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Micromagnetic simulations require the numerically challenging preservation of the Euclidean norm during the whole simulation. This can be accomplished by applying a priori length preserving methods, renormalization algorithms, or penalization strategies. The latter one includes both the penalty method and the Lagrangian multiplier. The penalty method requires the definition of a penalty parameter during the initiation of the simulation which, depending on its size, can lead to an unsatisfied constraint or stiff and difficult to solve systems of equations. The Lagrange multiplier always penalizes in problem-dependent intensity, hence, an additional degree of freedom is added to the system of equations to the drawback of higher computational costs. This paper proposes a method that utilizes a perturbed Lagrangian multiplier and an element level static condensation to condensate the additional degree of freedom. This guarantees fast simulations, and no parameter fitting in advance. Suitable numerical examples are conducted to prove the workability of the outlined scheme and to highlight the efficiency compared to the non-condensed formulation. [ABSTRACT FROM AUTHOR]

This study introduces an unstructured variational nodal method (UVNM-S N), also recognized as the hybridized discontinuous Galerkin (HDG) method, for solving heterogeneous neutron Boltzmann transport problems. The UVNM-S N solves the variational formulation of neutron Boltzmann transport equation (NBTE) by meshing the problem domain with non-overlapping nodes, i.e. the meshes. Lagrange multipliers are introduced along nodal interfaces enforcing neutron conservation. The interface unknowns are globally coupled and solved as the Dirichlet data to recover local within-node unknowns. Unstructured meshes are handled using the coordinate transformation technique, while the angular variables are discretized using the discrete-ordinates (S N) method. Furthermore, within the framework of the UVNM-S N , the nonlinear diffusion acceleration (NDA) is incorporated to tackle the issue of slow convergence of the power iteration (PI). Besides, the volume correction method is developed to facilitate the implementation of the UVNM-S N for heterogeneous problems. The 2D and 3D C5G7 benchmark problems and the SIMONS test problem are utilized to verify the suggested methods. According to numerical results, UVNM-S N exhibits geometric compatibility and precision in a variety of applications. Moreover, the volume correction method yields a speed-up ratio of around 10, and the NDA method provides a 6-12 speed-up ratio. [ABSTRACT FROM AUTHOR]

This paper describes a project assigned in a multivariable calculus course. The project showcases many fundamental concepts studied in a typical course, including the distance formula, equations of lines and planes, intersection of planes, Lagrange multipliers, integrals in both Cartesian and polar coordinates, parametric equations, and arc length. [ABSTRACT FROM AUTHOR]

Two-sample location-scale refers to a model that permits a pair of standardised random variables to have a common base distribution. Function-based hypothesis testing in these models refers to formal tests based on distributions functions, or direct transformations thereof, that would help decide whether or not two samples come from some location-scale family of distributions. For uncensored data, an approach of testing based on plug-in empirical likelihood (PEL) is carried out with sample means and standard deviations as the plug-ins. The method extends to censored data, where censoring adjusted moment estimators provide the requisite plug-ins. The large sample null distribution of the PEL statistic is derived. Since it is not distribution free, a two-sample location-scale appropriate resampling is employed to obtain thresholds needed for the testing. Numerical studies are carried out to investigate the performance of the proposed method. Real examples are presented for both the uncensored and censored cases. [ABSTRACT FROM AUTHOR]

This work introduces a stabilised finite element formulation for the Stokes flow problem with a nonlinear slip boundary condition of friction type. The boundary condition is enforced with the help of an additional Lagrange multiplier representing boundary traction and the stabilised formulation is based on simultaneously stabilising both the pressure and the traction. We establish the stability and the a priori error analyses, and perform a numerical convergence study in order to verify the theory. [ABSTRACT FROM AUTHOR]

We present a complete numerical analysis for a general discretization of a coupled flow–mechanics model in fractured porous media, considering single-phase flows and including frictionless contact at matrix–fracture interfaces, as well as nonlinear poromechanical coupling. Fractures are described as planar surfaces, yielding the so-called mixed- or hybrid-dimensional models. Small displacements and a linear elastic behavior are considered for the matrix. The model accounts for discontinuous fluid pressures at matrix–fracture interfaces in order to cover a wide range of normal fracture conductivities. The numerical analysis is carried out in the Gradient Discretization framework (see J. Droniou, R. Eymard, T. Gallouët, C. Guichard, and R. Herbin [ The gradient discretisation method , Springer, Cham, 2018]), encompassing a large family of conforming and nonconforming discretizations. The convergence result also yields, as a by-product, the existence of a weak solution to the continuous model. A numerical experiment in 2D is presented to support the obtained result, employing a Hybrid Finite Volume scheme for the flow and second-order finite elements (\mathbb {P}_2) for the mechanical displacement coupled with face-wise constant (\mathbb P_0) Lagrange multipliers on fractures, representing normal stresses, to discretize the contact conditions. [ABSTRACT FROM AUTHOR]

