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The comment disputes some of the inferences in the paper "Helmert Transformation Problem. From Euler Angles Method to Quaternion Algebra", published in this journal. The key points in the dissent are the following: (1) The number of unknown parameters in the reverse transformation problem using dual quaternions. (2) The reliability of both data and the results. (3) There should be no differences between Euler angles and quaternion methods. Our response is summarized as follows: (1) The problem can be solved using either eight or nine unknown parameters. (2) All the data and results are real. (3) There should be differences between methods because of different calculations. [ABSTRACT FROM AUTHOR]

We investigate the cosmological evolution of the universe for a spatially flat FLRW background space within the context of f (T , B) gravity, which is a recently formulated teleparallel theory that connects both f (T) and f (R) gravity under suitable limits. The analysis focuses on four different f (T , B) cosmological models corresponding to various choices of scale factor, namely, emergent, logamediate, and intermediate. In addition to this, we assume a power law-like function of f (T , B) gravity. The reconstruction of f (T , B) gravity considers the Holographic Ricci Dark Energy (HRDE) as the background fluid. We analyze the equation of state parameters and the squared speed of sound for the reconstructed models. Finally, we conduct a thermodynamical analysis for each reconstructed model. The generalized second law of thermodynamics (GSLT) is valid for the four different f (T , B) cosmological models. [ABSTRACT FROM AUTHOR]

In geotechnical engineering, a scale factor “n” is a numerical ratio that relates the physical properties of a physical model to those of a prototype. The effect of scale factor on the dynamic response of a frame foundation used for high-speed turbo machines is examined through numerical analyses to clarify the influence of scaling dimensions, frequency, static and dynamic loads, and scaled models’ material on the dynamic responses of the frame foundation. The static and dynamic analyses were conducted using Ansys Workbench software. The total number of analyses used to investigate the scale factor effect was 28. Both modal and harmonic analyses were performed to calculate the natural frequencies and displacement responses of the scaled and prototype models under the scaled dynamic loading. Five scale factors were used in this study for concrete models (1, 20, 25, 32, and 40), and two additional analyses on steel models of scale (1 and 20) were used to study the material scaling. The prototype results were first verified, and then the models were investigated after scaling the dynamic loads and dimensions. The results of this study revealed the importance of scaling the frequency when studying the high-speed turbo machine foundation models to reflect the correct responses of the prototype foundation.

We investigate the cosmological evolution of the universe for a spatially flat FLRW background space within the context of f(T,B) gravity, which is a recently formulated teleparallel theory that connects both f(T) and f(R) gravity under suitable limits. The analysis focuses on four different f(T,B) cosmological models corresponding to various choices of scale factor, namely, emergent, logamediate, and intermediate. In addition to this, we assume a power law-like function of f(T,B) gravity. The reconstruction of f(T,B) gravity considers the Holographic Ricci Dark Energy (HRDE) as the background fluid. We analyze the equation of state parameters and the squared speed of sound for the reconstructed models. Finally, we conduct a thermodynamical analysis for each reconstructed model. The generalized second law of thermodynamics (GSLT) is valid for the four different f(T,B) cosmological models.

Copyright of Journal of Geodesy & Geodynamics (1671-5942) is the property of Editorial Board Journal of Geodesy & Geodynamics and its content may not be copied or emailed to multiple sites or posted to a listserv without the copyright holder's express written permission. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract. (Copyright applies to all Abstracts.)

The scale factor serves as a ruler for converting raw phase measurements into physical displacements and significantly impacts the preprocessing of data from the Laser Ranging Interferometer (LRI) in laser ranging systems. In the current GRACE Follow-On (GRACE-FO) mission for low–low tracking gravity satellites, most of the existing LRI scale factor estimation algorithms heavily rely on cross-calibration between instantaneous/biased ranges from the Ka-Band Ranging Interferometer (KBR) and the LRI. However, due to the nonlinearity of the objective function (which includes terms involving the product of scale and time shifts), the scale factor estimation may absorb errors from timing noise. Moreover, future gravity missions or gravity detection tasks may no longer incorporate KBR ranging instruments. To address these challenges, this paper proposes an energy-based method for scale factor estimation using inter-satellite baseline solutions. Comparative analysis indicates that the proposed method effectively disentangles two parameters in the objective function and can be applied in scenarios where KBR data are unavailable, demonstrating promising prospects for practical application. The experimental results show that when the KBR validation residuals are lower than 0.8 mm, the SYSU LRI1B V01 products exhibit residuals below the payload design accuracy thresholds in the frequency band of 2 mHz to 0.1 Hz. Additionally, the stability of the scale factors obtained from the baseline can reach 10−7. Although this is still below the required precision of better than 10−8 for the laser frequency stability in next-generation gravity satellites, advancements in orbit determination technology and the enhanced stability of GPS receivers offer potential for future precision improvements. Currently, this method appears suitable for roughly extracting the scale factor as a stochastic mean over several months or serving as a backup validation strategy for future missions, but it is not well suited to measure day-to-day variations. [ABSTRACT FROM AUTHOR]

