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

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

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

In this paper, we investigate the dynamics of following higher order difference equation x_{n+1}=A+B((x_{n})/(x_{n-m}²)) with A,B and initial conditions are positive numbers, and m∈{2,3,⋯}. Especially we study the boundedness, periodicity, semi-cycles, global asymptotically stability and rate of convergence of solutions of related higher order difference equations.

For the solution existence condition of the Navier-Stokes equation, we propose a conjecture as follows: "\emph{The Navier-Stokes equation has a solution if and only if the determinant of flow velocity gradient is not zero, namely $\det (\bm \nabla \bm v)\neq 0$.}"

The authors intend to establish new oscillation criteria for a class of generalized third order functional difference equation of the form \begin{equation}{\label{eq01}} \Delta_{\ell}\left(a_2(n)\left[\Delta_{\ell}\left(a_1(n)\left[\Delta_{\ell}z(n)\right]^{\beta_1}\right)\right]^{\beta_2}\right)+q(n)f(x(g(n)))=0, ~~n\geq n_0, \end{equation} where $z(n)=x(n)+p(n)x(\tau(n))$. We also present sufficient conditions for the solutions to converges to zero. Suitable examples are presented to validate our main results.

The Cordoba Guitar Festival is one of the most important cultural events in Spain. This article analyses the musical preferences, satisfaction, attitudinal loyalty and behavioural loyalty of spectators who attended the 36th festival held in July 2016, as well as the festival’s economic impact on the city. To achieve this aim, a structural equation model (SEM) was used. The results show the goodness-of-fit of the model and indicate that the observed data fit the expected dataset.

In this paper we study the class of mixed-index time fractional differential equations in which different components of the problem have different time fractional derivatives on the left hand side. We prove a theorem on the solution of the linear system of equations, which collapses to the well-known Mittag-Leffler solution in the case the indices are the same, and also generalises the solution of the so-called linear sequential class of time fractional problems. We also investigate the asymptotic stability properties of this class of problems using Laplace transforms and show how Laplace transforms can be used to write solutions as linear combinations of generalisedMittag-Leffler functions in some cases. Finally we illustrate our results with some numerical simulations.

This paper attempts to address the phenomenon of normal vibrations, (referred to as dynamic vibrations) occurring on a surface which is already in vibrational motion due to other kinematic phenomena. Such a surface will have a metric tensor, normal, and ambient velocity which diverges from the surface’s original various dynamic tensorial descriptors. This paper formulates the wave equation defined in a coordinate space, and extends the equation to observe vibrations on a surface with the use of the Laplace-Beltrami operator in a tensorial fashion drawing on conventions from the newly established Calculus of Moving Surfaces (CMS). The Paper then identifies the way which these normal vibrations will manifest within ambient space. Finally, a counter-intuitive relation between the magnitude of such dynamic vibrations and dynamic surface’s time-dependent mean curvature presents itself, for which dynamic vibrations superimposed on original dynamic motion will eliminate the other, and the surface remains static under an arbitrary initial motion. From this condition, resubstitution within the wave equation yields a novel coupled PDE system which within contains the time-evolution of the surface’s mean curvature and its dynamic vibrations. This analysis can have application for algorithms designed for mechanical stabilization during seismic activity, as well as analyzing stabilization algorithms for other various applications and can also have application with respect to biotechnological innovations for analyzing properties defined on the surface of cell-Like biological entities such as metabolism, lipid content, and actin dynamics.

Giant unilamellar vesicles (GUVs) are membrane model used to study membrane properties. Electroformation is one of the methods used to produce GUVs. During electroformation protocol dry lipid film is formed. Drying of the lipid film induce Cholesterol (Chol) demixing artifact, in which Chol forms anhydrous crystals, where these crystals does not participate in formation of vesicles. This leads to a lower Chol concentration in the vesicle bilayers compared to the Chol concentration in the initial lipid solution. To address this problem, we propose novel electroformation protocol that includes rapid solvent exchange, plasma cleaning and spin-coating methods to produce GUVs. We tested the protocol focusing on vesicles with high Chol content using different spin-coating durations and vesicle types deposition. Additionally, we compared the novel protocol using completely dry lipid film. The optimal spin-coating duration for vesicles made out of phosphatidylcholine/Chol mixture was 30 s. Mulitlamellar vesicles (MLVs), large unilamellar vesicles (LUVs) obtained by extrusion of MLVs through 100 nm membrane pores and LUVs obtained by extrusion of previously obtained LUVs through 50 nm membrane pores were deposited on electrode for 1.5/1 Chol/phosphatidylcholine lipid mixture and the results were compared. Electroformation using all three deposited vesicle types gave a high GUVs yield, but deposition of LUVs obtained by extrusion of MLVs through 100 nm membrane pores gave the most reproducible results. Using deposition of these LUVs, we produced GUVs with high yield for 6 different Chol concentrations (from 0 % to 71.4%). Using protocol that includes dry lipid film GUVs yield was lower and Chol demixing artifact was induced, proving that the lipid film should never undergo drying when Chol content is high.

Nanocrystalline silicon oxide (nc-SiOx:H) is a multipurpose material with its varied application in solar cells as a transparent front contact, intermediate reflector, back reflector layer and even tunnel layer for passivating contacts, owing to easy tailoring of its optical properties. In this work, we systematically investigate the influence of gas mixture (SiH4, CO2, PH3 and H2), RF power and process pressure on the optical, structural and passivation properties of thin n-type nc-SiOx:H films prepared in an industrial, high throughput, plasma-enhanced chemical vapor deposition (PECVD) reactor. We provide a detailed description of the n-type nc-SiOx:H material develop-ment using various characterization techniques (SEM, EDX, Raman spectroscopy, and spectro-scopic ellipsometry) with a focus on the relationship between the material properties and the pas-sivation they provide to n-type c-Si wafers characterized by their effective carrier lifetime (τeff). Further, we also outline the parameters to be kept in mind while developing different n-type nc-SiOx:H layers for different solar cell applications. We report a tunable optical gap (1.8 – 2.3 eV) for our n-type nc-SiOx:H films as well as excellent passivation properties with τeff up to 3.5 ms (iVoc ~ 715 mV) before annealing. Oxygen content plays an important role in determining the crystallinity and hence passivation quality of the deposited nanocrystalline silicon oxide films.

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

In this paper, we propose a partial differential equation model based on phase-field for sentiment analysis in the field of hotel comment texts. The comment texts are converted into word vectors using the Word2Vec tool, and then we utilize the multifractal detrended fluctuation analysis (MF-DFA) model to extract the generalized Hurst exponent of the word vector time series to achieve dimensionality reduction of the word vector data. The dimensionality reduced data is represented in a two-dimensional computational domain, and the modified Allen-Cahn (AC) function is used to evolve the phase values of the data to obtain a stable nonlinear boundary, thereby achieving automatic classification of hotel comment texts. The experimental results show that the proposed method can effectively classify positive and negative samples and achieve excellent results in classification indicators. We compared our proposed classifier with traditional machine learning models and the results indicate that our method possesses a better performance.

In this study, we actually want to explore the time-fractional Phi-four equation via two methods, the exp _a function method and the hyperbolic function method. We transform a fractional order dierential equation into an ordinary differential equation using a wave transformation and the fractional derivative in conformable form. Then, the resulting equation has successfully been explored for new explicit exact solutions. The procured solutions are simply showed the effectiveness and plainness of the projected methods.

Here is shown method for the hydraulic solution of a looped gas-pipeline networks. Calculation of presented network is done according to principles of Hardy Cross method. The optimization was carried out by iteration of the pipes diameters, node consumptions are known and flow velocities through pipes have to stand below certain values. Accent is on determination of appropriate friction factor, and on selection of representative equation for natural gas flow under presented conditions in the network. Inappropriate usage of friction factor, equally as inappropriate usage of gas flow equation can lead to inaccurate final results. Here is shown new facts in comparison to previous calculation of gas distribution network in Kragujevac, Serbia which is done in 1994. After the implementation, measurements in situ have performed, and real measured values deviate from calculated. Causes for these errors are investigated, and improved and more accurate procedure is shown.

