Corporate identity has played a vital role in the Halal industry to create a strong foundation for its reputation in the long run. This paper used two modeling analyses for two different data. The first analysis aims to predict the relationship between Corporate Identity Management between Internal Brand and Employee Brand Support (consequence) mediated by CIM using partial-least squares-structural equation modeling (PLS-SEM). A total of 206 employees from Malaysia’s Halal food SMEs took part in the survey. The second analysis to identify topic proportions patterns using the topic modeling approach on Halal brand identity Machine learning approach of knowledge mining was applied for this analysis. Metadata of 1,091 articles were mined from the Scopus database on Halal studies across all social sciences fields. The result revealed that there was a partial relationship between Internal Brand (antecedent) and Employee Brand Support (consequence) mediated by CIM. This finding was supported by the identified topic proportions patterns from the topic modeling approach that pointed out a weak topic proportion on the Halal brand identity discussion globally, interestingly the result also found that the Halal brand identity discussion involving the Halal food industry is almost non-existed in Malaysia’s Halal food SMEs. The contributions of this paper were apparent in three major areas which are methodology, theoretical and future suggestions. The utilization of two different model analyses was able to confirm the consistency of the major findings with the literature review which opens up more possibilities for future researchers.

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

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

This study presents the solution of the second type of a two-dimensional nonlinear integral equation in Banach space. Also, the existence and uniqueness of this equation’s solution are discussed. We utilize a numerical approach involving hybrid and block-pulse functions to obtain the approximate solution of a two-dimensional nonlinear integral equation. Nonlinear integral equation in two dimensions is reduced numerically to a system of nonlinear algebraic equations that can be solved using numerical methods. This study focuses on showing the convergence analysis for the numerical approach and obtaining an error estimate. Some numerical examples have been provided to demonstrate the approach’s viability and efficacy

In this paper, the notion of θ∗-weak contraction is introduced, which is utilized to prove some fixed point results. These results are helpful to give a positive response to certain open question raised by Kannan [Amer. Math. Monthly 76:1969] and Rhoades [Contemp. Math. 72:1988] on the existence of contractive definition which does not force the mapping to be continuous at the fixed point. Some illustrative examples are also given to support our results. As applications of our result, we investigate the existence and uniqueness of a solution of non-linear matrix equations and integral equations of Volterra type as well.

In cosmology, the cosmic curvature $K$ and the cosmological constant $\Lambda$ are two most important parameters, whose values have strong influence on the behavior of the universe. By analyzing the energy-momentum tensor and equations of state of ideal gas, scalar, spinor and vector potential in detail, we find that the total mass density of all matter is always positive, and the initial total pressure is negative. Under these conditions, by qualitatively analyzing the global behavior of the dynamical equation of cosmological model, we get the following results: (i) $K= 1$, namely, the global spatial structure of the universe should be a 3-dimensional sphere $S^3$. (ii) $0\le\Lambda < 10 ^ {-24} {\rm ly} ^ {-2}$, the cosmological constant should be zero or an infinitesimal. (iii) $a(t)>0$, the initial singularity of the universe is unreachable, and the evolution of universe should be cyclic in time. This means that the initial Big Bang is impossible at all. Since the matter components considered are quite complete and the proof is very elementary and strict, these logical conclusions should be quite reliable. Obviously, these conclusions will be much helpful to correct some popular misconceptions and bring great convenience to further research other problems in cosmology such as property of dark matter and dark energy.

The complete-lattice approach to optimization problems with a vector- or even set-valued objective already produced a variety of new concepts and results and was successfully applied in finance, statistics and game theory. For example, the duality issue for multi-criteria and vector optimization problems could be solved using the complete-lattice approach, compare [11]. So far, it has been applied to set-valued dynamic risk measures (in the stochastic case), as discussed in Feinstein, Rudloff etc. (see [11], for example), but it has not been applied to deterministic calculus of variations and optimal control problems. In this paper, the following problem of set-valued optimization is considered: minimize the functional $$ \overline J_t[y]=\int_0^t \overline L(s,y(s),\dot y(s))\ ds + U_0(y(0)) $$ over all admissible arcs $y$, where $\overline L$ is the associated multifunction to a vector-valued Lagrangian $L$, the integral is in the Aumann sense and $U_0$ is the initial cost. A new concept of \emph{value function}, for which a Bellman's optimality principle holds, is introduced. Also the classical result of the Hopf-Lax formula holds for the generalized value function. Finally, a derivative with respect to the time $t$ and a directional derivative with respect to $x$ of the value function are defined, based on ideas close to the concepts in [12]. The value function is proved to be solution of a suitable Hamilton-Jacobi equation.

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

In this paper we give approximations to the Mittag-Leffler functions in terms of elementary functions using different methods. This allowed us to establish a practical method we called integerization principle. This principle states that many fractional nonlinear oscillators may be solved by means of the solution to some integer-order Duffing oscillator equation. The accuracy of the obtained results is illsutrated in concrete examples. Formulas for estimating the errors in the approximations are also provided.

Evaporating liquid sessile drop deposited on horizontal surface is an important object of applications (printing technologies, electronics, sensorics, medical diagnostics, hydrophobic coatings, etc.) and theoretical investigations (microfluidics, self-assembly of nanoparticle, crystallization of the solute, etc.). The arsenal of formulas for calculating the slow evaporation of an axisymmetric drop of capillary dimensions deposited on a flat solid surface is reviewed. Such characteristics as vapor density, evaporation flux density, total evaporation rate are considered. Exact solutions obtained in the framework of the Maxwellian model, in which the evaporation process of the drop is limited by vapor diffusion from the drop surface to the surrounding air, are presented. The summary covers both well-known results obtained during the last decades and new results published by us in the last few years, but practically unknown to the wide scientific community. The newest formulas, not yet published in refereed publications, concerning exact solutions for a number of specific contact angles are also presented. In addition, new approximate solutions are presented for the first time (total evaporation rate and mass loss per unit surface area per unit time in the whole range of contact angles ), which can be used in modeling without requiring significant computational resources.

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

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

A model of space-time is presented, whose origin is set before the appearance of any universe. It uses concepts of previous work, a central one being that the information about the laws of nature is stored locally everywhere in space such that all physical processes obey them. Since information storage is bound to matter or energy, space is assumed to consist of dark energy (DE), which thus assumes an importance far beyond its function as a stopgap for an energy deficit in our universe ( U ). The primordial state (PS) is a timeless and relatively large space of 3 dimensions described by a Wheeler DeWitt (WDW) equation, whose solution is interpreted as an arrangement of very many space quanta and possesses properties that remind of the time-honored concept of the unmoved mover. The comparison of WDW solutions belonging to different mass densities of the DE favors one in which the space quanta are mini black holes. This allows the space quanta to be imagined as mass points which are kept at a distance compatible with the quantum volume by the Pauli principle or something equivalent. Triggered by a dramatic increase in probability, the PS is followed by a time-controlled sequence of quantized expansion states (ES i ). The concomitant emergence of time occurs in a lightning huge crash, consuming almost all DE of the PS. The subsequent quantized ES i emerge from a WDW equation, novelly derived from a solution of the modified cosmic momentum equation, which classically describes an exponential space expansion (CS). The huge volme of the ES i is also used as size of the PS. Information is assumed to be geometrically stored in arrangements of space quanta similar to how genetic information is stored in DNA molecules. During the CS information must be transferred from already existing "information quanta" to new ones. This requires time, slows down the expansion and is taken into account by a friction term in the cosmological momentum equation thus modified. Since the Friedmann-Lemaître (FL) equation remains fully valid, the model is widely based on recognized equations, so that some results may be understood as interpretations.

Multivariate Time Series Classification (MTSC) is one of most important tasks in time series analysis, aiding in activities such as human motion recognition and medical diagnostics. Existing methods for MTSC do not explicitly model temporal differences and generalize the idea of temporal difference into a efficient temporal module. Additionally, existing methods are not yet able to capture cross-variable relationships well during network training. As a result, they are unable to achieve convincing feature representation, leading to suboptimal classification accuracy. In this paper, we propose a novel MTSC model called Temporal Difference and Cross-variate Fusion Network (TDCFN), which integrates a two-stream differential LSTM network and a cross-variate feature extraction network to enhance feature representation. TDCFN achieves superior classification accuracy by capturing dynamic temporal evolution and inter-variable relationships. The experimental results show that TDCFN can achieve competitive performance with state-of-the-art multivariate time series classification approaches.