A Friedmann–Lemaitre–Robertson–Walker space–time model with all curvatures k = 0 ,   ± 1 is explored in f (R , T) gravity, where R is the Ricci scalar, and T is the trace of the energy–momentum tensor. The solutions are obtained via the parametrization of the scale factor that leads to a model transiting from a decelerated universe to an accelerating one. The physical features of the model are discussed and analyzed in detail. The study shows that f (R , T) gravity can be a good alternative to the hypothetical candidates of dark energy to describe the present accelerating expansion of the universe. [ABSTRACT FROM AUTHOR]

In this paper, we investigate in this paper the Type IV singular bouncing in the framework of f (R ,) theory of gravity where R and mean the curvature scalar and the Gauss–Bonnet invariant, respectively. Cosmological f (R ,) models constrained by the slow-roll evolution is reconstructed and their explicit forms are provided near the bounce and far away from it. One obtains finally two models whose stability is numerically analyzed in this work. Our results show that the stability of the reconstructed models is very affected by their parameters. The model far from the singularity recovers stability quickly than the model near the singularity. [ABSTRACT FROM AUTHOR]

This study proposes a universal adaptive control algorithm for an unknown multi-input multi-output (MIMO) system using recursive least squares (RLS) and parameter self-tuning. The issue of adjusting the control and system parameters in response to changes in the platform was discussed. The development of a control algorithm that can consistently achieve reliable and robust control performance in various systems is important. This study aimed to develop a control algorithm that can track the reference value for any unknown MIMO system. For the controller design, an nth-order differential error dynamic model was designed, and an RLS with a scale factor was used to estimate the coefficients of the error dynamics. In the current scenario, the numbers of control inputs and error states in the error dynamics were assumed to be equal. It was designed such that the control input is derived based on the Lyapunov stability concept using the estimated coefficients. The scale factor in the RLS and injection term in the control input based on the sliding-mode approach were computed using a self-tuning methodology. The performance of the proposed universal adaptive control algorithm was evaluated using an actual DC motor and CarMaker (version 8.1.1) software tests under various scenarios. [ABSTRACT FROM AUTHOR]

This paper considering two buildings different in height as a case study to inquiries into the effect of recorded and spectrally matched ground motions (simulated ground motion). Model of structures are developed using design procedure of Chapter 12 of ASCE 7-22 and linear analysis is adopted using requirements of Chapter 16 of ASCE 7-22. In this study, the effects of recorded and simulated ground motions on drift distribution and also floor acceleration are investigated. It could be seen that all of the structures, when subjected to simulated ground motions, give acceptable performance, even though this is not the case with amplitude-scaled ground motions. [ABSTRACT FROM AUTHOR]

The numerous factors that influence the technological process and cause errors during manufacture of parts complicate the problem of ensuring the required accuracy of required dimensions. The article proposes a method for determining coefficients of simulation models using probabilistic statistical methods, the versatility of which makes them applicable to a wide range of problems. [ABSTRACT FROM AUTHOR]

Copyright of Micronanoelectronic Technology is the property of Micronanoelectronic Technology Editorial Office and its content may not be copied or emailed to multiple sites or posted to a listserv without the copyright holder's express written permission. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract. (Copyright applies to all Abstracts.)

In order to explore the formation mechanism of corrugation in railway systems, the corrugation phenomenon is analyzed in detail from points of view of micro contact and material wear using the self-designed scale twin discs test rig. The results show that the longitudinal creep force is not a sufficient condition for corrugation formation, and the transverse creep force is indeed an important condition. Considering the scale factor (1:4) of the test model, it can be obtained that the passing frequency of corrugation on the rail wheel surface of 1700.78 Hz corresponds to the passing frequency of corrugation in the actual system of 425.20 Hz. Due to the frequency-fixed characteristic of corrugation, the above frequency is consistent with the line measurement results in the relevant literatures. The stick-slip analysis shows that the transverse slip of 0.0084∼0.3437 mm is greater than the longitudinal one of 0.0003∼0.1205 mm in the contact area. Combining experimental tests with the numerical analysis, it can be concluded that the theoretical mechanism of corrugation formation is that under the condition of transverse creep force saturation, the unstable vibration at a specific frequency causes the wear to have the frequency-fixed characteristic and eventually form corrugation, and the transverse wear has a greater influence on the evolution of corrugation. [ABSTRACT FROM AUTHOR]

The annular array Airy beam (AAAB) possesses excellent optical properties, and it exhibits great potential in optical particle manipulation, light bullet, and so on. When the power of the laser system is relatively high, the B-integral greatly affects the generation and transmission of AAABs. We numerically study the nonlinear propagation of AAABs based on the Schrödinger equation. The variation of the maximum peak intensity of the AAAB with the nonlinear coefficient at different parameters are discussed. The influence of the truncation coefficient, lateral offsets, scale factor, and rotation factor on the AAAB affected by B-integral are also taken into consideration. We show that the AAAB gradually evolves into solitons in the transmission process as the nonlinear coefficient increases. The intensity of AAAB is altered due to the B-integral, and the effect of the B-integral on the transmission of the AAAB cannot be ignored. The research results will be a great boost to the application of the AAAB in biomedicine, particle manipulation, and various other fields. [ABSTRACT FROM AUTHOR]

