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

An analysis of the consistency of the Abraham and Minkowski momenta in the determination of the photon trajectory was carried out considering a new principle of conservation of the photon's mechanical energy, in which the photon conserves translational energy in orbital angular momentum when transiting between two media, introducing the relativistic energy wave (REW). The confrontation between REW and the recent theory of space-time waves (ST) was considered, pondering your differences. Throughout this study it was possible to verify that the Abraham momentum appears a relativistic photon ignition device in the transition between two media, acting as the hidden momentum of the Minkowski’s relativistic momentum. The wavy behavior in the matter is relativistic, and the relativistic trajectory appears with delays and advances, with points of synchronization between source-observer. The classical or relativistic trajectories are determined as a function of the angle of incidence and the relative refractive index, by one of two distinct non-additive torques, the classic by Abraham or the relativistic by Minkowski. It was found that the same analysis conducted under the principle of conservation of the mechanical energy of the photon can be treated by an new Doppler, Relativistic Apparent, that can be confused with other Dopplers in the treatment of redshift from distant sources. It was found that the conservation of energy in Orbital Angular Momentum (OAM), in the interaction with matter, explains that the synchronization instants are found in the inversion of the OAM, where the advances and delays of REW occur under negligible variations of the OAM, however, opposites.

Dearth of information on extent of genetic variability in cassava limits the genetic improvement of cassava in Sierra Leone. This study aimed at assessing the genetic variability and relationships within 103 cassava genotypes using agro-morphological and culinary markers. A field trial was conducted in the School of Agriculture and Food Sciences research site. The experiment was laid in an augmented randomized block design. Morphological classification based on qualitative and quantitative traits categorized the germplasm into three different groups. A total of ten principal components (PCs) in the qualitative and six PCs in the quantitative trait sets accounted for 66.74% and 67.27% of the total genetic variation, respectively. Traits with significantly strong and positive correlations included presence of fruit (PFRT) and presence of seed (PSE)(r = 0.86***),root yield per plant (RYPP) and number of storage root (NSR) (r = 0.76***), RYPP and number of commercial root (NCR) (r = 0.68***), length of leaf lobe (LLL) and width of leaf lobe (WLL) (r = 0.66***),and between NSR and NCR (0.84***). Cooking time, cooking percentage, texture, mealiness, taste and aroma varied widely among the accessions. Findings established that the cassava germplasm possess useful genetic variability that could be exploited through selection for short term release programme, genetic conservation of valuable germplasm and genetic improvement of the crop.

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

A panorama of the current historiography on the Supernova of 1054 is outlined. Shklovsky (1968) [1], and Murdin (1985) [2] show how the interpretation of this phenomenon converged on a Su-pernova event. Here we reconsider the historical data, assuming a Gamma-Ray Burst (GRB) as its source. A Supernova correlated with the GRB explains well the fading time observed by the an-cient Chinese astronomers, in daytime and in night time, while the GRB power-law explains the present X-rays and GeV emission of the Crab. On the ground of recent understanding of the first episode of binary driven Hypernova GRB (BDHN GRB) in terms of the collapse of a ten solar masses core, we propose the possible identification of the real Supernova event at earlier time than Chinese chronicles. This work allows a new understanding of the significance of historical astronomical observations, including a fireball, due to gamma-rays air shower observation, and a plague of acute radiation syndrome, documented with several thousands of victims in the Eura-sian area (Egypt, Iraq and Siria).

By using Modified simple equation method, we study the Cahn Allen equation which arises in many scientific applications such as mathematical biology, quantum mechanics and plasma physics. As a result, the existence of solitary wave solutions of the Cahn Allen equation is obtained. Exact explicit solutions interms of hyperbolic solutions of the associated Cahn Allen equation are characterized with some free parameters. Finally, the variety of structure and graphical representation make the dynamics of the equations visible and provides the mathematical foundation in mathematical biology, quantum mechanics and plasma physics.

The study investigated farmers’ perception on pests and diseases management strategies, agricultural practices, production constraints and selection criteria of elite varieties using a survey research design. A total of 700 questionnaires were administered to smallholder farmers who were farming for household consumption, those producing for sale and household consumption and those who were mainly producing for sale because their primary goal was to produce for the market. Findings revealed that the most prevalent pests identified were whiteflies (Bemisia tabaci), grasshoppers (Zonocerus variegatus), aphids (Aphis gossypii), mealybugs (Phenacoccus manihoti), termites (Isoptera), and grasscutters (Thryonomys swinderianus). The three most common diseases of cassava limiting growth and yield with mixed infection include viral, bacterial, and fungal. The study also revealed that only 12.5% of farmers cultivated improved cassava varieties. The management practices implemented encompassed field sanitation and the application of pesticides. Lack of capital and no availability of market were the most important production and marketing constraints faced by farmers in the study area, whereas poundability and high storage root yield are the most preferred traits farmers consider in selecting a new variety. Results suggest that smallholder farmers should endeavor to undergo various developmental programs to develop themselves to increase their competitive advantage in their locality and in the local and global agricultural sectors. In addition, governments and other policy makers should strategize plans and programs that would contribute to smallholder farmers’ agriculture, community and national development.

Using a scaling symmetry, it is shown how to compute polynomial conservation laws, generalized symmetries, recursion operators, Lax pairs, and bilinear forms of polynomial nonlinear partial differential equations thereby establishing their complete integrability. The Gardner equation is chosen as the key example for it comprises both the Korteweg-de Vries and modified Korteweg de Vries (mKdV) equations. The Gardner and Miura transformations which connect these equations are also computed using the concept of scaling homogeneity. Exact solitary wave solutions and solitons of the Gardner equation are derived using Hirota’s method and other direct methods. The nature of these solutions depends on the sign of the cubic term in the Gardner equation and the underlying mKdV equation. It is shown that flat (table-top) waves of large amplitude only occur when the sign of the cubic nonlinearity is negative (defocusing case) whereas the focusing Gardner equation has the standard elastically colliding solitons. The paper’s aim is to provide a review of integrability properties and solutions of the Gardner equation and illustrate the applicability of the scaling symmetry approach. The methods and algorithms used in this paper have been implemented in Mathematica but can be adapted for major computer algebra systems.

In this paper we study the initial boundary value problem for logarithmic Higher Order Wave equation. Introducing the Logarithmic Sobolev inequality and using the combination of Galerkin method, we consider the theorem of existence of a global weak solution to problem for the initial boundary value problem of the logarithmic wave equation. By constructing an appropriate Lyapunov function, we obtain the decay estimates of energy for logarithmic Higher Order Wave equation. The proof of the main theorem is given.

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

Formulating a relativistic equation for particles with arbitrary spin remains an open challenge in theoretical physics. In this study, the main algebraic approaches used to generalize the Dirac and Kemmer–Duffin equations for particles of arbitrary spin are investigated. It is proved that an irreducible relativistic equation formulated using spin matrices satisfying the commutation relations of the de Sitter group leads to inconsistent results, mainly as a consequence of violation of unitarity and the appearance of a mass spectrum that does not reflect the physical reality of elementary particles. However, the introduction of subsidiary conditions resolves the problem of unitarity and restores the physical meaning of the mass spectrum. The equations obtained by these approaches are solved and the physical nature of the solutions is discussed.

In the Majorana equation for particles with arbitrary spin, the wave packet is due not only to the uncertainty affecting position and momentum but also to the infinite components with decreasing mass forming the Majorana spinor. In this paper we prove that such components contribute to increase the spreading of the wave packet. Moreover, as occurs in the time propagation of the Dirac wave packet, also in that of Majorana the Zitterbewegung takes place, but it shows a peculiar fine structure. Finally, the group velocity always remains subluminal and the contributions due to the infinite components decrease progressively increasing the spin.

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.

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

This paper attempts to address the phenomenon of normal vibrations, (referred to as dynamic vibrations) occurring on a surface which is already in vibrational motion due to other kinematic phenomena. Such a surface will have a metric tensor, normal, and ambient velocity which diverges from the surface’s original various dynamic tensorial descriptors. This paper formulates the wave equation defined in a coordinate space, and extends the equation to observe vibrations on a surface with the use of the Laplace-Beltrami operator in a tensorial fashion drawing on conventions from the newly established Calculus of Moving Surfaces (CMS). The Paper then identifies the way which these normal vibrations will manifest within ambient space. Finally, a counter-intuitive relation between the magnitude of such dynamic vibrations and dynamic surface’s time-dependent mean curvature presents itself, for which dynamic vibrations superimposed on original dynamic motion will eliminate the other, and the surface remains static under an arbitrary initial motion. From this condition, resubstitution within the wave equation yields a novel coupled PDE system which within contains the time-evolution of the surface’s mean curvature and its dynamic vibrations. This analysis can have application for algorithms designed for mechanical stabilization during seismic activity, as well as analyzing stabilization algorithms for other various applications and can also have application with respect to biotechnological innovations for analyzing properties defined on the surface of cell-Like biological entities such as metabolism, lipid content, and actin dynamics.