The National Institute of Justice reported that current methods for processing sexual assault samples have a high failure rate, with 60 to 80 percent of tested kits unable to produce usable DNA profiles. Even when samples test positive for male DNA, 34 percent of sexual assault kits (SAK) do not yield recovered male DNA after differential extraction. Less than 30% recovery of available sperm DNA contributes to this low success rate. The SpermX™ method (SX) has been shown to recover 80 percent or more of sperm DNA from sexual assault samples. An interlaboratory evaluation compared SX to standard differential extraction (DE) protocols. Mock samples with known ratios of female epithelial cells and sperm cells were processed using both methods. Results revealed that SX consistently provided CODIS up-loadable DNA profiles, even with as few as 25 sperm cells, whereas DE failed to produce usable results. On average, SX yielded a seven-fold increase in the recovery of unshared male alleles compared to DE. In conclusion, SX outperformed DE in recovering higher quantities of male DNA with minimal female carryover in sexual assault-type samples. This improved success rate in obtaining usable DNA profiles can significantly aid in solving sexual assault cases. Keywords: Differential extraction, Sexual Assault Kit (SAK), Sperm DNA, STRmix™, Combined DNA Index System (CODIS), Forensic DNA analysis, Low Sperm Samples, DNA Mixtures, Autosomal STR Analysis, SpermX.

The Eliezer and Gray physical interpretation of the Ermakov-Lewis invariant is applied as a guiding principle for the derivation of the special relativistic analog of the Ermakov-Milne-Pinney equation and associated first integral. The special relativistic extension of the Ray-Reid system and invariant is obtained. General properties of the relativistic Ermakov-Milne-Pinney are analyzed. The conservative case of the relativistic Ermakov-Milne-Pinney equation is described in terms of a pseudo-potential, reducing the problem to an effective Newtonian form. The non-relativistic limit is considered as well. A relativistic nonlinear superposition law for relativistic Ermakov systems is identified. The generalized Ermakov-Milne-Pinney equation has additional nonlinearities, due to the relativistic effects.

Land Surface Temperature (LST) estimation has been studied for several purposes, while the optimal method of estimating the LST has not been criticized yet. This research explores the optimum method in Land Surface Temperature (LST) estimation using LANDSAT-8 imagery data. Four different LST retrieval approaches, the Radiative Transfer Equation-based method (RTE), the Improved Mono-Window method (IMW), the Generalized Single-Channel method (GSC), and the Split-Window algorithm (SW), were calculated to present the LSTs over Buriram Town Municipality, Thailand. The calculated LSTs from these four methods were compared with the ground-based temperature data, taken on the same date and time of the employed LANDSAT-8 images. For this reason, the optimum method of the LST calculation was justified by considering the lowest normalized root means square error (NRMSE) values. As a result, the SW algorithm presents an optimum method in LST estimation. Regarding the SW, this algorithm requires not only the atmospheric profiles during satellite acquisition but also the retrieval of several coefficients. Besides, the LST retrieval method based on the SW algorithm is sensitive to water vapor content and coefficients. Although the SW algorithm is an optimum method explored in this study, it is emphasized that the adjustable values of coefficient response to the atmospheric state may be recommended. With these conditions, the SW algorithm can generate the land-surface temperature over the mixed land-use and land cover on the LANDSAT-8 images.

Plants have evolved tightly regulated strategies to adapt and acclimate to a changing environment to ensure their survival. Various environmental factors affect plant distribution, growth and yield. Low temperature belongs to those abiotic factors which significantly constrain range boundaries of plant species. Exposing plants to low but non-freezing temperature induces a multigenic processes termed cold acclimation, which finally results in an increased freezing tolerance. Cold acclimation comprises reprogramming of the transcriptome, proteome and metabolome and affects communication and signaling between subcellular organelles. Reprogramming of the central carbohydrate metabolism plays a key role in cold acclimation. This review summarizes current knowledge about the role of carbohydrate metabolism in plant cold acclimation. A focus is laid on subcellular metabolic reprogramming, its thermodynamic constraints under low temperature and mathematical modelling of metabolism.

This study addresses the latent construct of attitudes towards environmental conservation based on study participant’s responses. We measured and evaluated the latent scale based on an 18-item scale instrument, over four experimental strata (N=945) in the US Virgin Islands and the Caribbean. We estimated the latent scale reliability and validity. We further fitted multiple alternative two-parameter logistic (2PL) and graded response models (GRM) from Item-Response Theory. We finally constructed and fitted equivalent structural and generalized structural equation models (SEM/GSEM) for the attitudinal latent scale. All scale measures (composite, alpha-based, IRT-based and SEM-based) were consistently and reliably valid measures of the study participants’ latent attitudes toward conservation. We found statistically significant differences among participant’s attributes relating to socio-demographic, physical and core environmental characteristics of participants. We assert that the nature of relationship between cognitive attitudes and individual as well as social behavior related to environmental conservation.

Understory plants are important components of forest ecosystem productivity and diversity. Compared to biomass models of overstory canopy trees, few are available for understory saplings and shrubs and therefore their roles in estimation of forest carbon pools are often ignored. In this study, we harvested 24 understory species including 4 saplings, 9 tree-like shrubs and 11 typical shrubs in coniferous and broadleaved mixed forest in northeastern China and developed the best fit allometric equations of above- and below-ground and total biomass by species-specific or multispecies using morphological measurements of basal diameter, height and crown area as independent variables. The result showed that single basal diameter, height or crown area had good explanatory power for both species-specific and multispecies (p<0.001). The best-fit models included only basal diameter in sapling and tree-like shrubs, and combinations of crown area, height, and basal diameter in typical shrubs. The logarithmic model was most desired among the 4 model forms of linear, quadratic, multiple linear and logarithmic, for species-specific and multispecies. The models we developed should help the estimation of forest ecosystem carbon stocks, especially for belowground component, and provide tools for quantification of individual species biomass of understory plants.

Let {$\Gamma(k)$} denote {$(k-1)!$}, and let {$\Gamma_{n}(k)$} denote {$(k-1)!$}, where {$n \in \{3,\ldots,16\}$} and {$k \in \{2\} \cup [2^{\textstyle 2^{n-3}}+1,\infty) \cap \mathbb N$}. For an integer {$n \in \{3,\ldots,16\}$}, let $\Sigma_n$ denote the following statement: if a system of equations {${\mathcal S} \subseteq \{\Gamma_{n}(x_i)=x_k:~i,k \in \{1,\ldots,n\}\} \cup \{x_i \cdot x_j=x_k:~i,j,k \in \{1,\ldots,n\}\}$} with $\Gamma$ instead of $\Gamma_{n}$ has only finitely many solutions in positive integers {$x_1,\ldots,x_n$}, then every tuple {$(x_1,\ldots,x_n) \in (\mathbb N \setminus \{0\})^n$} that solves the original system ${\mathcal S}$ satisfies {$x_1,\ldots,x_n \leqslant 2^{\textstyle 2^{n-2}}$}. Our hypothesis claims that the statements {$\Sigma_{3},\ldots,\Sigma_{16}$} are true. The statement {$\Sigma_6$} proves the following implication: if the equation {$x(x+1)=y!$} has only finitely many solutions in positive integers $x$ and $y$, then each such solution {$(x,y)$} belongs to the set {$\{(1,2),(2,3)\}$}. The statement {$\Sigma_6$} proves the following implication: if the equation {$x!+1=y^2$} has only finitely many solutions in positive integers $x$ and $y$, then each such solution {$(x,y)$} belongs to the set {$\{(4,5),(5,11),(7,71)\}$}. The statement {$\Sigma_9$} implies the infinitude of primes of the form {$n^2+1$}. The statement {$\Sigma_9$} implies that any prime of the form {$n!+1$} with {$n \geqslant 2^{\textstyle 2^{9-3}}$} proves the infinitude of primes of the form {$n!+1$}. The statement {$\Sigma_{14}$} implies the infinitude of twin primes. The statement {$\Sigma_{16}$} implies the infinitude of Sophie Germain primes.

