Search Results (18)

After the interruption of the timing service, the increase in clock offset is a critical issue for the global navigation satellite system (GNSS)-disciplined oven-controlled crystal oscillator (OCXO). Current timekeeping methods for GNSS-disciplined OCXO have some drawbacks, such as high computational complexity, inadequate consideration of temperature effects, and insufficient separation of the impacts of temperature and aging. To address this issue, this study proposes a timekeeping method using a dual iterative algorithm. First, the external iteration separates the clock offset caused by temperature and aging. Then, the internal Gauss–Seidel iterative algorithm estimates the temperature and aging coefficients. During the timing service interruption phase, the model estimates and compensates for the frequency offset in real time using the coefficients. The proposed method demonstrates improved performance compared with OCXO in the free state and compensated by a second-order polynomial model, with better accuracy, drift rate, and long-term stability. The time offset is better than 4 μs over 24 h, representing an improvement of over 95% compared with the OCXO in the free state. Full article

Background: Given the lack of standardization in stimulus types for assessing accommodation, we aimed to evaluate accommodative response (AR) and Zernike coefficients using four different stimuli. Methods: Sixteen healthy subjects aged 22–32 years participated. Four black transilluminated stimuli (Snellen 6/12 “E”, 6/6 “e”, Maltese Cross 6/12 “X”, 6/6 “x”) were used to stimulate accommodation from 0 D to 5 D, in 1 D increments, using the irx3 aberrometer. From the results, AR was calculated with Seidel defocus and the change in Zernike coefficient value between the non-accommodative state and the fully accommodative state (5 D) was determined. Results: Larger pupils were observed with stimulus “E” (p-value < 0.05). The mean AR at the maximum accommodative level (5 D) for the different stimuli was −1.88 ± 1.00 for “E”, −2.60 ± 1.44 for “X”, −2.00 ± 1.32 for “e”, and −2.40 ± 1.27 for “x”. No statistically significant differences were found between AR and Zernike coefficients with the four different accommodative stimuli (p-value > 0.05, one-way ANOVA). Conclusions: The study evaluated accommodative stimulus design and size on AR and Zernike coefficients and found no significant differences. However, stimuli with higher spatial frequencies (“e” and “E”) provided larger ARs compared to the other stimuli. Full article

Assessment of the environmental impact of organic chemicals has become an important subject in chemical science. Efficient quantitative descriptors of their impact are their partition coefficients logP_ow, logK_oa and logK_aw. We present a group-additivity method that has proven its versatility for the reliable prediction of many other molecular descriptors for the calculation of the first two partition coefficients and indirectly of the third with high dependability. Based on the experimental logP_ow data of 3332 molecules and the experimental logK_oa data of 1900 molecules at 298.15 K, the respective partition coefficients have been calculated with a cross-validated standard deviation S of only 0.42 and 0.48 log units and a goodness of fit Q² of 0.9599 and 0.9717, respectively, in a range of ca. 17 log units for both descriptors. The third partition coefficient logK_aw has been derived from the calculated values of the former two descriptors and compared with the experimentally determined logK_aw value of 1937 molecules, yielding a standard deviation σ of 0.67 log units and a correlation coefficient R² of 0.9467. This approach enabled the quick calculation of 29,462 logP_ow, 27,069 logK_oa and 26,220 logK_aw values for the more than 37,100 molecules of ChemBrain’s database available to the public. Full article

In this paper, we develop a novel method to construct Goethals–Seidel (GS) sequences with special structures. In the existing methods, utilizing Turyn sequences is an effective and convenient approach; however, this method cannot cover all GS sequences. Motivated by this, we are devoted to designing some sequences that can potentially construct all GS sequences. Firstly, it is proven that a quad of $\pm 1$ polynomials can be considered a linear combination of eight polynomials with coefficients uniquely belonging to $\{0,\pm 1\}$. Based on this fact, we change the construction of a quad of Goethals–Seidel sequences to find eight sequences consisting of 0 and $\pm 1$. One more motivation is to obtain these sequences more efficiently. To this end, we make use of the k-block, of which some properties of (anti) symmetry are discussed. After this, we can then look for the sequences with the help of computers since the symmetry properties facilitate reducing the search range. Moreover, we find that one of the eight blocks, which we utilize to construct GS sequences directly, can also be combined with Williamson sequences to generate GS sequences with more order. Several examples are provided to verify the theoretical results. The main contribution of this work is in building a bridge linking the GS sequences and eight polynomials, and the paper also provides a novel insight through which to consider the existence of GS sequences. Full article

