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

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

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

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

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

The present article seeks to study whether there is any relationship between the equation of the rhythmic figures (Lugos Abarca, 2023) and cardiac auscultation using Field's method, which consists of representing cardiac sounds by means of musical notation (Field, 2010). A new meaning is given to the equation, concluding a mathematical equality between the equation of the rhythmic figures and the formula for calculating the RR Interval.

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

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

The present study aimed to develop a mathematical model to estimate the performance of an indoor rowing event of 6000m through an 500 m all out test in junior athletes. We selected141 subjects from the Brazilian rowing confederation database (15.9 ± 1.0 years), subsequently randomised the sample to the development (~70%) and cross-validation (~30%) groups of the mathematical model. Performance data for 500m and 6000m were collected (there was a 48h washout between one test and anoth-er).Subsequently, the mathematical model: Time(min) 6000m = { [( Time(s) 500-m * 6) * 2] / 60} + 1.3, was developed by arithmetic modeling using machine learning and Regression analysis, being tested by intraclass correlation coefficient (ICC), Concordance correlation coefficient (CCC), Validity (Cb ), preci-sion (ρ) and bland-Altman plotting. The prediction of the result of 6000m through the mathematical model utilizando apenas o desempenho de 500m “all-out” test showed a significant reliability in de-velopment group (r2 = 0.730, ICC = 0.753; CCC = 0.895, Cb = 0.879, ρ: 0.957, pure error: 0.2 secounds (1.0% estimative error)); and in cross-validation group (r2 = 0.710, ICC = 0.747; CCC = 0.888, Cb = 0.875, ρ: 0.903, pure error: 0.3 secounds (1.4% estimative error)). When comparing the estimated re-sults of the 6000m performance by the mathematical model with the real performance of 6000m per-formed in indoor rowing, no statistical differences were observed. In addition, the mathematical model did not present a significant proportion bias in relation to the 6000 m performance in both groups. The mathematical model for predicting 6000m performance through a 500m fast test was significant for national level junior rowing athletes.

Modern physics is situated on the fine line between scientific research and an attempt to answer metaphysical questions. Contemporary scholars such as Henry Stapp and Roger Penrose attempt to create an ontological interpretation of Schrödinger's equation in superposition state and its reduction or collapse to classical state. In this short essay I will try to explore how Immanuel Kant's metaphysics and the concept of noumena can be possibly integrated with quantum physics and Schrödinger's equation.

A model for cell proliferation in developmental fields is derived from information theory using a few biological postulates. The model provides an explanation for the success of the Gompertz equation in describing the growth of embryonic, neoplastic, and regenerative systems. Although this equation has been applied to many growth phenomena, its use has been entirely empirical. A theoretical justification for the use of the Gompertz equation in characterizing developmental processes is presented. The model also accounts for a reported relationship among the parameters of the Gompertz equation. A method for quantification and comparison of the determination of developmental fields at different levels of organization is suggested.

By solving a Marchenko equation, Green's functions at an arbitrary (inner) depth level inside an unknown elastic layered medium can be retrieved from single-sided reflection data, which are to be collected at the top of the medium. So far, an exact solution could only be obtained if the medium obeys stringent monotonicity conditions and if all forward-scattered (non-converted and converted) transmissions between the acquisition level and the inner depth level are known a-priori. We introduce an alternative Marchenko equation by revising the window operators that are applied in its derivation. We also introduce an auxiliary equation for transmission data, which are to be collected at the bottom of the medium, and a coupled equation, which is based on both reflection and transmission data. We show that the joint system of the Marchenko equation, the auxiliary equation and the coupled equation can be succesfully inverted when broadband reflection and transmission data are available. This results in a novel methodology for elastodynamic Green's function retrieval from two-sided data. Apart from these data, our approach requires P- and S-wave transmission times between the inner depth level and the top of the medium, as well as two angle-dependent amplitude scaling factors, which can be estimated from the data by enforcing energy conservation.

In this paper, inspired by Jleli and Samet [journal of inequalities and applications 38 (2014) 2 1–8] we introduce two new classes of auxiliary functions and utilize the same to define (q, y)R-weak 3 contractions. Utilizing (q, y)R-weak contractions, we prove some fixed point theorems in the setting 4 of relational metric spaces. We employ some examples to substantiate the utility of our newly proved 5 results. Finally, we apply one of our newly proved results to ensure the existence and uniqueness of 6 solution of a Volterra-type integral equation.

Rough volatility models are popularized by \cite{gatheral2018volatility}, where they have shown that the empirical volatility in the financial market is extremely consistent with rough volatility. Fractional Riccati equation as a part of computation for the characteristic function of rough Heston model is not known in explicit form as of now and therefore, we must rely on numerical methods to obtain a solution. In this paper, we give a short introduction to option pricing theory and an overview of the current advancements on the rough Heston model.