In this paper after introducing a model of binary data matrix for physical measurements of an evolving system (of particles), we develop a Hilbert space as an ambient space to derive induced metric tensor on embedded parametric manifold identified by associated joint probabilities of particles observables (parameters). Parameter manifold assumed as space-like hypersurface evolving along time axis, an approach that resembles 3+1 formalism of ADM and numerical relativity. We show the relation of endowed metric with related density matrix. Identification of system density matrix by this metric tensor, leads to the equivalence of quantum Liouville equation and metric compatibility condition ∇₀g_ij = 0 while covariant derivative of metric tensor has been calculated respect to Wick rotated time coordinate. After deriving a formula for expected energy of the particles and imposing the normalized Ricci flow as governing dynamics, we prove the equality of this expected energy with local scalar curvature of related manifold. Consistency of these results with Einstein tensor, field equations and Einstein-Hilbert action has been verified. Given examples clarify the compatibility of the results with well-known principles. This model provides a background for geometrization of quantum mechanics compatible with curved manifolds and information geometry.

We introduce a model of a passive optical cavity based on the two-dimensional Lugiato-Lefever equation, with a localized pump carrying intrinsic vorticity S, and the cubic or cubic-quintic nonlinearity. Up to S = 5, stable vortex-ring states (vortex pixels) are produced by a variational approximation and in a numerical form. Surprisingly, vast stability areas of the vortex states are found, for both the self-focusing and defocusing signs of the nonlinearity, in the plane of the pump-strength and loss parameters. When the vortex-rings are unstable, they are destroyed by azimuthal perturbations which break the axial symmetry. The results suggest new possibilities for mode manipulations in nonlinear optical media.

There are many problems based on solving non-autonomous differential equations of the form x¨(t)+ω2(t)x(t)=0, where x(t) represents the coordinate of a material point and ω is the angular frequency. The inverse problem involves finding the bounded coefficient ω. Continuity of the function ω(t) is not required. The trajectory x(t) is unknown, but the initial and final values of the phase variables are given. The variation principle of minimum time for the entire dynamic process allows for the determination of the optimal solution {x(t),ω(t)}. Thus, the inverse problem is an optimal control problem. No simplifying assumptions were made.

In our latest studies with the help of the self-similar Ansatz we derived new type of 1 solutions for the regular diffusion equation which are much more complex than the well-known 2 Gaussian and error functions. These solutions contain additional Kummer’s M and Kummer’s U 3 functions with quadratic argument. In the present treaties we perform an analogous analysis for the 4 regular diffusion equation which has a complex diffusion coefficient. Formally, it is equivalent to 5 the free Schrödinger equation however it is far from being trivial how the solutions can be given 6 quantum mechanical interpretation. We investigate both the one dimensional Cartesian and the 7 spherical symmetric equations. We find solutions which fulfill the L2 integrability criteria therefore 8 might have quantum mechanical relevance in the future.

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.

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.

ObjectivesThe present study is aimed at characterizing and identifying the important research trends of the application of structural equation modelling (SEM) in nursing research by bibliometric analysis, and further providing reference for nursing researchers to conduct SEM research.MethodsA descriptive bibliometric analysis of publications in the application of SEM in nursing research. Literatures were retrieved from the Web of Science (WoS) core collection database On April 30, 2022. CiteSpace 6.1.R1 and VOSviewer 16 software were used for visualization and bibliometric analysis.ResultsThe annual publication indicated an increasing trend in the future. The intellectual structures of the application of SEM in nursing researches included patient safety, cross-cultural comparison, compassion fatigue, benchmarking, patient discharge, China, psychometrics, and policy. The hotpots and development trends include job satisfaction, nursing home, and nursing student.ConclusionThe hotspots and development trends related to the application of SEM in nursing research mentioned in this study may be helpful for researchers to explore new directions in this field. The intellectual structures and development trends were found in the application of SEM in nursing researches in this study. The awareness of the clusters and bursts in this field can help nursing researchers avoid overlooking some important issues when conducting SEM, and provide nurse researchers with good practice guidelines for conducting SEM.

In this study, we have considered for numerical solution of a Poisson equation in a domain. we have presented a first and second order finite difference method for solving the system of the intial boundary value. We have presented the numerical solution of the Poisson equations in a two-dimensional finite region. Numerical Solution and exact solution for the presented method has been compared and the figures presented. The present error analysis tables demonstrate the efficiency of the method.

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.

The purpose of this research is to determine if the tradeoffs that Kissick proposed among cost containment, quality, and access remain as rigidly interconnected as originally conceived in the contemporary health care context. Although many have relied on the Kissick model to advocate for health policy decisions, to our knowledge, the model has never been empirically tested. Some have called for policy makers to come to terms with the premise of the Kissick model tradeoffs, others have questioned the model given the proliferation of quality enhancing initiatives, automation, and information technology in the health care industry. One wonders whether these evolutionary changes alter or disrupt the originality of the Kissick paradigms themselves. Methods: Structural Equation Modeling (SEM) was used to evaluate the Kissick hypothetical relationships among the unobserved constructs of cost, quality, and access in hospitals for the year 2018. Hospital data were obtained from Definitive Healthcare a subscription site which contains Medicare data as well as non-Medicare data for networks, hospitals, and clinics (final n= 2,766). Results: Reporting significant net effects as defined by our chosen study variables, we find that as quality increases costs increase, as access increases quality increases, and as access increases, costs increase. Policy and Practice Implications: Our findings lend continued relevance to a balanced approach to health care policy reform efforts. Simultaneously bending the health care cost curve, increasing access to care, and advancing quality of care is as challenging now as it was when the Kissick model was originally conceived.

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

An equation for the Fermi level of impurity isotropic semiconductors is considered when the bottom of the conduction band and the top of the valence band are at the center of the first Brillouin zone. The energy of charge carriers in the valence and conduction bands of semiconductors is considered taking into account the real positions of the top of the valence band and the bottom of the conduction band in the first Brillouin zone. A universal equation for determining the Fermi levels of impurity isotropic semiconductors is presented.

The acceleration of the universe is described as a consequence of the extrinsic curvature of the space-time embedded in a bulk space, defined by the Einstein-Hilbert. Using the linear approximation of Nash-Green theorem, we obtain the related perturbed equations in which just the gravitational-tensor field equations contribute to propagation of cosmological perturbations. In accordance with Big Bang Nucleosynthesis and solar constraints, we calculate numerically the effective Newtonian function Geff to constrain the related parameters of the model. We numerically solve the growth density equation for two possible family of solutions leading to an interesting overdensity and, in some cases, a mild damping of the growth profiles, with a top amplification of the growth perturbations around 14% in comparison with LCDM model and quintessence. The effective gravitational Phi and Newtonian curvature Psi are also analysed showing mild perturbations in early times induced only by the extrinsic curvature differently from the LambdaCDM standards.

In this paper, we consider the generalized sextic functional equation \begin{align*} \sum_{i=0}^{7}{}_7 C_{i} (-1)^{7-i}f(x+iy) = 0. \end{align*} And by applying the fixed point theory in the sense of L. C\u adariu and V. Radu, we will discuss the stability of the solutions for this functional equation.

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.

Widely used in hydraulics, the Colebrook equation for flow friction relates implicitly to the input parameters; the Reynolds number, Re and the relative roughness of inner pipe surface, ε/D with the output unknown parameter; the flow friction factor, λ; λ=f(λ, Re, ε/D). In this paper, a few explicit approximations to the Colebrook equation; λ≈f(Re, ε/D), are generated using the ability of artificial intelligence to make inner patterns to connect input and output parameters in explicit way not knowing their nature or the physical law that connects them, but only knowing raw numbers, {Re, ε/D}→{λ}. The fact that the used genetic programming tool does not know the structure of the Colebrook equation which is based on computationally expensive logarithmic law, is used to obtain better structure of the approximations which is less demanding for calculation but also enough accurate. All generated approximations are with low computational cost because they contain a limited number of logarithmic forms used although for normalization of input parameters or for acceleration, but they are also sufficiently accurate. The relative error regarding the friction factor λ, in best case is up to 0.13% with only two logarithmic forms used. As the second logarithm can be accurately approximated by the Padé approximation, practically the same error is obtained also using only one logarithm.

