Moment Properties Research Articles

Nonlinear Stable Least Trimmed Squares for Regression Models with Stable Errors

The common method for estimating nonlinear regression coefficients with Gaussian errors is nonlinear least squares. It is not robust for regression with heavy-tailed errors. The nonlinear least trimmed squares method is an efficient procedure for regression with heavy-tailed errors. We are introducing nonlinear least trimmed squares for the nonlinear regression with non-Gaussian stable errors and estimate the parameters of the stable distributions based on the order statistics. The traditional least trimmed squares regression algorithm is adopted for errors with infinite variance by modifying the trimming procedure. This paper estimated the nonlinear regression coefficients with stable errors through the proposed nonlinear least trimmed squares algorithm based on a new trimming procedure based on the properties of stable order statistics moments. The proposed algorithm was applied to real and simulated datasets and evaluated using a bootstrap standard deviation estimator.

Investigating the acceptor tuned effect on INPOD-based efficient D-π-A organic chromophores for optoelectronic utilization through quantum chemical analysis

In this study, the dye-sensitized solar cells and non-linear optical capabilities of newly designed ((E)-2-amino-5-((5-(4-p-tolyl-1,2,3,3a, 4,8 b-hexahydrocyclopenta [b]indol-7-yl)thiophen-2-yl)methylene)thiazol-4(5H)-one (INPOD)-based A1-A6 organic chromophores were examined. To create a D-π-A structure, the A1-A6 molecules were positioned on the electron donor, spacer, and acceptor, respectively. The use of hybrid functionals including PBEPBE, CAM-B3LYP, and MPW1PW91 was evaluated for the maximum absorption wavelength of INPOD. According to the calculated outcomes, MPW1PW91 exhibited λmax closest to INPOD. Consequently, the optical absorption spectra of A1-A6 were employed by this method to identify the key factors. The photovoltaic characteristics of these compounds in dye-sensitized solar cells were studied theoretically. The acceptor category affected the photovoltaic performance of A1-A6. Through the quantum chemical technique in time-dependent density functional theory methods, the electronic charge distribution and intramolecular charge transfer inside the A1-A6 were found. Time-dependent density functional theory calculations revealed that all A1-A6 had a λmax, that was greater than the INPOD (437 nm) in the range of 564–806 nm. A6 demonstrated an electron reorganization energy of 0.2340 eV, while a hole reorganization energy of 0.1006 eV. These values represent the maximum mobility of holes and electrons among all values. Additionally, the open circuit voltage was calculated after coupling each compound with a PTB7-Th. By the Voc of 2.10, 2.06, 2.22, and 2.08 eV, the A1, A3, A4, and A5 dyes produced the best results, respectively. The A1-A6 sensitizers were used to derive the non-linear optical properties of the dipole moment, polarizability, and first-order hyperpolarizability. It was noticed from the calculated results that the A2 and A6 molecules have the best options for non-linear optical activity. It tested how well the A1-A6 dyes performed in terms of charge transfer, dye regeneration, electron injection driving force, light harvesting efficiency, transition density matrix, molecular electro-potential, and density of states. The computed result showed that A2 and A6 chromophores are excellent candidates for dye-sensitized solar cells. Finally, those dye derivatives would certainly work effectively as tuning-A in optoelectronic applications.

An improved analytical method for rarefied aerothermodynamics on a complex geometry in free-molecular flows

A numerical method for high altitude aerothermodynamic analysis code for Very Low Earth Orbit (VLEO) satellite and spacecraft, named as HACS, is presented in this article. HACS is a computational tool that addresses the challenges by integrating the free-molecular gas kinetic model with novel particle sampling method and robust particle tracing algorithm to predict the shadow region on surfaces. To ensure the reliability and accuracy of the HACS, a rigorous verification and validation process has been systematically conducted by comparing the aerothermodynamic properties of forces, moments, and heat flux with the direct simulation Monte-Carlo (DSMC) results. The HACS is applied to the realistic geometries of VLEO satellite, the Apollo re-entry module, and spacecraft including fin and wing shapes. Results demonstrate that HACS provides the aerothermodynamic properties within the time frame of 60 seconds for the complex geometries and the accuracy of the HACS is guaranteed above 120 km altitude. The maximum relative error of the aerothermodynamic properties is less than 5% compared to the DSMC results at the lowest altitude of about 120 km, and has smaller relative errors as the altitude increases.