In this paper, we review a new treatment of classical radiation damping, which resolves a well-known contradiction in the Abraham-Lorentz equation that has long been a concern. This radiation damping problem has already been solved in quantum mechanics by the method introduced by Friedrichs. Based on Friedrichs’ treatment, we solved this long-standing problem by classicizing quantum mechanics by replacing the canonical commutation relation in quantum mechanics with the Poisson bracket relation in classical mechanics. As an application of our new approach, we will analyze the anomalous damping experienced by electrons undergoing cyclotron motion inside a waveguide near the cut-off frequency. This anomalous damping cannot be described using the existing Abraham-Lorentz equation.

In this study, we mainly focus on the behavior of an electron gas produced by argon plasma that is bounded by a moving rigid flat plate. The effects of an external magnetic field on the electrons collected with each other, with positive ions, and with neutral atoms in the plasma fluid are investigated. We used the BGK model of the Boltzmann kinetic equation, which is fundamental in the study of the gas dynamics from the continuum flow to the free-molecular regimes with Maxwellian velocity distribution functions of the various species. An exact analytical solution of the model equations for the unsteady flow is given using the moment and the traveling wave methods. The behavior of the mean velocity of electrons is illustrated, which compatible with the variation of the shear stress, viscosity coefficient, and the initial and boundary conditions. Besides, the thermodynamic prediction is investigated by applying the principles of irreversible thermodynamics and Gibbs formula. It is found that the thermodynamic variables verify the Boltzmann’s H–theorem, the principle of Le Chatelier, and the Thermodynamics Second Law for the non-equilibrium processes of the system. Qualitative agreements with previous related papers are introducing. 3-Dimensional graphics for the calculating variables are offering, and their behavior is deeply discussed.

This paper presents a quantum formulation for classical abstract dynamical systems (ADS), defined by coupled sets of first order differential equations. They are referred as “abstract” because their dynamical variables can be of different interrelated nature, not necessarily corresponding to physics, such as populations, socioeconomic variables, behavioural variables, etc. A first order classical Hamiltonian in canonical moments can be derived for ADS by using Dirac’s dynamics for singular Hamiltonian systems. And also a corresponding first order Schrödinger equation (which involves the existence of a system Planck constant particular of each system) can be derived from this Hamiltonian. However, Bohm and Hiley’s reinterpretation of quantum mechanics produces no further information about the mathematical formulation of ADS. However, a second order classical Hamiltonian in canonical moments can be also derived for ADS, as well as a corresponding second order Schrödinger equation. In this case, Bohm and Hiley’s reinterpretation of quantum mechanics provides a quantum Hamiltonian that does provide the quantum formulation for ADS, which provides new quantum variables interrelated dynamically with the classical variables. An application case is presented: the one-dimensional autonomous system given by the logistic dynamics, where the differences between the classical and the quantum trajectories are highlighted.

The present paper reports an alternative solution of the measurement problem in quantum theory. The measurement problem can be characterized as that the U procedure verses the R procedure. The R-procedure is tested by the Yes/No measurement originally proposed by von Neuman and discussed in details by Penrose. We propose a novel stochastic sampling method to tackle the measurement paradox. Each testing sample produces a pair of Yes-number c and No-number d, which in turn generates a sample phase with respect to the exponential form of . All the sample phases form a group, write Taking as the sampling potential, the revised Schrödinger equation has the form . This equation has a solution , where is the dynamic phase, while is the sample phase. Based on the Born rule, the probability of a sample is given by the squared magnitude of . Some metaproperties of the new U-R model, such as natural transformation, consistency, and completeness, are presented. The present work provides a new picture of quantum mechanics and alike

Evapotranspiration (ET) is a major component of water budget in Bottomland Hardwood Forests (BHF) and is driven by a complex intertwined suite of meteorological variables. The understanding of these interdependencies leading to seasonal variations in ET is crucial in better informing water resource management in the region. We used a structural equation modeling approach to analyze the drivers of ET using Eddy covariance water and heat flux data collected from a BHF, located in the Russel Sage Wildlife Management Area (RSWMA). It consists of mature closed-canopy deciduous hardwood trees with an average canopy height of 27 m. Factor analysis was used to characterize the shared variance among drivers and path analysis was used to quantify independent contributions of individual drivers. In our results, ET and net radiation (Rn) showed similar variability patterns with Vapor Pressure Deficit (VPD) and temperature in Spring, Summer, and Autumn seasons while they differ in Winter season. The path analysis shows that Rn has the strongest influence on ET variations via direct and indirect pathways. In the deciduous forests like BHFs, our results suggest ET is more energy-dependent during growing season (Spring and Summer) and early non-growing season (Autumn) while more temperature-dependent during winter season.

Fractional-time Schrödinger equation (FTSE) describes the evolution of quantum processes endowed with memory effects. FTSE manifestly breaks all consistency requirements of quantum field theory (unitarity, locality and compliance with the clustering theorem), unless the order of fractional differentiation and integration ( ) falls close to the standard index . Working in the context of the minimal fractal manifold (where , ), we confirm here that FTSE approximates the attributes of gravitational metric and provides an unforeseen generation mechanism for massive fields.

While current studies have focused on adoption and the relevant content of the app to become a decision support system, very few studies have focused on the farmer's intention and initial decision to adopt. Based on a survey of 394 smallholder farmers this study investigated Mexican farmers’ willingness to adopt an agricultural advice app. A Structural Equation Modelling approach, based on the Unified Theory of Acceptance and Use of Technology (UTAUT) was applied. To understand farmers’ adoption decision, extended constructs were studied (e.g. mastery-approach goals) along with farmers’ age and participation in an innovation hub. Results showed that the intention to adopt the app is predicted by how farmers believe that technical infrastructure exists and by the expectation of the farmers using the app to acquire new knowledge. The multi-group analysis revealed that performance expectancy is a relevant predictor of the intention to adopt, whereas the mastery-approach goal is relevant only for younger and farmers not connected to the innovation hub. The results may well be a baseline to research further suitable non-financial incentives for different farmers’ groups, then encourage initial adoption and enhance uptake. The findings are useful for practitioners and app developers designing digital decision support tools.

Helmholtz energy of ice VII-X is determined in a pressure regime extending to 450 GPa at 300 K using local basis functions in the form of b splines. The new representation for the equation of state is embedded in a physics-based inverse theory framework of parameter estimation. Selected pressures as a function of volume from 14 prior experimental studies and two theoretical studies constrain the behavior of Helmholtz energy. Separately measured bulk moduli, not used to construct the representation, are accurately replicated below about 20 GPa and above 60 GPa. In the intermediate range of pressure, the experimentally determined moduli are larger and have greater scatter than values predicted using the Helmholtz representation. Although systematic experimental error in the experimental elastic moduli is possible and likely, the alternative hypothesis is a slow relaxation time associated with changes in proton mobility or the ice VII to X transition. A correlation is observed between anomalies in the pressure derivative of the predicted bulk modulus and previously suggested higher-order phase transitions. Improved determinations of elastic properties at high pressure would allow refinement of the current equation of state. More generally, the current method of data assimilation is broadly applicable to other materials in high-pressure studies.

Advanced methods of treatment are needed to fight the threats of virus-transmitted deseases and pandemics. Often they are based on an improved biophysical understanding of virus replication strategies and processes in their host cells. For instance, an essential component of the replication of the Hepatitis C virus (HCV) proceeds under the influence of non-structural HCV proteins (NSPs) that are anchored to the endoplasmatic reticulum (ER), such as the NS5a protein. The diffusion of NSPs has been studied by in-vitro fluorescence recovery after photobleaching (FRAP) experiments. The diffusive evolution of the concentration field of NSPs on the ER can be described by means of surface partial differential equations (sufPDE). Knodel et al, Viruses 2018, 10, 28 estimated the diffusion coefficient of the NS5a protein by minimizing the discrepancy of an extended set of sufPDE simulations and experimental FRAP time series data. Here, we provide a scaling analysis of the sufPDEs that describe the diffusive evolution of the concentration field of NSPs on the ER. This analysis provides an estimate of the diffusion coefficient that is based only on the ratio of the membrane surface area in the FRAP region and its contour length. The quality of this estimate is explored by comparison to numerical solutions of the sufPDE for a flat geometry and for ten different 3D embedded 2D ER grids that are derived from fluorescence z-stack data of the ER. Finally, we apply the new data analysis to the experimental FRAP time-series data analyzed in our previous paper, and we discuss the opportunities of the new approach.