Based on previous research results, we propose a new preprocessing HSS iteration method (PHSS) for the generalized Lyapunov equation. At the same time, the corresponding inexact PHSS algorithm (IPHSS) is given from the angle of application. All the new methods presented in this paper have given the corresponding convergence proof. The numerical experiments are carried out to compare the new method with the existing methods, and the improvement effect is obvious. The feasibility and effectiveness of the proposed method are proved from two aspects of theory and calculation.

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

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

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

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

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

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

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

An expansion method based on time fractional Sine-Gordon equation is implemented to construct some real and complex valued exact solutions to the Korteweg-de Vries and modified Korteweg-de Vries equation in time fractional forms. Compatible fractional traveling wave transform plays a key role to be able to apply homogeneous balance technique to set the predicted solution. The relation between trigonometric and hyperbolic functions based on fractional Sine-Gordon equation allows to form the exact solutions with multiplication of powers of hyperbolic functions.

This paper is devoted to investigate charged vector particles tunneling via horizons of a pair of accelerating rotating charged NUT black hole under the influence of quantum gravitational effects. For this purpose, we use the modified Proca equation incorporating generalized uncertainty principle. Using the WKB approximation to the field equation, we obtain a modified tunneling rate and the corresponding corrected Hawking temperature for this black hole. Moreover, we analyze the graphical behavior of corrected Hawking temperature T'_H with respect to the event horizon for the given black hole. By considering quantum gravitational effects on Hawking temperatures, we discuss the stability analysis of this black hole. For a pair of black holes, the temperature T'_H increases with the increase in rotation parameters α and w, correction parameter β, black hole acceleration α and arbitrary parameter k and decreases with the increase in electric e and magnetic charges g.

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

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

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

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

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

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

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

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

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

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

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

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

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

We prove: (1) the set of all Diophantine equations which have at most finitely many solutions in non-negative integers is not recursively enumerable, (2) the set of all Diophantine equations which have at most finitely many solutions in positive integers is not recursively enumerable, (3) the set of all Diophantine equations which have at most finitely many integer solutions is not recursively enumerable, (4) analogous theorems hold for Diophantine equations D(x₁, …, x_p) = 0, where p ∈ N\{0} and for every i ∈ {1, …, p} the polynomial D(x₁, …, x_p) involves a monomial M with a non-zero coefficient such that x_i divides M, (5) the set of all Diophantine equations which have at most k variables (where k ≥ 9) and at most finitely many solutions in non-negative integers is not recursively enumerable.

In this paper, we define new kind of Daehee numbers, the degenerate Daehee numbers of the third kind, using degenerate log function as generating function. We obtain some identities for the degenerate Daehee numbers of the third kind associated with the Daehee, degenerate Daehee and degenerate Daehee numbers of the second kind. In addition, we derive a differential equation associated with the degenerate log function. We deduce some identities from the differential equation.

Abstract: The article proposes to consider the possibility of connecting the problems of engineering synthesis of frequency control systems for asynchronous electric drives with the basic provisions of the theory of identification of asynchronous electric motors based on the equations of a generalized AC electric machine.The article presents the results of experimental studies of load parrying processes in asynchronous electric drives with vector and scalar controls. These results indicate the absence of fundamental advantages as processes in a drive with vector control. This advantage should have manifested itself in a more efficient formation of the moment and fast transients. It is suggested that the reason for this is in too significant errors, assumptions and simplifications of the equations adopted in the derivation of vector control and which are its theoretical basis. A method is proposed for describing asynchronous electric motors by nonlinear transfer functions, which made it possible to formulate the principle of correction of electric drives and a method for assessing their efficiency.The article shows. that the correction based on the proposed nonlinear transfer functions of the induction motor is much more efficient than the traditional vector control, which was confirmed by detailed experiments and modeling. The results of the most important of which are given in the article. An assumption was made. that the advantage in efficiency is due to a more accurate identification of the dynamics of an asynchronous electric motor with a gear function instead of vector equations.

In the framework of the self-consistent Maxwell-Pauli theory, the non-linear Pauli equation is obtained. Stationary and nonstationary solutions of the nonlinear Pauli equation for the hydrogen atom are studied. We show that spontaneous emission and the related rearrangement of the internal structure of an atom, which is traditionally called a spontaneous transition, have a simple and natural description in the framework of classical field theory without any quantization and additional hypotheses. The behavior of the intrinsic magnetic moment (spin) of an electron wave in an external magnetic field is considered. We show that, according to the self-consistent Maxwell-Pauli theory, in a weak magnetic field, the intrinsic magnetic moment of an electron wave is always oriented parallel to the magnetic field strength vector, while in a strong magnetic field, depending on the initial orientation of the intrinsic magnetic moment, two orientations are realized: either parallel or antiparallel to the magnetic field strength vector.

