Orthogonal Solution Research Articles

Development of a high-resolution ionospheric VTEC model over Nigeria using spherical harmonics with orthogonal transformation solution

Abstract One important ionosphere element that impacts radio signal transmission is the Vertical Total Electron Content (VTEC). Accurate estimation of VTEC is important for diverse applications such as satellite positioning, space weather forecasting, satellite communication. In regions with a sparse network of receivers, especially Nigeria, the spatial and temporal resolutions of the Global Ionospheric Maps (GIM) regularly provided by the International GNSS Service (IGS), Center for Orbit Determination in Europe (CODE), and the International Reference Ionosphere (IRI) are limited. This limits their potential to uncover local ionospheric phenomena in such areas. To address this limitation, we have developed a VTEC model for estimating high temporal-resolution VTEC and Differential Code Bias (DCB) over Nigeria using spherical harmonic expansions with an orthogonal transformation solution. Our novel method makes use of GNSS measurements from the Global Positioning System (GPS) and Global Navigation Satellite System (GLONASS) to precisely estimate VTEC and DCB. GNSS datasets in Receiver Independent EXchange (RINEX), satellite orbit (SP3) and Ionospheric Exchange (IONEX) formats from 2011 across 9 GNSS receivers in the Nigerian Geodetic Network sampled at 30-second intervals were used for this study. For this investigation, code pseudo-range observations were also smoothed using carrier phase observations. To assure data quality, we also carried out several preprocessing procedures utilizing the Melbourne-Wubbena linear and geometry-free linear combinations using an internal ITB-GNSSTEC FORTRAN application based on batch processing and least squares approaches. To validate our model, we compared the estimates with the IGS, CODE, and IRI-2020 models. Results demonstrated strong agreement with the other models with a standard deviation between 2.80 and 6.50 TECU and a correlation coefficient of not less than 0.92 at the evaluation stations. Notably, the new model aligned more closely with CODE and IGS than the IRI model. Also, the new model enabled the detection of local ionospheric VTEC post-sunset enhancement missed by GIM models. Our model also showed a strong positive correlation with the other models for quiet and disturbed days of geomagnetic activity. In Conclusively, this research has developed a high-resolution VTEC method for areas with sparse distribution of GNSS receivers, achieving a temporal resolution of 10 minutes. The ionospheric modeling in areas like Nigeria with sparse GNSS networks has greatly benefited from this research. The approach improves the precision of GNSS-based applications, such as location and navigation, by precisely calculating VTEC and DCBs. It also addresses the issue of sparse observational data in equatorial regions, offering insightful information for atmospheric and geodetic research.

Orthogonal Stability and Solution of a Three-Variable Functional Equation in Extended Banach Spaces

This manuscript introduces a novel three-variable cubic functional equation and derives its general solution. Employing both the direct and fixed-point methods, we investigate the orthogonal stability of this equation within the frameworks of quasi-β-Banach spaces and multi-Banach spaces. Additionally, the study explores the stability of the equation in various extended Banach spaces and provides a specific example illustrating the absence of stability in certain cases.

Theoretical modeling and vibration analysis of composite laminated wing-box structures of hydrogen-electric aircraft under hygrothermal environment

For the sake of achieving the goal of ultra-low or even zero carbon emissions during flight, hydrogen-electric aircraft has been receiving increasing emphasis. Nevertheless, the hydrogen-electric aircraft owns an all-composite fuselage configuration and is subjected hygrothermal environment, which have a significant effect on the aircraft dynamics, especially for wing structure. In this study, an improved orthogonal polynomial solution based on the Rayleigh-Ritz method is developed for the dynamic analysis of composite laminated wing-box structures (CLWBSs) of hydrogen-electric aircraft with humid and hot environment and elastic boundary. In this solution approach, the potential energy, kinetic energy, elastic potential energy and hygrothermal potential energy of CLWBSs are derived from the framework of Kirchhoff thin plate hypothesis. A set of artificial springs is imported to the free edges of CLWBSs to simulate the elastic boundary and connection between two plates. The convergence, accuracy and computational efficiency of the proposed formulation are validated by experiment and finite element analysis. The effect of the coupling parameters and the elastic boundaries due to flexible composite fuselage in hygrothermal environment created by the hydrogen fuel cells are systematically investigated which have been confirmed by theoretical research, finite element analysis and experiment. The related findings indicate that the present approach provided an effective formulation for the vibration analysis and optimization of flexible composite wing-box structures. It can be applied in the field of aerospace and navigation industry at the same time.

