ARTICLE | doi:10.20944/preprints202209.0252.v1
Subject: Computer Science And Mathematics, Probability And Statistics Keywords: alternative parameterization; normal distribution; dispersion estimators; location-invariance; scale-invariance; scale-and-location-invariance
Online: 19 September 2022 (02:06:09 CEST)
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.
ARTICLE | doi:10.20944/preprints202307.0750.v1
Subject: Social Sciences, Psychology Keywords: measurement invariance; MGCFA; alignment method; configural invariance; latent means; P-GAT
Online: 12 July 2023 (07:31:52 CEST)
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.
ARTICLE | doi:10.20944/preprints202304.1107.v1
Subject: Physical Sciences, Nuclear And High Energy Physics Keywords: neutrino; supernova; Lorentz Invariance violation; mass
Online: 28 April 2023 (04:31:14 CEST)
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.
ARTICLE | doi:10.20944/preprints202103.0489.v1
Online: 18 March 2021 (16:50:18 CET)
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
Subject: Physical Sciences, Astronomy And Astrophysics Keywords: Gamma rays; UHECR; Lorentz invariance violation
Online: 15 May 2020 (15:25:49 CEST)
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.
ARTICLE | doi:10.20944/preprints202005.0491.v1
Subject: Physical Sciences, Fluids And Plasmas Physics Keywords: Conductivity Invariance Phenomenon; Conductivity invariance lift-off; Sensor design; Eddy current testing; Electrical conductivity; Non-destructive testing
Online: 31 May 2020 (18:37:15 CEST)
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.
ARTICLE | doi:10.20944/preprints202306.1551.v1
Subject: Physical Sciences, Thermodynamics Keywords: Scale invariance; Quantitative Geometrical Thermodynamics; Lagrange multipliers
Online: 21 June 2023 (12:38:58 CEST)
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.
COMMUNICATION | doi:10.20944/preprints202106.0636.v1
Subject: Computer Science And Mathematics, Algebra And Number Theory Keywords: geometry; geometrical transformations; symmetry; invariance, perspectivity, Möbius transformations.
Online: 28 June 2021 (10:23:43 CEST)
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.
ARTICLE | doi:10.20944/preprints202006.0034.v1
Subject: Computer Science And Mathematics, Mathematics Keywords: factor model; 2PL model; linking; invariance alignment; Haberman linking; partial invariance; item response model; structural equation model; differential item functioning
Online: 4 June 2020 (13:25:49 CEST)
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.
ARTICLE | doi:10.20944/preprints202304.0816.v1
Subject: Computer Science And Mathematics, Applied Mathematics Keywords: discrete-time dynamic systems; positive invariance; ellipsoid; Lorenz cone; optimization
Online: 24 April 2023 (04:10:49 CEST)
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.
ARTICLE | doi:10.20944/preprints201810.0542.v1
Subject: Environmental And Earth Sciences, Geophysics And Geology Keywords: Climate sensitivity; scale invariance; long-range persistence; climate variability; emergent constrains
Online: 23 October 2018 (15:59:17 CEST)
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.
ARTICLE | doi:10.20944/preprints201806.0459.v1
Subject: Physical Sciences, Thermodynamics Keywords: fractal structure; non extensive statistics; Tsallis statistics; self-similarity; scale invariance
Online: 28 June 2018 (05:30:41 CEST)
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.
ARTICLE | doi:10.20944/preprints201810.0624.v1
Subject: Physical Sciences, Particle And Field Physics Keywords: conformal invariance; brane world models; U(1) scalar-gauge field; dilaton field
Online: 26 October 2018 (10:33:55 CEST)
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 $n$.
ARTICLE | doi:10.20944/preprints201809.0147.v1
Subject: Physical Sciences, Astronomy And Astrophysics Keywords: Lorentz invariance; Standard-Model extension; polarization; Active Galactic Nuclei; Gamma-ray Bursts
Online: 9 September 2018 (09:04:03 CEST)
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.
ARTICLE | doi:10.20944/preprints202110.0452.v2
Subject: Physical Sciences, Astronomy And Astrophysics Keywords: Lorentz invariance violation; FRW metric; general relativity; quantum mechanics; uncertainty principle; quantum gravity
Online: 7 December 2021 (11:37:55 CET)
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.
ARTICLE | doi:10.20944/preprints202104.0387.v2
Subject: Engineering, Automotive Engineering Keywords: Eddy current testing; lift-off invariance; property measurement; multi-frequency; non-destructive testing.
Online: 22 April 2021 (09:16:48 CEST)
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.
ARTICLE | doi:10.20944/preprints202006.0035.v1
Subject: Computer Science And Mathematics, Mathematics Keywords: linking; item response model; 2PL model; Haebara linking; differential item functioning; partial invariance
Online: 4 June 2020 (13:28:42 CEST)
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.
ARTICLE | doi:10.20944/preprints201806.0424.v4
Subject: Physical Sciences, Astronomy And Astrophysics Keywords: Gravitation - Fundamental Problems and General Formalism; Electrodynamics; Scale Invariance; Mach Principle; Dark Energy
Online: 3 October 2018 (15:35:51 CEST)
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.
ARTICLE | doi:10.20944/preprints202302.0426.v1
Subject: Physical Sciences, Optics And Photonics Keywords: gauge invariance; symmetry; time’s arrow; nonlocality; wave-particle duality; double slit; delayed-choice experiment
Online: 24 February 2023 (09:52:05 CET)
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.
REVIEW | doi:10.20944/preprints202208.0347.v1
Subject: Physical Sciences, Quantum Science And Technology Keywords: General relativity; uncertainty principle; geodesics; black hole singularity; quantum gravity; Planck star; Lorentz invariance violations.