We introduce a class of logarithmic wave equation. We study the global existence of week solution for this class of equation. We deal with the initial boundary value problem of this class. Using the Galerkin method and the Gross logarithmic Sobolev inequality we establish the main theorem of existence of week solution for this class of equation arising from Q-Ball Dynamic in particular.

A method based on ultra performance liquid chromatography with diode array detector (UPLC-DAD) was developed for quantitative analysis of five active compounds and chemical fingerprint analysis of Rosa rugosa. Ten batches of Rosa rugosa collected from different plantations in the Xinjiang region of China were used to establish the fingerprint. The feasibility and advantages of the used UPLC fingerprint were verified for its similarity evaluation by systematically comparing chromatograms with professional analytical software recommended by State Food and Drug Administration (SFDA) of China. In quantitative analysis, the five compounds showed good regression (R²=0.999 5) within the test ranges and the recovery of the method was in the range of 94.2–103.8%. The similarities of the fingerprints of 10 batches of the samples were more than 0.981. The developed UPLC fingerprint method is simple, reliable and validated for the quality control and identification of Rosa rugosa. Additionally, simultaneous quantification of five major bioactive ingredients in the Rosa rugosa samples was conducted to interpret the consistency of the quality test. The results indicated that the UPLC fingerprint as a characteristic distinguishing method combining similarity evaluation and quantification analysis, can be successfully used to assess the quality and to identify the authenticity of Rosa rugosa.

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

Huperzine A is an herbal reversible inhibitor of Acetylcholinesterase (AChE). A molecular docking analysis on Huperzine A molecule has been carried out to understand its structure, conformational flexibility, intermolecular interaction and the binding affinity in the active site of AChE enzyme. Further, the charge density distribution of huperzine A molecule (lifted from the active site of AChE) was determined from the high level quantum chemical calculations coupled with charge density analysis. The binding affinity of Huperzine A towards AChE was calculated from the molecular docking; the lowest docked energy is -8.46 kcal/mol. In the active site, huperzine A molecule interacts with acyl binding pocket-Phe330 of AChE, that is, the bicyclo ring group of huperzine A forms an intermolecular interaction with the oxygen atom of main chain of the amino acid residue Phe330 at the distances 3.02 and 3.25 Å respectively. On the other hand, a gas phase study on huperzine A molecule also performed using HF and DFT (B3LYP) methods with the basis set 6-311G**. The molecular structure, conformation, and the charge density distribution of huperzine A molecule in the gas phase have determined using quantum chemical calculations and the charge density analysis. The comparative studies between the gas phase and the active site forms of huperzine A molecule, explicitly reveals the degree of conformational modification and the charge density redistribution of huperzine A when present in the active site. The dipole moment of the molecule in the active site is 6.85 D, which is slightly higher than its gas phase value (5.91 D). The electrostatic potential (ESP) surface of active site molecule clearly shows the strong electronegative and positive ESP regions of the molecule, which are the expected strong reactive locations of the molecule.

One of the tools for optimal crop production is regular monitoring and assessment of crops. During the growing season of fruit trees, the bloom period has increased photosynthetic rates that correlate with the fruiting process. This paper presents the development of an image processing algorithm to detect peach blossoms on trees. Images of an experimental peach orchard were acquired from the Parma Research and Extension Center of the University of Idaho using an off-the-shelf unmanned aerial system (UAS), equipped with a multispectral camera (Near-infrared, Green, Blue). The orchard has different stone fruit varieties and different plant training system. Individual tree images (high-resolution) and arrays of trees images (low-resolution) were acquired to evaluate the detection capability. The image processing algorithm was based on different vegetation indices. Initial results showed that the image processing algorithm could detect peach blossoms and demonstrate good potential as a monitoring tool for orchard management.

Tellurium exhibits exceptional intrinsic electronic properties. However, investigations into the modulation of tellurium's electronic properties through physical modification are notably scarce. Here, we present a comprehensive study focused on the evolution of the electronic properties of tellurium crystal flakes under plasma irradiation treatment by employing conductive atomic force microscopy and Raman spectroscopy. The plasma-treated tellurium experienced a process of defect generation through lattice broken. Prior to the degradation of electronic transport performance due to plasma irradiation treatment, a remarkable observation emerged: in the low-energy region of hydrogen plasma-treated tellurium, a notable enhancement in conductivity was unexpectedly detected. The mechanism underlying this enhancement in electronic transport performance was thoroughly elucidated by comparing it with the electronic structure induced by argon plasma irradiation. This study not only fundamentally uncovers the effects of plasma irradiation on tellurium crystal flakes, but also unearths an unprecedented trend of enhanced electronic transport performance at low irradiation energies when utilizing hydrogen plasma. This abnormal trend bears significant implications for guiding the prospective application of tellurium-based 2D materials in the realm of electronic devices.

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.

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

Construction projects are usually operating in a complex and dynamic environment in which the accumulation of many interrelated factors causes high uncertainty. Construction projects are complex and frequently involve substantial uncertainties including process complicatedness, intricate organization structure, dynamic environment, and financial strain. The study aims to categorize the influencing factors into three groups, namely construction project system, economic-market climate, and external environment. It attempts to adopt a novel analysis tool to examine the relationship between the project cost and multiple influencing factors by using Bayesian SEM. While the Bayesian SEM method has been receiving increasing attention in exploring the relationship between latent variables, construction studies still heavily rely on the covariance-based SEM approach. This study introduces several advantages of Bayesian SEM that make it more flexible and powerful than covariance-based SEM and provides the foundation of Bayesian SEM estimation and inference by illustrating this method in a project cost application.

Construction projects are usually operating in a complex and dynamic environment in which the accumulation of many interrelated factors causes high uncertainty. Construction projects are complex and frequently involve substantial uncertainties including process complicatedness, intricate organization structure, dynamic environment, and financial strain. The study aims to categorize the influencing factors into three groups, namely construction project system, economic-market climate, and external environment. It attempts to adopt a novel analysis tool to examine the relationship between the project cost and multiple influencing factors by using Bayesian SEM. While the Bayesian SEM method has been receiving increasing attention in exploring the relationship between latent variables, construction studies still heavily rely on the covariance-based SEM approach. This study introduces several advantages of Bayesian SEM that make it more flexible and powerful than covariance-based SEM and provides the foundation of Bayesian SEM estimation and inference by illustrating this method in a project cost application.

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.

The Cohen-Macaulay vertex splittable ideals are characterized. As a consequence, we recover several Cohen-Macaulay classifications of families of monomial ideals known in the literature by new simpler combinatorial proofs.

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

The 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.

We provide methodology and numerical results for the Hattendorff differential equa- tion for the continuous time evolution of the variance of L(j)t , the loss at time t random variable for a multi-state process, given that the state at time t is j.

Queretaro is currently one of the states with the highest growth rate in the automotive industry. In the last five years, the number of companies has increased, reaching more than 300 small and medium-sized companies in the sector. However, they show a high degree of ignorance and lack of strategic foresight, which translates into poor planning in the short, medium and long term and low competitiveness, leading many of them to failure. This paper presents the results of a study within a strategic foresight evaluation with the development of a Structural Equation Model that allows the analysis of foresight and strategic planning within the automotive SMEs in the state of Queretaro. The study analyzes the necessary indicators to be evaluated and establishes the relationship of dependence between the variables, which is necessary to create the constructs of the model. It is confirmed that the adjustment of the model used is adequate for the evaluation of SMEs. The contributions of the research were: A theoretical contribution related to strategic foresight within SMEs and the construction of the structural equation model to evaluate strategic foresight in automotive SMEs in the state of Queretaro.

