A way of systematizing different geometries by geometrical transformations is presented by using Klein’s perspective. Symmetry is considered the basic precedent, and different groups of transformations are introduced by using Erlangen program ideas. So, to focus on the importance of geometric transformations, two purposes are shown: first, the classification of geometries is based on the invariants of geometric transformations; and second, the construction of geometry unlike the theory of deduction can be done by means of geometric transformations.

Location-and-scale transformation of a random variable underpins normal distribution, but it is however fundamentally incorrect for scale estimation such as relative dispersion. In this paper, a parametrized alternative to a normal distribution, called scaloc-normal distribution, is proposed that efficiently works and is fundamentally correct with absolute and relative dispersion estimators. The Monte Carlos simulation experiment was used to generate a total of 600,000 artificial datasets in 600 different simulation scenarios from loc-normal (normal) and scaloc-normal distributions. The absolute and relative dispersion were estimated and compared from the two distributions. The results show that scaloc-normal distribution is a good parametrized alternative to loc-normal distribution, fundamentally correct and efficient with both standard deviation and coefficient of variation. The key statistical advancement from loc-normal to scaloc-normal distribution is its fundamental correctness (i.e., scale-invariant property) with an efficient relative estimator of dispersion (i.e., coefficient of variation). Parametrically, the loc-normal and scaloc-normal distributions are very different, but both have linear transformations.

The scope of this study was twofold: first, to introduce a new method in examining measurement invariance, especially with large-scale studies where a large number of group comparisons are involved: the alignment approach, where only configural invariance is necessary to achieve measurement invariance. Second, to evaluate the psychometric robustness of this approach using real-life data. Particularly, we applied this approach to examine whether the factor structure of a cognitive ability test (PGAT) exhibits measurement invariance across the 26 universities of the Kingdom of Saudi Arabia. The sample consisted of 9,849 graduate students from 26 universities around the Kingdom. The results indicated a robust configural model suggesting that the P-GAT subscales were invariant across the 26 universities. Finally, the aligned factor mean values were estimated, and factor mean comparisons of every group’s mean with all other group means were conducted for both cognitive domains (Verbal and Quantitative). In both domains, King Saud University had the highest mean score among all universities. Moreover, its mean factor score was significantly higher than any other university besides Dammam University. On the other hand, several universities allocated at the northern and Southern borders of the country exhibited the lowest factor mean scores.

We analyze the expected arrival time spectrum of supernova neutrinos using simulated luminosity and computing the expected number of events in future detectors such as the DUNE Far Detector and Hyper-Kamiokande. We develop a general method using minimum square statistics that can compute the sensitivity to any variable affecting neutrino time of flight. We apply this method in two different situations: First, we compare the time spectrum changes due to different neutrino mass values to put limits in electron (anti)neutrino effective mass. Second, we constrain Lorentz Invariance Violation through the mass scale, MQG, at which it would occur. We consider two main neutrino detection techniques: 1. DUNE-like liquid argon TPC, for which the main detection channel is νe+40Ar→e−+40K*, related to the supernova neutronization burst, and 2. HyperK-like water Cherenkov detector, for which ν¯e+p→e++n is the main detection channel. We consider a fixed supernova distance of 10 kpc and two different masses of the progenitor star: (i) 15 M⊙ with neutrino emission time up to 0.3 s and (ii) 11.2 M⊙ with neutrino emission time up to 10 s. The best mass limits at 3σ are of O(1) eV. For νe, the best limit comes from a DUNE-like detector if the mass ordering happens to be inverted. For ν¯e, the best limit comes from a HyperK-like detector. The best limit for the Lorentz Invariance Violation mass scale at 3σ level, considering superluminal or subluminal effect, is MQG≳1013 GeV (MQG≳5×105 GeV) for linear (quadratic) energy dependence.

The aim of this study was to evaluate the psychometric evidence of the original and brief version of the Santa Clara Strength of Religious Faith Questionnaire (SCSRFQ) in Spanish in a sample of 245 Peruvian adolescents and adults (mean age = 21.04 years, SD = 3.07, 47.8% male and 52.2% female), selected by non-probabilistic convenience sampling. Additionally, the Coronavirus Anxiety Scale and the Satisfaction with Life Scale were applied. Confirmatory Factor Analysis, internal consistency reliability methods, hierarchical sequence of variance models and Graded Response Model were used. Results indicate that both versions of the SCSRFQ showed robust psychometric properties: adequate unidimensional structure, adequate difficulty and discrimination parameters, and significant relationships with the measures of fear of COVID-19 and satisfaction with life. The original version of the SCSRFQ showed evidence of strict measurement invariance by gender and age; whereas the short version showed strict invariance by gender and configural invariance by age. Both versions showed acceptable reliability indices. In conclusion, the original and brief versions of the SCSRFQ show evidence of psychometric indicators that support their use to assess the strength of religious faith

In this review, we present the latest exclusion limits obtained with astroparticles for Lorentz Invariance Violation (LIV) in the photon sector. We discuss the techniques known as energy-dependent time delay or time lag, subluminal pair production threshold shift, superluminal photon decays and superluminal photon splitting. Perspectives for future results in LIV with the next generation of experiments are also addressed.