This study aims to statistically analyze wind speed data of Tarnab, Peshawar, for the period 2004-2023. The data was recorded at the Agriculture Research Institute, Tarnab, Peshawar. Two statistical models (two-parameter Weibull and Rayleigh distribution functions) were applied to find the distributions of wind speeds. For the estimation of shape and scale parameters of Weibull and Rayleigh, two methods were employed: the method of moments and the energy pattern factor. Three statistical tools (mean percentage error, mean absolute percentage error, and root mean square deviation) were applied to check the error percentage of both models. The results of the Weibull distribution were much closer to the observed data than those of the Rayleigh distribution. The average values of wind speeds tended to increase from winter to summer and vice versa. The highest recorded annual and seasonal wind speeds were 26.19 in/s and 41.57 in/s, respectively, while the lowest values were 7.11 in/s and 4.95 in/s, respectively. Thus, while ruling out the possibility of harnessing wind as a significant source of energy, the findings are still useful for the crops produced in the region.

The comment disputes some of the inferences in the paper “Helmert Transformation Problem. From Euler Angles Method to Quaternion Algebra”, published in this journal. The key points in the dissent are the following: (1) The number of unknown parameters in the reverse transformation problem using dual quaternions. (2) The reliability of both data and the results. (3) There should be no differences between Euler angles and quaternion methods. Our response is summarized as follows: (1) The problem can be solved using either eight or nine unknown parameters. (2) All the data and results are real. (3) There should be differences between methods because of different calculations.

The present study investigates the Friedmann–Lemaitre–Robertson–Walker models (often FLRW models) with time varying G and Λ in the general theory of relativity. In this communication the Einstein field equations have been solved by considering the deceleration parameter q(t) as a varying function of time t and the Hubble parameter H defined as q = - l (t - t 0) + β - 1 and q = - 1 + 2 α (H - 1) H , where l , t 0 , β , α are non-negative constants. We have analyzed the values of different constants that will generate a transition for the universe from an early decelerating phase to a recent acceleration phase. The physical and graphic behaviour have also been planned to study in this communication. [ABSTRACT FROM AUTHOR]

Copyright of Computer Measurement & Control is the property of Magazine Agency of Computer Measurement & Control and its content may not be copied or emailed to multiple sites or posted to a listserv without the copyright holder's express written permission. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract. (Copyright applies to all Abstracts.)

Traditional methods of orthogonal basis function decomposition have been extensively used to detect magnetic anomaly signals. However, the determination of the relative velocity between the detection platform and the magnetic target remains elusive in practical detection. And, the non-ideal uniform motion of the magnetic target further complicates the process and adversely impacts the detector's performance. To address this challenge, this paper introduces an adaptive scale factor method based on orthogonal basis function decomposition. This new method can be used to adjust the relative velocity between the detection platform and the magnetic target and to refine the characteristic time in the basis functions. In this paper, a mathematical relationship between the scale factor and the relative velocity is established, which is subsequently fitted into a Gauss function curve. The optimal scale factor, denoted as β, is adaptively chosen from the fitting curve when the magnetic target moves at a non-ideal uniform velocity with an unknown motion state. The results of simulations indicate that the scale factor improves the signal-to-noise ratio of the magnetic anomaly signals in a non-ideal state. And, this method can improve the energy value of OBF decomposition by 17.7%. Simultaneously, this method ensures that the moment the magnetic target passes the CPA coincides with the energy peak of the orthogonal basis detection, which improves the accuracy by 54.1% compared with the traditional method. The effectiveness and precision of the proposed method are verified using simulations and practical experiments. [ABSTRACT FROM AUTHOR]

An anastomosing river is a stable multiple-channel system separated by inter-channel wetlands, and there are serious difficulties in observing the hydrodynamics of such river patterns in situ. Therefore, there are few reports on the hydrodynamic data of such rivers, for example, the upper Columbia and Pearl Rivers. In order to obtain the hydrodynamic parameter values at flow cross-sections of anastomosing rivers, without having to observe hydraulic radius, this study proposes a method called the Expression of Channel Morphological Parameters (ECMP) for hydrodynamic estimation. The calculation formula of the ECMP method is based on the shape factor (width–depth ratio), scale factor (mean depth), and gradient factor of the channel cross-sections of anastomosing rivers below a given water level as independent variables. This method can be used to calculate the mean velocity, discharge, specific stream power, and gross stream power of the flow cross-section at different water levels, only requiring the measurements of channel morphological parameters such as the mean depth, width–depth ratio, and gradient at the channel cross-section below the corresponding water level. The applicability of the ECMP method was verified using measured hydrological data. The results showed that the ECMP method is a practical estimation method with higher accuracy that is convenient for calculating the hydrodynamic parameters of anastomosing rivers. It can also be used to reconstruct ancient anastomosing rivers using the channel morphological parameters revealed from the fill sediments in ancient channels. [ABSTRACT FROM AUTHOR]

