Amplitude-frequency Characteristics Research Articles

Modeling Thermal Impedance of IGBT Devices Based on Fractional Calculus Techniques

The thermal impedance characteristics of insulated gate bipolar transistor (IGBT) modules are critical for the thermal management and design of electronic devices. This paper proposes a fractional-order equivalent thermal impedance model, which is inspired by the correlation between multi-time-scale dissipation characteristics of heat conduction processes and fractional calculus. The fractional-order equivalent thermal impedance model is derived based on the connection between fractional-order calculus and the Foster thermal network model in mathematical operations, with only two parameters to be identified: heat capacity C and fractional order α. Moreover, this paper provides a parameter identification method for the proposed fractional-order equivalent thermal impedance model based on the multi-objective particle swarm optimization (MOPSO) algorithm. In order to validate the effectiveness and superiority of this work, experiments and comparative works are provided in this paper. The results indicate that the fractional-order equivalent thermal impedance model can accurately describe the frequency domain characteristic curves of the thermal impedance of the Foster thermal network model for IGBT modules, with the difference between the amplitude frequency characteristics not exceeding 1 dB and the difference between the phase frequency characteristics not exceeding 1° within the operating frequency range of (1 kHz, 1 MHz).

Application of the Algebraic Extension Method to the Construction of Orthogonal Bases for Partial Digital Convolutions

Mathematical tools have been developed that are analogous to the tool that allows one to reduce the description of linear systems in terms of convolution operations to a description in terms of amplitude-frequency characteristics. These tools are intended for use in cases where the system under consideration is described by partial digital convolutions. The basis of the proposed approach is the Fourier–Galois transform using orthogonal bases in corresponding fields. As applied to partial convolutions, the Fourier–Galois transform is decomposed into a set of such transforms, each of which corresponds to operations in a certain Galois field. It is shown that for adequate application of the Fourier–Galois transform to systems described by partial convolutions, it is necessary to ensure the same number of cycles in each of the transforms from the set specified above. To solve this problem, the method of algebraic extensions was used, a special case of which is the transition from real numbers to complex numbers. In this case, the number of cycles varies from p to pn/k, where p is a prime number, n and k are integers, and an arbitrary number divisor of pn can be chosen as k. This allows us to produce partial Fourier–Galois transforms corresponding to different Galois fields, for the same number of cycles. A specific example is presented demonstrating the constructiveness of the proposed approach.

Investigation of the spatial distribution of deformations in quartz piezo elements by x-ray topography

Using X-ray topography on laboratory and synchrotron X-ray sources, the distribution of deformations in the volume of two types of AT-cut quartz resonators of different sizes were obtained. From a comparison of X-ray data and the amplitude-frequency characteristics of the resonators, a correlation between the deformation patterns and the features of oscillatory processes for operating modes and their harmonics, as well as for parasitic modes, was established. A connection between oscillations in parasitic modes, which manifest themselves in the amplitude inhomogeneity, and the topology of the resonators is found. The applied significance of the obtained results for the development and optimization of new designs of piezoelectric elements and the development of their manufacturing technology is noted.

Study on the influence mechanism of gate oxide degradation on DM EMI signals in SiC MOSFET

This paper investigates gate oxide degradation and its influence on Differential Mode(DM) EMI signals. The study reveals that changes in the parasitic capacitance within the chip, resulting from gate oxide degradation, can modify the amplitude-frequency characteristics of DM EMI signals, leading to unexpected transmission outcomes. This paper subjects SiC MOSFET modules to periodic high-temperature gate bias stress, extracts the spectrum characteristics of DM EMI, and assesses the impact of junction temperature. The analysis explores the impact of gate oxide degradation on low and high frequency DM EMI signals. Experimental results reveal distinct sensitivities of amplitude-frequency characteristics in the DM EMI signals to temperature variations and responses to gate oxide degradation at various frequency bands. The extrapolation of the correlation between the frequency-domain characteristics of the DM EMI signals and the degree of gate oxide degradation introduces a novel approach to evaluate the lifespan of power electronic devices.

