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This study aims to quantify and graphically illustrate the negative lingering effect that the COVID-19 pandemic had on the sales in South African Rands (ZAR) of the food and beverage sector using the time series seasonal autoregressive integrated moving average with exogenous components (SARIMAX) intervention model. The SARIMAX 2 ,   1 ,   0 0 ,   1 ,   2 12 intervention model provided the best fit, supported by the lowest values of the model selection and error metrics (Akaike's information criterion, Bayesian information criterion, and root mean square error). The total estimated loss of sales in the 52 months during the intervention period (March 2020 to June 2024) amounts to ZAR 130,579 million. The most affected months were April 2020 and May 2020 with estimated losses of ZAR 7719 million and ZAR 7633 million, respectively. The findings of this study align with the Statistics South Africa® statistical report based on empirical estimation without any model fitting, thus highlighting the effectiveness of the SARIMAX intervention model in quantifying the effects of the pandemic. The lingering negative impact of the COVID-19 pandemic still continues to threaten the sustainability of the South African food and beverage sector, violating the United Nations' Sustainable Development Goal, Number 2, which is to end hunger, achieve food security, improve nutrition, and promote sustainable agriculture. [ABSTRACT FROM AUTHOR]

Topology optimization is a powerful tool for structural design, while its computational cost is quite high due to the large number of design variables, especially for multilateral systems. Herein, an incremental interpolation approach with discrete cosine series expansion (DCSE) is established for multilateral topology optimization. A step function with shape coefficients (i.e., ensuring that no extra variables are required as the number of materials increases) and the use of the DCSE together reduces the number of variables (e.g., from 8400 to 120 for the optimization of the clamped-clamped beam with four materials). Remarkably, the proposed approach can effectively bypass the checkerboard problem without using any filter. The enhanced computational efficiency (e.g., a ~89.2% reduction in computation time from 439.1 s to 47.4 s) of the proposed approach is validated via both 2D and 3D numerical cases. [ABSTRACT FROM AUTHOR]

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

We construct three-dimensional dynamical systems with block-linear discontinuous right-hand side that simulate the simplest molecular oscillators. The phase portrait of each of these systems contains a unique equilibrium point and a cycle lying in the complement of the basin of attraction of this point. There are no other equilibrium points in these phase portraits. [ABSTRACT FROM AUTHOR]

In this paper, we propose a method for approximating the solution of the linear Fredholm integral equation of the second kind which is defined on a closed contour τ in the complex plane. The right-hand side of the equation is a piecewise continuous function that is numerically defined on a finite set of points on τ. To approximate the solution, we use a linear combination of B-spline functions and Heaviside step functions defined on τ. We discuss both theoretical and practical aspects of the pointwise convergence of the method, including its performance in the vicinity of the points where discontinuities occur. [ABSTRACT FROM AUTHOR]

In mathematical physics, time-dependent Green’s functions (GFs) are the solutions of differential equations of the first and second time derivatives. Habitually, the time-dependent GFs are Fourier transformed into the frequency space. Then, analytical continuation of the frequency is extended to below or above the real axis. After inverse Fourier transformation, retarded and advanced GFs can be obtained, and there may be arbitrariness in such analytical continuation. In the present work, we establish the differential equations from which the retarded and advanced GFs are rigorously solved. The key point is that the derivative of the time step function is the Dirac δ function plus an infinitely small quantity, where the latter is not negligible because it embodies the meaning of time delay or time advance. The retarded and advanced GFs defined in this paper are the same as the one-body GFs defined with the help of the creation and destruction operators in many-body theory. There is no way to define the causal GF in mathematical physics, and the reason is given. This work puts the initial conditions into differential equations, thereby paving a way for solving the problem of why there are motions that are irreversible in time. [ABSTRACT FROM AUTHOR]

