The aim of this study is to investigate and determine the key factors guiding customer attitudes towards social media influencers, and on that base to explore their effects on purchase intentions towards advertised products or services. A total of 376 fulfilled questionnaires from an online survey were analysed. The main characteristics of digital influencers’ behaviour, affecting consumer perceptions have been systematized and categorized through a combination of both traditional and advanced data analysis methods. Structural Equation Modelling (SEM), machine learning and multi-criteria decision-making (MCDM) methods were selected to uncover the hidden dependencies between variables from the perspective of social media users. The developed models elucidate the underlying relationships that shape the acceptance mechanism of influencers’ messages. The results obtained provide specific recommendations for stakeholders across the social media marketing value chain. Marketers can make informed decisions and optimize influencer marketing strategies to enhance user experience and increase conversion rates. Working collaboratively, marketers and influencers can create impactful and successful marketing campaigns that resonate with the target audience and drive meaningful results. Customers benefit from more tailored and engaging influencer content that aligns with their interests and preferences, fostering a stronger connection with brands and potentially affecting their purchase decisions. As the perception of customer satisfaction is individual and evolving process, stakeholders should organize regular evaluations of influencer marketing data and explore the possibilities to ensure continuous improvement of this e-marketing channel.

According to our current understanding of quantum mechanics, a `measurement' violates unitarity. In other words as the act of measurement `resets' the probabilities described by the Schrödinger equation, in the very `moment' of the collapse of the wavefunction, conservation of probability does not hold. To make progress in our understanding of the measurement problem it is thus expected that one must encompass in a single equation both otherwise mutually-exclusive processes of measurement and unitary evolution. In this light, turning to the continuity equation, we realize the possibility that if we allow for existence of sources and sinks in the `fluid of probability' we get closer to such a theory by arriving at nonlinear generalizations of Schrödinger and Klein-Gordon equations. The generalized equations derived are then shown to satisfy all conditions that are expected from a proper generalization: simplification to their linear counterparts by a well-defined dynamical condition, and Galilean and Lorentz invariance.

Biohydrogen is a versatile energy carrier for the generation of electric energy from renewable sources. Hydrogenases can be used in enzymatic fuel cells to oxidize dihydrogen. The rate of electron transfer (ET) at the anodic side between the [NiFe]-hydrogenase enzyme distal iron-sulfur cluster and the electrode surface can be described by the Marcus equation. All parameters for the Marcus equation are accessible from DFT calculations. The distal cubane FeS-cluster has a three cysteine and one histidine coordination [Fe₄S₄](His)(Cys)₃ first ligation sphere. The reorganization energy (inner- and outer-sphere) is almost unchanged upon a histidine-to-cysteine substitution. Differences in rates of electron transfer between the wild-type enzyme and the all-cysteine mutant can be rationalized by a diminished electronic coupling between the donor and acceptor molecules in the [Fe₄S₄](Cys)₄ case. The fast and efficient electron transfer from the distal iron-sulfur cluster is realized by a fine-tuned protein environment which facilitates the flow of electrons. This study enables the design and control of electron transfer rates and pathways by protein engineering.

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

In this paper, I investigate Hyers-Ulam-Rassias stabilities of the general quintic functional equation and the general sextic functional equation.

We consider a Mean Field Games model where the dynamics of the agents is given by a controlled Langevin equation and the cost is quadratic. A change of variables, introduced in [13], transforms the Mean Field Games system into a system of two coupled kinetic Fokker-Planck equations. We prove an existence result for the latter system, obtaining consequently existence of a solution for the Mean Field Games system.

Motivated by empirical observations, we propose a possible extension of Gibrat's law. By applying it into the random growth theory of income distribution (Gabaix, 2009), we find that the income distribution is described by a generalized Pareto-type distribution (GPD) with three parameters. We observe that there is a parameter /elta in the GPD that plays a key role in determining the shape of income distribution. By using the Kolmogorov-Smirnov test, we empirically show that, for typical market-economy countries, /elta is close to 0 significantly, such that the income distribution is characterized by a two-class pattern in which the bottom 90% of the population is approximated by an exponential distribution and the richest 1%~3% is approximated by an asymptotic power law. However, we empirically find that, for China both in planned economy period and in early stages of market reformation (from 1978 to 1990), /elta is significantly deviated from 0, such that the bottom of the population no longer conforms to an exponential distribution.

Maxwell's electric equation and Schrödinger quantum equation are used to find useful expressions for the probability of electrons existence and the electrons transport. The first expression which uses special relatively also shows that the probability of the electrons existence is higher for lower energy states compared to higher energy states where the probability is low. This means that electrons transport takes place from higher energy states to lower states. This conforms to the laws of chemistry where the atom tends to be stable by forcing electrons to occupy lower energy states. The second expression used the momentum velocity relation instead of special relatively. This expression shows also electrons transport from higher to lower states. It also shows that the probability of the electrons existence is higher for lower electrons density regions and lower for higher electrons density regions. This means that the electrons transport is from higher density regions to lower density regions. This conforms to the diffusion law.

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

Traditional population-based metaheuristic algorithms are effective in solving complex real-world problems but require careful strategy selection and parameter tuning. Parameter-less population-based optimization algorithms have gained importance due to their simplicity and efficiency. However, research on their applicability for solving large systems of nonlinear equations is still incipient. In this paper, a systematic review and detailed description of metaphor-less optimization algorithms is made, including the Jaya algorithm, the main Jaya variants for continuous optimization problems, with a focus on the Enhanced Jaya (EJAYA) algorithm, the three Rao algorithms, the best-worst-play (BWP) algorithm, and the very recent max-min-greedy-interaction (MaGI) algorithm. This paper also discusses a few previous parallelizations of the Jaya optimization algorithm, as well as recent GPU-based massively parallel implementations of the Jaya, Enhanced Jaya (EJAYA), Rao, and BWP algorithms developed by the authors. In addition, a novel GPU-accelerated version of the MaGI algorithm is proposed. The GPU-accelerated versions of the metaphor-less algorithms developed by the authors were implemented using the Julia programming language and tested primarily on GeForce RTX 3090 and NVIDIA A100 GPUs, as well as on Tesla V100S and Tesla T4 GPUs, using a set of difficult, large-scale nonlinear equation system problems. The computational experiments carried out produced quite significant speedups, which highlights the efficiency of the GPU-based versions of the metaphor-less algorithms developed for solving large-scale systems of nonlinear equations.

Recently several papers have been published on the Liénard equation x'' +L x+m x^3+n x^5=0, where the authors studied their explicit solutions and their applications. Here we describe the complete dynamics of these differential equations in the Poincar\'e disc. The Poincar\'e disc is the closed disc centered at the origin of coordinates of radius one, the whole plane R^2 is identified with the interior of this disc, and its boundary, the circle $\sss^1$ is identified with the infinity of R^2.

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

This paper presents a complete derivation and design of a physics-informed neural network (PINN) applicable to solve initial- and boundary value problems described by linear ordinary differential equations. The objective not to develop a numerical solution procedure which is more accurate and efficient than standard finite element or finite difference based methods, but to give a fully explicit mathematical description of a PINN and to present an application example in the context of hydrodynamic lubrication. It is, however, worth noticing that the PINN developed herein, contrary to FEM and FDM, is a meshless method and that training does not require big data which is typical in machine learning.