In our previous papers [1,3], using only the concepts of the zero-point energy and quantized space–times, all the fields including gravity were explained. However, the previous papers had the following limitations: First, the concept of the quantized space-time must be experimentally confirmed. Second, we should clarify the meaning of the quantized Einstein’s gravity equation, which is derived in [1]. Moreover, in another paper [2], we succeeded in describing the neutrinos’ self-energy and their oscillations. However, this paper assumes the rest energy of 3-leptons in advance, which is why we needed to uncover the reason why leptons have 3-generations. As mentioned, using the concepts of the zero-point energy and quantized space–times, we derived the quantized Einstein’s gravity equation in our previous paper [1]. The paper provides an analytical solution of this equalized Einstein’s equation, which implies the conservation of angular momentum in terms of quantized space–times. Employing this solution and without the standard big bang model, a unique form of acceleration equation for the acceleration-expansion universe is derived. Moreover, the temperature of the cosmic microwave background (CMB) emission is also obtained. Further, this solution results in an analytical (not numerical) derivation of the gravity wave. Moreover, based on the configuration of quantized space–times in terms of both electric and magnetic fields, we analytically attempted to calculate every equation in terms of electromagnetic and gravity fields, using the solution of the quantized Einstein’s gravity equation. As a result of this theory, first the calculated acceleration and temperature of CMB emission agree with the measurements. Furthermore, the analytical solution of the quantized Einstein’s gravity equation resulted in all the laws of electromagnetic and gravity fields in addition to the analytically derived gravity wave, which agrees well with the recent measurements. Moreover, the calculations of the energies in the basic configuration of the quantized space–times resulted in all 3-leptons’ rest energies. Considering this basic configuration is uniformly distributed everywhere in the universe, we can conclude that τ-particles or static magnetic field energy derived from the basic configuration of the quantized space–times is the identity of dark energy, which also distributes uniformly in the universe.

The structure and phenomena arising from charge transfer in cold field emission modus in a single closed carbon nanotube under cold field emission conditions were studied. By studying microphotographs in various microscopes - AFM, SEM, TEM it was found inhomogeneities in the form of two types of superlattices. The conductivity of the emitter section of a nanodiode circuit with an emitter made of an individual closed carbon nanotube (CNT) and arrays of closed CNTs was studied. High values of cold field emission were observed, as well as nonlinearity and anomalies of the current-voltage characteristic (I-V characteristics), which manifested themselves in the form of peaks at low and high current values. Peaks in the CVC have distinct areas of negative differential conductivity. It is argued, that the anomalously high currents in the I–V characteristics of cold field emission of electrons from a nanoemitter made of closed CNTs can be associated with a sharp increase in the density of electron states at energies near the van Hove singularity.

In this work, an improved collocation method based on the Bernoulli polynomials is presented to solve the Volterra integral equation (VIE) of the second kind. The main idea of the proposed method is to improve the results of the classic Bernoulli collocation method (BCM) by dividing the interval into some sub-intervals and considering the collocation points on each of them. Here, the zeros of the shifted Chebyshev polynomials (SCPs) are considered as collocation points. Then, BCM is applied step by step from the first sub-interval to the last one. By this process, a system of algebraic equations is attained for each sub-interval that could be easily solved. Convergence of the scheme is analyzed. For the purpose of demonstrating the validity, applicability, and efficiency of the suggested scheme several numerical examples are provided. Numerical results illustrate that the accuracy of the improved Bernoulli collocation method (IBCM) is more than BCM.

The paper examines common elements between Lévai’s and Milson’s potentials obtained by Liouville transformations of two rational canonical Sturm-Liouville equations (RCSLEs) with even density functions which are exactly solvable via Jacobi polynomials in a real or accordingly imaginary argument. We refer to the polynomial numerators of the given rational density function as ‘tangent polynomial’ (TP) and thereby term the aforementioned potentials as ‘e-TP’ A special attention is given to the overlap between the two potentials along symmetric curves which represent two different forms of the Ginocchio potential exactly quantized via Gegenbauer and Masjed-Jamei polynomials respectively. Our analysis reveals that the actual interconnection between Lévai’s parameters for these two rational realizations of the Ginocchio potential is much more complicated than one could expect based on the striking resemblance between two quartic equations derived by Lévai for ‘averaged’ Jacobi indexes.

The requirement for developing tools capable of detecting and monitoring heavy metals (HMs) has recently taken on more significance due to worries about their toxic effect on human health and aquatic habitats. In this study, a simple electrochemical sensing carbon paste electrode (CPE) based on composite of Zinc/Iron layered double hydroxide (LDH) and polyaniline (PANI) was developed for the determination of lead ions in aquatic solutions. For this purpose, Zn-Fe LDH/PANI was prepared and characterized by Fourier transform infrared (FTIR), X ray diffraction (XRD), and scanning electron microscopy (SEM). Modified carbon electrode based Zn-Fe LDH/PANI was electrochemically characterized compared with unmodified electrode in FCN as a redox probe using cyclic voltammetry (CV). Thus, Zn-Fe LDH/PANI was utilized as sensing material for the electrochemical determination of lead ions using differential pulse voltammetry (DPV). Zn-Fe LDH/PANI/CPE show limits of detection (LOD) and quantification (LOQ) of 167.8 nM and 559.4 nM, respectively. Zn/Mg/Fe LDH was prepared using co-precipitation method and characterized by XRD, FTIR, SEM and BET, used for removal of Pb+2 ions. Removal process was investigated at different conditions as pH, metal ion concentrations, starting adsorbent dose at first and contact time. Zn/Mg/Fe LDH was evaluated as an effective adsorbent material for lead ions elimination in aquatic solutions, with capacity of adsorption 700 mg/g. The elimination of lead ions on Zn/Mg/Fe LDH fitted the pseudo first-order kinetics model and the isotherm was matched with Langmuir model. Studies revealed that the ideal removal conditions were pH = 5.0, an adsorbent mass of 0.05 g, and 20 ml of 50 ppm metal ion concentration at 60 min. The Zn-Fe LDH/PANI composite also showed potential anti-cancer properties against lung cancer cells (A549) while maintaining safety for normal lung fibroblast cells (WI-38). Collectively, advancements in electrochemical sensors offer promising solutions for lead ion detection, with wide-reaching applications in wastewater treatment and cytotoxicity assessment. These innovations have the potential to enhance environmental monitoring and public health safety.

The extent of micro-phase separation in polyurethanes (PUs) depended on the molecular weight, the chemical nature and the structure of the polyol/soft segments. Balanced properties in PUs were obtained by using blends of polyols during synthesis. No previous studies have been devoted to understand the interactions between the soft segments that affect the properties of the PUs. In this study, different blends of two polyols of different nature (polyester – PE - and polycarbonate diol - CD) and similar molecular weight were prepared and their structural, thermal, surface, viscoelastic and self-adhesion properties were assessed. PE showed larger number of structural repeating units and higher number of polar groups than CD, but the carbonate-carbonate interactions in CD were stronger than the ester-ester interactions in PE. The blending of CD and PE imparted synergic structural properties, particularly in the ones containing less than 50 % PE, they were associated to the disrupt of carbonate-carbonate interactions in CD and the formation of new ester-carbonate and hydroxyl-carbonate interactions. Therefore, higher glass transition temperatures, a new diffraction peak at 2θ = 24°, one additional thermal degradation at 426-436 °C, and less steeper decline of the storage moduli to lower temperature were found in CD+PE blends with less than 50 wt.% PE. Furthermore, the different interactions between the polyol chains in the blends were also evidenced on their surface properties, and all CD+PE blends showed self-adhesion property which seemed related to the existence of ester-carbonate and carbonate-carbonate interactions.

The morphology of virgin reactor powder (RP) of high-density polyethylene HDPE with MW = 160,000 g/mol was investigated with the help of DSC, SEM, SAXS and WAXS methods. The morphological SEM analysis showed, that the main morphological units of RP are macro- and micro-shish kebab structures with significantly different geometric dimensions, as well as individual lamellae of folded chain crystals. Quantitative analysis of an asymmetric SAXS reflection made it possible to reveal the presence of several periodic morphoses in the RP with long periods from 20 nm to 60 nm and to correlate them with the observed powder morphology. According to the DSC crystallinity data, the thickness of the lamellae in each long period was estimated. Their surface energy was calculated in the framework of the Gibbs-Thompson theory. The presence of regular and irregular folds on the surface of the different shish-kebab lamellae is discussed. The percentage of identified morphoses in the RP was calculated. It has been suggested that the specific structure of HDPE RP is due to the peculiarity of polymer crystallization during suspension synthesis in a quasi-stationary regime, in which local overheating and inhomogeneous distribution of shear stresses in a chemical reactor are possible.