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

This study investigates how customers’ technological readiness affects service quality and the adoption of self-service banking by developing an empirical model. The model was proposed to explore the relationships between technology readiness, self-service quality, and customer satisfaction. The hypotheses and stability of the model were tested using structural equation modeling. The findings revealed that technology readiness, including the optimism, innovation, and insecurity dimensions, had a significant positive impact on self-service quality. In addition, service quality fully mediated the relationship between technological readiness and customer satisfaction. These results suggest that when customers are ready to embrace and use new technology, their evaluation of service quality is high. Thus, bank managers should drive customer perceptions of the quality of self-service banking by improving their technological readiness through various measures. Furthermore, based on the mediating effect of self-service quality, banks must be aware that improving service quality can enhance customer satisfaction and maintain a competitive advantage.

A concise proof of the Riemann Hypothesis is presented by clarifying the Hadamard product expansion over the zeta zeros, demonstrating that the Riemann Hypothesis is true.

In this paper, we analyze the Hawking radiation phenomenon for types of Banados-Teitelboim-Zanelli-like (BTZ-like) black holes. For this purpose, using the Hamilton-Jacobi method, we consider semi-classical WKB approximation to calculate the tunneling probabilities of massive boson particles. For these particles, we use the equation of motion for the Glashow-Weinberg-Salam model. Using quantum tunneling process of charged massive bossons, we compute the corresponding Hawking temperatures. Furthermore, we discuss the effects of rotation parameter on tunneling probability and temperature.

We propose a generalization of Nambu-Hamilton equation in superspace $\mathbb R^{3|2}$ with three real and two Grassmann coordinates. We construct the even degree vector field in the superspace $\mathbb R^{3|2}$ by means of the right-hand sides of proposed generalization of Nambu-Hamilton equation and show that this vector field is divergenceless in superspace. Then we show that our generalization of Nambu-Hamilton equation in superspace leads to family of ternary brackets of even degree functions defined with the help of Berezinian. This family of ternary brackets is parametrized by the infinite dimensional group of invertible second order matrices, whose entries are differentiable functions on the space $\mathbb R^{3}$. We study the structure of ternary bracket in a more general case of a superspace $\mathbb R^{n|2}$ with $n$ real and two Grassmann coordinates and show that for any invertible second order functional matrix it splits into the sum of two ternary brackets, where one is usual Nambu-Poisson bracket, extended in a natural way to even degree functions in a superspace $\mathbb R^{n|2}$, and the second is a new ternary bracket, which we call $\Psi$-bracket, where $\Psi$ can be identified with invertible second order functional matrix. We prove that ternary $\Psi$-bracket as well as the whole ternary bracket (the sum of $\Psi$-bracket with usual Nambu-Poisson bracket) is totally skew-symmetric, satisfies the Leibniz rule and the Filippov-Jacobi identity (Fundamental Identity).

The article proposes a mathematical model for creating playlists based on the emotional utility of the consumer, aiming to maintain high user interest in music streaming platforms (Lugos Abarca, 2024). The proposed method follows these steps: first, it calculates the MEEPE of Songs on the digital platform; subsequently, it quantitatively defines the Consumer's MEEPI before exposure to music; then, it operates the MEEPE of the Songs with the consumer's initial MEEPI using the known resolution process (Lugos Abarca, 2023); finally, it employs an emotional utility function to determine possible levels of emotional satisfaction and establish the playback order. This results in the creation of an efficient theoretical model. It is recommended to expand the computational study of the model in future research by using a broader set of songs and considering various initial MEEPI of the consumer. The article's originality lies in its ability to predict, quantitatively and theoretically, the level of satisfaction a music consumer could experience when listening to a playlist.

The objective of this research is to propose a utility function that calculates the possible level of satisfaction that a music consumer would achieve after listening to a song according to the emotional response obtained from a song. Assuming that the consumer's musical preferences are satisfied if the predominant emotions of his current emotional state increase; the probabilistic emotional-musical model (Lugos Abarca, 2023) is used to construct such a utility function. By posing a hypothetical scenario, realistic results were obtained, which guarantee, in principle, its use in theoretical practice. The originality of this research lies in proposing a mathematical tool to study, quantitatively, the decision making of a musical consumer influenced by his emotions. The main conclusion being its importance in the music industry, since the function could predict, theoretically, whether a song will be accepted or rejected by the consumer in comparison with the competition.

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

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

Proposed in 1889 by Svante Arrhenius, the Arrhenius equation is an important result in physical chemistry which aims to find the relationship between temperature and reaction rates. It is also an essential equation for analytic chemistry which helps to determine the energy barrier for a given reaction. In this article, we will go through a detailed derivation of the exponential factor in the Arrhenius Equation based on the Boltzmann distribution of particle energy probability. Then, we will attempt to model the pre-exponential factor in accordance with the principles of collision theory for bi-molecular reaction with gaseous reactants. Understanding the basic principles of chemical reaction provides valuable tools to analyze complex reaction mechanisms in the perspective of optimizing existing industrial processes.