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

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

Predicting ground reaction forces (GRFs) and ground reaction moments (GRMs) through a biomechanical model-based approach offers advantages for biomechanical analysis, particularly in situations where the application of a statistical model is limited by insufficient training data. However, the current prediction method is unsuitable for clinical applications due to its long computational time. The present study developed a new optical motion capture (OMC)-based method to predict GRFs, GRMs, and joint torques. The proposed approach performed the estimation process by distributing external forces, as determined by the equation of motion, between the left and right feet based on foot deformations, thereby predicting the GRFs and GRMs without relying on machine learning or optimization techniques. We investigated the prediction accuracy during walking by comparing a conventional analysis using a force plate with the OMC results. The comparison revealed excellent or strong correlations between the prediction and measurement for all GRFs, GRMs, and lower limb joint torques. The proposed method, which provides practical estimation with low computational cost, facilitates efficient biomechanical analysis and rapid feedback of analysis results, thereby increasing its applicability for kinetics estimation in clinical settings.

The cellular model we teach and have theorized assumes that the cell is the basic unit of multicellular living beings. This fundamental element has been the subject of many theories concerning its properties and the exchanges that exist with its environment. In this article, we demonstrate that certain functional aspects, in particular the electrical aspects related to diffusion, have not been correctly assumed or that certain initial conditions have been purely ignored and are in contradiction with physics, chemistry and thermodynamics.

The ordinary 3D wave equation for nondissipative, homogeneous, isotropic media admits solutions where the point sources are permitted to move, but it does not admit solutions where the receiver is allowed to move. To overcome this limitation, the new wave equation is derived, permitting both the receiver and the source to move. This new wave equation is a generalization of the standard wave equation, and it reduces to the standard wave equation when the receiver is at rest. To derive this new wave equation, we first mathematically define a diverging spherical wave caused by the stationary point source. From this purely mathematical definition, the wave equation for the stationary source and the moving receiver is derived together with the corresponding free-space Green's function. Utilizing the derived Green's function, it was shown that this new wave equation also permits the solutions where both the receiver and the source are permitted to move. In conclusion, this paper demonstrates that, instead of an ordinary wave equation, the wave equation for the moving source and the moving receiver governs the waves emitted by the moving point sources and received by the moving receivers.

In this short note we present a technique using which one attributes frequency and wavevector to (almost) arbitrary scalar fields. Our proposed definition is then applied to the classical wave equation to yield a novel nonlinear PDE.

With continued scaling of semiconductor devices , the value of predictive analysis through 1 accurate quantum transport modeling is exponentially increasing. Quantum transmitting Boundary 2 method (QTBM) has been a well-known method of choice to model quantum transport in simple 1-D 3 devices. Here, we present an extension of the QTBM to the 2-D domain and apply it for more realistic 4 devices for accurate performance analysis.

In this paper, we study nonlocal problems for a fractional diffusion equation and a degenerate hyperbolic equation with singular coefficients in the lower terms. The uniqueness of the solution to the problem is proved by the method of energy integrals. The existence of a solution is equivalently reduced to the question of the solvability of Volterra integral equations of the second kind and a fractional differential equation. For a particular solution of the proposed problem, its visualization is carried out for various values of the order of the fractional derivative. It is shown that the order of the derivative affects the intensity of the diffusion process (subdiffusion), as well as the shape of the wave front.

We investigate the exact travelling wave solutions of the Tzitzéica-Dodd–Bullough–Mikhailov (TDBM) and Tzitzéica-type (TT) equations, appear in nonlinear optics, using simple ansatz approach. We use the Painlevé and traveling wave transformations to convert the mentioned nonlinear equations into nonlinear ordinary differential equations. Then, the simple ansatz approach has been employed to procure wave solutions, in terms of bright, singular soliton and trigonometric functions, for the Tzitzéica-Dodd–Bullough–Mikhailov (TDBM) and Tzitzéica-type (TT) equations. The study shows that the simple ansatz approach is straightforward and easy to implement for solving nonlinear problems.

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

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

This paper secures the analytical soliton solutions of the perturbed NLSE gives to (1). The existence criteria have been demonstrated and the wave speed of the soliton befall out. To achieve all the results obtained we used the mathematical technique. In view of the results obtained, some new additional one have been reported in left-handed metamaterials.

The resilience of towns and cities refers to their ability to adapt and recover when confronted with pressures or challenges. This study employs ten variables as indicators to assess the resilience of urban areas by analyzing official data and constructing a multilevel mixed-effects structural equation model. The empirical findings demonstrate that enhancing resilience significantly influ-ences urban service functions, such as strengthening healthcare systems, stabilizing the real estate market, and addressing socio-economic challenges. Specifically, factors such as healthcare re-sources, housing demand, population structure, and social security exhibit varying levels of resil-ience, which profoundly impact the spatial distribution of these factors and socio-economic de-velopment. Disparities in healthcare resource allocation, demographic aging trends, and shifts in the housing market closely correlate with resilience levels in different regions. Additionally, the study emphasizes that improving resilience not only boosts the reliability and security of urban services but also ensures that communities receive necessary support and protection during times of adversity. Consequently, policymakers should recognize the pivotal role of urban resilience in resource allocation and social equity, devising corresponding strategies to enhance the resilience of these areas.

We examine a family of nonlinear q-difference-differential Cauchy problems obtained as a coupling of linear Cauchy problems containing dilation q-difference operators, recently investigated by the author, and quasi-linear Kowalevski type problems that involve contraction q-difference operators. We build up local holomorphic solutions to these problems. Two aspects of these solutions are explored. One facet deals with asymptotic expansions in the complex time variable for which a mixed type Gevrey and q-Gevrey structure is exhibited. The other feature concerns the problem of confluence of these solutions as q tends to 1.

A linear Cauchy problem with polynomial coefficients wich combines q-difference operators for q>1 and differential operators of irregular type is examined. A finite set of sectorial holomorphic solutions w.r.t the complex time is constructed by means of classical Laplace transforms. These functions share a common asymptotic expansion in the time variable which turns out to carry a double layers structure which couples q-Gevrey and Gevrey bounds. In the last part of the work, the problem of confluence of these solutions as q tends to 1 is investigated.

The space time fractional Korteweg-de Vries equation, modified Equal Width equation and Benney-Luke Equations are solved by using simple hyperbolic tangent Ansatz method. A simple compatible wave transformation in one dimension is employed to reduce the governing equations to integer ordered ODEs. Then, the ansatz approximation is used to derive exact solutions. Some illustrative examples are presented for some particular choices of parameters and derivative orders.

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

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

Finding a solution for Euler's equations is a classic mechanics problem. This study revisits the problem with numerical approaches. For ease of teaching and research, a Maple code comprising 2 lines is written to find a numerical solution for the problem. The study's results are validated by comparing these with previous studies. Our results confirm the correctness of the principle of maximum moment of inertia of the rotating body, which is verified by thermodynamics. As an essential part of this study, the Maple code is provided.

