Social media and other web 2.0 tools have provided users the platform to interact and also disclose personal information not only with their friends and acquaintances, but also with relative strangers with unprecedented ease. This has enhanced the ability of people to share more about themselves, their families, and their friends through a variety of media including text, photo, and video, thus developing and sustaining social and business relationships. The purpose of the paper is to identify the factors that predict self-disclosure on social networking sites within the Ghanaian context. Data was collected from 452 students in three leading universities in Ghana and analyzed with Partial Least Square-Structural Equation Modeling. Results from the study revealed that all variables in the proposed model with the exception of interaction and perceived control were significant predictors of self-disclosure with privacy risk being the most significant predictor. In all, the model accounted for 54.6 percent of the variance in self disclosure. The implications and limitations of the current study are discussed and directions for future research proposed.

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

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

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

We changed the symmetry of the Weak Force from SU(2) to the quaternion group $Q_8$, and found that spin spacetime separates into two complementary spaces: a spin polarization spacetime of even parity states, and a spin coherence space, in the $S^3$ hypersphere, of odd parity coherent states. Under the quaternion group, spin is a boson of spin 1 in free flight and a fermion of spin $\frac{1}{2}$ when measured. It immediately follows that neutrinos are not needed to balance spin and conserve energy in beta decay. Additionally, we find the boson electrons emitted in beta decay are odd to parity, leading to parity conservation even though the observed beta distribution is asymmetrical.

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

Sensory Processing Sensitivity (SPS) is a trait describing inter-individual differences in sensitivity to environments, both positive and negative ones. SPS has attracted growing societal interest. However, (neuro)scientific evidence is lagging behind. We critically discuss how to measure SPS, how it relates to other theories of Environmental Sensitivity and other temperament and personality traits, how SPS interacts with environments to influence (a)typical development, what the underlying aetiologies and mechanisms are, and its relation to mental disorders involving sensory sensitivities. Drawing on the diverse expertise of the authors, we set an agenda for future research to stimulate the field. We conclude that SPS is a heritable, evolutionarily conserved trait, linked to increased risk for psychopathology and stress-related problems in response to negative environments, as well as to greater benefits (e.g., intervention responsivity, positive mood) in positive environments. We need advances in objective assessment of SPS, understanding mechanisms, differentiating it from (seemingly) related mental disorders, to exploit the potential of SPS to improve mental health, preserve human capital, and prevent adverse effects.

In this review we collect some recent achievements in the accurate and efficient solution of the Nonlinear Schrödinger Equation (NLSE), with the preservation of its Hamiltonian structure. This is achieved by using the energy-conserving Runge-Kutta methods named Hamiltonian Boundary Value Methods (HBVMs) after a proper space semi-discretization. The main facts about HBVMs, along with their application for solving the given problem, are here recalled and explained in detail. In particular, their use as spectral methods in time, which allows efficiently solving the problems with spectral space-time accuracy.

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

Taste signaling is a complex process that is linked to obesity and its associated metabolic syndromes. The sweet taste is mediated through a heterodimeric G protein coupled receptor (GPRC) in a species-specific manner and at multi-tissue specific levels. The sweet receptor recognizes a large number of ligands with structural and functional diversities to modulate different amplitudes of downstream signaling pathway(s). The human sweet-taste receptor has been extremely difficult to study by biophysical methods due to inadequate methods for producing large homogeneous quantities of the taste-receptor protein and a lack of reliable in vitro assays to precisely measure productive ligand binding modes leading to activity upon their interactions with the receptor protein. We report a multimodal high throughput assays to monitor ligand binding, receptor stability and conformational changes to model the molecular interactions between ligand-receptor. We applied saturation transfer difference nuclear magnetic resonance spectroscopy (STD-NMR) complemented by differential scanning calorimetry (DSC), circular dichroism (CD) spectroscopy, and intrinsic fluorescence spectroscopy (IF) to characterize binding interactions. Our method using complementary NMR and biophysical analysis is advantageous to study the mechanism of ligand binding and signaling processes in other GPCRs.

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.

We study in this work a dilute granular gas immersed in a thermal bath made of smaller particles with nonnegligible masses as compared with the granular ones. The kinetic theory for this system is developed and described by an Enskog--Fokker--Planck equation for the one-particle velocity distribution function. Granular particles are assumed to have inelastic and hard interactions, losing energy in collisions as accounted by a constant coefficient of normal restitution. The interaction with the thermal bath is based on a nonlinear drag force plus a white-noise stochastic force. To get explicit results of the temperature aging and steady states, Maxwellian and first Sonine approximations are developed. The latter takes into account the coupling of the excess kurtosis with the temperature. Theoretical predictions are compared with direct simulation Monte Carlo and event-driven molecular dynamics simulations. While good results for the granular temperature are obtained from the Maxwellian approximation, a much better agreement, especially as inelasticity and drag nonlinearity increase, is found when using the first Sonine approximation. The latter approximation is, additionally, crucial to account for memory effects like Mpemba and Kovacs-like ones.

Background: The purpose was to develop a novel hypothetical method to increase the size of coronary arteries. Methods: In the long-term observation the coronary sizes were dilated in three unexpected scenarios. The coronary artery sizes were observed in patients with mitral stenosis (n=59) by angiogram prior to percutaneous balloon mitral valvuloplasty or valve replacement surgery for severe mitral stenosis. The coronaries of patients with patent ductus arteriosus who underwent surgical closure in the past (n=12) were examined by echocardiogram. Patients with renal failure on long-term dialysis through peripheral arterio-venous fistula without left ventricular hypertrophy (n=17) were studied by echocardiography. Normal age, weight and sex matched coronary sizes served as controls in the study. All these observations were made over a period of 11.5 years. Results: The sizes of coronaries in patients with mitral stenosis, patients who underwent closure for patent ductus arteriosus, and in patients on hemodialysis through arteriovenous fistulas were higher than normal controls (p<0.05, for all). A hypothetical model to increase the coronary sizes could be developed based on the analysis of the differential equations of Poiseuille’s. The proposed method is creating a peripheral arterio-venous fistula, which could be closed later electively by a percutaneous method/surgery. The closure time needs to be determined by experimental studies. The other methods could be a continuous exercise program or usage of beta-blockers. Conclusion: A novel hypothetical method of peripheral arteriovenous fistula formation could potentially increase the size of the coronaries, and this could be closed later.

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.

Metabolomics studies require a deep understanding of enzyme dynamics and their responses to environmental disturbances within a complex metabolic network. This paper presents a novel approach to modeling enzyme activity as a dynamic topological manifold, where each enzyme is represented as a node, and their interactions are described by differential equations. These equations account for both compensatory interactions and external perturbations, simulating how enzymes dynamically stabilize their activities in response to varying conditions. We explore the application of this model to visualize enzyme interactions, using graph theory to represent the network structure and color gradients to illustrate interaction intensities. Multiple disturbances are introduced to analyze the network's resilience and adaptability over time. The results provide insights into the compensatory mechanisms within enzymatic networks, offering a comprehensive visualization through both static and dynamic representations. Our approach allows for a better understanding of how enzymatic systems buffer against mutations and environmental stressors, contributing to the broader field of systems biology and metabolomics.

A methodology for selecting rational parameters of atmospheric aircrafts at the initial stages of design using an optimization algorithm of differential evolution and numerical mathematical modeling of aerodynamics problems is proposed. The technique involves the implementation of weight and aerodynamic balance in the main flight modes, has the ability to consider atmospheric aircrafts with one or two lifting surfaces, apply parallel calculations and automatically generate a three-dimensional geometric model of aircraft appearance based on the optimization results. A method for accelerating the process of optimizing the parameters of an aircraft in terms of take-off weight by more than three times by introducing a objective function into a set of design variables is proposed and demonstrated. The results of assessing the reliability of the used mathematical models of aerodynamics and the correctness of the calculation the objective function, taking into account various constraints, are presented. A comprehensive test of the performance and efficiency of the methodology is considered by solving demonstration problems to optimize more than ten main design parameters the appearance of two existing heavy-class unmanned aerial vehicles with known characteristics from open sources.