Optimization of Aluminum Alloy Formwork Geometry Parameters Based on a PSO-BP Neural Network

To assist in addressing the problem where an aluminum alloy formwork (AAF) deforms more greatly under the action of lateral pressure and therefore does not meet the requirements of plaster-free engineering, we propose a method for determining the geometric parameters of this formwork based on a PSO algorithm and BP neural network with ABAQUS as the platform. The influence of six geometric parameters of the formwork on the maximum deflection value of the panel under the action of lateral pressure is studied using finite element analysis. The maximum deflection value of the panel is used as the index, and the influence of each factor is analyzed with an orthogonal test, and a set of optimal geometric parameters is obtained via extreme difference analysis and analysis of variance. The sample data are obtained via finite element simulation, and the PSO-BP neural network model is established using the six factors of the orthogonal test as input values and the maximum deflection of the panel as the output value, and the optimal geometric parameters are optimized using the PSO algorithm. The results indicate that the maximum deflection for the panel in the orthogonal scheme is 1.446 mm. The PSO-BP neural network prediction model demonstrates greater accuracy and a 31.74% reduction in running time compared to the BP neural network prediction model. The optimized PSO-BP neural network prediction model scheme reveals a maximum panel deflection of 1.296 mm, a 10.37% decrease compared to the orthogonal solution. These findings offer technical guidance and a foundation for optimizing AAF designs, presenting practical applications.

과도 결정 선형 시스템에서의 보통과 수직 거리 최소 제곱 해에 대한 대수 및 기하적 분석

In this paper, we make an in-depth analysis on the ordinary least-squares solution and the orthogonal distance least-squares solution to an overdetermined linear system, having the number n of constraints greater than the number m of unknowns. Using the barycentric coordinate, algebraic and geometric analysis is made for the case of n=2 and m=3, yielding a constraint triangle, and for the case of n=3 and m=4, yielding a constraint tetrahedron. First, for an n-dimensional overdetermined system, the ordinary least squares solution that minimizes the sum of the squares of m residuals and the orthogonal distance least squares solution that minimizes the sum of the squares of m orthogonal distances are formulated. Next, for the cases of n=2 and m=3, and n=3 and m=4, the following analysis is made: The relationship between the ordinary least-squares solution and the centroid of the constraint triangle/tetrahedron is identified, the changing pattern of the ordinary least-squares solution due to the scaling of an overdetermined system is examined, and the relationship between the orthogonal distance least squares solution and the symmedian point of the constraint triangle/tetrahedron is identified. Finally, to demonstrate the applicability of the ordinary least-squares and the orthogonal distance least-squares solutions, the velocity estimation of a mobile robot using a polygonal array of optical mice is provided.

Thermally Activated Aromatic Ionic Dopants (TA‐AIDs) Enabling Stable Doping, Orthogonal Processing and Direct Patterning

AbstractDoping plays a critical role in organic electronics, and dopant design has been central in the development of functional and stable doping. In this study, there is departure from conventional molecular dopants and a new class of dopants are reported – aromatic ionic dopants (AIDs). AIDs consist of a pair of aromatic cation and anion that are responsible for molecular doping reaction and charge balancing separately. It is shown that the first AID made from cycloheptatrienyl (tropylium) cation and pentacyanocyclopentadienide anion (PCCp), abbreviated as T‐PCCp, can function as an effectivep‐type dopant to dope polydioxythiophenes. Here, tropylium cation induces the doping reaction while the PCCp anion stabilizes the generated polarons and bipolarons. With T‐PCCp, a highly doped (≈120 S/cm) and stable system is achieved up to 150 °C, an orthogonal (sequential)solution processing resulting from the immiscibility of the dopant and the polymer host, and a high‐resolution direct micropatterning with laser writing resulted from a thermally activated doping process.