A simple mechanical model of turbulence

This work examines the control and stabilization problems of vibrations in a hierarchical chain of oscillators with hysteresis couplings. Hysteresis coupling is formalized within the Bouc — Wen phenomenological model. The mass, stiffness, and damping properties of the oscillators are set to follow a specific scaling rule and decrease exponentially along the chain, thus forming a hierarchy. The model is verified using Kolmogorov’s hypotheses. To do this, energy spectra are constructed under hysteresis in coupling and without it at different amplitudes of the external excitation. As a result of computational experiments, it is shown that for a chain with hysteresis couplings at a high amplitude of excitation, the energy spectrum curve sufficiently corresponds to Kolmogorov’s hypotheses. The amplitude-frequency characteristics of the system are calculated under hysteresis in coupling using the frequency scanning method. In numerical experiments, frequency ranges of external excitation are identified, which correspond to the chaotic behavior of oscillators and their synchronization.

Applying heterogeneous building materials for the protection of people against electromagnetic radiation

The object of this study is the processes of shielding electromagnetic radiation by building and facing materials. The research is aimed at solving the problem of ensuring the electromagnetic safety of people by improving the composition and structures of building and facing materials. Means for improving the electromagnetic safety of people under industrial and domestic conditions using non-homogeneous building materials have been determined. The shielding properties of reinforced concrete structures were studied. A methodology for increasing their efficiency depending on the amplitude-frequency characteristics of the radiation that needs shielding has been devised. The efficiency of electromagnetic radiation shielding by heterogeneous dielectric building materials based on cement concrete and basalt fibers was determined. It was established that shielding through the refraction of electromagnetic waves on inhomogeneities does not give an acceptable effect. The expediency of covering basalt fibers with a conductive substance to increase the protective properties of materials was substantiated. The protective properties of flat facing material with carbonyl iron content were studied. It has been shown that the properties of materials can be effectively controlled by adjusting the filler. The material's transmission coefficient of ultra-high frequency electromagnetic radiation does not exceed 0.40, and the reflection coefficient – 0.25 with a filler content in the base of 14–15 % by volume. This makes it possible to simultaneously ensure the electromagnetic safety of people and the stable functioning of wireless communication devices. The advantage of the material is the low coefficients of reflection of electromagnetic waves, which does not lead to deterioration of the electromagnetic situation in other areas where people stay. It has been established that the addition of boron nitride to the facing material significantly increases the thermal insulation characteristics of the coating and contributes to the solution of energy saving problems. Adding a layer containing boron nitride to the material provides thermal conductivity coefficients of 0.030–0.031 W/m·K, which is better than known analogs

Intelligent Diagnosis of Bearing Failures Based on Recurrence Quantification and Energy Difference

Bearing health is key for maintaining good performance and safety in rotating machinery. As the diagnosis of mechanical faults develops toward intelligence and automation, accurate and systematic fault diagnosis algorithms are imperative. Focusing on the diagnosis of rolling bearing failures, this study utilizes a sliding time window to extract essential data segments. A series of signal processing techniques, including filtering, amplitude–frequency analysis, Hilbert envelope analysis, and energy analysis, is applied to establish a comprehensive dataset. For extraction of the hidden properties of the data, the recurrence quantity spectrum is defined for the input of the neural network. The goal is to obtain a cleaner dataset with enhanced features. A convolution neural network is constructed. Different activation functions in the activation layer are compared for better fault diagnosis algorithms. The established feature matrices are specifically defined to accurately identify the subtlest defects of bearings, thereby facilitating early detection. The proposed procedure distinguishes various fault modes. As for the multidimensional complexities of fault signals, this study carries out a comprehensive comparison of energies, recurrence quantification, and amplitude–frequency characteristics of bearing fault detection to assess the accuracy, computational efficiency, and robustness of bearing fault diagnosis. The proposed method and bearing fault detection procedures have potential in practical applications.

A Hybrid Network Integrating MHSA and 1D CNN–Bi-LSTM for Interference Mitigation in Faster-than-Nyquist MIMO Optical Wireless Communications