Genetic diversity is very important in crop improvement. This study was carried out to assess the genetic diversity and the number of unique multilocus genotypes (MLGs) in cassava collection in Burkina Faso. To achieve this objective 130 cassava accessions were genotyped using 32 simple sequence repeat (SSR) markers. The results revealed that among these markers, twelve (12) were highly informative, with the PIC values greater than 0.50, twelve (12) were moderately informative, with the PIC values ranged between 0.25 and 0.50, and eight (8) were not very informative, with the PIC values lower than 0.25. A moderate level of genetic diversity was found for the population, indicated by the average expected heterozygosity (0.45) and the observed heterozygosity (0.48). About 83.8% of unique multilocus genotypes were found in the cassava collection indicating that SSR markers seem to be most appropriate for MLGs identification. Population structure analysis based on hierarchical clustering identified two subpopulations and Bayesian approach suggested five clusters. Additionally, DAPC analysis separated the cassava accessions into 13 subpopulations. The comparison of these results and the previous study using SNP, suggest that each type of markers can be used to assessment the genetic structure of cassava grown in Burkina Faso.

Stueckelberg-Horwitz-Piron (SHP) electrodynamics formalizes the distinction between coordinate time (measured by laboratory clocks) and chronology (temporal ordering) by defining 4D spacetime events x^μ as functions of an external evolution parameter τ. Classical spacetime events x^μ (τ) evolve as τ grows monotonically, tracing out particle worldlines dynamically and inducing the five U(1) gauge potentials through which events interact. Since Lorentz invariance imposes time reversal symmetry on x⁰ but not τ, the formalism resolves grandfather paradoxes and related problems of irreversibility. The action involves standard first order field derivatives but includes a higher order τ derivative that while preserving gauge and Lorentz invariance removes certain singularities and makes the related QFT super-renormalizable. The resulting field equations are Maxwell-like but τ-dependent and sourced by a current that represents a statistical ensemble of instantaneous events distributed along the worldline. The width λ of this distribution defines a correlation time for the interactions and a mass spectrum for the photons that carry the interaction. As λ becomes very large, the photon mass goes to zero and the field equations become τ-independent Maxwell’s equations. Maxwell theory thus emerges as an equilibrium limit of SHP, in which λ is larger than any other relevant time scale. Particles and fields are not constrained to mass shells in SHP theory, and by exchanging mass may produce pair creation/annihilation processes at the classical level. On-shell evolution with fixed particle masses is restored through a self-interaction associated with the 5D wave equation.

This research focuses on deriving the equation of motion for fermions on a ring. The paper proposes an alternative equation for fermions on the ring, incorporating a self-rotation angle denoted as $\Delta$, and explores its relationship with the original equation.

We introduce a class of logarithmic wave equation. We study the global existence of week solution for this class of equation. We deal with the initial boundary value problem of this class. Using the Galerkin method and the Gross logarithmic Sobolev inequality we establish the main theorem of existence of week solution for this class of equation arising from Q-Ball Dynamic in particular.

One of the oldest problems in physics is that of calculating the motion of N particles under a specified mutual force: the N-body problem. Much is known about this problem if the specified force is non-relativistic gravity, and considerable progress has been made by considering the problem in one spatial dimension. Here I review what is known about the relativistic gravitational N-body problem. Reduction to one spatial dimension has the feature that gravitational radiation is absent, thereby allowing for a clear comparison between the physics of one-dimensional relativistic and non-relativistic self-gravitating systems. After describing how to obtain a relativistic theory of gravity coupled to N point particles, I discuss in turn the 2-body, 3-body, 4-body, and N-body problems. Quite general exact solutions can be obtained for the 2-body problem, unlike the situation in general relativity in 3 spatial dimensions for which only highly specified solutions exist. The 3-body problem exhibits mild forms of chaos, and provides one of the first theoretical settings in which relativistic chaos can be studied. For N4 other interesting features emerge. Relativistic self-gravitating systems have a number of interesting problems awaiting further investigation, providing us with a new frontier for exploring relativistic many-body systems.

Physical processes are usually described using four-dimensional vector quantities - coordinate vector, momentum vector, current vector. But at the fundamental level they are characterized by spinors - coordinate spinors, momentum spinors, spinor wave functions. The propagation of fields and their interaction takes place at the spinor level, and since each spinor uniquely corresponds to a certain vector, the results of physical processes appear before us in vector form. For example, the relativistic Schrödinger equation and the Dirac equation are formulated by means of coordinate vectors, momentum vectors and quantum operators corresponding to them. In the Schrödinger equation the wave function is represented by a single complex quantity, in the Dirac equation a step forward is taken and the wave function is a spinor with complex components, but still coordinates and momentum are vectors. For a closed description of nature using only spinor quantities, it is necessary to have an equation similar to the Dirac equation in which momentum, coordinates and operators are spinors. It is such an equation that is presented in this paper. Using the example of the interaction between an electron and an electromagnetic field, we can see that the spinor equation contains more detailed information about the interaction than the vector equations. This is not new for quantum mechanics, since it describes interactions using complex wave functions, which cannot be observed directly, and only when measured goes to probabilities in the form of squares of the moduli of the wave functions. In the same way spinor quantities are not observable, but they completely determine observable vectors.In Section 2 of the paper, we analyze the quadratic form for an arbitrary four-component complex vector based on Pauli matrices. The form is invariant with respect to Lorentz transformations including any rotations and boosts. The invariance of the form allows us to construct on its basis an equation for a free particle combining the properties of the relativistic wave equation and the Dirac equation. For an electron in the presence of an electromagnetic potential it is shown that taking into account the commutation relations between the momentum and coordinate components allows us to obtain from this equation the known results describing the interactions of the electron spin with the electric and magnetic field. In section 3 of the paper this quadratic form is expressed through momentum spinors, which makes it possible to obtain an equation for the spinor wave function in spinor coordinate space by replacing the momentum spinor components by partial derivative operators on the corresponding coordinate spinor component. Section 4 presents a modification of the theory of the path integral, which consists in considering the path integral in the spinor coordinate space. The Lagrangian densities for the scalar field and for the electron field, along with their corresponding propagators, are presented. An equation of motion for the electron is proposed that is relativistically invariant, in contrast to the Dirac equation, which lacks this invariance. This novel equation permitted the construction of a relativistically invariant procedure for the second quantization of the fermion field in spinor coordinate space.

The statistical analysis of impact of the top 50 solar flares of X-class (1997-2023) on the global seismic activity, as well as on the earthquake preparation zones located in illuminated part of the globe and in the area of 5000 km radius around the subsolar point was carried out. It is shown by a method of epoch superposition that for all cases the increase of seismicity is observed, especially in the region around the subsolar point (up to 38%) during 10 days after the solar flare in comparison with preceding 10 days. The case study of aftershock sequence of strong M=9.1 earthquake (Su-matra-Andaman Islands, 26.12.2004) after the solar flare of X7.2 class (20.01.2005) demonstrated that the number of aftershocks with magnitude M≥2.5 increases more than 20 times after the solar flare with a delay of 7 days. For the case of the Darfield earthquake (M=7.1, 04.09.2010, New Zealand) it was shown that strong solar flares of class X and M probably triggered two strong aftershocks (M>6) with the same delay of 6 days on the Port Hills fault, which is the most sensitive to external electromagnetic impact from point of view of the fault electrical conductivity and orientation. Based on the obtained results the possible application of natural electromagnetic triggering of earthquakes is discussed for a short-term earthquake prediction using confidently recorded strong external electromagnetic triggering impacts on the specific earthquake preparation zones, as well as ionospheric perturbations due to aerosol emission from the earthquake sources recorded by satellites.

Wave and tidal energy, recognized as vital renewable resources, harness the ocean's kinetic and potential power. This study aims to provide an in-depth patent analysis of the technological landscape within these sectors. We applied a dual approach: first, a descriptive analysis was conducted to explore patent publication trends, technology lifecycle stages, patent activity by country, top assignees, and IPC classifications. Our analysis provided a detailed overview of the sector's growth and the key players involved. Second, we utilized topic modeling, specifically BERTopic enhanced with large language models (LLMs), to identify and fine-tune key technolog-ical themes within the patent data. In this study, we identified seven distinct clusters each for wave and tidal energy using this approach. This method led to a novel categorization of the pa-tents, revealing latent themes within the patent data. Although our categorization differs from traditional methods, it provides deeper insights into the thematic focus of the patents, highlight-ing emerging trends and areas of innovation within wave and tidal energy technologies to better exploit and optimize ocean energy conversion infrastructure.

This paper proposed a time two-mesh (TT-M) finite difference numerical scheme to improve the efficiency of solving the symmetric regularized long wave (SRLW) equation. The TT-M Crank-Nicolson discretization and finite difference method are employed in time and space approximation respectively. The scheme involves three main steps: firstly, the time interval is divided into coarse and fine time meshes, then the nonlinear system is solved on the coarse time mesh; secondly, coarse numerical solutions on the fine time mesh are computed using an interpolation formula based on the solutions derived in the step one; lastly, the TT-M finite difference numerical solutions can be obtained through constructing the linearized fine time mesh system using Taylor’s formula. Compared to the currently existing TT-M numerical methods, the novelty of this study is that the nonlinear term including derivatives is linearized by Taylor’s formula for a function with three variables, whose error analysis is more complex. Finally, some numerical examples, including computational time and accuracy, preservation of conservation laws, are given to verify the efficiency of the scheme. By comparing it with the standard nonlinear finite difference scheme, this method can reduce CPU time without sacrificing accuracy.

In this paper, the functional variable method is used to establish solitary wave solutions and periodic wave solutions of the loaded quadratic non-linear Klein-Gordon equation, the loaded cubic non-linear Klein-Gordon equation and the loaded coupled non-linear Klein-Gordon equation. All solutions of these equations have been examined and three dimensional graphics of the obtained solutions have been drawn by using the Matlab software. The main advantage of the proposed functional variable method over other methods is that it provides more new exact traveling wave solutions along with additional free parameters. The graphical representations of the soliton solutions and the periodic wave solutions by using distinct values of random parameter are demonstrated to better understand their physical features. The exact solutions have its great importance to reveal the internal mechanism of the physical phenomena.