Previously, a conductivity invariance phenomena (CIP) has been discovered – at a certain lift-off, the inductance change of the sensor due to a test sample is immune to conductivity variations, i.e. the inductance – lift-off curve passes through a common point at a certain lift-off, termed as conductivity invariance lift-off. However, this conductivity invariance lift-off is fixed for a particular sensor setup, which is not convenient for various sample conditions. In this paper, we propose using two parameters in the coil design – the horizontal and vertical distances between the transmitter and the receiver to control the conductivity invariance lift-off. The relationship between these two parameters and the conductivity invariance lift-off is investigated by simulation and experiments and it has been found that there is an approximate linear relationship between these two parameters and the conductivity invariance lift-off. This is useful for applications where the measurements have restrictions on lift-off, e.g. uneven coating thickness which limits the range of the lift-off of probe during the measurements. Therefore, based on this relationship, it can be easier to adjust the configuration of the probe for a better inspection of the test samples.

The Fourier Continuous Derivative ($D_C$) offers a unique perspective on fractional differentiation grounded in the theory of Fourier series. This approach has the potential to address problems across various disciplines, including physics, engineering, and mathematics. The primary insight underpinning this approach is that a convex function defined on $\mathbb{Z}$ retains its convexity on $\mathbb{R}$. This paper delves into the Fourier Continuous Derivative, compares it with traditional fractional derivatives, and outlines its possible real-world applications, such as modeling viscoelastic materials, solving wave equations, and financial data analysis.

The Principle of Indifference (“PI”: the simplest non-informative prior in Bayesian probability) has been shown to lead to paradoxes since Bertrand (1889). Von Mises (1928) introduced the “Wine/Water Paradox” as a resonant example of a “Bertrand paradox”, and which has been presented as demonstrating that the PI must be rejected. We now resolve these paradoxes by a Maximum Entropy (MaxEnt) treatment of the PI that also includes information provided by Benford’s “Law of Anomalous Numbers” (1938). We show that the PI should be understood to represent a family of informationally-identical MaxEnt solutions; each solution being identified with its own explicitly justified boundary condition. In particular, our solution of the Wine/Water Paradox exploits Benford’s Law to construct a non-uniform distribution representing the universal constraint of scale invariance, which is a physical consequence of the Second Law of Thermodynamics.

The exact, non perturbative, response theory developed within the field of nonequilibrium molecular dynamics, also known as TTCF (Transient Time Correlation Function) applies to quite general dynamical systems. Its key element is called dissipation function, because it represents the power dissipated by external fields acting on the particle system of interest, whose coupling with the environment is given by deterministic thermostats. This theory has been initially developed for time independent external perturbations, and then it has been extended to time dependent perturbations. It has also been applied to dynamical systems of different nature, and to oscillator models undergoing phase transitions, which cannot be treated withe.g. linear response theory. The present work includes time dependent stochastic perturbations, in the theory, using the Karhunen-Loeve theorem. This leads to three different investigations of a given process. One in which a single realization of the stochastic coefficients is fixed, and averages are taken only over the initial conditions, as in a deterministic process. In the second, the initial condition is fixed, and averages are taken with respect to the distribution of stochastic coefficients. In the last investigations, one averages over both initial conditions and stochastic coefficients. We conclude illustrating the applicability of the resulting exact response theory with simple examples.

Cyberaggression is an important problem today; it can affect adolescents in different ways. Therefore, reliable and valid measures are necessary to better study the phenomenon. The aim of the present study was to generate validity and reliability evidence for a Spanish-language cyberaggression scale in a population of adolescents from northwestern Mexico. The results of this study contribute to the research and focus on cyberaggression in adolescents in Mexico. The measure in this article differs from other measures by detecting the different roles, including the bystander, contributing to the state of knowledge about cyberaggression, ratifying the presence of this actor that has not been sufficiently explored in the cyber context.

The comparison of group means in latent variable models plays a vital role in empirical research in the social sciences. The present article discusses extensions of invariance alignment and Haberman linking concerning the choice of linking functions for comparisons of many groups. Robust linking functions are proposed for invariance alignment and robust Haberman linking that are particularly suited to item response data under partial invariance. In a simulation study, it is shown that both linking approaches have comparable performance, and in some conditions, the newly proposed robust Haberman linking outperforms invariance alignment.

