This paper presents modified Lagrange–Jacobi functions derived from the sine, exponential, and hyperbolic tangent coordinate transformations. The resulting Lagrange–Jacobi functions and their respective matrix elements for observables can...
Special polynomials play an important role in several subjects of mathematics, engineering, and theoretical physics. Many problems arising in mathematics, engineering, and mathematical physics are framed in terms of differential equations. In this pa...
The Euler-Lagrange equations are useful for solving optimization problems in mechanics. In this paper, we study the B-spline solutions of the Euler-Lagrange equations associated with the general functionals. The existing conditions of B-spline soluti...
Consider a compact manifold with boundary, homeomorphic to the N-dimensional disk, and a Tonelli Lagrangian function defined on the tangent bundle. In this paper, we study the multiplicity problem for Euler-Lagrange orbits that satisfy the conormal b...
The augmented Lagrange multiplier as an important concept in duality theory for optimization problems is extended in this paper to generalized augmented Lagrange multipliers by allowing a nonlinear support for the augmented perturbation function. The...
By means of the Lagrange interpolation, we derive two trigonometric identities that are utilized to evaluate, in closed forms, eight classes of power sums of trigonometric functions over equally distributed angles around the unit circle. When the mth...
This paper presents a unified framework for constructing transfinite finite elements with arbitrary node distributions, using either Lagrange or Bernstein polynomial bases. Three distinct classes of elements are considered. The first includes element...
The purpose of this paper is to construct a unified generating function involving the families of the higher-order hypergeometric Bernoulli polynomials and Lagrange–Hermite polynomials. Using the generating function and their functional equations, we...
The D’Alembert–Lagrange principle is a fundamental concept in analytical mechanics that simplifies the analysis of multi-degree-of-freedom mechanical systems, facilitates the dynamic response prediction of structures under various loads,...
The time evolution of stochastic reaction networks can be modeled with the chemical master equation of the probability distribution. Alternatively, the numerical problem can be reformulated in terms of probability moment equations. Herein we present...
The convergence rate of the augmented Lagrangian method (ALM) for solving the nonlinear semidefinite optimization problem is studied. Under the Jacobian uniqueness conditions, when a multiplier vector
This work presents the modified Lagrange interpolating polynomial (MLIP) method, which aims to provide a straightforward procedure for deriving accurate analytical approximations of a given function. The method introduces an exponential function with...
The article considers a model system that describes a dynamically symmetric rigid body in the Lagrange case with a suspension point that performs high-frequency oscillations. This system, reduced to axes rigidly connected to the body, after the avera...
While the established theory of computer-aided geometric design (CAGD) suggests that rational Bernstein–Bézier polynomials associated with control points can be used to accurately represent conics and quadrics, this paper shows that the same goal can...
The security framework in Ad-hoc Networks (ANET) continues to attract the attention of researchers, although significant work has been accomplished already. Researchers in the last couple of years have shown quite an improvement in Identity Dependent...
In this paper, we review two related aspects of field theory: the modeling of the fields by means of exterior algebra and calculus, and the derivation of the field dynamics, i.e., the Euler–Lagrange equations, by means of the stationary action princi...
The latest generation of standard versatile video coding (VVC) continues to utilize hybrid coding architecture to further promote compression performance, where the intra-mode decision module selects the optimal mode to balance bitrate and coding dis...
Vehicle trajectory usually suffers from a large number of outliers and observation noises. This paper proposes a novel framework for reconstructing vehicle trajectories. The framework integrates the wavelet transform, Lagrange interpolation and Kalma...
Recently, a new blind adaptive deconvolution algorithm was proposed based on a new closed-form approximated expression for the conditional expectation (the expectation of the source input given the equalized or deconvolutional output) where the outpu...
The capacitated multi-item lot-sizing problem, referred to as the CLSP, is to determine the lot sizes of products in each period in a given planning horizon of finite periods, meeting the product demands and resource limits in each period, and to min...
This study presents a method for deriving closed-form solutions for Lagrange multipliers in worst-case performance optimization (WCPO) beamforming. By approximating the array-received signal autocorrelation matrix as a rank-1 Hermitian matrix using t...
This research aims to investigate the Noether symmetry and conserved quantity for the fractional Lagrange system with nonholonomic constraints, which are based on the Herglotz principle. Firstly, the fractional-order Herglotz principle is given, and...
Acoustic Emission tomography (AET) has the potential to visualize damage in existing structures, contributing to structural health monitoring. Further, AET requires only the arrival times of elastic waves at sensors to identify velocity distributions...
In this paper, we investigate a trajectory control problem for Euler-Lagrange systems with unknown quantization on the actuator channel. To address such a challenge, we proposed a quantization-mitigation-based trajectory control method, wherein adapt...
Equations of a heavy rotating body with one fixed point can be deduced starting from a variational problem with holonomic constraints. When applying this formalism to the particular case of a Lagrange top, in the formulation with a diagonal inertia t...