This research presents the design and characteristics of new wideband polarizer based on the square waveguide with irises. Matching and polarization characteristics of the polarizer have been simulated and optimized. Frequency dependences of the characteristics are presented. Developed polarizer can be applied in satellite information systems.

The study aimed to know the direct effect of strategic leadership on the quality of service represented by wireless communications services, in addition to knowing the indirect effect of strategic leadership on the quality of service when using performance as an intermediary variable. This research was conducted in government institutions in the Republic of Yemen. Represented by the offices of the Ministry of Communications and Information Technology in five Yemeni cities, it targeted senior management employees, boards of directors, and middle management concerned with strategic planning and strategic leadership. To measure and evaluate the factors of strategic leadership and service quality in Offices of the Yemeni Ministry of Communications Ministry of Communications and Information Technology of the Republic of Yemen. Moreover, performance. A questionnaire was formulated and distributed to the study sample, and data was collected through questionnaires for 150 individuals in some offices of the Yemeni Ministry of Communications. This study uses structural equation model analysis from the Partial Least Squares program through the Smart Plus 4 programs. The study reached a set of results, including that all models show a direct, positive and significant effect of strategic leadership on the quality of service represented by the quality of services in the offices of the Ministry of Communications. As well as the positive relationship between them, as well as the direct and positive impact of performance on the quality of service, as well as the positive and significant relationship between them. While the results indicated a positive and significant indirect effect of strategic leadership on service quality, there is also a positive and significant indirect relationship between strategic leadership on service quality when using performance as an intermediary variable.

The European Power Exchange has introduced day-ahead auctions and continuous trading spot markets to facilitate the insertion of renewable electricity. These markets are designed to balance excess or lack of power in short time periods, which leads to a large stochastic variability of the electricity prices. Furthermore, the different markets show different stochastic memory in their electricity price time series, which seem to be the cause for the large volatility. In particular, we show the antithetical temporal correlation in the intraday 15 minutes spot markets in comparison to the day-ahead hourly market. We contrast the results from Detrended Fluctuation Analysis (DFA) to a new method based on the Kramers–Moyal equation in scale. For very short term (< 12 hours), all price time series show positive temporal correlations (Hurst exponent H > 0.5) except for the intraday 15 minute market, which shows strong negative correlations (H < 0.5). For longer term periods covering up to two days, all price time series are anti-correlated (H < 0.5).

Recent astronomical observations with respect to measurements in distant supernovas, cosmic microwave background and weak gravitational lensing confirm that the Universe is undergoing a phase of accelerated expansion and it has been proposed that this cosmological behavior is caused by a hypothetical dark energy which has a strong negative pressure that allows explain the expanding universe. Several theoretical ideas and models related dark the energy includes the cosmological constant, quintessence, Chaplygin gas, braneworld and tachyonic scalar fields. In this paper, we have obtained new relativistic stellar configurations considering an anisotropic fluid distribution with a charge distribution which could represents a potential model of a dark energy star. In order to investigate the effect of a quadratic equation of state in this anisotropic model we specify particular forms for the gravitational potential that allow solving the Einstein-Maxwell field equations. For these new solutions we checked that the radial pressure, metric coefficients, energy density, anisotropy factor, charge density , mass function are well defined and are regular in the interior of the star. The solutions found can be used in the development of dark energy stars models satisfying all physical acceptability conditions but the causality condition and strong energy condition are violated. We expect that these models have multiple applications in astrophysics and cosmology.

The thymus hosts the development of a specific type of adaptive immune cells called T cells. T cells orchestrate the adaptive immune response through recognition of antigen by the highly variable T-cell receptor (TCR). T-cell development is a tightly coordinated process comprising lineage commitment, somatic recombination of Tcr gene loci and selection for functional, but non-self-reactive TCRs, all interspersed with massive proliferation and cell death. Thus, the thymus produces a pool of T cells throughout life capable of responding to virtually any exogenous attack while preserving the body through self-tolerance. The thymus has been of considerable interest to both immunologists and theoretical biologists due to its multiscale quantitative properties, bridging molecular binding, population dynamics and polyclonal repertoire specificity. Here, we review mathematical modelling strategies that were reported to help understand the flexible dynamics of the highly dividing and dying thymic cell populations. Furthermore, we summarize the current challenges to estimating in vivo cellular dynamics and to reaching a next-generation multiscale picture of T-cell development.

There are numerous approaches to model an influence of manufacturing parameters on the dissolution and disintegration of solid dosage forms. A modern approach for modelling and simulating complex and heterogeneous systems such as pharmaceutical tablets focuses on computationally-intensive finite-element or discreet element methods. Industrial challenges such as Process Analytical Technology (PAT) and Quality by Design are stimulating computer-based technologies to design, control and improve the quality of pharmaceutical compacts and their performance. In this study the disintegration and dissolution model based on the numerical solutions of the Noyes-Whitney equation and cellular automata supported disintegration model are proposed and evaluated. The results from in vitro release studies of the mefenamic acid formulations were compared to the calculated release patterns from the tablet structures obtained from microtomography experiments and the purely algorithmically created virtual tablets.

We delve into nonrelativistic quantum electrodynamics within a background magnetic field, ensuring gauge invariance via a vector potential. Our exploration extends to the Lagrangian, which incorporates electron self-interactions and electromagnetic field interactions. Through the path integral formalism, we elucidate the effective action, with a specific focus on the photon propagator and screening effects. Examining density and current components reveals Laurent expansions in the hydrodynamic limit. The equations of motion in real space are derived, leading to discussions on phenomena such as Poiseuille-like flow and the Navier-Stokes equation. To ground our theoretical framework at practical contexts, we consider applications such as the fluid dynamics at binary star systems. Depending on the velocity of the expelled fluid, our analysis allows for both nonrelativistic and relativistic treatments, providing a versatile tool for understanding the intricacies of fluid behavior at astrophysical scenarios. Additionally, we recognize that at the presence of a magnetic field, magnetohydrodynamics becomes crucial. While our current focus is at nonrelativistic quantum electrodynamics, the insights gained here contribute to a broader understanding, offering a comprehensive foundation for quantum electrodynamics analysis at diverse physical systems.

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

In crystal structure prediction, Newton's second law can always be applied to particles (atoms or ions) in a cell to determine their positions. However the values of the period vectors (crystal cell edge vectors) should be determined as well. Here we applied the dynamical equations of period vectors derived recently based on Newton's laws (doi:/10.1139/cjp-2014-0518) for that purpose, where the period vectors are driven by the imbalance between the internal and external pressures/stresses. For equilibrium states, they became equations of state, which essentially turn out the equilibrium conditions of crystals from mechanical point of view. For external pressure, by ignoring some effects, they reduced to the Mie-Gruneisen equation. Since the internal stress has both a full kinetic energy term and a full interaction term, the influences of both external temperature and stress/pressure on crystal structures can be calculated, then thermodynamical properties and processes were presented. Contrary to usual ideas, the equations show that pure harmonic vibrating phonons can result in thermal expansion in crystals when the external temperature is changed. Finally, crystal system collapse due to temperature and/or stress/pressure change was discussed.

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

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.

This manuscript presents a novel approach to estimating the potential within Schrödinger equations, with a particular focus on applications to the Navier-Stokes problem in fluid dynamics. By establishing new theoretical estimates, we delve into the intricate dynamics of fluid flow, aiming to unveil previously obscured aspects of the Navier-Stokes equations. Through a rigorous mathematical framework, we explore how these new potential estimates can provide a fresh perspective on fluid mechanics, contributing to the ongoing quest to solve some of its most persistent challenges.