(1) Background: Parents of children with autism spectrum disorders often experience psychological distress, which can affect the quality of childcare they provide. It is crucial to screen for psychiatric symptoms among these parents. The Core Symptom Index (CSI) is a widely used tool for assessing general symptoms such as depression, anxiety, and somatic symptoms, with demonstrated validity and reliability across various populations. However, there is limited research on the validity and reliability of the CSI in the general Chinese population. This study aimed to investigate the psychometric properties of the Chinese version of the CSI among parents of children with autism spectrum disorders using Confirmatory Factor Analysis (CFA). (2) Methods: A total of 794 Chinese parents raising children with autism participated in this study. All completed the CSI, along with the social inhibition subscale of the Interpersonal Problems Inventory and the Couple Satisfaction Index. Factorial validity was assessed using CFA to determine how well the bifactor three-factor model fits the data. Various structural models were compared using model fit indices. Convergent and discriminant validity were examined by exploring correlations with the social inhibition subscale and the Couple Satisfaction Index. Invariance testing of the CSI was conducted across multiple groups based on gender, age, and education using CFA. The reliability of the CSI was evaluated using McDonald’s omega coefficients. (3) Results: The bifactor model emerged as the best-fitting model for the data, suggesting that the total score of the CSI adequately represents overall psychiatric symptoms. The CSI exhibited significant correlations with the social inhibition subscale (r = 0.41, p < 0.01) and smaller correlation coefficients with the Couple Satisfaction Index (r = -0.16, p < 0.05), indicating both convergent and discriminant validity. Invariant tests supported scalar invariance levels based on gender and age but only partial invariance for education. The Chinese version of the CSI demonstrated high consistency, with McDonald's omega coefficients ranging between 0.86 and 0.95. (4) Conclusions: The bifactor model of the Chinese version of the CSI is validated, making it a suitable tool for measuring depression, anxiety, and somatization symptoms among parents of children with autism spectrum disorders. Further research on other Chinese populations is encouraged.

Positive invariant set is an important concept of dynamic systems. The purpose of this paper is to study the sufficient and necessary conditions that the set of ellipsoids and the Lorenz cone are positive invariant sets of discrete time systems. By means of nonlinear programming and induced norm, the problem of positive invariance is formulated as an optimization problem, and the equivalent dual form optimization is also presented using the dual optimization method. Our results provide more alternative methods for determining the positive invariance of quadratic form convex sets from the point of view of optimization and dual optimization. The effectiveness of this method is demonstrated by numerical examples.

It is universally accepted that Maxwell equations do not remain invariant under the Galilean transformation. This conflicts the principle of relativity which states that the physical law must remain invariant in the mathematical form in all inertial frames of reference. For this reason, the Lorentz transformation is invented, and the Galilean transformation is nowadays superseded by the Lorentz transformation. However, this paper challenges this widely held belief that the Maxwell equations are not invariant under the Galilean transformation. By applying the Galilean transformation to Lienard-Wiechert electromagnetic fields it is mathematically proven that the Maxwell equations indeed remain invariant under the Galilean transformation. In addition, the critical error in Lorentz's proof of Galilean non-invariance of Maxwell equations is pointed out, and it turns out that Lorentz's conclusion that Maxwell equations are not invariant under the Galilean transformation is the result of a mathematical error.

Earth's global surface temperature shows variability on an extended range of temporal scales and satisfies an emergent scaling symmetry. Recent studies indicate that scale invariance is not only a feature of the observed temperature fluctuations, but an inherent property of the temperature response to radiative forcing, and a principle that links the fast and slow climate responses. It provides a bridge between the decadal- and centennial-scale fluctuations in the instrumental temperature record, and the millennial-scale equilibration following perturbations in the radiative balance. In particular, the emergent scale invariance makes it possible to infer equilibrium climate sensitivity (ECS) from the observed relation between radiative forcing and global temperature in the instrumental era. This is verified in ensembles of Earth system models (ESMs), where the inferred values of ECS correlate strongly to estimates from idealized model runs. For the range of forcing data explored in this paper, the method gives best estimates of ECS between 2.3 and 3.4 K.

The role played by non extensive thermodynamics in physical systems has been under intense debate for the last decades. With many applications in several areas, the Tsallis statistics has been discussed in details in many works and triggered an interesting discussion on the most deep meaning of entropy and its role in complex systems. Some possible mechanisms that could give rise to non extensive statistics have been formulated along the last several years, in particular a fractal structure in thermodynamics functions was recently proposed as a possible origin for non extensive statistics in physical systems. In the present work we investigate the properties of such fractal thermodynamical system and propose a diagrammatic method for calculations of relevant quantities related to such system. It is shown that a system with the fractal structure described here presents temperature fluctuation following an Euler Gamma Function, in accordance with previous works that evidenced the connections between those fluctuations and Tsallis statistics. Finally, the fractal scale invariance is discussed in terms of the Callan-Symanzik Equation.