We have introduced a sign operator of energy, analogous to the operator helicity, but in the direction of what we call energy vector. However, this energy vector needs a time vector. To give physical senses to the components of such a time vector, we try to explain the time dilation in special relativity and try to relate the components of the time vector to the tunneling times when an electron crosses a potential barrier.

In this paper, we solve KG-oscillator in the five-dimensional cosmic string space-time background with a uniform magnetic field and quantum flux subject to a scalar potential of Cornell-type using KaluzaKlein theory, and observe the gravitational analogue of the AharonovBohm effect. We show that the energy eigenvalue and eigenfunction depends on the global parameters of the space-time, and also a quantum effect is seen due to the dependence of magnetic field on the quantum numbers of the system

The potential of Thai industrial product design is still inferior to those of leading competitors in world market that give more importance on the design during their product development to increase their competitive edges on commercial scale. The product design is very important part for sustainable growth in this industry. Thus, this research aims at investigating footwear design strategies for Thai footwear industry to be excellence in world market. The research has been designed with the mixed method of both qualitative and quantitative study. The quantitative data were collected through semi-structure interview from 500 designers who presented their designs to join the award competition. The results revealed that the footwear design strategies consisted of 4 factors, i.e. 1) design, 2) market analysis, 3) innovation, and 4) information technology. This paper utilizes the method of Structural Equation Modeling (SEM) to establish a strategies model for competitive advantage in Thai footwear industry. The analysis results indicated that the footwear design strategies model could help make more effective policies and organization strategies for enterprises and designers to develop themselves to be excellence in world market.

Project complexity is usually considered as one of main causes of cost overruns, resulting in poor performance and thus project failure. However, empirical studies focused on evaluating its effects on project cost remain lacking. Given this circumstance, this study attempts to develop the relationships between project cost and the multidimensional project complexity elements. We establish complexity as a multidimensional factor including the task, organization, market, legal, and environment complexities. This study uses an empirical evidence-based structural model to account for the relationships between project cost and project complexity. By doing so, a quantitative assessment of multi-dimensional project complexity has been developed. The findings suggest that task and organization complexities have direct effects on project cost, while market, legal and external environment complexities have indirect effects on project cost. The practical contribution is that the findings can improve the understanding of which dimension of complexity significantly influence project cost, and the need to focus efforts on strategically addressing that complexities.

Recently a new class of experiments in the field of surface gravity waves has emerged. These experiments serve as demonstration of an analogy to a broad variety of phenomena in optics and quantum mechanics. In particular, experiments involving Airy water-wave packets were carried out. The Airy wave packets have attracted tremendous attention in optics and quantum mechanics owing to their unique properties, spanning from an ability to propagate along parabolic trajectories without spreading, and to accumulating a phase that scales with the cubic power of time. Non-dispersive Cosine-Gauss wave packets and self-similar Hermite-Gauss wave packets, also well known in the field of optics and quantum mechanics, were recently studied using surface gravity waves as well. These wave packets demonstrated self-healing properties in water wave pulses as well, preserving their width despite being dispersive. Finally, this new approach also allows to observe diffractive focusing from a temporal slit with finite width.

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

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

We consider a family of nonlinear singularly perturbed PDEs whose coefficients involve a logarithmic dependence in time with confluent Fuchsian singularities that unfold an irregular singularity at the origin and rely on a single perturbation parameter. We exhibit two distinguished finite sets of holomorphic solutions, so-called outer and inner solutions, by means of a Laplace transform with special kernel and Fourier integral. We analyze the asymptotic expansions of these solutions relatively to the perturbation parameter and show that they are (at most) of Gevrey order 1 for the first set of solutions and of some Gevrey order that hinges on the unfolding of the irregular singularity for the second.

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

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

Understanding the stability limit of crystalline materials under variable tensile stress conditions is of capital interest for their technological applications. In this study, we present results from first-principles density functional theory calculations that quantitatively account for the response of selected covalent and layered materials to general stress conditions. In particular, we have evaluated the ideal strength along the main crystallographic directions of 3C and 2H polytypes of SiC, hexagonal ABA stacking of graphite and 2H-MoS2. Transverse superimposed stress on the tensile stress was taken into account in order to evaluate how the critical strength is affected by these multi-load conditions. In general, increasing transverse stress from negative to positive values leads to the expected decreasing of the critical strength. Few exceptions found in the compressive stress region correlate with the trends in the density of bonds along the directions with the unexpected behavior. In addition, we propose a modified spinodal equation of state able to accurately describe the calculated stress-strain curves. This analytical function is of general use and can also be applied to experimental data anticipating critical strengths and strains values and providing informattion on the energy stored in tensile stress processes.