This research provides a computationally efficient numerical tool for predicting 3-D turbulent flows over hydrofoils. It addresses a gap in existing numerical methods by extending the capabilities of the laminar VIScous Vorticity Equation (VISVE) solver to handle 3-D turbulent flow scenarios. The implementation integrates the k − ω SST model into the 3-D VISVE solver using the Finite Volume Method (FVM), extending its capability to handle turbulent flows. The turbulence model is also parallelized to improve computational efficiency. The application of the newly developed model to 3-D hydrofoil cases expands its scope and serves as preparatory work for future rotational propeller applications. Rigorous testing includes a convergence analysis concerning grid numbers and time step sizes, and validation against a Reynolds-Averaged Navier-Stokes (RANS) solver ensures the reliability and accuracy of the enhanced VISVE solver for turbulent flow simulations. The turbulent VISVE solver offers advantages such as reduced computational domain and costs through a vorticity-based approach. Turbulence concentration within boundary layers and free shear flows does not compromise the advantages of the small computational domain. The simplified meshing process, automatically generated by denoting the number of panels on the hydrofoil, makes the solver accessible for researchers and engineers.

A mathematical model that comprehensively captures the real behavior of riverbed deformation, encompassing all pertinent effects, is developed. The underwater slope reformation process, with the generatrix aligned along the flow velocity in the model, is considered. A numerical model is introduced to calculate the flow involving a deformable bottom, and the model's validation is established through rigorous analysis of experimental findings. The research firmly confirms the suitability of the proposed mathematical and numerical model for describing deformations in uneven and unsteady river flows, including the movement of dredging slots and channel quarries. The model's minimal equation count and reliance on empirical constants demonstrate the model's efficiency. The model's predictions align strongly with experimental data, although optimal values of empirical coefficients vary slightly across different experiments. Hence, there is a call for further investigation to derive more universally applicable closure relationships for the model. The importance of validating the model with reliable field data and its potential extension to accommodate hydraulically diverse soils is emphasized. Such an extension is feasible due to the concentration transfer equation, enabling independent calculations for particle fractions of varying sizes as long as the total particle concentration in the stream remains within reasonable limits. This dedicated research contributes significantly to understanding riverbed deformations and advancing accurate modeling and management of riverine environments.

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

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

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

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 nonlocal boundary value problem, dtρu(t)+Au(t)=f(t) (0&lt;ρ&lt;1, 0&lt;t≤T), u(ξ)=αu(0)+φ (α is a constant and 0&lt;ξ≤T), in an arbitrary separable Hilbert space H with the strongly positive selfadjoint operator A, is considered. The operator dt on the left hand side of the equation expresses either the Caputo derivative or the Riemann-Liouville derivative; naturally, in the case of the Riemann - Liouville derivatives, the nonlocal boundary condition should be slightly changed. Existence and uniqueness theorems for solutions of the problems under consideration are proved. The influence of the constant α on the existence of a solution to problems is investigated. Inequalities of coercivity type are obtained and it is shown that these inequalities differ depending on the considered type of fractional derivatives. The inverse problems of determining the right-hand side of the equation and the function φ in the boundary conditions are investigated.

The ordinary continuity equation relating the current and density of a system is extended to incorporate systems with dual (longitudinal and transverse) currents. Such a system of equations is found to have the same mathematical structure as that of Maxwell equations. The horizontal and transverse currents and the densities associated with them are found to be coupled to each other. Each of these quantities are found to obey a wave equation traveling at the velocity of light in vacuum. London's equations of super-conductivity are shown to emerge from some sort of continuity equations. The new London's equations are symmetric and are shown to be dual to each other. It is shown that London's equations are Maxwell's equations with massive electromagnetic field (photon). These equations preserve the gauge invariance that is broken in other massive electrodynamics. The duality invariance may allow magnetic monopoles to be present inside superconductors. The new duality is called the comprehensive duality transformation.

There is need to accurately design pipelines to transport the expected increase of CO₂ captured from industrial processes after the signing of the Paris Climate Agreement in 2016. This paper reviews several aspects of CO₂ pipeline design with emphasis on pressure drop and models for the calculation of pipeline diameter. Two categories of pipeline equations were identified. The first category is independent of pipeline length and has two different equations. This category is used to specify adequate pipeline diameter for the volume of fluid transported. The optimum economic pipe diameter equation (Eq. 17) with nearly uniform resultant velocity values at different flow rates performed better than the standard velocity flow equation (Eq. 20). The second category has four different equations and is used to calculate pipeline pressure drop or pipeline distance for the installation of booster stations after specifying minimum and maximum pipeline pressures. The hydraulic equation is preferred because it gave better resultant velocity values and the closest diameter value obtained using Aspen HYSYS (V.10) simulation. The effect of impurities on the pressure behaviour and optimal pipeline diameter and pressure loss due to acceleration were ignored in the development of the models. Further work is ongoing to incorporate these effects into the models.

Correlations between the air permeability coefficient and various pore structure indicators in cementitious materials were examined to determine the pore structure indicator that best evaluated air permeability using data from previous studies of air permeabilities and pore structures. The determination coefficients of air permeability with total pore volume, critical pore diameter, and ordinary threshold pore diameter were low, although these have often been used as indicators. The median and threshold pore diameters obtained by percolation theory showed high determination coefficients. The equation using the threshold pore diameter better estimated the air permeability coefficient than the Katz–Thompson equation.

Let $f\left(1\right)=1$ , and let $f(n+1)=2^{2^{f\left(n\right)}}$ for every positive integer n. We consider the following hypothesis: if a system S ⊆ {x_i · x_j = x_k : i, j, k ∈ {1, . . . , n}} ∪ {x_i + 1 = x_k : i, k ∈{1, . . . , n}} has only finitely many solutions in non-negative integers x₁, . . . , x_n, then each such solution (x₁, . . . , x_n) satisfies x₁, . . . , x_n ≤ f (2n). We prove: (1) the hypothesisimplies that there exists an algorithm which takes as input a Diophantine equation, returns an integer, and this integer is greater than the heights of integer (non-negative integer, positive integer, rational) solutions, if the solution set is finite; (2) the hypothesis implies that there exists an algorithm for listing the Diophantine equations with infinitely many solutions in non-negative integers; (3) the hypothesis implies that the question whether or not a given Diophantine equation has only finitely many rational solutions is decidable by a single query to an oracle that decides whether or not a given Diophantine equation has a rational solution; (4) the hypothesis implies that the question whether or not a given Diophantine equation has only finitely many integer solutions is decidable by a single query to an oracle that decides whether or not a given Diophantine equation has an integer solution; (5) the hypothesis implies that if a set $\mathfrak{M}$ ⊆ has a finite-fold Diophantine representation, then $\mathfrak{M}$ is computable.

A Natural gas is increasingly being sought after as a vital source of energy, given that its production is very cheap and does not cause the same environmental harms that other resources, such as coal combustion, do. Understanding and characterizing the behavior of natural gas is essential in hydrocarbon reservoir engineering, natural gas transport, and process. Natural gas compressibility factor, as a critical parameter, defines the compression and expansion characteristics of natural gas under different conditions. In this study, a simple second-order polynomial model based on the group method of data handling (GMDH) is presented to determine the compressibility factor of different natural gases at different conditions, using corresponding state principles. The accuracy of the model evaluated through graphical and statistical analyses. The results show that the model is capable of predicting natural gas compressibility with an average absolute error of only 2.88%, a root means square of 0.03, and a regression coefficient of 0.92. The performance of the developed model compared to widely known, previously published equations of state (EOSs) and correlations, and the precision of the results demonstrates its superiority over all other correlations and EOSs.

In this paper, we consider the effects of a radial electric field and a constant magnetic field induced by Lorentz symmetry violation on a generalized relativistic quantum oscillator by choosing a function f(r) = b1 r + b2/r in the equation subject to a Cornell-type potential S(r) = ηL r + ηc/ r introduce by modifying the mass term in the equation. We show that the analytical solutions to the Klein-Gordon oscillator can be achieved, and a quantum effect is observed due to the dependence of the angular frequency of the oscillator on the quantum numbers of the system

Fear extinction requires coordinated neural activity within the amygdala and medial prefrontal cortex (mPFC). Any behavior has a transcriptomic signature that is modified by environmental experiences, and specific genes are involved in functional plasticity and synaptic wiring during fear extinction. Here, we investigated the effects of optogenetic manipulations of prelimbic (PrL) pyramidal neurons on amygdala gene expression to analyze the specific transcriptional pathways involved in adaptive and maladaptive fear extinction. To this aim, transgenic mice were (or not) fear-conditioned and during the extinction phase they received optogenetic (or sham) stimulations over PrL pyramidal neurons. At the end of behavioral testing, electrophysiological (neural cellular excitability and Excitatory Post-Synaptic Currents) and morphological (spinogenesis) correlates were evaluated in the PrL pyramidal neurons. Furthermore, transcriptomic cell-specific RNA-analyses (differential gene expression profiling and functional enrichment analyses) were performed in amygdala pyramidal neurons. Our results show that the optogenetic activation of PrL pyramidal neurons in fear-conditioned mice induces fear extinction deficits, reflected in an increase of cellular excitability, excitatory neurotransmission, and spinogenesis of PrL pyramidal neurons, and in strong modifications of the transcriptome of amygdala pyramidal neurons. Understanding the electrophysiological, morphological and transcriptomic architecture of fear extinction may facilitate the comprehension of fear-related disorders.