This study focuses on the cosmological evolution of Barrow holographic dark energy (BHDE) in a flat FLRW-universe. We take into account a time-dependent scale factor a (t) = [ sinh (k t) ] 1 n , where k and n are positive values, to find the solutions to field equations. This scale factor results in a smooth transition of the universe from its previous decelerating stage to its most recent accelerating stage. Using the Granda–Oliveros cut-off, we examine the chronology of the deceleration parameter, equation of state parameter, and density parameter, and we analyze the positive aspects of the BHDE model. Negative pressure values in this model suggest dark energy dominance, resulting in the universe's acceleration. We use the statefinder parameters (r , s) to improve the accuracy of the results of the dark energy model that is similar to the Λ -CDM model. [ABSTRACT FROM AUTHOR]

Abstract—The effect of the scale factor on the elastic modulus determined by instrumented indentation in the elastic and elastoplastic regions of indentation diagrams has been studied. A significant increase in the elastic modulus has been established upon transition to micro- and nanoscale indentation. The reasons for the effect of the scale factor on the elastic modulus determined by instrumented indentation are outlined. [ABSTRACT FROM AUTHOR]

A revived figure of teenage Albert Einstein is confronted at the threshold of the second millennium with a problem of a graphical likeness of the Lambert W function-based cosmological equations to a logarithmic-exponential discontinuous function that he has just plotted. To puzzle the issue out his mind is put onto an imaginary mathematical-philosophical-physical trail ride around the Universe. Euler’s identity that he invited to ride pillion on his Pegasus of Imagination spanks the cavalier’s horse to carry him on wings of Leibniz’ zero-nothingness unity-infiniteness array towards a non-Euclidean landscape of novel cosmological equations – which describe behaviour of principal cosmological parameters as an exclusive function of the scale factor. Zero, unity, p, and Euler’s number become in the rider’s eyes a quaternion of linesmen – and the imaginary unit the one who as a chief referee opens and controls on the space-time playground a collective mass-energy game. And while the young cavalier observes from a horseback of his mount that within the playground expansion the cosmic match is running into the order of timelessness and spacelessness the Universe with all of its ever existing forms and events, thoughts and memories, unveils to him its all-encompassing face of eternity and immortality attributable to God.

The scale factor serves as a ruler for converting raw phase measurements into physical displacements and significantly impacts the preprocessing of data from the Laser Ranging Interferometer (LRI) in laser ranging systems. In the current GRACE Follow-On (GRACE-FO) mission for low–low tracking gravity satellites, most of the existing LRI scale factor estimation algorithms heavily rely on cross-calibration between instantaneous/biased ranges from the Ka-Band Ranging Interferometer (KBR) and the LRI. However, due to the nonlinearity of the objective function (which includes terms involving the product of scale and time shifts), the scale factor estimation may absorb errors from timing noise. Moreover, future gravity missions or gravity detection tasks may no longer incorporate KBR ranging instruments. To address these challenges, this paper proposes an energy-based method for scale factor estimation using inter-satellite baseline solutions. Comparative analysis indicates that the proposed method effectively disentangles two parameters in the objective function and can be applied in scenarios where KBR data are unavailable, demonstrating promising prospects for practical application. The experimental results show that when the KBR validation residuals are lower than 0.8 mm, the SYSU LRI1B V01 products exhibit residuals below the payload design accuracy thresholds in the frequency band of 2 mHz to 0.1 Hz. Additionally, the stability of the scale factors obtained from the baseline can reach 10−7. Although this is still below the required precision of better than 10−8 for the laser frequency stability in next-generation gravity satellites, advancements in orbit determination technology and the enhanced stability of GPS receivers offer potential for future precision improvements. Currently, this method appears suitable for roughly extracting the scale factor as a stochastic mean over several months or serving as a backup validation strategy for future missions, but it is not well suited to measure day-to-day variations.

A Friedmann–Lemaitre–Robertson–Walker space–time model with all curvatures k=0, ±1 is explored in f(R,T) gravity, where R is the Ricci scalar, and T is the trace of the energy–momentum tensor. The solutions are obtained via the parametrization of the scale factor that leads to a model transiting from a decelerated universe to an accelerating one. The physical features of the model are discussed and analyzed in detail. The study shows that f(R,T) gravity can be a good alternative to the hypothetical candidates of dark energy to describe the present accelerating expansion of the universe.

