ATP Synthase is an essential molecule in cell and molecular biology. It is responsible for the production of ATP during cellular respiration, a molecule that provides the energy required to drive a number of cellular processes. In this paper, I explore the rotational physics of ATP Synthase’s rotor, a part of the protein that spins during the production of ATP. Firstly, I discuss some elementary rotational kinematics of the rotor. I then derive two alternate formulations for the total linear acceleration of the rotor. Finally, I derive formulas for the moment of inertia, angular momentum, net torque, and kinetic energy of the rotor. Through this, I hope to provide a theoretical and mathematical insight into the mechanics of ATP Synthase during the production of ATP.

After UV excitation, gas phase thymine returns to ground state in 5 to 7 ps, showing multiple time constants. There is no consensus on the assignment of these processes, with a dispute between models claiming that thymine is trapped either in the first (S1) or in the second (S2) excited states. In the present study, nonadiabatic dynamics simulation of thymine is performed on the basis of ADC(2) surfaces, to understand the role of dynamic electron correlation on the deactivation pathways. The results show that trapping in S2 is strongly reduced in comparison to previous simulations considering only non-dynamic electron correlation on CASSCF surfaces. The reason for the difference is traced back to the energetic cost for formation of a CO p bond in S2.

Computational neuroscience combines mathematics, computer science models, and neurosciences for theorizing, investigating, and simulating neural systems involved in the development, structure, physiology, and cognitive abilities of the brain. Computational models constitute a major stake in translational neuroscience: the analytical understanding of these models seems fundamental to consider a translation towards clinical applications. Method: We propose a minimal typology of computational models, which allows distinguishing between more realistic models (e.g., mechanistic models) and pragmatic models (e.g., phenomenological models). Result: Understanding the translational aspects of computational models goes far beyond the intrinsic characteristics of models. First, we assume that a computational model is rarely uniquely mechanistic or phenomenological. Idealization seems necessary because of i) the researcher’s perspectives on the phenomena and the purposes of the study (i.e., by the relativity of the model); ii) The complexity of reality across different levels and therefore the nature and number of dimensions required to consider a phenomenon. Especially, the use of models goes far beyond their function, and requires considering external characteristics rooted in path dependence, interdisciplinarity, and pluralism in neurosciences. Conclusion: The unreasonable use of computational models, which are highly complex and subject to a shift in their initial function, could be limited by bringing to light such factors.

This review presents an updated overview of research concerning Leishmania protein structures, primarily sourced from the Protein Data Bank (PDB), that play a role in the metabolic pathways of the Leishmania parasite. Furthermore, we assess the current progress in the identification and development of bioactive chemical agents aimed at addressing this substantially overlooked tropical disease. We have analyzed experimental data obtained from in vitro, in vivo and in silico sources. This data has been categorized into four main areas: a) vector taxonomy and geographic distribution; b) parasite taxonomy and geographic distribution; c) enzymatic functions of proteins engaged in parasite/host interactions throughout various developmental stages (such as oxidoreductases, transferases, hydrolases, lyases, isomerases, ligases, and cytokines); and d) established and experimental treatments employing bioactive chemical compounds. Our objective is to establish a foundational point of reference for research efforts concentrating on the elucidation of interaction mechanisms and the processes of ligand-protein activation/inactivation, specifically linked to Leishmania infections. Consequently, we emphasize enzymes recognized for their involvement in the biochemical pathways incited during Leishmania infection episodes. This review encapsulates the current understanding, offering insights to inform and direct future explorations aimed at targeting proteins and pathways to enhance the management of Leishmania-related diseases.

In recent years, the economies of many countries of the world are in a situation of intense shock processes. The current situation urgently needs to change the economic paradigm in the near future, which objectively requires the development of new conceptual models. The purpose of the paper is to develop the basic theoretical provisions of a new macroeconomics based on impulse and jump processes. Research problems are the following: 1) to describe the main types of impulse and jump functions with examples from economic theory and practice; 2) to perform an analytical representation of impulse and jump functions; 3) to select macroeconomic characteristics for the analysis of rapidly changing processes in the economy; 4) to create models and mechanisms for predicting impulsive and abrupt changes in macroeconomics. The approaches to the development of macroeconomic theory and its methods proposed in the article are not associated with the use of evolutionary continuous functions, for example, power functions, which is typical for many canonical macroeconomic models. These approaches do not include management decisions to achieve optimal values of given target functions, which is typical for recursive macroeconomic models of dynamic programming. This article is about formulating the foundations of macroeconomic theory and its methods, which, with some degree of accuracy, could give a forecast about the impending possibility of abrupt changes (impulse, shock, jump, stepwise and others) in the macroeconomic situation. The research methodology is statistical analysis, special methods for studying impulse and jump processes developed by the author. As a result of the study, the main provisions of the macroeconomic theory based on rapid impulse and spasmodic changes were formulated, approaches were outlined for constructing the tools of this theory, problems and tasks for further research were identified.

The formation of rock fractures in nature has a certain relationship with water seepage. In order to analyze the shape of rock fracture, we propose a rock deformation theoretical model in three-dimensional space considering with the condition of seepage water pressure, and establish the mass conservation equation, seepage equation, surrounding rock displacement equation, so as to deduce the rock deformation control equation under seepage pressure action. The numerical analysis of the nonlinear quadratic partial differential equation obtains the fracture deformation distribution in the example, and verifies with the calculated fracture morphology. And we further use this principle to analyze the fracture morphology in nature and prove the rationality of the theory.

X-ray crystallographic and theoretical charge density data for a series of compounds [(Co(Ts3tren))M(Co(Ts3tren))] (M = Mg, Ca, Sr and Ba) is examined. The crystal structures are isostructural and the alkaline earth metal ions have the same arrangement of donor oxygen atoms despite the large variation in ionic radii. The isomorphism of these molecules is surprising and a theoretical examination of the electronic structures, with the different metal ions along the series, provides detailed insight into their stabilities. The theoretical and experimental data are consistent and agree well. The local properties of the Co(II) ion and its donor atoms are relatively independent of the alkali earth metal.

The manuscript presents the applicability of the Gumbel distribution in the frequency analysis of extreme events in hydrology. The advantages and disadvantages of using the distribution are highlighted, as well as recommendations regarding its proper use. A literature review was also carried out regarding the methods of estimating the parameters of the Gumbel distribution. Thus, for the verification of the methods, case studies are presented regarding the determination of the maximum annual flows and precipitations using nine methods for parameter estimation. The influence of the observed data lengths on the estimation of the statistical indicators, the parameters and the quantiles corresponding to the field of low annual exceedance probabilities (p <1%) is also highlighted. The results are compared to those obtained with the Generalized Extreme Value distribution, respectively the Burr and the Wakeby distributions with parameters estimated using the L-moments. The results highlight and reaffirm the statistical, mathematical and hydrological recommendation regarding the avoidance of using the Gumbel distribution in Flood Frequency Analysis and its use with reservations in the case of maximum precipitation, especially when the statistical indicators of the analyzed data are not close to the characteristic ones and unique to the distribution.