In this paper, we study quantum gravity effect on the symmergent black hole which is derived from quadratic-curvature gravity. To do so, we use the Klein-Gordon equation which is modified by generalized uncertainty principle (GUP). After solving the field equations, we examine the symmergent black hole's tunneling and Hawking temperature. We explore the graphs of the temperature through the outer horizon to check the GUP influenced conditions of symmergent black hole stability. We also explain how symmergent black holes behave physically when influenced by quantum gravity. The impacts of thermal fluctuations on the thermodynamics of a symmergent black holes spacetime are examined. We first evaluate the model under consideration's thermodynamic properties, such as its Hawking temperature, angular velocity, entropy, and electric potential. We evaluate the logarithmic correction terms for entropy around the equilibrium state in order to examine the impacts of thermal fluctuations. In the presence of these correction terms, we also examine the viability of the first law of thermodynamics. Finally, we evaluate the system's stability using the Hessian matrix and heat capacity. It is determined that a stable model is generated by logarithmic corrections arising from thermal fluctuations.

In the upper charged layers of the atmosphere, the plasma is very rarefied. The collisions between its molecules are almost non-existent, and the driving forces behind them are the Lorentz forces resulting from the electric and magnetic fields. For this reason, we are interested in studying the behavior of non-collision plasmas because of its essential applications, such as the movement of satellites in the charged atmosphere. In this paper, the flow problem of collisionless gaseous plasma is examined. For that propose, we solve the unsteady Vlasov-Maxwell system of non-linear partial differential equations analytically. Methods of moments and traveling wave parameters are used to acquire an exact solution. Specific macroscopic properties of collisionless gaseous plasma are calculated along with electrical and magnetic fields. Further, thermodynamic estimation, such as entropy and entropy production, is presented. Those calculations allow us to measure the consistency with the laws of non-equilibrium thermodynamics. Relations between internal energy modification participations are predicted using Gibbs' equation for collisionless plasma. The modification effect of internal energies due to electro-magnetic fields is found to be small compared with the internal energy change due to the effect of entropy. That is because these fields are self-induced by plasma particles due to the sudden movement of the rigid plane plate. The results are accomplished according to the typical argon gaseous plasma model. Three-dimensional diagrams showing the measured variables are drawn to investigate and discuss their behavior. The problem has many commercial applications for the movement of objects in the charged atmosphere.

In this paper, we obtain the existence and uniqueness theorem for solutions of Caputo type fractional stochastic delay differential systems (FSDDSs) with Poisson jumps by utilizing delayed perturbation of Mittag-Leffler function. Moreover, by using Burkholder-Davis-Gundy's inequality, Doob's martingale inequality and Holder inequality, we prove that the solution of the averaged FSDDSs converges to that of the standard FSDDSs in the sense of Lp. Some known results in the literature are extended.

In the present work we study the existence of solutions for hybrid nonlinear fractional integrodifferential equations. We developed an algorithm by using the operator theoretical techniques in order to obtain the approximate solutions. The main results depend on the Dhage iteration method that were incorporated with the modern hybrid fixed point theorems. The approximate solutions were obtained by using Lipschitz conditions and weaker form of mixed partial continuity. Further, we provide some examples to explain the hypotheses and the related results.

We introduce the linear subgroup of volume-preserving diffeomorphism as the underlying symmetry to construct an action within the effective field theory framework and the Schwinger-Keldish formalism. The formulated action is posited to effectively incorporate dissipative effects into the Navier-Stokes equations.

In this work, we study a Klein-Gordon oscillator subject to Cornelltype potential in the background of the Lorentz symmetry violation determined by a tensor out of the Standard Model Extension. We introduce a Cornell-type potential S(r) = (η_L\,r + \frac{η_c}{r} ) by modifying the mass term via transformation $M → M + S(r)$ and then coupled oscillator with scalar particle by replacing the momentum operator $\vec{p}→ (\vec{p}+ i\,M\,ω\,\vec{r})$ in the relativistic wave equation. We see that the analytical solution to the Klein-Gordon oscillator equation can be achieved, and a quantum effect characterized by the dependence of the angular frequency of the oscillator on the quantum numbers of the relativistic system is observed

For the KdV-Burgers equations on cylindrical and spherical waves the development of a regular profile starting from an equilibrium under a periodic perturbation at the boundary is studied. The equations describe a medium which is both dissipative and dispersive. Symmetries, invariant solutions and conservation laws are investigated. For an appropriate combination of dispersion and dissipation the asymptotic profile looks like a periodical chain of shock fronts with a decreasing amplitude (sawtooth waves). The development of such a profile is preceded by a head shock of a constant height and equal velocity which depends on spatial dimension as well as on integral characteristics of boundary condition; an explicit asymptotic for this head shock and a median of the oscillating part is found.

A recently proposed classical field theory comprised of four field equations that geometrically couple electromagnetism and gravitation in a fundamentally new way is reviewed. The cornerstone of the theory equates the derivatives of the Maxwell tensor to a vector field contracted with the Riemann-Christoffel curvature tensor. The new theory’s field equations show little resemblance to the field equations of classical physics, but both Maxwell’s equations of electromagnetism and Einstein’s equation of General Relativity augmented by a term that can mimic the properties of dark matter and dark energy are shown to be a consequence. Emphasized is the unification brought to electromagnetic and gravitational phenomena as well as the consistency of solutions of the new theory with those of the classical Maxwell and Einstein field equations. Unique to the four field equations reviewed here and based on specific solutions to them are: the emergence of antimatter and its behavior in gravitational fields, the emergence of dark matter and dark energy mimicking terms in the context of General Relativity, an underlying relationship between electromagnetic and gravitational radiation, the impossibility of negative mass solutions that would generate repulsive gravitational fields or antigravity, and a method for quantizing the charge and mass of particle-like solutions.

Since crystals are made of periodic structures in space, predicting their three period vectors starting from any values based on the inside interactions is a basic theoretical physics problem. For the general situation where crystals are under constant external stress, we derived dynamical equations of the period vectors in the framework of Newtonian dynamics, for pair potentials recently (doi:/10.1139/cjp-2014-0518). The derived dynamical equations show that the period vectors are driven by the imbalance between the internal and external stresses. This presents a physical process where when the external stress changes, the crystal structure changes accordingly, since the original internal stress can not balance the external stress. The internal stress has both a full kinetic energy term and a full interaction term. It is extended to many-body interactions in this paper. As a result, all conclusions in the pair-potential case also apply for many-body potentials.

This work presents results of property researches of fabricated samples of silica few-mode optical fiber (FMF) with induced chirality under twisting 10 and 66 revolutions per meter, core diameter 11 µm, typical “telecommunication” cladding diameter 125 µm and improved height of quasi-step refractive index profile. Proposed FMF supports 4 guided modes over “C”-band. We represent results of computed characteristics, as well as experimentally measured spectral responses of laser-excited optical signals, including researches and analysis of few-mode effects, occurring after fiber Bragg grating writing.