Coupled canonical polyadic decomposition of multi-group fMRI data with spatial reference and orthonormality constraints

Multi-group fMRI data may possess different types of subjects, tasks, scans, etc. Fortunately, coupled canonical polyadic decomposition (CCPD) requires multiple tensor datasets to share one or more factor matrices. Considering that spatial variability is generally smaller than temporal variability, we attempt CCPD to decompose multi-group fMRI data into shared spatial maps (SMs), group-specific time courses (TCs) and subject intensities. As spatial references of interested components are generally available and the spatial orthonormality can reduce crosstalk among components, we propose a novel CCPD by adding spatial reference and orthonormality constraints. Specifically, based on accelerated alternating least squares, we further update shared SMs twice: 1) we orthonormalize shared SM components by orthogonal Procrustes solution; 2) after identifying the interested components by maximizing Pearson correlation coefficients between shared SMs and spatial references, we update interested shared SMs by minimizing the square error between magnitude part of normalized shared SMs and corresponding normalized spatial references. The results of two-group simulated and experimental task-related fMRI data as well as resting-state fMRI data with 24 healthy controls (HCs) and 24 schizophrenia patients (SZs) all show outperformed performance for the proposed method compared with unconstrained CCPD, CCPD with a spatial orthonormality constraint, widely-used tensor independent component analysis (ICA) and semi-blind group information guide ICA in both magnitude-only analysis and complex-valued analysis. Moreover, by using AdaBoost, resting-state group-specific TCs estimated by the proposed method significantly exhibit larger group differences, especially for the sensorimotor network, and thus provide a potential biomarker for schizophrenia.

Estimation Method for Mixed Near-Field and Far-Field Sources Based on Four-Order Cumulant and Polarization Sensitive Array

A new multidimensional parameters joint estimation method of mixed near-field and far-field sources based on polarization sensitive array, fourth-order cumulant, joint diagonalization technology, and propagator method is presented, which can realize the joint estimation of DOA (Direction of Arrival), range, frequency, polarization auxiliary angle, and polarization phase difference without multidimensional spectral peak searching and parameter pairing, and it is suitable for any additive Gaussian noise environment and effective for reducing the loss of array aperture. The algorithm skillfully constructs the fourth-order cumulant matrix by using the output on the label of specific dipole pairs of the received array, which effectively avoids the matrix rank reduction caused by the far-field sources coexistence situation. In addition, the presented algorithm utilizes the orthogonal propagation algorithm for subspace decomposition and uses the total least square solution to replace the orthogonal solution of singular value decomposition, which effectively reduces the computational complexity. The experiment proved the effectiveness of the proposed algorithm.

Causal attributions for success and failure among athletes: Validation of the Croatian version of the revised Causal dimension scale (CDS-II)

Background and Study Aim. Researchers since the late 1970s have been interested in finding out the reasons attributed to outcomes. To facilitate attribution research in Croatia we translated and validated The Revised Causal Dimension Scale (CDS-II) and examined its invariance when attributing most and least successful competition performances.
 Materials and methods. To achieve our stated aim, 384 kinesiology students completed the translated CDS-II. To test the latent structure of the questionnaire, we used CFA and tested two alternative models (orthogonal solution and model with correlated latent variables). Additionally, we examined the CDS-II invariance when attributing the most and the least successful competition performance in sport using longitudinal CFA. The reliability was tested using Cronbach alpha coefficients. Lastly, we tested differences in latent means between most and least successful performance using pairwise t-test.
 Results. Similar to the originally published findings, CFA indicated the CDS-II structure with correlated latent variables had an adequate and better fit than the orthogonal solution in both situations. Furthermore, we confirmed configural, metric and scalar invariance, as well as partial strict invariance since one item’s residuals differed significantly from the others. Cronbach alpha coefficients were adequate across both situations. Lastly, athletes attributed their most successful performances to more internal, stable and controllable reasons than their least successful performances.
 Conclusions. We confirmed that the Croatian version of the CDS-II has adequate psychometric properties and is therefore suitable for research in sport situations.