High density of buildings and the large traffic volume of cities give rise to narrow spaces and high passenger flows in most subway stations. When evacuation is required during an emergency, these problems may trigger issues in operational safety. Therefore, it is imperative to comprehensively assess subway station emergency evacuation times and capacities during the operating process to ensure the design is safe, science-based, and rational. To further enhance safe evacuation capacity, this paper proposes an overall evacuation time model that considers the multielement charac-teristics of subway stations in multiple segments. The evacuation route is decomposed into five stages according to the critical nodes in the evacuation process. An overall emergency evacuation time model is established based on the diversity of bottlenecks in the five stages, integrating elements such as the horizontal movement velocity of passengers, subway equipment parameters, and human density. Taking Xi’an Wulukou Subway Station as an example, this paper verifies the outcomes of the theoretical model against the Pathfinder software and conducts additional anal-yses of the evacuation conditions of stairs and exits. The results show that the error between the theoretical emergency evacuation time and simulation evacuation time was 5.4%, The emergency evacuation model established in this study boasts strong robustness and stability.

Counting in terms of cycles allows modeling many processes of Nature. We make use of a slight numerical incongruence within the numbering system to find a translational mechanism which connects sequential ↔ commutative properties of assemblies. The algorithms allow picturing the logical syntax Nature uses when reading the DNA. Ordering a collection on two different properties of its members will impose two differing sequences on the members. The coordinates of a point on a plane of which the axes are the two sorting orders sidestep the logical contradiction arising from the different linear assignments. During a reorder, elements aggregate into cycles. Using an etalon collection of simple logical symbols (which are pairs of natural numbers), which we reorder, we see typical movement patterns along the path of the string of elements that are members of the same cycle. We split the {value, position} descriptions of a natural number and observe the places the unit occupies at specific instances of time among its peers, while being a member of a cycle, under different orders prevailing. Which places elements occupy among their peers, under specific order conditions, is determined by numeric properties of the natural numbers that make up the element. The model presented is therefore tautologic, and can be compared to a hybrid of sudokus with the ultimate form of Rubik‘s cube. It is necessary for the reader to do some self-education on the matter of cycles as a prerequisite to understanding the working principle of the model. The contraption being a new development, it can’t have references in literature.One cannot lose a bet on the idea that sorting and ordering a collection of elementary logical elements will turn up typical patterns and that these archetypes of patterns will be of interest to Theoretical Physics, Chemistry, Biology, Information Theory, and some other fields, too.

Featured Application: Bio-electronic devices take advantages of some specific duties of biological matter. The specific ability of some proteins to use sunlight is considered for the realization of photo-electronic devices . Here the focus is on the role of the pH, whose variations seem to affect the protein conductance

In cotton cultivars, an insect that causes irreversible damage is the Spodoptera frugiperda, known as the fall armyworm. Since the visual detection of plants is a burdensome task for human inspection, the spectral information related to plant damage, registered on a spectral scale, can be useful. These measurements, associated with machine learning techniques, produce useful information for a rapid and non-invasive inspection method development. To contribute to this gap fulfillment, this paper proposes a machine learning framework to model the spectral response of cotton plants under the attack of the fall armyworm. Additionally, a theoretical model is presented, built from the results of the machine learning analysis, to infer this damage with up-to-date orbital sensors. The data was composed of the reflectance measurements collected at a cotton field with control plants and plants submitted to Spodoptera frugiperda damage. Their spectral response was recorded with a hand-held spectroradiometer ranging from 350 to 2,500 nm, for eight consecutive days. Different machine learning models were evaluated and the overall best model was defined by accuracies comparisons on a testing-set. A ranking approach was adopted based on the model accuracy, returning the most contributive wavelengths for the classification. Sequentially, an unsupervised neural network (Self-Organizing Map - SOM) was implemented to reduce data-dimensionality and assist in the definition of important spectral regions. The regions were associated with the spectral bands of the two sensors (OLI and MSI) and a theoretical model using a band simulation process with the overall best machine learning model was proposed. The results indicated that the Random Forest (RF) algorithm is the most suitable to predict cotton-plants damaged by insects and that the last day of analysis (8th day) was better to separate it, with F-measure equals 0.912. The ranking approach combined with the SOM method indicated the spectral regions at the red to near-infrared (650 to 1,350 nm) and shortwave infrared (1,570 to 1,640 nm) as the most important regions to the analysis. The proposed theoretical model simulated with the OLI and MSI sensor-bands returned an F-Measure of 0.865 and 0.886, respectively. In conclusion, this framework can be used to map cotton-plants under insect-attack. The theoretical model presents high accuracy to infer the insect-damaged on cotton plants based on multispectral bands from other sensors, being a useful tool for future research that intends to evaluate it in other areas and at different field scales.

In recent years, advances in science, technology, and the way in which we view our world have led to anincreasingly broad use of the term “intelligence”. As we learn more about biological systems, we find more and more examples of complex and precise adaptive behavior in animals and plants. Similarly, as we build more complex computational systems, we recognize the emergence of highly sophisticated structures capable of solving increasingly complex problems. These behaviors show characteristics in common with the sort of complex behaviors and learning capabilities we find in humans, and therefore it is common to see them referred to as “intelligent”. These analogies are problematic as the term "intelligence" is inextricably associated with human-like capabilities. While these issues have been discussed by leading researchers of AI and renowned psychologists and biologists highlighting the commonalities and differences between AI and biological intelligence, there have been few rigorous attempts to create an interdisciplinary approach to the modern problem of intelligence. This article proposes a comparative framework to discuss what we call “purposeful behavior”, a characteristic shared by systems capable of gathering and processing information from their surroundings and modifying their actions in order to fulfill a series of implicit or explicit goals. Our aim is twofold: on the one hand, the term purposeful behavior allows us to describe the behavior of these systems without using the term "intelligence", avoiding the comparison with human capabilities. On the other hand, we hope that our framework encourages interdisciplinary discussion to help advance our understanding of the relationships among different systems and their capabilities.

Chiroptical responses have been an essential tool over the last decades for chemical structural elucidation due to their exceptional sensitivity to geometry and intermolecular interactions. In recent times, there has been an increasing interest for the search of more efficient sensing by the rational design of tailored chiroptical systems. In this Review article, advances on chiroptical systems towards their implementation in sensing applications are summarized. Strategies to generate chiroptical responses are illustrated. Theoretical approaches to assist in the design of these systems are discussed. Development of efficient chiroptical reporters in different states of matter, essential for the implementation in sensing devises, is reviewed. In the last part, remarkable examples of chiroptical sensing applications are highlighted.