The zero offset voltage in anti-aliasing low-pass filters (LPF) included at the ADC input has a significant effect on the effective bit rate of the ADC. The article discusses methods for minimizing the systematic component of the zero offset voltage (V_OS) of operational amplifiers (Op-Amp) in the structure of the LPF, due to the degradation of the current gain of the base (b) of bipolar transistors for an extremely common subclass of Op-Amp with one high-impedance node. The methods of matching a high-impedance Op-Amp node and a buffer amplifier with the help of special correcting SCM^p and SCMⁿ multipolars are proposed. Methods of description and formation of the given coefficients of weak current asymmetry of typical Op-Amp functional units (current mirrors, input DS, buffer amplifiers, SRC, etc.) are presented. As an example, the results of computer simulation of GaAs Op-Amp with small V_OS performed on JFET field and p-n-p bipolar transistors are given.

Transcriptional regulations have been widely studied as one of the main bridges between biology and other basic sciences as well as medicine. The traffic across it has been mostly unidirectional: chemistry and physics provided a lot of tools for biology, although the supply is now saturating. The traffic in opposite direction, the supply of subjects to develop chemistry and physics, has been only a little. However, if there are any, the supply will be at least from transcription, because the notion of chemical reaction is the strongest. This topic is aimed to increase the opposite traffic by introducing the forefront of physicochemical studies of transcription.

Protein import into the endoplasmic reticulum (ER) is the first step in the biogenesis of about 10,000 different soluble and membrane proteins in humans. It involves co- or post-translational targeting of precursor polypeptides to the ER and their subsequent membrane insertion or translocation. So far, three pathways for ER targeting of precursor polypeptides plus four pathways for ER targeting of mRNAs were described. Typically, these pathways deliver their substrates to the Sec61 polypeptide-conducting channel in the ER membrane. Next, the precursor polypeptides are inserted into the ER membrane or translocated into the ER lumen, which may involve auxiliary translocation components, such as the TRAP and Sec62/Sec63 complexes, or auxiliary membrane protein insertases, such as EMC and the TMCO1 complex. Recently, the PEX19/PEX3-dependent pathway, which has a well-known function in targeting and inserting various peroxisomal membrane proteins into pre-existent peroxisomal membranes, was also found to act in targeting and, putatively, inserting monotopic hairpin proteins into the ER. These either remain in the ER as resident ER membrane proteins or are pinched off from the ER as components of new lipid droplets. Therefore, the question arose if this pathway may play a more general role in ER protein targeting, i.e. represents a fourth pathway for ER targeting of precursor polypeptides. Thus, we addressed the client spectrum of the PEX19/PEX3-dependent pathway in both PEX3-depleted HeLa cells and PEX3-deficient Zellweger patient fibroblasts by an established approach, which involves label-free quantitative mass spectrometry of the total proteome of depleted or deficient cells and differential protein abundance analysis. The negatively affected proteins included twelve peroxisomal proteins and two hairpin proteins of the ER, thus confirming two previously identified classes of putative PEX19/PEX3-clients in human cells. Interestingly, fourteen collagen-related proteins with signal peptides or N-terminal transmembrane helices and belonging to the secretory pathway were also negatively affected by PEX3-deficiency, which may suggest compromised collagen biogenesis as a hitherto unknown contributor to organ failures in the respective Zellweger patients.

We show how the Poincar\'e--Riemann--Hilbert boundary-value problem enables us to construct effective estimates of the potential in the Schr\"odinger equation. The apparatus of the three-dimensional inverse problem of quantum scattering theory is developed for this. It is shown that the unitary scattering operator can be studied as a solution of the Poincar\'e--Riemann--Hilbert boundary-value problem. This allows us to go on to study the potential in the Schr\"odinger equation

A method is proposed for describing the dynamics of systems of interacting particles in terms of an auxiliary field, which in the static mode is equivalent to given interatomic potentials, and in the dynamic mode is a classical relativistic composite field. It is established that for interatomic potentials, the Fourier transform of which is a rational algebraic function of the wave vector, the auxiliary field is a composition of elementary fields that satisfy the Klein-Gordon equation with complex masses. The interaction between particles carried by the auxiliary field is nonlocal both in space variables and in time. The temporal non-locality is due to the dynamic nature of the auxiliary field and can be described in terms of functional-differential equations of retarded type. Due to the finiteness mass of the auxiliary field, the delay in interactions between particles can be arbitrarily large. A qualitative analysis of the dynamics of few-body and many-body systems with retarded interactions has been carried out, and a non-statistical mechanisms for both the thermodynamic behavior of systems and synergistic effects has been established.

The stability properties of the Hill equation are discussed, and especially those of the Mathieu equation that characterize ion motion in electrodynamic traps. The solutions of the Mathieu equation for a trapped ion are characterized by using the Floquet theory and Hill's Method solution, which yields an infinite system of linear and homogeneous equations whose coefficients are recursively determined. Stability is discussed for parameters $a$ and $q$ that are real. Characteristic curves are introduced naturally by the Sturm-Liouville problem for the well known even and odd Mathieu equations $ce_m(z,q)$ and $se_m(z,q)$. We illustrate the stability diagram for a combined (Paul and Penning) trap and represent the frontiers of the stability domains for axial and radial motion. In case of a Paul trap the stable solution corresponds to a superposition of harmonic motions. The problem of evaluating the maximum amplitudes of stable oscillations for the ideal conditions (taken into consideration) is also approached. Anharmonic corrections are discussed within the frame of the perturbation theory, while the frontiers of the modified stability domains are determined as a function of the chosen perturbation parameter. The results apply to 2D and 3D ion traps used for different applications in quantum engineering, among which optical clocks, quantum logic and quantum metrology, but not restricted only to these.

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

Contemporary theories of Universe, such as the Friedmann-Lemaître Robertson - Walker (FLRW) model of the cosmos, assume that space and time marches on at a uniform, constant pace from its beginning. But what if that is not the case? It is proposed that the big bang was not the first beginning of the Universe, but rather the Big Bang may have been just a particular moment in the evolution of this always-existing universe, not a true beginning. Universe started from the shortest meaningful length, Planck Length, and the shortest meaningful measure of time, Planck Time. The observed accelerated expansion, which relates the change in the space, to change in the stretching of shrink space for the new theory, is derived. As pressure of shrink space decreases, the expansion of space increases, that is although in general, decelerate in the pressure of shrink space leads to accelerate the stretching of space. (pressure of shrink space approaching zero at the end of accelerated expansion, or all the shrinked space stretches), no need however, for dark energy. The new definition of eternal space enables us to describe a sequence of events from the Big Bang to the Big Crunch.

Many authors proposed analytical methods for solving fully fuzzy Sylvester matrix equation (FFSME) based on Vec-operator and Kronecker product. However, these methods are restricted to nonnegative fuzzy numbers and cannot be extended to FFSME with near-zero fuzzy numbers. The main intention of this paper is to develop a new numerical method for solving FFSME with near-zero trapezoidal fuzzy numbers that provides a wider scope of trapezoidal fully fuzzy Sylvester matrix equation (TrFFSME) in scientific applications. This numerical method can solve the trapezoidal fully fuzzy Sylvester matrix equation with arbitrary coefficients and find all possible finite arbitrary solutions for the system. In order to obtain all possible fuzzy solutions, the TrFFSME is transferred to a system of non-linear equations based on newly developed arithmetic fuzzy multiplication between trapezoidal fuzzy numbers. The fuzzy solutions to the TrFFSME are obtained by developing a new two-stage algorithm. To illustrate the proposed method numerical example is solved.

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.

We consider a multitude of topics in mathematics where unification constructions play an important role: the Yang–Baxter equation and its modified version, Euler’s formula for dual numbers, means and their inequalities, topics in differential geometry, etc. It is interesting to observe that the idea of unification (unity and union) is also present in poetry. Moreover, Euler’s identity is a source of inspiration for the post-modern poets.

We derive time evolution equations, namely the Schrodinger-like equations and the Klein-Gordon equations for coherent fields and the Kadanoff-Baym (KB) equations for quantum fluctuations, in Quantum Electrodynamics (QED) with electric dipoles in 2 + 1 dimensions. Next we introduce a kinetic entropy current based on the KB equations in the 1st order of the gradient expansion. We show the H-theorem for the Leading-Order self-energy in the coupling expansion (the Hartree-Fock approximation). We show a conserved energy in the spatially homogeneous systems in the time evolution. We derive aspects of the super-radiance and the equilibration in our single Lagrangian. Our analysis can be applied to Quantum Brain Dynamics, that is QED with water electric dipoles. The total energy consumption to maintain super-radiant states in microtubules seems to be within the energy consumption to maintain the ordered systems in a brain.