I localize gravity to match its measurements with the local inertial frame of special relativity. I find a geometric interpretation of the speed of light and mass. I find also a relation between every mass measured and the black hole entropy which introduces information-matter equation from gravity. Through localization of gravity, a timeless state of the universe emerges and the uncertainty principle does not hold since the velocity concept is replaced by distance in this timeless state. This would resolve the problem of time because timeless state of the universe emerges naturally and mathematically consistent. This would suggest that gravity form the hidden one variable of quantum mechanics which would complete the relation between quantum mechanics and gravity. The experimental evidence of timeless state of the universe is the quantum entanglement. Since the spin measurement is the manifestation of quantum entanglement. Therefore, the spin of quantum particle can be originated from geometrical or gravitational red-shift. We introduce also a principle of least computation which is achieved when the ratio equal to the difference in the process of local gravitational measurements.

Four methods in two different families have been constructed to derive the exact solutions to Benjamin-Bona-Mahony equation in two space dimensions. Simply defined hyperbolic tangent, hyperbolic secant and hyperbolic cosecant ansatzes and the expansion method based on the Sine-Gordon equation in two dimensions are directly substituted into the governing ODE reduced from the two dimensional BBM equation. Classical algebraic method is used to find the relations among the target parameters representing the nonzero coefficients in the predicted solutions and the wave transform parameters. Some complex and real solutions have been constructed in explicit forms.

Empirical Colebrook equation from 1939 is still accepted as an informal standard to calculate friction factor during the turbulent flow (4000 < Re < 10⁸) through pipes from smooth with almost negligible relative roughness (ε/D→0) to the very rough (up to ε/D = 0.05) inner surface. The Colebrook equation contains flow friction factor λ in implicit logarithmic form where it is, aside of itself; λ, a function of the Reynolds number Re and the relative roughness of inner pipe surface ε/D; λ = f (λ, Re, ε/D). To evaluate the error introduced by many available explicit approximations to the Colebrook equation, λ ≈ f(Re, ε/D), it is necessary to determinate value of the friction factor λ from the Colebrook equation as accurate as possible. The most accurate way to achieve that is using some kind of iterative methods. Usually classical approach also known as simple fixed point method requires up to 8 iterations to achieve the high level of accuracy, but does not require derivatives of the Colebrook function as here presented accelerated Householder’s approach (3^rd order, 2^nd order: Halley’s and Schröder’s method and 1^st order: Newton-Raphson) which needs only 3 to 7 iteration and three-point iterative methods which needs only 1 to 4 iteration to achieve the same high level of accuracy. Strategies how to find derivatives of the Colebrook function in symbolic form, how to avoid use of the derivatives (Secant method) and how to choose optimal starting point for the iterative procedure are shown. Householder’s approach to the Colebrook’s equations expressed through the Lambert W-function is also analyzed. One approximation to the Colebrook equation based on the analysis from the paper with the error of no more than 0.0617% is shown.

GNSS have been widely used in navigation, positioning and timing. Nowadays, the multipath errors previously considered detrimental may be re-utilized for the remote sensing of geophysical parameters (soil moisture, vegetation and snow depth), e.g. GPS- Multipath Reflectometry (GPS-MR). In this paper, a new element describing bistatic scattering properties of vegetation is incorporated into the traditional GPS-MR model. This new element is the first-order radiative transfer equation model. The new forward GPS multipath simulator is able to explicitly link the vegetation parameters with GPS multipath observables (signal-to-noise-ratio (SNR), code pseudorange and carrier phase observables). The trunk layer and its corresponding scattering mechanisms are ignored since GPS-MR is not suitable for high forest monitoring due to the coherence of direct and reflected signals. Based on this new model linking the GPS observables (SNR, phase and pseudorange) with detailed vegetation parameters, the developed simulator can present how the GPS signals (L1 and L2 carrier frequencies, C/A, P(Y) and L2C modulations) are transmitted (scattered and absorbed) through vegetation medium and received by GPS receivers. Simulation results show that wheat will decrease the amplitudes of GPS multipath observables, if we increase the vegetation moisture contents or the scatters sizes (stem or leaf), the amplitudes of GPS multipath observables (SNR, phase and code) decrease. Although the Specular-Ground component dominates the total specular scattering, vegetation covered ground soil moisture has almost no effects on the final multipath signatures. Our simulated results are consistent with published results for environmental parameter detections with GPS-MR.

In the present study, we derive a new B-spline technique namely trigonometric B-spline collocation algorithm to solve some initial boundary value problems for the nonlinear Klein-Gordon equation. In order to carry out the time integration with Crank-Nicolson implicit method, the order of the equation is reduced to give a coupled system of nonlinear partial differential equations. The collocation approximation based on trigonometric cubic B-splines for spatial discretization is followed by the linearization of the nonlinear term. The efficiency and accuracy of the present method are validated by measuring the error between the numerical and analytical solutions when exist. The conservation laws representing momentum and energy are also computed for all problems.

Chitosan (CS) nanoparticles are under investigation for a wide range of applications in nanomedicine. The structural, molecular and physicochemical properties of chitosan nanoparticles have a direct bearing on their efficacy in drug conjugation and delivery, gene delivery, and tissue engineering. Herein we report on the structural, morphological and molecular properties of chitosan nanoparticles synthesized using the ionic gelation method with the intended purpose of being used for drug delivery. The chitosan nanoparticles (CS-NPs) were prepared in the 0.25 to 1.0% w/v concentration range, whereas separate samples of the 1.0% w/v CS-NPs were also functionalized with polyethylene oxide (PEO) alone and with a diblock copolymer of PEO and polypropylene glycol (PPG). The average size of the CS-NPs was determined from TEM imaging to be in the range of 11.3 to 14.8 nm. The XRD and TEM analyses show that the CS-NPs have semi-crystalline structure with the degree of crystallinity depending upon the nature of synthesis. Our results show that functionalizing the 1.0% w/v CS-NPs with PEO increases the degree of crystallinity whereas functionalizing with the diblock copolymer PEO - PPG results in a significant increase in their degree crystallinity. The CS/TPP concentration (CS:TPP fixed at 1:1 ratio) had no apparent effect on the degree of crystallinity of the CS-NPs. The results from the FTIR analysis confirm incorporation of TPP with CS in the CS-NPs. Additionally, FTIR analysis shows an enhancement of hydrogen bonding that is consistent with the increase in the degree of crystallinity of the CS-NPs.

We review time expansion wave theory and refine our model showing it to accurately match observed cosmological luminosity data. The theory augments general relativity to create a container within which quantum effects can be explained by treating time as an artefact of a fourth spatial dimension that we observe as the expansion of the universe. This leads us to explain mass creation, the speed of light limit, gravity, black holes without singularities and other macroscopic effects. Our model leads to an expansion velocity of 6.87 0.36 × 106 ms-1, which results in a Hubble expansion rate constant of 71.3 3.7 km/s/Mpc. Because of the finite window of time in which we exist, an extra a degree of freedom is available leading to interesting interpretations at the subatomic level. At this size range, then a spin is allowed within the time dimension explaining why wave particle duality occurs and explains the electromagnetic force and other quantum mechanical properties. It provides a solution to the double slit conundrum and can explain how quantum entangled partners can behave in a quantum way and pass seemingly time-defying information. The potential quantitative origin of the fine structure constant which governs the size of the electromagnetic force is also strongly indicated by this theory.

As matrix representations of magic labelings of related hypergraphs, magic squares and their various variants have been applied to many domains. Among various subclasses, trimagic squares have been investigated for over a hundred years. The existence problem for trimagic squares with singly even orders and orders 16n has been solved completely. However, very little is known for the existence of trimagic squares with other even orders except for the only three examples and three families. We construct normal trimagic squares by using product constructions, row-square magic rectangles, and trimagic pairs of orthogonal diagonal Latin squares. We give a new product construction: For positive integers p, q, and r having the same parity other than 1, 2, 3, 6, if normal p × q and r × q row-square magic rectangles exist, then a normal trimagic square with order pqr exists. As its application, we construct normal trimagic squares of orders 8q^3 and 8pqr for all odd integers q not less than 7 and p,r ∈ {7, 11, 13, 17, 19, 23, 29, 31, 37}. Our construction can easily be extended to construct multimagic squares.