Synthesis, crystal structure, spectroscopic, electronic and vibrational properties of N′-[(E)-3-pyridinylmethylene]nicotinohydrazide trihydrate: Experimental and computational study

N′-[(E)-3-pyridinylmethylene]nicotinohydrazide trihydrate (C12H10N4O·3(H2O)) was synthesized and its structure was determined by single crystal X-ray diffraction method. X-ray analysis showed that the compound crystalized in the triclinic system P-1 with a = 7.1134 (3) Å, b = 10.0208 (4) Å, c = 10.3601 (4) Å, α = 96.386 (3)°, β = 96.995 (3)°, γ = 101.219 (4)°, V = 712.05 (5) Å3 and Z = 2 and exhibits that the title compound (I) consists of N′-[(E)-3-pyridinylmethylene]nicotinohydrazide (II) (C12H10N4O), and three water molecules of crystallization. The two water molecules are attached to the third water molecule through intermolecular two OH…O hydrogen bonds. At the same time, this water molecule is linked to the NH amide group of the hydrazone by an intermolecular NH…O hydrogen bond. Hirshfeld surface (HS) analyses were carried out are to visualise the intermolecular interactions in the crystals of Compound I. The geometric optimization of the titled compound has been carried out by different computational methods such as by Hatree Fock (HF) and Density Functional Theory (DFT) methods with the 6–311++G (d,p) basis set. The vibrational frequency, dipole moment (μ), polarizability (α), hyperpolarizability (β), and electronic properties including the highest occupied molecular orbital-lowest unoccupied molecular orbital (HOMO–LUMO) of the compound have been calculated at the level of both theories. In the results of crystal analysis and geometry calculations of the compound I, it was observed that intermolecular hydrogen bonds, N2H2A…O3, O3H31…O2 and O3H32…O4, were formed. The energy band gap (Eg = ELUMO-EHOMO) values were also obtained by using ELUMO and EHOMO at the level of both theories. The value of equilibrium (ground state) dipole moment of the studied molecule was calculated to be 8.31 Debye in B3LYP and 7.55 Debye in HF. The calculated hyperpolarizability values at the B3LYP/6–311++G(d,p) of the compound are 2.53 × 10−30 esu and this value corresponds to 6.79 times the hyperpolarizability value of urea.

Dual-Vacancy-Engineered ZnIn2S4 Nanosheets for Harnessing Low-Frequency Vibration Induced Piezoelectric Polarization Coupled with Static Dipole Field to Enhance Photocatalytic H2 Evolution.

This study investigates the impact of In- and S-vacancy concentrations on the photocatalytic activity of non-centrosymmetric zinc indium sulfide (ZIS) nanosheets for the hydrogen evolution reaction (HER). A positive correlation between the concentrations of dual In and S vacancies and the photocatalytic HER rate over ZIS nanosheets is observed. The piezoelectric polarization, stimulated by low-frequency vortex vibration to ensure the well-dispersion of ZIS nanosheets in solution, plays a crucial role in enhancing photocatalytic HER over the dual-vacancy engineered ZIS nanosheets. The piezoelectric characteristic of the defective ZIS nanosheets is confirmed through the piezopotential response measured using piezoelectric force microscopy. Piezophotocatalytic H2 evolution over the ZIS nanosheets is boosted under accelerated vortex vibrations. The research explores how vacancies alter ZIS's dipole moment and piezoelectric properties, thereby increasing electric potential gradient and improving charge-separation efficiency, through multi-scale simulations, including Density Functional Theory and Finite Element Analysis, and a machine-learning interatomic potential for defect identification. Increased In and S vacancies lead to higher electric potential gradients in ZIS along [100] and [010] directions, attributing to dipole moment and the piezoelectric effect. This research provides a comprehensive exploration of vacancy engineering in ZIS nanosheets, leveraging the piezopotential and dipole field to enhance photocatalytic performances.