We study the center of energy (CE) before and after the separation of superposed wave from a moving medium (MM). It is assumed that two out-of-phase mechanical transverse waves propagating from the opposite directions on a medium moving at non-relativistic speeds are superposed and the superposed portion (SP) is separated from the MM at that moment. We consider the CE of the SP before and after the separation from the MM. The location of CE (LCE) of the SP seems to be at the center of it at the moment of superposition. The SP rotates due to the separation from the MM since the velocity of each portion symmetric with respect to the center of the SP is equal in magnitude and opposite in direction. The magnitudes of velocities of the symmetric portions become different as soon as the SP begins to rotate with the separation from the MM. Then the energies of their symmetric portions are not the same, so the LCE of the SP is not at the center of it. As a result, the LCE of it looks different before and after the separation from the MM. We must find a solution to keep the LCE of the SP constant. We propose that two out-of-phase mechanical transverse waves (MTWs) propagating from the opposite directions on a MM originally have hidden difference in relativistic energy and it suddenly appears within the range observable in Newtonian mechanics when the SP starts rotating. This means that the point of view of hidden difference in relativistic energy is necessary to keep the LCE constant.

We develop an action principle for producing a single fluid, two-constituent system with dissipation in general relativity. The two constituents in the model are particles and entropy. The particle flux creation rate is taken to be zero, while the entropy creation rate is non-zero. Building on previous work, it is demonstrated that a new term (the proper time derivative of the matter space ``metric'') is required in the Lagrangian in order to produce terms typically associated with bulk and shear viscosity. Equations of motion, entropy creation rate, and energy-momentum-stress tensor are derived. Using an Onsager approach of identifying thermodynamic ``forces'' and ``fluxes'' a model is produced which delivers the same entropy creation rate as the standard, relativistic Navier-Stokes equations. This result is then contrasted with a model generated in the spirit of the action principle, which takes as its starting point a specific Lagrangian and then produces the equations of motion, entropy creation rate, and energy-momentum-stress tensor. Unlike the equations derived from Onsager reasoning, where the analogs of the bulk and shear viscosity coefficients are prescribed ``externally'', we find that the form of the coefficients in the second example are a direct result of the specified Lagrangian. Furthermore, the coefficients are shown to satisfy evolution equations along the fluid worldline; also a product of the specific Lagrangian.

In this paper we address the approximation of the coupling problem for the wave equation and Maxwell's equations of electromagnetism in the time domain in terms of the electric field, by means of a nodal linear finite-element discretization in space, combined with a classical'explicit finite-difference scheme for the time discretization. Our study applies to the particular case where the dielectric permittivity has a constant value outside a sub-domain, whose closure does not intersect the boundary of the domain where the problem is defined. Inside this sub-domain Maxwell's equations hold. Outside this sub-domain the wave equation holds, which may correspond to the Maxwell's equations with a constant permittivity under certain conditions. We consider as a model the case of first order absorbing boundary conditions. Optimal error estimates that hold in natural norms under reasonable assumptions are given, among which lies a typical CFL condition for hyperbolic equations.

Relativistic shocks are one of the most plausible sites of the emission of strongly variable, polarized multi-wavelength emission from relativistic jet sources such as blazars, via diffusive shock acceleration (DSA) of relativistic particles. This paper summarizes recent results on a self-consistent coupling of diffusive shock acceleration and radiation transfer in blazar jets. We demonstrate that the observed spectral energy distributions (SEDs) of blazars strongly constrain the nature of hydromagnetic turbulence responsible for pitch-angle scattering by requiring a strongly energy-dependent pitch-angle mean free path. The prominent soft X-ray excess (``Big Blue Bump'') in the SED of the BL Lac object AO 0235+164 can be modelled as the signature of bulk Compton scattering of external radiation fields by the thermal electron population, which places additional constraints on the level of hydromagnetic turbulence. It has further been demonstrated that internal shocks propagating in a jet pervaded by a helical magnetic field naturally produce polarization-angle swings by 180$^o$, in tandem with multi-wavelength flaring activity, without requiring any helical motion paths or other asymmetric jet structures. The specific application of this model to 3C279 presents the first consistent, simultaneous modeling of snap-shot SEDs, multi-wavelength light curves and time-dependent polarization signatures of a blazar during a polarization-angle (PA) rotation. This model has recently been generalized to a lepto-hadronic model, in which the high-energy emission is dominated by proton synchrotron radiation. It is shown that in this case, the high-energy (X-ray and $\gamma$-ray) polarization signatures are expected to be significantly more stable (not showing PA rotations) than the low-energy (electron-synchrotron) signatures.

The advent of modern satellite technology has transformed observational astronomy and astrophysics, offering unprecedented insights into the large-scale behavior of gravitation and challenging established cosmological models. This technological progress has reinvigorated the study of relativistic cosmology, leading to a critical reassessment of foundational assumptions, particularly the cosmological principle, which posits that the universe is homogeneous and isotropic on large scales. While this principle underpins the Standard Cosmological Model and the Friedmann-Lemaitre-Robertson-Walker metric, emerging data has increasingly been challenging its validity. Central to this investigation are the redshift-distance and light intensity-distance relations, essential for testing cosmological models. The integration of both parametric and nonparametric redshift models provides a more comprehensive analysis, addressing discrepancies in our understanding of the universe's structure and evolution. However, unresolved mysteries, particularly concerning dark matter and dark energy, complicate these models. This research critically examines the cosmological principle using the latest observational data and scrutinizes the Friedmann model's assumptions. The study shows that galaxy formation was most rapid in the early universe, especially within the redshift range of , with notable peaks around at and These two characteristic redshift values, predicted by our standard Friedmann redshift model used in this work, are confirmed by the observational data utilized in this research. The research also highlights that dark matter plays a significantly more critical role than dark energy in the process of galaxy formation. While dark energy primarily affects the large-scale expansion of the universe, dark matter seems to go beyond the domination of local galaxy formation and evolution of cosmic structures. These findings underscore the limitations of current models and contribute to the ongoing refinement of cosmological theories, offering a clearer understanding of the universe’s evolution.

This paper analyses the application of deep learning techniques for predicting wave overtopping events in port environments using sea state and weather forecasts as inputs. The study was conducted in the outer port of Punta Langosteira, A Coruña, Spain. A video recording infrastructure was installed to monitor overtopping events from 2015 to 2022, identifying 3709 overtopping events. The data collected was merged with actual and predicted data for the sea state and weather conditions during the overtopping events, creating three datasets. We used these datasets to create several machine learning models to predict whether an overtopping event would occur based on sea state and weather conditions. The final models achieved a high accuracy level during the training and testing stages: 0.81, 0.73, and 0.84 average accuracy during training and 0.67, 0.48, and 0.86 average accuracy during testing, respectively. The results of this study have significant implications for port safety and efficiency, as wave overtopping events can cause disruptions and potential damage. Using deep learning techniques for overtopping prediction can help port managers take preventative measures and optimize operations, ultimately improving safety and helping to minimize the economic impact that overtopping events have on the port's activities.

This paper, based on the "Unified Theory of Forces," rigorously proves the formula of de Broglie's wave function. This helps us better understand the following important issues: 1) Theoretically prove and understand the essence of de Broglie's wave function; 2) Prove that when the particle's momentum P is determined, the greater the mass of the particle, the more concentrated its wave function distribution, and the weaker the interference effect; 3) Correct the spatial distribution of the wave function of free particles, proving that the wave function of free particles is strictly constrained within a finite spatial range, which is consistent with the facts we observe.

In this paper, we consider the Cauchy problem of a time fractional nonlinear diffusion equation. According to the Kaplan’s first eigenvalue method, we first prove the blow-up of the solutions in finite time for some sufficient conditions. We next give sufficient conditions for the existence of global solutions by using the result of Zhang and Sun. In conclusions, we find the second critical exponent for the existence of global and non-global solutions via the decay rates of the initial data at spatial infinity.

The Schwarzschild metric emerges independent of Einstein's field equations, offering a straightforward derivation solely reliant on Newtonian mechanics and Minkowskian proper acceleration. This approach provides a clear path to understanding the gravitational field around a spherically symmetric mass without the need for the complexities of Einstein's full theory of General Relativity. Transitioning to our exploration of the cosmic Friedmann equations, we adopt a novel perspective rooted in a Lagrangian formulation grounded in Newtonian mechanics and the first law of thermodynamics. Our investigation operates under the assumption that the universe is populated by either a perfect fluid or a scalar field. By elucidating the intricate interplay between the Lagrangian formulation and the cosmic Friedmann equations, we uncover the fundamental principles governing the universe's dynamics within the framework of these elemental constituents. In our concluding endeavor, we embark on the task of harmonizing the classical equations—namely, the conservation, Euler, and Poisson equations—with the principles of General Relativity. This undertaking seeks to extend these foundational equations to encompass the gravitational effects delineated by General Relativity, thus providing a comprehensive framework for understanding the behavior of matter and spacetime in the cosmic context.

The extremely high rotation of some SMBHs is the origin of their relativistic rotational energy that results in their relativistic mass. Relativistic mass creates their relativistic gravity which is a partial answer to the missing dark matter.