To mitigate inter-symbol interference (ISI) caused by Faster-than-Nyquist (FTN) technology in a multiple input multiple output (MIMO) optical wireless communication (OWC) system, we propose an ISI cancellation algorithm that combines multi-head self-attention (MHSA), a one-dimensional convolutional neural network (1D CNN), and bi-directional long short-term memory (Bi-LSTM). This hybrid network extracts data features using 1D CNN and captures sequential information with Bi-LSTM, while incorporating MHSA to comprehensively reduce ISI. We analyze the impact of antenna numbers, acceleration factors, wavelength, and turbulence intensity on the system’s bit error rate (BER) performance. Additionally, we compare the waveform graphs and amplitude–frequency characteristics of FTN signals before and after processing, specifically comparing sampled values of four-pulse-amplitude modulation (4PAM) signals with those obtained after ISI cancellation. The simulation results demonstrate that within the Mazo limit for selecting acceleration factors, our proposal achieves a 7 dB improvement in BER compared to the conventional systems without deep learning (DL)-based ISI cancellation algorithms. Furthermore, compared to systems employing a point-by-point elimination adaptive pre-equalization algorithm, our proposal exhibits comparable BER performance to orthogonal transmission systems while reducing computational complexity by 31.15%.

Determination of stability indicators as the main criteria for assessing the development of special endurance of cadets

The paper investigates the main biomechanical indicators of the statokinesiogram to assess the coordination criteria of resistance before and after load in physical training classes of cadets of Military Higher Education Institutions (VHE), as well as the registration of posture indicators that characterize the development of the main muscles of the trunk, i.e.: amplitude- frequency, vector and integral indicators of oscillations of the general center of mass. Back in the 20th century, the Hungarian physician Romberg introduced into clinical practice the observation of the upright position of the body and developed a method for assessing the degree of body oscillation and tremor of the limbs. He found that the assessment of the vertical position of the body due to quantitative biomechanical stability criteria is an important indicator of the functional state of the cadets' body and their health [3; 4; 5;7;10]. In the practice of physical training, various static positions and postures are often encountered. Such static positions include various racks, hangs, stops in gymnastic exercises, starting positions in athletics, swimming and other sports, postures of weightlifters, shooters, etc. The role of these positions and postures as elements of sports technique can be completely different if we consider their main three phases - initial, intermediate and final. Depending on which of these phases the studied static posture belongs to, it is possible to specifically assess its role in the effective solution of the motor task. The significant role of static positions and postures in sports is also evidenced by the fact that in competitions for the court, the girls' rules regulate the fixation of static postures [ 1, 2, 8, 9, 11]. Object of research. Cadets of the main group of 1-4 courses with an average level of development of physical condition (Fig. 1). Subject of research. Oscillations of the CMR of the body during stabilometry, where the leading human sensory systems: vestibular, proprioceptive and visual systems unequally integrate their contribution. As a result of the research, the leading role of proprioceptive, amplitude-frequency characteristics of CMR oscillations in the control of equilibrium has been proved, which is confirmed by the studies of M.O. Bernstein (1947), V.S. Gurfinkel (1965-1980), Bretz (1993) and other specialists [3; 4; 6; 7; 9]. Thus, the stabilographic method can be useful in assessing the body's response to stress, as well as in assessing and predicting the effectiveness of the development of special endurance of cadets in various conditions of professional activity.

Intrapulmonary electronic auscultation for asthma and chronic obstructive pulmonary disease

The aim of the study was to develop and perform clinical testing of the intrapulmonary electronic auscultation method for audio and video recording at various levels of the tracheobronchial tree for the diagnosis of asthma and chronic obstructive pulmonary disease (COPD).Methods. We examined 31 patients with moderate (n = 17) and severe (n = 14) COPD with severe symptoms outside of exacerbation and 35 patients with moderate (n = 19) and severe (n = 16) partially controlled asthma. Traditional bronchoscopy was performed, including intrabronchial recording of acoustic noise with a microphone (introduced into the instrumental channel of the bronchoscope) at various levels of the tracheobronchial tree. Video recording in various modes revealed the causes of wheezing. At the same time, pulmonary sounds were recorded in the interscapular region of the chest at the projection points of the bronchoscope in the tracheobronchial tree using a 3M™ Littmann® 3200 electronic stethoscope (USA).Results. The greatest intergroup differences between patients with moderate and severe COPD were demonstrated by intrapulmonary sound parameters (frequency and duration of wheezing, р < 0.0001) and frequency response (amplitude-frequency characteristics) of wheezing in the lumen of the 4th order bronchi (р < 0.0001), significantly exceeded the corresponding sound phenomena during auscultation from the surface of the chest (р < 0.01). The most significant intergroup differences in the groups of BA patients with moderate and severe disease were observed in the frequency response of wheezing during intrapulmonary auscultation in the lumen of the 3rd order (р < 0.0001) and 4th order (р < 0.0001) bronchi; smaller differences were observed in the frequency response during auscultation from the chest surface (р < 0.001).Conclusion. Intrapulmonary auscultation is a modern auscultatory method which can improve the quality and efficiency of diagnosis of asthma and COPD in pulmonology.

