Maximum Absolute Value Research Articles

Large Magnetocaloric Effect of PrNi Compound at Liquid-Hydrogen Temperatures

In the work, polycrystalline PrNi compound was synthesized by the arc-melting method. The crystal structure is determined as CrB type orthorhombic structure (Space group Pnma). The Curie temperature (T <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">C</sub> ) is determined to be 21.0 K according to the maximum absolute value of first derivative of magnetization. The slope of the Arrott plots is positive around phase transition temperature, indicating of the second-order phase transition characteristic. The magnetic entropy change (-ΔS <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">M</sub> ) was calculated from the isothermal magnetization data based on the Maxwell’s relationship. The maximum value of -ΔS <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">M</sub> is calculated to be 7.3 and 13.0 J/kg K for the magnetic field changes of 0-2 T and 0-5 T, respectively. The large magnetocaloric effect (MCE) around 21.0 K with second-order phase transition feature indicates that PrNi is a great potential in the application of magnetic refrigeration for hydrogen liquefaction.

Research on the application of ergonomics in UI interface design

Abstract This paper firstly discusses the design method and design process of UI interface based on ergonomics, focusing on applying ergonomics principles on interactive UI interface, and discusses the design of UI interface text and color respectively. Secondly, a resilient optimization design model based on the human-computer interaction UI interface is proposed, and the constraints of the first stage and the first stage resilient sub-model are constrained using the equivalence planning method, respectively. The results show that the new version of the interactive UI interface based on ergonomics has a maximum absolute value of 26.83 for the visual coefficient and a minimum of 0.58 for the short-term memory, which is significantly more inclusive than the old version of the UI interface. This paper’s research results are expected to offer a more scientific and reliable design method for UI interface design, which will have greater practical application value and promotion prospects.

Nonlinear position control of electro-hydraulic servo system based on lyapunov robust integral backstepping controller

In electro-hydraulic servo systems (EHSS), high nonlinearity and time-varying features limit the hydraulic actuator performance. In feedback-based systems, linearization reduces nonlinearities. Their cancellation may produce instability when modeling uncertainty exists. This work uses a robust nonlinear controller based on Lyapunov theory to control the nonlinear position of the electro-hydraulic servo system (EHSS). The dynamics of the system were modeled as extensively as possible, and then a simplified mathematical model based on the EHSS dynamics was created for the controller design. Integral backstepping was used to design the nonlinear robust controller utilizing the Lyapunov theory of nonlinear systems. Lyapunov functions theoretically ensured closed-loop stability. Comparative simulation analysis and experimental investigation in real-time with the proportional integral derivative (PID) controller optimized offline for position tracking control were carried out. Besides tracking performance and steady-state error, the mean square error (MSE), the root mean square error (RMSE), the maximum absolute value of tracking errors and the standard deviation of tracking errors (σ) was utilized to evaluate the controllers’ performance. The simulation analysis and experimental verification were accomplished under various sinusoidal trajectories using different testing conditions (amplitudes, frequencies, and external disturbance), in all testing conditions the effectiveness of the robust nonlinear integral backstepping controller was demonstrated.

Dual-Matrix Domain Wall: A Novel Technique for Generating Permutations by QUBO and Ising Models with Quadratic Sizes

The Ising model is defined by an objective function using a quadratic formula of qubit variables. The problem of an Ising model aims to determine the qubit values of the variables that minimize the objective function, and many optimization problems can be reduced to this problem. In this paper, we focus on optimization problems related to permutations, where the goal is to find the optimal permutation out of the n! possible permutations of n elements. To represent these problems as Ising models, a commonly employed approach is to use a kernel that applies one-hot encoding to find any one of the n! permutations as the optimal solution. However, this kernel contains a large number of quadratic terms and high absolute coefficient values. The main contribution of this paper is the introduction of a novel permutation encoding technique called the dual-matrix domain wall, which significantly reduces the number of quadratic terms and the maximum absolute coefficient values in the kernel. Surprisingly, our dual-matrix domain-wall encoding reduces the quadratic term count and maximum absolute coefficient values from n3−n2 and 2n−4 to 6n2−12n+4 and 2, respectively. We also demonstrate the applicability of our encoding technique to partial permutations and Quadratic Unconstrained Binary Optimization (QUBO) models. Furthermore, we discuss a family of permutation problems that can be efficiently implemented using Ising/QUBO models with our dual-matrix domain-wall encoding.