The increasing demand for higher power in rocket launchers is driving the development of higher power nozzles, achieved essentially by increasing the expansion ratio. However, this can lead to flow separation and resulting unsteady, asymmetrical forces, called side loads, which can limit the life of both the nozzle itself and other engine components. If this problem can be overcome, engine performance can be significantly increased. Therefore, various separation control methods have been proposed, but none have been fully implemented to date due to the uncertainties associated with modeling and predicting the flow phenomena. A numerical study of high area ratio rocket engine is presented to analyze the aeroelastic performance of the structure under the condition of flow separation. The finite volume method, the 2nd order upwind scheme and the extended wall function are used to analyze the flow inside the rocket nozzle and the transition of the Free Shock Separation (FSS) to Restricted Shock Separation (RSS) separation pattern ) to be discussed in detail. Since the location of the flow separation point depends heavily on the flow.

Dual generalized commutative quaternions have broad application prospects in many fields. Additionally, the matrix equation AXB = C has important applications in mathematics and engineering, especially in control systems, economics, computer science, and other disciplines. However, research on the matrix equation AXB = C over the dual generalized commutative quaternions remains relatively insufficient. In this paper, we derive the necessary and sufficient conditions for the solvability of the dual generalized commutative quaternion matrix equation AXB = C. Furthermore, we provide the general solution expression for this matrix equation, when it is solvable. Finally, a numerical algorithm and an example are provided to confirm the reliability of the main conclusions.

In a multivariable system there are usually a number of relaxation times. When some of the relaxation times are shorter than others, the corresponding variables will decay to their equilibrium value faster than the others. After the fast variables have decayed, the system can be described with a smaller number of variables. From the theory of nonequilibrium thermodynamics, as formulated by Onsager, we know that the coefficients in the linear flux-force relations satisfy the so-called Onsager symmetry relations. The question we will address in this paper is how to eliminate the fast variables such that the coefficients in the reduced description for the slow variables still satisfy the Onsager relations. As the proof Onsager gave of the symmetry relations does not depend on the choice of the variables, it is equally valid for the subset of slow variables. Elimination procedures that lead to symmetry breaking are possible, but do not consider systems that satisfy the laws of nonequilibrium thermodynamics.

This study delves into the intricate dynamics of classical mechanics, exploring the interplay between force, mass, and energy. Through fundamental principles and mathematical formulations, it elucidates key relationships governing physical systems. Beginning with an overview of classical mechanics, the study establishes the foundational principles laid down by Newton, emphasizing concepts such as inertia, acceleration, and the relationship between force and motion. Central to the investigation is Newton's second law of motion, highlighting the direct proportionality between force and acceleration, and the inverse relationship between acceleration and mass when acted upon by a force. The study extends to the concept of effective mass, elucidating how the application of force influences the inertial mass of an object and contributes to its effective mass through the acquisition of kinetic energy. Furthermore, the study examines the total energy composition of systems, emphasizing the holistic nature of energy as a combination of potential and kinetic forms. Through the work-energy theorem, a direct link between force and kinetic energy is established, revealing how mechanical work done on an object results in changes in its kinetic energy and effective mass. Mathematical formulations and conceptual analyses provide deeper insights into the intricate relationships between force, mass, and energy, shedding light on the underlying mechanisms governing classical mechanical systems. Through validation against empirical observations and experimental data, the study ensures the accuracy and reliability of derived equations, contributing to a richer understanding of classical mechanics and paving the way for further exploration in the field of physics.

We describe here the coherent formulation of electromagnetism in the nonrelativistic quantummechanical many-body theory. We use the mathematical frame of the field theory and its quantization in the spirit of the QED. This is necessary because of the manifold of misinterpretations emerging from the hystorical development of quantum mechanics, starting from the Schrödinger equation of a single particle in the presence of given electromagnetic fields, followed by the many-body theories of many charged identical particles having just Coulomb interactions inspired from the classical electromagnetic theory of point-like charges. However, this later is known to be inconsistent due to the self-interaction. This way could not be continued further to include properly the magnetic forces between the charged particles and lead to a lot of confusion about the interpretation of the magnetic field in the Hamiltonian, as well as about the gauge invariance. We emphasize the importance of the distinction between the applied (external fields) and the field in the matter. All these problems are length properly solved within the non-relativistic QED, nevertheless the confusion dominates in all the problems related to the magnetic properties of the solid state.

From the theory of relativistic chemical kinetics [M. W. Baig, Int. J. Mod. Phys. B 31, 1750177 (2017)] relativistic thermodynamics and kinetics for electrode processes have been developed to explain time dilation for electrode processes. For a moving observer moving at fractions of the speed of light, cell potential is observed to decrease. This results in the slower oxidation and reduction of ions at the respective electrodes. The newly formulated Lorentz transformation of the electrode and cell potential is explained in terms of generation of spin 2-boson “gravitons” from fusion of spin-1 boson “virtual-photons” mediating electrostatic force of attraction between ions and electrodes. It is postulated that birth of spin 2-boson i.e. gravitons is followed by their eventual escape in any of higher 4+n dimensions. To demonstrate the effectiveness of the present theory, the Daniel cell is considered as a numerical example.

In the study of relativistic jets one of the key open questions is their interaction with the environment on the microscopic level. Here, we study the initial evolution of both electron–proton (e^- - p⁺) and electron–positron (e^±) relativistic jets containing helical magnetic fields, focusing on their interaction with an ambient plasma. We have performed simulations of "global" jets containing helical magnetic fields in order to examine how helical magnetic fields affect kinetic instabilities such as the Weibel instability, the kinetic Kelvin-Helmholtz instability (kKHI) and the Mushroom instability (MI). In our initial simulation study these kinetic instabilities are suppressed and new types of instabilities can grow. In the e^- - p⁺ jet simulation recollimation-like instability occurs and jet electrons are strongly perturbed. In the e^± jet simulation a recollimation-like instability occurs at early times followed by a kinetic instability and the general structure is similar to a simulation without helical magnetic field. Simulations using much larger systems are required in order to thoroughly follow the evolution of global jets containing helical magnetic fields.

By introducing environmental mediator, for avoiding randomness in selecting indicators and subjectivity in deciding interaction path coefficients to reveal interaction mechanism among forest industry, ecology and environmental capacity, structural Pressure–State–Impact–Response (PSIR) and quantitative Structural Equation Modeling (SEM) are utilized with data on thirty–one provinces of China. We can find that: (i) forest industry has a negative influence on ecology, whereas ecology has a positive influence on industry; (ii) the destructive influence that industry has on ecology is much greater than the positive effect ecology has on industry; and (iii) environmental capacity plays a partial mediating role between industry and ecology. According to these results we can conclude that: (i) forest industry and ecology are not in a symbiotic relationship and have not reached a level of ecological security; (ii) the interaction between industry and ecology is in a period of transition from antagonistic to beneficial; and (iii) industry dominates ecology. However, we prospect the following advice: (i) methods of forest industry should be changed; (ii) new modes of industrial integration and circular economy should be developed; and (iii) the ability of the environment to sustain itself should be enhanced. The level of forest ecological security to discuss the symbiotic mechanism of industry and ecology will propose to be measured in future.

This paper investigates the ion-acoustic wave structures in fluid ions for the Benjamin-Bona-Mahony-Peregrine-Burgers (BBMPB) equation. The various types of wave structures, are extracted including the three-wave hypothesis, breather wave, lump periodic, mixed-type wave, periodic cross-kink, cross-kink rational wave, M-shaped rational wave, M-shaped rational wave solution with one kink wave and M-shaped rational wave with two kink wave solutions. The Hirota bilinear transformation is a powerful tool that allows us to accurately solutions and predict the behavior of these wave structures. Through our analysis, we gain a better understanding of the complex dynamics of ion-acoustic waves and their potential applications in various fields. Moreover, our findings contribute to the ongoing research in plasma physics that utilize ion-acoustic wave phenomena. To show the physical behavior of the solutions, some 3D plots have been performed and their respective contour level, choosing different values of the parameters.

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

The extra precession of Mercury - 42.9 seconds of arc per century - explained by General Relativity (GR), is the result of a secular addition of 5.02 × 10⁻⁷ rad. at the end of every orbit around the Sun. We will analyze, the instantaneous precession and its addition along one orbit, determine the magnitude and oscillations around the mean value, comparing key theoretical proposals. This angular precession, should be the result reaction of Mercury to the gravitoelectric action produced by the geometric curve space-time at each single point of the elliptic orbit. The better we should know about this instantaneous precession, the better we will determine the external action and its quantum core nature, if that is the case. The Doppler tracking of the MESSENGER spacecraft, produces only 1 m error, enough precision to deduce the complete geodesic orbit of Mercury as an open free-fall path, isolated from other planets gravitational interference. The aim of this article is also to encourage JPL, IMCCE. and other scientific teams to do so because, as far as I know, it has not been entirely measured yet, by accurately tracking that motion.

It is discovered that the gravitational field on the surface of a neutron star is with a relativistic mass density of 2.65*10¹⁶~5.87*10¹⁸kgm^-3 which can be larger than the mass density of the neutron star (~10¹⁷kgm^-3). And, the total relativistic mass of the gravitational field of the Sun is ~10⁷ times the mass of the Sun. For different stars, the relativistic mass of the gravitational field is larger as the mass density of the star is larger. In the Milky Way, the total relativistic mass of the gravitational fields is much larger than the total mass of the stars, planets and gas. And, the relativistic mass density of the observed strongest magnetic field is 2.17*10⁸kgm^-3. This discovery should be a new frame to understand the fundamental problem of physics.