Self-sustained learning (SSL) is considered a crucial factor in promoting students’ long-term learning and development in a sustainable society. To deepen the understanding of SSL, especially in the context of learning English as a second language, the current study examined the influence of intercultural communicative skills, language mindset, and positive L2 self on SSL in English learning among 1,238 college students in China. The results showed that students not only had a strong language mindset, positive L2 self, and intercultural communicative skills but also scored higher in long-term self-sustained English learning. Findings from the Structural Equation Modeling indicated that both language mindset and intercultural communicative skills positively predicted positive L2 self and self-sustained English learning. Furthermore, language mindset and intercultural communicative skills had an indirect impact on self-sustained English learning through positive L2 self. These findings suggest that to promote English learners’ SSL, instructors should help facilitate students’ intercultural communicative skills and foster a growth language mindset, as well as positive language learning beliefs.

We prove general stability theorems for $n$-dimensional quartic-cubic-quadratic-additive type functional equations of the form \begin{eqnarray*} \sum_{i=1}^\ell c_i f \big( a_{i1}x_1 + a_{i2}x_2 + \cdots + a_{in}x_n \big) = 0 \end{eqnarray*} by applying the direct method. These stability theorems can save us much trouble of proving the stability of relevant solutions repeatedly appearing in the stability problems for various functional equations.

Today, Colebrook’s equation is mostly accepted as an informal standard for modeling of turbulent flow in hydraulically smooth and rough pipes including transient zone in between. The empirical Colebrook’s equation relates the unknown flow friction factor (λ) with the known Reynolds number (R) and the known relative roughness of inner pipe surface (ε/D). It is implicit in unknown friction factor (λ). Implicit Colebrook’s equation cannot be rearranged to derive friction factor (λ) directly and therefore it can be solved only iteratively [λ=f(λ, R, ε/D)] or using its explicit approximations [λ≈f(R, ε/D)]. Of course, approximations carry in certain error compared with the iterative solution where the highest level of accuracy can be reached after enough number of iterations. The explicit approximations give a relatively good prediction of the friction factor (λ) and can reproduce accurately Colebrook’s equation and its Moody’s plot. Usually, more complex models of approximations are more accurate and vice versa. In this paper, numerical values of parameters in various existing approximations are changed (optimized) using genetic algorithms to reduce maximal relative error. After this improvement computational burden stays unchanged while accuracy of approximations increases in some of the cases very significantly.

In this article, we introduce a relatively new concept of multi-valued (θ;R)-contractions and utilize the same to prove some xed point results for a new class of multi-valued mappings in metric spaces endowed with an amorphous binary relation. Illustrative examples are also provided to exhibit the utility of our results proved herein. Finally, we utilize some of our results to investigate the existence and uniqueness of a positive solution for the integral equation of Volterra type.

The Sine-Gordon expansion method is implemented to construct exact solutions some conformable time fractional equations in Regularized Long Wave(RLW)-class. Compatible wave transform reduces the governing equation to classical ordinary differential equation. The homogeneous balance procedure gives the order of the predicted polynomial-type solution that is inspired from well-known Sine-Gordon equation. The substitution of this solution follows the previous step. Equating the coefficients of the powers of predicted solution leads a system of algebraic equations. The solution of resultant system for coefficients gives the necessary relations among the parameters and the coefficients to be able construct the solutions. Some solutions are simulated for some particular choices of parameters.

Background: While greenness has been associated with lower depression, the generalizability of this association in arid landscapes remains undetermined. We assessed the association between depression and greenness among nursing students living in El Paso, Texas (the Chihuahuan desert). Methods: Depression was measured with the Patient Health Questionnaire-9 scale, and greenness with the normalized difference vegetation index (at buffer sizes =250m, 500m, 1000m). Using data from the National Land Cover Database two additional measures of land patterns were analyzed: grayness and brownness. Structural equation models were used to assess the relationships of these land patterns to depression and quantify the indirect effects of peer alienation. Results: After adjusting for individual characteristics, at buffers 250 m greenness was associated with a decrease in the Incidence Rate Ratios (IRR) of depression by 49% (IRR, 0.51; 95%CI, 0.12-2.10), greyness with increases by 64% (IRR, 1.64; 95%CI, 1.07-2.52) and brownness with decreases by 35% (IRR, 0.65; 95%CI, 0.42-0.99). At buffer 250 m peer alienation explained 17.43% (95% CI, -1.79-36.66) of the association between depression and brownness, suggesting a pathway to depression. Conclusions: We did not observe an association between depression and residential greenness in El Paso, Texas. However, we did observe a protective association between brownness and depression as well as an adverse association with grayness. These results have theoretical implications as based on commonly used frameworks in this literature and adverse association of brownness (and the lack of greenness) and depression was expected.

We investigate the determinants of U.S. bilateral imports of olive oil and their dynamics from shocks in foreign supplies and changes in U.S. olive oil demand, using an augmented gravity framework that leads to an equilibrium of bilateral trade flows from olive oil exporters to the U.S. market. The empirical specification is applied at the disaggregated HS-6 level in a panel dataset, and three estimation techniques (truncated OLS, PPML, Heckman), for which the latter two account for zero trade flows, the extensive margin of trade and the potential censored distribution of exports with zero trade flows. We run Reset and HPC tests to qualify our results. On the supply side, exporters’ capacity to exports, multilateral trade resistance, and immigrants’ networks into the US are strong determinants of the bilateral trade flows for both aggregate olive oil exports and for virgin olive oil exports, On the consumer side, U.S. GDP, the import unit value, and immigrant network effects are robust determinants of bilateral flows as well for aggregate and virgin olive oil trade flows. Migrants’ stock, exporters’ GDP and population, and total exports revenues increase the probability of an exporter entering the U.S. market. We could not find robust evidence of consumer behavior being influenced by popular press measures of the emergence of Mediterranean diet and olive oil, or measures of cultural globalization of U.S. consumers.

This paper establishes a real integral representation of the reciprocal $\Gamma$ function in terms of a regularized hypersingular integral. The equivalence with the usual complex representation is demonstrated. A regularized complex representation along the usual Hankel path is derived.

These counterexamples have shown the relationships between the power of a Pythagorean equation and Pythagorean’s triples. There are three positive integers that satisfy Fermat’s equation when the power n is equal to 2 in the case of the Pythagorean theorem and it’s applicable relationships in right triangles. On the other hand, as the power varies from positive to negative integers or any integers other than 2, such as in the case of Fermat’s last theorem, the hypotenuse z of a right triangle tends to be equal to one of the sides x or y of the triangle and the other side tends to be equal to zero. And the application of this idea describes the behavior of a mass object in motion. Since the total energy of the object is the sum of its energy in motion and its rest energy, at a particular power n, the total energy of the object tends to be equal to either the rest energy or the photon energy.

Sums of M consecutive squared integers (a+i)^2 equaling squared integers (for a<=1, 0<= i<= M-1) yield remarkable regular linear features when plotting values of M in function of a. These features correspond to groupings of pairs of a values for successive same values of M around straight lines of equation mu*M = 2a and are characterized in this paper for rational values of mu.