The deep neural network with step function activation (0/1 DNNs) is a fundamental composite model in deep learning which has high efficiency and robustness to outliers. However, due to the discontinuity and lacking subgradient information of the 0/1 DNNs model, prior researches are largely focused on designing continuous functions to approximate the step activation and developing continuous optimization methods. In this paper, by introducing two sets of network node variables into the 0/1 DNNs and by exploring the composite structure of the resulted model, the 0/1 DNNs is decomposed into a unary optimization model associated with the step function and three derivational optimization subproblems associated with the other variables. For the unary optimization model and two derivational optimization subproblems, we present a closed form solution, and for the third derivational optimization subproblem, we propose an efficient proximal method. Based on this, a globally convergent step function based recursion method for the 0/1 DNNs is developed. The efficiency and performance of the proposed algorithm are validated via theoretical analysis as well as some illustrative numerical examples on classifying MNIST, FashionMNIST and Cifar10 datasets. • We analyse the relevant optimal conditions for 0/1 deep neural networks. • We develop a globally convergent step function based recurtion method for solving 0/1 deep neural networks. • We investigate the proposed method on three classifying datasets: MNIST, FashionMNIST and Cifar10. [ABSTRACT FROM AUTHOR]

In this paper we propose an efficient algorithm for approximating piece- wise continuous functions, defined on a closed contour Γ in the complex plane. The function, defined numerically on a finite set of points of Γ, is approximated by a linear combination of B-spline functions and Heaviside step functions, defined on Γ. Theoretical and practical aspects of the convergence of the algorithm are presented, including the vicinity of the discontinuity points. [ABSTRACT FROM AUTHOR]

In this paper, we describe a new method for speaker clustering in an audio file. The main idea is to replace the speech signal with a step function having a limited number of levels. The research goal is to determine the signal characteristics obtained from the analysis of the step function produced. The step function is created by setting multiple levels that divide the signal range into non-overlapping strips. All the source signal values, which are inside a stip, are changed for the strips mark. Using the sine function as a template, we get recommendations for choosing the sources best-keeping features. We employ the obtained results to solve the problem of speaker diarization. The developed diarization algorithm requires little computer resources. The experiments show the suitability of the developed results to the conditions of the online diarization process.

Molecular dynamics characteristics have important significance in studying the interaction between biomolecules, such as drug screening, environmental monitoring and evaluation of virus infectivity. In this work, a simulation method based on step function is proposed to study the molecular binding and dissociation processes, which is further coupled with surface plasmon wave evanescent field. A complete simulation model is established from biomolecular reaction to surface plasmon resonance (SPR) optical detection, which is consistent with the experimental process. Furthermore, experimental verification studies were carried out on human serum albumin (HSA), a marker of the urinary protein disease. The effects of microchannel size, liquid flow rate, molecular concentration, complex samples and other conditions on the molecular dynamics binding characteristics were studied under the conditions of antibody fixation and antigen–antibody binding reaction. Optimized parameters are obtained such as microchannel size and liquid flow rate, which can save reaction reagents reduce the experimental process and improve the experimental detection accuracy. Therefore, the established simulation and experimental methods include a complete process from biological information to optical information, which is expected to be a powerful tool for molecular interaction analysis in the future. [ABSTRACT FROM AUTHOR]

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

To assist physically disabled people with impaired upper limb function， a new exoskeleton robot is developed， which named motion assistive robotic-exoskeleton for superior extremity to ease daily upper limb movements and to provide effective rehabilitation therapy to the superior extremity. Firstly， the entire wearable robot is designed and modeled in ergonomics. The D-H coordinates are established by the exoskeleton upper limb kinematics model， and use Lagrange method to analyze its dynamics， and the theoretical driving torque of each joint is solved. The dynamics analysis software Adams is used to simulate the robot. By planning the end and active trajectory and speed settings， the changes of torque， speed and acceleration of each joint are obtained. The correctness of the dynamics model is verified in reverse， and the foundation for further optimization of robot is laid.

Because of driving experience and comfort of electric vehicle， the working performance of its dive system must be well in the diving process. Structural analysis and dynamical system calculating of a two speed transmission are carried out， which based on a certain type of electric vehicle， and the flexible simulation model of the transmission system is designed and established based on Adams/View platform. The dive speed of electromotor in different gears is constructed by using Step function， and in the simulation conditions of 0~50 km/h and 50~80 km/h speed range， the kinematics characteristics and impact load on axle head which under first gear and second gear are calculated， analyzed and compared， on the basis of the results， the driving transfer process and variable speed performance of the transmission are verified. The dynamics optimization of input axis is carried out by modal analysis and zero order optimization algorithm， and then dynamic stability of the transmission system is enhanced effectively. All of above provide some technical reference for dynamic design and performance study of new energy vehicle transmission system.