When presenting special relativity, it is customary to single out the so-called paradoxes. One of these paradoxes is the formal occurrence of speeds exceeding the speed of light. An essential part of such paradoxes arises from the incompleteness of the relativistic calculus of velocities. In special relativity, the additive group is used for velocities. However, the use of only group operations imposes artificial restrictions on possible computations. Naive expansion to vector space is usually done by using non-relativistic operations. We propose to consider arithmetic operations in the special theory of relativity in the framework of the Cayley–Klein model for projective spaces. We show that such paradoxes do not arise in the framework of the proposed relativistic extension of algebraic operations.

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

This article lays the foundation for Extended Relativity (ER) – a unified geometric approach to the electromagnetic and gravitational field and relativistic dynamics in them. We explain here the basic tenets of ER, including the influenced spacetime of an object and the Extended Principle of Inertia. These two new ideas enable a unified theory of these fields. We introduce local scaling functions for describing the geometry of a spacetime influenced by a field and construct a simple, universal local scaling function which unifies electromagnetism and gravity. We recover the full electromagnetic theory, including Maxwell’s equations. For gravitation, ER passes all of the tests of General Relativity. Despite the non-linearity of relativistic gravitation, we obtain a method of combining fields from multiple sources. Finally, we identify the differences in the relativistic treatment of the electromagnetic field by Special Relativity and of the gravitational field by General Relativity and indicate how these differences are resolved in ER.

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.

In this work, we consider a one-dimensional laminated beam in the case of non-equal wave speeds with only one infinite memory on the effective rotation angle. In this case, we establish the general decay result for the energy of solution without any kind of internal or boundary control. The main result is obtained by applying the method used in Guesmia et al. (Electron. J. Differential Equations 193: 1-45, 2012) and the second-order energy.

The fractional advection-dispersion equation FADE plays an important role, especially in explaining the process of solute-transport in natural porous media with different degrees of heterogeneity. However, studies of the flow and transport of contaminants in the underground environment are based on the knowledge of many functional parameters of the subsoil. The delay factor caused by nonlinear absorption is one of these parameters inheriting significant ambiguities in its estimation in heterogeneous media. In the study, a fractional advection-dispersion FADE model was developed by the implicit Euler method, based on a Grunwald and Caputo-Liousville approximation to explicitly evaluate and simulate the transport mechanism of contaminants in media with unsaturated porous materials subjected to a nonlinear sorption model. Better solute mass retention was observed for fractional advection-dispersion FADE model. Moreover, the absorption parameter of the retardation coefficient has a better impact on the motion of the solute in a saturated porous medium. In other words, it has a significant effect on the dispersion of pollutants in aquifers. This study highlights the need to characterize the aquifer to predict solute transport in porous media.

The effect of wave forces on the structural safety of fixed oscillating water-column (OWC) devices is critical. In this study, a three-dimensional numerical model of an oscillating water column (OWC) device is constructed using the computational fluid dynamics software OpenFOAM. Subsequently, the hydrodynamic performance of the numerical model is comprehensively validated. Finally, the hydrodynamic performance data are analyzed in detail to obtain meaningful conclusions. The results indicate that the horizontal wave force on the OWC device is approximately 6.6 to 7.9 times greater than the vertical wave force, whereas the lateral wave force is relatively small. Both the horizontal and vertical wave forces decrease as the relative water depth increases under a constant wave period and height. The horizontal wave force increases linearly with the wave height, whereas the vertical wave force increases with the square of the wave height. In addition, the highest dynamic water pressure is observed at the interface between the water surface and device, both within and outside the front wall of the gas chamber. The dynamic water pressure at different locations on the front chamber increases and subsequently decreases as the wave frequency increases.

In previous papers we have shown how Schr\"{o}dinger's equation which includes an electromagnetic field interaction can be deduced from a fluid dynamical Lagrangian of a charged potential flow that interacts with an electromagnetic field. The quantum behaviour was derived from Fisher information terms which were added to the classical Lagrangian. It was thus shown that a quantum mechanical system is drived by information and not only electromagnetic fields. This program was applied also to Pauli's equations by removing the restriction of potential flow and using the Clebsch formalism. Although the analysis was quite successful there were still terms that did not admit interpretation, some of them can be easily traced to the relativistic Dirac theory. Here we repeat the analysis for a relativistic flow, pointing to a new approach for deriving relativistic quantum mechanics.

In this paper, we study the relativistic correction to Bekenstein-Hawking entropy in the canonical ensemble and isothermal-isobaric ensemble and apply it to the cases of non-rotating BTZ and AdS-Schwarzschild black holes. This is realized by generalizing the equations obtained using Boltzmann-Gibbs(BG) statistics with its relativistic generalization, Kaniadakis statistics, or κ-statistics. The relativistic corrections are found to be logarithmic in nature and it is observed that their effect becomes appreciable only in the high-temperature limit suggesting that the entropy corrections must include these relativistically corrected terms while taking the aforementioned limit. The non-relativistic corrections are recovered in the κ → 0 limit.

The relativistic effects of the dynamical properties of light at angular incidence were analyzed from the perspectives of Bohr indeterminacy and Heisenberg uncertainties and statistical dispersion. It was found that these effects report minimal uncertainties that agree with one or the other according to the angular range of incidence and that decrease with increasing refringence of the medium, constituting a specific relativistic uncertainty at angular incidence. An anomaly is indicated for the uncertainty principle in the Quantum Theory (QT) setting for small angles of incidence, where the accuracy of the angular position does not imply an increase in the uncertainty of the linear momentum. The anomalies arise because TQ does not predict the alternation between the classical and relativistic regimes of photon inertia at angular incidence. Specific relativistic uncertainty particularizes the uncertainty principle in the transmission of light between media pairs at angular incidence for the relativistic scenario, considering an observer that registers the relativistic effects of measurements that interfere with the observed system, in another inertial referential.

The geodesics on a relativistic manifold are given by the well-known equation involving the Christoffel coefficients. This equation can be solved numerically step by step and transposed into a quantization. We study here the effect of this quantization on the Schwarzschild spacetime, more precisely in the Kruskal-Szekeres map.

In ultra-relativistic collisions of heavy ions, the strongly interacting Quark Gluon Plasma (sQGP) is created. The fluid nature of the sQGP was one of the important discoveries of high energy heavy ion physics in the last decades. Henceforth the explosion of this matter may be described by hydrodynamical models. Besides numerical simulations, it is important to study the analytic solutions of the equations of hydrodynamics, as these enable us to understand the connection of the final and initial states better. In this paper we present a perturbative, accelerating solution of relativistic hydrodynamics, on top of a known class of solutions describing Hubble-expansion. We describe the properties of this class of perturbative solutions, and investigate a few selected solutions in detail.

A novel nano-laminated GdB2C2 material was successfully synthesized using GdH2, B4C, and C via an in-situ solid state reaction approach for the first time. The formation mechanism of GdB2C2 was revealed based on the microstructure and phase evolution investigation. A purity of 96.4 wt. % GdB2C2 was obtained at a low temperature of 1500 ℃, while a near full pure GdB2C2 can be obtained at a temperature over 1700 ℃. The as-obtained GdB2C2 presented excellent thermal stability at high temperature of 2100 ℃ in Ar atmosphere due to the stable frame work formed by the high covalent four-members and eight-members B-C rings in GdB2C2. The minimum reflection loss value (RLmin) of -47.01 dB with an effective absorption bandwidth (EAB) of 1.76 GHz at a thickness of 3.44 mm was obtained for the GdB2C2 synthesized at 1500 ℃. The possible EMWA mechanism could be ascribed to the nano-laminated structure and appropriate electrical conductivity, which facilitated to the good impedance matching, remarkable conduction loss, interfacial polarization as well as multiple interface reflection and scattering. The as-obtained GdB2C2, with excellent EMWA performance as well as remarkable ultra-high temperature thermal stability, could be a promising candidate for the EMWA materials applications in extreme ultra-high temperatures.

In this paper, a semi-empirical model of air waves induced by falling rock is described. The model is composed of a uniform motion phase (velocity close to 0 m·s^-1) and an acceleration movement phase. The uniform motion phase was determined based on experimentally and the acceleration movement phase was derived by theoretical analysis. A series of experiments were performed to verify the semi-empirical model and elucidated the law of the uniform motion phase. The acceleration movement phase accounted for a larger portion with a greater height of the falling rock. Experimental results of different falling heights of the goaf showed close agreement with theoretical analysis values. The semi-empirical model could accurately and conveniently estimate the velocity of air wave induced by falling rock. Thus, the semi-empirical model can provide a reference and basis for estimating the speed of air waves and designing protective measures in mines.

Wave steepness is presented as an extension and a valuable add-on to the conventional set of sea state parameters retrieved from satellite altimetry data. Following physical model based on recent advances of weak turbulence theory wave steepness is estimated from directly measured spatial gradient of wave height. In this way the method works with altimetry trajectories rather than with point-wise data. Moreover, in contrast to widely used parametric models this approach provides us with instantaneous values of wave steepness and period. Relevance of single-track estimates of wave steepness (period) is shown for wave climate studies and confirmed by a simple probabilistic model. The approach is verified via comparison against buoy and satellite data including crossover points for standard 1 second data of Ku-band altimeters. High quality of the physical model and robustness of the parametric ones are examined in terms of global wave statistics. Prospects and relevance of both approaches in the ocean wave climate studies are discussed.