Effect of the electric field orientation on stark shift, dipole moment and electronic properties in a circular toroidal quantum ring: Presence of shallow donor impurity

This research investigates the influence of electric field orientation on the physical properties of a Gallium Arsenide (GaAs) Circular Toroidal Quantum Ring (CTQR) in the presence of shallow donor impurity. Using the effective mass approximation and an infinite potential well, we delve into how electric field directions specifically 0, 45, and 90 degrees on the xy-plane affect physical behaviors such as binding energy, electronic energy, the Stark effect, dipole moment and donor impurity position. Utilizing the finite difference method for our numerical analysis, we discovered interesting size-dependent behaviors. Our findings reveal intriguing insights. Initially, we observed that the electronic energy exhibits minimal sensitivity to the direction of the electric field in smaller CTQR. Notably, the ground state energy increases when the electric field’s direction shifts from φF=0 to φF=90∘. The electric field’s influence on the binding energy varies depending on its orientation. In larger structures, we observe a lower binding energy. Thus, our study unveils the influence of the electric field’s direction on Stark shifts and dipole moment which opens pathways for a deeper understanding of potential applications in this domain.

Molecular Structures, Dipole Moments, and Electronic Properties of β-HMX under External Electric Field from First-Principles Calculations.

In order to investigate the impact of an external electric field on the sensitivity of β-HMX explosives, we employ first-principles calculations to determine the molecular structure, dipole moment, and electronic properties of both β-HMX crystals and individual β-HMX molecules under varying electric fields. When the external electric field is increasing along the [100], [010], and [001] crystallographic directions of β-HMX, the calculation results indicate that an increase in the bond length (N1-N3/N1'-N3') of the triggering bond, an increase in the main Qnitro (N3, N3') value, an increase in the minimum surface electrostatic potential, and a decrease in band gap all contribute to a reduction in its stability. Among these directions, the [010] direction exhibits the highest sensitivity, which can be attributed to the significantly smaller effective mass along the [010] direction compared with the [001] and [100] directions. Moreover, the application of an external electric field along the Y direction of the coordinate system on individual β-HMX molecules reveals that the strong polarization effect induced by the electric field enhances the decomposition of the N1-N3 bonds. In addition, due to the periodic potential energy of β-HXM crystal, the polarization effect of β-HMX crystal caused by an external electric field is much smaller than that of a single β-HXM molecule.

Coefficientwise Hankel-total positivity of the row-generating polynomials for the output matrices of certain production matrices

Total positivity of matrices is deeply studied and plays an important role in various branches of mathematics. The aim of this paper is to study the criteria for coefficientwise Hankel-total positivity of the row-generating polynomials of generalized m-Jacobi-Rogers triangles and their applications.Using the theory of production matrices, we present the criteria for coefficientwise Hankel-total positivity of the row-generating polynomials of the output matrices of certain production matrices. In particular, we gain a criterion for coefficientwise Hankel-total positivity of the row-generating polynomial sequence of the generalized m-Jacobi-Rogers triangle. This immediately implies that the corresponding generalized m-Jacobi-Rogers triangular convolution preserves the Stieltjes moment property of sequences and its zeroth column sequence is coefficientwise Hankel-totally positive and log-convex of higher order in all the indeterminates. In consequence, for m=1, we immediately obtain some results on Hankel-total positivity for the Catalan-Stieltjes matrices. In particular, we in a unified manner apply our results to some combinatorial triangles or polynomials including the generalized Jacobi Stirling triangle, a generalized elliptic polynomial, a refined Stirling cycle polynomial and a refined Eulerian polynomial. For the general m, combining our criterion and a function satisfying an autonomous differential equation, we present different criteria for coefficientwise Hankel-total positivity of the row-generating polynomial sequence of exponential Rirodan arrays. In addition, we also derive some results for coefficientwise Hankel-total positivity in terms of compositional functions and m-branched Stieltjes-type continued fractions. Finally, we apply our criteria to: (1) rook polynomials and signless Laguerre polynomials (confirming a conjecture of Sokal on coefficientwise Hankel-total positivity of rook polynomials), (2) labeled trees and forests (proving some conjectures of Sokal on total positivity and Hankel-total positivity), (3) rth-order Eulerian polynomials (giving a new proof for the coefficientwise Hankel-total positivity of rth-order Eulerian polynomials, which in particular implies the conjecture of Sokal on the coefficientwise Hankel-total positivity of reversed 2th-order Eulerian polynomials), (4) multivariate Ward polynomials, labeled series-parallel networks and nondegenerate fanout-free functions, (5) an array from the Lambert function and a generalization of Lah numbers and associated triangles, and so on.

