Second-order Curve Research Articles

Latent growth curve analyses of emotional awareness and emotion regulation in early and middle adolescence

The importance of emotional awareness (EA) and emotion regulation (ER) for children’s and adolescents’ development has been suggested in numerous studies, but longitudinal trajectories of these aspects of emotional competence have rarely been examined. Therefore, the main aim of this study was to investigate developmental trends of EA and ER in early and middle adolescence over a 1-year period. Longitudinal increases of different aspects of EA (emotion differentiation, bodily unawareness, attention to others’, and analyses of own emotions) and dysfunctional ER, and decreases of functional ER were expected. Furthermore, it was explored whether these trajectories as well as their initial levels were associated with gender and age. Three-wave longitudinal self-report data of N = 1,225 German adolescents (aged 10–15 years at initial assessment, 54% female) who had completed the Emotion Awareness Questionnaire and the Regulation of Emotions Questionnaire were analyzed. After establishing at least partial scalar measurement invariance for the longitudinal models, the second-order Latent Growth Curve Models (LGCMs) were computed. Regarding EA, increases of emotion differentiation and bodily unawareness, as well as adolescents’ attention to others’ emotions, but also a decrease of their willingness to analyze own emotions were found. For ER, results suggested stability of dysfunctional and decreases of functional strategies. Conditional LGCMs (including gender, age, and the interaction between both) indicated that the increase of emotion differentiation and the decrease in the use of selected functional ER strategies were more pronounced for younger participants. Gender differences were found only for baseline but not for developmental trends, and no significant interaction with age was found. Overall, this study illustrates the developmental trajectories of EA and ER over the course of 1 year and emphasizes that adolescents have difficulties in applying functional ER strategies with increasing age, despite improvements in EA.

Temporal development of student burnout symptoms: Sociodemographic differences and linkage to university dropout intentions

Considering the demanding higher education context, university students are at risk to experience burnout symptoms such as emotional exhaustion, cynicism, and reduced professional efficacy. Theoretical models (e.g., Job Demands-Resources Model) state that burnout symptoms develop over time, vary between individuals, and bear adverse consequences. To date, the temporal development of student burnout symptoms within semesters, inter-individual differences in their development, and the role of their development for academic outcomes like student dropout are understudied. To complement this limited research, we used date of a three-wave longitudinal study with N = 1435 undergraduate students over one semester. First, we modeled unconditional second-order latent growth curves to examine the initial levels and trajectories of each burnout symptom (emotional exhaustion, cynicism, and reduced professional efficacy). We then modeled conditional second-order latent growth curves to examine whether initial levels and trajectories differed depending on students’ sociodemographic characteristics (gender, age, study progress, and academic major) and associated with students’ intentions to drop out from university. Results indicated a linear increase in student burnout symptoms over the semester. Sociodemographic differences existed in the initial levels of emotional exhaustion and reduced professional efficacy and the trajectories of each symptom. Generally, female, STEM, and higher- and lower- semester students were particularly affected by burnout symptoms. Further, higher initial levels and an increase in each symptom corresponded with higher dropout intentions. Summarizing, the results highlighted that student burnout symptoms increase as the semester progresses, seem more pronounced among certain student groups, and operate as strong predictors for dropout intentions.

Trajectories of distress from pregnancy to 15-months post-partum during the COVID-19 pandemic.

The COVID-19 pandemic has particularly burdened pregnant and postpartum women. It remains unclear how distress levels of pregnant and postpartum people have changed (or persisted) as the pandemic continues on and which factors may contribute to these trajectories of distress. This longitudinal study included 304 pregnant people, who were followed during pregnancy, 6-weeks, 6-months and 15-months postpartum. At each time point, a latent "distress" factor was estimated using self-reported depressive symptoms, anxiety symptoms, and stress. Reported negative impact of COVID-19 and social support were assessed during pregnancy as risk and protective factors related to distress. Second-order latent growth curve modeling with a piecewise growth function was used to estimate initial levels and changes in distress over time. Mean distress was relatively stable from the pregnancy to 6-weeks postpartum and then declined from 6-weeks to 15-months postpartum. Higher education, greater social support, and lower negative impact of COVID-19 were associated with a lower distress during pregnancy. Unexpectedly, negative impact of COVID-19 was associated with a faster decrease in distress and more social support was associated with a greater increase in distress from pregnancy to 6-weeks postpartum. However, these effects became non-significant after controlling for distress during pregnancy. Findings indicate high but declining levels of distress from pregnancy to the postpartum period. Changes in distress are related to social support and the negative impact of the pandemic in pregnancy. Findings highlight the continued impact of COVID-19 on perinatal mental health and the need for support to limit the burden of this pandemic on pregnant people and families.