In this article, we are first concerned with the existence of multiple normalized solutions to the following fractional p-Laplace problem: { (- Δ) p s ⁢ v + 풱 ⁢ (ξ ⁢ x) ⁢ | v | p - 2 ⁢ v = λ ⁢ | v | p - 2 ⁢ v + f ⁢ (v) in ⁢ ℝ N , ∫ ℝ N | v | p ⁢ 푑 x = a p , where a , ξ > 0 , p ≥ 2 , λ ∈ ℝ is an unknown parameter that appears as a Lagrange multiplier, 풱 : ℝ N → [ 0 , ∞) is a continuous function, and f is a continuous function with L p -subcritical growth. We prove that there exists the multiplicity of solutions by using the Lusternik–Schnirelmann category. Next, we show that the number of normalized solutions is at least the number of global minimum points of 풱 , as ξ is small enough via Ekeland's variational principle. [ABSTRACT FROM AUTHOR]

Communication plays a pivotal role in distributed optimization problems, where unavoidable communication delays are presented. This research studies the distributed constrained optimization problem concerning second‐order multi‐agent systems with double‐integrator under time‐varying communication delays. An adaptive distributed optimization algorithm using multi‐agent system consensus technique and Karush–Kuhn–Tucker conditions is developed to deal with this problem. The local constraint term is solved adaptively through local dual Lagrange multipliers. When the cost function is strongly convex, and the communication topology is undirected and connected, we employ the Lasalle invariance principle to analyze the delay effects on convergence analysis. Moreover, we give an upper bound on communication delay. Finally, the provided numerical simulation examples demonstrate that the developed method is robust for the limited communication delay and the derived results are conservative. [ABSTRACT FROM AUTHOR]

In this paper we consider the following focusing mass-critical Hartree equation with a defocusing perturbation and harmonic potential i ∂ t ψ = - Δ ψ + | x | 2 ψ - (| x | - 2 ∗ | ψ | 2 ) ψ + ε | ψ | p - 2 ψ , in R + × R N , where N ≥ 3 , 2 < p < 2 ∗ = 2 N / (N - 2) and ε > 0 . We mainly focus on the normalized ground state solitary waves of the form ψ (t , x) = e i μ t u ε , ρ (x) , where u ε , ρ (x) is radially symmetric-decreasing and ∫ R N | u ε , ρ | 2 d x = ρ . Firstly, we prove the existence and nonexistence of normalized ground states under the L 2 -subcritical, L 2 -critical ( p = 4 / N + 2 ) and L 2 -supercritical perturbations. Secondly, we characterize perturbation limit behaviors of ground states u ε , ρ as ε → 0 + and find that the ε -blow-up phenomenon happens for ρ ≥ ρ c = ‖ Q ‖ L 2 2 , where Q is a positive radially symmetric ground state of - Δ u + u - (| x | - 2 ∗ | u | 2) u = 0 in R N . We prove that ∫ R N | ∇ u ε , ρ (x) | 2 d x ∼ ε - 4 N (p - 2) + 4 for ρ = ρ c and 2 < p < 2 ∗ , while ∫ R N | ∇ u ε , ρ | 2 d x ∼ ε - 4 N (p - 2) - 4 for ρ > ρ c and 4 / N + 2 < p < 2 ∗ , and obtain two different blow-up profiles corresponding to two limit equations. Finally, we study the limit behaviors as ε → + ∞ , which corresponds to a Thomas–Fermi limit. The limit profile is given by the Thomas–Fermi minimizer u TF = μ TF - | x | 2 + 1 p - 2 , where μ TF is a suitable Lagrange multiplier with exact value. Moreover, we obtain a sharp vanishing rate for u ε , ρ that ‖ u ε , ρ ‖ L ∞ ∼ ε - N N (p - 2) + 4 as ε → + ∞ . [ABSTRACT FROM AUTHOR]

A displacement‐only finite‐element formulation of strain‐gradient models requires elements with C1$$ {C}^1 $$ continuous interpolation. Mixed formulations have been proposed to allow the use of more common C0$$ {C}^0 $$ element shape functions. These mixed formulations are based on the interpolation of two different fields, displacement and some kind of displacement gradient, with the relation between the two fields enforced using either Lagrange multipliers or penalty methods. All elements proposed in the literature for such formulations use a distinct set of degrees of freedom to discretise each field. In this work, we introduce for the first time shared degrees of freedom, that lead to a mixed formulation with a significantly better numerical performance. We describe how this novel mixed formulation can be derived, present individual elements implementing this, and discuss the significance of the results. [ABSTRACT FROM AUTHOR]