Thermal stresses in bimetallic plate under induction heating by nonstationary electromagnetic field

A thermomechanical problem is formulated for a bimetallic plate subjected to induction heating by a nonstationary electromagnetic field. As the object of the study, a plate with layers made of stainless steel and copper is selected. The stress intensities in the constituent layers of the plate are numerically analyzed on its external surfaces and at the contact interface of the constituent layers. The analysis is conducted based on the amplitude-frequency characteristics and the duration of the nonstationary electromagnetic action. The research is carried out for two cases of electromagnetic carrier wave frequencies including those equal to the first resonance frequency and those extending outside the resonance frequency range of the electromagnetic field.

Quantitative evaluation and optimization of synergistic regulation performance considering wear in short-term response of hybrid pumped storage systems

Amid the extensive integration of renewable energy sources and rapid development of variable-speed pumped storage systems (VPSSs), demanding regulation tasks introduce risks to hydraulic-mechanical systems, revealing a growing trade-off between wear and regulation. From the economic and safe operation perspective, this paper aims to accurately quantify and enhance comprehensive regulation performance of hybrid pumped hydro storage systems (HPHSSs) with VPSS. First, a generic framework is established to quantitatively evaluate synergistic regulation performance (SRP), combining regulation intensity and frequency suppression effect of each unit type. Next, a frequency-division coordinated control method is proposed based on the amplitude-frequency characteristics, designed to leverage the rapid response capabilities of VPSS, and the coupling mechanism between this method and the conventional speed limiter module in affecting system dynamics is elucidated. Finally, comprehensive evaluations of HPHSS under typical disturbance scenarios are conducted, with frequency-division parameter further optimized for different system configurations. The results indicate that HPHSS exhibits excellent global stability with the coordinated control, reducing magnitude of average frequency deviation from 10−3 to 10−4, greatly enhancing the SRP. Additionally, an optimal cut-off frequency is identified within 0.05–0.5 Hz, showing an increasing trend as VPSS proportion decreases. These findings provide a novel sight for the safe and optimized operation of HPHSS.

Maximum power point tracking control of wind turbines based on speed hysteresis loop to reduce drive-train loads

By adding compensation torque based on the optimal torque, the torque compensation control method expands the unbalanced torque at varying wind speeds, thereby improving the maximum power point tracking (MPPT) performance of wind turbines (WT). However, while improving the wind energy capture efficiency, such methods will lead to drastic fluctuations of generator torque, resulting in significantly increased drive-train loads. To solve this problem, based on the amplitude-frequency characteristics analysis of the WT system transfer function, it is found rotor speed information can not only reflect the main trend of wind speed changes, but also has the characteristics of not being easily affected by the high-frequency component of wind speed. Therefore, setting compensation torque according to it can effectively alleviate the above phenomenon. On this basis, the MPPT control of WT based on speed hysteresis loop to reduce drive-train loads is proposed. The speed information is used to replace the torque information to set the compensation torque amplitude term, and the speed hysteresis loop is introduced to improve the design of the compensation torque symbol term, which can significantly decreased drive-train loads without compromising on power capture. Finally, the effectiveness of the proposed method is verified by the experiments.

Study on the influence of guide vane opening on pressure pulsation of pump-turbine under zero flow pump condition

Abstract Reversible pump-turbine is the key equipment of energy conversion in large pumped storage power station, and it is the core of stable operation of power station. Under the pump condition, the internal pressure pulsation law of the pump-turbine has an important influence on the stable operation of the pump. In order to study the pressure pulsation characteristics of pump-turbine in pump mode under zero flow condition, this study carried out unsteady numerical simulation on three kinds of guide vane openings, and analyzed the amplitude frequency characteristics of pressure pulsation in turbine under different head and the influence of internal flow characteristics on pressure pulsation. The research shows that in the pump mode, when the guide vane opening of the turbine increases, the influence of the blade frequency and the shaft frequency on the vaneless area increases, resulting in the maximum pressure fluctuation amplitude in the vaneless area under the pump condition, especially when GVO = 19 °. At the same time, due to the influence of dynamic and static interference, the larger turbulent kinetic energy appears in the vaneless area and the connection between the guide vane flow channel and the runner flow channel, resulting in an increase in hydraulic loss. Both the experimental and simulation results show that the guide vane opening of 19 ° should be avoided to reduce the hydraulic loss in the vaneless area when the turbine is operated under the zero flow pump condition.