For a positive function f on the interval [0, 1], the power mean of order p ∈ R is defined by ∥ f ∥p = (∫¹0 fp(x) dx)1/p (p ≠ 0), ∥ f ∥0 = exp (∫¹0lnf(x)dx). Assume that 0 < A < B, 0 < θ < 1 and consider the step function gA[θ,1], where χE is the characteristic function of the set E. Let -∞ < p < q < +∞. The main result of this work consists in finding the term Cp = max0≤θ≤1 ∥ gA ∥q/∥ gA ∥p. For fixed p < q, we study the behaviour of Cp and θp with respect to β = B/A ∈ (1,+∞). The cases p = 0 or q = 0 are considered separately. The results of this work can be used in the study of the extremal properties of classes of functions, which satisfy the inverse Hölder inequality, e.g. the Muckenhoupt and Gehring ones. For functions from the Gurov-Reshetnyak classes, a similar problem has been investigated in [4]. [ABSTRACT FROM AUTHOR]

Abstract In the Wind Farm Cabling Problem (WCP) the task is to design the internal cabling of a wind farm such that all power from the turbines can be transmitted to the substations and the costs for the cabling are minimized. Cables can be chosen from several available cable types, each of which has a thermal capacity and cost. Until now, solution approaches mainly use Mixed-integer Linear Programs (MILP) or metaheuristics. We present our current state of research on a fast heuristic specifically designed for WCP. We introduce an algorithm that iteratively improves a cable layout by finding and canceling negative cycles in a suitably defined network. Our simulations on publicly available benchmark sets show that the heuristic is not only fast but it tends to produce good results. Currently our algorithm gives better solutions on large wind farms compared to an MILP solver. However, on small to medium instances the solver performs better in terms of solution quality, which represents a starting point for future work.

Aiming at the problem of force transmission through wire-steel and pulley in previous cam lifting, a new type of negative cam shedding mechanism with spring return was designed and developed on the basis of plane bar group, gear drive, tension spring and disk-cam mechanism with swinging roller follower. The stiffness and initial tension of the spring for coarse cotton fabric were determined through mechanism analysis, derivation of mechanical model and warp tension calculation. Functional simulation prototype of the mechanism was established on ADAMS/View platform. In view of real work situation on the mechanism, dynamic warp tension simulated by Step function was loaded into the heald frame which effectively improved dynamic design accuracy and reliability for lifting process of the heald frame. Based on that, the feasibility of cam lifting and spring return were verified by kinematic and dynamic simulation analysis. The results indicate that in the process of opening and closing, the travel range of heald frame is about 14. 5 mm and angular range of swing bar on the cam is 12. 4°, which can meet the technological requirements of negative cam shedding. [ABSTRACT FROM AUTHOR]

Actuator rate limit phenomenon is ubiquitous in control systems, but it has always been neglected in practical engineering. Especially, few papers are published to investigate the system identification while considering the rate limit. Step function is commonly used in parameter estimation and its first‐order derivative at the step time goes to infinity, which is not affordable by real actuators. As a result, the rate limit slows down the system response speed, misleads the parameter identification, and subsequently affects the controller design and deteriorates the control performance. This study proposes both graphical method and curve fitting method to identify the first‐order plus time‐delay (FOPTD) systems with consideration of the actuator rate limit effect whose limit value is unknown. Quantitative analyses of the parameter mismatch in the traditional FOPTD model and parameter sensitivity analyses are also carried out. Both simulation results and experimental results have shown the necessity and feasibility of defining a new model structure which includes the rate limit value. [ABSTRACT FROM AUTHOR]

To enable targeted therapies and enhance medical decision-making, biomarkers are increasingly used as screening and diagnostic tests. When using quantitative biomarkers for classification purposes, this often implies that an appropriate cutoff for the biomarker has to be determined and its clinical utility must be assessed. In the context of drug development, it is of interest how the probability of response changes with increasing values of the biomarker. Unlike sensitivity and specificity, predictive values are functions of the accuracy of the test, depend on the prevalence of the disease and therefore are a useful tool in this setting. In this paper, we propose a Bayesian method to not only estimate the cutoff value using the negative and positive predictive values, but also estimate the uncertainty around this estimate. Using Bayesian inference allows us to incorporate prior information, and obtain posterior estimates and credible intervals for the cut-off and associated predictive values. The performance of the Bayesian approach is compared with alternative methods via simulation studies of bias, interval coverage and width and illustrations on real data with binary and time-to-event outcomes are provided. [ABSTRACT FROM AUTHOR]