Magnon Orbital Nernst Effect in Honeycomb Antiferromagnets without Spin-Orbit Coupling.

Recently, topological responses of magnons have emerged as a central theme in magnetism and spintronics. However, resulting Hall responses are typically weak and infrequent, since, according to present understanding, they arise from effective spin-orbit couplings, which are weaker compared to the exchange energy. Here, by investigating transport properties of magnon orbital moments, we predict that the magnon orbital Nernst effect is an intrinsic characteristic of the honeycomb antiferromagnet and therefore, it manifests even in the absence of spin-orbit coupling. For the electric detection, we propose an experimental scheme based on the magnetoelectric effect. Our results break the conventional wisdom that the Hall transport of magnons requires spin-orbit coupling by predicting the magnon orbital Nernst effect in a system without it, which leads us to envision that our work initiates the intensive search for various magnon Hall effects in generic magnetic systems with no reliance on spin-orbit coupling.

Portfolio optimisation of international real estate investment trusts market during COVID-19: A behavioural perspective

This paper employs the cumulative prospect theory to investigate how deviation from rational investor asset selection improves portfolio optimisation. Firstly, asset portfolios are constructed by utilising the cumulative prospect theory, which captures investors’ psychology and risk tolerance and is herein referred to as a behavioural portfolio (BF). Secondly, the cluster technique is also used to build behavioural-centred investment portfolios that capture all the relevant moment properties of the asset return distribution as well as investors’ psychological dynamics and risk appetite, herein called the cluster moment behavioural portfolio (CMBF). The constructed portfolios are optimised by copula and differential evolution techniques. The analysis of optimisation of the constructed portfolios indicates that for behavioural portfolios (BF), in all phases of our sample period, portfolios with higher behavioural scores outperformed those with lower behavioural scores. And in the cluster moment behavioural portfolio (CMBP), for the pre-COVID and the COVID phases, the portfolios with lower behavioural scores outperform those with higher behavioural scores; however, for the full sample phase, the portfolio with a higher behavioural score outperforms the portfolio with the lower behavioural scores. The optimisation results of all the constructed portfolios largely favour portfolios with higher behavioural scores over those with lower scores. The results offer investment suggestions to guide investors with varying risk tolerance levels and those who deviate from the rational investor on how they can enhance their portfolio optimisation.

Removal of caffeine from aqueous and vacuum environments using Si12C12, Si11GeC12, Si11BC12 fullerenes: A DFT and TDDFT studies

Caffeine (CFI) adsorption upon the perfect, boron-doped (Si11BC12 and Si12BC11), and germanium-doped (Si11GeC12 and Si12GeC11) silicon carbide (SiC) fullerenes have been studied to assess the feasibility of caffeine removal from aqueous and vacuum environments by using density functional theory (DFT) and time-dependent density functional theory (TDDFT) calculations. The adsorption energy and charge transfer of caffeine through its nitrogen atom of the imidazole ring upon the surface of Si12C12 nano-cage is stronger than that of the oxygen atoms of the pyrimidinedione ring with moderate adsorption energy. The theoretical infrared (IR) spectrum shows that the vibrational frequency of CFI changes after interacting with the pure Si12C12 fullerene, and this change is comparable to the experimental data. According to the TDDFT method, Ultraviolet–Visible (UV–Vis) techniques reveal that the optical features of the pure, Si11BC12, Si11GeC12 fullerenes changed after interacting with CFI. The density of state (DOS) analysis confirmed that the caffeine adsorption via imidazole ring with a robust electron hybridization can be remarkably altered the electronic features of Si12C12 fullerene, being too sensitized to the binding of caffeine. The results demonstrate that CFI adsorption on Si12C12 is stronger than on Si11BC12 and Si11GeC12 fullerenes. The presence of a boron (B) atom in the Si11BC12 fullerene improves the dipole moment and optical properties as compared to the Si11GeC12 fullerene. Upon caffeine adsorption, the Si12C12 and Si12BC11 fullerenes could be promising adsorbents for caffeine removal and detection because of the strong interaction, increasing dipole moment, and short recovery time.