We investigate solutions of the classical Mathieu-Hill (MH) equation which characterizes the dynamics of trapped ions, based on the Floquet theory and starting from a well known analytical model. The analytical model we introduce demonstrates that the equations of motion are equivalent to those of the harmonic oscillator (HO). Two independent approaches are used, based on two classes of complex solutions of the MH equation. The paper addresses both the damped HO and parametric oscillator (PO) for an ion confined in an electrodynamic (Paul) trap. Stability and instability regions for the periodic orbits associated to the MH equation which describes a HO (PO) confined in an electrodynamic trap are also discussed, depending on the values of the Floquet exponent, for very small values of the $q$ parameter. The main objective of the paper is to identify stable and bounded solutions for the dynamics of a HO levitated in an electrodynamic trap. This paper represents a follow-up of a recently published article in Photonics, 11 (6) 551.

Two distinct measures of information, connected respectively to the amplitude and phase of the wave function of a particle, are proposed. There are relations between the time derivatives of these two measures and their gradients on the configuration space, which are equivalent to the wave equation. The information related to the amplitude measures the strength of the potential coupling of the particle (which is itself aspatial) with each volume of its configuration space, i.e. its tendency to participate in an interaction localized in a region of ordinary physical space corresponding to that volume. The information connected to the phase is that required to obtain the time evolution of the particle as a persistent entity starting from a random succession of bits. It can be considered as the information provided by conservation principles. The meaning of the so-called "quantum potential" in this context is briefly discussed.

The stability properties of the Hill equation are discussed, and especially those of the Mathieu equation that characterize ion motion in electrodynamic traps. The solutions of the Mathieu equation for a trapped ion are characterized by using the Floquet theory and Hill's Method solution, which yields an infinite system of linear and homogeneous equations whose coefficients are recursively determined. Stability is discussed for parameters $a$ and $q$ that are real. Characteristic curves are introduced naturally by the Sturm-Liouville problem for the well known even and odd Mathieu equations $ce_m(z,q)$ and $se_m(z,q)$. We illustrate the stability diagram for a combined (Paul and Penning) trap and represent the frontiers of the stability domains for axial and radial motion. In case of a Paul trap the stable solution corresponds to a superposition of harmonic motions. The problem of evaluating the maximum amplitudes of stable oscillations for the ideal conditions (taken into consideration) is also approached. Anharmonic corrections are discussed within the frame of the perturbation theory, while the frontiers of the modified stability domains are determined as a function of the chosen perturbation parameter. The results apply to 2D and 3D ion traps used for different applications in quantum engineering, among which optical clocks, quantum logic and quantum metrology, but not restricted only to these.

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

In this article, we describe a simple procedure for evaluating the sterility of nutrient media using a shear-horizontal surface acoustic wave (SH-SAW) biosensor. We used the SH-SAW biosensor platform to monitor the time-dependent phase responses of the material for the media that binds to a monolayer of 3-mercaptopropanyl-N-hydroxy succinimide on the biosensor surface. Increases in the phase shift less than 50% of the starting phase shift recorded 180 minutes after the sterilization indicate a successful sterility test of the media. Our devices were then applied to sterility testing using a viable Escherichia coli (E. coli) K-12 solution to confirm our hypothesis. Filtered LB Broth was the negative control, and a 24-hour culture of E. coli was the positive control. Before testing, the cell solution was pelleted, the media decanted, and then replaced with a 1x phosphate-buffered saline solution (1x PBS). Since we know that the N-hydroxysuccinimide residues will bind to amine groups, only in cases where microbial species are present will the surface binding increase greater than 50%. We confirmed our hypothesis using SH-SAW biosensors and overnight E. coli cultures. The sensitivity for our 250 MHz quartz SH-SAW sensors was calculated based on the response from the E. coli K-12 solution over the linear dynamic range, which appears to be 2x10^4 – 2x10^7 CFU per ml and has a sensitivity of S = 1.655x10^5 o m2 Kg-1. The limit of detection (LOD) for these sensors was calculated to be approximately 2x10^-9 grams (g), which is estimated to be approximately 2,000 Escherichia coli (E. coli) K-12 cells. However, the sensitivity and insertion loss remained approximately unchanged before and after coating the sensor with 3,3'-Dithiobis(succinimidyl) Propionate (DSP).

In this paper, we consider a fourth-order suspension bridge equation with nonlinear damping term |u_t|^m-2u_t and source term |u|^p-2u. We give necessary and sufficient condition for global existence and energy decay results without considering the relation between m and p. Moreover, when p>m, we give sufficient condition for finite time blow-up of solutions. The lower bound of the blow-up time T_max is also established. It worth to mention that our obtained results extend the recent results of Wang (J. Math. Anal. Appl., 2014) to the nonlinear damping case.

Continuous-wave photocathode guns are capable of delivering electron beams with high repetition rates and high average currents. However, they are limited by relatively low accelerating gradients and cathode fields. This limitation leads to a larger beam size at the gun exit due to space charge forces, making the beam more sensitive to optical aberrations and posing challenges for low-emittance electron beam transmission. This paper focuses on the aberrations induced by multipole fields. We analyze the effects of quadrupole, sextupole, and higher-order fields on beam profile and transverse emittance and propose a beam-based method for the rapid characterization and correction of these multipole fields. Furthermore, we present an experimental study conducted on the DC-SRF-II photocathode gun equipped with dedicated correctors. Both simulation and experimental results demonstrate that our approach effectively mitigates beam aberrations caused by multipole fields, resulting in improved beam symmetry and reduced emittance.

Fire detection from satellite sensors relies on an accurate estimation of the unperturbed state of a target pixel, from which an anomaly can be isolated. Methods for estimating the radiation budget of a pixel without fire depend upon training data derived from the location's recent history of brightness temperature variation over the diurnal cycle, which can be vulnerable to cloud contamination and the effects of weather. This study proposes a new method that utilises the common solar budget found at a given latitude in conjunction with an area's local solar time to aggregate a broad-area training dataset, which can be used to model the expected diurnal temperature cycle of a location. This training data is then used in a temperature fitting process with the measured brightness temperatures in a pixel, and compared to pixel-derived training data and contextual methods of background temperature determination. Results of this study show similar accuracy between clear-sky medium wave infrared upwelling radiation and the diurnal temperature cycle estimation compared to previous methods, with demonstrable improvements in processing time and training data availability. This method can be used in conjunction with brightness temperature thresholds to provide a baseline for upwelling radiation, from which positive thermal anomalies such as fire can be isolated.

We describe a family of paraxial and quasi-monochromatic optical wave packets with finite energy and smoothly shaped amplitude in space and time that develops a singularity in the intensity when spatiotemporally focused by imparting a converging spherical wave front and a negative temporal chirp. This singular behavior upon ideal focusing is manifested in actual focusing with finite apertures and in media with high-order dispersion in an "exploding" behavior featuring indefinitely increasing concentration of the energy when opening the aperture radius, thus exercising a continuous control on the focal intensity and spatial and temporal resolution. These wave packets offer a new way of focusing that outperforms what can be achieved with standard Gaussian wave packets in terms of focal intensity and resolution, and new possibilities in applications where energy concentration and its control are crucial.

In 2018, Iran witnessed approximately 21,000 fatalities resulting from road accidents, ranking it as the fifth leading cause of death across all age groups. These incidents carry substantial economic and social burden for the nation, claiming more than 5% of its GDP. Human behavior emerges as a significant contributing factor to high-risk driving offenses. It has been proposed that by influencing general deterrence, a rigorous defense can be established against such violations. Various theories posit that by reinforcing or diminishing influential factors, general deterrence perception can be molded, presenting a potential avenue for an effective deterrent against traffic infractions. This study examines deterrence perceptions prevailing among the public in Iran regarding the enforcement of traffic laws. Employing Structural Equation Modeling (SEM), we delve into the intricate relationships between variables, allowing for a comprehensive exploration of the factors influencing general deterrence. The study draws on the data derived from a survey comprising 548 questionnaires for modeling purposes. An innovative concept, private sector enforcement, is introduced and incorporated into the questioning and modeling process. The findings reveal that socioeconomic status (p-value<0.01), police enforcement (p-value<0.05), private sector enforcement (p-value<0.05), specific deterrence (p-value<0.01), and the use of technology (p-value<0.01) have direct and indirect impacts on the general deterrence perception of drivers.

This study presents a comparative analysis of length deformation in Classical and Relativistic Mechanics, specifically investigating 10-gram objects accelerating to 1% of the speed of light. By employing Hooke's Law in Classical Mechanics and the Relativistic Lorentz Factor, the research explores the implications of acceleration dynamics and the limitations inherent in Relativistic Mechanics. The results reveal significant differences in predicted length changes between the two frameworks, emphasizing the necessity of considering relativistic effects beyond velocity alone. This study underscores the critical importance of addressing the incomplete treatment of acceleration dynamics in Relativistic Mechanics to achieve a more accurate depiction of length deformation in high-speed scenarios.

We all have in mind Einstein's famous thought experiment in the elevator where we observe the free fall of a body, and then the trajectory of a light ray. Simply here, in addition to the qualitative aspect, we carry out the exact calculation, and for the first time the worldlines equations are given. We consider a uniformly accelerated reference frame in rectilinear translation, and we show that the trajectories of the particles are semi-ellipses with the center on the event horizon. The frame of reference is non-inertial, the space-time is flat, and the computations are performed within the framework of special relativity. Some experimental consequences are discussed, especially the experiment with the accelerated Michelson-Morley interferometer is solved, and we described an experiment where a new relativistic paradox appears --- a particle of matter seems to go faster than light. The differences, compared to the classical case, are important at large scale and close to the horizon, but they are small in the lift where the interest is above all theoretical. The concepts of metric, coordinated velocity and horizon are discussed, and the analogy with the black hole is made.