The article presents studies of the influence of scale factor on the strength properties of artificial leathers. The method of simulation modeling enables to determine general patterns of influence of linear dimensions of surface-retentive materials on their strength properties. Simulation was performed by the type and parameter of the law of distribution of the breaking load for specimens consisting of one section, the breaking load of which along the length is constant. In order to identify the influence of the geometric dimensions of the sample on the average value of its breaking load, the same experiments were simulated for man-made leather samples with variable length and width. In order to experimentally verify the preliminary conclusions, an experimental evaluation of the breaking load of artificial leather at various geometric dimensions was carried out. The object of the study was double-layered man-made leather, item Hongxin 11022-16. Sample thickness of 0.9 mm, surface density is 435 g/m2. Tests were conducted using TIME WDW-5 universal testing machine on samples of rectangular shape. As a result of this research, the possibility of practical use of the test simulation method for studying the influence of the scale factor on the strength properties of man-made leather was shown. Цель работы – оценка влияния масштабного фактора на прочностные характеристики искусственных кож, путем использования метода имитационного моделирования, применение которого позволяет выявить общие закономерности влияния линейных размеров поверхностно-протяженных материалов на их прочностные характеристики. Осуществлено моделирование испытаний с учетом вида и параметра закона распределения разрывной нагрузки для образцов, состоящих из некоторого числа n структурных элементов по длине и некоторого числа m структурных элементов по ширине образца. Для выявления влияния геометрических размеров образца на среднее значение его разрывной нагрузки проводилось моделирование таких же экспериментов для образцов искусственной кожи с переменной длиной и шириной. С целью проверки предварительных выводов была произведена экспериментальная оценка разрывной нагрузки искусственной кожи при разных геометрических размерах пробы. В качестве объекта исследования была выбрана двухслойная искусственная кожа артикула Hongxin 11022-16. Испытания проводились с помощью универсальной испытательной машины TIME WDW-5 на пробах прямоугольной формы. В результате проведенных исследований показана возможность практического использования метода имитационного моделирования испытаний для изучения влияния масштабного фактора на прочностные характеристики искусственной кожи.

Magnetic field gradients interfere with the coherence of the atomic ensemble and degrade the performance of the spin-exchange relaxation-free (SERF) atomic magnetometer. In this paper, the influence of magnetic field gradients is incorporated into the response model of single-beam atomic magnetometer, and the theoretical models of transverse relaxation rate, spin polarization and scale factor are established. Based on this model, we find that magnetic field gradients in different directions can cause varying degrees of degradation in the performance parameters of the magnetometer. The magnetic linewidths under different light power and magnetic field gradients are measured using the designed dedicated magnetic field gradients coils, and the spin polarization and magnetic field gradients relaxation rate are obtained through fitting. An unevenness and deviation of the curve are also observed in the experiments, indicating the presence of the magnetic field gradient of approximately 2 nT/cm in the magnetic shields. Furthermore, in a magnetic field gradient environment of 20 nT/cm, the mean of the long-term sensitivity decreased by 3.5 times and the standard deviation increased by 11 times. It shows that the magnetic field gradients will not only affect the signal-to-noise ratio, but also make the magnetometer more vulnerable to external interference when working. The sensitivity and stability of magnetometer will be greatly reduced. The research in this article provides a theoretical and experimental basis for eliminating the influence of magnetic field gradients and improving the accuracy of magnetic field measurements.

This study proposes a method to determine the location, magnitude, and sequence of line heating to form a target shape using the strain directed as boundary (SDB) method. The analysis model was constructed by considering the phase transformation caused by line heating. The results of the analytical model were compared with the experimental results. The deformation at an arbitrary heating location and heating magnitude was calculated using a verified model. The locations and magnitudes were determined by optimization. The deformation reflecting the optimization result confirmed an error of 5.91 % compared to the experimental results. The scale factor for the optimal heating sequence was determined via optimization by line heating sequence. The deformations caused by the heating sequence of the concave and saddle shapes confirmed errors of 7.04 % and 8.59 %, respectively. The proposed method provides guidelines for heat forming. [ABSTRACT FROM AUTHOR]

Copyright of Engineering Mechanics / Gongcheng Lixue is the property of Engineering Mechanics Editorial Department and its content may not be copied or emailed to multiple sites or posted to a listserv without the copyright holder's express written permission. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract. (Copyright applies to all Abstracts.)

The results of studying the effect of filamentary striae with birefringence 3 to 15 nm/cm in sitall [glass-ceramic] SO-115M on the quality of manufacturing of optical components of ring lasers and the accuracy characteristics of laser gyroscopes based on them are presented. It is shown that the presence of streaks with stresses not exceeding 15 nm/cm in sitall SO-115M does not affect the manufacturing accuracy of the resonator optical circuit and its assembly quality. The streaks in the output mirror of a ring laser serve as a source of additional backscattering and can increase the lock-in zone width. Proper adjustment of the output mirror makes it possible to reduce the amount of scattering and minimize the growth of the lock-in zone in a laser gyroscope. It is shown that the accuracy of a laser gyroscope is determined by the quality of the mirror substrates, the body geometry, and the level of backscattering inside the resonator. [ABSTRACT FROM AUTHOR]