The neurobiology of wellness: 1H-MRS correlates of agency, flexibility and neuroaffective reserves in healthy young adults

Proton magnetic resonance spectroscopy (1H-MRS) is a noninvasive imaging technique that measures the concentration of metabolites in defined areas of the human brain in vivo. The underlying structure of natural metabolism-emotion relationships is unknown. Further, there is a wide range of between-person differences in metabolite concentration in healthy individuals, but the significance of this variation for understanding emotion in healthy humans is unclear. Here we investigated the relationship of two emotional constructs, agency and flexibility, with the metabolites glutamate and glutamine (Glx), N-acetylaspartate (tNAA), choline (Cho), creatine (tCr), and myo-inositol (Ins) in the right dorsal anterior cingulate cortex (dACC) in medically and psychiatrically healthy volunteers (N = 20, 9 female; mean age = 22.8 years, SD = 3.40). The dACC was selected because this region is an integrative hub involved in multiple brain networks of emotion, cognition and behavior. Emotional traits were assessed using the Multidimensional Personality Questionnaire Brief Form (MPQ-BF), an empirically derived self-report instrument with an orthogonal factor structure. Phenotypes evaluated were positive and negative agency (MPQ-BF Social Potency, Aggression), emotional and behavioral flexibility (MPQ-BF Absorption, Control-reversed), and positive and negative affect (MPQ-BF Social Closeness; Stress Reaction, Alienation). The resting concentration of tNAA in the dACC was robustly positively correlated with Absorption (r = +0.56, unadjusted p = .005), moderately positively correlated with Social Potency (r = +0.42, unadjusted p = .03), and robustly negatively correlated with Aggression (r = -0.59, unadjusted p = .003). Absorption and Aggression accounted for substantial variance in tNAA (R2 = 0.31, 0.35; combined R2 = 0.50), and survived correction for multiple comparisons (Holm-Bonferroni adjusted p = .032, 0.021, respectively). dACC Glx and Cho had modest relationships with behavioral flexibility and social affiliation that did not survive this multiple correction, providing effect sizes for future work. Principal Component Analysis (PCA) revealed a three-factor orthogonal solution indicating specific relationships between: 1) Glx and behavioral engagement; 2) Cho and affiliative bonding; and 3) tNAA and a novel dimension that we term neuroaffective reserves. Our results inform the neurobiology of agency and flexibility and lay the groundwork for understanding mechanisms of natural emotion using 1H-MRS.

On elliptic trigonometric form of the Zernike system and polar limits

The Zernike system provides orthogonal polynomial solution bases on the unit disk that separate in coordinates that are generically elliptic. This is a superintegrable system whose optical realization is a scalar wavefield on the plane of a circular pupil. Here we describe the solution set in the trigonometric form of elliptic coordinates expressed in terms of special functions, and examine closely the two limits where the explicit form of the wavefunctions in elliptic coordinates reduce to wavefunctions in polar coordinates.

A fourth-order orthogonal spline collocation solution to 1D-Helmholtz equation with discontinuity

In this paper, we use orthogonal spline collocation methods (OSCM) for the one dimensional Helmholtz equation with discontinuous coefficients. We discuss the existence uniqueness results and establish optimal error estimates. We use piecewise Hermite cubic basis functions to approximate the solution. Finally, we perform some numerical experiments and validate the theoretical results. Comparative to existing methods, we prove that the orthogonal spline collocation methods (OSCM) handles the discontinuous coefficients effectively and gives optimal order of convergence for $$\Vert y-y_h\Vert _{L^{\infty }}$$ -norm and superconvergent result for $$\Vert y'-y'_h\Vert _{L^{\infty }}$$ -norm at the grid points.

