Quadratic-exponential functionals of Gaussian quantum processes

This paper is concerned with exponential moments of integral-of-quadratic functions of quantum processes with canonical commutation relations of position-momentum type. Such quadratic-exponential functionals (QEFs) arise as robust performance criteria in control problems for open quantum harmonic oscillators (OQHOs) driven by bosonic fields. We develop a randomised representation for the QEF using a Karhunen–Loeve expansion of the quantum process on a bounded time interval over the eigenbasis of its two-point commutator kernel, with noncommuting position-momentum pairs as coefficients. This representation holds regardless of a particular quantum state and employs averaging over an auxiliary classical Gaussian random process whose covariance operator is specified by the commutator kernel. This allows the QEF to be related to the moment-generating functional of the quantum process and computed for multipoint Gaussian states. For stationary Gaussian quantum processes, we establish a frequency-domain formula for the QEF rate in terms of the Fourier transform of the quantum covariance kernel in composition with trigonometric functions. A differential equation is obtained for the QEF rate with respect to the risk sensitivity parameter for its approximation and numerical computation. The QEF is also applied to large deviations and worst-case mean square cost bounds for OQHOs in the presence of statistical uncertainty with a quantum relative entropy description.

Флуктуационно-диссипативная теорема и частотные моменты функций реакции плотной плазмы на электромагнитное поле

The fluctuation-dissipative theorem and frequency moments for quadratic functions of the reaction of a dense plasma in a constant magnetic field to an electromagnetic field are considered. The frequency moments of the corresponding correlation functions are studied. A model approach is proposed to calculate quadratic reaction functions that determine nonlinear phenomena caused by the quadratic interaction of electromagnetic waves in a dense charged medium (Coulomb systems, plasma) in a constant magnetic field. Keywords: dense plasma, nonlinear fluctuation-dissipative theorem, quadratic reaction functions, nonlinear phenomena.

Accelerated Reduced Gradient Algorithm with Constraint Relaxation in Differential Inverse Kinematics

The Moore-Penrose pseudoinverse-based solution of the differential inverse kinematic task of redundant robots corresponds to the result of a particular optimization underconstraints in which the implementation of Lagrange’s ReducedGradient Algorithm can be evaded simply by considering the zero partial derivatives of the ”Auxiliary Function” associated with this problem. This possibility arises because of the fact that the cost term is built up of quadratic functions of the variable of optimization while the constraint term is linear function of the same variables. Any modification in the cost and/or constraint structure makes it necessary the use of the numerical algorithm. Anyway, the penalty effect of the cost terms is always overridden by the hard constraints that makes practical problems in the vicinity of kinematic singularities where the possible solution stillexists but needs huge joint coordinate time-derivatives. While in the special case the pseudoinverse simply can be deformed, inthe more general one more sophisticated constraint relaxation can be applied. In this paper a formerly proposed acceleratedtreatment of the constraint terms is further developed by the introduction of a simple constraint relaxation. Furthermore, thenumerical results of the algorithm are smoothed by a third order tracking strategy to obtain dynamically implementable solution.The improved method’s operation is exemplified by computation results for a 7 degree of freedom open kinematic chain

A study of wire tool surface topography and optimization of wire electro-spark machined UNS N06690 using the federated mode of RSM-ANN

PurposeThe purpose of this study is to examine the postprocessed wire tool surface using scanning electron microscopy and find out the streamlined conditions of input process variables using multi-objective optimization techniques to get minimum wire wear values.Design/methodology/approachA federated mode of response surface methodology (RSM) and artificial neural network (ANN) is used to optimize the process variables during the machining of a nickel-based superalloy.FindingsThe study explores that with the rise in spark-off time and spark gap voltage, the rate of wire tool consumption also escalates.Originality/valueMost of the researchers used the RSM technique for the optimization of process variables. The RSM generates a second-order regression model during the modeling and optimization of a manufacturing process whose major limitation is to fit the collected data to a second-order polynomial. The leading edge of ANN on the RSM is that it has comprehensive approximation capability, i.e. it can approximate virtually all types of nonlinear functions, including quadratic functions also.

The Application of Fuzzification for Solving Quadratic Functions

This paper describes an approximation algorithm for solving standard quadratic optimization problems(StQPs) over the standard simplex by using fuzzification technique. We show that the approximate solution of the algorithm is an epsilon -critical point and satisfies epsilon-delta condition. The algorithm is compared with IBM ILOG CPLEX (short for CPLEX). The computational results indicate that the new algorithm is faster than CPLEX. Especially for infeasible problems. Furthermore, we calculate 100 instances for different size StQP problems. The numerical experiments show that the average computational time of the new algorithm for calculating the first local minimizer is in BigO(n) when the size of the problems is less or equal to 450.

On Solving Bi-level Multi-Objective Fully Quadratic Fractional Optimization Model with Fuzzy Demands

This paper has been designed to introduce the method for solving the Bi-level Multi-objective (BL-MO) Fully Quadratic Fractional Optimization Model through Fuzzy Goal Programming (FGP) approach by utilising non-linear programming. In Fully Quadratic Fractional Optimization Model, the objective functions are in fractional form, having quadratic functions in both numerator and denominator subject to quadratic constraints set. The motive behind this paper is to provide a solution to solve the BL-MO optimization model in which number of decision-makers (DM) exists at two levels in the hierarchy. First, the fractional functions with fuzzy demand, which are in the form of fuzzy numbers, are converted into crisp models by applying the concept of α-cuts. After that, membership functions are developed which are corresponding to each decision-maker’s objective and converted into simpler form to avoid complications due to calculations. Finally, the model is simplified by applying FGP approach, and a compromised solution to the initial model is obtained. An algorithm, flowchart and example are also given at the end to explain the study of the proposed model.