We show that the Einstein field equations for a five-dimensional warped spacetime, where only gravity can propagate into the bulk, determine the dynamical evolution of the warp factor of the four-dimensional brane spacetime. This can be explained as a holographic manifestation. The warped 5D model can be reformulated by considering the warp factor as a dilaton field ($\omega$) conformally coupled to gravity and embedded in a smooth $M_4 \otimes R$ manifold. On the brane, where the U(1) scalar-gauge fields live, the dilaton field manifests itself classically as a warp factor and enters the evolution equations for the metric components and matter fields. We write the Lagrangian for the Einstein-scalar-gauge fields in a conformal invariant setting. However, as expected, the conformal invariance is broken (trace-anomaly) by the appearance of a mass term and a quadratic term in the energy-momentum tensor of the scalar-gauge field, arising from the extrinsic curvature terms of the projected Einstein tensor. These terms can be interpreted as a constraint in order to maintain conformal invariance. By considering the dilaton field and Higgs field on equal footing on small scales, there will be no singular behavior, when $\omega\rightarrow 0$ and one can deduce constraints to maintain regularity of the action. Our conjecture is that $\omega$, alias warp factor, has a dual meaning. At very early times, when $\omega \rightarrow 0$, it describes the small-distance limit, while at later times it is a warp (or scale) factor that determines the dynamical evolution of the universe. We also present a numerical solution of the model and calculate the (time-dependent) trace-anomaly. The solution depends on the mass ratio of the scalar and gauge fields, the parameters of the model and the vortex charge $n$.

Theories of quantum gravity suggest that Lorentz invariance, the fundamental symmetry of the Theory of Relativity, may be broken at the Planck energy scale. While any deviation from conventional Physics must be minuscule in particular at attainable energies, this hypothesis motivates ever more sensitive tests of Lorentz symmetry. In the photon sector, astrophysical observations, in particular polarization measurements, are a very powerful tool because tiny deviations from Lorentz invariance will accumulate as photons propagate over cosmological distances. The Standard-Model Extension (SME) provides a theoretical framework in the form of an effective field theory that describes low-energy effects due to a more fundamental quantum gravity theory by adding additional terms to the Standard Model Lagrangian. These terms can be ordered by the mass dimension d of the corresponding operator and lead to a wavelength, polarization, and direction dependent phase velocity of light. In this paper, we analyze optical polarization measurements from 63 Active Galactic Nuclei (AGN) and Gamma-ray Bursts (GRBs) in order to search for Lorentz violating signals. We derive the first set limits on each of the 10 individual birefringent coefficients of the minimal SME with d = 4, with 95% confidence limits on the order of 10⁻³⁴ on the dimensionless coefficients.

Most quantum gravity theories endow space-time with a discreet nature by space quantization on the order of Planck length (lp ). This discreetness could be demonstrated by confirmation of Lorentz invariance violations (LIV) manifested at length scales proportional to lp. In this paper, space-time line elements compatible with the uncertainty principle are calculated for a homogeneous, isotropic expanding Universe represented by the Friedmann-Lemaitre-Robertson-Walker solution to General Relativity (FLRW or FRW metric). To achieve this, the covariant geometric uncertainty principle (GeUP) is applied as a constraint over geodesics in FRW geometries. A generic expression for the quadratic proper space-time line element is derived, proportional to Planck length-squared and dependent on two contributions. The first is associated to the energy-time uncertainty, and the second depends on the Hubble function. The results are in agreement with space-time quantization on the expected length orders, according to quantum gravity theories and experimental constraints on LIV.

Eddy current testing can be used to interrogate steels but it is hampered by the lift-off distance of the sensor. Previously, the lift-off point of intersection (LOI) feature has been found for the pulsed eddy current (PEC) testing. In this paper, a lift-off invariant inductance (LII) feature is proposed for the multi-frequency eddy current (MEC) testing, which merely targets the ferromagnetic steels. That is, at a certain working frequency, the measured inductance signal is found nearly immune to the lift-off distance of the sensor. Such working frequency and inductance are termed as the lift-off invariant frequency (LIF) and LII. Through simulations and experimental measurements of different steels under the multi-frequency manner, the LII has been verified to be merely related to the sensor parameters and independent of different steels. By referring to the LIF of the test piece and using an iterative inverse solver, one of the steel properties (either the electrical conductivity or magnetic permeability) can be reconstructed with a high accuracy.

The comparison of group means in item response models constitutes an important issue in empirical research. The present article discusses an extension of Haebara linking by proposing a flexible class of robust linking functions for comparisons of many groups. These robust linking functions are particularly suited to item response data that are generated under partial invariance. In a simulation study, it is shown that the newly proposed robust Haebara linking approach outperforms existing approaches of Haebara linking. In an empirical application using PISA data, it is illustrated that country means can be sensitive to the choice of linking functions.