The corrosion inhibition performance of pyridine derivatives (4-methylpyridine and its quaternary ammonium salts) and sulfur-containing compounds (thiourea and mercaptoethanol) with different molar ratios on carbon steel in CO2-saturated 3.5 wt.% NaCl solution was investigated by weight loss, potentiodynamic polarization, electrochemical impedance spectroscopy and scanning electron microscopy. The synergistic corrosion inhibition mechanism of mixed inhibitors was elucidated by the theoretical calculation and simulation. The molecule of pyridine derivatives compound with larger volume has the priority to adsorb on the metal surface, while the molecules of sulfur-containing compounds with smaller volume fill in vacancies. A dense adsorption film would be formed when 4-PQ and sulfur-containing compounds are added at a proper mole ratio.

The coal mine underground reservoir is an appropriate solution between coal mining and groundwater resource protection and utilization. By calculating the storage capacity of a groundwater reservoir, the storage coefficient has been proved to be always an empirical value. Based on the mathematical derivation of the vertical fracture area ratio and the horizontal fracture area rate of the collapse zone and the fissure zone in the goaf area of the coal seam, the mathematical models of tem are derived, and the model for calculating the water storage coefficient is derived. The water storage coefficient derived from the theoretical model had more basis and more advanced than the traditional empirical value. By using this method, the practical calculation of No.1 underground reservoir of the DaLliuta Coalmine in Shenhua Shendong, has got a perfect matching with the actual groundwater storage capacity.

The theoretical limit of link prediction is a fundamental problem in this field. Taking the network structure as object to research this problem is the mainstream method. This paper proposes a new viewpoint that link prediction methods can be divided into single or combination methods, based on the way they derive the similarity matrix, and investigates whether there a theoretical limit exists for combination methods. We propose and prove necessary and sufficient conditions for the combination method to reach the theoretical limit. The limit theorem reveals the essence of combination method that is to estimate probability density functions of existing links and nonexistent links. Based on limit theorem, a new combination method, theoretical limit fusion (TLF) method, is proposed. Simulations and experiments on real networks demonstrated that TLF method can achieve higher prediction accuracy.

In recent years, concerns regarding the environmental impact of microplastics (MPs) have led to increased international attention on these pollutants. Although initial focus was largely directed toward marine environments, land-based pollution sources, including MP release, has been recognized to directly affect marine ecosystems. Therefore, soil-, atmosphere-, groundwater-, and river-based research is ongoing. However, when considering sources of MP, it is necessary to examine the circular system of plastic in terms of raw materials, production, consumption, discharge, and disposal (recycling). Accordingly, the present study proposes a strategy to effectively manage MPs using this circular system. First, the factors influencing MPs in the circular system were identified, and MPs at the system’s final stage, i.e., at the waste treatment facility, were subsequently investigated. Using the concept of MP waste (MPW), strategies were then developed for effective MP management within the circular system. Applying the proposed theoretical strategy to the Korean waste management system revealed that the new policy framework improves the current MP management system. Overall, this study provides fundamental data for establishing new or improved MP management schemes from a waste sector perspective.

In this short paper we will propose a new equation for the proton charge radius which is inversely proportional to the Rydberg constant and directly proportional to the running value of the fine structure constant on the protonic scale. This will define the proton charge radius only by the effective value of the fine structure constant and the Rydberg constant. This new equation also disproves the old value of the proton charge radius 0.877(50) which was measured by using electron-proton scattering and further solidifies the newer and smaller values 0.8414(19) provided by NIST.

Effective communication in automated chat systems hinges on the ability to understand and respond to context. Traditional models often struggle with determining when additional context is necessary for generating appropriate responses. This paper introduces Context-Aware BERT (CA-BERT), a transformer-based model specifically fine-tuned to address this challenge. CA-BERT innovatively applies deep learning techniques to discern context necessity in multi-turn chat interactions, enhancing both the relevance and accuracy of responses. We describe the development of CA-BERT, which adapts the robust architecture of BERT with a novel training regimen focused on a specialized dataset of chat dialogues. The model is evaluated on its ability to classify context necessity, demonstrating superior performance over baseline BERT models in terms of accuracy and efficiency. Furthermore, CA-BERT's implementation showcases significant reductions in training time and resource usage, making it feasible for real-time applications. The results indicate that CA-BERT can effectively enhance the functionality of chatbots by providing a nuanced understanding of context, thereby improving user experience and interaction quality in automated systems. This study not only advances the field of NLP in chat applications but also provides a framework for future research into context-sensitive AI developments.

The water exit problem, which is ubiquitous in ocean engineering, is one of the significant research topics in the interaction between navigators and water. The study of the water exit problem can help to improve the structure design for marine ships and underwater weapons for better strength and movement status. However, the water exit problem involves complex processes such as gas-liquid-solid three-phase coupling, cavitation, water separation, liquid surface deformation and fragmentation, making it challenging to study. According to the works carried out by many researchers towards this issue, we summarize the recent developments from three aspects, i.e. theoretical research, numerical simulation and experimental results. In theoretical research, the improved von Kaman model and linearized water exit model are introduced. Several classical experimental devices, data acquisition means and cavitation are introduced in experimental development. Three methods, namely, BEM(boundary element method), FVM(finite volume method) and LES(large eddy simulation) are concluded for numerical simulation. The limitations and shortcomings of these three aspects are then analyzed. Finally, an outlook on the future research improvements and developments of the water exit problem is provided.

In engineering, connections between components are often weak areas. Unreasonable connection methods can easily reduce the strength of components, resulting in unpredictable failure modes. In nature, numerous connection methods for biological structures with excellent mechanical properties have evolved. Studying the connection methods of organisms in nature can inspire new ideas for bionic connection methods. When the diabolical ironclad beetle is under pressure, the elytra are not easy to separate, which ensures the stability of the beetle's external structure, thus making the beetle extremely resistant to pressure. The reason for this is the interlocking and toughening effect of the unique jigsaw connection between the elytra. Therefore, in this paper a theoretical analysis model is established and used to analyze the mechanical behavior of the diabolical ironclad beetle's jigsaw connection during the drawing process and determine the influence of factors such as quantity, angle, and geometric characteristics on the mechanical properties of the jigsaw connection. The results of the theoretical analysis are then compared with the results of experiments and ABAQUS finite element simulation.