Solving various real-life problems ultimately requires solving systems of linear equations. However, the parameters involved in such real-life problems may be pervaded with uncertainty, which results in fuzzy parameters rather than crisp parameters. Intuitionistic fuzzy parameters are more suitable for some cases, since they allow us to tackle the feeling of fear or hesitation when making a decision. These are characteristics of human beings that occur when applying knowledge and skills. The intuitionistic fuzzy linear system (IFLS) resulting from real-life problem involves large number of equations and equally large number of unknowns. When IFLS is in matrix-vector form, the resulting coefficient matrix will have a sparse structure, which makes iterative methods necessary for their solution. In this paper, the known Gauss–Seidel and SOR iterative methods for solving linear system of equations are discussed, to the best of our knowledge for the first time, to solve (IFLS). The single parametric form representation of intuitionistic fuzzy numbers (IFN) makes it possible to apply these iterative techniques to IFLS. Finally, a problem of voltage input output in an electric circuit has been considered to show the applicability and the efficiency of these methods. Full article

Obtaining an approximation for the majority of sparse linear systems found in engineering and applied sciences requires efficient iteration approaches. Solving such linear systems using iterative techniques is possible, but the number of iterations is high. To acquire approximate solutions with rapid convergence, the need arises to redesign or make changes to the current approaches. In this study, a modified approach, termed the “third refinement” of the Gauss–Seidel algorithm, for solving linear systems is proposed. The primary objective of this research is to optimize for convergence speed by reducing the number of iterations and the spectral radius. Decomposing the coefficient matrix using a standard splitting strategy and performing an interpolation operation on the resulting simpler matrices led to the development of the proposed method. We investigated and established the convergence of the proposed accelerated technique for some classes of matrices. The efficiency of the proposed technique was examined numerically, and the findings revealed a substantial enhancement over its previous modifications. Full article

In a continuation and extension of an earlier publication, the calculation of the refractivity and polarizability of organic molecules at standard conditions is presented, applying a commonly applicable computer algorithm based on an atom group additivity method, where the molecules are broken down into their constituting atoms, these again being further characterized by their immediate neighbor atoms. The calculation of their group contributions, carried out by means of a fast Gauss–Seidel fitting calculus, used the experimental data of 5988 molecules from literature. An immediate subsequent ten-fold cross-validation test confirmed the extraordinary accuracy of the prediction of the molar refractivity, indicated by a correlation coefficient R² and a cross-validated analog Q² of 0.9997, a standard deviation σ of 0.38, a cross-validated analog S of 0.41, and a mean absolute deviation of 0.76%. The high reliability of the predictions was exemplified with three classes of molecules: ionic liquids and silicon- and boron-containing compounds. The corresponding molecular polarizabilities were calculated indirectly from the refractivity using the inverse Lorentz–Lorenz relation. In addition, it could be shown that there is a close relationship between the “true” volume and the refractivity of a molecule, revealing an excellent correlation coefficient R² of 0.9645 and a mean absolute deviation of 7.53%. Full article

A novel computational approach is developed to investigate the mixed convection, boundary layer flow over a nonlinear elastic (stretching or shrinking) surface. The viscous fluid is electrically conducting, incompressible, and propagating through a porous medium. The consequences of viscous dissipation, Joule heating, and heat sink/source of the volumetric rate of heat generation are also included in the energy balance equation. In order to formulate the mathematical modeling, a similarity analysis is performed. The numerical solution of nonlinear differential equations is accomplished through the use of a robust computational approach, which is identified as the Spectral Local Linearization Method (SLLM). The computational findings reported in this study show that, in addition to being simple to establish and numerically implement, the proposed method is very reliable in that it converges rapidly to achieve a specified goal and is more effective in resolving very complex models of nonlinear boundary value problems. In order to ensure the convergence of the proposed SLLM method, the Gauss–Seidel approach is used. The SLLM’s reliability and numerical stability can be optimized even more using Gauss–Seidel approach. The computational results for different emerging parameters are computed to show the behavior of velocity profile, skin friction coefficient, temperature profile, and Nusselt number. To evaluate the accuracy and the convergence of the obtained results, a comparison between the proposed approach and the bvp4c (built-in command in Matlab) method is presented. The Matlab software, which is used to generate machine time for executing the SLLM code, is also displayed in a table. Full article