As gravitation and electromagnetism are closely analogous long-range interactions, and gravitation is formulated in terms of geometry in general relativity (GR), we expect the latter also to appear through the geometry. This unification has however remained an unfulfilled goal. The goal is achieved here in a new theory, which results from the principles of equivalence and Mach supplemented with a novel insight that the field tensors in a geometric theory of gravitation and electromagnetism must be traceless, since these long-range interactions are mediated by virtual exchange of massless particles whose mass is expected to be related to the trace of the field tensors. Hence the Riemann tensor, like the analogous electromagnetic field tensor, must be traceless. Thence emerges a scale- invariant, Machian theory of gravitation and electrodynamics unified, wherein the vanishing of the Ricci tensor appears as a boundary condition. While the field equations of the theory are given by the vanishing divergence of the respective field tensors and their duals, the matter and charge emerge from the spacetime. A quantitative formulation of the emergent fields embodied in ‘energymomentum super tensors’ follows from the respective Bianchi identities for the two fields. The resulting theory is valid at all scales and explains the observations without invoking the non-baryonic dark matter, dark energy or inflation. Moreover, it answers the questions that the GR-based standard paradigm could not address.

It is argued that all physical knowledge ultimately stems from observation and that the simplest possible observation is that an event has happened at a certain space-time location . Considering historic experiments, which had been groundbreaking in the evolution of our modern ideas of matter on the atomic, nuclear and elementary particle scales, it is shown that such experiments produce as outputs macroscopically observable events which represent binary decisions with regard to simple alternatives and which accumulate in the course of time into spatio-temporal patterns whose forms allow decisions to be taken concerning conceivable alternatives of explanation. Working towards elucidating the physical and information-theoretic characteristics of those elementary pieces of information we arrive at the conclusion that - unlike the events of relativity which are mere 4-tuples of spacetime coordinates - the events of observation are pieces of information endowed with the properties of physical action, spacetime extension, and Lorentz invariance. Another important aspect is that such events are produced at the expense of irreversibly dissipating energy which can be stated in Landauer diction in the form that more energy needs to be spent in the erasure of events than had previously been invested in their initiation.

Particles and photons appear to be total opposites; the former has rest mass which requires space to exist; the latter has kinetic energy which requires time to occur (oscillate). But they do share certain properties (e.g., quantization) that remain invariant when one is transformed (swapped) for the other. This gauge invariance is developed in some detail.The symmetry between particle and photon turns out to be one of inversion. It is the equalities of special relativity that support this inversion and the accompanying invariances: mass transformed to energy; space transformed to time. The great advantage of these symmetries (inversions) is that they provide guidance for an object little understood (the photon) based upon an object well understood (the particle). On this basis, progress can be made in the understanding of some long-standing issues: wave-particle duality, time’s arrow, the constant speed of light and nonlocality.

This article introduces the Theory of Inverse Discrete Dynamical Systems (TIDDS), a novel methodology for modeling and analyzing discrete dynamical systems via inverse algebraic models. Key concepts such as inverse modeling, structural analysis of inverse algebraic trees, and the establishment of topological equivalences for property transfer between a system and its inverse are elucidated. Central theorems on homeomorphic invariance and topological transport validate the transfer of cardinal attributes between dynamic representations, offering a fresh perspective on complex system analysis. A significant application presented is an alternative proof of the Collatz Conjecture, achieved by constructing an associated inverse model and leveraging analytical property transfers within the inverted tree structure. This work not only demonstrates the theory's capability to address and solve open problems in discrete dynamics but also suggests vast implications for expanding our understanding of such systems.

This article introduces the Theory of Inverse Discrete Dynamical Systems (TIDDS), a novel methodology for modeling and analyzing discrete dynamical systems via inverse algebraic models. Key concepts such as inverse modeling, structural analysis of inverse algebraic trees, and the establishment of topological equivalences for property transfer between a system and its inverse are elucidated. Central theorems on homeomorphic invariance and topological transport validate the transfer of cardinal attributes between dynamic representations, offering a fresh perspective on complex system analysis. A significant application presented is an alternative proof of the Collatz Conjecture, achieved by constructing an associated inverse model and leveraging analytical property transfers within the inverted tree structure. This work not only demonstrates the theory's capability to address and solve open problems in discrete dynamics but also suggests vast implications for expanding our understanding of such systems

