Multiplier Technique Research Articles

Optimizing FIR Filter Efficiency with Advanced Hybrid Multiplier Techniques

Optimizing FIR Filter Efficiency with Advanced Hybrid Multiplier Techniques

Local discontinuous Galerkin methods with implicit–explicit BDF time marching for Newell–Whitehead–Segel equations

The Newell–Whitehead–Segel type equations with time-dependent Dirichlet boundary conditions are solved by the local discontinuous Galerkin (LDG) method coupled with the implicit–explicit backward difference formulas (IMEX-BDF). With a suitable setting of numerical fluxes and by the aid of the multiplier technique and the a priori error assumption technique, the optimal error estimate for the corresponding fully discrete LDG-IMEX-BDF schemes is obtained by energy analysis, under the condition τ ≤ C h 1 / s , where h and τ are mesh size and time step, respectively, the positive constant C is independent of h, and s = 1 , … , 5 is the order of the IMEX-BDF method. Numerical experiments are also presented to verify the accuracy of the considered schemes.

Why the action?

In this note, I present two variations of the principle of stationary action in order to provide alternative ways for students to think about the action that they may find more intuitive than the traditional approach. These methods involve Lagrange multiplier techniques and are, therefore, best suited for students who are encountering the stationary action principle for a second or third time, perhaps in an advanced undergraduate mathematical methods course or a graduate classical mechanics course.

Well-posedness and exponential stability of piezoelectric beam with thermal effect and boundary or internal distributed delay

In this work, we focus on a one-dimensional initial-boundary value problem of a thermoelastic piezoelectric beam in the presence of magnetic effects with distributed delay acting in the mechanical equation. The well-posedness of the system is initially demonstrated by applying semigroup theory (Hille-Yosida theorem). Also, based on the construction of a Lyapunov functional, which is equivalent to the energy functional of the problem through multiplier techniques, we show that a unique dissipation through frictional damping is strong enough to ensure exponential stabilization of the model. Next, the results are compared to those of the electrostatic or quasi-static approaches. Moreover, we consider the fully dynamic and electrostatic or quasi-static piezoelectric beams with thermal effects, boundary feedback controllers and boundary distributed delays and using the multipliers technique, we establish an exponential stability result of the solution. Our results are related to the distributed delay weights. Finally, we give some numerical tests to illustrate the theoretical result.

Partially and fully implicit multi-step SAV approaches with original dissipation law for gradient flows

The scalar auxiliary variable (SAV) approach was considered by Shen et al. in Shen et al. (2019) and has been widely used to simulate a series of gradient flows. However, the SAV-based schemes are known for the stability of a ‘modified’ energy. In this paper, we construct a series of modified SAV approaches with unconditional energy dissipation law based on several improvements to the classic SAV approach. Firstly, by introducing the three-step technique, we can reduce the number of constant coefficient linear equations that need to be solved at each time step, while retaining all of its other advantages. Secondly, the addition of energy-optimal technique and Lagrange multiplier technique can make the numerical schemes have the advantage of preserving the original energy dissipation. Thirdly, we use the first-order approximation of the energy balance equation in the GSAV approach, instead of discretizing the dynamic equation of the auxiliary variable, so that we can construct the high-order unconditional original energy stable numerical schemes. Finally, representative numerical examples show that the efficiency and accuracy of the proposed schemes are improved.

Core allocation to minimize total flow time in a multicore system in the presence of a processing time constraint

Data centers are a vital and fundamental infrastructure component of the cloud. The requirement to execute a large number of demanding jobs places a premium on processing capacity. Parallelizing jobs to run on multiple cores reduces execution time. However, there is a decreasing marginal benefit to using more cores, with the speedup function quantifying the achievable gains. A critical performance metric is flow time. Previous results in the literature derived closed-form expressions for the optimal allocation of cores to minimize total flow time for a power-law speedup function if all jobs are present at time 0. However, this work did not place a constraint on the makespan. For many diverse applications, fast response times are essential, and latency targets are specified to avoid adverse impacts on user experience. This paper is the first to determine the optimal core allocations for a multicore system to minimize total flow time in the presence of a completion deadline (where all jobs have the same deadline). The allocation problem is formulated as a nonlinear optimization program that is solved using the Lagrange multiplier technique. Closed-form expressions are derived for the optimal core allocations, total flow time, and makespan, which can be fitted to a specified deadline by adjusting the value of a single Lagrange multiplier. Compared to the unconstrained problem, the shortest job first property for optimal allocation is maintained; however, a number of other properties require revising and other properties are only retained in a modified form (such as the scale-free and size-dependence properties). It is found that with a completion deadline the optimal solution may contain groups of simultaneous completions. In general, all possible patterns of single- and group-completion need to be considered, producing an exponential search space. However, the paper determines analytically that the optimal completion pattern consists of a sequence of single completions followed by a single group of simultaneous completions at the end, which reduces the search space dimension to being linear. The paper validates the Lagrange multiplier approach by verifying constraint qualifications.