In general, a superconductor has zero resistance, although it requires significant refrigeration or high pressures with high manufacturing costs, which prevents it into practical applications. In other words, solving these issues implies main superconducting researches. To solve these problems, this paper describes a new type of superconductivity, which is independent for temperatures and which operates without pressures. The principles of the presented system are as follows:First a voltage source, a current source and a load are connected in series. Then, the voltage of the voltage source is adjusted to balance the voltage of the load. Under this condition, the balance of the two voltages provides a zero voltage between the taps of the current source and the generated current from the voltage source becomes zero because of the internal infinite resistance of the current source. As a result, the electric powers generated by the two sources are zero, and therefore, the load cannot generate Joule heating because of energy conservation. However, the current from the current source (not the voltage source) is not zero; therefore, we can predict that the resistance of the load must be zero. As a theory, we derived a new electric field and transient attractive force, which result in a very short coherence of an electron pair because there is not the Coulomb repulsive force due to the existence of the above transient attractive force. Note that both the forces are derived by the Poisson equation, which implies that they cannot be compatible. Therefore, the pair combination energy from spins becomes extremely strong, which is not destroyed by the normal heat energy. Moreover, every center-of-mass motion of electron pair results in the Bose-Einstein condensation and the macroscopic wave function, which produces the London equation (i.e., the Meissner effect). Moreover, by introducing the equivalent circuit, this paper conducted numerical calculations. As a result, we could derive numerically zero resistance and responses for additional static magnetic fields as a discharged current, which implies the Meissner effect. Note that this paper has prepared Appendix section, which provides a guide to reproduce actual experiments and preliminary experimental results. These results in the Appendix indicate the zero resistances and Meissner effects.

The Lagrangian formalism is developed for the population dynamics of interacting species that are described by several well-known models. The formalism is based on standard Lagrangians, which represent differences between the physical kinetic and potential energy-like terms. A method to derive these Lagrangians is presented and applied to selected theoretical models of the population dynamics. The role of the derived Lagrangians and the energy-like terms in the population dynamics is investigated, and it is shown that the obtained standard Lagrangians can be used to study oscillatory behavior of the models and the period of their oscillations, which may have ecological and environmental implications. These and other physical and biological insights gained from the derived standard Lagrangians are discussed.

An overview is presented of several diverse branches of work in the area of effectively 2D fluid equilibria which have in common that they are constrained by an infinite number of conservation laws. Broad concepts, and the enormous variety of physical phenomena that can be explored, are highlighted. These span, roughly in order of increasing complexity, Euler flow, nonlinear Rossby waves, 3D axisymmetric flow, shallow water dynamics, and 2D magnetohydrodynamics. The classical field theories describing these systems bear some resemblance to perhaps more familiar fluctuating membrane and continuous spin models, but the fluid physics drives these models into unconventional regimes exhibiting large scale jet and eddy structures. From a dynamical point of view these structures are the end result of various conserved variable forward and inverse cascades. The resulting balance between large scale structure and small scale fluctuations is controlled by the competition between energy and entropy in the system free energy, in turn highly tunable through setting the values of the conserved integrals. Although the statistical mechanical description of such systems is fully self-consistent, with remarkable mathematical structure and diversity of solutions, great care must be taken because the underlying assumptions, especially ergodicity, can be violated or at minimum lead to exceedingly long equilibration times. Generalization of the theory to include weak driving and dissipation (e.g., non-equilibrium statistical mechanics and associated linear response formalism) could provide additional insights, but has yet to be properly explored.

This work is a top-level summary of several contributions published in the last three decades. It makes the case that complex dynamics of nonlinear systems lies at the heart of foundational physics.

Different forces play a key-role in the stability of food colloid dispersions. Focus is here on those controlling attraction and/or repulsion, which concur to stabilization, phase separation, coagulation, and are quite evident in water-based systems. Combination of attractive and repulsive forces favors, or hinders, the association of colloid entities; such processes are often met in food technology. The above processes depend on the forces at work, and on colloid concentration in the medium (i.e. on inter-particle distance). Worked examples deals with milk manipulation procedures, ending in cheese formation. The whole milk-working sequence is controlled by the combination of forces leading to aggregation and phase separation of casein and other milk components. Thereafter, one gets either fresh, for prompt consumption, or aged cheeses. The combination of attractive (van der Waals, vdW, and depletion) with repulsive (double layer, DL, but also with steric) forces results in the dominance of aggregation versus dispersion modes in all steps of milk transformation, which depend on the distance among colloid particles, on the amplitude of the mentioned forces, and on their decay length. The combined role of double layer and van der Waals (vdW) forces is at the basis of the DLVO theory on colloid stability, which is properly modified when these forces overlap with steric stabilization and, eventually, with depletion. Steric effects are dispersive, depletion ones favor colloid nucleation in a single phase. The milk manipulation chain is a worked example of the intriguing association features controlled by the mentioned forces (and of ancillary ones, as well), and indicates which forces favor the formation of products such as Parmesan or Mozzarella cheese, but are not alien to the preparation of many other dairy products.

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

This feature study attempts on setting a granules involving mesoscopic matter-aggregation context as a problem of passing locally by the matter-aggregating system from classical stochastic (mesoscopic limit) to a quantum description (nanoscale quantum-size effect limit). A d-dimensional entropy-production aggregation of the granules-involving matter is considered in terms of a (sub)diffusive realization. It turns out that when taking a full d-dimensional pathway of the aggregation toward the nanoscale, one is capable of disclosing a Heisenberg type (diffusional) relation, setting up an upper uncertainty bound for the (sub)diffusive very slow granules-including environment that matches the quantum limit of h/2pm (m– average mass of a granule; h – the Planck’s constant) for the diffusion coefficient of the aggregation, likely first proposed by Fürth in 1933, and qualitatively foreseen by Schrödinger some years before, both in the context of a diffusing particle cluster. The classical-quantum passage uncovered here, also termed insightfully the quantum-size effect (as borrowed from the quantum dots’ parlance), works properly for the three-dimensional (d=3) case, making use of a substantial physical fact that the (nano)granules interact readily via their surfaces with the also granular surroundings in which they are immersed. This natural observation is embodied in the basic averaging construction of the diffusion coefficient of the aggregation of interest. Certain, possibly biomedical, applications of the model can also be viewed by prospective inspection of tiny inhomogeneities in nanofibrillar and/or lamellar matter for which certain numerical realizations are plausible to prepare based on thorough nanoscale experiments.

The purpose of this paper is to demonstrate the existence of an artificial magnetic monopole and to introduce new electromagnetic equations by altering an electric field and a magnetic field vectors.As a principle device, a cylindrical condenser is prepared, and a superconducting loop is inserted into it. By this conduction, radial electric fields take a role as the centripetal force and both counterclockwise and clockwise motions are induced. As a result, a stationery wave is formed in which the nodes take a part in creating a monopole as follows.First, employing the Lorentz conservations and because node of the stationary wave has no phases, the momentum k and the vector potential A vanish and instead a magnetic potential appears in order to maintain the Lorentz conservation. This magnetic potential has relationship with an electric potential, and thus consequently, a dependent relationship is obtained between an electric field and a magnetic field vectors. Using this conclusive dependent relationship, we can derive new Maxwell equation assembly which are created by altering the electric field and the magnetic field vectors. In this process, we derive a divergent equation of magnetic fields which is not zero, i.e., the existence of a magnetic monopole. Employing these newly derived Maxwell equation, an electromagnetic wave is derived whose speed is the same as one the existing Maxwell equations provide. As a monopole configuration, this paper discusses the energy gap of the vacuum, which is a result of the Dirac equation and describes a monopole as pairs between two Cooper pairs (i.e. four electrons) whose interaction is a photon. As mentioned, because the total momenta and phases are zero, this paper defines the wave function as the Dirac function and demonstrate the condensation, employing the Bloch’s theorem. Moreover, using the macroscopic basic equations, we retrace the creation of the divergent magnetic field in view of macroscopic phenomenon., which provides results in this paper.In Result section in this paper, we succeeded in demonstrating the distribution of the divergent magnetic field of monopole in terms of both microscopic and macroscopic scales. Furthermore, Discussion section describes properties a magnetic monopole should follow.