The well-known equations for the process of powder compaction (PCP) in a rigid die published over the period from the beginning of the last century to the present are considered. Most of the considered equations are converted into the dependence of the densification pressure on the relative density. The equations were analyzed and their ability to describe PCP was assessed by determining the coefficient of determination when approximating experimental data on the compaction of various powders. It is shown that most of the equations contain two constants, the values of which are determined by fitting the mathematical dependence to the experimental curve. Such equations are able to describe PCP with high accuracy in the case of compaction of powders up to a relative density of 0.9-0.95. It is also shown that different equations can describe PCP in the range of density change from the initial to 0.9 with the same and sufficiently high accuracy, but when the process of compaction is extrapolated to higher values of density, the curves diverge. This indicates the importance of equations that can unambiguously describe PCP to a relative density equal to or close to 1.0. For an adequate description of PCP to a relative density greater than 0.95, equations containing three or four constants have proven themselves well.

Clifford algebra is unified language and efficient tool for geometry and physics. In this paper, we introduce this algebra to derive the integrable conditions for Dirac and Pauli equations. This algebra shows the standard operation procedure and deep insights into the structure of the equations. Usually, the integrable condition is related to the special symmetry of transformation group, which involves some advanced mathematical tools and its availability is limited. In this paper, the integrable conditions are only regarded as algebraic conditions. The commutators expressed by Clifford algebra have a neat and covariant form, which are naturally valid in curvilinear coordinate system and curved space-time. For Pauli and Schr\"odinger equation, many solutions in axisymmetric potential and magnetic field are also integrable. We get the scalar eigen equation in dipole magnetic field. By the virtue of Clifford algebra, the physical researches may be greatly promoted.

Legendre’s equation is key in various branches of physics. Its general solution is a linear function space, spanned by the Legendre functions of first and second kind. In physics however, commonly the only acceptable members of this set are the Legendre polynomials. Quantization of the eigenvalues of Legendre’s operator is a consequence of this. We present and explain a stand-alone, in-depth argument for rejecting all solutions of Legendre’s equation, but the polynomial ones, in physics. We show that the combination of the linearity, the mirror symmetry and the signature of the regular singular points of Legendre’s equation is quintessential to the argument. We demonstrate that the evenness or oddness of the Legendre polynomials is a consequence of the same ingredients.

This article aims to discuss, the stability and boundedness character of the solutions of the rational equation of the form \begin{equation}\label{eql21.1} y_{t+1}=\frac{\nu\epsilon^{-y_t}+\delta\epsilon^{-y_{t-1}}}{\mu+\nu y_t+\delta y_{t-1}},\quad t\in N(0). \end{equation} Here, $\epsilon>1, \nu,\delta,\mu\in (0,\infty)$ and $y_0, y_1$ are taken as arbitrary non-negative reals and $N(a)=\{a,a+1,a+2,\cdots \}$. Relevant examples are provided to validate our results. The exactness is tested using MATLAB.

In this study the tachyon-like Dirac equation, formulated by Chodos to describe superluminal neutrino, is solved. The analytical solutions are Gaussian wave packets obtained using the envelope method. It is shown that the superluminal neutrino behaves like a pseudo-tachyon, namely a particle with subluminal velocity and pure imaginary mass that fulfils the energy-momentum relation typical of classical tachyons. The obtained results are used to prove that the trembling motion of the particle position around the median, known as Zitterbewegung, also takes place for the superluminal neutrino, even if the oscillation velocity is always lower than the speed of light. Finally, the pseudo-tachyon wave packet is used to calculate the probability of oscillation between mass states, obtaining a formula analogous to the one obtained for the ordinary neutrino. This suggest that in the experiments concerning neutrino oscillation is not possible to distinguish tachyonic neutrinos from ordinary ones.

J. C. Maxwell, B. Riemann and H. Poincaré have proposed the idea that all microscopic particles are sink flows in a fluidic aether. Following this research program, a previous theory of gravitation based on a mechanical model of vacuum and a sink flow model of particles is generalized by methods of special relativistic continuum mechanics. In inertial coordinate systems, we construct a tensorial potential which satisfies the wave equation. Inspired by the equation of motion of a test particle, a definition of a metric tensor of a Riemannian spacetime is introduced. Applying Fock's theorem, a generalized Einstein's equation in inertial systems is derived based on some assumptions. This equation reduces to Einstein's equation in case of weak field in harmonic coordinate systems. In some special non-inertial coordinate systems, a second generalized Einstein's equation is derived based on some assumptions. If the field is weak and the coordinate system is quasi-inertial and harmonic, the second generalized Einstein's equation reduces to Einstein's equation. Thus, this theory may also explains all the experiments which support the theory of general relativity. There exists some fundamental differences between this theory and Einstein's theory of general relativity.

In an era characterized by technological disruption and unprecedented challenges posed by the COVID-19 pandemic, this scholarly investigation explores the role of Artificial Intelligence (AI) in shaping Leadership Dynamics in Higher Education Institutions (LDHE) within the specific socio-cultural and regulatory environment of China. Utilizing Structural Equation Modeling (SEM) as operationalized through the SMART_PLS software, this research harnessed data from a robust sample of 381 key stakeholders in China higher education. The study's empirical findings indicate a noteworthy impact of AI-informed decision-making processes on LDHE, which was further mediated by the variable of AI Literacy among leadership. Moreover, the consequences of the ongoing pandemic served as a moderating factor in this relationship. These nuanced outcomes not only contribute to the theoretical discourse surrounding educational leadership and technological integration but also provide actionable insights for policy formulation and institutional strategies in an increasingly complex educational landscape.

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

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

The effects on Raychaudhuri's equation of an intrinsically discrete or particle nature of spacetime are investigated, through consideration of null congruences emerging from, or converging to, a generic point of spacetime, i.e. in geometric circumstances somehow prototypical of singularity issues. This is done from an effective point of view, meaning through a (continuous) description of spacetime modified to embody the existence of an intrinsic discreteness on the small scale, adding to previous results for non-null congruences. Various expressions for the effective rate of change of expansion are derived. They in particular provide finite values for the limiting effective expansion and its rate of variation when approaching the focal point; this on top of resulting non vanishing the limiting cross-sectional area itself of the congruence.

In this paper, we investigate the equilibrium points, stability of two equilibrium points, convergences of negative equilibrium point, periodic solutions, and existence of bounded or unbounded solutions of a system of nonlinear difference equations x_n+1 =x_n-1y_n - 1, y_n+1 = y_n-1x_n - 1 n = 0,1,..., where the initial values are real numbers. Additionally we present some numerical examples to verify our theoretical results.