Phytochemical Composition and Medicinal Properties of Psidium guajava, Artocarpus heteorphyllus, Anona muricata and Passiflora edulis: A Critical Review

Artocarpus heterophyllus Lam, a part of the Moraceae family, is known by distinctive names in different districts over the globe. The jackfruit tree's significant alleviating impacts have made it a well-known choice for characteristic cures. Its bioactive compounds, counting lignans, flavones, and saponins, contribute to its momentous therapeutic properties, which incorporate anti-cancer, anti-ulcer, anti-hypertensive, and anti-aging impacts. As a result, the jackfruit tree holds awesome importance in conventional medication and characteristic mending hones. Guanabana, soursop, graviola, or Brazilian paw paw, scientifically known as A. muricata, is a plant native to Central America but can be found in abundance across Southeast Asia, South America, and the African rainforest.. This plant has appeared various advantageous properties counting anticancer, antiulcer, antidiabetic, antiprotozoal, antidiarrhea, antibacterial, antiviral, antihypertensive, and wound mending impacts. Psidium guajava includes a wealthy history of restorative employments, with all parts of the tree being esteemed for their helpful properties. From the takes off to the natural products, each component of Psidium guajava has been utilized for different wellbeing benefits throughout a long time. Its restorative centrality includes to the by and large significance of this tropical tree totally different societies and conventional hones. Energy natural products, which have a place to the sort Passiflora, comprise of around 450 species. Among them, Passiflora edulis is the foremost well-known and commonly utilized. Later thinks about have too highlighted its anti-inflammatory potential, especially within the frame of tea made from the imbued clears out. Passiflora alata and P. edulis have both found applications in various pharmaceutical arrangements and are broadly utilized within the nourishment industry. The anti-oxidant substances present in P. Edulis have sparked a growing interest in this plant. Even though it is important, no audit of this species has been included in the logical writing up to this point. The notable and recent literature on the botany, traditional uses, phytochemistry, pharmacological effects, and harmfulness of this ponder plant is surveyed and summarized here. This overview may prove beneficial for subsequent research aimed at misusing the beneficial attributes of this priceless, curative species.

The study of electronic structure and magnetic properties of ferromagnetic Kondo-lattice CePd2P2 from the first-principles

The electronic structure of ferromagnetic CePd2P2 Kondo lattice crystallizing in the tetragonal ThCr2Si2-type structure is investigated by means of the Density Functional Theory (DFT) and Time-Depedent DFT (TDDFT) methods. The calculated electronic properties from DFT are presented and compared to those of the non-magnetic LaPd2P2 compound. The differences in the FS topologies upon changing magnetic states (paramagnetic → ferromagnetic) is also examined. Including the relativistic effects of without or with spin-orbit coupling, and Hubbard corrections in the calculations, ferromagnetic ground state with an ordered magnetic moment of ∼ 0.8-0.9 μB is corroborated. Meaningful changes in the magnetic moment and electronic properties of CePd2P2 are discussed in terms of effects brought by the Coulomb interaction (U), and the Hund coupling (J). In particular, the reduction in magnetic moment and simultaneously enhancement of DOS at the Fermi energy due to decreasing J are in quantitative concordance with the Kondo lattice characteristic. Furthermore, dynamical model used in TDDFT calculations exhibits that 4 f electrons in CePd2P2 tend to be delocalized. The frequency-temperature behavior of response function allows to estimate the Kondo temperature to amount 19 K.

Correlation between the horizontal transition dipole moment and luminescence properties of dopants in organic light-emitting diodes

MD simulations provide molecular horizontal transition dipole moments and intermolecular van der Waals interactions, while TD-DFT provides emitters’ luminescence properties, which can be used to screen for promising OLED materials.

Fine-tuning of organic optical double-donor NLO chromophores with DA-supported functional groups.