Magneto-Thermoelastic Principal Parameter Resonance of a Functionally Graded Cylindrical Shell with Axial Tension

The principal parameter resonance of a ferromagnetic functionally graded (FG) cylindrical shell under the action of axial time-varying tension in magnetic and temperature fields is investigated. The temperature dependence of physical parameters for functionally graded materials (FGMs) is considered. Meanwhile, the tension bending coupling effect is eliminated by introducing the physical neutral surface. The kinetic and strain energies are gained with the Kirchhoff–Love shell theory. Based on the nonlinear magnetization characteristics of ferromagnetic materials, the electromagnetic force acting on the shell is calculated. The nonlinear vibration equations are obtained through Hamilton’s principle. Afterward, the vibration equations are discretized and solved by Galerkin and multiscale methods, respectively. The stability criterion for steady-state motion is established utilizing Lyapunov stability theory. After example analysis, the effects of magnetic field intensity, temperature and power law index on the static deflection are elucidated. Subsequently, the impacts of these parameters, as well as axial tension, on the amplitude-frequency characteristics, resonance amplitude, and multiple solution regions are discussed explicitly. Results indicate that the stiffness can be enhanced due to the generation of static deflection. The amplitude decreases with increasing magnetic field intensity, temperature, and power law index. When the magnetic field intensity surpasses a threshold, the resonance phenomenon disappears.

Theoretical Analysis of Viscoelastic Friction System Characteristics of Robotic Arm Brake Based on Fractional Differential Theory

In engineering practice, the nonlinear vibration effect can easily lead to chaos in the system, which will not only reduce the performance of the system but also lead to premature fatigue of components, control failure, and increased safety risks. In view of the core position of the robotic arm in modern industry, this study relies on the robotic arm brake system to explore the theoretical basis of integrated viscoelastic materials as a vibration isolation layer. By analyzing the dynamic characteristics of the friction braking system with fractional differential terms, it aims to provide a new perspective for understanding and controlling the chaotic phenomena of a class of nonlinear friction systems. Firstly, we construct a model of a friction system and analyze its dynamic characteristics in detail. The self-excited vibration of the system under disturbance is studied. The relationship between amplitude and frequency is calculated by a nonlinear approximate analytical algorithm, and the accuracy of this relationship is verified by a numerical algorithm. Then, we compare the differences between non-fractional systems and fractional systems. It is found that with the increase in the fractional order term, the vibration amplitude of the system decreases significantly, which helps to reduce the nonlinear characteristics generated by the friction system and narrow the range of unstable solutions. Secondly, we also study the influence of parameter coefficients on the amplitude–frequency characteristics and analyze the local static bifurcation characteristics through singularity theory. Finally, we study the dynamic bifurcation behavior under different parameter perturbations and find that the change in system parameters will lead to the alternation of periodic motion and chaotic motion.

Damage characterisation of GFRP composites based on clustering acoustic emission events utilizing single-failure-cause tests as reference

A new method to identify causes of fracture in composites based on acoustic emission (AE) and clusterization of AE data based on reference datasets is presented within the manuscript. Acoustic Emission (AE) is a widely used non-destructive method for fracture analysis, but data due to their multidimensionality are not easy to analyze especially if the acoustic events appear simultaneously and have similar parameters even if they are an effect of different failure mechanisms. In this research, we utilize an unsupervised learning algorithm besides the simplest K-means, through fuzzy c-means to Gaussian Mixture Model (GMM) and spectral clustering to investigate the dataset obtained from the three-point bending test manufactured by us composite. The analysis is preceded by data curation, feature determination (Laplacian score) and the best number of cluster investigations (DB index, Caliński-Harabasz score, and Silhouette method) To enable interpretation of the clustering we run an additional three groups of tests covering fibre breakage (two methods), resin fracture (in tension and in compression) and delamination (DCB test) creating reference datasets. These datasets were statistically analyzed and kernel density estimators were generated for each AE feature as well as amplitude-frequency characteristics. Clusters obtained for the main dataset were then assigned to particular causes of failure by comparing them with the reference dataset. It was found that clusters generated using spectral clustering were the most realistic ones, as it was possible to assign the cause of failure to them.