A tomographic microscopy system can achieve instantaneous three-dimensional imaging, and this type of microscopy system has been widely used in the study of biological samples; however, existing chromatographic microscopes based on off-axis Fresnel zone plates have degraded image quality due to geometric aberrations such as spherical aberration, coma aberration, and image scattering. This issue hinders the further development of chromatographic microscopy systems. In this paper, we propose a method for the design of an off-axis Fresnel zone plate with the elimination of aberrations based on double exposure point holographic surface interference. The aberration coefficient model of the optical path function was used to solve the optimal recording parameters, and the principle of the aberration elimination tomography microscopic optical path was verified. The simulation and experimental verification were carried out utilizing a Seidel coefficient, average gradient, and signal-to-noise ratio. First, the aberration coefficient model of the optical path function was used to solve the optimal recording parameters. Then, the laminar mi-coroscopy optical system was constructed for the verification of the principle. Finally, the simulation calculation results and the experimental results were verified by comparing the Seidel coefficient, average gradient, and signal-to-noise ratio of the microscopic optical system before and after the aberration elimination. The results show that for the diffractive light at the orders 0 and ±1, the spherical aberration W040 decreases by 62–70%, the coma aberration W131 decreases by 96–98%, the image dispersion W222 decreases by 71–82%, and the field curvature W220 decreases by 96–96%, the average gradient increases by 2.8%, and the signal-to-noise ratio increases by 18%. Full article

The calculation of the heats of combustion ΔH°_c and formation ΔH°_f of organic molecules at standard conditions is presented using a commonly applicable computer algorithm based on the group-additivity method. This work is a continuation and extension of an earlier publication. The method rests on the complete breakdown of the molecules into their constituting atoms, these being further characterized by their immediate neighbor atoms. The group contributions are calculated by means of a fast Gauss–Seidel fitting calculus using the experimental data of 5030 molecules from literature. The applicability of this method has been tested by a subsequent ten-fold cross-validation procedure, which confirmed the extraordinary accuracy of the prediction of ΔH°_c with a correlation coefficient R² and a cross-validated correlation coefficient Q² of 1, a standard deviation σ of 18.12 kJ/mol, a cross-validated standard deviation S of 19.16 kJ/mol, and a mean absolute deviation of 0.4%. The heat of formation ΔH°_f has been calculated from ΔH°_c using the standard enthalpies of combustion for the elements, yielding a correlation coefficient R² for ΔH°_f of 0.9979 and a corresponding standard deviation σ of 18.14 kJ/mol. Full article

Commonly based on the liquid diffusion theory, drying theoretical studies in porous materials has been directed to plate, cylinder, and sphere, and few works are applied to non-conventional geometries. In this sense, this work aims to study, theoretically, the drying of solids with oblate spheroidal geometry based on the thermodynamics of irreversible processes. Mathematical modeling is proposed to describe, simultaneously, the heat and mass transfer (liquid and vapor) during the drying process, considering the variability of the transport coefficients and the convective boundary conditions on the solid surface, with particular reference to convective drying of lentil grains at low temperature and moderate air relative humidity. All the governing equations were written in the oblate spheroidal coordinates system and solved numerically using the finite-volume technique and the iterative Gauss–Seidel method. Numerical results of moisture content, temperature, liquid, vapor, and heat fluxes during the drying process were obtained, analyzed, and compared with experimental data, with a suitable agreement. It was observed that the areas near the focal point of the lentil grain dry and heat up faster; consequently, these areas are more susceptible to the appearance of cracks that can compromise the quality of the product. In addition, it was found that the vapor flux was predominant during the drying process when compared to the liquid flux. Full article