This paper is a continuation of previous papers on unification theories publishes in AXIOMS. We present results about the (modified) Yang-Baxter equation, Euler’s formula, dual numbers, coalgebra structures, non-associative structures, differential geometry, and (mean) inequalities. We will also attempt to relate our discussion to some Brain Studies and Machine Learnig.

We consider several unification problems in mathematics. We refer to transcendental numbers. Also, we present some ways to unify the main non-associative algebras (Lie algebras and Jordan algebras) and associative algebras.

Today, two very efficient methods for calculation of flow distribution per branches of a looped gas pipeline are available. Most common is improved Hardy Cross method, while the second one is so-called unified node-loop method. For gas pipeline, gas flow rate through a pipe can be determined using Colebrook equation modified by AGA (American Gas Association) for calculation of friction factor accompanied with Darcy-Weisbach equation for pressure drop and second approach is using Renouard equation adopted for gas pipeline calculation. For the development of Renouard equation for gas pipelines some additional thermodynamic properties are involved in comparisons with Colebrook and Darcy-Weisbach model. These differences will be explained. Both equations, the Colebrook’s (accompanied with Darcy-Weisbach scheme) and Renouard’s will be used for calculation of flow through the pipes of one gas pipeline with eight closed loops which are formed by pipes. Consequently four different cases will be examined because the network is calculated using improved Hardy Cross method and unified node-loop method. Some remarks on optimization in this area of engineering also will be mentioned.

An inverse aeroacoustic problem for a helicopter rotor combined with aerodynamic constraint is proposed based on Ffowcs Williams and Hawkings equation in subsonic. The rotor noise includes thickness noise and loading noise when quadrupole noise is neglected. Thickness noise is related to geometry and motion conditions. Loading noise is related to the pressure on the wall. Therefore, the equation between pressure on the wall and far-field noise can be established, thus the pressure on the wall can be obtained by solving this equation. Since this equation is an ill-posed, the singular value decomposition combined with the regulation method is applied and the aerodynamic constraint is taken into account. The direct noise prediction is verify firstly and then the inverse problem is solved. The reconstruction pressure is compared to the input data. The result is in good agreement with the input value. At the same time, the influence of interference noise is also considered. Under low signal-to-noise ratio, the reconstruction result is also reasonable.

In this work, linear confinement of a relativistic scalar particle under the effects of Lorentz symmetry violation is investigated. We introduce a scalar potential by modifying the mass via transformation M → M + S(r) in the wave equation, and analyze the effects on the eigenvalues and the wave function. We see that the solution of the bound state to the wave equation can be achieved, and the energy eigenvalues and the wave function modified by the Lorentz symmetry breaking parameters as well as potential

We present a geometric field theory in which the action and field equation are constructed from an ultra-high-density vector field and its covariant derivative and have full general covariance in a higher-dimensional spacetime. The field equation is the simplest possible generalisation of the Poisson equation for gravity consistent with general covariance and the equivalence principle. It contains the Ricci tensor and metric acting as operators on the vector field. If the covariant derivative is diagonalisable across a neighbourhood under real changes of coordinate basis, spacetime coincides with a product manifold. The dimensionalities of the factor spaces are determined by its eigenvalues and hence by its algebraic invariants. Tensors decompose into multiplets which have both Lorentz and internal symmetry indices. The field equation has a `classical vacuum' solution which is a product of Minkowski spacetime and an Einstein manifold. A worked example is provided in six dimensions. Away from this classical vacuum, connection components in appropriate coordinates include $SO(N)$ gauge fields. The Riemann tensor includes their field strength. Unitary gauge symmetries act indirectly on tensor fields and some or all of the unitary gauge fields are found amongst the $SO(N)$ gauge fields. Symmetry restoration occurs at the zero-curvature `decompactification limit', in which all dimensions appear on the same footing.

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.

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 eighty years old empirical Colebrook function widely used as an informal standard for hydraulic resistance relates implicitly the unknown flow friction factor , with the known Reynolds number and the known relative roughness of a pipe inner surface ; . It is based on logarithmic law in the form that captures the unknown flow friction factor in a way from which it cannot be extracted analytically. As an alternative to the explicit approximations or to the iterative procedures that require at least a few evaluations of computationally expensive logarithmic function or non-integer powers, this paper offers an accurate and computationally cheap iterative algorithm based on Padé polynomials with only one -call in total for the whole procedure (expensive -calls are substituted with Padé polynomials in each iteration with the exception of the first). The proposed modification is computationally less demanding compared with the standard approaches of engineering practice, but does not influence the accuracy or the number of iterations required to reach the final balanced solution.

We construct a family of two-step optimal fourth order iterative methods for finding single root of non-linear equations. We generalize these methods to simultaneous iterative methods for determining all the distinct as well as multiple roots of single variable non-linear equations. Convergence analysis is present for both cases to show that the order of convergence is four in case of single root finding method and is twelve for simultaneous determination of all roots of non-linear equation. The computational cost, Basin of attraction, efficiency, log of residual and numerical test examples shows, the newly constructed methods are more efficient as compared to the existing methods in literature.

We suggest that momentum should be redened in order to help make physics more consistent and more logical. In this paper, we propose that there is a rest-mass momentum, a kinetic momentum, and a total momentum. This leads directly to a simpler relativistic energy momentum relation. As we point out, it is the Compton wavelength that is the true wavelength for matter; the de Broglie wavelength is mostly a mathematical artifact. This observation also leads us to a new relativistic wave equation and a new and likely better QM. Better in terms of being much more consistent and simpler to understand from a logical perspective.

The magnetic field of the earth plays an important role in the ecosystem, and the magnetic field of celestial bodies is also important in the formation of cosmic large-scale structures, but the origin and evolution of the celestial magnetic field is still an unresolved mystery. Many hypotheses to explain the origin have been proposed, but there are some insurmountable difficulties for each one. At present, the theory widely accepted in scientific society is the dynamo model, it says that, the movement of magnetofluid inside celestial bodies, which can overcome the Ohmic dissipative effect and generate persistent weak electric current and macroscopic magnetic field. However, this model needs an initial seed magnetic field, and the true values of many physical parameters inside the celestial body are difficult to obtain, and there is no stable solution to the large range of fluid motion. These are all difficulties for the dynamo model. Furthermore, it is difficult for the dynamo to explain the correlation between the dipole magnetic field and angular momentum of a celestial body. In this paper, by calculating the interaction between spin of particles and gravity of celestial body according to Clifford algebra, we find that a rotational celestial body provides a field $\Omega^\alpha$ for spins, which is similar to the magnetic field of a dipole, and the spins of charged particles within the celestial body are arranged along the flux line of $\Omega^\alpha$, then a macroscopic magnetic field is induced. The calculation shows that the strength of $\Omega^\alpha$ is proportional to the angular momentum of the celestial body, which explains the correlation between the magnetic intensity and angular momentum. The results of this paper suggest that further study of the effects of internal variables such as density, velocity, pressure and temperature of a celestial body on $\Omega^\alpha$ may provide some new insights into the origin and evolution of celestial magnetic field.

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

Polyvinyl Alcohol (PVA)/ Graphene Quantum Dots (GQDs) polymer nanocomposite films have been prepared, and the relationship between their structural, thermal and nanoscale morphologi-cal properties, and their photoluminescent response, has been investigated. Although according to X-ray Diffraction (XRD), Fourier-Transform Infrared Spectroscopy (FT-IR) and Differential Thermal Analysis (DTA) the incorporation of GQDs does not significantly affect the percentage crystallinity of the PVA matrix, for a range of added GQD concentrations, Atomic Force Micros-copy (AFM) showed the formation of islands with apparent crystalline morphology on the surface of the PVA/GQD films, with GQD presumably acting as a nucleating agent for island growth. The incorporation of GQD also led to the formation of characteristic surface pores with increased stiffness and frictional contrast, according to Ultrasonic Force Microscopy (UFM) and Frictional Force Microscopy (FFM) data. The photoluminescence (PL) spectra of the films were found to de-pend both on the amount of GQD incorporated and on the film morphology. For GQD loads > 1,2wt%, a GQD-related band was observed at ~ 1650 cm-1 in FT-IR, along with an increase in the PL band at lower energy. For a load of ~2wt% GQD, the surface morphology was characterized by extended cluster aggregates with lower stiffness and friction than the surrounding matrix, and the PL signal decreased.

