Dynamic Event-Triggered Quadratic Nonfragile Filtering for Non-Gaussian Systems:Tackling Multiplicative Noises and Missing Measurements

This paper focuses on the quadratic nonfragile filtering problem for linear non-Gaussian systems under multiplicative noises,multiple missing measurements as well as the dynamic event-triggered transmission scheme.The multiple missing measurements are characterized through random variables that obey some given probability distributions,and thresholds of the dynamic event-triggered scheme can be adjusted dynamically via an auxiliary variable.Our attention is concentrated on designing a dynamic event-triggered quadratic nonfragile filter in the well-known minimum-variance sense.To this end,the original system is first augmented by stacking its state/measurement vectors together with second-order Kronecker powers,thus the original design issue is reformulated as that of the augmented system.Subsequently,we analyze statistical properties of augmented noises as well as high-order moments of certain random parameters.With the aid of two well-defined matrix difference equations,we not only obtain upper bounds on filtering error covariances,but also minimize those bounds via carefully designing gain parameters.Finally,an example is presented to explain the effectiveness of this newly established quadratic filtering algorithm.

Representation of an Integer by a Quadratic Form through the Cornacchia Algorithm

Cornachia’s algorithm can be adapted to the case of the equation x2+dy2=nand even to the case of ax2+bxy+cy2=n. For the sake of completeness, we have given modalities without proofs (the proof in the case of the equation x2+y2=n). Starting from a quadratic form with two variables f(x,y)=ax2+bxy+cy2and n an integer. We have shown that a primitive positive solution (u,v)of the equation f(x,y)=nis admissible if it is obtained in the following way: we take α modulo n such that f(α,1)≡0modn, u is the first of the remainders of Euclid’s algorithm associated with n and α that is less than 4cn/| D |) (possibly α itself) and the equation f(x,y)=n. has an integer solution u in y. At the end of our work, it also appears that the Cornacchia algorithm is good for the form n=ax2+bxy+cy2if all the primitive positive integer solutions of the equation f(x,y)=nare admissible, i.e. computable by the algorithmic process.

Relaxed Stability Criteria for Time-Delay Systems:A Novel Quadratic Function Convex Approximation Approach

This paper develops a quadratic function convex approximation approach to deal with the negative definite problem of the quadratic function induced by stability analysis of linear systems with time-varying delays.By introducing two adjustable parameters and two free variables,a novel convex function greater than or equal to the quadratic function is constructed,regardless of the sign of the coefficient in the quadratic term.The developed lemma can also be degenerated into the existing quadratic function negative-determination(QFND)lemma and relaxed QFND lemma respectively,by setting two adjustable parameters and two free variables as some particular values.Moreover,for a linear system with time-varying delays,a relaxed stability criterion is established via our developed lemma,together with the quivalent reciprocal combination technique and the Bessel-Legendre inequality.As a result,the conservatism can be reduced via the proposed approach in the context of constructing Lyapunov-Krasovskii functionals for the stability analysis of linear time-varying delay systems.Finally,the superiority of our results is illustrated through three numerical examples.

Performance Study of a Quadratic Boost Converter

Energy is the driving force behind all economic and industrial development. Africa is the least advanced continent in terms of energy consumption and production. Paradoxically, it is the sunniest continent, which is why our objective is to exploit this energy potential in order to produce and use sufficient energy. To achieve this, we are carrying out a series of studies aimed at developing a device capable of converting solar photovoltaic energy into electrical energy. This device is a two-stage converter, the first of which is a quadratic boost and the second a full bridge. Initially, this paper is devoted to studying the performance of the quadratic boost.