Stress Measurements of GIS Epoxy Composite with Transverse Waves Based on the Ultrasonic Pulse-Echo Method

The mechanical reliability of the gas-insulated metal-enclosed switchgear (GIS) is critical to the safe and stable operation of a power system. The internal stress induced in GIS insulators, which typically lead to cracking, can degrade the mechanical properties and compromise the reliability of the GIS. In this work, ultrasonic nondestructive measurements of the internal stress in a GIS 126 kV epoxy composite with the transverse waves are demonstrated for the first time. Our results show that the velocities of ultrasonic transverse waves increase linearly with the compressive stress and decrease linearly with the tensile stress. The acoustoelastic coefficients are −1.18 × 10−4/MPa and −1.96 × 10−4/MPa for measurements with transverse waves polarized vertically and parallelly to stress, respectively. Based on these acoustoelastic coefficients, the internal stresses are calculated, and the maximum absolute values of relative errors are 35.4% and 26.3% for measurements with the transverse wave polarized vertically and parallelly to stress, respectively.

Finite-time dissipative control for discrete-time memristive neural networks via interval matrix method

This paper addresses the problems of finite-time dissipative analysis and control for discrete-time memristive neural networks (DMNNs). With the help of interval matrix method (IMM), the challenges posed by the mismatched state-dependent parameters of DMNNs can be solved, which is different from the maximal absolute value operation-based method (MAVOM) in most existing literature. Based on a discrete-time Lyapunov-Krasovskii functional (LKF) and some inequality techniques, several sufficient conditions are established for achieving both finite-time bounded (FTB) behavior and finite-time (Q,S,R)−γ dissipative (FTD). Moreover, the control gains are obtained by solving a series of linear matrix inequalities (LMIs) and convex optimization problems. Finally, the validity of our main findings and the superiority of the control strategies are verified through numerical simulations.

Aniseikonia after reduced-fluence photodynamic therapy in patients with central serous chorioretinopathy

This study investigated aniseikonia after reduced-fluence photodynamic therapy (RFPDT) for central serous chorioretinopathy (CSC). We examined 48 eyes of 48 patients (38 men; mean age, 49.2 ± 9.9 years) with CSC resolved after RFPDT. Horizontal and vertical aniseikonia were measured using the New Aniseikonia Test at baseline, 6 months, and 12 months after RFPDT. The maximum absolute value of the horizontal and vertical measurements indicated the aniseikonia score. The aniseikonia score was 2.2 ± 2.3 at 6 months and 2.2 ± 2.0 at 12 months after RFPDT, both of which improved significantly from the baseline score of 4.1 ± 2.9 (P < 0.05 and P < 0.01, respectively). The 12-month aniseikonia score significantly correlated with the baseline aniseikonia score (P = 0.047), outer nuclear thickness at baseline (P = 0.027) and 12 months after RFPDT (P = 0.014), baseline SRD area (P = 0.005), and ellipsoid zone disruption at 12 months after RFPDT (P = 0.021). In multivariate analysis, baseline serous retinal detachment (SRD) area (P = 0.034) was significantly associated with aniseikonia score at 12 months after RFPDT. Eyes with a larger SRD area might have higher aniseikonia scores even after SRD resolution following RFPDT.

Automatic monitoring and control of excavation disturbance of an ultra-deep foundation pit extremely adjacent to metro tunnels

This paper proposes an automatic monitoring and control system to control the construction disturbances of an ultra-deep foundation pit extremely adjacent to the operational metro tunnels. By real-time monitoring the structural response of tunnels and foundation pits, the reinjection wells and servo support system were automatically controlled to change the groundwater level and support axial force, respectively. All the relevant monitoring and control equipment was integrated into the system through Internet of Things technology. The field observations revealed that the proposed automatic monitoring-control system and framework can well control the excavation disturbance in adjacent metro tunnels. Under the ultra-deep excavation depth of 42.25 m and ultra-close spacing of 3.0 m, the maximum absolute value of the observed tunnel displacement was less than 5 mm. All the relevant structural responses of the tunnel and foundation pit were within limits. The wall deformation of the servo side is different from the common bulging deformation curve and is approximately 2 times smaller compared to the non-servo side. The observed tunnel deformation mainly changed at the excavation stage within the buried depth of tunnels. The presented system, data, advised control index and framework can provide useful guidance for similar scenarios.