We review the main features of the non-local gauge, named the contour gauge. The contour gauge belongs to the axial type of gauges and extends the local gauge used in the most of approaches. The geometry of gluon fields and the path-dependent formalism are the essential tools for the description of non-local gauges. The principle feature of the contour gauge is that there are no the residual gauges which are left in the finite domain of space. In the review, we present the useful correspondence between the contour gauge conception and the Hamiltonian (Lagrangian) formalism. The Hamiltonian formalism is turned out to be a very convenient framework for the understanding of contour gauges. The comprehensive comparison analysis of the local and non-local gauges advocates the advantage of the contour gauge use. As an example of practical worth, we consider the Drell-Yan process and discuss the gauge invariance of the corresponding hadron tensor. We show that the appropriate use the contour gauge leads to the existence of extra diagram contributions. These additional contributions, first, restore the gauge invariance of the hadron tensor and, second, give the important terms for the observable quantities. We also demonstrate the significant role of the additional diagrams to form the relevant contour in the Wilson path-ordered exponential. Ultimately, it leads to the spurious singularity fixing. Moreover, in the present review, we discuss in detail the problem of spin and orbital angular momentum separation. We show that in SU(3) gauge theories the gluon decomposition on the physical and pure gauge components has a strong mathematical evidence provided the contour gauge conception has been used. In addition, we prove that the contour gauge possesses the special kind of residual gauge that manifests at the boundary of space. Besides, the boundary field configurations can be associated with the pure gauge fields.

Quantum gravity theories rely on a minimal measurable length for their formulations, which clashes with the classical formulation of the uncertainty principle and with Lorentz invariance from general relativity. These incompatibilities led to the development of the generalized uncertainty principle (GUP) from string theories and its various modifications. GUP and covariant formulations of the uncertainty principle are discussed, together with implications for space-time quantization.

The redefined vacuum approach, which is frequently employed in the many-body perturbation theory, proved to be a powerful tool for formula derivation. Here, we elaborate this approach within the bound-state QED perturbation theory. In addition to general formulation, we consider the particular example of a single particle (electron or vacancy) excitation with respect to the redefined vacuum. Starting with simple one-electron QED diagrams, we deduce first- and second-order many-electron contributions: screened self-energy, screened vacuum polarization, one-photon exchange, and two-photon exchange. The redefined vacuum approach provides a straightforward and streamlined derivation and facilitates its application to any electronic configuration. Moreover, based on the gauge invariance of the one-electron diagrams, we can identify various gauge-invariant subsets within derived many-electron QED contributions.

I examine the groups which underly classical mechanics, non-relativistic quantum mechanics, special relativity, relativistic quantum mechanics, quantum electrodynamics, quantum flavourdynamics, quantum chromodynamics, and general relativity. This examination includes the rotations SO(2) and SO(3), the Pauli algebra, the Lorentz transformations, the Dirac algebra, and the U(1), SU(2), and SU(3) gauge transformations. I argue that general relativity must be generalized to Einstein-Cartan theory, so that Dirac spinors can be described within the framework of gravitation theory.

A Berry geometrical phase is identified in a strongly metastable system containing dynamically responsive clathrate hydrate structures within a crystal-fluid material. High energy degeneracy in the associated chemistry produces local stability and false vacuum conditions that lead to non-extensive and non-additive contributions in the fundamental thermodynamic relation. Application of Ginzburg-Landau theory and the scaling laws reveals a coherence length and a penetration depth for a macro-scale dual superconductor. The coherence length determines non-extensive volume changes whilst its inverse gives the Higgs mass. The penetration depth determines the extent of QCD vacuum suppression whilst its inverse gives the vector boson mass together with indirect manifestation as non-additive hyperbolic curvature. Simultaneous emergence of the Ginzburg-Landau superconducting phase transition is consistent with gauge-invariant coupling of the scalar field to the Yang-Mills action in QCD. The discovery of an energy gap in the gradient energy term of the system Lagrangian is associated with a critical correlation length revealed in the transition from a gapped to a gapless superconducting state. Together with the emergence and absorption of the Higgs-like scalar field, a mechanism for describing a renormalized QCD mass gap arises.

The star matter composed of nucleons deep inside the compact star like a neutron star is believed to be very dense and various new types of concepts and physical phenomena due to the nontrivial strong correlations are naturally expected. Peudo-conformality in dense star matter has been discussed recently assuming the hidden underlying scale symmetry, which is partly supported by the recent discussions of infrared conformal window of QCD. It is found that the appearance of dilaton and the dilatonic mean field calculation of nucleonic matter lead to the density independent nucleon mass at higher density regime than normal nuclear matter density. Non-vanishing constant nucleon mass can be considered as a chiral invariant mass of the parity doublet model, in which the chiral symmetry is manifested even in the massive nucleon sector provided with a parity doubling. In this paper we will discuss how the chiral and scale symmetry are correlated to lead the parity doublet symmetry inside the core of the compact star. A simple schematic model is adopted. The star matter at T=0 is basically composed of the nucleons. As a first approximation, they can be treated as free fermions with the effective mass filled up to fermi surface. There is a nontrivial feature due to the interplay between vector meson and nucleon(or equivalently dilaton, χ). The trace of energy momentum tensor approaches density independent, the pseudo-conformal phase. Local fluctuations inside the star matter will be travelling with the speed of sound which depends on the equation of state. In the pseudo-conformal phase, the speed of sound approaches to the conformal velocity for the scale symmetric matter, vc=13c. The excitations of the parity doublets in the compact star matter as an emerging phenomena in pseudo-conformal phase will be discussed in connection to the chiral symmetry. The possible implication on the corespondence of hadrons to quark degrees of freedom will be briefly discussed.