A single constructive algorithm for constructing foci of second-order curves

The article is devoted to the analysis of some geometric schemes and discussion of the issues arising in this connection of the theory of constructing second-order curves by methods of constructive synthesis. The article shows that the currently used definitions of the center of the second-order curve and the diameters of these curves conflict with the principle of indistinguishability of conics in projective geometry. The ways of eliminating these contradictions are proposed and a unified algorithm for constructing foci of second-order curves is developed on their basis. The author's reasoning, based on the apparatus of projective geometry, will reveal a number of contradictions in the currently existing definitions relating to second-order curves, and their elimination will provide an opportunity to develop a unified approach to the construction of some geometric images initiated by second-order curves and give them a general constructive justification. As a result of the analysis of geometric schemes, a number of concepts of projective geometry were clarified, which made it possible to unify the solution of problems related to the construction of focal points of second-order curves. A unified algorithm for constructing all four foci of the second-order curve is presented. Thus, the basis has been laid for expanding the fields of application of geometric models to imaginary geometric images covered by the concept of a "second-order curve", and conducting research on the resulting geometric images and schemes.

Novel tumor localization model and prediction of ablation zone using an intertwined helical antenna for the treatment of hepatocellular carcinoma.

Hepatocellular carcinoma has been the leading cause of death in recent centuries and with the advent of newer technologies, several thermal and cryo-ablation techniques have been introduced in the recent past. In this regard, microwave ablation has developed into a promising method for thermal ablation technique. However, due to clinical obligations, in-vivo analysis is not feasible and ex-vivo analysis is inaccurate due to changes in the electrical and thermal properties of the tissue. Therefore, in this study, temperature-dependent permittivity, electrical conductivity, and thermal conductivity along with phase change effect due to temperature reaching above 100°C are incorporated using finite element method model. Further, using an intertwined normal mode helical antenna ablation probe, a change in resonant frequency (Δf) and reflection coefficient (ΔS11 ) from the actual value (antenna parameter in the air at 5GHz) is modeled using second-order polynomial curve fitting to predict the surrounding permittivity in the range of 30-70. A maximum deviation of 0.8 value in permittivity from the actual value is observed. However, to obtain a generalized methodology, XG Boost and CAT Boost algorithms are used. Further, since ablation diameter plays a crucial role in achieving optimal tumor ablation, an artificial neural network (ANN) algorithm with three different optimizers is incorporated to predict ablation diameter using five critical parameters. Such an ANN algorithm which can predict the transversal and axial ablation zone may provide optimal ablation outcomes.

Temperature dependence of magnetization reversal mechanism in misch-metal substituted Nd-Fe-B magnets sintered by dual alloy method

The substitution of Nd by misch-metal (MM) in Nd-Fe-B permanent magnets has attracted extensive attention due to the effective reduction of production cost and rational utilization of rare earth resources. In particular, multi-main phase (MMP) magnets prepared by dual alloy method possess a higher permanent magnetic performance than that of single main phase (SMP) magnets. However, the coercivity mechanism of MMP magnets is different from the nucleation and propagation of SMP magnets, especially the interactions of different 2:14:1 main phases have not been clarified. In this study, we investigated the temperature dependence of magnetization reversal mechanism in (MM,Nd)-Fe-B magnets by using recoil loops, minor hysteresis loops, first-order and second-order reversal curves. It found that with the increase of temperature, the magnetic moments motion is mainly affected by long-range magnetostatic interaction rather than exchange coupling. The weakened coupling interaction makes the demagnetization process of softer and harder magnetic phases asynchronous. The thermal activation energy barrier index related to coercivity mechanism is 1.45, 1.18 and 1.0 at 200 K, 300 K and 380 K, respectively. It indicates that nucleation and expansion of reversed domains are the main mechanisms controlling the magnetization reversal process at low temperature. While the coercivity at high temperature is mainly determined by the domain wall pinning mechanism. In addition, we noted that both two coercivity mechanisms coexist in MMP magnets at 300 K. Micromagnetism has also been used to verify the coercivity mechanism of (MM,Nd)-Fe-B magnets sintered by dual alloy method, which is of great significance for improving the magnetic properties of high abundance rare earth magnets.