The wealth of data obtained during the past 20 years using Laser-Induced Breakdown Spectroscopy (LIBS) indicates that the technique is very promising to detect small chemical contents of alloying elements. The potential of LIBS was looked more seriously during the past two decades or so as more data were obtained on Aluminum and steel to study the phenomena in the condition of local thermodynamic equilibrium and time-delay between a Q-switch laser and an intensified CCD camera. Since the past decade, some data on compounds were also shown to be useful in determining small concentrations of harmful elements. This manuscript is intended to show that the technique of LIBS performance is very promising in fields such as micro-machining, in alloying element analysis, surface cleaning and environmental applications even with lightweight spectrometers having a relatively low resolution, which can potentially be air-borne.

Soccer is the leading cause of all sports-related ocular injuries in Europe and Israel and leads to blindness at a disproportionately high rate, especially among children (Thompson et al., 2019). With soccer being the most popular sport in the world, it is surprising the only solution to ocular injuries are sports glasses which can cause direct damage to the eye and impair peripheral vision by 15%, calling for an alternative (Smith & Jones, 2020). This work, based on an imported facial model, focuses on both the qualitative and quantitative aspects of building a personalized, low-cost (through optimizing material needed), superior apparatus to conventional sports glasses. The quantitative side examines a modified and model-validated (through a SRS of thirty unique extrapolated points) multivariate linear regression equation, based on horizontal and vertical rotation angles (n=60) trained with residual and computer simulation data, that can accurately extrapolate and quantify ocular impact from all horizontal and vertical rotation angles and a modified Hertzian Contact Stress Equation to determine the thickness of the apparatus using the elasticity modulus, impact force, and geometrical facial and soccer-ball features. The qualitative side examines where firstly, ocular impact is most prevalent, and secondly, where most impact is seen from rotating the ball horizontally and vertically through analysis of Pearson’s Correlation Coefficient at the supraorbital, medial canthus, infraorbital, and lateral canthus regions from both regression equations as well as a cost-benefit analysis for comparison with conventional sports glasses. The findings discovered in this work lay the groundwork for future research to build a customized low-cost ocular injury prevention device which can simultaneously ensure complete ocular safety while enhancing athletic performance for over 250,000,000 players (Johnson & Garcia, 2022).

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.

The main idea of this paper is to investigate the exact solutions and dynamic properties in optical nanofibers, which is modeled by space-time fractional perturbed nonlinear schr\"odinger equation involving Kerr law nonlinearity with conformal fractional derivative. Firstly, by the complex fractional traveling wave transformation, the traveling wave system of the original equation is obtained, then a conserved quantity, namely the Hamiltonian is constructed, and the qualitative analysis of this system is conducted via this quantity by classifying the equilibrium points. Moreover, the prior estimate of the existence of the soliton and periodic solution is established via the bifurcation method. Furthermore, all exact traveling wave solutions are constructed to illustrate our results explicitly by the complete discrimination system for polynomial method.

Interaction of an electromagnetic field with matter in a laser cavity without the assumption of a fixed direction of the transverse electric field, described by the two-level Maxwell-Bloch equations, is studied. By using a perturbative nonlinear analysis, performed near the laser threshold, we report on the derivation of the laser (3+1)D vectorial complex cubic-quintic complex Ginzburg-Landau equation. Furthermore, we study the modulational instability of the plane waves both theoretically using the linear stability analysis, and numerically, using direct simulations via the split-step Fourier method. The linear theory predicts instability for any amplitude of the primary waves. Our numerical simulations confirm the theoretical predictions of the linear theory as well as the threshold of the amplitude of perturbations. The system understudy shows a deep dependence on the laser cavity parameters, for which there appear wave patterns in accordance with the predictions from the gain spectrum.

The Colebrook equation is a popular model for estimating friction loss coefficients in water and gas pipes. The model is implicit in the unknown flow friction factor . To date, the captured flow friction factor can be extracted from the logarithmic form analytically only in the term of the Lambert -function. The purpose of this study is to find an accurate and computationally efficient solution based on the shifted Lambert -function also known as the Wright -function. The Wright -function is more suitable because it overcomes the problem with the overflow error by switching the fast growing term of the Lambert -function to the series expansions that further can be easily evaluated in computers without causing overflow run-time errors. Although the Colebrook equation transformed through the Lambert -function is identical to the original expression in term of accuracy, a further evaluation of the Lambert -function can be only approximate. Very accurate explicit approximations of the Colebrook equation that contains only one or two logarithms are shown. The final result is an accurate explicit approximation of the Colebrook equation with the relative error of no more than 0.0096%. The presented approximations are in the form suitable for everyday engineering use, they are both accurate and computationally efficient.

The purpose of the research is to investigate the unique solvability of a nonlocal boundary value problem for a loaded equation of parabolic-hyperbolic type in a special domain. Methods: Using representations of a general regular solution, the existence and uniqueness of the problem posed is proved. Results: A new method for proving the unique solvability of nonlocal boundary value problems for one loaded equation of mixed type in a special domain has been formed and developed. Conclusions: The obtained results make it possible to solve some problems of genetics, immunology, transonic gas dynamics and thermal physics, which are associated with displacement.

Some qualitative results are provided on the cylindrical version of the Lane-Emden equation. Although the explicit form of the solution is not exactly known, we establish some properties on the critical points of the solution in some specific cases and we propose a technique to evaluate the distance between a pair of solutions in small intervals.

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

Einstein’s field equation is a highly general equation. However, the equation itself provides limited information about the universe unless it is solved with different boundary conditions. Multiple solutions have been utilized to predict cosmic scales, and among them, the Friedmann-Lemaître-Robertson-Walker solution that is the back-bone of the development into todays standard model of modern cosmology: the Λ-CDM model. However this is naturally not the only solution to Einsteins field equation. We will investigate the extremal solutions of the Reissner-Nordström, Kerr, and Kerr-Newman metrics. Interestingly, in their extremal cases, these solutions yield identical predictions for horizons and escape velocity. These solutions can be employed to formulate a new cosmological model that resembles the Friedmann equation. However, a significant distinction arises in the extremal universe solution, which does not necessitate the ad hoc insertion of the cosmological constant; instead, it emerges naturally from the derivation itself. To the best of our knowledge, all other solutions relying on the cosmological constant do so by initially ad hoc inserting it into Einstein’s field equation. This clarification unveils the true nature of the cosmological constant, suggesting that it serves as a correction factor for strong gravitational fields, accurately predicting real-world cosmological phenomena only within the extremal solutions of the discussed metrics, all derived strictly from Einstein’s field equation.

The use of allometric tools allows estimating the biomass of a plant species with greater precision. Tree roots are the least studied part of the vegetation due to the difficulty in obtaining complete root systems. For this reason, the objective was to generate an allometric model to estimate the amount of biomass accumulated in the root system of Abies religiosa trees in El Chico National Park, Hidalgo. For this purpose, 61 trees of A. religiosa were extracted from 0.06 to 3.56 m in height, using a backpack sprayer of pressurized water that detached the soil from the root. The response variable was root fresh weight and the independent variables were height, diameter and age+1, according to the fit of the models tested. Diameter was the variable with the best fit (r2 = 0.95 ± 0.04), obtaining the following equation PFR = (20.918 + D (2.4475)). The allometric model accurately estimates the below-ground biomass contained in the roots, which will allow us to obtain the complete biomass of an A. religiosa forest by having access to data on both the aerial and root components.

The main objective of this study is to apply structural equation modeling with partial least squares and based on covariance to assess the satisfaction of residential electricity consumers. The methodology used compares the results of both structural equation models to indicate the model that best fits the problem of measuring the satisfaction of residential consumers of electricity concessionaires and licensees. The sample used in the survey contained questionnaire responses from 86.175 individuals considering the period from 2014 to 2018. The constructs evaluated were satisfaction, quality, value, loyalty, and trust. Confidence interval analysis shows that all weights are significant, demonstrating the importance of all the indicators that represent the constructs. The trust, quality, and value constructs can explain 74.4% of the variability of the satisfaction construct, so the explanatory capacity of this relationship is considered substantial. Finally, the evaluation of the performance of the service provided by the electric energy concessionaires/licensees, measured by customer satisfaction, allows for the continuous improvement of services and meeting, even if minimally, the expectations of its consumers.