A reduced-dimension (RD) method based on the proper orthogonal decomposition (POD) technology and the linearized Crank-Nicolson mixed finite element (CNMFE) scheme for solving the 2D nonlinear Extended Fisher-Kolmogorov (EFK) equation is proposed. The method reduces CPU runtime and error accumulation by reducing the dimension of the unknown CNMFE solution coefficient vectors. For this purpose, The CNMFE scheme of the EFK equation is established and the uniqueness, stability and convergence of the CNMFE solutions are discussed. Subsequently, the matrix-based RDCNMFE scheme is derived by applying the POD method. Furthermore, the uniqueness, stability and error estimates of the linearized RDCNMFE solution are proved. Finally, numerical experiments are carried out to validate the theoretical findings. In addition, we contrast the RDCNMFE method with the CNMFE method, highlighting the advantages of the dimensionality reduction method.

Uncertainty relations in hydrodynamics are numerically studied. We first give a review for the formulation of the generalized uncertainty relations in the stochastic variational method (SVM), following the work by two of the present authors [Phys.\ Lett.\ A\textbf{382}, 1472 (2018)]. In this approach, the origin of the finite minimum value of uncertainty is attributed to the non-differentiable (virtual) trajectory of a quantum particle and then both of the Kennard and Robertson-Schr\"{o}dinger inequalities in quantum mechanics are reproduced. The same non-differentiable trajectory is applied to the motion of fluid elements in the Navier-Stokes-Fourier equation or the Navier-Stokes-Korteweg equation. By introducing the standard deviations of position and momentum for fluid elements, the uncertainty relations in hydrodynamics are derived. These are applicable even to the Gross-Pitaevskii equation and then the field-theoretical uncertainty relation is reproduced. We further investigate numerically the derived relations and find that the behaviors of the uncertainty relations for liquid and gas are qualitatively different. This suggests that the uncertainty relations in hydrodynamics are used as a criterion to classify liquid and gas in fluid.

DGJ (Daftardar-Gejii-Jafaris) method is used to obtain numerical solution of the third order fractional differential equation. Providing the DGJ method converges, the approximate solution is a good and effective numerical result which is close to the exact solution or the exact solution. For this,the examples of the explaning the method are presented. The proposed method is implemented for the approximation solution of the third order nonlinear fractional partial differential equations. The method was shown to be unsuitable and inconsistent for an example of a nonlinear fractional partial differential equation depend on initial-boundary value conditions. The fact that these numerical results are not consistent can be explained by the fact that the method is not convergent.

We apply utilized the extended form of the auxiliary equation method to obtain extensively reliable exact travelling wave solutions of perturbed Gerdjikov–Ivanov equation (GIE) that is widely used as a model in the field theory of quanta and non-linear optics. The method is based on a simple first order second degree ODE. The new form of the approach gives more solutions to the governing equation efficiently.

A probabilistic description is essential for understanding the dynamics of stochastic systems far from equilibrium. To compare different Probability Density Functions (PDFs), it is extremely useful to quantify the difference among different PDFs by assigning an appropriate metric to probability such that the distance increases with the difference between the two PDFs. This metric structure then provides a key link between stochastic processes and geometry. For a non-equilibrium process, we define an infinitesimal distance at any time by comparing two PDFs at times infinitesimally apart and sum these distances in time. The total distance along the trajectory of the system quantifies the total number of different states that the system undergoes in time and is called the information length. By using this concept, we investigate classical and quantum systems and demonstrate the utility of the information length as a unique Lagrangian diagnostic to quantify the information change as a system continuously evolves in time and to map out attractor structure. We further elucidate quantum effects (uncertainty relation) and the dual role of the width of PDF in quantum systems.

Using a nonclassical symmetry of nonlinear reaction-diffusion equations, some exact multi-dimensional time-dependent solutions are constructed for a fourth-order Allen-Cahn-Hilliard equation. This models a phase field that gives a phenomenological description of a two-phase system near the critical temperature. Solutions are given for the changing phase of a cylindrical or spherical inclusion, allowing for a 'mushy zone' with mixed state that is controlled by imposing a pure state at the boundary. The diffusion coefficients for transport of one phase through the mixture, depend on the phase field value, since the physical structure of the mixture depends on the relative proportions of the two phases. A source term promotes stability of both of the pure phases but this tendency may be controlled or even reversed through the boundary conditions.

Complex and real valued exact solutions to some reaction-diffusion equations are suggested by using homogeneous balance and Sine-Gordon equation expansion method. The predicted solution of finite series of some hyperbolic functions are determined by using some relations between the hyperbolic functions and trigonometric functions based on Sine-Gordon equation and traveling wave transform. The Newel-Whitehead-Segel and Zeldovich equations are solved explicitly. Some real valued solutions are depicted for some particular choice of parameters.

Many systems in nature and laboratories are far from equilibrium and exhibit significant fluc- tuations, invalidating the key assumptions of small fluctuations and short memory time in or near equilibrium. A full knowledge of Probability Distribution Functions (PDFs), especially time- dependent PDFs, becomes essential in understanding far-from-equilibrium processes. We consider a stochastic logistic model with multiplicative noise, which has gamma distributions as stationary PDFs. We numerically solve the transient relaxation problem, and show that as the strength of the stochastic noise increases the time-dependent PDFs increasingly deviate from gamma distributions. For sufficiently strong noise a transition occurs whereby the PDF never reaches a stationary state, but instead forms a peak that becomes ever more narrowly concentrated at the origin. The addition of an arbitrarily small amount of additive noise regularizes these solutions, and re-establishes the existence of stationary solutions. In addition to diagnostic quantities such as mean value, standard deviation, skewness and kurtosis, the transitions between different solutions are analyzed in terms of entropy and information length, the total number of statistically distinguishable states that a system passes through in time.

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

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

In a recent article, the author derived a new generalized Langevin equation and its associated Fokker-Planck equation of a Brownian particle in a parabolic potential where the thermal bath, consisting of $N$ harmonic oscillators, interacts bilinearly with the external field. The time needed for the system to reach a steady state is longer than that for the classical version where such an interaction is off. We find that there is a marked effect of the field-bath interaction on the average heat and entropy production of the bath represented through strong oscillations in such properties. The new theory applied to the system should improve the physical description of previous works done with the classical approach.

Chemotherapy-related deaths, the result of treatment with faulty medications, account for nearly 10% of all breast cancer deaths (Rashbass, 2016). Patient-specific, personalized medicine is evidently required to administer optimized therapeutics and prevent treatment-related mortality. In order to develop a predictive model for breast cancer therapy, the following study analyzed the mRNA data of 4,704 genes derived from 20 breast cancer patients before and after doxorubicin treatment for 16 weeks (O’brien et al., 2006; Perou et al., 2000). The genomic data of each patient was first stratified into 9 groups (corresponding to the 9 Mechanisms defined in Figure 4) based on mRNA expression in response to the tumor and to the doxorubicin treatment. The study then employed the Planckian Distribution Equation (PDE) discovered at Rutgers University to model the stratified samples by transforming each mechanism into a single long-tailed histogram fitted by the PDE. Our PDE model is based on 3 parameters - A, B, and C - of which 2 were extracted from each model to generate the plots seen in figures 5e and 5f. The drug-induced slopes of the A vs C plots were then determined for all 9 mechanisms of each patient. The study observed an increase in post-treatment mRNA levels for longer surviving patients in 6 mechanisms. Further analysis displayed how the drug treatment uniquely altered each of the mechanisms based on the length of patient survival. These results indicate that the PDE-based procedures described herein may provide a novel tool for discovering potential anti-breast cancer pharmaceuticals.