НЕКОТОРЫЕ ЗАДАЧИ НА КРИВЫЕ ВТОРОГО ПОРЯДКА С ПАРАМЕТРОМ

The methodological aspects of teaching the section "second-order curves" in the course of analytical geometry at a technical university are considered. The necessity of including non-standard problems in the course, in particular, tasks with parameters for deeper assimilation of educational material, is discussed. Such tasks are designed to form students' research and analytical skills. Problems on a tangent to a second-order curve are considered as problems with a parameter. A sheaf of curves intersecting at the same points is investigated as a family of lines described by a second-order equation with a parameter.

Циклические поверхности, сопровождающие нелинейчатые квадрики вращения

The paper considers the shaping of cyclic surfaces based on nonlinear rotation, in which the axis of rotation and the generatrix in the general case are three-dimensional smooth curves. As a tool for shaping surfaces of non-linear rotation, the method of the accompanying Frenet trihedron, known in the differential geometry of curved lines, is used. The geometric scheme of surface shaping is based on a construction that includes: a curvilinear axis of rotation and a one-parameter set of its normal planes; a generatrix whose points describe in normal planes circular trajectories centered on a curvilinear axis. A mathematical model of shaping the surface of non-linear rotation for the general case of specifying the axis of rotation and the generatrix is given. On the basis of this model, test examples of the formation of surfaces of nonlinear rotation, which are cyclic surfaces, each of which accompanies the corresponding nonlinear quadric of rotation, are considered. In the examples of shaping, the original rectilinear axis of a non-linear quadric of revolution and its generating line, a second-order curve, are functionally interchanged: the secondorder curve becomes the rotation axis, and the rectilinear axis becomes the generatrix. The resulting family of surfaces of non-linear rotation belongs to the well-known class in the theory of analytic surfaces "Normal cyclic surfaces". It complements this class and fundamentally differs in the method of shaping.

Numerical and experimental investigation of a negative-curvature variable-shell flextensional transducer.

Type IV flextensional transducers do not have broadband characteristics due to the deep valley between their first- and second-order response curves arising from the sound pressure cancellation produced by the vibration in different areas of the shell. In this paper, the cause of the deep valley is examined by analyzing the equivalent radiated sound field of the transducer. Simplifying the three-dimensional vibration equation to a two-dimensional equation shows that the vibration state of the shell is related to the positive and negative curvature. Therefore, a variable-shell flextensional transducer with a negative curvature is proposed, which changes the second-order vibration of the transducer by introducing a negative curvature structure. The transducer avoids acoustic pressure cancellation, achieves broadband characteristics, and has continuous high efficiency in the frequency band. After optimization, a prototype of the transducer is fabricated and a pool test is completed. The test results show that the transducer realizes the coupling of the first three vibration mode, forming a broad band with an in-band fluctuation of less than 8 dB at 1200-5600 Hz, and the efficiencies of the first to third resonance peaks are 30.2 %, 16.6 %, and 9.4 %, respectively.

Magnetic loss in grain-oriented Fe–Si sheets under different harmonic excitation and high indication

This paper presents an improved loss calculation method that takes into account the effects of harmonics and skinning effects, thus extending the loss prediction of soft magnetic materials to a larger frequency and induction range. First, the first-order and second-order slew curves are concurrently fitted into a nonlinear Preisach model to determine the hysteresis loss. Then, integrating the effects of high frequency harmonics and high induction, the fixed-point technique based on the H–B magnetic intrinsic relationship is introduced into the finite element calculation in order to calculate the flux density distribution of the silicon steel sheet more accurately. Then, the classical loss at high flux density is further calculated more accurately. Finally, losses for soft magnetic materials in the 1 kHz range are computed under various harmonic excitations. This method is compared to the traditional method and the experimental results, and this method is closer to the experimental results.

Determination of the angle of rotation of the diffraction grating by the method of conical diffraction

Diffractograms of rotated polyaniline fiber grating were studied experimentally. Based on the obtained results, the diffraction patterns were analyzed and set of experimental data obtained after image digitization was approximated by the least squares method. The angle of rotation of the diffraction grating was calculated using the determined coefficients of the second-order curves.