A reliable and efficient rail track defect detection system is essential for maintaining rail track integrity and avoiding safety hazards and financial losses. Eddy current (EC) testing is a non-destructive technique that can be employed for this purpose. The trade-off between spatial resolution and lift-off should be carefully considered in practical applications to distinguish closely spaced cracks such as those caused by rolling contact fatigue (RCF). A multi-channel eddy current sensor array has been developed to detect defects on rails. Based on the sensor scanning data, defect reconstruction along the rails is achieved using an inverse algorithm that includes both direct and iterative approaches. In experimental evaluations, the EC system with the developed sensor is used to measure defects on a standard test piece of rail with a probe lift-off of 4-6 mm. The reconstruction results clearly reveal cracks at various depths and spacings on the test piece.

Wind loads have become one of the key influence factors for the running safety of vehicles and comfort of passengers. Investigation on the wind speed spectrum characteristics of a moving vehicle under turbulent crosswinds is of great influence. Expressions of the wind speed spectrum of a moving vehicle was obtained from the von Kármán spectrum based on Taylor’s frozen flow hypothesis. The influence factors, including the ratio of the vehicle speed to the wind speed and the wind yaw angle from 15° to 175°, were analyzed. The maximum value of the wind speed spectrum and the corresponding frequency were studied as well. The results show that the maximum values of the wind speed spectrum of the moving vehicle were larger than those of the static vehicle. The maximum value of the wind speed spectrum corresponding to the moving vehicle first increased and then decreased as the wind yaw angle increased. Some of the frequencies corresponding to the longitudinal wind speed spectrum values of the moving vehicles were smaller than those of the static vehicle. For moving vehicles, the frequency values corresponding to the maximum values of the longitudinal wind speed spectrum first increased and then decreased as the ratio of the vehicle speed to the wind speed and the wind yaw angle increased.

A new copper(I) complex, [Cu2(L)2dppm](PF6)2 (1) [L = 3-(2-Pyridyl)-5,6-diphenyl-1,2,4-triazine and dppm: Bis(diphenylphosphino)methane] was prepared and characterized by IR, 1H-NMR, 31P-NMR spectroscopy, elemental and thermogravimetric analysis, and single-crystal X-ray diffraction technique. Complex 1 is a dinuclear compound, showing that L and dppm act as tridentate and bidentate chelating ligands, respectively. The two Cu(I) atoms exhibit a distorted tetrahedral coordination sphere embedded in N3P environments. The supramolecular interactions in the solid-state structure are characterized by C−H···N, C−H···F, C-H···π and π···π intermolecular interactions that were analyzed by inspection of the Hirshfeld surface and fingerprint plots. Additionally, the complex was studied experimentally in solution by UV–Vis spectroscopy and cyclic voltammetry; also, theoretical studies with Time-Dependent Density Functional Theory (TD-DFT) were performed. Moreover, the optical and electrochemical properties have been studied, focusing on the band gap. Compound 1 has been used as a co-sensitizer in a dye-sensitized solar cell, showing good activity.

This article, inspired by Dr. Jürgen Essletzbichler’s chapter namely “Locating Location Models” in The SAGE Handbook of Economic Geography (2011), delves into the legacy and significance of location theory. By examining its integration of historical analysis and theoretical abstraction, the study highlights the crucial role played by historical and geographical contexts in shaping spatial patterns. It emphasizes the importance of complementing abstract models with historical analysis to gain a deeper understanding of real-world spatial phenomena. Acknowledging the delay in the development of location theory attributed to the dominance of the German historical school, the article recognizes its enduring value and resurgence in the realm of modern evolutionary economic geography. Ultimately, the abstract underscores the contributions of location theory to our comprehension of spatial dynamics and its potential for further advancements in the field of economic geography.

This paper proposes a curved link-slab (CLS) structure, simplified into a hingeless-arch model, to address the current cracking phenomenon of CLS concrete. The stress formula of the hingeless arch under various loads is derived based on the classical mechanic's method. Based on an actual bridge example, the mechanical properties of CLS are analyzed under different loads and load combinations. The results show that: (1) the CLS stress is significantly lower than that of the flat link-slab structure (FLS), (2) its stress values are less than the concrete tensile limit, and (3) the CLS can effectively solve the concrete cracking phenomenon on the link-slab. The rationality of the stress formula derived from the simplified model of the hingeless arch is verified using the finite element method (FEM). The parametric sensitivity analysis shows that variation of the reinforcement ratio of the CLS has a limited impact on it. Considering both the concrete tensile and compressive limit, the thickness of the CLS should be 15 cm to 20 cm, and its design span should be about 5% to7.5% of the main beam length.

Here we use the flat Friedmann-Lemaitre-Robertson-Walker metric describing a spatially homogeneous and isotropic universe to derive the cosmological redshift distance in a way which differs from that which can be found in the astrophysical literature. We use the co-moving coordinate r_e (the subscript e indicates emission) for the place of a galaxy which is emitting photons and r_a (the subscript a indicates absorption) for the place of an observer within a different galaxy on which the photons - which were traveling thru the universe - are absorbed. Therefore the real physical distance - the way of light - is calculated by D = a(t₀) r_a - a(t_e) r_e. Here means a(t₀) the today’s (t₀) scale parameter and a(t_e) the scale parameter at the time of emission (t_e) of the photons. Nobody can doubt this real travel way of light: The photons are emitted on the co-moving coordinate place r_e and are than traveling to the co-moving coordinate place r_a. During this traveling the time is moving from t_e to t₀ (t_e ≤ t₀) and therefore the scale parameter is changing in the meantime from a(t_e) to a(t₀). Using this right way of light we calculate some relevant classical cosmological equations (effects) and compare these theoretical results with some measurements of astrophysics. As one result we get e.g. the today’s Hubble parameter H_0a ≈ 62.34 km/(s Mpc). This value is smaller than the Hubble parameter H_0,Planck ≈ 67.66 km/(s Mpc) resulting from Planck 2018 data [12] which is discussed in the literature.

The theoretical limits of water sorbate based chemical sorption heat storage are investigated in this study. First, a classification of \textit{thermochemical heat storage} is proposed based on bonding typology. Then, thermodynamics of chemical solid/gas sorption is introduced. The analysis of the reaction enthalpy from the literature indicates that this value is only slightly varying for one mole of water. Using this observation, and with the help of thermodynamical considerations, it is possible to derive conclusions on energy efficiency of closed and open heat storage systems. Whatever the salt, the main results are 1) the energy required for evaporation of water is, at least, 65% of the available energy of reaction and 2) the maximum theoretical energy efficiency of the system is about 1.8.