Accounting for Quadratic and Cubic Invariants in Continuum Mechanics–An Overview

The differential equations of continuum mechanics are the basis of an uncountable variety of phenomena and technological processes in fluid-dynamics and related fields.These equations contain derivatives of the first order with respect to time.The derivation of the equations of continuum mechanics uses the limit transitions of the tendency of the volume increment and the time increment to zero.Derivatives are used to derive the wave equation.The differential wave equation is second order in time.Therefore,increments of volume and increments of time in continuum mechanics should be considered as small but finite quantities for problems of wave formation.This is important for calculating the generation of sound waves and water hammer waves.Therefore,the Euler continuity equation with finite time increments is of interest.The finiteness of the time increment makes it possible to take into account the quadratic and cubic invariants of the strain rate tensor.This is a new branch in hydrodynamics.Quadratic and cubic invariants will be used in differential wave equations of the second and third order in time.

Experimental Study of a Quadratic Boost: The Cascaded Connected Single Switch

The quadratic boost is studied under its real model. The equations, of the continuous conduction mode, descriptive of this model are established. From these equations, the expressions of the voltage gain and the efficiency are extracted. These two quantities are plotted as a function of the duty cycle in order to appreciate them in different operating points of the transistor. The values of the different components have also been extracted for the fabrication of a prototype of the converter. Thanks to a set of experimental measurements at the input as well as at the output of the prototype converter, the voltage gain and the efficiency could also be observed. These were also plotted for different loads to observe converter behavior. The theoretical curves were compared with the experimental curves which allowed to validate the proposed mathematical models on a large range of duty cycles.

Nonparametric Statistical Feature Scaling Based Quadratic Regressive Convolution Deep Neural Network for Software Fault Prediction

The development of defect prediction plays a significant role in improving software quality. Such predictions are used to identify defective modules before the testing and to minimize the time and cost. The software with defects negatively impacts operational costs and finally affects customer satisfaction. Numerous approaches exist to predict software defects. However, the timely and accurate software bugs are the major challenging issues. To improve the timely and accurate software defect prediction, a novel technique called Nonparametric Statistical feature scaled QuAdratic regressive convolution Deep nEural Network (SQADEN) is introduced. The proposed SQADEN technique mainly includes two major processes namely metric or feature selection and classification. First, the SQADEN uses the nonparametric statistical Torgerson–Gower scaling technique for identifying the relevant software metrics by measuring the similarity using the dice coefficient. The feature selection process is used to minimize the time complexity of software fault prediction. With the selected metrics, software fault perdition with the help of the Quadratic Censored regressive convolution deep neural network-based classification. The deep learning classifier analyzes the training and testing samples using the contingency correlation coefficient. The softstep activation function is used to provide the final fault prediction results. To minimize the error, the Nelder–Mead method is applied to solve non-linear least-squares problems. Finally, accurate classification results with a minimum error are obtained at the output layer. Experimental evaluation is carried out with different quantitative metrics such as accuracy, precision, recall, F-measure, and time complexity. The analyzed results demonstrate the superior performance of our proposed SQADEN technique with maximum accuracy, sensitivity and specificity by 3%, 3%, 2% and 3% and minimum time and space by 13% and 15% when compared with the two state-of-the-art methods.

A Modified Lagrange Method for Solving Convex Quadratic Optimization Problems

In this paper, a modified version of the Classical Lagrange Multiplier method is developed for convex quadratic optimization problems. The method, which is evolved from the first order derivative test for optimality of the Lagrangian function with respect to the primary variables of the problem, decomposes the solution process into two independent ones, in which the primary variables are solved for independently, and then the secondary variables, which are the Lagrange multipliers, are solved for, afterward. This is an innovation that leads to solving independently two simpler systems of equations involving the primary variables only, on one hand, and the secondary ones on the other. Solutions obtained for small sized problems (as preliminary test of the method) demonstrate that the new method is generally effective in producing the required solutions.