New strategic chromophores with updated fine-tuning of previously reported BLD1 and BLD3 chromophores were designed. BLD1 and BLD3 have silicon functional groups on the donor unit, and the bridge has a good chance of self-assembling, so in the present study we fine-tuned the isolating groups to the bulky cyclic alkene to improve their dipole moment and organic electro-optic (OEO) properties as well. To demonstrate the impact of cyclic alkenes on the electron-donating groups in sensible NLO chromophore designs, a thorough analysis and comparison of the chromophore synthesis, UV-Vis calculations, solvatochromic behavior of the chromophore, DFT quantum mechanical calculations, thermal stabilities, and much lower dipole moments was conducted.

EQUATIONS OF MOTION OF AN ISOTROPIC SPHERICAL MOMENT ELASTIC SHELL*2

Using the previously obtained equations of motion of thin moment elastic shells of constant thickness with an arbitrary middle surface, the equations of motion of an isotropic moment spherical shell in terms of forces and “displacements” (kinematic parameters) are constructed. In this case, the metric of the middle spherical surface is taken into account, as the curvilinear coordinates of which two angular coordinates of the standard spherical coordinate system with the origin at the center of the middle surface are used. First, a closed system is written down, which includes the equations of motion in the physical components of the tensors of internal forces and moments, as well as additional similar characteristics corresponding to the moment properties of the model, and physical relationships. Then, by excluding physical relations, it is reduced to twelve equations of motion in kinematic parameters, written in operator form. In this case, the coefficients of partial derivative operators are simplified by neglecting terms that have a higher order of smallness relative to the thickness of the shell. Despite the bulkiness of the system, it is written in a compact form. Boundary conditions are not written, since the shell is considered closed. By introducing additional hypotheses similar to those used in the classical theory of shells (neglecting the compression of a normal fiber, the Kirchhoff – Love hypothesis about the connection between the tangential components of the rotation angle vector of a normal fiber and normal displacement, as well as the hypothesis about the connection between the normal to the middle surface part of the coordinate of the rotation angle vector and its tangential components) the number of equations and unknowns decreases. To carry out this procedure, a variational Hamilton equation is constructed, which takes into account the connections between kinematic parameters imposed by the hypotheses, and then the corresponding one is transformed using the generalized Ostrogradsky – Gauss theorem.

Study of Geometrical, Electronic Structure, Spectral, and NLO Properties of Phenyl‐Based Azo Dyes of Dye Sensitizer for Solar Cells: A Theoretical Study

AbstractThe molecular geometry, electronic structure, and absorption spectra of some important phenyl derivatives are investigated by using DFT and TD‐DFT with B3LYP and CAM‐B3LYP functional. The highest HOMO–LUMO energy gap, Non‐linear optical properties of dipole moment, polarizability, and hyperpolarizability are calculated. In both methods hyperpolarizability PDP values (16.77 × 10−30 and 16.59 × 10−30 esu) are higher than PDNA, PDN, and MPAN dye. The Molecular electrostatic potential shows that PDNA dye has more electronegative potential. Comparing all the dyes, PDP dye shows a higher light harvesting efficiency in the UV–vis region. The vibrational frequencies are assigned based on the potential energy distribution (PED) using the VEDA‐4 program.