Density is a crucial parameter for quantitatively describing the physical properties of liquids. It serves as an important indicator for scientific research, production process control, pipeline transportation, and other aspects. In oil pipeline transportation and raw material processing, real-time online measurement of liquid density is of great significance. This paper analyzes the working principle of an on-line vibrating tube densitometer and derives the fitting equation for temperature, pressure, and density；it also conducts experiments with an on-line vibrating tube liquid densitometer and establishes a traceability chain for the experimental device. The experimental setup includes a desktop densitometer system, a multi-temperature field constant temperature stirring system, a walk-in constant temperature box, an automatic blowing system, and a frequency acquisition and calculation system. The uncertainty of the device's evaluation is U= 0.08kg/m3, k=2.The experimental research on the on-line vibrating tube liquid densitometer can be carried out within the range of (650~1400) kg/m3, (10~70)℃, (0~50)bar the metrological performance of the vibrating tube densitometer can be researched by utilizing the straight tube type and the elbow type on-line vibrating tube densitometer. A preliminary study was conducted on the effects of different densities, temperatures, and pressures on the vibrating tube system's vibration cycle. The fit coefficient and error were calculated, and the experimental results were compared to the theoretical analysis to confirm the device's conformity. The study verified the device's scientific and reasonable design, and demonstrated that it is feasible to use the device for follow-up research.

We provide a detailed analysis of the electronic properties of graphene-like materials with charge carriers living on a curved substrate, focusing in particular on constant negative-curvature spacetime. An explicit parametrization is also worked out in the remarkable case of Beltrami geometry, with an analytic solution for the pseudoparticles modes living on the curved bidimensional surface. We will then exploit the correspondent massless Dirac description, to determine how it affects the sample local density of states.

A simple model has been used to investigate the nature of chemical order in Na-Pb and Na-Hg liquid binary alloy at 700K and 673K respectively. The energy parameter obtained from the model was used to calculate the concentration dependent mixing properties such as Gibb’s free energy of mixing, Concentration fluctuations in the long wavelength limit and the Warren-Cowley chemical short range order parameter. Results obtained showed that both alloys are hetero-coordinated throughout the entire concentration and there is tendency for segregation and demixing to take place in the liquid alloys. We observed that Na-Hg liquid alloy is more strongly interacting binary alloy and chemically ordered than Na-Pb liquid alloy.

As is known, the Maxwell stress-energy tensor typically used in electromagnetism is not a canonical tensor in the sense of Noether, since its four-divergence is not zero in the presence of sources, in other words, outside of free space. Indeed, the result provided by the calculation of the four-divergence of this tensor is the opposite of the four-vector generalizing the Lorentz force density. The idea is to associate with it a tensor constructed from potentials and sources, such that its four-divergence is the opposite of that of the Maxwell tensor. The distribution of sources will also be analyzed in light of fluid mechanics, allowing us to account for its influence in terms of generated pressure.

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

The energy efficiency of ice hockey arenas is a central concern for the administrations, as these buildings are well known to consume a large amount of energy. Since they are composite, complex systems, solutions to such a problem can be approached from many different areas, from managerial to technological to more strictly physical. In this paper we consider heat transfer processes in an ice hockey hall, during operating conditions, with a bottom-up approach based upon on-site measurements. Detailed heat flux, relative humidity and temperature data for the ice pad and the indoor air are used for a heat balance calculation in the steady-state regime, which quantifies the impact of each single heat source. We then solve the heat conduction equation for the ice pad in transient regime, and obtain a generic analytical formula for the temperature profile that can be used in practical applications. We then apply this formula to the resurfacing process for validation, and find good agreement with an analogous numerical solution. Since it is given with implicit initial condition and boundary conditions, it can be used not only in ice hockey halls, but in a large variety of engineering applications.

Considering the important demand of fresh water and its scarce availability, water desalination is an interesting technology, producing about 44 Mm³/year worldwide, but, in general the most common desalination techniques are highly energy demanding. Freezing-Melting (F/M) desalination uses just up to 70% less thermal energy, but is the least used process mainly, due to the difficulty of the salt separation. This study proposes a model able to analyses the thermodynamic potential that allows the salt diffusion during the F/M process, using an aqueous solution of sodium chloride. This should allow to obtain a sensitive analysis of the process to promote the separation between the high concentration brine and the ice with liquid separation by physical process. The unidimensional model is based on the evolution of both processes: thermal and mass diffusions, depending on temperature and saline gradients, predicting whether the salt will remain inside the ice or not. Thus, the thermal potential is adjusted to frozen only when the salt has been "pushed" towards the brine. Mostly models have base their results on the assumption of a “certain value of saline concentration of the liquid fraction”, value in which there is great disagreement. In this paper the calculations are based on the concentration in the solid-liquid interface, which has been extensively studied and there is a coincidence in those results, being the main advantage of the proposed model.

This article explores the enduring mysteries of consciousness and the afterlife, two enigmatic topics that have fascinated humanity for ages. Despite extensive scientific efforts, the existence of an afterlife remains unproven, and understanding consciousness remains a significant challenge. The research introduces new hypotheses through simple experiments with empirical evidence and theoretical foundations. It delves into the complexities of consciousness, its relationship with the brain, and the need for interdisciplinary approaches. Boldly contemplating the probability of a continuous consciousness after death, the study argues that existing evidence strongly supports this idea. In other words, if we do not accept the hypothesis of an afterlife, we may not be able to discuss the experimental results in the context of any alternative theories. Beyond theoretical implications, it envisions practical outcomes, suggesting that insights into these mysteries could enhance human well-being and contribute to a more harmonious world. This article sheds light on age-old questions about consciousness and the afterlife. Through fresh methodologies, it seeks to provide new perspectives that could reshape our understanding of existence and inspire intellectuals to positive individual and societal advancements including psychological well-being and intelligence.

Ecologists use the net biotic interactions among plants as a major factor to predict other ecosystem features, such as species diversity, community structure, or plant atmospheric carbon uptake. By adopting this approach, ecologists have built a giant body of theory founded on observational evidence. However, growing evidence points out that this may not be the right approach. The literature addressing the biophysical mechanisms underlying the plant interactions is much scarcer. A rising number of scientists claim the need for a mechanistic understanding of plant interactions due to the limitations that a phenomenological approach raises both in empirical and theoretical studies. Scattered studies have recently taken such a mechanistic approach, but we still lack a general theoretical framework to study mechanistically plant interactions. In this review, we first recapitulate the elementary units of plant interactions, i.e., all the known biophysical processes affected by the presence of an influencing plant and the possible phenotypic responses of plants influenced by those processes. Second, we discuss how a net interaction between two plants emerges from the simultaneous effect of these elementary units. Third, we touch upon the spatial and temporal variability of the net interaction and discuss the links between this variability and the underlying biophysical processes. We conclude by discussing how to integrate these processes into a mechanistic framework for plant interactions that must necessarily focus on the individual scale and explicitly incorporate the spatial structure of the community and environmental factors: the plant interaction models (PIM). A PIM incorporates a pair or few plants interacting with their physical environment so that the biotic interaction is not imposed but emerges from the model. This type of model can provide concise, mechanistic hypotheses to be tested empirically. This review calls for a paradigm shift in the ecology of plant interactions, from the classic species interaction study towards a more mechanistic individual-level approach. It also presents a comprehensive foundation for studying the mechanisms underpinning the net interaction between two plants.

