Iterated socles and integral dependence in regular rings

Let $R$ be a formal power series ring over a field, with maximal ideal $\mathfrak m$, and let $I$ be an ideal of $R$ such that $R/I$ is Artinian. We study the iterated socles of $I$, that is the ideals which are defined as the largest ideal $J$ with $J\mathfrak m^s\subset I$ for a fixed positive integer $s$. We are interested in these ideals in connection with the notion of integral dependence of ideals. In this article we show that the iterated socles are integral over $I$, with reduction number one, provided $s \leq \text{o}(I_1(\varphi_d))-1$, where $\text{o}(I_1(\varphi_d))$ is the order of the ideal of entries of the last map in a minimal free $R$-resolution of $R/I$. In characteristic zero, we also provide formulas for the generators of iterated socles whenever $s\leq \text{o}(I_1(\varphi_d))$. This result generalizes previous work of Herzog, who gave formulas for the socle generators of any ${\mathfrak m}$-primary homogeneous ideal $I$ in terms of Jacobian determinants of the entries of the matrices in a minimal homogeneous free $R$-resolution of $R/I$. Applications are given to iterated socles of determinantal ideals with generic height. In particular, we give surprisingly simple formulas for iterated socles of height two ideals in a power series ring in two variables. These generators are suitable determinants obtained from the Hilbert-Burch matrix

Controls of the hydraulic safety–efficiency trade-off

C.G. was supported by the Swiss National Science Foundation SNF (5231.00639.001.01). A.V. was supported by WSL visiting fellowship and IMAGINA project (Prometeo program 2019/110-Generalitat Valenciana). The CEAM Foundation is supported by Generalitat Valenciana

MECHANICAL ENERGY DIFFERENCES BETWEEN WALKING AND RUNNING AT DIFFERENT VELOCITIES ON TREADMILL

INTRODUCTION: Cavanagh (1990) described a variation from 170 to 1700 W in power output for the same movement (running at 3.6 m/s) calculated by six different authors. These differences occurred mainly due to different procedures for energy calculation and generated data that are not comparable. The purpose of this investigation was to describe, analyze, and compare the mechanical energy curves (total, internal and external energies) for six subjects while walking and running on treadmill, by using the same procedure for energy calculation. METHODS: Six male subjects were filmed with two video-cameras (Sony-50Hz) while walking at 1.5 m/s and running at 3.0 and 4.0 m/s on a treadmill. After a manual digitizing process, a 3D analysis was performed from the kinematics. The analysis was based on a 13 segment model. Positions of segmental centers of gravity, segmental weights, and moments of inertia were estimated on the basis of tables devised by Dempster (1955) as revised by Winter (1979). The components of mechanical energy were calculated at each instant of time, using the equations described by Zatsiorsky et al. (1987). RESULTS AND DISCUSSION: In relation to the differences between walking and running, the following observations were made: a) in walking the greatest contribution to the total change derived from the internal energy, while in running it derives from the external energy; b) the internal and external energy were in phase in walking, and in opposition in running. Comparing the variations in the two velocities of running, the following conclusions were drawn: a) the average value of the absolute total energy at 3.0 m/s was 1237.9 J and at 4.0 m/s 1544.2 J; b) there was a linear correlation (r = 0.84) between the change in velocity and the change in total energy; b) with the increase in velocity, the average increase in the total contribution of the change in internal energy was about 72% and of the external energy 36%; c) there was no change in the contribution of the potential energy to the change in external energy; d) the increase in the internal energy was chiefly dependent on the increase in the kinetic energy. CONCLUSION: Although the results related to the shape of the curves for mechanical energy for walking and running are already a matter of consensus in the field of biomechanics, it would appear that the numerical results are still open to broad discussion

Bistatic Experiment Using TerraSAR-X and DLR’s new F-SAR System

A bistatic X-band experiment was successfully performed early November 2007. TerraSAR-X was used as transmitter and DLR’s new airborne radar system F-SAR, which was programmed to acquire data in a quasi-continuous mode to avoid echo window synchronization issues, was used as bistatic receiver. Precise phase and time referencing between both systems, which is essential for obtaining high resolution SAR images, was derived during the bistatic processing. Hardware setup and performance analyses of the bistatic configuration are pre-sented together with first processing results that verify the predicted synchronization and imaging performance

Resilience support in software-defined networking:a survey

Software-defined networking (SDN) is an architecture for computer networking that provides a clear separation between network control functions and forwarding operations. The abstractions supported by this architecture are intended to simplify the implementation of several tasks that are critical to network operation, such as routing and network management. Computer networks have an increasingly important societal role, requiring them to be resilient to a range of challenges. Previously, research into network resilience has focused on the mitigation of several types of challenges, such as natural disasters and attacks. Capitalizing on its benefits, including increased programmability and a clearer separation of concerns, significant attention has recently focused on the development of resilience mechanisms that use software-defined networking approaches. In this article, we present a survey that provides a structured overview of the resilience support that currently exists in this important area. We categorize the most recent research on this topic with respect to a number of resilience disciplines. Additionally, we discuss the lessons learned from this investigation, highlight the main challenges faced by SDNs moving forward, and outline the research trends in terms of solutions to mitigate these challenges

Recurrent Neural Network Model for On-Board Estimation of the Side-Slip Angle in a Four-Wheel Drive and Steering Vehicle

A valuable quantity for analyzing the lateral dynamics of road vehicles is the side-slip angle, that is, the angle between the vehicle’s longitudinal axis and its speed direction. A reliable real-time side slip angle value enables several features, such as stability controls, identification of understeer and oversteer conditions, estimation of lateral forces during cornering, or tire grip and wear estimation. Since the direct measurement of this variable can only be done with complex and expensive devices, it is worth trying to estimate it through virtual sensors based on mathematical models. This article illustrates a methodology for real-time on-board estimation of the side-slip angle through a machine learning model (SSE—side-slip estimator). It exploits a recurrent neural network trained and tested via on-road experimental data acquisition. In particular, the machine learning model only uses input signals from a standard road car sensor configuration. The model adaptability to different road conditions and tire wear levels has been verified through a sensitivity analysis and model testing on real-world data proves the robustness and accuracy of the proposed solution achieving a root mean square error (RMSE) of 0.18 deg and a maximum absolute error of 1.52 deg on the test dataset. The proposed model can be considered as a reliable and cheap potential solution for the real-time on-board side-slip angle estimation in serial cars