Enhancing Proficiency in Quadratic Equations and Functions Through the MILAPlus Strategy

This study investigates the efficacy of the Mathematics Independent Learning Activity Practice and Play Unite Scheme(MILAPlus)as an instructional strategy to improve the proficiency levels of Grade 9 students in quadratic equations and functions through a study carried out at Quezon National High School.The research involved 116 Grade 9 students and utilized a quantitative approach,incorporating both pre-assessment and post-assessment measures.The research utilizes a quasi-experimental design,examining the academic performance of students before and after the introduction of MILAPlus.The pre-assessment establishes a baseline,and the subsequent post-assessment measures the impact of the instructional strategy.Statistical analyses,including t-tests,assess the significance of differences in mean scores and mean percentage scores,providing quantitative insights into the effectiveness of MILAPlus.Findings from the study revealed a statistically significant improvement in both mean scores and mean percentage scores after the utilization of MILAPlus,indicating enhanced proficiency in quadratic equations and functions.The Mean Proficiency Scores(MPS)also showed a substantial increase,demonstrating a marked improvement in overall proficiency levels among Grade 9 students.In light of the results,recommendations were given including the continued utilization of MILAPlus as an instructional strategy and aligning its development with prescribed learning competencies.Emphasizing the consistent adherence to policies and guidelines for MILAPlus implementation is suggested for sustaining positive effects on students’long-term performance in mathematics.This research contributes valuable insights into the practical application and effectiveness of MILAPlus within the context of Grade 9 mathematics education at Quezon National High School.

Theoretical Study of Double Cost Function Linear Quadratic Regulator(LQR)

Double cost function linear quadratic regulator (DLQR) is developed from LQR theory to solve an optimal control problem with a general nonlinear cost function. In addition to the traditional LQ cost function, another free form cost function was introduced to express the physical need plainly and optimize weights of LQ cost function using the search algorithms. As an instance, DLQR was applied in determining the control input in the front steering angle compensation control (FSAC) model for heavy duty vehicles. The brief simulations show that DLQR is powerful enough to specify the engineering requirements correctly and balance many factors effectively. The concept and applicable field of LQR are expanded by DLQR to optimize the system with a free form cost function.

采用转角补偿LQR的自动驾驶集卡路径跟踪控制

为了解决自动驾驶集卡中半挂车在行驶过程中的路径偏移问题,提出了一种引入铰接角偏差和转角补偿的线性二次调节器(LQR)控制方法。基于集卡三自由度动力学模型建立了考虑铰接角偏差的路径跟踪误差模型;通过采用比例-积分-微分(PID)算法进行转角补偿设计了LQR路径跟踪控制器;通过MATLAB/Simulink和TruckSim搭建联合仿真平台,在不同工况下进行仿真分析验证。结果表明:通过采用提出的路径跟踪算法,引入PID转角补偿,牵引车平均距离偏差降低62%以上,半挂车平均距离偏差降低31%以上,航向偏差和铰接角偏差也均有所改善。因此,该文提出的控制算法具有较好的路径跟踪性能,提高了对期望路径跟踪的精度和稳定性。

Sequential quadratic programming-based non-cooperative target distributed hybrid processing optimization method

The distributed hybrid processing optimization problem of non-cooperative targets is an important research direction for future networked air-defense and anti-missile firepower systems. In this paper, the air-defense anti-missile targets defense problem is abstracted as a nonconvex constrained combinatorial optimization problem with the optimization objective of maximizing the degree of contribution of the processing scheme to non-cooperative targets, and the constraints mainly consider geographical conditions and anti-missile equipment resources. The grid discretization concept is used to partition the defense area into network nodes, and the overall defense strategy scheme is described as a nonlinear programming problem to solve the minimum defense cost within the maximum defense capability of the defense system network. In the solution of the minimum defense cost problem, the processing scheme, equipment coverage capability, constraints and node cost requirements are characterized, then a nonlinear mathematical model of the non-cooperative target distributed hybrid processing optimization problem is established, and a local optimal solution based on the sequential quadratic programming algorithm is constructed, and the optimal firepower processing scheme is given by using the sequential quadratic programming method containing non-convex quadratic equations and inequality constraints. Finally, the effectiveness of the proposed method is verified by simulation examples.