To date, radiation adaptation response has been reported as a low-dose related phenomenon and has been associated with radiation hormesis. Well-known cancers are caused by non-radiation active reactants, in addition to radiation. A model of suppression for radiation-specific cancers was previously reported, but the model did not target radiation-nonspecific cancers. In this paper, we describe kinetic models of radiation-induced suppressors for general radiation non-specific cancers, estimating the dose that induces the maximum hormesis effect while satisfying the condition that the risk is approximately proportional to dose above 100 mSv. It was found that the radiation hormesis effect is maximal at about 20 mSv when the rate constant for generation is the same as the rate constant for decomposition. When the two rate constants are different, the dose at which the radiation hormesis effect is maximized depends on both rate constants, but the dose increases as the two rate constants approach each other, reaching a maximum of about 20 mSv. This conclusion may lead to the discovery of unknown cancer suppressors at low doses and the development of cancer suppression methods in the future.

The research showsThis paperstudy presents a theoretical model of sustainable tourism in protected areas based on the experiences obtained in fromthrough field work carried out in the Machalilla national park. The units of analysis that compose it and their theoretical–-methodological foundation, and as well as the indications for their practical implementation in the face of the changes imposed by future tourism are exposed. Using the deductive method, the an analysis of the problem and the general theories linked to sustainable tourism in protected areas was carried out., the This involved establishingment of the premises and the developingment of the objectives to reach conclusions on the topic studied. A qualitative investigation is presented that allowed for the integration of contributions from the analyszes carried out for the treatment and processing of information. Among the results, the systematization of theoretical models linked to tourism in protected areas and, from a practical point of view, the application of a sustainable tourism model was were achieved. The results show the relevance of the proposed theoretical model that is proposed as a contribution to the scientific development of tourism. This model highlights, the systemic nature of its components from a new perspective of analysis, which considerings the need for changes as a development factor.

In this part of the two-part series of essays, we first derive some equations for further physical redshift distances. We then analyze a catalog with 132,975 quasars, for which both the apparent magnitude m and the redshift z are given, in order to find the today’s value of the parameter β₀ of the theory presented. We then use this value to determine the today’s value of the radius R_0a of the Friedmann sphere using a magnitude redshift diagram of 19 SNIa. With the help of the known values of R_0a and β₀, statements about astrophysical data from the black hole in the galaxy M87 can be made. In addition, the today’s Hubble parameter H₀ results from both parameters. Furthermore, we calculate the values of the further physical redshift distances for the black hole in M87 and all 19 SNIa. The resulting parameter values are: β₀ ≈ 0.731, R_0a ≈ 2,712.48 Mpc and H₀ ≈ 65.638 km / (s ∙ Mpc). The today’s mass density of the Friedmann sphere is ρ₀ ≈ 4.843 x 10^-27 g / cm 3. For the mass of the Friedmann sphere we find M_FK ≈ 1.206 x 10⁵⁶ g. Annotation: Knowledge of the first part [1] of the series of articles is a prerequisite for understanding this article.

Aero submarines (aerosubs) are vehicles that can both fly both in air and travel under water. The concept of dual aerial and aquatic vehicles emerged in 1939 when Russian engineer Boris Ushakov proposed the “flying submarine”[1], and this was followed by further developments including RFS1 [2], convair project in 1964[3] , etc. however, to date, limited attempt has been diverted towards the advanced development of such aircraft. This is heavily influenced by challenges associated with the design and operation of the same. Based on the review of literature the authors aim to introduce a theoretical design for an aerosub (QFS-20) with a view to address the design and operation issues including power, entry to and exit from water.

Deep learning is based on matrix computing with a large amount of hidden parameters that is not visible outside the computing module. Deep learning is a non-linear system and a linear approach is not possible. It is natural for people to visualize the algorithm and to follow some hidden parameters. In this paper, we propose a simple graphical programming of a nonlinear system based on drawing the simplest unit, such as a single neuron model. A more complex scheme of a classical neural network is obtained by commands copy-move-place of one neuron. The number of neurons and layers can be chosen arbitrarily. Once the scheme is complete, the implementation code is evaluated with symbolic parameters and nonlinear activation functions. This cannot be done manually. With the symbolic expression of outputs in terms of inputs and symbolic parameters, including symbolic activation pure functions, some other properties can be derived in closed form. This unique original approach can help scientists and developers and design numerical algorithms for machine learning and to understand how deep learning algorithms work.

Orthogonal operators can successfully be used to calculate eigenvalues and eigenvector compositions in complex spectra. Orthogonality ensures least correlation between the operators and thereby more stability in the fit, even for small interactions. The resulting eigenvectors are used to transform the pure transition matrix into realistic intermediate coupling transition probabilities. Calculated transition probabilities for close lying levels illustrate the power of the complete orthogonal operator approach.

The out-of-time-ordered correlation (OTOC) function is an important new probe in quantum field theory which is treated as a significant measure of random quantum correlations. In this paper, with the slogan "Cosmology meets Condensed Matter Physics" we demonstrate a formalism using which for the first time we compute the Cosmological OTOC during the stochastic particle production during inflation and reheating following canonical quantization technique. In this computation, two dynamical time scales are involved, out of them at one time scale the cosmological perturbation variable and for the other the canonically conjugate momentum is defined, which is the strict requirement to define time scale separated quantum operators for OTOC and perfectly consistent with the general definition of OTOC. Most importantly, using the present formalism not only one can study the quantum correlation during stochastic inflation and reheating, but also study quantum correlation for any random events in Cosmology. Next, using the late time exponential decay of cosmological OTOC with respect to the dynamical time scale of our universe which is associated with the canonically conjugate momentum operator in this formalism we study the phenomena of quantum chaos by computing the expression for {\it Lyapunov spectrum}. Further, using the well known Maldacena Shenker Stanford (MSS) bound, on Lyapunov exponent, λ≤2π/β, we propose a lower bound on the equilibrium temperature, T=1/β, at the very late time scale of the universe. On the other hand, with respect to the other time scale with which the perturbation variable is associated, we find decreasing but not exponentially decaying behaviour, which quantifies the random correlation at out-of-equilibrium. Finally, we have studied the classical limit of the OTOC to check the consistency with the large time limiting behaviour.