Modeling Growth in the Presence of Changing Measurement Properties between Persons and within Persons over Time: A Bayesian Regularized Second-Order Growth Curve Model

"Modeling Growth in the Presence of Changing Measurement Properties between Persons and within Persons over Time: A Bayesian Regularized Second-Order Growth Curve Model." Multivariate Behavioral Research, ahead-of-print(ahead-of-print), pp. 1–2

An automatic parallel scheme to design an augmented hydrokinetic river turbine using a simulation-based optimization approach

The effect of diffuser-enhanced flow on the energy extraction performance of hydrokinetic turbines is widely reported in the literature. In this context, this work combines automatic scripting for geometry construction and meshing, together with a simulation-based approach using particle-swarm optimization with Computational Fluid Dynamics (CFD) to design an augmented hydrokinetic river turbine (HKRT). The goal is to achieve an increase in mass flow in the throat of the diffuser and then to design an ad-hoc set of rotor blades. The optimization is performed in two separate stages: Continuous optimization for the diffuser and discrete optimization for the rotor blades. The complex shape of the rotor blades in terms of the chord, twist, and thickness distribution was parametrized with second-order Bezier curves, which facilitates the correlation between the blade’s shape and its performance, proving to be more intuitive to the experienced designer. Furthermore, a novel search and discrete arrangement of feasible design variables are proposed, which allows for reducing the computational costs of this large optimization problem. Results show that the optimized diffuser achieved a flow rate increase of 279%, and the ad-hoc 1.5 [m] in diameter rotor delivers a power of 11.98 [kW] with an efficiency of 0.3385%.

Beyond Big Five trait domains: Stability and change in personality facets across midlife and old age.

Accumulated evidence indicates both stable and malleable parts of inter-individual differences in the broad Big Five domains. Less is known, however, about stability and change at the more diversified facet level. With the current study, we fill this gap by investigating personality stability and change across midlife and old age. We apply local structural equation measurement models and second-order growth curve models to four waves of data obtained with the full NEO Personality Inventory (NEO-PI-R) collected over 11 years from 1667 adults (Mage =62.69 years, SDage =15.62, 55% female) who participated in the Seattle Longitudinal Study. Measurement invariance analyses indicated that the psychometric properties of the NEO-PI-R facets are comparable across time and age. Results revealed substantial rank-order stabilities across all facets, yet the exact pattern varied strongly between facets of the same trait and across traits. Mean-level change of facets from midlife to old age largely mirrored the mean-level change observed for the broader traits. We discuss conceptual implications and argue that in the face of overall stability across midlife and old age, changes in the rank-ordering of people reveals a much more complex and diverse pattern of development than analyses at the trait level suggest.

Algorithms for Planning Smoothed Individual Trajectories of Ground Robots

The article is devoted to the development of an algorithm for constructing the trajectory of a robotic platform moving in an environment with obstacles. This algorithm is based on the application of a special local optimization procedure at each planning step and allows us to obtain feasible program trajectories without increasing the computational complexity of algorithms compared to existing methods. The algorithm is based on the application of the improved method of potential fields and subsequent smoothing of the resulting trajectory. The improving of the potential field method consists in a new way of detecting and avoiding local minima. When a local minimum is detected, it is added to the map as an additional obstacle, which makes it possible to avoid it during further trajectory planning. To circumvent obstacles that can be approximated by polygons, the method of the effective point to the obstacle is proposed, which is the equivalent of the latter in relation to the current location of the moving robotic platform when using this planning method. A two-stage technique for smoothing piecewise linear trajectories is proposed. It is assumed that there is some initial suboptimal curve found by any planning method. This curve is optimized using a functional that includes the length of the trajectory and the deviation of the optimized curve from the original curve. At the second stage, the linear segments of the planned straight line are conjugated with second-order curves. As a result, the planned trajectory of motion is a quadratic-linear curve with a smooth function of the trajectory velocity. At the same time, the proposed method of coupling rectilinear sections of the trajectory does not require sudden changes in speed when passing turns. Simulation results confirming the effectiveness of the proposed method of planning the trajectories of robots are considered and discussed.

Adolescents' developing awareness of inequality: Racial and ethnic differences in trajectories.