Conditional heteroskedastic financial time series are commonly modelled by (G)ARCH processes. ARCH(1) and GARCH were recently established in C[0,1] and L^2[0,1]. This article provides sufficient conditions for the existence of strictly stationary solutions, weak dependence and finite moments of (G)ARCH processes for any order in C[0,1] and L^p[0,1]. It deduces explicit asymptotic upper bounds of estimation errors for the shift term, the complete (G)ARCH operators and the projections of ARCH operators on finite-dimensional subspaces. The operator estimaton is based on Yule-Walker equations, and estimating the GARCH operators also involves a result estimating operators in invertible linear processes being valid beyond the scope of (G)ARCH. Moreover, our results regarding (G)ARCH can be transferred to functional AR(MA).

In this study, we introduce a novel framework for the estimation of residual renal function (RRF), based on the population compartmental kinetic behavior of Beta 2 Microglobulin (B2M) and its dialytic removal. Using this model, we simulated a large cohort of patients with various levels of RRF receiving either conventional high-flux hemodialysis or on-line hemodiafiltration. These simulations were used to estimate a novel population kinetic (PK) equation for RRF (PK-RRF) that was validated in an external public dataset of real patients. We assessed the performance of the resulting equation(s) against their ability to estimate urea clearance using cross-validation. Our equations derived entirely from computer simulations and advanced statistical modeling, and had extremely high discrimination (AUC 0.808 – 0.909) when applied to a human dataset of measurements of RRF. A clearance-based equation that utilized pre and post dialysis B2M measurements, patient weight, treatment duration and ultrafiltration had higher discrimination than an equation previously derived in humans. Furthermore, the derived equations appeared to have higher clinical usefulness as assessed by Decision Curve Analysis, potentially supporting decisions that for individualizing dialysis frequency in patients with preserved RRF.

Background: Ultrasonography (US) represents the gold standard imaging method for the assessment of testicular lesions (TL). The gray-scale (GSUS) and color-Doppler (CDUS) ultrasound examination allow sonographers to investigate size, margins, echotexture and vascular features of TL, with the effort to differentiate benign from malignant lesions. Recently, the use of contrast-enhanced US (CEUS) and sonoelastography (SE) led to further improvements in the differential diagnosis of TL. Although GSUS and CDUS are often sufficient to suggest the benign or malignant nature of TL, CEUS can be decisive in the differential diagnosis of unclear findings, while SE can help to strengthen the diagnosis. The contemporary combination of GSUS, CDUS, CEUS and SE led to a new diagnostic paradigm named multiparametric US (mp-US), able to provide a more detailed characterization of TL than the single techniques alone. This narrative and pictorial review is aimed to describe the mp-US appearance of several TL. Methods: An extensive Medline search was performed identifying studies in the English language focusing on mp-US evaluation of TL. Results: a practical mp-US “identity card” and iconographic characterization of several benign and malignant TL is provided herein. Conclusions: the mp-US characterization of TL reported herein can be useful in daily clinical practice.

We explore the relationship between the exact renormalization group (RG) equation and quantum mechanics. The central idea is to rewrite the exact Wilsonian RG equation as a Schrödinger-type equation, opening avenues for analysis. By introducing a functional transformation, the RG equation takes on a form analogous to a quantum mechanical Schrödinger equation. The study investigates solutions to this equation and draws parallels with quantum mechanics, paving the way for understanding the infrared behavior of quantum field theories. Furthermore, we extends its insights to a one-dimensional toy model, providing illustrative examples. The discussion encompasses the implications of these findings in multiple dimensions and quantum field theory, with a brief exploration of their relevance in the context of inflationary cosmology.

This study addresses the central question that how can a precise measurement of the gluon Parton Distribution Function (PDF) be attained, thereby enhancing our understanding of the intricate quark-gluon composition within nucleons? Through a dual approach involving Quantum Chromodynamics (QCD) and high-energy particle collisions, the research combines computational tools and experimental techniques, focusing on protons and neutrons. Scattering experiments and advanced detectors are utilized to probe nucleon structure. Theoretical frameworks like QCD equations and the Momentum Sum Rule investigate Parton Distribution Functions at specific momentum fractions and energy scales. The primary goal is to achieve an accurate measurement of the gluon PDF, crucial for unraveling strong force complexities and internal nucleon dynamics. The study's theoretical plots and equations illustrate hypothetical behaviors of gluon distribution, quark distribution, and splitting functions, contributing to a deeper understanding of fundamental particles.

Applying a procedure similar to that of E.S. Bring, by using a 4^th degree Tschirnhaus transformation, it was possible to transform the Bring-Jerrard normal quintic (BJQ) equation into a De Moivre form (DMQ), so that it could be solved by radicals. The general solution by radicals of the De Moivre equations of any degree is presented. By the same procedure the BJSx (normal sextic) equation was taken to another one without the 2^nd, 4^th and 6^th terms which was transformed into a cubic (solvable) equation. By applying a 6^th degree Tschirnhaus transformation to the BJSp (normal septic) equation its binormal (without the 2^nd, 3^rd, 4^th and 5^th terms) form was obtained.

Applying a procedure similar to that of E.S. Bring, by using a 4^th degree Tschirnhaus transformation, it was possible to transform the Bring-Jerrard normal quintic (BJQ) equation into a De Moivre form (DMQ), so that it could be solved by radicals. The general solution by radicals of the De Moivre equations of any degree is presented. By the same procedure the BJSx (normal sextic) equation was taken to another one without the 2^nd, 4^th and 6^th terms which was transformed into a cubic (solvable) equation. By applying a 6^th degree Tschirnhaus transformation to the BJSp (normal septic) equation its Bring-Jerrard binormal (without the 2^nd, 3^rd, 4^th and 5^th terms) form was obtained.

It is shown that the 5D geodetic equations and 5D Ricci identities give us a way to create a new viewpoint on some problems of Modern Physics, Astrophysics, and Cosmology. Specifically, the application of the 5D geodetic equations in (4+1) and (3+1+1) splintered forms obtained with the help of the monad and dyad methods made it possible to introduce a new, effective generalized concept of the rest mass of the elementary particle. The latter leads one to novel connections between the General Relativity and quantum field theories, as well as all of that, including the (4+1) splitting of the 5D Ricci identities, brings about a better understanding of the magnetic monopole problem and the vital difference in the origins of the Maxwell equations and gives rise to surprising connections between them. The obtained results also provide new insight into the mechanism of the 4D Universe’s expansion and its following acceleration.

The selection equation (replicator equation) has been independently discovered not only in various fields of biology (population genetics, ecology, prebiotic evolution, and sociobiology), but also in laser theory, where it accounts for the emergence of coherent light. Selection theory (replicator dynamics) is an ensemble theory, i. e., it describes the entire system rather than individual events, neglecting details in favor of a statistical view. However, the underlying processes at the individual level are well known in biology. For light quanta, this is not the case, because quantum theory says nothing about individual events. In the Copenhagen interpretation even the existence of causality on "quantum level" is denied. A large number of recent publications, however, makes this interpretation seem questionable.In the present paper, therefore, an attempt is made to describe the basic interactions between light and matter, as far as they are relevant for the emergence of coherent light in the laser (a photon pair interaction mediated by matter is postulated), and to apply replicator dynamics on this basis. Starting point are papers of A. Einstein about the interaction of light and matter as well as the photoelectric effect. Both theories are slightly modified. Furthermore, the double-slit experiment is investigated and finally the emergence of coherent light by density-dependent selection of photons of different phase in a laser-like model. The relationship between “mean fitness”, information content of the photon ensemble and the amplitude of the light is also analyzed.