Animal-assisted interventions (AAI) are a unique class of complementary medical treatments that can improve a patient’s quality of life, both physically and psychologically. Part I of this two-paper systematic literature review series focused on the study methods and quantitative results of researchers in this field. We continue this in-depth review here in Part II by discussing the common theories associated with AAI in the context of cancer. Of all the factors at work in human-animal interactions, researchers explicitly cite compatible animal personality, physical touch, physical movement, distraction/entertainment, and increased human interaction as the mechanisms responsible for the positive clinical outcomes observed in AAI. In various combinations, these mechanisms group under broader theoretical frameworks that attempt to fully explain the AAI context as it relates to cancer care. The social support hypothesis and the conception of a human-animal bond are the most referenced overarching frameworks. The cognitive activation theory of stress, the science of unitary human beings, and the self-object hypothesis are also referenced. We briefly consider other relevant theories commonly noted in the human-animal interactions literature that have the potential to clarify aspects of cancer-related AAI. We also discuss the neurobiological transduction mechanisms needed to connect theoretical frameworks and their mechanisms directly to the observed clinical outcomes. To advance the field, researchers should consider overarching theories with testable hypotheses when designing studies, and use consistent terminology when reporting results. This review lays a foundation for progress towards a unified theoretical framework and for effective treatment of the whole cancer patient.

Polymer flooding is one of the most successful chemical EOR methods, and is primarily implemented to accelerate oil production by sweep improvement. However, other benefits have extended the utility of polymers. During the last decade, it has been evaluated for an increasing number of fields, both offshore and onshore. This is a consequence of improved polymer properties, which extends the use to HTHS (high temperature high salinity) conditions and of improved understanding of flow mechanisms such as for heavy oil mobilization. A key issue in understanding polymer performance is to control and predict in-situ porous medium rheology. The first part of this paper reviews recent developments in understanding polymer flow in porous medium. Especially, polymer in-situ rheology and injectivity is discussed. The second part of this paper reports polymer flow experiments using the most applied polymer for EOR processes, HPAM (partially hydrolyzed polyacrylamide). The experiments address high rate near-wellbore behavior (radial flow) as well as reservoir rate steady state flow (linear flow) and discuss differences observed in terms of flow conditions. In addition, impact of oil on polymer rheology was investigated, and compared to single-phase polymer flow in Bentheimer sandstone rock material. Presence of oil leads to a reduction in apparent viscosity.

As digital technologies rapidly integrate into Health Professions Education (HPE), gaining a comprehensive understanding of cyberethics becomes crucial. This scoping review aimed to explore the pedagogy of cyberethics within HPE, with an emphasis on its definitions, conceptualizations, theoretical foundations, and interventions. Drawing from 37 documents spanning 2012-2022, primarily originating from the U.S. and encompassing both peer-reviewed and grey literature, the study highlighted a significant gap in the explicit definition and conceptualization of cyberethics. Additionally, the evident lack of specific theoretical frameworks in the majority of these documents could hamper the progression and replicability of research. Among the reviewed articles, only four introduced cyberethics educational interventions, indicating a substantial avenue for future research. While the study utilized comprehensive search methods, limitations such as language biases and the potential omission of pertinent documents were present. Future investigations should broaden the cyberethics discourse to encompass emerging technologies and their ethical implications within HPE. Crafting comprehensive, culturally sensitive, and inclusive guidelines is pivotal in nurturing ethical digital practices in the health care community.

In order to meet the military requirements of the fuze, such as precision strike, efficient mutilates ability and low collateral damages, the microminiaturization is an inevitable trend of secure system. Based on the silicon-based MEMS S&A device designed by our term, the design principles of each module and fabrication process are introduced. The average fracture strength and Young's modulus of the silicon are 726 MPa and 175 GPa from the tensile test, respectively. From Hopkinson impact experiment, we can get the threshold-value judging mechanism being safety under the impact overload of 20526 g, and this value is much more than the standard of the drop overload 12000g; the arming value under the centrifugal overload obtained from theory, simulation and experiment is at the range of 28200 g and 32000 g, it shows that the threshold-value judging mechanism can be arming compared with the value 35951g of design principle. Therefore, the threshold-value judging mechanism can meet the design requirements of overload. Furthermore, the relationship of fracture threshold-values obtained by different theories is found out through parametric design method, as shown in Figure 14, it provides the theory evidence to the follow parametric design.

This study delves into the essential characteristics of the Metaverse and its impact on the real world. The Metaverse, a parallel universe composed of countless 3D virtual worlds, has become a hot topic in technology. With the development of advanced technologies such as Virtual Reality (VR), Augmented Reality (AR), blockchain, and Artificial Intelligence, the Metaverse is gradually changing people's lifestyles and work methods, expanding the boundaries of the digital economy. This study profoundly investigates the attributes of the Metaverse, such as asset digitization, application scenario-based, scope economy, industry universality, integrated innovation, and the platform ecosystem. Additionally, we propose a theoretical framework to aid in understanding and shaping this emerging field. We conducted a thorough study and analysis of a specific case, explored the key features of the Metaverse, unveiled the profound impact of Metaverse characteristics on social and economic development, and verified our theoretical framework with this case. This research provides new perspectives and methods for academic studies and offers robust support and guidance for practical applications and decision-making.

The Hyper-Torus Universe Model (HTUM) proposes a novel framework to unify quantum mechanics, cosmology, and consciousness. This paper introduces HTUM's core concept: a higher-dimensional hyper-torus encompassing all possible states of existence. HTUM suggests that the universe functions as a quantum system where all outcomes are inherently connected, with consciousness playing a significant role in actualizing reality. The model introduces several key innovations, including the universe's 4-dimensional toroidal structure (4DTS), providing a new geometric interpretation of spacetime. HTUM presents dark matter and dark energy as nonlinear probabilistic phenomena within this toroidal framework, offering a unique perspective on their nature and interactions. The model proposes a mechanism for wave function collapse through universal self-observation, bridging quantum mechanics and gravity. It introduces a Topological Vacuum Energy Modulator (TVEM) function, offering a potential resolution to the cosmological constant problem. Furthermore, HTUM integrates consciousness as a fundamental aspect of the universe, influencing quantum state actualization and potentially resolving the hard problem of consciousness. The model explores the implications of a timeless singularity and the emergence of time as a product of causal relationships within the toroidal structure. This framework addresses critical challenges in modern physics, including the nature of quantum entanglement, the origin and fate of the universe, and the relationship between mind and matter. The paper discusses the mathematical formulation of HTUM, its implications for quantum mechanics and cosmology, and its potential to bridge the gap between science and philosophy. We present detailed predictions for the cosmic microwave background (CMB) power spectrum, gravitational wave signatures, and large-scale structure formation, demonstrating how HTUM differs from the standard ΛCDM model. Our analysis reveals distinctive oscillatory patterns in the relative difference between HTUM and ΛCDM predictions, with deviations reaching up to ±20% at certain scales. The paper also explores the unification of fundamental forces within the HTUM framework, proposing novel approaches to particle physics and quantum field theory. It introduces the concept of unified mathematical operations, suggesting a more holistic approach to mathematical thinking that aligns with the model's interconnected view of the universe. Additional testable predictions and proposed experimental approaches are discussed, including advanced space-based tests and laboratory experiments probing quantum gravity effects. These specific, quantifiable predictions offer multiple avenues for empirical validation, highlighting HTUM's potential to be distinguished from ΛCDM and other alternative cosmological models. HTUM represents a significant new perspective in our understanding of the universe, inviting further research and exploration into the nature of reality, consciousness, and the fundamental structure of the cosmos. By providing a comprehensive framework that unifies various aspects of physics, cosmology, and consciousness studies, HTUM offers a promising path toward a more complete understanding of our universe.