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

The purpose of this study was to assess the extent to which self-esteem and depression mediated the influence of internalized stigma on life satisfaction among Korean out-of-school youths. Cross-sectional data on 318 youths provided information on perceived stigma, self-esteem, depression, life satisfaction, and personal characteristics. A multinomial logistic regression analysis was followed by structured path analysis to investigate the mediation effects. Internalized stigma was negatively associated with life satisfaction. Self-esteem significantly mediated the influence of stigma on depression and the influence of depression on life satisfaction. Further, stigma directly and significantly influenced depression. This study demonstrated that self-esteem and depression were important to the relationship between internalized stigma and life satisfaction. Implications for possible policies and programs with the aim of helping out-of-school youths to integrate and lead successful satisfying lives are discussed.

Restoration experience is a positive response against the ever-increasing problem of stress. It is recovery of attentional capacity, clearing random thoughts and feelings of relaxation and calmness. Although there is a body of research on investigating the impact of open green space characteristics on psycho- logical restoration through attention restoration theory and supportive environment theory, there is little knowledge on how the interaction among these characteristics could promote restorative outcomes. To address this problem, using Perceived Sensory Dimension (PSD) for open green space qualities and Perceived Restorativeness (PR) as the property of restorative environment, this study assessed the extent to which the PSD and PR impact on restoration experience. Using 444 screened surveys, a Partial Least Square Structural Equation Model (PLS-SEM) was developed and the validity and reliability of it, was demonstrated. Extensive analysis of the results showed how environmental qualities can promote restoration experience using a sample of university students. These results provide information for landscape architecture and planning researchers to promote the development of open spaces as a resource of psychological restoration and stress relief.

The application of transformations of the state equations of continuous linear and bilinear systems to the canonical form of controllability allows one to simplify the computation of Gramians of these systems. In the paper we developed the method and obtain algorithms for computation of the controllability and observability Gramians of continuous linear and bilinear stationary systems with many inputs and one output, based on the method of spectral expansion of the Gramians and the iterative method for computing the bilinear systems Gramians. An important feature of the concept is the idea of separability of the Gramians expansion: sep333arate computation of the scalar and matrix parts of the spectral Gramian expansion reduces the sub-Gramian matrices computation to calculation of numerical sequences of their elements. For the continuous linear systems with one output the method and the algorithm of the spectral decomposition of the controllability Gramian are developed in the form of Xiao matrices. Analytical expressions for the diagonal elements of the Gramian matrices are obtained, making use of which the rest elements can be calculated. For continuous linear systems with many outputs the spectral decompositions of the Gramians in the form of generalized Xiao matrices are obtained, which allows to significantly reduce the number of calculations. The obtained results are generalized for continuous bilinear systems with one output. Iterative spectral algorithms for computation of elements of Gramians of these systems are proposed. Examples are given that illustrate theoretical results.

The aim of the study is to explore how sharing status updated and receiving Likes on Facebook, as a form of positive social feedback, correlates with current and perceived changes in Quality of Life (QoL) Sample consisted of 1577 adult Facebook users (76.3% females; 65.9% aged 18-24, 21.9% aged 25-30, 12.3% aged &gt; 30 years old). The study employed a longitudinal approach, collecting Facebook data from adult users over a 12-month period using the Graph API. Data were divided into 12 monthly segments. Two monthly indicators were calculated: the percentage of textual status updates and the average number of Likes per post. Current and perceived changes in Quality of Life (QoL) were administered as self-report measures. The findings indicated a positive correlation between the frequency of textual Facebook posts and the average received Likes. Furthermore, receivign more Likes was positively associated with a higher current QoL, and perceived improvements in QoL correlated with an increase in Likes over time. The study suggests that online positive social feedback, measured through Likes on Facebook, is associated with both current QoL and perceived improvements in QoL among adult Facebook users. This highlights the potential impact of online social interactions on individual well-being.

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

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

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

This paper inquires on the options pricing modeling using Artificial Neural Networks to price Apple(AAPL) European Call Options. Our model is based on the premise that Artificial Neural Networks can be used as functional approximators and can be used as an alternative to the numerical methods to some extent, for a faster and an efficient solution. This paper provides a neural network solution for two financial models, the BlackScholes-Merton model, and the calibrated-Heston Stochastic Volatility Model, we evaluate our predictions using the existing numerical solutions for the same, the analytic solution for the Black-Scholes equation, COS-Model for Heston’s Stochastic Volatility Model and Standard Heston-Quasi analytic formula. The aim of this study is to find a viable time-efficient alternative to existing quantitative models for option pricing.

This paper describes the development of a two-dimensional water quality model that solves hydrodynamic equations tied to transport equations with reactions mechanisms inherent in the processes. This enable us to perform an accurate assessment of the pollution in a coastal ecosystem. The model was developed with data drawn from the ecosystem found in Mexico's southeast state of Tabasco. The coastal ecosystem consists of the interaction of El Yucateco lagoon with the Chicozapote and Tonalá rivers, that connect the lagoon with the Gulf of Mexico. We present the results of pollutants transport simulation in the coastal ecosystem, focusing on toxic parameters for two hydrodynamic scenarios: wet and dry seasons. As it of interest in the zone, we study the transport of four metals: Cadmium, Chromium, Nickel and Lead. In order to address our objectives we solved numerically a self-posed mathematical problem,which is based on the measured data. The performed simulations show to characterise metal transport within the acceptable range of accuracy and in accordance with the measured data. The performed simulations show to characterise metals transport with an acceptable accuracy, agreeing well with measured data in total concentrations in four control points along the water body. Although for the accurate implementation of the hydrodynamic-based water quality model herein presented, boundary (geometry, tides, wind, etc.) and initial (concentrations measurements) conditions are required, it poses as an excellent option when the distribution of solutes with high accuracy is required, easing environmental, economic and social management of coastal ecosystems.