We propose a model for gravity based on the gravitational polarization of space. With this model, we can relate the density parameters within the Friedmann model, and show that dark matter is bound mass formed from massive dipoles set up within the vacuum surrounding ordinary matter. Aggregate matter induces a gravitational field within the surrounding space, which reinforces the original field. Dark energy, on the other hand, is the energy density associated with gravitational fields both for ordinary matter, and bound, or induced dipole matter. At high CBR temperatures, the cosmic susceptibility, induced by ordinary matter vanishes, as it is a smeared or average value for the cosmos as a whole. Even though gravitational dipoles do exist, no large scale alignment or ordering is possible. Our model assumes that space, i.e., the vacuum, is filled with a vast assembly (sea) of positive and negative mass particles having Planck mass, called planckions, which is based on extensive work by Winterberg. These original particles form a very stiff two component superfluid, where positive and negative mass species neutralize one another already at the submicroscopic level, leading to zero net mass, zero net gravitational pressure, and zero net entropy, for the undisturbed medium. It is theorized that the gravitational dipoles form from such material positive and negative particles, and moreover, this causes an intrinsic polarization of the vacuum for the universe as a whole. We calculate that in the present epoch, the smeared or average susceptibility of the cosmos equals, , and the overall resulting polarization equals, . Moreover, due to all the ordinary mass in the universe, made up of quarks and leptons, we calculate a net gravitational field having magnitude, . This smeared or average value permeates all of space, and can be deduced by any observer, irrespective of location within the universe. This net gravitational field is forced upon us by Gauss’s law, and although technically a surface gravitational field, it is argued that this surface, smeared value holds point for point in the observable universe. A complete theory of gravitational polarization is presented. In contrast to electrostatics, gravistatics leads to anti-screening of the original source field, increasing the original value, , to, , where is the induced or polarized field. In the present epoch, this leads to a bound mass, , where is the sum of all ordinary source matter in the universe, and equals the relative permittivity. A new radius, and new mass, for the observable universe is dictated by the density parameters in Friedmann's equation, and Gauss’s law. These lead to the very precise values, , and, , respectively, somewhat larger than current less accurate estimates.

We introduce the Symplectic Structure of Information Geometry based on Souriau’s Lie Group Thermodynamics model, with a covariant definition of Gibbs equilibrium via invariances through co-adjoint action of a group on its moment space, defining physical observables like energy, heat, and moment as pure geometrical objects. Using Geometric (Planck) Temperature of Souriau model and Symplectic cocycle notion, the Fisher metric is identified as a Souriau Geometric Heat Capacity. Souriau model is based on affine representation of Lie Group and Lie algebra that we compare with Koszul works on G/K homogeneous space and bijective correspondence between the set of G-invariant flat connections on G/K and the set of affine representations of the Lie algebra of G. In the framework of Lie Group Thermodynamics, an Euler-Poincaré equation is elaborated with respect to thermodynamic variables, and a new variational principal for thermodynamics is built through an invariant Poincaré-Cartan-Souriau integral. The Souriau-Fisher metric is linked to KKS (Kostant-Kirillov-Souriau) 2-form that associates a canonical homogeneous symplectic manifold to the co-adjoint orbits. We apply this model in the framework of Information Geometry for the action of an affine Group for exponentiel families, and provide some illustrations of use cases for multivariate Gaussian densities. Information Geometry is presented in the context of seminal work of Fréchet and his Clairaut-Legendre equation. Souriau model of Statistical Physics is validated as compatible with Balian gauge model of thermodynamics. We recall the precursor work of Casalis on affine group invariance for natural exponential families.

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

It has been more than a century since Erlang published his paper in 1909. The classical queueing system for the M/D/c queue has been investigated by many authors. The key is to find the roots of an equation using explicit or numerical methods. We present an alternate form of explicit solution(s) of this/these root(s) using the Lambert-W function in this paper. In addition, the unsaturated probabilities of the number of customers in the system is derived explicitly in terms of this/these root(s). Finally, the mean number of customers in the system and the mean queueing delay are obtained from these probabilities. The exact queueing delay formula for the M/D/c queue is expressed in closed-form in terms of the root(s). Numerical results show that they are in excellent agreement with the numerical results published by Seelen, Tijms and Van Hoorn.

We present a new mathematical model of disease spread reflecting specialties of covid-19 epidemic by elevating the role social clustering of population. The model can be used to explain slower approaching herd immunity in Sweden, than it was predicted by a variety of other mathematical models; see graphs Fig. \ref{GROWTH2}. The hierarchic structure of social clusters is mathematically modeled with ultrametric spaces having treelike geometry. To simplify mathematics, we consider homogeneous trees with $p$-branches leaving each vertex. Such trees are endowed with algebraic structure, the $p$-adic number fields. We apply theory of the $p$-adic diffusion equation to describe coronavirus' spread in hierarchically clustered population. This equation has applications to statistical physics and microbiology for modeling {\it dynamics on energy landscapes.} To move from one social cluster (valley) to another, the virus (its carrier) should cross a social barrier between them. The magnitude of a barrier depends on the number of social hierarchy's levels composing this barrier. As the most appropriate for the recent situation in Sweden, we consider {\it linearly increasing barriers.} This structure matches with mild regulations in Sweden. The virus spreads rather easily inside a social cluster (say working collective), but jumps to other clusters are constrained by social barriers. This behavior matches with the covid-19 epidemic, with its cluster spreading structure. Our model differs crucially from the standard mathematical models of spread of disease, such as the SIR-model. We present socio-medical specialties of the covid-19 epidemic supporting our purely diffusional model.

The description of the microscopic world in quantum mechanics is very different from that in classical physics, and there are some points of view that are contrary to intuition and logic. The first is the loss of reality, the behavior of micro particles shows randomness and hopping. The second is the loss of certainty, the conjugate physical variables of a system cannot be determined synchronously, they satisfy the Heisenberg uncertainty principle. The third is the non-local correlation. The measurement of one particle in the quantum entanglement pair will change the state of the other entangled particle simultaneously. In this paper, some concepts related to quantum entanglement, such as EPR correlation, quantum entanglement correlation function, Bell's inequality and so on, are analyzed in detail. Analysis shows that the mystery and confusion in quantum theory may be caused by the logical problems in its basic framework. Bell's inequality is only a mathematical theorem, but its physical meaning is actually unclear. The Bell state of quantum entangled pair may not satisfy the dynamic equation of quantum theory, so it cannot describe the true state of microscopic particles. In this paper, the correct correlation functions of spin entanglement pair and photonic entanglement pair are strictly derived according to normal logic. Quantum theory is a more fundamental theory than classical mechanics, and they are not parallel relation in logic. However, there are still some unreasonable contents in the framework of quantum theory, which need to be improved. In order to disclose the real relationship between quantum theory and classical mechanics, we propose some experiments which show the wave-particle duality simultaneously and provide intuitionistic teaching materials for the new interpretation of quantum theory.

We apply principles of Gibbs phase plane chemistry to and across the entire ocean-atmospheric interface. Surface tension increments support a two dimensional, tangential pressure well known to determine rates of bulk gas, bubble, salt, spray and momentum transfer plus both sensible and latent heat fluxes. Hence it is worth asking whether tension mapping follows from current understanding of two dimensional composition. A history is provided dating back centuries and demonstrating that detrital organic macromolecules are central; subtle surfactant functional variation creates a microforcing field which dissipates turbulent energy at the sub-meter scale. Since we have just distributed major biopolymeric classes emitted as primary organic aerosol, further climate links can be established by considering full planar thermochemistry. Organic microlayer behaviors are reviewed with attention to confined, analog phase transitions among two dimensional “solid, liquid, (and) gaseous” states serving as elasticity indicators. We also discuss surfactant properties of general marine dissolved organic carbon, demonstrating that only proteins and lipids are capable of occupying significant local micro-area. The literature often suggests albumin and stearic acid as best proxies, and so we distribute their concentrations through multilevel global ecodynamic simulations. Consensus distributions are obtained in order to control adsorptive equilibria. Working from conservation of planar free energy, a parametric equation of state is devised relating excess coverage to the surface pressure-modulus. Constant settings for the proxy pair are drawn from laboratory study, and they successfully reproduce frequencies for surfactant solid-to-gas occurrence in ambient compression experiments. Functionally resolved organic measurements are rare and so we group them into super-ecological province tables showing that our bulk concentration estimates are reasonable. Outputs are then fed into a coverage-tension-elasticity code. Resulting contours traverse the critical range for piston velocity, bubble-spray and damping effects on either a regional or seasonal basis. There is also a possibility for widespread microlayer crystallization in polar seas. The concepts are a direct extension of our organic aerosol work, and the two approaches could be inserted into Earth System Models in tandem. Uncertainties in the logic are enumerated and include kinetic and thermochemical factors at multiple scales. But the problems are reducible through molecular modeling coupled to renewed laboratory and field study. Connections to marine colloids-gels, microlayer iron chelation, and linings of the ice channel network are discussed additionally.