The temperature effect plays an important role for an accurate determination of the polar free energy, polar thermodynamic parameters, and enthalpic and entropic Lewis’s acid base properties of oxides, polymers and composites polymers/oxides. The adsorption of polymers on other solid surfaces is crucial in many industrial applications, coatings, paints, catalysis, colloids and adhesion processes. (1) Background: Inverse gas chromatography at infinite was used for the physico-chemical characterization of solid substrates by determining the thermodynamic parameters of adsorption of model organic solvents on solid surfaces such as polymers, metallic oxides, carbon fibers, pharmaceutical or 3D/4D printing substrates. (2) Methods: A new method based on the London dispersion equation was applied with a new parameter associating the deformation po-larizability and the harmonic mean of the ionization energies of solvent. More accurate values of the dispersive and polar interaction energies of the various organic solvents adsorbed on PMMA in bulk phase and PMMA/silica at different recovery fractions were obtained as well as the Lewis acid-base parameters and the transition temperatures of the different composites. (3) Results: This new methodology gave very interesting results on the behavior of PMMA adsorbed on silica. An important effect of the temperature and the recovery fraction on the various physicochemical and thermodynamic properties was highlighted. The variations of all interaction parameters showed the presence of three transition temperatures for the different PMMA adsorbed on silica with the various coverage rates with a shift of these temperatures for a recovery fraction of 31% (4) Con-clusions: An important variation of the polar enthalpy and entropy of adsorption, the Lewis ac-id-base parameters and the intermolecular separation distance as a function of the temperature and the recovery fraction of PMMA on silica.

Prior studies have focused on the overall behavior of randomly moving particle swarms. However, the characteristics of the stochastic-constrained particles that form ubiquitously within these swarms remain oblivious. This study demonstrates a generalized diffusion equation for stochastic-constrained particles that considers the velocity and location aggregation effects observed from their parent particle swarm (i.e., a completely random particle swarm). This equation can be approximated as the form of Schr\"odinger equation in the microcosmic case (low relative density) and describe the dynamics of the total mass distribution in the macrocosmic case (high relative density). The predicted density distribution of the particle swarm in the stable aggregation state is consistent with the total mass distribution of massive, relaxed galaxy clusters (at least in the range of r < r_s), preventing cuspy problems in the empirical Navarro-Frenk-White (NFW) profile. This study opens a window to observe the dynamics of stochastic-constrained particles from a third perspective, from which the aggregation effect of particles without gravitation can be saw.

We address the dynamics of two-dimensional Navier-Stokes models with infinite delay and hereditary memory, whose kernels are a much larger class of functions than the one considered in the literature, on a bounded domain. We prove the existence and uniqueness of weak solutions by means of Faedo-Galerkin method. Moreover, we establish the existence of global attractor for the system with the existence of a bounded absorbing set and asymptotic compact property.

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

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

The entropic gravity conception proposes that what has been traditionally interpreted as unobserved dark matter might be merely the product of quantum effects. These effects would produce a novel sort of positive energy that translates into dark matter via $E=mc^2$. In the case of axions, this perspective as been shown to yield quite sensible, encouraging results [DOI:10.13140/RG.2.2.17894.88641] . There, a simple Schrodinger mechanism was utilized, in which his celebrated equation is solved with a potential function based on the microscopic Verlinde's entropic force advanced in [Physica A {\bf 511} (2018) 139]. In this effort we revisit such technique with regards to fermions' behavior (specifically, baryons).

Quaternion algebra is used both for the description of the motion of material objects in 4D space-time and for the representation of the energy-momentum density tensor in the same quaternion basis, accurate to some arbitrary scalar fields. Quaternionic generating operators applied repeatedly to the energy-momentum density tensor lead to the gravitomagnetic equations that are parent equations for the series of physical equations ranging from the wave equations up to the quantum mechanical ones. Before finally deducing the gravitomagnetic equations, it is necessary to use the Lorentz gauge at a certain stage to cut off the arbitrary scalar fields. We declare that these superfluous scalar fields, inaccessible to direct observation, represent dark matter and dark energy. We show in what way the dark matter can provide a flat profile of the orbital speed of the galaxy's arm rotations.

The article outlines a creative approach by fusing ideas from fuzzy contractions, graph mappings, and Kannan mappings to create a brand-new notion known as "Kannan-graph-fuzzy contraction." This combination of concepts makes it possible to create a unique framework for resolving real-world issues controlled by nonlinear models. It is anticipated that using Kannan-graph-fuzzy contractions will offer a fresh approach to discussing solution existence in situations where these ideas overlap. This strategy might have a significant impact on a lot of real-world applications, proving how practical multidisciplinary techniques are for tackling issues in the real world originating from technology and engineering. The article includes several illustrated examples based on computer simulations, making the results more explicit.

In this paper, we work with a diffusion-perturbed risk model comprising a surplus generating process and an investment return process. The investment return process is of standard Black-Scholes type, that is, it comprises a single risk-free asset that earns interest at a constant rate and a single risky asset whose price process is modelled by a geometric Brownian motion. Additionally, the company is allowed to purchase noncheap proportional reinsurance priced via the expected value principle. Using the Hamilton-Jacobi-Bellman approach, we derive a second-order Volterra integrodifferential equation which we transform into a linear Volterra integral equation of the second kind. We proceed to solve this integral equation numerically using the block-by-block method for the optimal reinsurance retention level that minimizes the ultimate ruin probability. The numerical results based on light- and heavy-tailed distributions show that proportional reinsurance and investments play a vital role in enhancing the survival of insurance companies. But the ruin probability exhibits sensitivity to the volatility of the stock price.

Inverse Sumudu transform multiple shifting properties are used to design methodology for solving ordinary differential equations. Then algorithm applied to solve Whittaker and Zettl equations to get their new exact solutions and profiles which shown through Maple complex graphicals. Table of inverse Sumudu transforms for elementary functions given for supporting the differential equations solving using inverse Sumudu transform.

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

The generalized dual-kinetic-balance approach for axially symmetric systems is employed to solve the two-center Dirac problem. The spectra of one-electron homonuclear quasimolecules are calculated and compared with the previous calculations. The analysis of the monopole approximation with two different choices of the origin is performed. Special attention is paid to the lead and xenon dimers, Pb82+–Pb82+–e− and Xe54+–Xe54+–e−, where the energies of the ground and several excited σ-states are presented in the wide range of internuclear distances. The developed method provides the quasicomplete finite basis set and allows for construction of the perturbation theory, including within the bound-state QED.

Background: Tourism is one of the prominent industry that has a capability to generate handsome income for developed as well as developing countries. However, the study to investigate specifically the perception of local residents towards tourism is still lacking. The perception of the locals is important since it could determine the extent of their support for tourism development. Plus, previous research found that male residents are more support better towards the tourism development. Thus, this factor is adapted as well in this study to examine whether this gender may influence to the tourism industry. 2) Methods: This study used Structural Equation Modeling (SEM) technique for determining the structural estimates between constructs. 3) Results: The respondents agree that positive perception, negative perception and tourism impact has a significant impact on support for tourism development in which has been recognized as Social Exchange Theory model. Moreover, the finding also revealed that gender has a potential to moderates the causal effect of tourism impact on tourism development. 4) Conclusion: The resident understand the tourism sector could strengthen economic nation but they also want the natural resources should be protected.

