As is known, quantum mechanics is inextricably linked with classical mechanics. Its justification is connected with the need to consider the interaction of a microparticle with a macroscopic classical measuring device [1]. The basic dynamical equation, the Schrödinger equation, was postulated by Schrödinger but actually derived from the Hamilton-Jacobi equation for action in classical mechanics by introducing the wave function in some form, which is now called the semiclassical approximation. The width of the levels, "inside which" the energy spectrum is continuous, is a sign of the partially classical nature of the dynamics in quantum systems. Quantum-classical mechanics is not a "mixture" of quantum mechanics and classical mechanics, but is a substantially modified quantum mechanics, in which the initial and final states are quantum in the adiabatic approximation, and the chaotic transient state due to chaos is classical. The Franck-Condon principle in molecular physics avoids the consideration of transient state dynamics, which is unreasonably assumed to be unimportant. Classicality, which is immanently inherent in quantum mechanics itself, in molecular physics, is supplemented by classicism, which is associated with the Franck-Condon principle. It is assumed that the quantum transition (fast jump) of an electron from the ground to the excited electronic state of the molecule occurs between the turning points of classically moving nuclei, where the nuclei are at rest. In fact, the classical nature of motion in molecular physics is not associated with the Franck-Condon principle, but with the chaotic dynamics of the motion of an electron and nuclei in a transient state. As is known, the theory of quantum transitions in quantum mechanics is based on the convergence of a series of time-dependent perturbation theory. This series converges in atomic and nuclear physics, as well as in molecular physics, provided that the Born-Oppenheimer adiabatic approximation and the Franck-Condon principle are strictly observed. If this condition is not met, the series of time-dependent perturbation theory diverges. Obviously, in real molecules, the adiabatic approximation is not strictly observed, which makes the application of Franck-Condon principle unfounded in theory, and with it the whole physical picture of molecular transitions based on it. The only physical way to eliminate the singularity of the series of time-dependent perturbation theory in molecular physics is the postulate of the presence of dynamics in the transient electron-nuclear(-vibrational) state, which the Franck-Condon principle ignores, and that this dynamics is chaotic. In this case, in the case of strong chaos, as in the case of the Franck-Condon picture of molecular transitions, the transition rates do not depend on the specific dynamics of the transient state, but depend only on the initial and final states, taken in the adiabatic approximation. In the case of weak chaos, against the background of chaos, the regular nature of the dynamics of the transient state manifests itself. Chaos, which is weak in the case of large molecules, may be strong in the case of small molecules. Therefore, the Franck-Condon picture of transitions often gives good agreement with experimental data on optical spectra in conventional molecular spectroscopy of small molecules. In photochemistry, where, as a rule, we deal with large molecules, where chaos is not strong, but weak, elements of dynamic self-organization often appear in the chaotic dynamics of the transient state. A striking example of this is the well-known narrow and intense J-band of J-aggregates of polymethine dyes, which can no longer be explained on the basis of quantum mechanics, but finds its explanation in quantum-classical mechanics. Thus, in the case of small molecules, the Franck-Condon principle gives the correct result, although an erroneous theory and an erroneous physical picture are used. In the case of large molecules, this erroneous theory and the erroneous physical picture no longer lead to the correct result. The analogue of this situation is well known. This analogue is the collision between two pictures of the world, namely, geocentric and heliocentric. As is well known, the correct picture is the heliocentric picture of the world, in which the Earth rotates both around the Sun and around its own axis. However, being on the surface of the Earth, the rotation of the Earth around its own axis is perceived by the observer as the movement of the Sun across the sky, which is well simulated by an erroneous geocentric picture. It is even customary to talk about the time of sunrise and the time of its sunset at a given particular point on the surface of the Earth. However, the exit from the surface of the Earth to a sufficiently large distance into space directly shows the fallacy of the geocentric picture of the world. At present, quantum-classical mechanics and the physical picture of molecular "quantum" transitions corresponding to it are based on their simplest example, namely, on the example of elementary electron transfers in condensed media. Here, chaos is introduced into the transient state by replacing the infinitely small imaginary additive in the energy denominator of the total Green's function of the system by a finite value [2]. This chaos is called dozy chaos.

[1] Landau, L.D.; Lifshitz, E.M. Quantum Mechanics, Non-Relativistic Theory, 3rd ed.; Elsevier: Amsterdam, The Netherlands, 1977.

[2] Egorov, V.V. Quantum–classical mechanics: Nano-resonance in polymethine dyes. Mathematics 2022, 10(9), 1443.

We study the structure of symplectic mock-Lie algebras, and we give a necessary and sufficient condition to construct a symplectic Lie algebra, starting from a symplectic mock Lie algebra. Moreover, we investigate the equivalence between the existence of a symplectic form on a mock-Lie algebra and the existence of a solution of the Yang-Baxter equation. Finally, we conclude the work with the salient results and discussion.

In this paper, we study the laminar, incompressible and steady flow of a biomagnetic fluid such as blood containing gold nanoparticles through a shrinking sheet in the presence of a magnetic dipole. Here, we consider blood as a biomagnetic fluid which is also taken as a base fluid and gold as non-magnetic particles. This model is consistent with both the principles of magnetohydrodynamics (MHD) and ferro-hydrodynamics (FHD). The main concentration is to study biomagnetic fluid flow with non-magnetic particles that passes through a two dimensional shrinking sheet under the influence of heat source, Brownian motion and thermophoresis in the presence of a blood with gold nanoparticles which has not been studied yet as far as best knowledge of authors. The flow equations, such as momentum and energy, are physically described by a system of coupled, non-linear partial differential equations with suitable boundary conditions, and they are transformed into a non-linear system of ordinary differential equations by using the appropriate similarity transformations. An effective numerical method that is based on an iterative process, tridiagonal matrix manipulation, and a common finite difference method with central differencing is used to generate the numerical solution. The velocity, temperature, concentration distribution and the skin friction coefficient, local Nusselt number and Sherwood number are all calculated numerically. The major numerical results show that the fluid velocity decreases as the ferromagnetic number increases whereas the skin friction coefficient shows the opposite behavior. As the ferromagnetic number increases, the rate of heat transfer with ferromagnetic interaction parameter is likewise observed and shown to be decreasing. There is a great deal of agreement between them and a previous study that is mentioned in the literature. Such findings are hoped to be helpful in the medical field, particularly in MRI, magnetic drug targeting, and magnetic hypothermia treatments.