We present a Quantum Space Model (QSM) of cosmic evolution based on the theory that space consists of energy quanta which participates in the evolution of the universe. It shows that Dark Energy is the energy of space which causes its accelerating expansion. We used the Friedmann equations to trace the history of the cosmos from a time before the Big Bang to its ultimate end. The universe started from a quantum size volume of space with high energy density.Quantum fluctuations triggered the release of energy in a Big Bang at very high temperature and pressure. It then expanded and cooled undergoing phase transitions to radiation, fundamental particles, and matter. Matter grew into galaxies, and was further consolidated by gravity into Dark Energy Stars/Black Holes, ending in a Big Crunch at about 1.380 trillion years, thus bringing the universe back to its initial state. It can stay in a Deep Feeeze inside a Black Hole and through fluctuations or other mechanism may start a new cycle in its life with a new Bang. If the Law of Conservation of Energy is universal, then the cosmos is eternal. Space and energy are equivalent just as matter and energy are. This is well founded in Planck’s energy equation. They are the two most fundamental quantities in the universe that govern cosmic evolution. The two principal long range forces are the gravitational force and the space force.The latter could be the fifth force in the universe. They may provide the clockwork mechanism that operates our eternal cyclic universe.

Rare earths are classified as most important and critical material for US economy and defense by Congress and a mandate has been set to increase their in-house production, domestic resource utilization and decrease reliance on foreign resources and reserves. They are widely available in earth crust as ore (bastnaesite (La, Ce)FCO₃, monazite, (Ce, La, Y, Th)PO₄, and xenotime, YPO₄), but their so-called economic reserves are sparsely located geographically. They may be produced by various means such as beneficiation (physical, chemical, mechanical, or electrical), reduction (direct or indirect), electrolysis (of aqueous or molten / fused single or mixed salt systems) at high temperature or hydrometallurgy. Out of these, direct reduction also known as metallothermic reduction (La and Ca reduction) is mostly utilized. Its variant, high temperature electrowinning of fused salts is also practiced widely. These processes are material and application specific. In this study, author will employ thermodynamics (Ellingham diagrams, free energy of formation, reduction potential, Nernst equation, Pourbaix (E_h-pH) diagrams, E-pO^-2 diagrams), kinetics and energetic of a chemical reaction (chemical metallurgy) to reduce rare earth oxide / salt to rare earth metals (REO/RES – REM). It is shown that materials and energy requirement vary greatly depending on type of mineral ore, production facility, and beneficiation / mineral processing method selected. Aim is to reduce dependence on coal deposits. It is anticipated this route will be able to produce rare earths with > 35% yield and > 98% purity which be described in subsequent studies and patents.

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

The Chebyshev collocation method (ChC) implemented as Chebfun is used in order to solve a class of second order one-dimensional singular and genuinely nonlinear boundary value problems. Efforts to solve these problems with conventional ChC have generally failed, and the outcomes obtained by finite differences or finite elements are seldom satisfactory. We try to fix this situation using the new Chebfun programming environment. However, for toughest problems we have to loosen the default Chebfun tolerance in Newton's solver as the ChC runs into trouble with ill-conditioning of the spectral differentiation matrices. Although in such cases the convergence is not quadratic the Newton updates decrease monotonically. This fact, along with the decreasing behaviour of Chebyshev coefficients of solutions, suggests that the outcomes are trustworthy, i.e., the collocation method has exponential (geometric) rate of convergence or at least an algebraic rate. We consider first a set of problems that have exact solutions or prime integrals and then another set of benchmark problems that do not possess these properties. Actually, for each test problem carried out we have determined how Chebfun solution converges, its length, the accuracy of the Newton method and especially how well the numerical results overlap with the analytical ones (existence and uniqueness).

To identify the exchange coefficients of a nonlinear polynomial tricompartmental general system of α+β , we follow the procedure; firstly, the recommended solution is to introduce an adequate time t*&gt;0 in a determinable manner. That is, after injecting quantity a into the main compartment, wait a moment for the exchange in the polynomial α+β order nonlinear general system to settle, and then compare this compartment to compartment 2 at t*. Secondly, applying the Taylor formula will linearize the system and identify the exchange coefficients. Finally, we will prove that the linearization method is stable.