The core motivation for this study emanates from Voronin S.'s seminal work on the universality of the zeta function. This universality positions the zeta function as a pivotal element in the conceptual framework of global artificial intelligence, suggesting its potential as a foundational component. A critical barrier to harnessing this promising universality has been the absence of efficient algorithms capable of actualizing this concept.

Dirac's Large Number Hypothesis (LNH), proposed in 1937, has captivated the scientific community with its exploration of profound correlations between cosmic and atomic scales. This hypothesis delves into the intricate interplay between the infinitesimally small and the vastly large, offering potential insights into the fundamental nature of the universe. As we continue to uncover the mysteries of the cosmos, the LNH oscillates on the precipice of scientific acceptance—neither fully validated nor entirely dismissed. In this review paper, we embark on a comprehensive journey through Dirac's LNH, shedding light on its theoretical underpinnings, its implications for universe models, and its resonance with the Anthropic Principle. We delve into the possibilities of variable gravitational constants and continuous mass creation, inviting further exploration into the intricacies of our cosmic symphony. By embracing the ongoing quest for understanding, we endeavor to unravel the profound harmonies that connect the infinitesimal with the infinite, contributing to the symphony of knowledge in theoretical physics and cosmology.

Dirac's Large Number Hypothesis (LNH), proposed in 1937, has captivated the scientific community with its exploration of profound correlations between cosmic and atomic scales. This hypothesis delves into the intricate interplay between the infinitesimally small and the vastly large, offering potential insights into the fundamental nature of the universe. As we continue to uncover the mysteries of the cosmos, the LNH oscillates on the precipice of scientific acceptance—neither fully validated nor entirely dismissed. In this review paper, we embark on a comprehensive journey through Dirac's LNH, shedding light on its theoretical underpinnings, its implications for universe models, and its resonance with the Anthropic Principle. We delve into the possibilities of variable gravitational constants and continuous mass creation, inviting further exploration into the intricacies of our cosmic symphony. By embracing the ongoing quest for understanding, we endeavor to unravel the profound harmonies that connect the infinitesimal with the infinite, contributing to the symphony of knowledge in theoretical physics and cosmology.

e Magnetic Ion Modulation (MIM) Theory presents a unified and groundbreaking mathematical framework for controlling and predicting ion behavior in both biological and non-biological systems using external magnetic fields. Central to the theory is the **Ion Modulation Constant** (Tn), a context-specific scaling factor that quantifies the number of ions modulated under specific conditions. This constant, although not universal, allows for accurate modeling of ion modulation in systems ranging from neuronal ion channels to plasma physics and quantum computing. The MIM equation incorporates ion properties such as magnetic moment and permeability, providing insights into neuromodulation for treating chronic pain and epilepsy, plasma confinement in fusion research, and stabilization of ion qubits in quantum computing. This paper includes detailed derivations of the Ion Modulation Constant, examples of its application to specific ions, and a comprehensive exploration of potential experimental validations.

This work is a physical review, with elements of additions and thinning, on the methods of theoretical studies of nonlinear electrophysical phenomena in crystals with ion-molecular chemical bonds (CIMB). Crystals of this class include ionic dielectrics (characterized by high ionic conductivity), layered crystals, a special case of which are hydrogen-bonded crystals (HBC), defined as proton semiconductors and dielectrics (PSD).A scientific review (comparative analysis and justification of various approximations) was carried out on the methods of constructing and solving a generalized quasi-classical kinetic equation describing the mechanism of nonlinear relaxation polarization and conductivity processes in dielectric materials with ion-molecular chemical bonds (a special case is hydrogen-bonded crystals (HBC)) in a wide temperature range (1-1550 K) and polarizing field strengths (0.1-1000 V/m) at alternating field frequencies of the order of 1 kHz - 1000 MHz. The most important variant of the equations of the kinetic theory of dielectric relaxation in this work is the generalized non-linear by polarizing field quasi-classical kinetic equation of ionic (in HBC, proton) relaxation, based on the particle number balance equation (conductivity ions) in potential wells and having (in these models) the meaning of the ion current continuity equation (in HBC, protons), solved by the method of successive approximations by decomposition into infinite power series by degrees of a small dimensionless comparison parameter. It was found that in the area of ​ ​ weak fields (0.1-1 MW/m) at temperatures T = 50 - 550 K, for a number of ionic dielectrics (including HBC and similar dielectric properties and lattice structure) the generalized quasi-classical kinetic equation transforms to the linearized Fokker – Planck equation and, in the region of low (50-100K) and higher temperatures (250-550 K) begin to manifest non-linear polarization effects due to respectively proton tunneling (in the case of HBC) and volume charge relaxation (in the case of the HBC and for a wider class of ionic dielectrics). At ultra-low (1-10 K) temperatures in the region of weak fields (0.1-1 MW/m) and ultra-high temperatures (550-1550 K) in the region of strong fields (10-1000 MW/m), the contribution of this kind of effects to polarization is significantly enhanced. The effect of nonlinearities on relaxation times for microscopic acts of proton transitions across a potential barrier (assumed to be parabolic) is investigated. Nonlinear effects at volume-charge polarization in the hydrogen-bonded crystals (HBC) in alternating electric field, in radio frequency range are investigated. From the solution of the system of nonlinear Fokker-Planck equations (macroscopic kinetic equation) and Poisson, with blocking electrodes, using Fourier series, a recurrent (convenient for use in any approximation of perturbation theory) expression is constructed for complex amplitudes of relaxation modes of volumetric charge. Complex dielectric permittivity (CDP) is calculated as a series decomposition over even frequency harmonics of a variable field. The effect of quantum proton transitions and polarizing field parameters (strength, frequency) on the nonlinear properties of proton semiconductors and dielectrics has been established.