Travelling wave solutions and conservation laws of the (2+1)-dimensional new generalized Korteweg–de Vries equation

In this study, we investigate the travelling wave solutions of the (2+1)-dimensional new generalized Korteweg–de Vries equation by employing Lie group analysis along with various techniques which include direct integration, simplest equation method and Kudryashov’s method. The results obtained consists of periodic, kink, soliton and hyperbolic solutions. The symbolic computation software Maple is used to check the accuracy of all solutions obtained. Finally, 3D, density, and 2D plots of the derived solution are displayed to show the physical appearance of the model. Furthermore, we utilize the general multiplier technique and Ibragimov’s method to derive its conserved vectors. Conservation of energy and momentum, amongst others were found. Conservation laws have many significant uses with regards to integrability, linearization and analysis of solutions.

Low-carbon optimal scheduling of park-integrated energy system based on bidirectional Stackelberg-Nash game theory

Multi-stakeholder participation is crucial in facilitating the development of park-integrated energy systems (PIES). Balancing the diverse interests of various stakeholders, each with its distinct requirements presents a notable challenge. Concurrently, the model's complexity increases due to the engagement of various stakeholders, posing challenges to its resolution through traditional methods. In this context, this paper aims to investigate an optimal scheduling model that incorporates shared energy storage (SES) system, microgrids operator (MGO), electric vehicles station (EVS), and user aggregator (UA) with multiple prosumers. To comprehensively address the interests of all stakeholders, this study introduces a tri-level optimization model. The proposed model integrates a bidirectional Stackelberg-Nash game framework, in which the SES acts as the leader, the MGO acts as the secondary leader, and the UA-EVS acts as the followers while allocating benefits based on the asymmetric Nash bargaining theory. The Stackelberg game model between MGO and UA-EVS is analyzed using the Karush-Kuhn-Tucker (KKT) condition, while the Stackelberg game model between SES and MGO is resolved using the bisection method. Meanwhile, the Nash bargaining method among users is solved using the alternating direction method of multipliers (ADMM) technique. The analysis indicates that the proposed strategy can reduce PIES's costs and carbon emissions, yielding a win-win situation for all stakeholders.

Indirect stabilization of locally weakly coupled second‐order evolution systems of hyperbolic type

The purpose of this work is to investigate the stabilization of locally weakly coupled second‐order evolution equations of hyperbolic type, where only one of the two equations is directly damped. As such system cannot be exponentially stable, we are interested in polynomial energy decay rates. Our main contributions concern strong abstract and polynomial stability properties based on stability properties of two auxiliary problems: the sole damped equation and the second equation with a damping related to the coupling operator. The main novelty is that the polynomial energy decay rates are obtained in different important situations not covered before; let us mention the case of a coupling operator not partially coercive and not necessarily bounded. The main tools are the use of the frequency domain approach combined with new multipliers technique based on the solutions of the resolvent equations of the two auxiliary problems mentioned before. Finally, our abstract framework is illustrated by several concrete examples not treated before.

Stability and regularity analysis of nonlinear wave equations with localised internal and Ventcell boundary conditions

This paper primarily focuses on analysing the exponential decay stability and regularity of the solution to a nonlinear wave equation with localised internal damping, characterised by a Carathéodory function and Ventcel-Dirichlet boundary conditions. Additionally, the regularity of the solution within this framework is investigated. Stability through exponential decay is established by formulating fresh Lyapunov functions and employing multiplier techniques. It's essential to underline the recognition of the memory term's influence at the boundary on the solution, thereby introducing a degree of uncertainty into the analysis.