Objectives: The high-precision registration of point cloud data is the key to ensure the integrity of 3D data on the surface of spatial objects. To address the problem that there are differences in position, attitude and scale of cloud data from neighboring stations, a method is proposed to solve the registration model of point cloud described by the dual quaternion under the constraints of point-planar feature. Methods: First, the rotation matrix and translation vector of the spatially similar transformation are represented by the dual quaternion, based on which the scale factor is taken into account and the vertical and parallel spatial topological relationships exist between the vectors constructed by the points in the plane and the points out of the plane respectively and the normal vectors of the plane, and this is used as the constraint of the spatially similar transformation to construct the parity model based on the least squares criterion. Then the Levenberg-Marquardt method is introduced to solve the level-difference model to avoid the possible non-convergence of the iterations in the level-difference treatment due to the inappropriateness of the initial values or due to the fact that the real symmetric matrix constructed by the Jacobi matrix is close to singularity. Result: Two sets of experiments are compared and analyzed with the existing methods, and the experimental results show that the proposed method can effectively achieve point cloud registration. Conclusions: Therefore, the method that takes into account the scale factor under the point-planar feature constraint and uses the dual quaternion to realize the spatial similarity transformation has a strong practical value. [ABSTRACT FROM AUTHOR]

The present paper reports a study on bounce realization with a truncated scale factor and the holographic fluid taken in the form of holographic Ricci Dark Energy, which is a particular case of holographic Nojiri–Odintsov model (Nojiri & Odintsov, 2006, Gen. Relativ. Gravit., 38(8), 1285). We have investigated the realization of bounce due to the application of a holographic fluid in the early scenario of the universe. We started with a de‐Sitter scale factor in our study and derived two modified forms using Taylor's series expansion. After studying the behavior of the resulting Hubble parameter, we identified a(t)=a01+H0(t−t0)+H022(t−t0)2$$ a(t)={a}_0\left(1+{H}_0\left(t-{t}_0\right)+\frac{H_0^2}{2}{\left(t-{t}_0\right)}^2\right) $$ as the suitable form of the scale factor to realize the bounce. It satisfied the conditions H<0$$ H<0 $$, H=0$$ H=0 $$, and H>0$$ H>0 $$ before, at, and after the turn‐around point. We have also observed that the resulting equation of state (EoS) parameter violates the null energy condition required by the bounce realization. We have studied the bounce scenario in a modified f(T)$$ f(T) $$ gravity framework and derived the slow roll parameters. We have studied the behavior of the potential along with the slow‐roll parameters in this bouncing scenario. [ABSTRACT FROM AUTHOR]

Approaches to guaranteeing the dimensional precision of machine parts are considered. It is difficult to formulate a uniform approach on account of the limited statistical data on which the corresponding theory may be based. In addition, numerous factors determining the operational errors in the manufacturing process must be taken into account. Accordingly, it is expedient to employ universal statistical and probabilistic methods in addressing the reliable dimensional precision of products. [ABSTRACT FROM AUTHOR]

The coupling efficiency of the fiber ring resonator has an important influence on the scale factor of the resonant fiber gyroscope. In order to improve the scale factor of the gyroscope, the coupling efficiency of the fiber ring resonator and its influential factors on the scale factor of the gyroscope are analyzed and tested. The results show that the coupling efficiency is affected by both the splitting ratio of the coupler and the loss in the cavity. When the coupling efficiency approaches 0.75 at the under-coupling state, the scaling factor of the gyroscope is the highest. This provides a theoretical reference and an experimental basis for the enhancement of the scaling factor of the resonant fiber gyroscope with the fiber ring resonator as the sensitive unit, providing options for multiple applications such as sea, land, sky and space. [ABSTRACT FROM AUTHOR]

The global bathymetry models are usually of low accuracy over the coastline of polar areas due to the harsh climatic environment and the complex topography. Satellite altimetric gravity data can be a supplement and plays a key role in bathymetry modeling over these regions. The Synthetic Aperture Radar (SAR) altimeters in the missions like CryoSat-2 and Sentinel-3A/3B can relieve waveform contamination that existed in conventional altimeters and provide data with improved accuracy and spatial resolution. In this study, we investigate the potential application of SAR altimetric gravity data in enhancing coastal bathymetry, where the effects on local bathymetry modeling introduced from SAR altimetry data are quantified and evaluated. Furthermore, we study the effects on bathymetry modeling by using different scale factor calculation approaches, where a partition-wise scheme is implemented. The numerical experiment over the South Sandwich Islands near Antarctica suggests that using SAR-based altimetric gravity data improves local coastal bathymetry modeling, compared with the model calculated without SAR altimetry data by a magnitude of 3.55 m within 10 km of offshore areas. Moreover, by using the partition-wise scheme for scale factor calculation, the quality of the coastal bathymetry model is improved by 7.34 m compared with the result derived from the traditional method. These results indicate the superiority of using SAR altimetry data in coastal bathymetry inversion.

This study proposes a universal adaptive control algorithm for an unknown multi-input multi-output (MIMO) system using recursive least squares (RLS) and parameter self-tuning. The issue of adjusting the control and system parameters in response to changes in the platform was discussed. The development of a control algorithm that can consistently achieve reliable and robust control performance in various systems is important. This study aimed to develop a control algorithm that can track the reference value for any unknown MIMO system. For the controller design, an nth-order differential error dynamic model was designed, and an RLS with a scale factor was used to estimate the coefficients of the error dynamics. In the current scenario, the numbers of control inputs and error states in the error dynamics were assumed to be equal. It was designed such that the control input is derived based on the Lyapunov stability concept using the estimated coefficients. The scale factor in the RLS and injection term in the control input based on the sliding-mode approach were computed using a self-tuning methodology. The performance of the proposed universal adaptive control algorithm was evaluated using an actual DC motor and CarMaker (version 8.1.1) software tests under various scenarios.