Temperature differences between the atmosphere and river water allow rivers to be used as a hydrothermal energy source. The river-water heat pump system is a relatively non-invasive renewable energy source; however, effluent discharged from the heat pump can cause downstream temperature changes which may impact sensitive fluvial ecosystems. In this study, the water temperature recovery distance of the effluent was estimated for a river section in the Han River Basin, Korea, using the heat transfer equation and the Environmental Fluid Dynamic Code (EFDC) model. Results showed that, compared to the EFDC model, the heat transfer equation tended to overestimate the water temperature recovery distance due to its simplified assumptions. The water temperature recovery distance could also be used as an objective indicator to decide the reuse of downstream river water. Furthermore, as the river system was found to support an endangered fish species that is sensitive to water environment changes, care should be taken to exclude the habitats of protected species affected by water temperatures within water temperature recovery distance.

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.

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

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

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

This article develops duality principles and related convex dual formulations suitable for the local optimization of non-convex primal formulations for a large class of models in physics and engineering. The results are based on standard tools of functional analysis, calculus of variations and duality theory. In particular, we develop applications to a Ginzburg-Landau type equation.

Time evolution operators of a strongly ionizing medium are calculated by a time-dependent unitary transformation (TDUT) method. The TDUT method has been employed in quantum mechanical system composed of discrete states. This method is especially helpful for solving molecular rotational dynamics in quasi-adiabatic regimes because the strict unitary nature of the propagation operator allows us to set the temporal step size large; a tight limitation on the temporal step size ($\delta t <<1$) can be circumvented by the strict unitary nature. On the other hand, in a strongly ionizing system where the Hamiltonian is not Hermitian, the same approach cannot be directly applied because it is demanding to define a set of field-dressed eigenstates. In this study, the TDUT method was applied to the ionizing regime using the Kramers-Henneberger frame, in which the strong-field-dressed discrete eigenstates are given by the field-free discrete eigenstates in a moving frame. Although the present work verifies the method for a one-dimensional atom as a prototype, the method can be applied to three-dimensional atoms, and molecules exposed to strong laser fields.

Boulder dynamics may provide essential data for the coastal evolution and hazards assessment and can be focused as a proxy for the onshore effect of intense storm waves. In this work, detailed observations of currently available satellite imagery of the Earth surface allowed to identify several coastal boulders displacements in the Southern Apulia coast (Italy), in a period between July 2018 and June 2020. Field surveys confirmed the displacements of several dozens of boulders up to several meters in size, also allowing the determination of the initial position for many of them. Archive weather analyses identified two possible causative storms during the same period, and calculations based on analytical equations are found in agreement with the displacement by storm waves for most of the observed boulders. The results help to give insights about the onshore effect of high storm waves on the coastal hydrodynamics and the possible future flooding hazard in the studied coast.

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.

In quantum approaches to consciousness, the authors try to propose a model and mechanism for the mind-brain interaction using modern physics and some quantum concepts which do not exist in the classical physics. The independent effect of mind on the brain has been one of the challenging issues in the history of science and philosophy. In some recent mind-brain interaction models, the direct influence of mind on matter is either not accepted (as in Stapp’s model) or not clear, and there have not been any clear mechanism for it (as in Penrose-Hameroff’s model or in Eccles’s model). In this manuscript we propose a model and mechanism for mind’s effect on the matter using an extended Bohmian quantum mechanics and Avicenna’s ideas. We show that mind and mental states can affect brain’s activity without any violation of physical laws. This is a mathematical and descriptive model which shows the possibility of providing a causal model for mind’s effect on matter. It is shown that this model guarantees the realistic philosophical constraints and respects the laws of nature. In addition, it is shown that it is in agreement with the Libet style experimental results and parapsychological data. To propose this model, we obtained a modified (non-unitary) Schrödinger equation via second quantization method which affects the particle through a modified quantum potential and a new term in the continuity equation. At the second quantized level, which is equivalent to quantum field theory level (QFT), we can use the path integral formalism of Feynman. We show that there are three methods to extend Bohmian QM via path integral formalism, which has different interpretations. By numerical simulation of trajectories in the two-slits experiment, we show their differences and choose one of these methods for our mind-brain model which can be the basis for explaining some phenomena which are not possible to explain in the standard Bohmian QM.

An eigenvalue equation representing symmetric (dual) quantum equation is introduced. The particle is described by two scalar wavefunctions, and two vector wavefunctions. The eigenfunction is found to satisfy the quantum Telegraph equation keeping the form of the particle fixed but decaying its amplitude. An analogy with Maxwellian equations is presented. Massive electromagnetic field will satisfy a quantum Telegraph equation instead of a pure wave equation. This equation resembles the motion of the electromagnetic field in a conducting medium. With a particular setting of the scalar and vector wavefunctions, the dual quantum equations are found to yield the quantized Maxwell's equations. The total energy of the particle is related to the phase velocity ($v_p$) of the wave representing it by $E=p\,|v_p|$, where $p$ is the matter wave momentum. A particular solution which describes the process under which the particle undergoes a creation and annihilation is derived. The force acting on the moving particle is expressed in a dual Lorentz-like form. If the particle moves like a fluid, a dissipative (drag) quantum force will arise.

Bringing toghether mathematical and philosophical ideas related to transcendental numbers, this paper begins with a survey on transcendence and transcendental numbers, it then presents several properties of the transcendental numbers e and π, and then it gives the proof of a new inequality for transcendental numbers. Also, in relationship with these topics, we study solutions to the Yang-Baxter equation from hyperbolic functions and from logical implication.

The meridian line is a basic instrument for positional astronomy, it was used to study the motion of Sun, Moon, planets and the position of stars by measuring position and time of their passage through the meridian plane. The accuracy of such positions was dependent on precise theories of the atmospheric refraction (Cassini, 1655 and Laplace, 1825) and by the use of reference marks present originally on the meridian line, and now cancelled by the centuries. From October 27, 2018 the new pinhole of the meridian line in the Basilica of S. Maria degli Angeli in Rome (1702) is a circle 25 mm wide and 6.11 mm thick and its position is fixed, in order to perform a series of observations of astrometric quality, the IGEA campaign. The comparison of the observed positions of the meridian passages of the Sun, Southern and Northern limbs, with the ephemerides of Calsky.org and Stellarium 0.20.2 for the Sun are examined for the dates of the ingresses into the zodiacal signs, when the ecliptic longitude is exactly 0°/180° (Aries and Libra, spring and fall equinox), 30°/150° (Taurus, Virgo), 60°/120° (Gemini, Leo), 90° (Cancer), 330°/210° (Pisces, Scorpio), 300°/240° (Aquarius/Sagittarius), 270° (Capricorn). The former geometrical calibration of the marks present on the line, with a total station, is compared with another calibration done with a metal and laser meter. The first star on the floor of the Basilica representing the position of the Sun on August 20, 1702 when the pope Clement XI visited the meridian line, financed by him, has been calibrated with the solar image. The present pinhole is 4.4±0.1 mm South with respect to the original one of 1702.

In this study, 12 organic waste materials were subjected to TG/DTG thermogravimetric analysis and DSC calorimetric analysis. These analyses provided basic information about thermochemical transformations and degradation rates during organic waste pyrolysis. Waste materials were chosen to cover the most abundant waste that can be found in the municipal solid waste stream. Based on TG results, kinetic parameters according to Coats–Redfern method were determined. The pyrolysis activation energy was the highest for cotton 134.5 kJ∙(mol∙K)-1 and the lowest for leather 25.2 kJ∙(mol∙K)-1. The DSC analysis showed number of transformations occurred during pyrolysis for each material. For each transformation, normalized energy required for transformation, or released during transformation were determined and then summarized to present energy balance. The study found that only for three waste materials: PET (-220.1 J⸱g-1), leather (-66.9 J⸱g-1), and chicken meat (-130.3 J⸱g-1) energy balance was negative, while the highest positive balance value was found for potato peelings (367.8 J⸱g-1). The obtained results may be applied for the modelling of energy and mass balance of municipal solid waste pyrolysis.