Economic dispatch using wind power plants plays a role in reducing the price of electricity production by dispatching power among different generating units for thermal and wind power plants, and supplying load demand while meeting the power system e...
An image reconstruction method is proposed based on Lagrange-Newton method for electrical impedance tomography (EIT) and ultrasound tomography (UT) dual-modality imaging. Since the change in conductivity distribution is usually accompanied with the c...
Throughout this study, we continue the analysis of a recently found out Gibbs–Wilbraham phenomenon, being related to the behavior of the Lagrange interpolation polynomials of the continuous absolute value function. Our study establishes the err...
Task-space cooperative tracking control of the networked multiple Euler–Lagrange systems is studied in this paper. On the basis of establishing kinematic and dynamic modeling of a Euler–Lagrange system, an innovative task-space coordinati...
In the present work we introduce an appropriate definition of the notion of a Lagrange (formal) adjoint system for homogeneous systems with incommensurate-order derivatives in Caputo’s sense and distributed delays. Under natural conditions, the...
In this work, we derive necessary optimality conditions for a class of fractional variational problems involving Caputo-type derivatives. We consider functionals defined on appropriate spaces of absolutely continuous functions and study both periodic...
The results of this research provide fixed-time fractional-order control for Euler–Lagrange systems that are subject to external disturbances. The first step in the process of developing a new system involves the introduction of a method known...
This paper investigates the problem of distributed interval estimation for multiple Euler–Lagrange systems. An interconnection topology is supposed to be strongly connected. To design distributed interval observers, the coordinate transformatio...
Different approaches to describing the kinematics and dynamics of a mobile robot equipped with four Mecanum wheels are compared. Due to the no-slip rolling condition, the kinematic constraints imposed on the system are nonholonomic; therefore, the eq...
Integration by parts plays a crucial role in mathematical analysis, e.g., during the proof of necessary optimality conditions in the calculus of variations and optimal control. Motivated by this fact, we construct a new, right-weighted generalized fr...
The modeling of the paint atomization process is a barrier in computational fluid dynamics numerical simulation for the whole process of air spraying, and seriously restricts robot intelligent spray gun trajectory planning and the improvement of coat...
The focus of this research is to develop a Lagrange multiplier (LM) test of spatial dependence for the spatial autoregressive model (SAR) with latent variables (LVs). It was arranged by the standard SAR, where the independent variables were replaced...
The atmospheric flow field and weather processes exhibit complex and variable characteristics at small scales, involving interactions between terrain features and atmospheric physics. To investigate the mechanisms of these process further, this study...
This paper addresses the problem of leader–follower synchronization of uncertain Euler–Lagrange systems under input constraints. The problem is solved in a distributed model reference adaptive control framework that includes positive
With the rise of the low-altitude urban traffic system, urban air mobility (UAM) has developed rapidly. As a critical component of the UAM system, the strategic layout of vertiports helps divert ground traffic pressure. To satisfy various demand patt...
This study on the local stability of quaternion-valued neural networks is of great significance to the application of associative memory and pattern recognition. In the research, we study local Lagrange exponential stability of quaternion-valued neur...
In this paper, a new Lagrange relaxation based decomposition algorithm for the integrated offshore oil production planning optimization is presented. In our previous study (Gao et al. Computers and Chemical Engineering, 2020, 133, 106674), a multiper...
Accuracy in property valuations is a fundamental element in the real estate market for making informed decisions and developing effective investment strategies. The complex dynamics of real estate markets, coupled with the high differentiation of pro...
We investigate the Lagrange formulation for the one-dimensional Saint Venant–Exner system. The system describes shallow-water equations with a bed evolution, for which the bedload sediment flux depends on the velocity,
Since current key management schemes are mainly designed for static and planar networks, they are not very suitable for the layer-cluster wireless sensor networks (WSNs), a WSN layer-cluster key management scheme based on quadratic polynomial and Lag...
Coordinated operation of hydrothermal scheduling with HVDC links considering network constraints becomes a vital issue due to their remote location and recent induction in the existing power system. The nonlinear and complex nature of the problem int...
Renewable energy sources are constantly increasing in the modern power systems. Due to their intermittent and uncertain potential, increased spinning reserve requirements are needed to conserve the reliability. On the other hand, each action towards...
Rate-distortion optimization (RDO) plays an essential role in substantially enhancing the coding efficiency. Currently, rate-distortion optimized mode decision is widely used in scalable video coding (SVC). Among all the possible coding modes, it aim...
This paper investigates the state prediction problems for uncertain Euler–Lagrange systems with large time delays during data transmissions. A set of sequential predictors is proposed to estimate the actual real-time states of the systems by us...
The goal of this paper is to find a stabilizing and optimal control policy for a class of systems dictated by Euler–Lagrange dynamics, that also satisfies predetermined response criteria. The proposed methodology builds upon two stages. Initial...
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