Our aim is to implement and test some less known numerical methods that might be used to solve an advection equation. The description is restricted to information necessary to implement and test the presented methods and it is given only for one-dimensional case.

In this study, a simple and direct numerical scheme is proposed for the similarity solution of Smoluchowski coagulation equation based on Taylor series expansion method of moment. The results show that the present method is convergence with high accuracy by comparison with previous work in the literatures.

Many causal factors to marine traffic accidents (MTA) influence each other and have associated effects. It is necessary to quantify the correlation path mode of these factors to improve accident prevention measures and their effects. In the application of human factors to the accident mechanisms, the complex structural chains on causes to MTA systems were analyzed combining the Human Failure Analysis and Classification System (HFACS) with theoretical Structural Equation Modeling (SEM). First, the accident causation model was established as a human error analysis classification in sight of MTA, and the constituent elements of the causes of accident was conducted. Second, a hypothetical model of Human factors classification was proposed applying the practice of the structural model. Third, with the data resource from ship accident cases, this hypothetical model was discussed and simulated, and as a result the relationship path dependency mode between the latent independent variable of the accident was quantitatively analyzed based on the observed dependent variable of human behaviors. Application examples show that relationships in HFACS are verified and in line with the path developing mode, and resource management factors have a pronounced influence and a strong relevance to the causal chain of the accidents. Appropriate algorithms for the theoretical model can be used to numerically understand the safety performance of marine traffic systems under different parameters through mathematical analysis. Hierarchical assumptions in the HFACS model are quantitatively verified.

Existing research indicates that mineralization of Carlin-type gold deposit is related to geological structures, but current studies mostly focus on the qualitative association, and lack quantitative analysis of the relationship between mineralization and structural features, which limits the potential for predictive mineral exploration. In this study, the Nibao Carlin-type gold deposit was selected as the research area to conduct three-dimensional geological modeling, spatial analysis, and three-dimensional prospectivity modeling. Spatial analysis revealed that the majority of gold ore bodies are situated near the main fault, with gold mineralization primarily occurring within a spatial range of approximately -80 meters to 20 meters from the main fault plane. This spatial distribution predominantly aligns in a SW-NE direction. Spatial characteristic extraction of fault slope indicators suggests that the slope angles are conducive to the migration and accumulation of ore-forming hydrothermal fluids, with ore body metal content rapidly increasing within an angle range of approximately 20° to 60°. The shape analysis of the mainfault indicates that the principal spaces of mineralization enrichment are within -10m to 20m of the fault plane undulations, where gold resources are concentrated in a relatively flat area. However, the degree of mineralization is more pronounced in the protruding sections than in the depressed areas. The areas with significant dip changes in faults display higher variations in orebody attitudes, with mineralization noticeably weaker in areas where the fault steepness changes markedly. Ore-bearing units exhibit significantly higher grades within the -17° to 3° interval of fault steepness transition. This interval also sees a rapid accumulation of gold resources. The Nibao gold mine's mineralization is derived from deep, ore-bearing hydrothermal fluids ascending along major fractures, precipitating, and accumulating in favorable ore-hosting spaces (faults, anticline cores) and lithological combinations (sedimentary tuffs, tuffs). Three deep potential gold targets were identified, highlighting the deep western edge of the F1 fault and the deep southeast-trending lower plate as prospective areas for future exploration. This study underscores the effectiveness of 3D prospective modeling as an indispensable tool for elucidating the spatial distribution of fault-controlled Carlin-type gold deposits and their tectonic determinants.

The spectra and global distributions of the X-ray emissions generated by the solar wind charge-exchange (SWCX) process in the terrestrial magnetosheath are investigated based on a global hybrid model and a global geocoronal hydrogen model. The solar wind O6+ ions which are the primary charge state for oxygen ions in solar wind are considered. The line emissivity of the charge-exchange born O5+ ions are calculated by Spectral Analysis System for Astrophysical and Lab oratory (SASAL). It is found that the emission lines from the O5+ ranges from 105.607 to 118.291 eV with the strong line at 107.047 eV. We then simulated the magnetosheath X-ray emission intensity distributions with a virtual camera at two positions of north pole and dusk at six stages during the passing of a perpendicular interplanetary shock combined with a tangential discontinuity structure through the Earth’s magnetosphere. During this process, the X-ray emission intensity increases with time, and the maximum value is 27.11 keV cm-2 s-1 sr-1 on the dayside, which is 4.5 times that before the solar wind structure reaches the Earth. A clear shock structure can be seen in the magnetosheath and moves earthward. The maximum emission intensity seen at dusk is always higher than that seen at north pole.

The chiral optical Tamm state (COTS) is a special localized state at the interface of a handedness-preserving mirror and a structurally chiral medium such as a cholesteric liquid crystal or a chiral sculptured thin film. The spectral behavior of COTS, observed as reflection resonances, is described by the temporal coupled-mode theory. Mode coupling is different for two circular light polarizations because COTS has a helix structure replicating that of the cholesteric. The mode coupling for co-handed circularly polarized light exponentially attenuates with the cholesteric layer thickness since the COTS frequency falls into the stop band. Cross-handed circularly polarized light freely goes through the cholesteric layer and can excite COTS when reflected from the handedness-preserving mirror. The coupling in this case is proportional to anisotropy of the cholesteric and theoretically it is only anisotropy of magnetic permittivity that can ultimately cancel this coupling. These two couplings being equal results in a polarization crossover (the Kopp--Genack effect) for which a linear polarization is optimal to excite COTS. The corresponding cholesteric thickness and scattering matrix for COTS are generally described by simple expressions.

Up to now, Schrödinger equation, Klein-Gordon equation (KGE) and Dirac equation are believed the fundamental equations of quantum mechanics. Schrödinger equation has a defect that there is no NKE solutions. Dirac equation has positive kinetic energy (PKE) and negative kinetic energy (NKE) branches. Both branches should have low momentum, or nonrelativistic, approximations: one is Schrödinger equation and the other is NKE Schrödinger equation. KGE has two problems: it is an equation of second time derivative, and calculated density is not definitely positive. To overcome the problems, it should be revised as PKE and NKE decoupled KGEs. The fundamental equations of quantum mechanics after the modification have at least two merits. They are of unitary in that everyone contains the first time derivative and are symmetric with respect to PKE and NKE. This reflects the symmetry of the PKE and NKE matters, as well as matter and dark matter, of our universe. The problems of one-dimensional step potentials are resolved by means of the modified fundamental equations for a nonrelativistic particle.

The equation of state of asymmetric nuclear matter as well as the neutron and proton effective masses and their partial-wave and spin-isospin decomposition are analyzed within the Brueckner–Hartree–Fock approach. Theoretical uncertainties for all these quantities are estimated by using several phase-shift-equivalent nucleon-nucleon forces together with two types of three-nucleon forces, phenomenological and microscopic. It is shown that the choice of the three-nucleon force plays an important role above saturation density, leading to different density dependencies of the energy per particle. These results are compared to the standard form of the Skyrme energy-density functional and we find that it is not possible to reproduce the BHF predictions in the (S,T) channels in symmetric and neutron matter above saturation density, already at the level of the two-body interaction, and even more including the three-body interaction.