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.

In a recent paper, Nicolas Gisin suggests that by conducting physics with intuitionistic rather than classical mathematics, rich temporality - that is, passage and tense, and specifically, the future’s openness - can be incorporated into physics. Physics based on classical mathematics is tenseless and deterministic, and that, so he holds, renders it incongruent with experience. According to Gisin, physics ought to represent the indeterminate nature of reality, and he proposes that intuitionistic mathematics is the key to succeeding in doing so. While I share his insistence on the reality of passage and tense, and on the future being real and open, I argue that the amendment he offers does not work. I show that, its attunement to time notwithstanding, intuitionistic mathematics is as tenseless as classical mathematics, and that physics is bound to remain tenseless regardless of the math it employs. There is much to learn about tensed time, but the task belongs to phenomenology and not to physics.

The prevalence of internet gaming disorders (IGD) is considerably high among youth, especially with social isolation imposed by the ongoing COVID-19 pandemic. IGD adversely affects mental health, quality of life, and academic performance. The Internet Gaming Disorder Scale (IGDS9-SF) is designed to detect IGD according to DSM-IV diagnostic criteria. However, inconsistent results are reported on its capacity to diagnose IGD evenly across different cultures. To ensure the suitability of the IGDS9-SF as a global measure of IGD, this study examined the psychometric properties of the IGDS9-SF in a sample of Sri Lankan university students (N = 322, mean age =17.2 ± 0.6, range = 16-18 years, 56.5% males) and evaluated its measurement invariance across samples from Sri Lanka, Turkey, Australia, and the USA. Among Sri Lankan students, a unidimensional structure expressed good fit, invariance across different groups (e.g., gender, ethnicity, and income), adequate criterion validity (strong correlation with motives of internet gaming, daily gaming duration, and sleep quality), and good reliability (alpha = 0.81). Males and online multiplayers expressed higher IGD levels, greater time spent gaming, and more endorsement of gaming motives (e.g., Social and Coping) than females and offline players. Across countries, the IGDS9-SF was invariant at the configural, metric, and scalar levels, albeit strict invariance was not maintained. The lowest and highest IGD levels were reported among Turkish and American respondents, respectively. In conclusion, the IGDS9-SF can be reliably used to measure IGD among Sri Lankan youth. Because the scale holds scalar invariance across countries, its scores can be used to compare IGD levels in the studied countries.

Mereology stands for the philosophical concept of parthood and is based on a sound set of fundamental axioms and relations. One of these axioms relates to the existence of a universe as a thing having part all other things. The present article formulates this logical expression first as an algebraic inequality and eventually as an algebraic equation reading in words: The universe equals the sum of all things. “All things” here are quantified by a “number of things”. Eventually this algebraic equation is normalized leading to an expression The whole equals the sum of all fractions. This introduces “1” or “100%” as a quantitative – numerical - value describing the “whole”. The resulting “basic equation” can then be subjected to a number of algebraic operations. Especially squaring this equation leads to correlation terms between the things implying that the whole is more than just the sum of its parts. Multiplying the basic equation (or its square) by a scalar allows for the derivation of physics equations like the entropy equation, the ideal gas equation, an equation for the Lorentz-Factor, conservation laws for mass and energy, the energy-mass equivalence, the Boltzmann statistics, and the energy levels in a Hydrogen atom. It further allows deriving a “contrast equation” which may form the basis for the definition of a length and a time scale. Multiplying the basic equation with vectors, pseudovectors, pseudoscalars and eventually hypercomplex numbers opens up the realm of possibilities to generate many further equations.

We point out an inconsistency in Newton's equations of celestial mechanics. A set of differential equations implied by Newton's equations are shown to be free of this inconsistency. We then investigate the integrals of motion associated with this relative difference system.

In this paper, a short survey of the existed results concerning the Jacobian Conjecture is first given. Then the 3-fold linear type polynomial map will be analyzed in detail. The expansion of the Jacobian condition is deduced to obtain its equivalent algebraic equations, and the Jacobian condition will be analyzed to derive two coordinate transformations that can maintain the invariance of the Jacobian condition. Finally, it is proved by mathematical induction method that one general chain expression presented in this paper is just the inverse polynomial map of 3-fold linear type polynomial map, i.e. LJC(n,[3]) holds such that the Jacobian Conjecture holds.