The theories of quantum mechanics and relativity dramatically altered our understanding of the universe ushering in the era of modern physics. Quantum theory deals with objects probabilistically at small scales, whereas relativity deals classically with motion in space and time. We show here that the mathematical structures of quantum theory and of relativity follow together from pure thought, defined and uniquely constrained by the same elementary ``combining and sequencing'' symmetries that underlie standard arithmetic and probability. The key is uncertainty, which inevitably accompanies observation of quantity and imposes the use of pairs of numbers. The symmetries then lead directly to the use of complex \sqrt{-1} arithmetic, the standard calculus of quantum mechanics, and the Lorentz transformations of relativistic spacetime. One dimension of time and three dimensions of space are thus derived as the profound and inevitable framework of physics.

A relativistic positioning system is a set of four emitters broadcasting their proper times by means of light signals. The four emitter times received at an event constitute the emission coordinates of the event. Covariant quantities associated with relativistic positioning systems are analysed relatively to an observer in Minkowski space-time by splitting them in their relative space-like and time-like components. The location of a user in inertial coordinates from a standard set of emission data (emitted times and satellite trajectories) is solved in the underlying 3+1 formalism. The analytical location solution obtained by Kleusberg for the GPS system is recovered and interpreted in a Minkowskian context.

In previous papers we have shown how Schrödinger’s equation which includes an electromagnetic field interaction can be deduced from a fluid dynamical Lagrangian of a charged potential flow that interacts with an electromagnetic field. The quantum behaviour was derived from Fisher information terms which were added to the classical Lagrangian. It was thus shown that a quantum mechanical system is driven by information and not only electromagnetic fields. This program was applied also to Pauli’s equations by removing the restriction of potential flow and using the Clebsch formalism. Although the analysis was quite successful there were still terms that did not admit interpretation, some of them can be easily traced to the relativistic Dirac theory. Here we repeat the analysis for a relativistic flow, pointing to a new approach for deriving relativistic quantum mechanics.

In a recent paper discussing Newton’s third law in the framework of special relativity for charged bodies, it was suggested that one can construct a practical relativistic motor provided high enough charge and current densities are available. As on the macroscopic scale charge density is limited by the phenomena of dielectric breakdown, it was suggested to take advantage of the high charge densities which are available on the microscopic scale. A preliminary analysis of this option denoted "nano relativistic scale" is studied in the current paper.

In this review article the study of the development of relativistic cosmology and introduction of inflation in it is carried out. We study the properties of standard cosmological model developed in the framework of relativistic cosmology and the geometric structure of spacetime connected coherently with it. We examine the geometric properties of space and spacetime ingrained into the standard model of cosmology. The big bang model of the beginning of the universe is based on the standard model which succumbed to failure in explaining the flatness and the large-scale homogeneity of the universe as demonstrated by observational evidence. These cosmological problems were resolved by introducing a brief acceleratedly expanding phase in the very early universe known as inflation. Cosmic inflation by setting the initial conditions of the standard big bang model resolves these problems of the theory. We discuss how the inflationary paradigm solves these problems by proposing the fast expansion period in the early universe.

Hamiltonians describing the relativistic quantum dynamics of a particle with an arbitrary spin are shown to exhibit a supersymmetric structure when the even and odd elements of the Hamiltonian commute. For such supersymmetric Hamiltonians an exact Foldy-Wouthuysen transformation exits which brings it into a block-diagonal form separating the positive and negative energy subspaces. Here the supercharges transform between energy eigenstates of positive and negative energy. The relativistic dynamics of a charged particle in a magnetic field is considered for the case of a scalar (spin-zero) boson obeying the Klein-Gordan equation, a Dirac (spin one-half) fermion and a vector (spin-one) boson characterised by the Proca equation.

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

Recent advancements in semiconductor photonic and electronic devices such as Uni-travelling-carrier photodiodes (UTC-PDs), have played a significant role in the development of Terahertz communication technology. However, a major challenge that still persists is the limited output power from a single UTC-PD required for practical transmission distances. To enhance the output power, we propose and demonstrate a novel Terahertz wave power combining technique using a photomixer device that comprises of two arrayed UTC-PDs monolithically integrated with a microstrip line-based 2 × 1 Wilkinson power combiner and a rectangular patch antenna on a Silicon Carbide (SiC) substrate at 300 GHz. At photocurrents of 8 mA and 10 mA from the two UTC-PDs, the device experimentally exhibited a 7.3 dB increase in power relative to the power obtained with 8 mA UTC-PD and a 4.4 dB increase in power relative to the power obtained with 10 mA UTC-PD, when both UTC-PDs were irradiated. This implies that power can be enhanced by a factor of N2 if the photocurrent is multiplied by a factor of N. This technology presents a holistic and cutting edge platform for further power multiplication by further increasing the number of arrayed UTC-PDs.

We review time expansion wave theory and refine our model showing it to accurately match observed cosmological luminosity data. The theory augments general relativity to create a container within which quantum effects can be explained by treating time as an artefact of a fourth spatial dimension that we observe as the expansion of the universe. This leads us to explain mass creation, the speed of light limit, gravity, black holes without singularities and other macroscopic effects. Our model leads to an expansion velocity of 6.87 0.36 × 106 ms-1, which results in a Hubble expansion rate constant of 71.3 3.7 km/s/Mpc. Because of the finite window of time in which we exist, an extra a degree of freedom is available leading to interesting interpretations at the subatomic level. At this size range, then a spin is allowed within the time dimension explaining why wave particle duality occurs and explains the electromagnetic force and other quantum mechanical properties. It provides a solution to the double slit conundrum and can explain how quantum entangled partners can behave in a quantum way and pass seemingly time-defying information. The potential quantitative origin of the fine structure constant which governs the size of the electromagnetic force is also strongly indicated by this theory.

The discovery by the Large Area Telescope on board Fermi of variable gamma-ray emission from radio-loud narrow-line Seyfert 1 (NLSy1) galaxies revealed the presence of a possible third class of AGN with relativistic jets in addition to blazars and radio galaxies. Considering that NLSy1 are usually hosted in spiral galaxies, this finding poses intriguing questions about the nature of these objects and the formation of relativistic jets. We report on a systematic investigation of the gamma-ray properties of a sample of radio-loud NLSy1, including the detection of new objects, using 7 years of Fermi-LAT data with the new Pass 8 event-level analysis. In addition we discuss the radio-to-very-high-energy properties of the gamma-ray emitting NLSy1, their host galaxy, and black hole mass in the context of the blazar scenario and the unification of relativistic jets at different scales.

Planetary waves in the mesosphere are studied using observational data and models to establish their origin, as there are indications of their generation independently of waves in the stratosphere. The quantitative relationships between zonal wave numbers m = 1 (wave 1) and m = 2 (wave 2) were studied with a focus on the mid-latitude mesosphere at 50N latitude. Aura Microwave Limb Sounder measurements were used to estimate wave amplitudes in geopotential height during the 2020–2021 winter major sudden stratospheric warming. The moving correlation between the wave amplitudes shows that, in comparison with the anticorrelation in the stratosphere, wave 2 positively correlates with wave 1 and propagates ahead of it in the mesosphere. A positive correlation r = 0.5–0.6, statistically significant at the 95% confidence level, is observed at 1–5-day time lag and in the 75–91 km altitude range, which is the upper mesosphere–mesopause region. Wavelet analysis shows a clear 8-day period in waves 1 and 2 in the mesosphere at 0.01 hPa (80 km), while in the stratosphere–lower mesosphere the period is twice as long at 16-days; this is statistically significant only in wave 2. Possible sources of mesospheric planetary waves are discussed.

First, we examine how spin is treated in special relativity and the necessity of introducing spin supplementary conditions (SSC) and how they are related to the choice of a center-of-mass of a spinning particle. Next, we discuss quantum electrodynamics and the Foldy-Wouthuysen transformation which we note is a position operator identical to the Pryce-Newton-Wigner position operator. The classical version of the operators are shown to be essential for the treatment of classical relativistic particles in general relativity, of special interest being the case of binary systems (black holes/neutron stars) which emit gravitational radiation.

A proof is given showing the Collatz Conjecture is true for all positive integers. The proof was possible once the perspective of the proof was changed from looking at the pattern of the positive integers to looking at the conjecture rules. The conjecture rule for even numbers organizes all positive integers into unique sets and the rule for odd numbers interconnects the unique sets into dendritic pathways to “1.” Infinite loops, other than the minor 4-2-1 loop after reaching “1,” and pathways to infinity are shown to be mathematically impossible. The proof predicted a general equation that shows all positive integers ultimately reach a final value of “1," and calculates the values and locations of the odd positive integers during the iterations for each tested positive integer.

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

Significant Wave Height(SWH) is a crucial parameter in oceanographic research, essential for understanding various marine and atmospheric processes. Traditional methods for obtaining SWH, such as ship-based and buoy measurements, face limitations like limited spatial coverage and high operational costs. With the advancement of Global Navigation Satellite Systems reflectometry(GNSS-R) technology, a new method for retrieving SWH has emerged, demonstrating promising results. This study utilizes Radio occultation sounder(GNOS) data from the FY-3E satellite and incorporates the latest Vision Transformer(ViT) technology to investigate GNSS-R-based SWH retrieval. We designed and evaluated various deep learning models, including ANN-Wave, CNN-Wave, Hybrid-Wave, Trans-Wave, and ViT-Wave. Through comparative training using ERA5 data, the ViT-Wave model was identified as the optimal retrieval model. The ViT-Wave model achieved an Root Mean Square Error(RMSE) accuracy of 0.4052 meters and Mean Absolute Error(MAE) accuracy of 0.2700 meters, significantly outperforming both traditional methods and newer deep learning approaches utilizing Cyclone Global Navigation Satellite Systems(CYGNSS) data. These results underscore the potential of integrating GNSS-R technology with advanced deep learning models to enhance SWH retrieval accuracy and reliability in oceanographic research.