Solution of the Elliptic Interface Problem by a Hybrid Mixed Finite Element Method

This paper addresses the elliptic interface problem involving jump conditions across the interface. We propose a hybrid mixed finite element method on the triangulation where the interfaces are aligned with the mesh. The second-order elliptic equation is initially decomposed into two equations by introducing a gradient term. Subsequently, weak formulations are applied to these equations. Scheme continuity is enforced using the Lagrange multiplier technique. Finally, we derive an explicit formula for the entries of the matrix equation representing Lagrange multiplier unknowns resulting from hybridization. The method yields approximations of all variables, including the solution and gradient, with optimal order. Furthermore, the matrix representing the final linear algebra systems is not only symmetric but also positive definite. Numerical examples convincingly demonstrate the effectiveness of the hybrid mixed finite element method in addressing elliptic interface problems.

Blockchain-enabled framework for transactive home energy management with cloud energy storage under uncertainties

In modern paradigm of smart grid, prosumers can trade energy peer-to-peer in a transactive energy market to reduce energy costs and improve energy efficiency. In addition, cloud energy storage (CES) is a type of shared energy storage systems with high economic efficiency that can provide energy storage services for prosumers and become an active player in energy trading. However, transactive energy implementation in power systems has several challenges such as data privacy and security. In existing researches, energy trading mechanisms rely on central authorities, where security and privacy cannot be maintained. Therefore, this paper presents a decentralized stochastic optimization model of transactive energy management based on blockchain in the presence of CES. In this framework, the smart contract based on Alternating Direction Method of Multipliers technique is deployed on the Ganache and Ethereum blockchains, and the YALMIP toolbox along with CPLEX solver handle decentralized optimization in the MATLAB software. The numerical results demonstrate that not only the capacity of distributed generations is fully utilized, but also total costs of smart homes are reduced by more than 27%, and the total grid’s delivery power to smart homes is decreased by more than 24% compared to the inflexible scheduling.

A High Step-Up Resonant Converter Based on Current-Fed Voltage Multiplier Technique

An extendable non-isolated resonant dc-dc converter based on current-fed voltage multiplier (VM) technique is proposed in this paper for high step-up applications. These VM cells capacitors participate in a resonant network; therefore, no additional elements are required to provide a resonant tank circuit to realize soft switching conditions for power switches. Zero voltage switching (ZVS) and zero current switching (ZCS) conditions are realized here for switches and diodes, respectively. Consequently, MOSFETs dominant switching losses and the diodes reverse recovery problems are well overcome. Furthermore, the input source current waveform is continuous. Also, using the VM cells reduces the power devices voltage stresses. Accordingly, low voltage rating devices can be used, which reduce conduction losses and cost, and improve the converter efficiency. Also, by using more VM cells, the proposed converter can be used for high-voltage applications, without using extremely high duty cycle values to regulate the output voltage. The operation principles, steady-state analysis, design guidelines, and main characteristics of the proposed converter are given here, in detail. Finally, an 800 W prototype converter, with 80–100V input voltage and 2 kV output voltage, has been implemented to validate the given analyses, simulation results, as well as to show the proposed converter main advantages.

A high step-up soft-single switched converter with three coupling inductors

ABSTRACT This paper presents a new high voltage gain converter, which bases on the incorporation of the voltage multiplier cell and the switched coupled inductor technique, having low voltage stress on the switch, which is far from the output voltage. The presented topology is well suited for high step-up applications. By integrating coupled inductors and voltage multiplier cell techniques, a high step-up voltage gain is achieved. All of the semiconductor devices are switched under soft switching conditions, which reduces the switching losses significantly. The switch turns on at ZCS and turns off at ZVS. All diodes have soft-switching features and their reverse recovery problem is obviated due to the leakage inductance. The operation principles and theoretical analysis of proposed converter are presented in details. At the end, the experimental results have been taken from a laboratory prototype rated at 100 W, input voltage of 24 V, output voltage of 300 V, and switching frequency of 100 kHz.

Optimal solution of nonlinear 2D variable-order fractional optimal control problems using generalized Bessel polynomials

This study aims to propose a new optimization method based on the generalized Bessel polynomials (GBPs) as a class of basis functions for a category of nonlinear two-dimensional variable-order fractional optimal control problems (N-2D-VOFOCPs) involved in fractional-order dynamical systems and Caputo derivatives. For the optimal solution of such problems, the optimization method is developed on the basis of operational matrices (OMs) scheme of derivatives, 2D Gauss–Legendre quadrature rule, and Lagrange multiplier technique. The state and control functions are expanded in terms of the GBPs to reduce the complexity of these problems. The proposed method focuses on a system of nonlinear algebraic equations in the process of finding solution to the problems. The convergence of the method based on GBPs is proved, and the accuracy of the method is analyzed by solving several examples.