This paper presents a new method for parameterizing the Lorentz group based on coupled parameters. From the Euler–Hamilton equations, an additional angular rapidity and perpendicular rapidity are obtained, and the Hamiltonian and Lagrangian of a relativistic particle are expanded into rapidity spectra. A so-called passage to the limit is introduced that makes it possible to decompose physical quantities into spectra in terms of elementary functions when explicit decomposition is difficult. New rapidity-dependent Lorentz-invariant coordinates are obtained, and the descriptions of particle motion using the old and new Lorentz-invariant forms as applied to plane waves are compared. Based on a classical model of particle motion in the field of a plane monochromatic electromagnetic wave and in that of a plane laser pulse, the rapidity-dependent spectral decompositions into elementary functions are presented, and the Euler–Hamilton equations are derived as rapidity functions in 3+1 dimensions.

Pure-compression shells have been the central topic in the form-finding of shells. This paper studies tension-compression mixed type shells by utilizing a NURBS-based isogeometric form-finding approach that analyzes Airy stress functions to expand the possible plan geometry. A complete set of smooth version graphic statics tools is provided to support the analyses. The method is validated using examples with known solutions, and a further example demonstrates the possible forms of shells that the proposed method permits. Additionally, a guideline to configure a proper set of boundary conditions is presented through the lens of asymptotic lines of the stress functions.

This paper revisits the analytical theory of fractional vibrations with the highlights in five aspects. First, we address the cases of structures with frequency dependent mass or damping or stiffness in Sections 2-4. Second, we introduce the theory based on the general second-order vibration motion equation with frequency dependent elements (mass, damping, stiffness) in Sections 5-7. Third, we present the analytical theory of seven specific classes of second-order vibration systems with frequency dependent mass or damping or stiffness in Sections 8 and 9. Fourth, we bring forward the analytical theory of seven classes of fractional vibration systems in Sections 10-12. Finally, as an application, we give the closed form expression of the forced response to multi-fractional Euler-Bernoulli beam in Section 13. The explanation of the nonlinearity of fractional vibrations is given in Section 14.

This study proposes a methodology for identifying time intervals in which time-of-use (ToU) energy tariffs can be set. This is achieved by analyzing the variability in electric power demand and esti-mating the potential for demand flexibility. The proposed methodology is as follows: first, data preprocessing is performed, focusing on the organization and cleaning of individual consumption records. Subsequently, the data are processed and classified by using consumption variability analysis and clustering techniques. Then, representative clusters are selected and time intervals are analyzed to identify periods of high electric power consumption variability. This methodology was tested with real data from smart meters in the Colombian electrical system, in which time intervals with potential for settinh ToU tariffs were ultimately identified. This work promotes the implementation of demand response strategies that enhance sustainability and facilitate the transition to a more resilient energy landscape both nationally and internationally. The findings are expected to contribute to the formulation of tariff schemes that encourage con-scious changes in electric energy consumption patterns.

A controlled ammonia (NH₃) release experiment was performed at a grassland site to quantify the effect of dry deposition, at the field scale between the source and the receptors (NH₃ measurement locations), on the estimates of emission rates by means of inverse dispersion modelling. NH₃ was released for 3 hours at a constant rate of Q = 6.29 mg s⁻¹ from a grid of 36 orifices spread over an area of 250 m². The increase in line-integrated NH₃ concentration was measured with open-path optical miniDOAS devices at different locations downwind of the artificial source. Using a backward Lagrangian stochastic (bLS) dispersion model (bLSmodelR), the fraction of the modelled release rate to the emitted NH₃ (Q_bLS/Q) was calculated from the measurements of the individual instruments. Q_bLS/Q was found to be systematically lower than 1, on average between 0.69 and 0.91, depending on the location of the receptor. We hypothesized that NH₃ dry deposition to grass and soil surfaces was the main factor responsible for the observed depletion of NH₃ between source and receptor. A dry deposition algorithm based on a deposition velocity approach was included in the bLS modelling. Model deposition velocities were evaluated from a ‘big‑leaf’ canopy resistance analogy. Canopy resistances (generally termed Rc) that provided Q_bLS/Q = 1 ranged from 75 to 290 s m⁻¹, showing that surface removal of NH₃ by dry deposition can plausibly explain the original underestimation of Q_bLS/Q. The inclusion of a dry deposition process in dispersion modelling is crucial for emission estimates, which are based on concentration measurements of depositing tracers downwind of homogeneous area sources or heterogeneously distributed hot spots, such as e.g. urine patches on pastures in the case of NH₃.

This study aims to categorize the morphological changes during cabbage (B. oleracea ssp. capitata) development: seedling, rosette, folding, and heading and to elucidate the cellular mechanisms of leaf curvature, essential for the formation of the leafy head. We followed the growth of two cabbage morphotypes with distinct head shapes (round and pointed); we phenotyped the size and volume of the whole-plant as well as the size, shape, and curvature of the leaves during growth. By integrating these phenotypic data, we determined the four vegetative stages for both cabbages. Cytological phenotypes of microtome sections from five distinct leaf positions of the rosette, folding, and heading leaves at two timepoints during leaf growth were quantified and revealed variations in cellular parameters among leaf types, between leaf positions, and between the adaxial and abaxial sides. We identified two synergistic cellular mechanisms contributing to the curvature of heading leaves: differential growth across the leaf blade, with increased growth at the leaf's centre relative to the margins; and increased expansion of the spongy parenchyma layer compared to the palisade parenchyma layer, resulting in the direction of the curvature, which is inwards. These two processes together contribute to the typical leafy heads of cabbages.

Whenever vegetated areas are monitored over time, phenological changes in land cover should be decoupled from changes in acquisition conditions, like atmospheric components, sun and satellite heights, and imaging instrument. This especially holds when the multispectral (MS) bands are sharpened for spatial resolution enhancement by means of a panchromatic (Pan) image of higher resolution, a process referred to as pansharpening. In this paper, we provide evidence that pansharpening of visible/near-infrared (VNIR) bands takes advantage from a correction of the path radiance term introduced by the atmosphere, during the fusion process. This holds whenever the fusion mechanism emulates the radiative transfer model ruling the acquisition of the Earth’s surface from space, that is, for methods exploiting a multiplicative, or contrast-based, injection model of spatial details extracted from the panchromatic (Pan) image into the interpolated multispectral (MS) bands. The path radiance should be estimated and subtracted from each band before the product by Pan is accomplished. Both empirical and model-based estimation techniques of MS path radiances are compared within the framework of optimized algorithms. Simulations carried out on two GeoEye-1 observations of the same agricultural landscape at different dates highlight that the de-hazing of MS before fusion is beneficial for an accurate detection of seasonal changes in the scene, as measured by the normalized differential vegetation index (NDVI).

Since its initial development in the 1970’s by Phil Burke and his collaborators, the R-matrix theory and associated computer codes have become the de facto approach for the calculation of accurate data for general electron-atom/ion/molecule collision and photoionization processes. The use of a non-orthonormal set of orbitals based on B-splines, now called the B-spline R-matrix (BSR) approach, was pioneered by Zatsarinny. It has considerably extended the flexibility of the approach and improved particularly the treatment of complex many-electron atomic and ionic targets, for which accurate data are needed in many modelling applications for processes involving low-temperature plasmas. Both the original R-matrix approach and the BSR method have been extended to the interaction of short, intense electromagnetic (EM) radiation with atoms and molecules. Here we provide an overview of the theoretical tools that were required to facilitate the extension of the theory to the time domain. As an example of a practical application, we show results for two-photon ionization of argon by intense short-pulse extreme ultraviolet radiation