Online: 18 August 2022 (11:06:06 CEST)
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.
ARTICLE | doi:10.20944/preprints202105.0284.v1
Subject: Physical Sciences, Acoustics Keywords: Bound-state QED; Lamb shift; relativistic atomic theory; vacuum redefinition; ground state redefinition; gauge invariance
Online: 13 May 2021 (11:29:01 CEST)
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.
ARTICLE | doi:10.20944/preprints201806.0446.v1
Subject: Physical Sciences, Nuclear And High Energy Physics Keywords: Einstein-Cartan theory, quantum gravity, energy-momentum tensor, Lorentz transformations, gauge invariance, quantum field theories
Online: 27 June 2018 (14:26:02 CEST)
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.
ARTICLE | doi:10.20944/preprints202307.1051.v4
Subject: Physical Sciences, Particle And Field Physics Keywords: Berry geometrical phase; symmetry groups; self-organized criticality; dual superconductivity; scale- and gauge-invariance; hyperbolic curvature; false vacuum; QCD mass gap
Online: 25 August 2023 (08:49:43 CEST)
Berry curvature is deemed responsible for generating mechanical work 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. The reciprocating action of a piston expander also confirms a net energy gain despite the crystal-fluid material maintaining almost constant density. Hyperbolic curvature produces non-extensive volume changes attributed to gluon emission and absorption in a U(2) electroweak symmetry group synchronized across the condensed matter system, the embedding vacuum manifold and associated quantum interactions. The property of asymptotic freedom is apparent across these three domains providing evidence for scale-invariance that dominates both the macro- and micro-scales of an associated Ginzburg-Landau superconducting phase transition. External pressure perturbations of the low-energy system initiate ‘rolling’ critical responses that conserve energy and momentum across the synchronized U(2) group and also reveal an emergent gauge field. Corresponding emergence of the Ginzburg-Landau superconducting phase transition is consistent with gauge-invariant coupling of this scalar field to the Yang-Mills action of QCD. The discovery of an energy gap in the gradient energy term of the system Lagrangian is associated with a critical correlation length and consistent with a complex energy band gap in the Berry phase. Coupled with the emergence and absorption of the Higgs-like scalar field, a mechanism for describing the QCD mass gap arises.
ARTICLE | doi:10.20944/preprints202005.0083.v1
Subject: Physical Sciences, Condensed Matter Physics Keywords: nonrelativistic QED; many-body theories; Lagrangian; gauge invariance; Coulomb gauge; Hamiltonian; external fields; quantization; 1/c2 approximation; current-current interaction
Online: 5 May 2020 (15:14:06 CEST)
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.
ARTICLE | doi:10.20944/preprints202202.0055.v2
Subject: Social Sciences, Psychology Keywords: Coronavirus disease 2019/COVID-19; Internet Gaming Disorder Scale9—Short form (IGDS9-SF); university students; factorial structure/psychometric properties/structural validity/validation; cultur*/collectivisti*/individualis*; invariance; gender; game type
Online: 21 March 2022 (11:04:57 CET)
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.
ARTICLE | doi:10.20944/preprints201907.0314.v1
Subject: Physical Sciences, Mathematical Physics Keywords: entropy; Boltzmann statistics; Lorentz-factor; mereology; analytical philosophy; conservation laws; vacuum energy; cosmologic constant problem; invariance; hypercomplex numbers; Octonions; energy-mass equivalence; Ur-Alternatives; mereotopology; mereophysics
Online: 28 July 2019 (14:39:59 CEST)
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.
ARTICLE | doi:10.20944/preprints202210.0277.v1
Subject: Computer Science And Mathematics, Mathematics Keywords: Newton's celestial mechanics equations; $N$-body problem; Kepler problem; relative difference; origin invariance; integrals of motion; conservation of energy; conservation of angular momentum; inertia; Lagrange-Jacobi formula; total collapse.
Online: 19 October 2022 (10:06:06 CEST)
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.
ARTICLE | doi:10.20944/preprints202307.1834.v2
Subject: Computer Science And Mathematics, Algebra And Number Theory Keywords: Jacobian Conjecture, 3-fold linear type map, General 3-fold linear type map, Homogeneous type map, Jacobian condition, Coordinate transformation, Equivalent algebraic equations, Invariance of the Jacobian condition, General chain expression, Inverse polynomial map, Injective problem
Online: 1 August 2023 (09:46:21 CEST)
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,) holds such that the Jacobian Conjecture holds.
ARTICLE | doi:10.20944/preprints202208.0176.v1
Subject: Social Sciences, Psychology Keywords: psychological distress/anxiety/depression; dementia; Alzheimer’s disease; Parkinson’s disease; short form of the Depression Anxiety Stress Scale 21; Depression Anxiety Stress Scale 8-items; factor structure; psychometric properties; structural validity; validation; measurement invariance; old age/elders/elderly; informal; family caregivers; spouse; adult children
Online: 9 August 2022 (08:44:11 CEST)
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.
ARTICLE | doi:10.20944/preprints202109.0014.v1
Subject: Social Sciences, Psychology Keywords: Coronavirus disease 2019/COVID-19; Depression Anxiety Stress Scales-21/DASS-21; DASS-8; shortened version*; shorter version* of the DASS-21; psychiatric disorders; factorial structure/psychometric properties/structural validity/validation; measurement invariance/multigroup analysis; psychological distress; discriminant validity; item coverage; good predictive validity
Online: 1 September 2021 (12:15:27 CEST)
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.