Stabilization of string–beam–string transmission systems with localized frictional damping and delay

In this paper, we consider two string–beam–string boundary transmission problems with localized frictional damping and delay. The first transmission problem is that the frictional damping and delay are in the left string equation and the right string equation is thermoelastic. The second transmission problem is that the damping and the delay are both only acting on the middle beam equation. Using the semigroup theory, we get the existence and the uniqueness of solution under suitable assumptions on the weight of the damping and the weight of the delay. Furthermore, we prove that the first transmission problem is exponentially stable and the second transmission problem is polynomially stable using the frequency domain method and the multiplier techniques.

Controllability and stabilization of a degenerate/singular Schrödinger equation

The aim of this paper is to prove controllability and stabilization properties for a degenerate and singular Schrödinger equation with degeneracy and singularity occurring at the boundary of the spatial domain. We first address the boundary control problem. In particular, by combining multiplier techniques and compactness-uniqueness argument, we prove direct and inverse inequalities for the associated adjoint system. Consequently, via the Hilbert Uniqueness Method, we deduce exact boundary controllability for the control system under consideration in any time T>0. Moreover, we investigate the stabilization problem for this class of equations in the range of subcritical coefficients of the singular potential. By introducing a suitable linear boundary feedback, we prove that the solution decays exponentially in an appropriate energy space.

Well posedness and stability result of Lord–Shulman system with microtemperature effects: The case ξμ∗=μ02

In this study, we investigate the Lord–Shulman porous elastic system with dissipation caused by the microtemperature effects. Here, the thermal conduction has a single‐phase‐lag that acts as a relaxation time and the energy associated with the solution is not required to be positive definite . We introduce a stability number and prove using the multiplier technique that the exponential decay of the system is valid if . Otherwise, we show that the system decays polynomially.

Determinants of Customer Satisfaction That Impact Electricity Repurchase Decisions: Evidence From Electricity Companies in Indonesia

The purpose of this study is to determine the effect of marketing mix and service quality on customer satisfaction and its impact on electricity repurchase decisions, a case study on electricity companies in Indonesia. This research uses power electricity product categories and customer service provided by electricity companies. The population of this study is electricity customers spread throughout the territory of Indonesia using questionnaires of 250 respondents. This study used a multiplier regression analysis technique with SPSS Statistical Version 25 statistical processing. Research results, First, electricity customer satisfaction is significantly influenced by price, distribution channels, promotions, and service quality; Second, customer satisfaction has a positive and significant effect on the decision to repurchase electricity, Third, simultaneously product, price, distribution channel, promotion, and service quality have a significant effect on customer satisfaction and repurchase decisions, Fourth, customer satisfaction can mediate the influence of price, distribution channels, promotions, and service quality on repurchase decisions, But it is unable to mediate the influence of the product. The results of this study enrich the empirical literature on Marketing Mix theory, Service Quality, Customer Satisfaction, and Purchasing Decisions. Electricity companies can implement a marketing mix and service quality to improve customer satisfaction and electricity repurchase decisions. The originality of this study on mediating customer satisfaction on the effect of marketing mix and service quality on electricity repurchase decisions, no previous study has examined its effect on electricity companies in Indonesia.

Structural stability of subsonic steady states to the hydrodynamic model for semiconductors with sonic boundary

The hydrodynamic model for semiconductors with sonic boundary, represented by Euler–Poisson equations, possesses the various physical steady states including interior-subsonic/interior-supersonic/shock-transonic/C 1-smooth-transonic steady states. Since these physical steady states result in some serious singularities at the sonic boundary (their gradients are infinity), this makes that the structural stability for these physical solutions is more difficult and challenging, and has remained open as we know. In this paper, we investigate the structural stability of interior subsonic steady states. Namely, when the doping profiles are as small perturbations, the differences between the corresponding subsonic solutions are also small. To overcome the singularities at the sonic boundary, we propose a novel approach, which combines the weighted multiplier technique, local singularity analysis, monotonicity argument and squeezing skill. Both the result itself and the technique developed here will give us some truly enlightening insights into our follow-up study on the structural stability of the remaining types of solutions. A number of numerical approximations are also carried out, which intuitively confirm our theoretical results.