Introduction: Heat is a kinetic process whereby energy flows from between two systems; hot-to-cold objects. In oro-dental implantology, conductive heat transfer/(or thermal stress) is a complex physical phenomenon to analyze and consider in treatment planning. Hence, ample research has attempted to measure heat-production to avoid over-heating during bone-cutting and -drilling for titanium (Ti) implant-site preparation and insertion, thereby preventing/minimizing early (as well as delayed) implant-related complications and failure. Objective: Given the low bone-thermal conductivity whereby heat generated by osteotomies is not effectively dissipated and tends to remain within the surrounding tissue (peri-implant), increasing the possibility of thermal-injury; this work attempts to obtain an exact analytical solution of the heat equation under exponential thermal-stress, modeling transient heat transfer and temperature changes in Ti implants upon hot-liquid intake. Materials and Methods: We investigate the impact of the material, the location point along implant length, and the exposure time of the thermal load on temperature changes. Results: Despite its simplicity, the presented solution contains all the physics and reproduces the key features obtained in previous numerical analyses studies. To the best of knowledge, this is the first introduction of the intrinsic time, a “proper” time that characterizes the geometry of the dental implant, where we show, mathematically and graphically, how the interplay between “proper” time and exposure time influences temperature changes in Ti implants, under the suitable initial and boundary conditions. Conclusions: This work aspires to accurately complement the overall clinical diagnostic and treatment plan for enhanced bone-implant interface, implant stability and success rates, whether for immediate or delayed loading strategies.

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.

Density distribution function of classical statistical mechanics is generally generalized as a product of a general complex function and its complex Hermitian conjugate function, and the average of classical statistical mechanics is generalized as the average of the quantum mechanics. Furthermore, this paper derives three ones of the five axiom presumptions of quantum mechanics, e.g., deduces Schrȍdinger equation by two general ways, makes the three axiom presumptions into three theorems of quantum mechanics, not only solves the crisis to hard understand, but also gets new theories and new discoveries, e.g., this paper solves the crisis of the origin of the wave-particle duality, derives operators, eigenvalues and eigenstates, deduces commutation relations for coordinate and momentum as well as the time and energy, and discovers quantum mechanics is just a generalization ( mechanics ) theory of the complex square root of ( real density function of ) classical statistical mechanics. Quantum mechanics being just a generalization theory of the complex square root of classical statistical mechanics is both new physics and revolutionary discovery, which are affecting people’s deep philosophical thinking for modern physics development, solve all the crisises of quantum mechanics, quantum information and so on, and make quantum mechanics have scientific solid bases being checked and both no basic axiom presumption and no all the quantum strange incomprehensible properties, because classical statistical mechanics and the complex square root of classical statistical mechanics have the scientific solid bases being checked. In addition, this paper discovers the reason no taking the time derivative of space coordinates in Schrȍdinger equation. Therefore, this paper gives solution to the crisis of the first quantization origin, and mainly deduces quantum physics no all the quantum current strange incomprehensible properties.

This paper aims to propose improvements for plastic waste management in Salvador – the Brazilian third most populated metropolis – via Partial Least Squares Structural Equation Modeling (PLS-SEM). All indicators, constructs, and hypotheses regarding collection, sorting, recycling, and disposal in the proposed PLS model were derived from the literature review, and the dependence of the performance construct on efficiency, effectiveness, municipality's socioeconomic aspects and municipality infrastructure is evaluated. Academic and practitioner publics were surveyed, and after analysis in both SmartPLS and RStudio software, suggestions for improvement regarding plastics recycling rate, market maturity, and infrastructural aspects for optimized reverse logistics were made. Since almost double the minimum number of respondents answered the survey questionnaire and the PLS-SEM statistics showed that the modeling presents consistency, the discussion is relevant. The model can and will evolve, but examples of suggested improvement are the installation of Deposit-Return Systems (DRS) in parks, streets, and avenues for increasing selective collection and the direct purchasing of waste from residents by municipal administration, compensating them with vouchers for food. The model can be a basis for other cities worldwide sharing analogous characteristics. By considering it, organizations can contribute to both reduced Greenhouse Gas (GHG) emissions and reduced terrestrial 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.

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

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

In this paper we totally discard the traditional trial-and-error algorithms of choosing acceptable shape parameter c in the multiquadrics $-\sqrt{c^{2}+\|x\|^{2}}$ when dealing with differential equations. Instead, we choose c directly by the MN-curve theory and hence avoid the time-consuming steps of solving a linear system required by each trial of the c value in the traditional methods. The quality of the c value thus obtained is supported by the newly born choice theory of the shape parameter. Experiments show that the approximation error of the approximate solution to the differential equation is very close to the best approximation error among all possible choices of c.

In this paper, the functional variable method is used to establish solitary wave solutions and periodic wave solutions of the loaded quadratic non-linear Klein-Gordon equation, the loaded cubic non-linear Klein-Gordon equation and the loaded coupled non-linear Klein-Gordon equation. All solutions of these equations have been examined and three dimensional graphics of the obtained solutions have been drawn by using the Matlab software. The main advantage of the proposed functional variable method over other methods is that it provides more new exact traveling wave solutions along with additional free parameters. The graphical representations of the soliton solutions and the periodic wave solutions by using distinct values of random parameter are demonstrated to better understand their physical features. The exact solutions have its great importance to reveal the internal mechanism of the physical phenomena.

The objective of this paper is to investigate the convergence of coupling-parameter expansion-based solutions to Ornstein-Zernike equation in liquid state theory. The analytically solved Baxter's adhesive hard sphere model is analyzed first using coupling-parameter expansion. It is found that the expansion provides accurate approximations to solutions - including the liquid-vapor phase diagram - in most parts of the phase plane. However, it fails to converge in the region where the model has only complex solutions. Similar analysis and results are, then, obtained using analytical solutions within the mean spherical approximation for the hard-core Yukawa potential. Next, convergence of the expansion is analyzed for the Lennard-Jonnes potential using an accurate density-dependent bridge function in the closure relation. Numerical results are presented which show convergence of correlation functions, compressibility versus density profiles, etc., in the single as well as two phase regions. Computed liquid-vapor phase diagrams, using two independent schemes employing the converged profiles, compare excellently with simulation data. Results obtained for the generalized Lennard-Jonnes potential, with varying repulsive exponent, also compare well with simulation data. All these results together establish the coupling-parameter expansion as a practical tool for studying single component fluid phases modeled via general pair-potentials.

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.

In this paper, we investigate an analytical solution of a class of nonlinear fractional integro-differential equation base on a generalized fractional power series expansion. The fractional derivatives are described in the conformable's type. The new approach is a modified form of the well-known Taylor series expansion. The illustrative examples are presented to demonstrate the accuracy and effectiveness of the proposed method

The Colebrook equation ζ is implicitly given in respect to the unknown flow friction factor λ ; λ=ζ(Re,ε*,λ) which cannot be expressed explicitly in exact way without simplifications and use of approximate calculus. Common approach to solve it is through the Newton-Raphson iterative procedure or through the fixed-point iterative procedure. Both requires in some case even eight iterations. On the other hand numerous more powerful iterative methods such as three-or two-point methods, etc. are available. The purpose is to choose optimal iterative method in order to solve the implicit Colebrook equation for flow friction accurately using the least possible number of iterations. The methods are thoroughly tested and those which require the least possible number of iterations to reach the accurate solution are identified. The most powerful three-point methods require in worst case only two iterations to reach final solution. The recommended representatives are Sharma-Guha-Gupta, Sharma-Sharma, Sharma-Arora, Džunić-Petković-Petković; Bi-Ren-Wu, Chun-Neta based on Kung-Traub, Neta, and Jain method based on Steffensen scheme. The recommended iterative methods can reach the final accurate solution with the least possible number of iterations. The approach is hybrid between iterative procedure and one-step explicit approximations and can be used in engineering design for initial rough, but also for final fine calculations.

In Mexico viticulture represents the second source of employment in the agricultural area after the fruit and vegetable sector. In developed countries, remote sensing is widely used for vineyard monitoring, however, this tool is barely used in developing countries of Iberoamerica. In this re-search, our overall objective is to characterize two vineyards in the state of Queretaro (Mexico) using Sentinel-2 and meteorological data, specifically spectral and thermal indices. Results showed that spectral indices obtained from Sentinel-2 bands have characterized adequately the phenolog-ical evolution of the different varieties of the vineyards. The Modified Soil-Adjusted Vegetation Index (MSAVI) was adequately used to discriminate the first stages of vineyards, while the Nor-malized Difference Vegetation Index (NDVI) was useful to monitor vineyards during the rest stages of vineyards. Thermal indices have shown that the best grape varieties were those that can adapt to both cooler and warmer temperatures, have a reasonable ripening period, and can produce wines with balanced acidity and flavors. In conclusion, the combination of meteorological (including thermal indices) and remote sensing data (NDVI and MSAVI) provide information for choosing the suitable grape variety for this region.