Defining integrals over volume element in curved spacetime together with the mass and energy densities within that region of spacetime is apparently equivalent to the given energy and mass of that body or particle. With this in mind equations involving energies and mass can be rewritten in terms of their densities and the integral over the volume element. The idea find its place in the Hamiltonian formulations, and can be carried over into quantum mechanical frameworks systematically accounting for the effect of spacetime volume structures and gravity on dynamics of quantum systems. This article briefly explores this concept and runs through various frameworks and equations relevant to this idea, particularly the schrodinger-Newton equation and discusses the cosmological constant as a vacuum energy density.

This study focuses on the optimal deployment problem, and determines the optimal size of a military force to send to the battle field. The decision is optimized, based on an objective function, that considers the cost of deployment, the cost of the time it takes to win the battle, and the costs of killed and wounded soldiers with equipment. The cost of deployment is modeled as an explicit function of the number of deployed troops and the value of a victory with access to a free territory, is modeled as a function of the length of the time it takes to win the battle. The cost of lost troops and equipment, is a function of the size of the reduction of these lives and resources. An objective function, based on these values and costs, is optimized, under different parameter assumptions. The battle dynamics is modeled via the Lanchester differential equation system based on the principles of directed fire. First, the deterministic problem is solved analytically, via derivations and comparative statics analysis. General mathematical results are reported, including the directions of changes of the optimal deployment decisions, under the influence of alternative types of parameter changes. Then, the first order optimum condition from the analytical model, in combination with numerically specified parameter values, is used to determine optimal values of the levels of deployment in different situations. A concrete numerical case, based on documented facts from the Battle of Iwo Jima, during WW II, is analyzed, and the optimal US deployment decisions are determined under different assumptions. The known attrition coefficients of both armies, from USA and Japan, and the initial size of the Japanese force, are parameters. The analysis is also based on some parameters without empirical documentation, that are necessary to include to make optimization possible. These parameter values are motivated in the text. The optimal solutions are found via Newton- Raphson iteration. Finally, a stochastic version of the optimal deployment problem is defined. The attrition parameters are considered as stochastic, before the deployment decisions have been made. The attrition parameters of the two armies have the same expected values as in the deterministic analysis, are independent of each other, have correlation zero, and have relative standard deviations of 20%. All possible deployment decisions, with 5000 units intervals, from 0 to 150000 troops, are investigated, and the optimal decisions are selected. The analytical, and the two numerical, methods, all show that the optimal deployment level is a decreasing function of the marginal deployment cost, an increasing function of the marginal cost of the time to win the battle, an increasing function of the marginal cost of killed and wounded soldiers and lost equipment, an increasing function of the initial size of the opposing army, an increasing function of the efficiency of the soldiers in the opposing army and a decreasing function of the efficiency of the soldiers in the deployed army. With stochastic attrition parameters, the stochastic model also shows that the probability to win the battle is an increasing function of the size of the deployed army. When the optimal deployment level is selected, the probability of a victory is usually less than 100%, since it would be too expensive to guarantee a victory with 100% probability. Some of many results of relevance to the Battle of Iwo Jima, are the following: In the deterministic Case 0 analysis, the optimal US deployment level is 66200, the time to win the battle is 30 days and 14000 US soldiers are killed or wounded. If the marginal cost of the time it takes to win a victory doubles, the optimal deployment increases to 75400, the time to win a victory is reduced to 26 days, and less than 12000 soldiers are killed or wounded. In the stochastic Case 0 analysis, the optimal US deployment level is 65000, the expected time to win the battle is 46 days and almost 25000 US soldiers are expected to be killed or wounded. If the cost per killed or wounded soldier increases from 0 to 5 M $US, the optimal deployment level increases to 75000. Then, the victory is expected to appear after 35 days and 19900 US soldiers are expected to be killed or wounded.

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

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

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

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

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

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

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

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

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

In this article, we present a comparative study between the Adomian Decomposition Method (ADM) and Variational Iteration Method (VIM). The study outlines the significant features of the two methods, for solving nonlinear Volterra-Fredholm integro-differential equations. From the computational viewpoint, the VIM is more efficient, convenient and easy to use. Moreover, we proved the existence and uniqueness results and convergence of the solution. Finally, an example is included to demonstrate the validity and applicability of the proposed techniques.

In this paper after introducing a model of binary data matrix (BDM) for physical parameters of an evolving system (of particles), we develop a Hilbert space as an ambient space to derive induced metric tensor on embedded parametric manifold identified by associated joint probabilities of particles observables (parameters). Parameter manifold assumed as space-like hypersurface evolving along time axis, an approach that resembles 3+1 formalism of ADM and numerical relativity. We show the relation of endowed metric with related density matrix. Identification of system density matrix by this metric tensor, leads to the equivalence of quantum Liouville equation and metric compatibility condition while covariant derivative of metric tensor has been calculated respect to Wick rotated time or spatial coordinates. After deriving a formula for expected energy per particles, we prove the equality of this expected energy with local scalar curvature of related manifold. We show the compatibility of BDM model with Hamilton-Jacobi formalism and canonical forms. On the basis of the model, I derive the Ricci flow like dynamics as the governing dynamics and subsequently derive the action of BDM model and Einstein field equations. Given examples clarify the compatibility of the results with well-known principles such as equipartition energy principle and Landauer’s principle. This model provides a background for geometrization of quantum mechanics compatible with curved manifolds and information geometry. Finally, we conclude a “bit density principle” which predicts the Planck equation, De Broglie wave particle relation, , Beckenstein bound and Bremermann limit.