Approximate semi-analytical solution for a penny-shaped rough-walled hydraulic fracture driven by turbulent fluid in an impermeable rock

The popularity of high injection rate hydraulic fracturing treatments using low viscosity fluids is driving a need to consider the turbulent and laminar-turbulent transition regimes of fluid flow in hydraulic fracture simulators. The radial model is one of the most important geometries both for benchmarking and as a starter solution for 3D and Planar 3D models. Here we provide a semi-analytical, orthogonal polynomial series solution for a rough-walled radial (penny-shaped) hydraulic fracture driven by a fully turbulent fluid. Embedding the appropriate pressure singularities in a family of orthogonal polynomials used for derivation of the solution leads to very rapid convergence of the series, requiring just two terms for an accurate result. We conclude with an investigation of the occurrence of this limiting regime by comparison with numerical simulations, illustrating that the fully turbulent regime is typically not encountered for the radial geometry, although the present solution remains necessary as a starter solution and benchmark for the numerical simulators that are required to capture the laminar-turbulent transition. By comparison with numerical simulations that consider the laminar-turbulent transition, we find that such an estimate is expected to be sufficient for practical purposes when the inlet opening predicted by the turbulent solution exceeds the inlet opening predicted by the laminar solution.

Orthogonal Collocation Method of the Two-dimensional Burgers Equations

In this paper, the semi-discrete orthogonal collocation method for two-dimensional Burgers equations is considered. And the existence and uniqueness of orthogonal collocation solution is proved and the error estimate is obtained.

Calidad de vida relacionada con la salud: análisis factorial exploratorio del RAND-26 en mujeres de Buenos Aires

This study presents the adaptation and validation of the Rand-36 Item Health Survey 1.0 (RAND-26) in women aged between 18 and 65 from Buenos Aires. Regarding construct validity, an exploratory factor analysis was developed. A principal component analysis with orthogonal rotation solution (varimax) was performed. A two-factor structure (physical and mental) was the most parsimonious and theoretically appropriate. The Cronbach´s Alpha was excellent for the full-scale (? = .911) and very good for both components (physical component: ? = .873 and mental component: ? = .881). Concurrent validity indicators were also found. In conclusion, this local version of the instrument shows appropriate indicators of validity and internal consistency. It is a valid measure of health-related and perceived quality of life.

Linear Partial Divided-Difference Equation Satisfied by Multivariate Orthogonal Polynomials on Quadratic Lattices

In this paper, a fourth-order partial divided-difference equation on quadratic lattices with polynomial coefficients satisfied by bivariate Racah polynomials is presented. From this equation we obtain explicitly the matrix coefficients appearing in the three-term recurrence relations satisfied by any bivariate orthogonal polynomial solution of the equation. In particular, we provide explicit expressions for the matrices in the three-term recurrence relations satisfied by the bivariate Racah polynomials introduced by Tratnik. Moreover, we present the family of monic bivariate Racah polynomials defined from the three-term recurrence relations they satisfy, and we solve the connection problem between two different families of bivariate Racah polynomials. These results are then applied to other families of bivariate orthogonal polynomials, namely the bivariate Wilson, continuous dual Hahn and continuous Hahn, the latter two through limiting processes. The fourth-order partial divided-difference equations on quadratic lattices are shown to be of hypergeometric type in the sense that the divided-difference derivatives of solutions are themselves solution of the same type of divided-difference equations.

Symmetry and Solutions to the Helmholtz Equation Inside an Equilateral Triangle

Solutions to the Helmholtz equation within an equilateral triangle which solve either the Dirichlet or Neumann problem are investigated. This is done by introducing a pair of differential operators, derived from symmetry considerations, which demonstrate interesting relationships among these solutions. One of these operators preserves the boundary condition while generating an orthogonal solution and the other leads to a bijection between solutions of the Dirichlet and Neumann problems.