In this note, we study a discontinuous three-term recurrence relation which arises from seeking the steady states of a cellular neural network with step control function. Several collections of periodic solutions are found. A necessary and sufficient condition for a solution to be periodic is stated and aperiodic solutions are found as consequences. We also show that any periodic solution can be derived from a primary periodic solution with least period not divisible by 5. Although the periodic or aperiodic solutions we found are not exhaustive, they are quite abundant and may reflect some of the rich physical phenomena in true biological systems. Our method in this note may also provide a general approach to analyze the periodicity of solutions of similar recurrence relations. [ABSTRACT FROM AUTHOR]

• Expand the application of singularity functions for cable configuration. • Provide the mathematical derivation defining the cable deflection and forces when subject to point loads. • Define the procedure to employ the developed method for determining cable configuration during varied construction stages. • Provide an example of determining cable configuration by using developed method when main span cable is subject to point loads from suspenders. This paper presents a solution procedure for cable configurations, such as the ones used for suspension and cable stayed bridges. It employs a semi analytical method with direct integration of singularity functions. The procedure is rigorous and more efficient than other solution techniques for this class of structures. It can include any number of discontinuous and continuous loads and can take into account the initial configuration of the cable. Because of its efficiency the solution process compared to other solution methods such as finite element analysis is suitable for parametric studies that are needed during the design and construction processes. The procedure may also be used for developing a macro element of cable and its suspenders for use in an efficient finite element solution. [ABSTRACT FROM AUTHOR]

The purpose of this paper was to propose a complete analysis and parameter estimations of a new simplified and highly nonlinear hafnium dioxide memristor model that is appropriate for high-frequency signals. For the simulations; a nonlinear window function previously offered by the author together with a highly nonlinear memristor model was used. This model was tuned according to an experimentally recorded current−voltage relationship of a HfO2 memristor. This study offered an estimation of the optimal model parameters using a least squares algorithm in SIMULINK and a methodology for adjusting the model by varying its parameters overbroad ranges. The optimal values of the memristor model parameters were obtained after minimizing the error between the experimental and simulated current−voltage characteristics. A comparison of the obtained errors between the simulated and experimental current−voltage relationships was made. The error derived by the optimization algorithm was a little bit lower than that obtained by the used methodology. To avoid convergence problems; the step function in the considered model was replaced by a differentiable tangent hyperbolic function. A PSpice library model of the HfO2 memristor based on its mathematical model was created. The considered model was successfully applied and tested in a multilayer memristor neural network with bridge memristor−resistor synapses

In view of the error influence of rigid structure,the flexible modeling technology is applied to drive system design of reducer. The finite element modeling and modal calculating about its parts are carried out by using ANSYS platform,and the flexible design of the reducer is realized through a way of replacing the parts’ MNF file,thus then a simulation model of the virtual prototype of flexible reducer is set up based on ADAMS /View platform. The driving rotational speed and load torque of the reducer are fitted with Step function,and then its flexible body dynamics simulation is carried out. The simulation results that more close to actual situation is calculated and analyzed,such as input and output torque,acceleration,dynamic load and 3D frequency spectrum,all of those provide some strong reference and basis for flexible design and precision analysis of mechanical drive system.

Let G be an abelian ℓ-group with a strong order unit u > 0. We call G u-clean after Hager, Kimber, and McGovern if every element of G can be written as a sum of a strong order unit of G and a u-component of G. We prove that G is u-clean if and only if u-components of G can be lifted modulo any ℓ-ideal of G. Moreover, we introduce a notion of u-suitable ℓ-groups (as a natural analogue of the corresponding notion in Ring Theory) and we prove that the ℓ-group G is u-clean when and only when it is u-suitable. Also, we show that if E is a vector lattice, then E is u-clean if and only if the space of all u-step functions of E is u-uniformly dense in E. As applications, we will generalize a result by Banaschewski on maximal ℓ-ideals of an archimedean bounded f-algebras to the non-archimedean case. We also extend a result by Miers on polynomially ideal C (X)-type algebras to the more general setting of bounded f-algebras. [ABSTRACT FROM AUTHOR]