贝莱斯芽胞杆菌LQ-3防治小麦纹枯病的效果及根际定殖能力

小麦纹枯病(wheat sharp eyespot)主要是由禾谷丝核菌(Rhizoctonia cerealis)侵染引起的一种土传真菌病害,严重威胁小麦生产安全。目前,利用生防细菌防治小麦纹枯病已成为研究热点,其中,研究最多的一类生防细菌为芽胞杆菌。为明确贝莱斯芽胞杆菌(Bacillus velezensis)LQ-3防治小麦纹枯病的效果及其在小麦根部定殖能力,本研究利用LQ-3发酵液灌根处理小麦苗,调查统计LQ-3对小麦纹枯病的防效。同时利用绿色荧光蛋白标记菌株LQ-3(pGFP78)灌根处理小麦根部,并结合抗生素平板回收检测、激光共聚焦显微镜观察方法,探明LQ-3在小麦根部的定殖动态。结果表明,LQ-3防治小麦纹枯病的效果为57.49%,与化学药剂27%苯醚·咯·噻虫悬浮种衣剂(酷拉斯)的防效(59.95%)相当。LQ-3(pGFP78)的生长趋势与野生型LQ-3相比并没有显著性差异,且仍具有游动性和生物膜形成能力。LQ-3(pGFP78)发酵液初始浓度为2.3×10^(8) cfu·mL^(-1),灌根处理5 d后,其在小麦根部的定殖量已达到9.63×10^(6)cfu·g^(-1),25 d后,定殖量仍有1.33×10^(6)cfu·g^(-1),表明LQ-3在小麦根部具有较好的定殖能力。

Entropy generation analysis from the time-dependent quadratic combined convective flow with multiple diffusions and nonlinear thermal radiation

Diffusions of multiple components have numerous applications such as underground water flow, pollutant movement, stratospheric warming, and food processing. Particularly, liquid hydrogen is used in the cooling process of the aeroplane. Further, liquid nitrogen can find applications in cooling equipment or electronic devices, i.e., high temperature superconducting(HTS) cables. So, herein, we have analysed the entropy generation(EG), nonlinear thermal radiation and unsteady(time-dependent) nature of the flow on quadratic combined convective flow over a permeable slender cylinder with diffusions of liquid hydrogen and nitrogen. The governing equations for flow and heat transfer characteristics are expressed in terms of nonlinear coupled partial differential equations. The solutions of these equations are attempted numerically by employing the quasilinearization technique with the implicit finite difference approximation. It is found that EG is minimum for double diffusion(liquid hydrogen and heat diffusion)than triple diffusion(diffusion of liquid hydrogen, nitrogen and heat). The enhancing values of the radiation parameter R_(d) and temperature ratio θ_(w) augment the fluid temperature for steady and unsteady cases as well as the local Nusselt number. Because, the fluid absorbs the heat energy released due to radiation, and in turn releases the heat energy from the cylinder to the surrounding surface.

Enhancement of the group delay in quadratic coupling optomechanical systems subjected to an external force

We theoretically study the effect of the quadratic coupling strength on optomechanical systems subjected to a continuous external force. Quadratic coupling strength originates from strong coupling between the optical and the mechanical degrees of freedom. We show that the quadratic coupling strength reduces the amplitude of the dispersion spectra at the resonance in both blue-and red-sideband regimes. However, it increases(decreases) the amplitude of the absorption spectrum in the blue-(red-)sideband regime. Furthermore, in both sideband regimes, the effective detuning between the pump and the cavity deviates with the quadratic coupling strength. Thereby, appropriate selection of the quadratic coupling strength results in an important magnification(in absolute value) of the group delay for both slow and fast light exiting from the optomechanical cavity.

Novel Method to Deal with Interval Quadratic Equations via Sign-Variation Analysis

In this article, analytical results are obtained apparently for the first time in the literature, for the lower and upper bounds of the roots of quadratic equations when two or all three coefficients a, b, c constitute an interval, with a method called the sign-variation analysis. The results are compared with the parametrization technique offered by Elishakoff and Miglis, and with the solution yielded by minimization and maximization commands of the Maple software. Solutions for some interval word problems are also provided to edulcorate the methodology. This article only focuses on the real roots of those quadratic equations, complex solutions being beyond this investigation.