In this paper we investigate the optimal investment strategy for a defined contribution (DC) pension plan during the decumulation phrase which is risk-averse and pays close attention to inflation risk. The plan aims to maximize the expected constant relative risk aversion (CRRA) utility from the terminal wealth by investing the wealth in a financial market consisting of an inflation-indexed bond, an ordinary zero coupon bond and a risk-free asset. We derive the optimal investment strategy in closed-form using the dynamic programming approach by solving the corresponding Hamilton-Jacobi-Bellman (HJB) equation. Our theoretical and numerical results reveal that under some rational assumptions, an inflation-indexed bond do has significant advantage to hedge inflation risk.

In this paper, a class of semi-linear elliptic equations involving Hardy-Sobolev critical exponents has been investigated. This problem comes from the consideration of standing waves in the anisotropic Schr\"{o}dinger equation, also it is very important in the field of hydrodynamics, glaciology, quantum field theory and statistical mechanics. By a detailed estimation for the extremum function and using Mountain Pass Lemma with $\left( PS\right) _{c}$ conditions, the existence of positive solutions has been obtained. On the other hand, by establishing Pohozaev-type identity and using the properties of Bessel function, the nonexistence of positive solution also has been obtained. These results are extensions of E. Jannelli's research (\cite[Theorem 1.A-1.C]{EJ}).

Inverse problems of recovering surface fluxes on the boundary of a domain from pointwise observations are considered. Sharp conditions on the data ensuring existence and uniqueness of solutions in Sobolev classes are exposed. They are smoothness conditions on the data, geometric conditions on the location of measurement points, and the boundary of a domain. The proof relies on asymptotics of fundamental solutions to the corresponding elliptic problems and the Laplace transform. The problem is reduced to a linear algebraic system with a nondegerate matrix.

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

Blood perfusion quantification is important vital parameters in different diagnostic procedure, using infrared thermography imaging; it is reliable to use this technique as non-contact, non-invasive blood flow measurement method. Therefore, we developed a measurement protocol for blood flow over the arm's anterior surface. By using the superficial brachial and radial veins to be monitored under the impact of cold-excitation of (2 °C to 5 °C), the blood perfusion signal was detected using thermal imager of long-wave infrared spectral range (LWIR, 7μm - 14 μm). The simulation of Penne's bioheat transfer equation was performed to be compared with results obtained from the infrared thermography. Furthermore, the proposed blood flow monitoring using external adjusting of the excitation temperature, by using (cold-compress, or cold air-stream) applied to the region under testing. The signal detected resembles to the hemodynamic pulse of the superficial veins, in the definition of systolic and diastolic phases of the cardiac cycle. Moreover, statistical analysis applied to the BFIRT signals from 24 subjects to estimate the skin's mean temperature after recovery from the thermal excitation.

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

The rapid growth of the organic food market in Italy and in other developed countries has drawn the attention of researchers and practitioners. The diffusion of pro-environmental concerns and sustainable lifestyles among consumers are often cited as two of the main drivers of the increase in demand for organic food products. Consequently, unveiling the factors that influence consumers’ demand of, and preference for organic food is essential for all the actors involved in the supply chain. This paper presents the results of a research model which relates organic food purchase intention to consumers’ green consciousness, health motivations, food safety concerns, organic product knowledge, family and social context and perception of the intrinsic quality of food. A questionnaire, based on the Theory of Planned Behavior (TPB) and the extant literature on organic food choice, was developed and presented to a sample of 600 Italian consumers. Causal relations among variables were then tested using Structural Equation Modelling. The results suggest that, besides the existence of green consciousness, other variables may affect consumers’ preference for organic food: among these, specific and closely interlinked elements, such as food safety concerns and perceived quality heavily affected the intention to buy organic food products.

In the paper, by virtue of techniques in combinatorial analysis, the authors simplify two families of nonlinear ordinary differential equations in terms of the Stirling numbers of the first kind.

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

The instability of traveling pulses in nonlinear diffusion problems is inspected on the example of Gunn domains in semiconductors. Mathematically the problem is reduced to the calculation of the "energy" of the ground state in Schrödinger equation with a complicated potential. A general method to obtain the bottom-part spectrum of such equations based on the approximation of the potential by square wells is proposed and applied. Possible generalization of the approach to other types of nonlinear diffusion equations is discussed.