The main goal of the paper is to compare the effects of the wave spectrum, computed using the Discrete Interaction Approximation (DIA) and the Webb–Resio–Tracy (WRT) methods, on statistical wave properties such as skewness and kurtosis. The statistical properties are obtained by integrating the three-dimensional free-surface Euler equations with a high-order spectral method combined with a phenomenological filter to account for the energy dissipation due to breaking waves. In addition, we investigate the minimum spatial domain size required to obtain meaningful statistical wave properties. The numerical simulations are performed over a physical domain of size 4.13 km × 4.13 km. The results indicate that statistical properties must be computed over an area of at least 4 km2. The results also suggest that selecting a more computationally expensive WRT method does not affect the statistical values to a great extent. The most noticeable effect is due to the energy dissipation filter that is applied. It is concluded that selecting the WRT or the DIA algorithm for computing the wave spectrum needed for the numerical simulations does not lead to major differences in the statistical wave properties. However, more accurate energy dissipation mechanisms due to wave breaking are needed.

A millimeter-wave microstrip leaky-wave antenna array based on the substrate-integrated waveguide (SIW) and the complementary split-ring resonator (CSRR) is proposed in this paper. The slow wave characteristics of the SIW are enhanced by etching two rows of symmetrical CSRR-type slots on the surface of the SIW layer. The magnetic coupling between the CSRR-SIW layer and equally spaced circular patches array on the upper layer realizes the radiation of electromagnetic energy. In the 23~30 GHz (relative bandwidth 26.4%) operating frequency band, the horizontal polarization radiation beam scanning from -62° to -2° is realized, with a peak gain of 9.6~11.7 dBi, and the cross-polarization ratio is more than 43.8 dB.

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

The article aims to present an alternative perspective on the relativistic expression of energy. This perspective is based on the virtual use of a Dempster mass spectrometer. In this spectrometer, it is possible to simulate Alfred Bucherer's experiment and conclude, using Lienard's relativistic equation, that the classical expression of energy predicted by Special Relativity is a more complete expression than the one presented by high school and college physics textbooks.

The theory of one-photon ionization and two-photon above-threshold ionization is formulated for applications to heavy atoms in attosecond science using the Dirac-Fock formalism. A direct comparison of the Wigner-Smith-Eisenbud delays for photoionization is made with delays from the Reconstruction of Attosecond Beating By Interference of Two-photon Transitions (RABBIT) method. Photoionization by an attosecond pulse train, consisting of monochromatic fields in the extreme ultraviolet range, is computed with many-body effects at the level of the Relativistic Random Phase Approximation (RRPA). Subsequent absorption and emission processes of infrared laser photons in RABBIT are evaluated using static ionic potentials as well as asymptotic properties of relativistic Coulomb functions. As expected, light elements, such as Argon, show negligible relativistic effects, while heavier elements, such a Krypton and Xenon, exhibit delays that depend on the fine-structure of the ionic target. The relativistic effects are notable close to ionization thresholds and Cooper minima with differences in fine-structure delays predicted to be as large as tens of attoseconds. The separability of relativistic RABBIT delays into a Wigner-Smith-Eisenbud delay and a universal continuum--continuum delay is studied with reasonable separability found for photoelectrons emitted along the laser polarization axis in agreement with prior non-relativistic results.

A well known technique to enhance the signal to noise ratio (SNR) of repetitive signals is to average them. The coherent parts of the signal add up constructively while the incoherent parts are averaged out. The prerequisite is that the signals are acquired under conditions of high repeatability, i.e.\ the signals must be sufficiently similar. In the present technical note we describe an efficient method for maintaining signal similarity by ensuring spatial and temporal proximity of laser waveform signals obtained by a sensor operated from an airborne platform. The method makes use of a few auxiliary parameters such as laser pulse repetition rate, mirror rotation rate, platform altitude, and flight speed. The method can be extended to be operated in real time.

The rational design of magnetic carbon composites, encompassing both composition and microstructure, holds significant potential for achieving exceptional electromagnetic wave absorbing materials (EAMs). In this study, FeCo@CM composites was efficiently fabricated through an advanced microwave plasma assisted reduction chemical vapor deposition (MPARCVD) technique, offering high efficiency, low cost, and energy-saving benefits. By depositing graphitized carbon microspheres, the dielectric properties were significantly enhanced, resulting in improved electromagnetic wave absorption performances through optimized impedance matching and a synergistic effect with magnetic loss. A systematic investigation revealed that the laminar-stacked structure of FeCo exhibited superior properties compared to its spherical counterpart, supplying a higher number of exposed edges and enhanced catalytic activity, which facilitated the deposition of uniform and low-defect graphitized carbon microspheres. Consequently, the dielectric loss performance of the FeCo@CM composites was dramatically improved due to increased electrical conductivity and the formation of abundant heterogeneous interfaces. At a 40 wt% filling amount and a frequency of 7.84 GHz, the FeCo@CM composites achieved a minimum reflection loss value of -58.2 dB with an effective absorption bandwidth (fE) of 5.13 GHz. This study presents an effective strategy for developing high-performance EAMs.

Background: Injury of the spinal cord causes motor and sensory dysfunction, and pathological reflexes, leading to paraplegia or tetraplegia. The sequelae of traumatic spinal cord injury (SCI) is a significant burden and impact on healthcare systems. Despite constant progress in medicine, traumatic SCI still remains irreversible. Till now, no satisfying treatment that can enable neuronal regeneration and recovery of function at the damaged level has been found. Hundreds of experiments have been conducted on various possibilities of influencing spinal regeneration, some of them have yielded promising results, but unfortunately, the successes obtained in experimental animals have not translated into humans. Methods: This narrative review article presents the application of Extracorporeal Shock Wave Therapy (eSWT) in Spinal Cord Injury. The article has been divided into parts: 1. Use of extracorporeal Shock Wave Therapy for regeneration of the spinal cord after traumatic Spinal Cord Injury. 2. Application of extracorporeal Shock Wave Therapy in spasticity after Spinal Cord Injury. In both cases, the hypotheses of possible mechanisms of action will be described. Results and conclusions: A small number of clinical trials have demonstrated the potential of eSWT to influence the regeneration of the spine, as an innovative, safe, and cost-effective treatment option for patients with SCI. Some reports have shown that eSWT can improve spasticity, walking ability, urological function, quality of life, and independence in daily life.

Current physiology attributes the mechanism of membrane potential generation to transmembrane ion transport, but ion adsorption could just as well play this fundamental role. The evidence shows that the ion adsorption mechanism accurately reproduces the experimentally measured membrane potential. The Goldman-Hodgkin-Katz equation (GHK eq.) and the Nernst equation (Nernst eq.) are the typical mathematical formulas representing the membrane potential in current physiology. However, the authors were able to show that the potential formulas by ion adsorption mechanism give identical results to GHK eq. and Nernst. eq. Our experimental and theoretical analyses suggest that there is a special relationship between the membrane potential and the membrane surface charge density, and this unique equation inevitably leads to the establishment of a GHK eq and/or a Nernst eq. The authors found that the unique equation is the foundation of thermodynamics “Boltzmann distribution”. Thus, the GHK eq. and the Nernst eq. are simply the natural consequence of thermodynamics from the view of the ion adsorption mechanism.

The study aimed to analyze thoracic and lumbar erector spinae muscle activations during 3D elongation exercises in individuals with adolescent idiopathic scoliosis (AIS). Participants included 24 adolescents, meeting specific criteria such as a Cobb angle between 10° and 20°, and not having undergone surgical or brace treatments. EMG data were collected to evaluate muscle activations. The study found no significant interaction between exercise type and the side of the curve, but a significant main effect of exercise type on muscle activation, irrespective of Cobb angle. Different exercise types significantly affected muscle activity, with the highest activations in the TheraBand exercise, followed by manual and without equipment conditions. This suggests that exercise type significantly impacts muscle engagement in AIS patients, providing valuable insights for targeted exercise program design. The study, however, focused on short-term muscle activation, not long-term Cobb angle progression, pointing to the need for further research in this area.

Wind energy is a kind of renewable energy with great potential for development. This study mainly investigated the application of shock waves generated by high-pressure gases (wind energy) for generating energy. In this study, we designed a new supersonic shock wave generator that can be reused without disassembling and assembling bolts and developed a supersonic shock wave monitoring system. This system monitored the velocity of the generated shock waves, which was Mach 3-5, and the output pressure was more than 100 times higher than the input pressure of the shock wave generator tank.Then, we developed a power generation system driven by supersonic shock waves based on the characteristics of the new shock wave generator, which can generate high-pressure and high-speed blast waves and can be reused. The shock wave generator can repeatedly generate high-pressure waves to drive the Tesla turbine and then the magnetic energy generator for power generation. We established a complete control process for power generation driven by shock waves by controlling the valve stem. The system can detect the tank pressure, output pressure, gas flow, rotation speed, voltage, and current during the control process for the performance analysis of power generation.