Dynamics of an Impulsive Stochastic Predator–Prey System with the Beddington–DeAngelis Functional Response

Taking impulsive effects into account, an impulsive stochastic predator–prey system with the Beddington–DeAngelis functional response is proposed in this paper. First, the impulsive system is transformed into an equivalent system without pulses. Then, by constructing suitable functionals and applying the extreme-value theory of quadratic functions, sufficient conditions on the existence of periodic Markovian processes are provided. The uniform continuity and global attractivity of solutions are also investigated. Additionally, we investigate the extinction and permanence in the mean of all species with the help of comparison methods and inequality techniques. Sufficient conditions on the existence and ergodicity of the stationary distribution of solutions for the autonomous and non-impulsive case are given. Finally, numerical simulations are performed to illustrate the main results.

EXPLORING GIFTED AND TALENTED MUSLIMS STUDENT’S PERFORMANCE USING GEOGEBRA IN TEACHING AND LEARNING MATHEMATICS

GeoGebra is a teaching tool that educators use in their lesson plans to improve the quality of teaching and learning. Instead of drawing on a sheet of paper, students can design a graph, adjust the actual graph shape, and examine the impact of changing graph pattern using GeoGebra in mathematics teaching and learning. Furthermore, students can keep all of their work materials in a structured manner for future reference. GeoGebra will make a school lecture more interesting, exciting, creative, and innovative. The goal of this study was to analyse the effects of GeoGebra software in Mathematics achievement in respect to quadratic functions among gifted and talented Muslims student’s at Kolej GENIUS Insan, Universiti Sains Islam Malaysia. The maximum or minimum point of quadratic function was determined by using GeoGebra software, and the characteristics of quadratic expressions in one variables was also identified. The results illustrate that the graph quadratic expression has the highest point or the lowest point based the values of coefficient a on the quadratic function. For the graph function with negative values of coefficient a on a quadratic function, there are highest values of coordinates x and y, which also known as maximum point, while the graph function with positive values of a on a quadratic function, there are lowest values of coordinates x and y, which also known as minimum point. When students utilize GeoGebra software, their performance in calculating the minimum and maximum points on quadratic functions improves. Keywords: Geogebra; Integrated naqli ‘aqli gifted education; Gifted muslims student; Mathematics achievement; Quadratic functions

PENDAMPINGAN PEMANFAATAN GEOGEBRA DALAM MENGEKSPLORASI KARAKTERISTIK GRAFIK FUNGSI KUADRAT SEBAGAI UPAYA MENINGKATKAN KEMANDIRIAN BELAJAR

GeoGebra provides many facilities that can help teachers in geometry animation and manipulation so that it can be used as a means of visualization and construction in finding mathematical concepts. Utilization of the GeoGebra program can provide students with a visual experience in exploring graphs of quadratic functions in mathematics learning. The use of GeoGebra software is not easy, for that we need assistance and guidance activities from experts that are packaged in the form of community service activities. Mentoring activities are carried out online for students of SMA Negeri 1 Pegandon, Kendal, Central Java, through the Zoom Meeting application. The first session is an introduction to GeoGebra and the slider tool in the GeoGebra application. The second session is an exploration of the graph characteristics of a quadratic function by manipulating GeoGebra. The results of the self-regulated learning response questionnaire show that 75% of students have the initiative to learn, 71.55% of students can diagnose learning needs, 75.86% of students can set learning targets, 71,55% of students view difficulties as challenges, 69.83% of students utilize relevant reference sources, 73.71% of students can set learning strategies, 74.14% of students can evaluate learning processes and outcomes, and 78.02% of students have the good self-concept. Through GeoGebra mentoring service activities, students can be motivated to solve quadratic function graph problems and increase learning independence.GeoGebra banyak memberikan fasilitas yang dapat membantu guru dalam animasi geometri dan manipulasi sehingga dapat dijadikan sebagai sarana visualisasi dan mengkonstruksi dalam menemukan konsep matematis. Pemanfaatan program GeoGebra dapat memberikan pengalaman kepada siswa dalam mengeksplorasi grafik fungsi kuadrat pada pembelajaran matematika. Penggunaan software GeoGebra yang tidak mudah sehingga membutuhkan kegiatan pendampingan dan bimbingan dari ahli. Kegiatan pendampingan dilakukan secara online terhadap siswa SMA Negeri 1 Pegandon kabupaten Kendal Jawa Tengah melalui aplikasi zoom meeting. Sesi pertama kegiatan pengabdian adalah pengenalan GeoGebra dan tool slider pada aplikasi GeoGebra dan pada sesi kedua berupa eksplorasi karakteristik grafik fungsi kuadrat dengan memanipulasi GeoGebra. Hasil angket kemandirian belajar menunjukkan bahwa 75% siswa mempunyai inisiatif belajar, 71,55% siswa dapat mendiagnosa kebutuhan belajar, 75,86% siswa dapat menetapkan target belajar, 71,55% siswa beranggapan kesulitan bagian dari tantangan, 69,83% siswa memilih sumber referensi, 73,71% siswa dapat menetapkan strategi belajar, 74,14% siswa dapat melakukan evaluasi hasil belajar, dan 78,02% siswa memiliki self-concept yang baik. Melalui program pengabdian pendampingan geogebra dapat menjadikan siswa termotivasi untuk menyelesaikan masalah grafik fungsi kuadrat dan meningkatkan kemandirian belajar