This paper presents the simplified and quick way to obtain an experimental measure of the modulus of elasticity(E) of a piece of metal rod using the Smartphone microphone and through the experimental configuration in mode of unsupport beam Euler-Bernoulli(E-B). To understand it, it is required to have knowledge about flexural vibration of E-B beams and to know the analysis of the spectogram of the audio signal. The methodology consists in measuring the flexural resonance frequency through an app installed on a Smartphone and using the E formula deduced from the E-B theoretical framework. The results of the experimental measurements have a discrepancy of less than 5% with respect to the factory value, for a carbon steel rod with circular cross section using the impact excitation technique. It describes the precision and accuracy of the experimental measurement. It is useful, because it helps to classify the materials in the Faculty of Engineering and it helps to make a more efficient quality control.

This article investigates hydraulic percolation in saturated porous media, focusing on containment systems using sheet pile walls and gravity concrete dams. The Laplace equation, which governs hydraulic flow in porous media, is solved using the Finite Element Method through the ANSYS software. The modeling of the porous media employs a planar quadratic element called Plane 55, originally used for thermal problems, composed of four nodes and one hydraulic degree of freedom per node. The numerical results of the water pressure acting on the hydraulic structure, flow rate, and hydraulic gradient at the outlet of the porous media are compared with results obtained in the technical-scientific literature using flow nets. Two different methodologies are used to obtain the rate of seepage: by using the average hydraulic velocity or by calculating the integral of the hydraulic gradient perpendicular to the flow area. Both methodologies are compared and validated in the numerical simulations. This work also demonstrates the importance of mesh refinement for obtaining the flow rate in the studied hydraulic systems.

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

The solutions of the radial Schrödinger equation for a pseudoharmonic potential and Kratzer potentials has been studied separately in the past. The Kratzer potential despite different reports, the basic theoretic quantity such as Fisher information has not been reported. In this study, the solution of the radial Schrödinger equation for the combination of the pseudoharmonic and Kratzer potentials in the presence of a constant-dependent potential is obtained using the concepts and formalism of the supersymmetric and shape invariance approach. The position expectation value and momentum expectation value are calculated employing the Hellmann-Feynman Theory. The expectation values are used to calculate the Fisher information for both the position and momentum spaces in both the absence and presence of the constant-dependent potential. The obtained results revealed that the presence of the constant-dependent potential leads to an increase in the energy eigenvalue, as well as in the position and momentum expectation values. The presence of the constant-dependent potential also increases the Fisher information for both position and momentum spaces. Furthermore, the product of the position expectation value and the momentum expectation value along with the product of the Fisher information, satisfies both the Fisher’s inequality and the Cramer-Rao’s inequality.

A mathematical expression to describe cation absorption of root is expressed with simulation results. The root cells selectively emit H+ ions with active transport consuming ATPs to establish electrical gradient. The gradient promotes external positive ions to flow into the roots, while carries negatively charged particles with symport. In this paper, a mathematical model whose independent variables are the concentrations of external and internal cation is presented. This differential equation is induced from Ohm’s law. The equation has terms for plant physiology, ion’s physical and electrical properties, growth of plant, and interaction between the root and the surroundings. Simulation showed that the physiology-related coefficient has important role on nutrition absorption.

A probabilistic description is essential for understanding the dynamics of stochastic systems far from equilibrium, given uncertainty inherent in the systems. To compare different Probability Density Functions (PDFs), it is extremely useful to quantify the difference among different PDFs by assigning an appropriate metric to probability such that the distance increases with the difference between the two PDFs. This metric structure then provides a key link between stochastic systems and information geometry. For a non-equilibrium process, we define an infinitesimal distance at any time by comparing two PDFs at times infinitesimally apart and sum these distances in time. The total distance along the trajectory of the system quantifies the total number of different states that the system undergoes in time, and is called the information length. By using this concept, we investigate the information geometry of non-equilibrium processes involved in disorder-order transitions between the critical and subcritical states in a bistable system. Specifically, we compute time-dependent PDFs, information length, the rate of change in information length, entropy change and Fisher information in disorder-to-order and order-to-disorder transitions, and discuss similarities and disparities between the two transitions. In particular, we show that the total information length in order-to-disorder transition is much larger than that in disorder-to-order transition, and elucidate the link to the drastically different evolution of entropy in both transitions. We also provide the comparison of the results with those in the case of the transition between the subcritical and supercritical states and discuss implications for fitness.

Around 1637, Pierre de Fermat famously wrote in the margin of a book that he had a proof for the equation $a^n + b^n = c^n$ having no positive integer solutions for exponents $n$ greater than 2. This statement, now known as Fermat's Last Theorem, remained unproven for centuries, despite the efforts of countless mathematicians. Andrew Wiles' work in 1994 finally provided a rigorous proof of Fermat's Last Theorem. However, Wiles' proof relied on advanced mathematical techniques that were far beyond the scope of Fermat's time, raising questions about whether Fermat could have truly possessed a proof using the methods available to him. Wiles's achievement was widely celebrated, and he was awarded the Abel Prize in 2016 in recognition of his groundbreaking work. The citation for the award described his proof as a "stunning advance" in mathematics. The present work offers a potential solution to Fermat's Last Theorem that may be more aligned with the original approach that Fermat claimed to have used.

We investigated the dynamics of a simple master equation describing the evolution of a probability distribution between two states, \( p_1 \) and \( p_2 \) (with \( p_1 + p_2 = 1 \)). Our focus is on the behavior of the entropy \( S \), the distance \( D \) from the uniform distribution (\( p_1 = p_2 = 1/2 \)), and the free energy \( F \). We define two ratios, \( \eta_S = \frac{dS/dt}{dF/dt} \) and \( \eta_D = \frac{dD/dt}{dF/dt} \), and find that both diverge to plus-minus infinity as the system evolves towards the uniform distribution. This divergence marks a critical transition point where the master equation temporarily loses physical meaning. However, after this divergence, the system settles into a new, well-behaved regime where the solutions stabilize at finite values, representing a new equilibrium or steady state. This two-regime behavior underscores the intricate dynamics of simple probabilistic systems as they approach and surpass equilibrium, providing insights into the complex interplay of entropy, distance, and free energy in statistical mechanics.

The crust region is a tiny fraction of neutron stars, but it has a variety of physical properties and plays an important role in astronomical observations. One of the properties characterizing the crust is the elasticity. In this review, with the approach of asteroseismology, we systematically examine neutron star oscillations excited by crust elasticity, adopting the Cowling approximation. In particular, by identifying the quasi-periodic oscillations observed in magnetar flares with the torsional oscillations, we make a constraint on the nuclear saturation parameters. In addition, we also discuss how the shear and interface modes depend on the neutron star properties. Once one detects an additional signal associated with neutron star oscillations, one can get a more severe constraint on the saturation parameters and/or neutron star properties, which must be a qualitatively different constraint obtained from terrestrial experiments, and help us to complementarily understand astrophysics and nuclear physics.