Photoluminescence and electroluminescence of cationic PtAu2 heterotrinuclear complexes with aromatic acetylides.

Cationic PtAu2 heterotrinuclear complexes [PtAu2(dpmp)2(C[triple bond, length as m-dash]CR)2]2+ (dpmp = bis(diphenylphosphinomethyl)phenylphosphine, R = aryl) of aromatic acetylides were prepared. The PtAu2 structures are supported through doubly bridging dpmp and stabilized by a significant Pt-Au interaction. They are highly phosphorescent in fluid CH2Cl2 solution (Φem = 23.5%-78.9%), the solid state (Φem = 15.4%-70.2%), the PMMA film (Φem = 39.9%-71.7%) and the doping film of 61% TCTA : 31% OXD-7 : 8% PtAu2 complex (Φem = 16.9%-67.9%). The phosphorescence arises mainly from 3[π (C[triple bond, length as m-dash]CR) → π* (dpmp)] 3LLCT and 3[π (C[triple bond, length as m-dash]CR) → s/p (PtAu2)] 3LMCT triplet excited states for carbazole-acetylide complexes, whereas other complexes display a 3LLCT character mixed with noticeable PtAu2 centered 3[d → s/p] parentage. Utilizing a mixed host composed of hole-transporting TCTA and electron-transporting OXD-7 doped with 8% PtAu2 species as a light-emitting layer and CuSCN as a hole-transporting layer through an orthogonal solution process, the devices exhibit highly efficient electrophosphorescence with the highest current efficiency (CEmax) of 51.7 cd A-1 and external quantum efficiency (EQEmax) of 14.5%. The efficiency roll-off is small in the practical brightness range of 500-5000 cd m-2. The PtAu2 complexes with carbazole-acetylides display a higher electroluminescence efficiency ascribed to their better hole-transporting character as well as more facile energy transfer from mixed host materials.

3D Metric-aligned and orthogonal solution adaptive mesh generation

A new 3D metric-orthogonal method for metric-based anisotropic tetrahedral mesh generation is presented. The approach uses an advancing-point type point placement that aligns the elements with the underlying metric field and creates quasi-structured local topology. It is based on well-proven methodology and adds novel point-placement strategies that produce solution-adapted anisotropic meshes that are optimal in size and alignment with the solution gradients upon which the metric field is based. The overall methodology is extended to 3D from a previously developed 2D process. Results for several analytical and actual CFD simulation examples are presented that demonstrate that aligned high-quality anisotropic tetrahedral meshes which are optimal for the solution process can be reliably generated.

The mechanics of intersecting echelon veins and pressure solution seams in limestone

Many studies that describe the formation of echelon vein arrays relate the causative stresses implicitly to the deformation, reliant on simple shear kinematics, such that the vein-to-array angle and the array width are the primary physical quantities. In contrast, we identify twelve physical quantities to describe echelon veins in two dimensions, including coeval, vein-intersecting, pressure solution seams. A finite element method is used to reproduce vein shapes in linear elastic and elastic-perfectly plastic model limestone. Model vein geometries are designed using values within the range of geometries measured from echelon veins at Raplee Anticline and Comb Monocline, Utah.Four physical quantities are significant for describing echelon vein shapes: vein spacing, vein-array angle, limestone elastic stiffness, and closing of orthogonal pressure solution seams. Pressure solution seam closing influences the mechanical interaction between adjacent veins, and for a range of conditions, causes a nearly linear vein opening distribution (triangular shapes) and encourages straight vein propagation, both of which approximate field measurements. Model results show that small spacing of veins with seams and large vein-array angles promote straight vein traces in limestone with stiffness typical of laboratory measurements, given the physical geologic conditions inferred from the burial history of the limestone strata.