Completing Dirac’s work. The Dirac electron is a 2D hologram

The QED-physical (QED-P) theory [J. H. Wilson, Phys. Essays 35, 5 (2022)] is actually the theory Dirac sought in 1962 in his attempt to predict the muon as an “extensible model of the electron.” Recently, Lerche attempted to produce a classical solution to Dirac’s equation for the radial motion of an extensible, basically classical, model of the electron. Both Dirac and Lerche proceeded in the wrong, classical direction in this effort. The QED-P center of charge (CoC) position operator is derived directly from the Dirac equation (DE) CoC velocity operator, cα with no ad hoc assumptions. QED-P was integrated with QED into a single theory, and that integration is proved by the highly accurate estimates of QED that are dependent on the DE velocity operator cα. Both QED and QED-P are based directly on the same Dirac Equation (DE) four current c(α,I) that QED couples with an external electromagnetic field. QED uses covariant perturbation theory to produce highly accurate results, except for the electron selfenergy, which is infinite. The DE velocity operator, cα, is the spatial part of the free electron four current, and has highly unusual properties compared to classical velocity vectors. QED could not produce highly accurate answers without the 4 × 4 complex matrix cα as the electron CoC “velocity” operator. QED-P simply integrates the same Dirac equation four current used so successfully in QED, and produces the discrete internal spatial and time coordinate operators (ISaTCOs) to give the electron field’s internal structure a very specific, but highly, nonclassical geometric description, with no ad hoc assumptions. QED and QED-P are complementary theories, and both are proven to be true by the accurate results of QED. The physical interpretation of QED-P is discussed in this paper as a two-dimensional, rapidly vibrating “point” charge, that is always located on a 2D CoC sphere in the electron rest frame, oscillating rapidly through eight eigenvalues with an ISaTCO period of ∼10−22 s. The fact that the CoC’s eight ISaTCO spatial eigenvectors are always are located on a 2D shell encompassing the electron’s 3D “space” inside the CoC’s 2D shell is a direct consequence of the DE, and nothing else. In this paper, it is shown that the “discrete” ISaTCOs produce a one dimensional, discrete quantum harmonic oscillator with its ISaTCOs always located on a 2D CoC shell. The CoC shell is an “2D hologram” emerging from a 3D volume inside the 2D CoC shell with a vibrational electronic clock” producing an internal phase that is propagated throughout space/time. The QED-P point electron charge rotates 720° to complete one internal electron discrete period. The electron’s spin and magnetic moment [J. H. Wilson, Phys. Essays 29, 402 (2016); ibid. 31(1), 59‐67 (2018); ibid. 34, 17 (2021)] are generated by the CoC ISaTCO in QED-P, and there is no need for “intrinsic” properties. The QED-P electron properties described above d are far different than the standard model’s very small point particle with intrinsic properties of spin and magnetic moment.

Modelling and diagnostic tests for Poisson and negative-binomial count time series

When modelling unbounded counts, their marginals are often assumed to follow either Poisson (Poi) or negative binomial (NB) distributions. To test such null hypotheses, we propose goodness-of-fit (GoF) tests based on statistics relying on certain moment properties. By contrast to most approaches proposed in the count-data literature so far, we do not restrict ourselves to specific low-order moments, but consider a flexible class of functions of generalized moments to construct model-diagnostic tests. These cover GoF-tests based on higher-order factorial moments, which are particularly suitable for the Poi- or NB-distribution where simple closed-form expressions for factorial moments of any order exist, but also GoF-tests relying on the respective Stein’s identity for the Poi- or NB-distribution. In the time-dependent case, under mild mixing conditions, we derive the asymptotic theory for GoF tests based on higher-order factorial moments for a wide family of stationary processes having Poi- or NB-marginals, respectively. This family also includes a type of NB-autoregressive model, where we provide clarification of some confusion caused in the literature. Additionally, for the case of independent and identically distributed counts, we prove asymptotic normality results for GoF-tests relying on a Stein identity, and we briefly discuss how its statistic might be used to define an omnibus GoF-test. The performance of the tests is investigated with simulations for both asymptotic and bootstrap implementations, also considering various alternative scenarios for power analyses. A data example of daily counts of downloads of a TeX editor is used to illustrate the application of the proposed GoF-tests.

Combined effects of hydrostatic pressure and temperature on diamagnetic susceptibility, dipole moment and optical band gap properties of Hemi-Quantum Ring: Presence of a single off-center donor atom

In this study, we have investigated the combined influence of hydrostatic pressure and temperature on the electronic and optical properties of an electron and a off-center atom confined in a Hemi Quantum Ring. To analyze the system, we employed the finite difference method, considering the effective mass approximation and an infinite confinement potential. Our study examines the permanent dipole moment and diamagnetic susceptibility under the influence of the donor atom’s position, temperature, and applied hydrostatic pressure in the three directions Rg, Rc and φ0. Our results reveal that the permanent dipole moment increases as the geometric confinement decreases, while the diamagnetic susceptibility exhibits a negative behavior and is influenced by temperature and hydrostatic pressure. Furthermore, we observed that the bandgap and the optical bandgap are sensitive to variations in temperature and the size of the HQR (Hemi Quantum Ring) nanostructure. The study on the combined influence of hydrostatic pressure and temperature on the electronic and optical properties of an electron and an off-center atom confined in a Hemi Quantum Ring has potential real-world applications in the development of electronic and optical devices.