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Not long ago, a novel gravitational scheme i.e, 4 D - E G B (Einstein-Gauss-Bonnet) gravity have been proposed by Glavan and Lin 2020. They rescaled the coupling factor α with α D - 4 and developed the field equations. The purpose of this paper is to workout the cosmic bounce with a cubic form of scale factor and workout the bouncing scenario under these assumptions. The flat FLRW metric is used along with the perfect fluid to study the energy conditions. The conditions are scrutinized by using different coupling factors α and cosmological constant Λ values. The stability of the assumed scale factor model is in evidence of universal expansion and allows the universal bounce by developing the validations of energy conditions. [ABSTRACT FROM AUTHOR]

In order to analyze Barrow holographic dark energy (BHDE) in a flat FRW universe, the time-dependent scale factor a (t) = [ sinh (α t) ] 1 n is employed. The Hubble horizon as the IR-cutoff is taken to investigate the cosmic consequences. We demonstrate the cosmic transition using the deceleration parameter and equation of state parameter. The characteristics of deceleration parameter for this model correspond well with the latest findings. The equation of state parameter behaves well and does not cross the phantom line. Depending on the values of Barrow exponent (Δ), our model is entirely quintessence and is eventually moving towards Λ -CDM model. We plotted the pressure diagram with various Barrow exponent (Δ) values to demonstrate dark energy dominance. The scalar field and potential that explain the universe's accelerating expansion are also reconstructed. [ABSTRACT FROM AUTHOR]

The current study examines the realisation of cosmic bounce in two situations involving two distinct scale factor selections, one of which is a scale factor already developed for bouncing and the other of which is a scale factor created by truncating a series expansion of a de Sitter scale factor. Generalized Chaplygin gas (GCG) is assumed to be the background fluid in both situations. When the scale factor is set to the first kind, the pre-bounce scenario's GCG energy density decreases due to contraction, reaches its lowest point at t = 0 during the bounce, and then rises as a result of expansion following the bounce. However, it is noted that the truncation has an impact on the density evolution from pre-bounce in the other scale factor scenario. The influence of bulk viscosity is shown in all circumstances, in addition to the influence of non-viscosity, and the test for stability makes use of the squared speed of sound. At the turn-around places, the null energy criterion is also violated. The final stage of the study includes a cosmographic analysis and a demonstration of the Hubble flow dynamics. In conclusion, we find that inflationary cosmology can also be realized with GCG as the background fluid for two-scale factor options. When the equivalent cosmic parameter is examined for pre-bounce and post-bounce scenarios, a symmetry is frequently seen. The symmetry occurs near the point of bouncing or turning. [ABSTRACT FROM AUTHOR]

The H-matrix best linear unbiased prediction (HBLUP) method has been widely used in livestock breeding programs. It can integrate all information, including pedigree, genotypes, and phenotypes on both genotyped and non-genotyped individuals into one single evaluation that can provide reliable predictions of breeding values. The existing HBLUP method requires hyper-parameters that should be adequately optimised as otherwise the genomic prediction accuracy may decrease. In this study, we assess the performance of HBLUP using various hyper-parameters such as blending, tuning, and scale factor in simulated and real data on Hanwoo cattle. In both simulated and cattle data, we show that blending is not necessary, indicating that the prediction accuracy decreases when using a blending hyper-parameter <1. The tuning process (adjusting genomic relationships accounting for base allele frequencies) improves prediction accuracy in the simulated data, confirming previous studies, although the improvement is not statistically significant in the Hanwoo cattle data. We also demonstrate that a scale factor, a, which determines the relationship between allele frequency and per-allele effect size, can improve the HBLUP accuracy in both simulated and real data. Our findings suggest that an optimal scale factor should be considered to increase prediction accuracy, in addition to blending and tuning processes, when using HBLUP. [ABSTRACT FROM AUTHOR]