LOS Deformation Correction Method for DInSAR in Mining Areas by Fusing Ground Data without Control Points

The traditional leveling, total station, and global navigation satellite system (GNSS) and the new differential interferometric synthetic aperture radar (DInSAR) and terrestrial laser scanning (TLS) systems have their own advantages and limitations in the deformation monitoring of mining areas. It is difficult to obtain accurate deformation information only using single-source measurement data. In this study, we propose an LOS deformation correction method for DInSAR in mining areas by fusing ground data without control points. Based on free space data, small deformations at the edges of mining influence areas accurately obtained using DInSAR. By combining leveling/GNSS and TLS methods, it was possible to obtain large deformations in central areas without the need for control points located outside the mining influence range. For overcoming the non-uniform coordinates of the “space–ground” data and the limited overlap of the effective measurement ranges, the subsidence prediction model was employed to assist in its fusion. In addition, in LOS deformation correction, we retained the non-full cycle phase of DInSAR and replaced the full cycle phase with the one from the data fusion. Engineering experiments have shown that the correction results preserve the differences in the LOS deformations at the edge areas of the mine influence range, and they recover the lost LOS deformations at the center areas. Using the difference in the LOS deformation before and after correction as the verification indicator, the maximum absolute value of the errors after correction was 143 mm, which was approximately 6.4% of the maximum LOS deformation. In addition, there were still two errors that were large (−112 mm and −89 mm, respectively), and the absolute values of errors were not more than 75 mm. For all errors, the mean absolute value was 36 mm. Compared with 399 mm before correction, the error was reduced by 91%. This study provides technical support and theoretical reference for deformation monitoring and control in mining areas.

Graphfool: Targeted Label Adversarial Attack on Graph Embedding

Graph embedding learns low-dimensional representations for nodes or edges on the graph, which is widely applied in many real-world applications. Excessive graph mining promotes the research of attack methods on graph embedding. Most attack methods generate perturbations that maximize the deviation of the prediction confidence. They are difficult to accurately misclassify the instances into the target label, and the nonminimized perturbations are more easily detected by defense methods. To address these problems, we propose Graphfool, a novel targeted label adversarial attack on graph embedding. It can generate adversarial graphs to attack graph embedding methods via classification boundary and gradient information in the target graph embedding method. Graphfool first estimates the classification boundaries of different categories. Then, it calculates the minimum perturbation matrix to misclassify the attacked node according to the target classification boundary. Finally, the adjacency matrix is modified according to the maximum absolute value of the perturbation matrix. Extensive experiments demonstrate that Graphfool achieves the state-of-the-art attack performance with minimum perturbations. Besides, the possible defense experiments further prove that the perturbations generated by Graphfool are more imperceptible.

Heterojunction Photocatalyst Loaded on Electrospun Nanofibers for Synergistic Enhanced Photocatalysis and Real-Time Temperature Monitoring.

Bi2WO6:Ho3+, Yb3+/g-C3N4 (BHY/CN) photocatalysts are successfully loaded on polyacrylonitrile (PAN) nanofibers by electrospinning technology, which combines an upconversion effect and heterojunctions to achieve dual-functional characteristics. Polymer-modified photocatalytic materials offer a large specific surface area of 24.1 m2/g and a pore volume of 0.1 cm3/g, promoting the utility of solar energy. The introduction of rare earth ions and g-C3N4 optimizes the structural band gap, which broadens the light absorption range and promotes electron transfer. Moreover, the heterojunction between Bi2WO6 and g-C3N4 has suppressed the complexation of photoinduced carriers, further improving catalytic performance. The optimized photocatalysts have higher photocatalytic activity with degrading 92.6% tetracycline-hydrochloride (120 min) under simulated sunlight irradiation. The optical thermometry has also been achieved based on the fluorescence intensity ratio technique, where the maximum absolute and relative sensitivity values of BHY/CN-1:6@PAN are 3.322% K-1 and 0.842% K-1, respectively. This dual-functional nanofibers with excellent mechanical properties provide noncontact temperature feedback and efficient catalytic performance for better wastewater treatment and ecological restoration in extreme harsh environments.