Dementia patients express a set of problematic and deteriorating symptoms, along self-care dependency. Overtime, the mental health of family caregivers of persons with dementia may suffer, putting them at a high risk for psychopathology, which may be associated with endangered wellbeing of demented people. This cross-sectional study examined the psychometric properties of the Depression Anxiety Stress Scale 8-items (DASS-8), DASS-12, DASS-21 in a convenient sample of 571 caregivers from northern Italy and southern Switzerland (Mean age = 53, SD = 12, range = 24–89 years). A bifactor structure of the three measures had the best fit; some items of the DASS-12/DASS-21 failed to load on their domain-specific factors. The three-factor structure was invariant across various groups (e.g., gender, education, etc.), expressed adequate reliability and convergent validity, and had strong positive correlation with the 3-item UCLA Loneliness Scale (UCLALS3). Dementia type had no effect on distress scores, which were higher among females, adult children caregivers, those caring for dependent patients, and those who received help with care. For 54.9 and 38.8% of the latter, care was provided by relatives and health professionals, respectively. Since the DASS-8 expresses adequate psychometrics comparable with the DASS-21, it may be used as a brief measure of distress in this population.

Despite extensive investigations of the Depression Anxiety Stress Scales-21 (DASS-21) since its development in 1995, its factor structure and other psychometric properties still need to be firmly established, with several calls for revising its item structure. Employing confirmatory factor analysis (CFA), this study examined the factor structure of the DASS-21 and five shortened versions of the DASS-21 among psychiatric patients (N = 168) and the general public (N = 992) during the COVID-19 confinement period in Saudi Arabia. Multigroup CFA, Mann Whitney W test, Spearman’s correlation, and coefficient alpha were used to examine the shortened versions of the DASS-21 (DASS-13, DASS-12, DASS-9 (two versions), and DASS-8) for invariance across age and gender groups, discriminant validity, predictive validity, item coverage, and internal consistency, respectively. Compared with the DASS-21, all three-factor structures of the shortened versions expressed good fit, with the DASS-8 demonstrating the best fit and highest item loadings on the corresponding factors in both samples (χ2(16, 15) = 16.5, 67.0; p = 0.420, 0.000; CFI= 1.000, 0.998; TLI = 0.999, 0.997; RMSEA = 0.013, 0.059, SRMR = 0.0186, 0.0203). It expressed configural, metric, and scalar invariance across age and gender groups. Its internal consistency was comparable to other versions (α = 0.94). Strong positive correlations of the DASS-8 and its subscales with the DASS-21 and its subscales (r = 0.97 to 0.81) suggest adequate item coverage and good predictive validity of this version. The DASS-8 and its subscales distinguished the clinical sample from the general public at the same level of significance expressed by the DASS-21 and other shortened versions, supporting its discriminant validity. Neither the DASS-21 nor the shortened versions distinguished patients diagnosed with depression and anxiety from other conditions. The DASS-8 represents a valid short version of the DASS-21, which may be useful in research and clinical practice for quick identification of individuals with potential psychopathologies. Diagnosing depression/anxiety disorders may be further confirmed in a next step by clinician-facilitated examinations. Brevity of the DASS-21 would save time and effort used for filling the questionnaire and support comprehensive assessments by allowing the inclusion of more measures on test batteries.

We delve into nonrelativistic quantum electrodynamics within a background magnetic field, ensuring gauge invariance via a vector potential. Our exploration extends to the Lagrangian, which incorporates electron self-interactions and electromagnetic field interactions. Through the path integral formalism, we elucidate the effective action, with a specific focus on the photon propagator and screening effects. Examining density and current components reveals Laurent expansions in the hydrodynamic limit. The equations of motion in real space are derived, leading to discussions on phenomena such as Poiseuille-like flow and the Navier-Stokes equation. To ground our theoretical framework at practical contexts, we consider applications such as the fluid dynamics at binary star systems. Depending on the velocity of the expelled fluid, our analysis allows for both nonrelativistic and relativistic treatments, providing a versatile tool for understanding the intricacies of fluid behavior at astrophysical scenarios. Additionally, we recognize that at the presence of a magnetic field, magnetohydrodynamics becomes crucial. While our current focus is at nonrelativistic quantum electrodynamics, the insights gained here contribute to a broader understanding, offering a comprehensive foundation for quantum electrodynamics analysis at diverse physical systems.

We introduce the linear subgroup of volume-preserving diffeomorphism as the underlying symmetry to construct an action within the effective field theory framework and the Schwinger-Keldish formalism. The formulated action is posited to effectively incorporate dissipative effects into the Navier-Stokes equations.