The calculation of the vapour pressure of organic molecules at 298.15 K is presented using a commonly applicable computer algorithm based on the group-additivity method. The basic principle of this method rests on the complete breakdown of the molecules into their constituting atoms, further characterized by their immediate neighbour atoms. The group contributions are calculated by means of a fast Gauss–Seidel fitting algorithm using the experimental data of 2036 molecules from literature. A ten-fold cross-validation procedure has been carried out to test the applicability of this method, which confirmed excellent quality for the prediction of the vapour pressure, expressed in log(pa), with a cross-validated correlation coefficient Q² of 0.9938 and a standard deviation σ of 0.26. Based on these data, the molecules’ standard Gibbs free energy ΔG°_vap has been calculated. Furthermore, using their enthalpies of vaporization, predicted by an analogous group-additivity approach published earlier, the standard entropy of vaporization ΔS°_vap has been determined and compared with experimental data of 1129 molecules, exhibiting excellent conformance with a correlation coefficient R² of 0.9598, a standard error σ of 8.14 J/mol/K and a medium absolute deviation of 4.68%. Full article

Aberrations and the image quality of holographic lenses were evaluated by a Hartmann–Shack (HS) wavefront sensor. Two lenses, one recorded with a symmetrical configuration and the other with an asymmetrical one, were stored in a photopolymer called Biophotopol. Each was reconstructed with two different wavelengths, 473 nm and 633 nm. Different metrics were applied to determine and quantify the aberration of the lenses (Zernike coefficients, Seidel coefficients, Marechal tolerances, root-mean-square (RMS), peak to valley, critical fraction of the pupil), and the quality of the image they provided (Strehl ratio, entropy, cutoff frequency, modulation transfer function (MTF), and area under the MTF). Good agreement between the metrics related to optical quality was obtained. The negative asymmetric holographic lenses had less aberration than the positive symmetric ones. Full article

The purpose of this paper is to discuss the variation of wellbore temperature and bottom-hole pressure with key factors in the case of coupled temperature and pressure under multi-pressure system during deep-water drilling circulation. According to the law of energy conservation and momentum equation, the coupled temperature and pressure calculation model under multi-pressure system is developed by using the comprehensive convective heat transfer coefficient. The model is discretized and solved by finite difference method and Gauss Seidel iteration respectively. Then the calculation results of this paper are compared and verified with previous research models and field measured data. The results show that when the multi-pressure system is located in the middle formation, the temperature of the annulus corresponding to location of the system is the most affected, and the temperature of the other areas in annulus is hardly affected. However, when the multi-pressure system is located at the bottom hole, the annulus temperature is greatly affected from bottom hole to mudline. In addition, the thermo-physical parameters of the drilling fluid can be changed by overflow and leakage. When only overflow occurs, the annulus temperature increases the most, but the viscosity decreases the most. When only leakage occurs, the annulus temperature decreases the most and the viscosity increases the most. However, when the overflow rate is greater than the leakage rate, the mud density and bottom-hole pressure increase the most, and both increase the least when only leakage occurs. Meanwhile, bottom-hole pressure increases with the increase of pump rate but decreases with the increase of inlet temperature. The research results can provide theoretical guidance for safe drilling in complex formations such as multi-pressure systems. Full article

The relationship between pollutant discharge and economic growth has been a major research focus in environmental economics. To accurately estimate the nonlinear change law of China’s pollutant discharge with economic growth, this study establishes a transformed nonlinear grey multivariable (TNGM (1, N)) model based on the nonlinear least square (NLS) method. The Gauss–Seidel iterative algorithm was used to solve the parameters of the TNGM (1, N) model based on the NLS basic principle. This algorithm improves the precision of the model by continuous iteration and constantly approximating the optimal regression coefficient of the nonlinear model. In our empirical analysis, the traditional grey multivariate model GM (1, N) and the NLS-based TNGM (1, N) models were respectively adopted to forecast and analyze the relationship among wastewater discharge per capita (WDPC), and per capita emissions of SO₂ and dust, alongside GDP per capita in China during the period 1996–2015. Results indicated that the NLS algorithm is able to effectively help the grey multivariable model identify the nonlinear relationship between pollutant discharge and economic growth. The results show that the NLS-based TNGM (1, N) model presents greater precision when forecasting WDPC, SO₂ emissions and dust emissions per capita, compared to the traditional GM (1, N) model; WDPC indicates a growing tendency aligned with the growth of GDP, while the per capita emissions of SO₂ and dust reduce accordingly. Full article