Mixture Representations for Generalized Burr, Snedecor–Fisher and Generalized Student Distributions with Related Results

In this paper, the representability of the generalized Student’s distribution as uniform and normal-scale mixtures is considered. It is also shown that the generalized Burr and the Snedecor–Fisher distributions can be represented as the scale mixtures of uniform, folded normal, exponential, Weibull or Fréchet distributions. New multiplication-type theorems are proven for these and related distributions. The relation between the generalized Student and generalized Burr distribution is studied. It is shown that the Snedecor–Fisher distribution is a special case of the generalized Burr distribution. Based on these mixture representations, some limit theorems are proven for random sums in which the symmetric and asymmetric generalized Student or symmetric and asymmetric two-sided generalized Burr distributions are limit laws. Also, limit theorems are proven for maximum and minimum random sums and absolute values of random sums in which the generalized Burr distributions are limit laws.

Influence of Hydrodynamic Effect on Dynamic Response of Bridge with Complex Piers Submerged in Reservoir

In order to clarify the influence of hydrodynamic on dynamic response of bridge with complex piers submerged in reservoir, based on the continuous beam of a 4-column pile column frame pier in Xiaolangdi Reservoir of Yellow River, taking 4-column pile column frame pier and bridge as the object separately, the numerical analysis model of bridge (pier) - water interaction is established by ANSYS. The flow around deep-water piers is analyzed. For the single pier (SP) and the pier of the bridge (BP), the dynamic responses of different flow velocities, water depths and wave heights and the combined action are studied. The research shows that detouring flow analysis shows that velocity field and pressure field of each column are asymmetric. Specifically, for this bridge, due to the columns interfere with each other, the velocity difference of 1#, 4# column is more obvious than that of 2#, 3# column. Maximum and stability values of the dynamic response of SP and BP increase with the increase of flow velocity and depth. Specifically, as the water flow velocity increases, the maximum response of the dynamic response increases linearly, while the stable response of the dynamic response increases in the form of a quadratic curve. When the water depth does not exceed 50 m, the maximum and stable values of the dynamic response gradually increase in the form of a quadratic curve. When the wave acts alone, the dynamic response of SP and BP is the largest at the wave crest and the smallest at the wave trough. The maximum dynamic response at the wave crest and trough increases with the increase of wave height. With the increase of water depth, the dynamic effects of waves on SP and BP are more significant. Under the combined action of wave and current, the dynamic response of SP and BP increases with the increase of wave height and water depth. For different flow velocities, the maximum value of dynamic response at wave crest increases with the increase of flow velocity, and the maximum absolute value of dynamic response at wave trough decreases with the increase of flow velocity. Dynamic response under the combined action of wave and current is not the superposition of the dynamic response under the separate action of wave and current. The maximum value of dynamic response appears in wave crest and wave trough, indicating that the current does not change the action of wave field, and the wave still plays a leading role. Specifically, the influence of water on the dynamic response of BP is: pier bottom bending moment > pier bottom shear force > pier top displacement and the influence of water on the dynamic response of SP is: pier bottom bending moment > pier top displacement > pier bottom shear force.

First-principles calculation of bonding and hydrogen trapping mechanism of Fe3C/α-Fe interface

The Fe3C/α-Fe interface in pearlite is the main hydrogen trapping site. The first-principles calculation method based on density functional theory was employed to investigate the bonding and hydrogen trapping mechanism of the Fe3C/α-Fe interface with three different orientation relationships, specifically the Bagaryatsky orientation, Isaichev orientation, and Pitsch-Petch orientation. The results showed that by calculating the interface energy and separation work, the theoretical bonding strength and stability of the three interfaces presented the following order: Isaichev orientation > Pitsch-Petch orientation > Bagaryatsky orientation. Hydrogen segregation energy revealed that H atoms were more likely to be trapped at the Fe3C/α-Fe interface region and the hydrogen trap ability of three interfaces was in the following order: Isaichev orientation > Pitsch-Petch orientation > Bagaryatsky orientation. The maximum absolute value of segregation energy was found at the interface with Isaichev orientation, which was 0.38 eV. The differential charge density, density of states, and Mulliken bond population calculations revealed that the formation of the interface was related to the covalent bond between C atoms in cementite and Fe atoms in ferrite, and affected by the spatial distribution of C atoms. The C atoms also repelled the H atoms, so the strength of H–Fe bond was identified as the dominant factor of hydrogen trapping behavior. Overall, these insights can potentially aid in improving the design and performance of materials with pearlite structures.