This study delves into the Schrödinger equation's new invariants, shedding light on their crucial implications for theoretical physics and beyond. Specifically, it explores the behavior of scattering amplitudes and bound states concerning the choice of coordinate systems. The research unveils that while the energy of bound states remains invariant under coordinate transformations, the phase of scattering amplitudes undergoes variations, underscoring its pivotal role in theories reliant on phase normalization. Moreover, these findings have played a pivotal role in constructing estimates for three-dimensional Navier-Stokes equations, enhancing our ability to model complex fluid dynamics with greater precision and reliability. Additionally, in seismic exploration, tomography, and ultrasound imaging, these properties allow researchers to optimize phase selection, facilitating the most effective interpretation of measurement results. This strategic phase manipulation ensures clearer insights into subsurface structures, tissue composition, and fluid dynamics, with the flexibility to seamlessly transition back to the original coordinate system post-interpretation. This interdisciplinary synergy underscores the profound impact of fundamental theoretical research on advancing practical applications across diverse scientific domains.

In this work, the analytical treatment of Fourth order pd equations has been discussed with the variational iteration algorithm with an auxiliary parameter. The technique has the capability of reducing the size of computational work and easily overcomes the difficulty of the perturbation method or Adomian polynomials. Comparison with the classic variational iteration algorithm- is carried out, showing that the modification is more efficient and reliable.

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

In this paper, we examine the weak abc conjecture and the strong abc conjecture using some functions. we attempt to discuss the possibilty that the negative consequence of the weak abc conjecture. Namely, we derive that the weak abc conjecture is not true. Additionally, we show that the strong abc conjecture is not true.

In the paper, the authors present an explicit form for a family of inhomogeneous linear ordinary differential equations, find a more significant expression for all derivatives of a function related to the solution to the family of inhomogeneous linear ordinary differential equations in terms of the Lerch transcendent, establish an explicit formula for computing all derivatives of the solution to the family of inhomogeneous linear ordinary differential equations, acquire the absolute monotonicity, complete monotonicity, the Bernstein function property of several functions related to the solution to the family of inhomogeneous linear ordinary differential equations, discover a diagonal recurrence relation of the Stirling numbers of the first kind, and derive an inequality for bounding the logarithmic function.

The diameter of a H13 steel tool with M6 threads and a pin diameter of 5.9 mm and a pin length of 5 mm was measured after each 25.4 mm length of friction stir processing (FSP) of 6061-T6 extrusions. The change in pin diameter with FSP time or distance did not exhibit any steady state and was found to have two distinct regions. Metallographic analysis of two tools subjected to FSP for 60 and 120 seconds showed that (i) threads fractured in early stages of FSP, (ii) a built-up layer formed between the threads, and (iii) threads progressively wore with processing time. The metallographic analysis of an embedded tool showed the presence of a fractured piece of the tool in the stir zone. These points are discussed in detail in the paper.

The crab’s fishery of the genus Callinectes is one of the most important fisheries in Mexico. Sonora and Sinaloa are the states in the eastern coast of the Gulf of California, the mainland coast. Sinaloa encompass the greatest production in Mexico of these species, in particular the Bahía Santa Maria La Reforma (BSMR), supply the most important catches. An administrative mandatory document for the fishery is the Management Plan of Crab. One of the main weaknesses found in it for Sonora and Sinaloa is the lack of fisheries assessment in both states. For this reason, a structured size method called CASA (Catch at Size Analysis) was applied in the BSMR, in the seasons 2000, 2011 and 2014 to C. bellicosus. The first catch size (CW50%) estimated for females were 97.5, 102.5 and 100 mm, while in males it was estimated at 117.5, 107.5 and 102.5 mm. In the specific case of fishing mortality (F), the algorithm allowed us to detect that in the larger sizes the greater fishing pressure is applied for both, females and males, yielding a weighted exploitation rate of 0.047 (2000), 0.119 (2011) and 0.426 (2014) for females and 0.045 (2000), 0.295 (2011) and 0.132 (2014) for males, all below 50% (E= 0.50), crab C. bellicosus in BSMR is not at risk of over exploitation.

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

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

Probability is an open question in the ontological interpretation of quantum mechanics. It has been discussed in some trajectory interpretations such as Bohmian mechanics and stochastic mechanics. New questions arise when the domain of probability extends to the complex space, including the generation of complex trajectories, the definition of the complex probability, the relation of the complex probability to the real quantum probability, and so on. The complex treatment proposed here applies the optimal quantum guidance law to derive the stochastic differential (SD) equation governing the particle’s random motions in the complex plane. The ensemble of the complex quantum random trajectories (CQRTs) solved from the complex SD equation is used to construct the probability distribution ρc(t,x,y) of the particle’s position over the complex plane z=x+iy. The correctness of the obtained complex probability is confirmed by the solution of the complex Fokker-Planck equation. The significant contribution of the complex probability is that it can be used to reconstruct both quantum probability and classical probability, and to clarify their relationship. Although quantum probability and classical probability are both defined on the real axis, they are obtained by projecting complex probability onto the real axis in different ways. This difference explains why the quantum probability cannot exactly converge to the classical probability when the quantum number is large.

In this paper, we investigate some kind of Dynkin game under $g$-expectation induced by backward stochastic differential equation (shortly for BSDE). We define the lower and upper value functions $\underline{V}_t=ess\sup\limits_{\tau\in{\mathcal{T}_t}} ess\inf\limits_{\sigma\in{\mathcal{T}_t}}\mathcal{E}^g_t[R(\tau,\sigma)]$ and $\overline{V}_t=ess\inf\limits_{\sigma\in{\mathcal{T}_t}}ess\sup\limits_{\tau\in{\mathcal{T}_t}}\mathcal{E}^g_t[R(\tau,\sigma)]$, respectively. Under some regular assumptions, a pair of saddle point is obtained and the value function of Dynkin game $V(t)=\underline{V}_t=\overline{V}_t$ follows. Furthermore, the constrained case of Dynkin game is also considered.

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

Some of the recent large-scale national projects in South Korea are delayed or suspended due to belated responses to risk occurring on site. Currently, the Far East District (FED) project is being implemented to relocate the US Army bases from Yongsan to Pyeongtaek. Because of lack of experience and understanding about the characteristics of such a project, the deadline of taking over to the US Army Korea has been missed. This study identifies problems of each participant in the Yongsan Relocation Plan (YRP) of the US Army Korea with respect to construction project management and establishes a risk management strategy reflecting characteristics of FED project. To derive significant risk factors influencing YRP, various field data like weekly and monthly reports and other reports on construction condition are analyzed, and experts’ advices are collected and a survey is conducted. Mediators and latent variables are ultimately obtained. Furthermore, a structural equation model is used to both analyze and evaluate complex causal relations among many variables of YRP. The impact of risk factors on the schedule, quality and cost of the project is analyzed. In particular, the case of Site A is examined to see how the project is affected by those risk factors.