A Novel Human Interaction Framework Using Quadratic Discriminant Analysis with HMM

Human-human interaction recognition is crucial in computer vision fields like surveillance,human-computer interaction,and social robotics.It enhances systems’ability to interpret and respond to human behavior precisely.This research focuses on recognizing human interaction behaviors using a static image,which is challenging due to the complexity of diverse actions.The overall purpose of this study is to develop a robust and accurate system for human interaction recognition.This research presents a novel image-based human interaction recognition method using a Hidden Markov Model(HMM).The technique employs hue,saturation,and intensity(HSI)color transformation to enhance colors in video frames,making them more vibrant and visually appealing,especially in low-contrast or washed-out scenes.Gaussian filters reduce noise and smooth imperfections followed by silhouette extraction using a statistical method.Feature extraction uses the features from Accelerated Segment Test(FAST),Oriented FAST,and Rotated BRIEF(ORB)techniques.The application of Quadratic Discriminant Analysis(QDA)for feature fusion and discrimination enables high-dimensional data to be effectively analyzed,thus further enhancing the classification process.It ensures that the final features loaded into the HMM classifier accurately represent the relevant human activities.The impressive accuracy rates of 93%and 94.6%achieved in the BIT-Interaction and UT-Interaction datasets respectively,highlight the success and reliability of the proposed technique.The proposed approach addresses challenges in various domains by focusing on frame improvement,silhouette and feature extraction,feature fusion,and HMM classification.This enhances data quality,accuracy,adaptability,reliability,and reduction of errors.

Theoretical calculations on Landé g-factors and quadratic Zeeman shift coefficients of nsnp ^(3)P_(0)^(o) clock states in Mg and Cd optical lattice clocks

The study of magnetic field effects on the clock transition of Mg and Cd optical lattice clocks is scarce.In this work,the hyperfine-induced Landég-factors and quadratic Zeeman shift coefficients of the nsnp ^(3)P_(0)^(o) clock states for ^(111,113)Cd and ^(25)Mg were calculated by using the multi-configuration Dirac–Hartree–Fock theory.To obtain accurate values of these parameters,the impact of electron correlations and furthermore the Breit interaction and quantum electrodynamical effects on the Zeeman and hyperfine interaction matrix elements,and energy separations were investigated in detail.We also estimated the contributions from perturbing states to the Landég-factors and quadratic Zeeman shift coefficients concerned so as to truncate the summation over the perturbing states without loss of accuracy.Our calculations provide important data for estimating the first-and second-order Zeeman shifts of the clock transition for the Cd and Mg optical lattice clocks.

A SUPERLINEARLY CONVERGENT SPLITTING FEASIBLE SEQUENTIAL QUADRATIC OPTIMIZATION METHOD FOR TWO-BLOCK LARGE-SCALE SMOOTH OPTIMIZATION

This paper discusses the two-block large-scale nonconvex optimization problem with general linear constraints.Based on the ideas of splitting and sequential quadratic optimization(SQO),a new feasible descent method for the discussed problem is proposed.First,we consider the problem of quadratic optimal(QO)approximation associated with the current feasible iteration point,and we split the QO into two small-scale QOs which can be solved in parallel.Second,a feasible descent direction for the problem is obtained and a new SQO-type method is proposed,namely,splitting feasible SQO(SF-SQO)method.Moreover,under suitable conditions,we analyse the global convergence,strong convergence and rate of superlinear convergence of the SF-SQO method.Finally,preliminary numerical experiments regarding the economic dispatch of a power system are carried out,and these show that the SF-SQO method is promising.

基于LQR的三有源桥变换器控制

针对三有源桥变换器解耦控制中工况远离稳态点解耦矩阵变化时控制性能较差的问题,提出一种基于线性二次型调节器(LQR)的三有源桥变换器控制方法。通过电路等效变换和端口功率传输方程建立状态空间模型,进一步设计基于状态反馈的LQR控制方法,在实现功率潮流控制的同时保持端口电压的稳定,通过仿真控制验证所提出方法的控制性能,对比传统PI解耦控制,在工况变化时,该控制方法具有更好的动态性能。