Up-Conversion Luminescence and Optical Temperature Sensing Behaviour of Y2O3:Ho3+, Yb3+ Phosphors

The up-conversion (UC) and temperature sensing behaviours of Y2O3:Ho3+, Yb3+ phosphors were investigated. A series of Y2O3:Ho3+, Yb3+ phosphors were synthesized using a solution combustion method. The cubic structure of the Y2O3 with an Ia3¯ space group was analysed by using X-ray powder diffraction. Scanning electron microscopy was conducted to study the surface morphologies of the UC phosphors. Under 980 nm excitation, the UC emissions of Ho3+ from the 5S2 → 5I8, 5F5 → 5I8 and 5S2 → 5I7 transitions were observed, which occurred through UC energy transfer (ET) processes. The Yb3+ ion concentration severely affected the UC emission. The sensing behaviour of the phosphor was investigated through the green (5F4, 5S2 → 5I8) to red (5F5 → 5I8) fluorescence intensity ratio (FIR). The maximum absolute and relative sensitivity values of SA = 0.08 K−1 and SR = 0.64% K−1 were obtained. The results revealed that the prepared Y2O3:Ho3+, Yb3+ phosphor is suitable for optical sensing at high temperatures.

Dynamic Analysis and Safety Assessment of Ships and Cables during Salvage Operations

The International Maritime Organization (IMO) emphasizes that shipwreck accidents frequently occur at sea and advocates for the safe recovery of shipwrecks. This paper examines the case of the Korean “Sewol” ferry salvage, where two lifting barges were symmetrically utilized to retrieve a substantial shipwreck. The dynamic analysis of the salvage operation is based on the computational fluid dynamics (CFD) approach. The main investigation covers two fundamental physical parameters: the motion response of the lifting barges and shipwreck and the tension response of the lifting cables. Using the parameters of the maximum absolute value (MA), root mean square (RMS), and coefficient of variation (CV), a unified criterion is established to quantitatively evaluate the safety of the salvage operation under different working conditions. The study demonstrates that by carefully considering the enhancement of safety and stability for the three vessels involved in the salvage process and by optimizing the safety performance of the lifting cables, suitable operating windows are determined at wave intervals of (115°, 155°) and (205°, 245°). Under most working conditions, curves illustrating the maximum tensions of lifting cables No. 1–15 and No. 16–30 show a distribution with a “middle part drooping” shape. The placement of connecting cables on the water’s surface at 1.1–1.2 times the salvage spacing between the two lifting barges or the arrangement of inclined lifting cables underwater proves advantageous in constraining the motion response of the three vessels. Reinforcing the lifting cables at the bow and stern ends is recommended. This study presents a methodology for salvaging a shipwreck using two lifting barges, which can be used as a reference for designing related salvage approaches.

Finite/fixed-time synchronization of inertial memristive neural networks by interval matrix method for secure communication

This paper investigates the finite/fixed-time synchronization problem of delayed inertial memristive neural networks (DIMNNs) using interval matrix-based methods within a unified control framework. By employing set-valued mapping and differential inclusion theory, two distinct methods are applied to handle the switching behavior of memristor parameters: the maximum absolute value method and the interval matrix method. Based on these different approaches, two control strategies are proposed to select appropriate control parameters, enabling the system to achieve finite and fixed-time synchronization, respectively. Additionally, the resulting theoretical criteria differ based on the chosen control strategy, with one expressed in algebraic form and the other in the form of linear matrix inequalities (LMIs). Numerical simulations demonstrate that the interval matrix method outperforms the maximum absolute value method in terms of handling memristor parameter switching, achieving faster finite/fixed-time synchronization. Furthermore, the theoretical results are extended to the field of image encryption, where the response system is utilized for decryption and expanding the keyspace.