In this paper, the effects of various fluid properties on two dimensional unsteady Biomagnetic fluid flow (blood) and heat transfer over a stretching sheet under the appearance of magnetic dipole is investigated. The governing boundary layer equations are simplified by suitable transformation which are then solved by bvp4c function aaproach in MATLAB software. The results indicate that fluid velocity and temperature are greatly influenced for ferromagnetic interaction parameter. Where, for ferromagnetic number fluid velocity drops but temperature rises upward. It is also found that the coefficient of skin friction and Nusselt number increase with the increment values of thermal conductivity parameter. For certain parameter values, the results are also compared with previously published studies and found in acceptable agreement.

In the current research, we develop sharp inequalities including generalized normalized δ-Casorati curvatures for several submanifolds of Riemannian manifolds endowed with metallic structures. For these submanifolds in the same ambient space form, we have also looked into generalized Wintgen inequalities. Additionally, submanifolds for which the equality cases hold are described as well.

Deep learning has become widely used in image analysis. Transfer learning can make use of information from other data sets for the analysis of this data set. When there is a small number of images at hand, the deep learning method will conduct transfer learning, which means using trained models or coefficients from other data sets. This is in contrast to deep learning with most model parameters re-estimated. Transfer learning will make use of trained models from other data sets and then apply them to images of this dataset to extract high-level features. High-level features can be fed into traditional machine learning models including a Neural network. We compare a range of combinations of traditional machine learning with deep learning for multi-view image analysis, with the objective of improving image analysis performances. The proposed methods have been applied to multi-view plant phenotyping data to evaluate the performance of various methods.

Valuation theory is an important area of investigation in algebra with applications in algebraic geometry and number theory. In 1957 M. Krasner introduced hyperfields, which are field-like structures with a multivalued addition, to describe some structures arising naturally from valued fields. We would like to discuss the possibility of generalising the notion of valuation to the multivalued setting and the potential that this higher point of view has in the understanding of classical valuation theory. For example, a valuation on a field K is nothing but a homomorphism of hyperfields from K onto a special type of hyperfield, which is called (generalised) tropical hyperfield.

The present work proposes new classes of models for random variables with support in the positive real line, these models explain the conditional quantile, and are an alternative for modeling data that indicate asymmetric behavior and heavy tails. The models are based on a reparametrization in the quantiles of the Burr XII (BXII) distribution, since the quantile is less sensitive than the average of heterogeneous populations and also suitable in the presence of outliers. A quantile regression model based on a new parameterization of the BXII distribution is proposed. We established a systematic structure in the quantiles of the response variable as a function of explanatory variables. We also introduce a model that makes it possible to model any quantile by a dynamic structure containing autoregressive terms and moving averages, time-varying regressors, unknown parameters and a link function. Three main and independent chapters make up the structure of this work. The first part presents a theoretical framework on the BXII distribution and discusses some of its generalizations and related regression models. In the second part, a study of the new proposal of the quantile regression model BXII is presented. The estimation of the parameters of the regression model is performed using the maximum likelihood method. Monte Carlo simulations and empirical applications are presented, showing the usefulness of the proposal to estimate the factors determining the salaries of the Major League Baseball players. Finally, the last part presents a new autoregressive moving average model based on the τ–th quantile of the BXII distribution (BXII ARMA). The conditional maximum likelihood method is considered to estimate the parameters and build the confidence intervals of the BXII-ARMA model. Furthermore, the performance of the model parameter estimators is evaluated through a Monte Carlo simulation study, as well as diagnostic tools and an empirical application are presented and discussed for the two proposed models.

This paper is investigating the prey-predator model, which includes a fear effect on susceptible prey through infected prey. Also, the predator consumes its prey in the form of Holling-type interactions. For the model, first we analyse the existence and local stability of possible non-negative equilibrium points. Further, we examine the Hopf-bifurcation analysis for the corresponding proposed model in the presence of the fear effect. Finally, we demonstrate some numerical simulation results to illustrate our main analytical findings.

The decision making process is of utmost importance since it dictates what will be chosen. Good decision making may lead to an ideal result that decision maker wishes to achieve. Decision making process is highly essential for the organization and investors to go through before making decisions. Proper and thorough planning can help the investors to make a good decision and hence, they are able to gain profits. As a result, it is important to conduct a financial distress analysis on the companies in order to understand their financial condition. In this study, the financial performance of the technology companies is assessed by Grover model. Financial ratios such as working capital to total asset, earnings before interest and taxes to total asset, and net income to total asset are analyzed in this study with Grover model. Each of the companies will obtain a G-score based on their financial performance. Grover model is capable to categorize the companies either into safe, grey or distress zones. The findings of this paper depict that 28 companies are financially sound. It indicates that these companies are performing well in terms of financial performance. Therefore, this provides insights to the investors to identify the companies with good financial performance for investment. Besides, the identified companies in safe zone can serve as a reference to other companies for benchmarking.