The wave energy converter (WEC) technology constantly develops new designs and models. To encourage its development within the energy sector, research is required to improve current designs and create durable and effective devices. However, it is also crucial to investigate the suitability of a WEC to a site-specific sea condition as this can impact its optimal power absorption and constructability. This study evaluates and compares the efficiency of a heaving buoy with varied geometries in one of the most energetic places along the Mexican coast. A statistical analysis of the wave climate on the coast of Ensenada during the last 42 years is performed to define the conditions to which the device is subjected. The location of the WEC in shallow waters is chosen using a computational model which solves the modified mild slope equation in its elliptic shape. The heaving buoy floater is studied using three distinct geometries: a semi-sphere, a cylinder, and a proposed rounded semi-rectangle. The hydrodynamic response of the three geometries is then analysed in the frequency and time domain using ANSYS AQWA. The hydrodynamic study involves the assessment of the floating body dynamics, exerted forces, the power absorbed as well as the suitability of the proposed power take-off (PTO) system. Findings reveal that the proposed geometry absorbs the most energy, with an annual power of 135.11 MW, and that the transmission PTO design is appropriate for this type of technology.

In this paper, we consider an epidemiological Susceptible-Infected-Susceptible (SIS) model in which the individuals cured from the infection return back into the group of people endangered by the infection. Delay differential equations were introduced to create more realistic models since many processes depend on past history. Many different mathematical methods, including the Susceptible-Infected-Recovered (SIR) model as well as derivatives thereof, can be used to prognose the spread of many various infectious diseases, including Covid-19.We use a nonlinear differential system with time delay as a mathematical formulation of this model. It is examined by the existence of a positive solution which is bounded by two functions $k_1, k_2\in C([t_0,\infty),(0,\infty))$ with constants $\lambda_1 > 0,\,\lambda_2 > 0$ where $0<\lambda_1\leq \lambda_2$. The conditions are put in place for existence of a positive solution that approaches zero in infinity, if $t\to\infty$. Infectious diseases accompany a person throughout their entire life, and in the history of mankind often appeared in frequent epidemics caused high mortality. The occurrence of infectious diseases in the population represents a serious health, social and economic problem. There is a lot of ambiguity concerning the time span and final spread of the epidemic thus making it very demanding for the governing bodies, healthcare institutions, and economic sector to precisely judge the future development.Several examples are shown at the end of this paper.

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.