Genetic Approach to Improve Cryptographic Properties of Balanced Boolean Functions Using Bent Functions

Recently, balanced Boolean functions with an even number n of variables achieving very good autocorrelation properties have been obtained for 12≤n≤26. These functions attain the maximum absolute value in the autocorrelation spectra (without considering the zero point) less than 2n2 and are found by using a heuristic search algorithm that is based on the design method of an infinite class of such functions for a higher number of variables. Here, we consider balanced Boolean functions that are closest to the bent functions in terms of the Hamming distance and perform a genetic algorithm efficiently aiming to optimize their cryptographic properties, which provides better absolute indicator values for all of those values of n for the first time. We also observe that among our results, the functions for 16≤n≤26 have nonlinearity greater than 2n−1−2n2. In the process, our search strategy produces balanced Boolean functions with the best-known nonlinearity for 8≤n≤16.

TRISO Burnup-Dependent Failure Analysis of a HTGR Design-Basis Accident Using BISON

This work assesses the failure behavior of the silicon carbide (SiC) layer in TRIstructural ISOtropic (TRISO) fuel particles with BISON during both steady-state and transient conditions for the MHTGR-350 design by General Atomics. A one-dimensional BISON model for a uranium oxycarbide–bearing TRISO is developed to simulate a power level of 50 mW/particles up to 12.4% fissions per initial metal atom (FIMA). Stress predictions for the materials of interest are presented as a function of burnup, along with the SiC failure probability computed using Weibull statistics under the assumption of realistic SiC quality. A design-basis accident (DBA) that involves control rod withdrawal is then simulated in BISON at various burnup levels. Boundary conditions during the DBA are obtained from RELAP5-3D. The predicted SiC failure probability is 3 × 10−14%. This value does not increase during the transient as a function of burnup since irradiation induces a compressive hoop stress state that reaches a maximum absolute value of around 300 MPa. This compressive stress compensates the tensile loading conditions introduced by the transient. The tensile components appear amplified at higher burnups since they increase from 100 to 140 MPa going from 6% FIMA to 12.4% FIMA. Nonetheless, burnup provides a negligible impact on the overall failure probability predictions for SiC, as transient conditions do not translate to a stress increase toward tensile values at any of the considered burnups. Additionally, a two-dimensional (2-D) exploratory BISON model is developed to determine the effects of inner pyrolytic carbon (IPyC) crack formation on SiC. IPyC failure is predicted using Weibull statistics at 105 days from the beginning of irradiation, which is set as the time for crack initiation using XFEM in the 2-D BISON model. Stress concentrations induced by the crack cause the SiC failure probability to increase with respect to the intact particle case by approximately 10 orders of magnitude. Maximum stress concentrations are found at the time of crack formation, after which stress relaxation is observed during remaining steady-state irradiations and subsequent transient simulations. Considerations are made on the results of the 2-D model being contingent on both mechanical and anisotropy properties for pyrolytic carbon. Recommendations are provided for future work involving higher dimensionality models, further investigations on uncertainties, material properties, and additional designs, such as the fluoride salt-cooled high-temperature reactor, that operate at higher burnups.

Electro-enhanced natural convection analysis for an Al2O3-water-filled enclosure by considering the effect of thermal radiation

One of the most crucial topics in the thermal sciences is the analysis of how an external electric field affects the natural convection flow. In this study, the heat transfer of electro-hydrodynamic natural convection in an enclosure with a wavy hot wall is numerically studied. Al2O3-water nanofluid is considered as the working fluid, and furthermore, the effect of thermal radiation on the characteristics of fluid flow is simulated. Non-dimensional forms of governing equations are numerically solved using control volume finite element method. The effects of operational parameters such as Rayleigh number, nanoparticles volume-fraction, Lorentz force number, Eckert number, charge diffusivity number, and electric field number on the maximum absolute value of stream function and the average Nusselt number are investigated. Two new parameters are defined to evaluate the contribution of the electrical field and radiation effects on the fluid flow. The results show that ascends 7.95% when increases from 0 to 0.05 at Also, the values of and increase 27.6% and 37.2%, respectively, when goes up from 0 to 0.5 at The values of and decrease 48.7% and 27.1%, respectively, with decreasing the amplitude parameter from 0.1 to 0.3 at