The mind-body problem is the central issue in both of philosophy and life science for several centuries. To date, there is still no conclusive theory to interpret the relation between the mind and the body, even just the mind alone. Here, we promote a novel model, a derived mathematic equation called the entropic system equation, to describe the innate characters of the mind and the mechanism of the mind-body coupling phenomenon. As the semi-open thermodynamic systems far from equilibrium, the living organisms could be logically considered as an entropic system. In the living organisms or the entropic systems, there also are three essential existing elements including mass, energy and information, in which the mind and the body are hypothetically coupled by free energy and entropic force.

Matiyasevich's theorem states that there is no algorithm to decide whether or not a given Diophantine equation has a solution in non-negative integers. Smorynski's theorem states that the set of all Diophantine equations which have at most finitely many solutions in non-negative integers is not recursively enumerable. We prove: (1) Smorynski's theorem easily follows from Matiyasevich's theorem, (2 ) Hilbert's Tenth Problem for Q has a negative solution if and only if the set of all Diophantine equations with a finite number of rational solutions is not recursively enumerable.

Following the coronavirus disease 2019 (COVID-19) pandemic, several studies have examined the possibility of correlating the virulence of severe acute respiratory syndrome coronavirus 2 (SARS-CoV-2), the virus that causes COVID-19, to the climatic conditions of the involved sites; however, inconclusive results have been generally obtained. Although either air temperature or humidity cannot be independently correlated with virus viability, a strong relationship between SARS-CoV-2 virulence and the specific enthalpy of moist air appears to exist, as confirmed by extensive data analysis. Given this framework, the present study involves a detailed investigation based on the first 20–30 days of the epidemic before public health interventions in 30 selected Italian provinces with rather different climates, here assumed as being representative of what happened in the country from North to South, of the relationship between COVID-19 distributions and the climatic conditions recorded at each site before the pandemic outbreak. Accordingly, a correlating equation between the incidence rate of the pandemic and the average specific enthalpy of atmospheric air was developed, and an enthalpy-based seasonal virulence risk scale was proposed as a tool to predict the potential danger of COVID-19 spread due to the persistence of weather conditions favorable to SARS-CoV-2 viability. For practical applications, a conclusive risk chart expressed in terms of coupled temperatures and relative humidity (RH) values was provided, showing that safer conditions occur in case of higher RH at the highest temperatures, and of lower RH at the lowest temperatures. The proposed risk scale was in agreement with the available infectivity data in the literature for a number of cities around the world.

Applying a procedure similar to that of E.S. Bring, by using a 4^th degree Tschirnhaus transformation, it was possible to transform the Bring-Jerrard normal quintic (BJQ) equation into a De Moivre form (DMQ), so that it could be solved by radicals. The general solution by radicals of the De Moivre equations of any degree is presented. By the same procedure the BJSx (normal sextic) equation was taken to another one without the 2^nd, 4^th and 6^th terms which was transformed into a cubic (solvable) equation. By applying a 6^th degree Tschirnhaus transformation to the BJSp (normal septic) equation its binormal (without the 2^nd, 3^rd, 4^th and 5^th terms) form was obtained.

Applying a procedure similar to that of E.S. Bring, by using a 4^th degree Tschirnhaus transformation, it was possible to transform the Bring-Jerrard normal quintic (BJQ) equation into a De Moivre form (DMQ), so that it could be solved by radicals. The general solution by radicals of the De Moivre equations of any degree is presented. By the same procedure the BJSx (normal sextic) equation was taken to another one without the 2^nd, 4^th and 6^th terms which was transformed into a cubic (solvable) equation. By applying a 6^th degree Tschirnhaus transformation to the BJSp (normal septic) equation its binormal (without the 2^nd, 3^rd, 4^th and 5^th terms) form was obtained.

This paper discusses approaches to the numerical integration of the coupled nonlinear Schrödinger equations system in case of few-mode wave propagation. The wave propagation assumes the propagation of up to nine modes of light in an optical fiber. In this case, the light propagation is described by the non-linear coupled Schrödinger equation system, where propagation of each mode is described by own Schrödinger equation with other modes interactions. In this case, the non-linear coupled Schrödinger equation system solving becomes increasingly complex, because each mode affects the propagation of other modes. The suggested solution is based on the direct numerical integration approach, which is based on a finite-difference integration scheme. The well-known explicit finite-difference integration scheme approach fails, due to the non-stability of the computing scheme. Due to this fact, the combined explicit/implicit finite-difference integration scheme, based on the implicit Crank–Nicolson finite-difference scheme, is used. It allows ensuring the stability of the computing scheme. Moreover, this approach allows separating the whole equation system on the independent equation system for each wave mode at each integration step. Additionally, the algorithm of numerical solution refining at each step and the integration method with automatic integration step selection are used. The suggested approach has performance gains (or resolutions) up to three or more orders of magnitude in comparison with the split-step Fourier method due to the fact that there is no need to produce direct and inverse Fourier transforms at each integration step. The main advantage of the proposed method is the ability to calculate the propagation of an arbitrary number of modes in the fiber.

The aim of the present work is to explore a different non-traditional approach to higher dimensional spacetime which differs from the usual approaches such as large extra space dimensions, warped extra space dimensions and multiple extra time dimensions. This approach will be referred to as "Dynamic" higher dimensional spacetime. By this term will be introduced a new kind of higher dimensional spacetime (more than the usual 3+1 dimensions), which behaves dynamically in the sense that time is not a fixed dimension but is the extra plus one dimension to the spatial dimensions of the phenomenon we are studying. For a higher dimensional phenomenon, the lower dimensional time will behave as space and the new time will be a plus one dimension, meaning if we study a 3-dimensional phenomenon then time is the usual 4th dimension but if we are studying a 4-dimensional phenomenon then its time will be an extra 5th dimension and for this phenomenon the 4th dimension will behave as space. All spatial dimensions are indistinguishable from each other and behave in the exact same way, which means that the important parameter is not the dimension we are studying (for example the 4th or the 5th) but the number of dimensions in which a phenomenon can interact and how higher dimensional phenomena interact with lower ones. This non-traditional approach to higher dimensional spacetime may appear confusing at first but will become clearer in the rest of the paper. For this reason, we will first associate the time dimension with propagation relative to space dimensions and change orthogonal to them in order to give the reader a better intuition. Following that, we will describe how higher - dimensional phenomena would appear to us, the 3 - dimensional observer and try to set some guidelines on how we should mathematically model higher - dimensional phenomena in order for us to make accurate predictions of their behaviour. Then we will express the general framework of a "Dynamic" higher - dimensional spacetime and turn our gaze to 4+1 – dimensional phenomena. We will explore how a mass term arises for 4 – dimensional waves by generalizing the frequency – speed – wavelength relation of 3D waves and give a basic description on a possible way to describe a 4+1 – dimensional disturbance in a scalar Energy Field in order to make accurate predictions on our 3+1 dimensional plane. In this framework we will derive the Klein – Gordon equation by generalizing the wave equation and ignoring all lower than 4+1 - dimensional disturbances and compere our mass term findings with the Klein – Gordon equation mass term and with results from gravity – induced quantum interference experiments. Lastly, we will describe how a "Dynamic" 5 - dimensional spacetime would appear in a 3D observer and examine whether our findings are compatible with quantum mechanics and the special theory of relativity.

A new framework in quantum chemistry has been proposed recently ("An approach to first principles electronic structure calculation by symbolic-numeric computation'' by A. Kikuchi). It is based on the modern technique of computational algebraic geometry, viz. the symbolic computation of polynomial systems. Although this framework belongs to molecular orbital theory, it fully adopts the symbolic method. The analytic integrals in the secular equations are approximated by the polynomials. The indeterminate variables of polynomials represent the wave-functions and other parameters for the optimization, such as atomic positions and contraction coefficients of atomic orbitals. Then the symbolic computation digests and decomposes the polynomials into a tame form of the set of equations, to which numerical computations are easily applied. The key technique is Grröbner basis theory, by which one can investigate the electronic structure by unraveling the entangled relations of the involved variables. In this article, at first, we demonstrate the featured result of this new theory. Next, we expound the mathematical basics concerning computational algebraic geometry, which are necessitated in our study. We will see how highly abstract ideas of polynomial algebra would be applied to the solution of the definite problems in quantum mechanics. We solve simple problems in "quantum chemistry in algebraic variety'' by means of algebraic approach. Finally, we review several topics related to polynomial computation, whereby we shall have an outlook for the future direction of the research.