To advance knowledge of critical consciousness development, this study examined age-related change in awareness of inequality by race and ethnicity, gender, parent education, generation status, and their interactions. With longitudinal data (2013-2017) from 5019 adolescents in grades 6-12 (55.0% female) from California, Minnesota, and West Virginia, multigroup second-order latent growth curves were estimated for Black (13.7%), Latinx (37.0%), Asian (8.1%), and white (41.3%) youth. Black, Latinx, and Asian adolescents increased awareness of inequality longitudinally; white youth showed no change. Multiracial youth accelerated awareness of inequality in mid-adolescence; changes in race and ethnicity predicted decline, followed by increases. Girls with more educated, immigrant-origin parents started out more aware of inequality. Results signal the need for race-specific and intersectional approaches to studying critical consciousness development.

New principles of shaping groove structures of high-aperture non-classical ruled toroidal diffraction gratings using pendulum-type ruling engines

Subject of study. Possible methods for increasing the range of optical parameters of fabricated high-aperture non-classical ruled toroidal diffraction gratings and new mathematical relations for describing the equations of curvilinear projections of grooves, laws of variation of the curvature radius of the closest vertex circle, and variable pitch for these groove projections are presented. Aim of study. The study aimed to improve the principles of designing pendulum-type ruling engines ensuring the implementation of a new method for fabricating high-aperture non-classical ruled concave toroidal diffraction gratings and derive analytical expressions for determining geometric parameters of curvilinear projections of the grooves of these gratings. Method of study. The investigation method was based on the theory of designing precision mechanisms, analytic geometry, and calculus. Main results. The possibility of solving the relevant issue of increasing the size, relative aperture, and relation between the curvature radii in meridional and sagittal cross-sections of high-aperture non-classical ruled toroidal diffraction gratings considering the optimization of their aberrations was demonstrated using pendulum-type ruling engines. In contrast to the available engines, pendulum-type ruling engines should be designed to ensure the intersection between the rotation axes of the diamond and blank carriages as well as alignment of the dimension chains of the structural parameters of the diamond and blank carriages according to the specified curvature radii in meridional and sagittal cross-sections of concave toroidal diffraction gratings. Considering that the cutting edge of the diamond tool must always be in contact with the concave toroidal surface of a substrate along the normal to the surface in all substrate points while ruling all grooves, we established that the system of curvilinear groove projections is described by a system of second-order curves, i.e., ellipse equations. With increasing discrete angle at which the grooves are ruled, the coordinates of the centers of the ellipses gradually shifted in the meridional cross-section from the origin of coordinates (grating vertex) in the direction of the edge light zone by a value directly proportional to the sine of the discrete angle and the difference between curvature radii in the meridional and sagittal cross-sections. Curvature radii of the closest vertex circles of the groove projections are variable parameters directly proportional to the product of curvature radii in the meridional and sagittal cross-sections of the grating and inversely proportional to the variable value of the specified coordinate. The variable pitch of the groove projections on the specified plane is a function that, to a first approximation, depends on the initial groove pitch at the grating vertex and the squared variable value of the specified coordinate and is inversely proportional to the squared curvature radius in the meridional cross-section of the grating. Practical significance. The proposed principles of shaping groove structures of the ruled toroidal diffraction gratings using pendulum-type ruling engines enable fabricating such gratings with extremely large relative aperture and optical size as well as increased range of ratios of their curvature radii in the meridional and sagittal cross-sections, which can be used to design novel advanced spectral instruments. The obtained analytical expressions describing the geometric parameters of the curvilinear groove projections enable correction of the first through third order aberrations of the gratings of the considered type.

Prediction of lower extremity strength by nerve conduction study in cauda equina syndrome.

