Remark on Algorithm 982: Explicit Solutions of Triangular Systems of First-order Linear Initial-value Ordinary Differential Equations with Constant Coefficients

Algorithm 982: Explicit solutions of triangular systems of first-order linear initial-value ordinary differential equations with constant coefficients provides an explicit solution for an homogeneous system, and a brief description of how to compute a solution for the inhomogeneous case. The method described is not directly useful if the coefficient matrix is singular. This remark explains more completely how to compute the solution for the inhomogeneous case and for the singular coefficient matrix case.

Parameter Adaptive Sliding Mode Trajectory Tracking Strategy with Initial Value Identification for the Swing in a Hydraulic Construction Robot

A novel trajectory tracking strategy is developed for a double actuated swing in a hydraulic construction robot. Specifically, a nonlinear hydraulic dynamics model of a double actuated swing is established, and a robust adaptive control strategy is designed to enhance the trajectory tracking performance. When an object is grabbed and unloaded, the inertia of a swing considerably changes, and the performance of the estimation algorithm is generally inadequate. Thus, it is necessary to establish an algorithm to identify the initial value of the moment of inertia of the object. To this end, this paper proposes a novel initial value identification algorithm based on a two-DOF robot gravity force identification method combined with computer vision information. The performance of the identification algorithm is enhanced. Simulations and experiments are performed to verify the effect of the novel control scheme.

Fast Computation of Highly Oscillatory ODE Problems: Applications in High-Frequency Communication Circuits

The paper demonstrates symmetric integral operator and interpolation based numerical approximations for linear and nonlinear ordinary differential equations (ODEs) with oscillatory factor x′=ψ(x)+χω(t), where the function χω(t) is an oscillatory forcing term. These equations appear in a variety of computational problems occurring in Fourier analysis, computational harmonic analysis, fluid dynamics, electromagnetics, and quantum mechanics. Classical methods such as Runge–Kutta methods etc. fail to approximate the oscillatory ODEs due the existence of oscillatory term χω(t). Two types of methods are presented to approximate highly oscillatory ODEs. The first method uses radial basis function interpolation, and then quadrature rules are used to evaluate the integral part of the solution equation. The second approach is more generic and can approximate highly oscillatory and nonoscillatory initial value problems. Accordingly, the first-order initial value problem with oscillatory forcing term is transformed into highly oscillatory integral equation. The transformed symmetric oscillatory integral equation is then evaluated numerically by the Levin collocation method. Finally, the nonlinear form of the initial value problems with an oscillatory forcing term is converted into a linear form using Bernoulli’s transformation. The resulting linear oscillatory problem is then computed by the Levin method. Results of the proposed methods are more reliable and accurate than some state-of-the-art methods such as asymptotic method, etc. The improved results are shown in the numerical section.

Performance Improvement of Supercapacitor Materials with Crushed 3D Structured Graphene

Conventional 2D-graphene sheets (2D-rGO) often demonstrate poor performance as capacitor materials, especially in cyclability due to the lamellar stacking and agglomeration of the electrode materials. Herein, we have proposed that crushed 3D-graphene (c-3D-rGO) can overcome the limitation. A simplistic way to prepare 3D-crushed graphene structures has been presented utilizing metal rGO core-shell (Ni@rGO) followed by acid leaching. The electrochemical performances of the prepared c-3D-rGO were evaluated as capacitor material using a three-electrode system with aqueous 0.5 M Na2SO4 solution through cyclic voltammetry and galvanostatic charge-discharge measurements. 2D-rGO was separately prepared to compare the performance with 3D-crushed graphene structures. It has been observed that the calculated specific capacitance (Csp) value of the prepared c-3D-rGO was 335 Fg-1 at a current density of 0.15 Ag-1, which was about three times higher than that of the 2D-rGO. The c-3D-rGO electrode retained 100% capacitance of its initial value after 10000 cycles, demonstrating the material’s excellent electrochemical stability. Furthermore, to show the performance in hybrid capacitor, manganese oxide (MnOx) with c-3D-rGO. The presence of c-3D-rGO significantly improved the capacitive performance MnOx.

The antioxidative potential of sea grapes (Caulerpa lentillifera, Chlorophyta) can be triggered by light to reach comparable values of pomegranate and other highly nutritious fruits

The interest in edible sea grapes (Caulerpa lentillifera) is increasing due to their potentially beneficial effect on human health. This macroalga, already used for direct and indirect human consumption, is grown in aquacultures in Vietnam and The Philippines. Here, the edible fronds of sea grapes were examined for their antioxidant activity (AOA) at light intensities from 140 to 300 µmol photons m−2 s−1 and compared to commercially dehydrated C. lentillifera and the renowned highly antioxidative fruits Pomegranates (Punica granatum), Goji (Lycium barbarum and L. chinense) and Aronia (Aronia melanocarpa) berries, using an ABTS+-assay for all samples. AOA of fronds exposed to 300 µmol photons m−2 s−1 for 14 days increased by about 320% from the initial value of 72.2 ± 5.6 to 232.2 ± 34.2 Trolox Equivalents (TE) mmol 100 g−1 dry weight (DW) onto the level of Pomegranates (272.8 ± 23.0 TE mmol 100 g−1 DW). This application could be used as a post-cultivation treatment in sea grape cultures to increase the quality and nutritional value of the product.

Encryption Management of Accounting Data Based on DES Algorithm of Wireless Sensor Network

The emergence of wireless sensor networks connects the physical world with the information world and changes the way humans interact with nature. With the rapid development of modern information technology, accounting information systems (AIS) have emerged at the historic moment. Under the information environment, accounting data exists in paper or paperless form. The use of information technology not only brings convenient and efficient services to enterprises but also has a huge impact on the internal control of the enterprise. Because the network is open and unstable, the system is vulnerable to illegal intrusion and viruses. Based on the above background, the research content of this article is to use DES algorithm to encrypt accounting data. DES (Data Encryption Standard) encryption algorithm is a symmetric password encryption method. It has the advantages of fast encryption speed, simple and practical algorithm, and consideration of both security and efficiency requirements. This paper discusses the application of DES encryption technology to accounting data processing. To achieve data security management goals. Therefore, this paper proposes a DES algorithm based on the logistic chaotic system. Through experimental simulation, the results show that the chaotic discrete model has initial value sensitivity and iterative nonrepetition. The resulting key space is independent and random. In the application, you can perform random key input according to the performance of software and hardware, which is flexible; there is only one “1186828” in the initial DES algorithm encryption process, but each set of plain text in the improved DES algorithm corresponds to a corresponding set of keys and independence. The test results show that they are maintained between 5 and 6.6. It is proved that using the initial value sensitivity of the logistic system and using the initial value as the key can realize the secure management of accounting data on the premise of ensuring efficiency.

New Fixed Point Theorem on Triple Controlled Metric Type Spaces with Applications to Volterra–Fredholm Integro-Dynamic Equations

The objective of the research article is two-fold. Firstly, we present a fixed point result in the context of triple controlled metric type spaces with a distinctive contractive condition involving the controlled functions. Secondly, we consider an initial value problem associated with a nonlinear Volterra–Fredholm integro-dynamic equation and examine the existence and uniqueness of solutions via fixed point theorem in the setting of complete triple controlled metric type spaces. Furthermore, the theorem is applied to illustrate the existence of a unique solution to an integro-dynamic equation.