Effects of rail models on aerodynamic characteristics of trains in crosswinds at a large yaw angle

Rail models may be simplified at different levels in wind tunnel tests and numerical simulations. This work used delayed detached eddy simulations to analyze and compare the aerodynamic loads (drag, side force, lift, and rolling moment), surface pressure, and flow characteristics around a train model placed on subgrades with three different rail models: no-rail, simplified rail, and realistic rail. The simulations were conducted at a large yaw angle of 60°. The mean aerodynamic characteristics of the car bodies and bogies were similar with the simplified rail model and realistic rail model, while those were completely different without the rail model. The difference in aerodynamic loads between the no-rail model and the realistic rail model was as high as 53.1%, whereas the difference between the simplified and realistic rail models was only 7.7%. And for fluctuating aerodynamic characteristics of the train, there was still differences between the cases with the simplified and realistic models. Further, the rail model significantly impacted the flow (such as the velocity, turbulent kinetic energy, and vorticity) around the train, especially under the train, resulting in significant differences in the aerodynamic loads in time and frequency domains. For accurate and precise measurements of mean aerodynamic loads, incorporating a rail model (with the simplified model being sufficient) can improve accuracy by 48.0% and precision by 66.9%. When focusing on fluctuating aerodynamic loads, using a realistic rail model is essential to accurately capture amplitude-frequency characteristics. The rail model setup recommendations outlined in this work aim to enhance the accuracy and reliability of various wind tunnel tests and numerical simulations related to train aerodynamics.

Characterization of ultrasonic vibration and polishing force in sapphire ultrasonic vibration-assisted flexible polishing: Insights from in-situ monitoring systems

Sapphire ultrasonic vibration-assisted flexible polishing (UVAFP) is a promising technique for comprehensively improving the surface integrity of machined parts. The technique was performed on an ultra-precision machine tool with the in-situ monitoring systems in this paper, which aims to provide a new perspective for understanding the material removal mechanisms in the sapphire UVAFP process. A Taguchi L9 (43) orthogonal experiment was conducted to investigate the effects of feed distance, spindle speed, ultrasonic vibration (UV), and polishing time on the surface finish and material removal in the process. In addition, the effect of a polyurethane ball tool is not trivial. A single-factor experiment was conducted for exploring it. Based on a laser displacement measurement system and an acoustic emission sensor system, the characteristics of time-dependent ultrasonic amplitude and ultrasonic frequency for the sapphire UVAFP system were analyzed, with the effectiveness of UV demonstrated. Based on a three-component force measurement system, the characteristics of normal force and its relationship with process parameters and tool deformation were analyzed, with macro- and micro-level examined. In conclusion, this paper presents the characterization of UV and polishing force in the sapphire UVAFP process, providing novel insights into understanding the material removal mechanisms of sapphire and even more manufacturing problems.

Gyroscopic rotor dynamics simulation with anisotropy of elastic and damping characteristics of the support

In the work, the differential equations of motion of the gyroscopic rotor, built taking into account the anisotropy of stiffness and damping of the flexible support, are solved analytically, by the method of harmonic balance, convenient for obtaining separately amplitude-frequency and phase-frequency characteristics in the direction of oscillations. The equations of the non-stationary process are obtained by the method of changing amplitudes. It has been found that when the linear stiffness of the elastic support is different in two orthogonal directions, two critical velocities and the corresponding resonant regions arise. In the area of each critical speed, there are two amplitude-frequency curves of oscillations of the main direction and the direction perpendicular to it, respectively. The geometric nonlinearity of damping suppresses the elevations of these amplitude-frequency curves more significantly than linear damping. If only one of the two directions has a damping nonlinearity, then its effect is on the amplitude-frequency curves of the corresponding critical speed. It is more efficient to control resonant amplitudes for smooth resonant transitions by enhancing the linear damping with geometrically nonlinear damping. The results of the analytical solution of the equations of motion agree well with the results of direct modeling and experimental studies.