An electrodiagnostic test is more useful than the lower extremity isometric strength test for objectively determining the degree of nerve damage and prognosis in cauda equina syndromes (CES). This study evaluated the correlation between nerve conduction study (NCS) parameters and the lower extremity isometric strength and manual muscle test (MMT) grades.The isometric strengths of knee extension (KE), ankle dorsiflexion (ADF), and ankle plantarflexion (APF) were measured. NCS parameters, MMT, and isometric strength of femoral, peroneal, and tibial nerves were evaluated, including their correlations with each other. A regression equation between the isometric strength and compound muscle action potential (CMAP) amplitudes was derived and cutoff values were used to confirm boundary values of strength and amplitude between the MMT grades.KE isometric strength and femoral nerve CMAP amplitude were significantly correlated (r = 0.738, P < .001). ADF isometric strength and peroneal nerve CMAP amplitude were significantly correlated (tibialis anterior, r = 0.707, P < .001). KE (r = 0.713, P < .001), ADF (r = 0.744, P < .001), and APF (r = 0.698, P < .001) isometric strengths were correlated with the MMT grades. For the regression curve, the second-order curve was more reasonable than the first-order curve. Cutoff femoral nerve CMAP amplitude and isometric strength cutoff values were ≥2.05 mV and 17.3, respectively, for MMT grades 2 to 3 and 2.78 ± 1.08 and 20.8 ± 9.33, respectively, for grade 3.The isometric strengths of the KE, ADF, and APF and the CMAP amplitude of the electrophysiologic parameters were correlated in CES patients and a significant correlation with MMT grade was also identified. Accordingly, it is possible to identify the precise neurological condition, objectively evaluate the degree of paralysis and disability, and determine the quantitative muscle strength from MMT in order to establish an appropriate rehabilitation treatment plan.

Lattice instability, anharmonicity and Raman spectra of BaO under high pressure: A first principles study

Alkaline-earth metal oxides, MgO and CaO dominate Earth's lower mantle, therefore, exploring high-pressure behavior of these compounds is of significant geophysical research interest. Among the alkaline-earth metal oxides, BaO exhibits rich polymorphism in the pressure range of 0–1.5 Mbar. Static enthalpy calculations revealed that BaO undergoes a pressure-induced structural phase transition from NaCl-type (B1) → NiAs-type (B8) → distorted CsCl-type (d-B2) → CsCl-type (B2) at 5.1, 19.5 and 120 GPa, respectively. Transitions B1 → B8 and B8 → d-B2 are found to be first order in nature whereas d-B2 → B2 is a second order or weak first-order phase transition with displacive nature. Interestingly, the d-B2 phase shows stability over a wide pressure range of ∼19.5–113 GPa. Mechanical and dynamical stabilities of ambient and high-pressure phases are demonstrated through the computed second-order elastic constants and phonon dispersion curves, respectively. Under high pressure, significant phonon softening and soft phonon mode along the M-direction are observed for B8, d-B2 and B2 phases, respectively. Pressure-dependent Raman spectra suggest a phase transition from d-B2 to a Raman inactive phase under high pressure. Overall, the present study provides a comprehensive understanding of lattice dynamics and the underlying mechanisms behind pressure-induced structural phase transitions in BaO.

Mineralization process of ferrous ions from ZnSO4-FeSO4 solution at a temperature range of 368.15–423.15 K

The abiotic mineralization of ferrous ions for ZnSO4-FeSO4 solution at temperatures of 368.15–423.15 K was investigated. The effect of kinetic factors including oxygen partial pressure, temperature, agitation speed, with presence of a neutralizer or not, and seeding on the ferrous oxidation process was evaluated in detail. Also, the rate constants for the ferrous oxidation process were calculated by a second-order kinetic curve of the partial concentration of [Fe2+] with time to realize the effect of the different kinetic factors as variables. Furthermore, the morphology of the minerals was identified using scanning electron microscopy electron dispersive spectroscopy measurements (SEM-EDS), and the phase composition was characterized by the X-ray diffraction (XRD), the thermogravimetric analysis (TGA) and differential thermal analysis (DTA). The research indicated that the ferrous oxidation process was accelerated by elevating temperature, increasing agitation speed, and adding a neutralizer. Conversely, increasing oxygen partial and seeding both decrease the rate constant of the oxidation process. The iron-rich precipitates produced comprise a wide range of chemical compositions, structures, sizes, and morphologies. They consisted primarily of goethite and hematite, with goethite being dominant below 403.15 K, and hematite above 403.15 K. Moreover, the iron-rich products were successfully obtained by abiotic mineralization of industrial ZnSO4 solution at 423.15 K, containing 59% of Fe and 1% of Zn, while the resultant ZnSO4 solution after removal of iron contained less than 1 g/L of iron ions. Thus, abiotic mineralization of ferrous ions for ZnSO4 is clean and energy-saving, and the iron-rich products can be used as raw materials for ironmaking.