With the state’s high attention to clean energy and the requirement to reduce the loss of power grid transmission lines, DC UHV has developed rapidly in recent years. It refers to DC transmission and related technologies with voltage levels of ±800 kV (±750 kV) and above. In the power system, DC high-voltage transmission is inseparable from power equipment, but the higher the transmission voltage level, the higher the voltage of DC withstand voltage preventive test. Before the transmission of UHV DC transmission lines, if the DC voltage withstand device is 800 kV or above, the voltage withstand test shall not be carried out for the high-voltage line. The traditional direct comparison method using voltage divider cannot be used to measure the DC output voltage of DC UHV withstand voltage device on site. This paper analyzes the method of full coverage of DC UHV system in limited voltage range and the method of out of range calibration using scale factor. In order to solve the problem of voltage traceability in the DC high voltage generator, especially the voltage traceability of the field DC UHV device, when the voltage output range of the calibrated DC high voltage generator exceeds the measurement range of the standard, the standard value of the voltage calibration point beyond the range can be determined by comparison and obtained through the linearity test. The comparison with the standard shall be conducted at a voltage not lower than 20% of the rated voltage of the calibrated DC high voltage generator, and compared to the maximum voltage of the standard voltage divider. The comparison is carried out at a (a ≥ 2) voltage point. When comparing at a point, the highest voltage level is equal to the upper limit of the standard. Under a voltage point, according to the mathematical relationship between the voltage standard value of the tested device and the current flowing through the linear load resistance, the fitting function can be obtained through the linear regression method. For b (b ≥ 4) calibration points beyond the measurement range of DC standard voltage divider, the standard value can be “extrapolated” from the linear load resistance current and the fitting function Yang (2002). Through comparison and verification, the method is feasible, which is of great significance to promote the compilation of calibration specification for DC high voltage generator.

Alternating current field measurement (ACFM) technology is widely used in defect detection of metal structures in manufacturing and other industrial fields. The angle deflection and crack location problems of single sensor in the process of unpredictable defect detection were studied. Firstly, through the COMSOL Multiphysics simulation results, it can be seen that the X and Y direction components of the field strength have a law of signal complementarity during the angular deflection process, and then the data augmented grey neural network model (DA-GNNM) prediction was realized by establishing a scale factor. At the same time, simulation prediction and regression prediction showed that DA-GNNM model has better prediction effect. In addition, the deflection crack was reconstructed by multigradient deflection simulation. Secondly, the DA-GNNM prediction model was verified to be reasonable by building an experimental platform and signal feature extraction, with an average prediction error of 2. 56% . Finally, the deflection of the reconstructed image of the crack in the non-parallel detection process is further improved through the prediction angle. [ABSTRACT FROM AUTHOR]

To obtain higher economic benefits, large eel breeding companies classify live eels by weight. Due to their strong mobility and smooth body surface, living eels are not suitable for traditional mechanical weight measurement. In this study, a live eel sorting machine based on machine vision was developed, and a novel method was developed for obtaining live eel weight measurements through images. First, a backlit workbench was designed to capture static images of eels, and then the projection area and skeleton length of the images were obtained by image preprocessing. For the eel's body shape, which is generally cylindrical and gradually transitions to a flat tail, the tail posture changes affect the shape of the images; thus, a weight measurement model combining the projected area and the skeleton length was proposed. The optimal scale division coefficient of the weight model was found to be 0.745 by experimentation. Then, select eels of different weight ranges were used for model error verification and to obtain the correction function of the error. The weight gradient was used to confirm the corrected eel weight model. Finally, the system calculation results were compared with the actual measurement results. The root mean square error (RMSE) was 12.94 g, and the mean absolute percentage error (MAPE) was 2.12%. The results show that the proposed method provided a convenient, fast, and low-cost non-contact weight measurement method for live eels, reduced the damage rate of live eels, and can meet the technical requirements of actual production. [ABSTRACT FROM AUTHOR]

The H-matrix best linear unbiased prediction (HBLUP) method has been widely used in livestock breeding programs. It can integrate all information, including pedigree, genotypes, and phenotypes on both genotyped and non-genotyped individuals into one single evaluation that can provide reliable predictions of breeding values. The existing HBLUP method requires hyper-parameters that should be adequately optimised as otherwise the genomic prediction accuracy may decrease. In this study, we assess the performance of HBLUP using various hyper-parameters such as blending, tuning, and scale factor in simulated and real data on Hanwoo cattle. In both simulated and cattle data, we show that blending is not necessary, indicating that the prediction accuracy decreases when using a blending hyper-parameter

Traditional methods of orthogonal basis function decomposition have been extensively used to detect magnetic anomaly signals. However, the determination of the relative velocity between the detection platform and the magnetic target remains elusive in practical detection. And, the non-ideal uniform motion of the magnetic target further complicates the process and adversely impacts the detector’s performance. To address this challenge, this paper introduces an adaptive scale factor method based on orthogonal basis function decomposition. This new method can be used to adjust the relative velocity between the detection platform and the magnetic target and to refine the characteristic time in the basis functions. In this paper, a mathematical relationship between the scale factor and the relative velocity is established, which is subsequently fitted into a Gauss function curve. The optimal scale factor, denoted as β, is adaptively chosen from the fitting curve when the magnetic target moves at a non-ideal uniform velocity with an unknown motion state. The results of simulations indicate that the scale factor improves the signal-to-noise ratio of the magnetic anomaly signals in a non-ideal state. And, this method can improve the energy value of OBF decomposition by 17.7%. Simultaneously, this method ensures that the moment the magnetic target passes the CPA coincides with the energy peak of the orthogonal basis detection, which improves the accuracy by 54.1% compared with the traditional method. The effectiveness and precision of the proposed method are verified using simulations and practical experiments.