κ Draconis is a binary system with a classical Be star as the primary component. Its emission-line spectrum consists of hydrogen lines, notably the Hα line with a peak intensity ratio (V/R) variations phase-locked with the orbital period P = 61.55 days. Among binaries demonstrating the Be phenomenon, κ Dra stands out as one of a few systems with a discernible mass of its secondary component. Based on more than 200 spectra obtained in 2014 − 2023, we verified the physical parameters and constructed the mass function. We used part of these data obtained in 2014 − 2021 to investigate regions in the circumstellar disk of the primary component that emit the Hα line using the Doppler tomography method. The results show that the disk has a non-uniform density distribution with a prominent enhancement at Vy≈ 99 km s−1 and Vx≈−6 km s−1 that corresponds to a cloud-like source of the double-peaked Hα line profile. We argue that this enhancement’s motion is responsible for the periodic variations of the Hα V/R ratio, which is synchronised in orbital phase with the radial velocity (RV) of absorption lines from the atmosphere of the primary component.

This article utilizes the Canny edge extraction algorithm based on contour curvature and the cross-correlation template matching algorithm to extensively study the impact of high-repetition-rate CO2 pulsed Laser on the target extraction and tracking performance of the infrared imaging detector. It establishes a quantified dazzling pattern for lasers on infrared imaging systems. By conducting laser dazzling and damage experiments, a detailed analysis of the normalized correlation between target and dazzling images is performed to quantitatively describe laser dazzling effects. Simultaneously, an evaluation system, including target distance and laser power evaluation factors, is established to determine the dazzling level and whether the target is recognizable. The research results reveal that laser power and target position are crucial factors affecting the detection performance of infrared imaging-guided weapon systems under laser dazzling. Different laser powers are required to successfully interfere with the recognition algorithm of infrared imaging-guided weapons at different distances. And laser dazzling will produce a lot of false edge information, which seriously affects the performance of pattern recognition algorithm. In laser damage experiments, the detector experienced functional damage, with a quarter of the image displaying as completely black. The energy density threshold required for functional damage to the detector is approximately 3 J/cm2. The dazzling assessment conclusions also apply to evaluating damage results. Finally, the proposed evaluation formula aligns with experimental results, objectively reflecting the actual impact of laser dazzling on the target extraction and tracking performance of infrared imaging systems. This study provides an in-depth and accurate analysis for understanding the influence of lasers on the performance of infrared imaging-guided weapons.

Potential dependent special relativity and Gauss's law for the electric field have been used for gravity by assuming vacuum energy to be generated when the energy is a minimum useful expression for vacuum energy has been found. This expression shows that elementary particles are generated by gravity vacuum filling their hollow balls; using Schrödinger equation for spherically symmetric particles vacuum energy is quantized. Treating mass as vibrating spheres thus solving Schrödinger, coordinate harmonic oscillator energy relation has been found.

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

The fear of missing out (FoMO) is characterized in the literature as a fear that others are having rewarding experiences while one is missing out, and a constant need to keep connected with one’s social network. Driven by Social Determination Theory (SDT) FoMO has been linked with Problematic Social Networking Sites use (PSNSU), negative affectivity (NA), self-esteem (SE) and sleep disturbances. The present study reports findings from 512 individuals (79.1% women, mean age 30.5 years, SD= 8.61). Structural equation modelling (SEM) suggests that the duration of SNSs use and the numbers of SNSs platforms actively used partially mediated the relationship between FoMO and PSNSU. In turns, PSNSU partially mediated the relationship between FoMO and NA. Furthermore, the present study has extended the literature by incorporating the Vulnerability Model in the FoMO concept, identifying that SE partially mediated the relationship between FoMO and NA, while NA fully mediated the relationship between FoMO and sleeping disturbances. Accordingly, the present has extended previous research findings in showing exercise as a potential protective factor to prevent against FoMO. Practical and theoretical implications are discussed.

The problem of Yukawa couplings being arbitrary parameters in the Standard Model Higgs mechanism is a long standing one due to their formulaic dependence on the Higgs Vacuum Expectation Value. We will attempt to solve this problem and provide a strong argument that the Yukawa couplings of charged leptons and down type quarks are not arbitrary parameters in the SM. A new methodology for predicting the Yukawa couplings will be presented by using Compton wavelengths, the Rydberg Constant and g-factors of charged leptons instead of relying on the Higgs VEV. We will then proceed to rewrite this new method in terms of an empirical formula that depends on the running of the fine-structure constant on the Q scale, charge and lepton quantum numbers and g-factors to predict the values of the Yukawa couplings for all three generations of charged leptons and d-type quarks. We will also touch on the subject of neutrinos both as Majorana and Dirac fermions respectively and make a prediction for the lightest possible Majorana neutrino and the differences between Dirac neutrinos and anti-neutrinos. We conclude that the Yukawa couplings are not arbitrary parameters in the SM and that this new formula provides very accurate results.

Based on our recent thermodynamic formulation of the Friedmann equation, we demon- strate how the age of the universe must be approximately 14.6 billion years. This is about 800 million years older than predicted by the Λ-CDM model and therefore greatly alleviates the early galaxy formation problem.

In this paper, we establish the necessary and sufficient conditions for solving a dual split quaternion matrix equation AXB=C, and present the general solution expression when solvability is achieved. As an application, we delve into the necessary and sufficient condition for the existence of Hermitian solution to this equation by using a newly defined real representation method. Furthermore, we obtain the solutions for the dual split quaternion matrix equations AX=C and XB=C. Finally, we provide a numerical example to demonstrate the findings of this paper.

One objective of this paper is to investigate bifurcation of solutions of Ornstein-Zernike equation in liquid state theory for the gas-liquid coexistence region of simple fluids. The analysis uses a discrete form of the Ornstein-Zernike equation in real space, together with a closure relation which provides nearly self consistent thermodynamic properties of fluids governed by interaction potentials like the Lennard-Jones potential. Accurate asymptotic forms of correlation functions are incorporated in the real space algorithm so as to mitigate the influence of cutoff length used in the discrete approximations. It is found that there is no spinodal on the vapor side on a sub-critical isotherm. But there are fold bifurcation points on the vapor and liquid sides together with a 'no-real-solution-region' in between. This is followed by a region of negative compressibility extending up to the spinodal on the liquid side. The emerging picture is quite similar to that in the case of the hypernetted-chain-closure. It is also found that complex solutions connect the physical solutions that exist outside the 'no-real-solution-region' as well as in region of negative compressibility. The second objective of the paper, in the light of bifurcation scenario, is to evolve an interpretation of the coupling-parameter expansion of correlation functions pertaining to the region of negative compressibility. It is shown that the expansion provides an accurate description of results of the restricted ensembles, implied in mean field theories and simulation methods. Bifurcation of singlet density to inhomogeneous distributions at a spinodal is also established using a simple equation, which uses the direct correlation function. Thus the paper reestablishes the fact that restriction to a homogeneous singlet density is the root cause of all inconsistencies found in the gas-liquid coexistence region.

In this paper we address the approximation of the coupling problem for the wave equation and Maxwell's equations of electromagnetism in the time domain in terms of the electric field, by means of a nodal linear finite-element discretization in space, combined with a classical'explicit finite-difference scheme for the time discretization. Our study applies to the particular case where the dielectric permittivity has a constant value outside a sub-domain, whose closure does not intersect the boundary of the domain where the problem is defined. Inside this sub-domain Maxwell's equations hold. Outside this sub-domain the wave equation holds, which may correspond to the Maxwell's equations with a constant permittivity under certain conditions. We consider as a model the case of first order absorbing boundary conditions. Optimal error estimates that hold in natural norms under reasonable assumptions are given, among which lies a typical CFL condition for hyperbolic equations.