A novel structural reliability analysis method that combines the improved beluga whale optimization (IBWO) and the arctangent function‐based maximum entropy method (AMEM) is proposed in this paper. It aims to augment the accuracy of failure probability prediction in structural reliability analysis based on the traditional maximum entropy method (MEM). First, the arctangent function is introduced to avoid the effects of truncation error and numerical overflow in the traditional MEM. The arctangent function can nonlinearly transform the structural performance function defined on the infinite interval into a transformed performance function defined on the bounded interval. Subsequently, the undetermined Lagrange multipliers in the maximum entropy probability density function (MEPDF) of the transformed performance function are obtained using IBWO at a swifter convergence speed with heightened convergence accuracy. Finally, the MEPDF of the transformed performance function can be obtained by combining the IBWO and AMEM, and the structural failure probability can be predicted. The analysis of the metro bogie frame as an engineering example reveals that compared with the traditional MEM using the genetic algorithm to solve the Lagrange multipliers, the proposed method diminishes the relative error in failure probability prediction from 20.51% to only 0.09%. This method significantly enhances the prediction accuracy of failure probability. [ABSTRACT FROM AUTHOR]

In this paper we study the existence and regularity results of normalized solutions to the following critical growth Choquard equation with mixed diffusion type operators: − Δ u + ( − Δ ) s u = λ u + g ( u ) + ( I α ∗ | u | 2 α ∗ ) | u | 2 α ∗ − 2 u in  R N , ∫ R N | u | 2 d x = τ 2 , where N ⩾ 3, τ > 0, I α is the Riesz potential of order α ∈ ( 0 , N ), ( − Δ ) s is the fractional laplacian operator, 2 α ∗ = N + α N − 2 is the critical exponent with respect to the Hardy Littlewood Sobolev inequality, λ appears as a Lagrange multiplier and g is a real valued function satisfying some L 2 -supercritical conditions. [ABSTRACT FROM AUTHOR]

Analysis-suitable G 1 (AS- G 1) multi-patch spline surfaces [7] are particular G 1 -smooth multi-patch spline surfaces, which ensure the construction of C 1 -smooth multi-patch spline spaces with optimal polynomial reproduction properties [20]. We present a local approach for the design of AS- G 1 multi-patch spline surfaces, which is based on the use of Lagrange multipliers. The presented method is simple and generates an AS- G 1 multi-patch spline surface by approximating a given G 1 -smooth but non-AS- G 1 multi-patch surface. Several numerical examples demonstrate the potential of the proposed technique for the construction of AS- G 1 multi-patch spline surfaces and show that these surfaces are especially suited for applications in isogeometric analysis by solving the biharmonic problem, a particular fourth order partial differential equation, with optimal rates of convergence over them. [ABSTRACT FROM AUTHOR]

The relaxation spectrum is a fundamental viscoelastic characteristic from which other material functions used to describe the rheological properties of polymers can be determined. The spectrum is recovered from relaxation stress or oscillatory shear data. Since the problem of the relaxation spectrum identification is ill-posed, in the known methods, different mechanisms are built-in to obtain a smooth enough and noise-robust relaxation spectrum model. The regularization of the original problem and/or limit of the set of admissible solutions are the most commonly used remedies. Here, the problem of determining an optimally smoothed continuous relaxation time spectrum is directly stated and solved for the first time, assuming that discrete-time noise-corrupted measurements of a relaxation modulus obtained in the stress relaxation experiment are available for identification. The relaxation time spectrum model that reproduces the relaxation modulus measurements and is the best smoothed in the class of continuous square-integrable functions is sought. Based on the Hilbert projection theorem, the best-smoothed relaxation spectrum model is found to be described by a finite sum of specific exponential–hyperbolic basis functions. For noise-corrupted measurements, a quadratic with respect to the Lagrange multipliers term is introduced into the Lagrangian functional of the model's best smoothing problem. As a result, a small model error of the relaxation modulus model is obtained, which increases the model's robustness. The necessary and sufficient optimality conditions are derived whose unique solution yields a direct analytical formula of the best-smoothed relaxation spectrum model. The related model of the relaxation modulus is given. A computational identification algorithm using the singular value decomposition is presented, which can be easily implemented in any computing environment. The approximation error, model smoothness, noise robustness, and identifiability of the polymer real spectrum are studied analytically. It is demonstrated by numerical studies that the algorithm proposed can be successfully applied for the identification of one- and two-mode Gaussian-like relaxation spectra. The applicability of this approach to determining the Baumgaertel, Schausberger, and Winter spectrum is also examined, and it is shown that it is well approximated for higher frequencies and, in particular, in the neighborhood of the local maximum. However, the comparison of the asymptotic properties of the best-smoothed spectrum model and the BSW model a priori excludes a good approximation of the spectrum in the close neighborhood of zero-relaxation time. [ABSTRACT FROM AUTHOR]

This article presents an adaptive remeshing strategy between the finite element method (FEM) and the discrete element method (DEM). To achieve this strategy, an edge‐to‐edge coupling method based on Lagrange multipliers has been set‐up to ensure the continuity of velocities at the interface. To switch from a computation initially purely FEM to a FEM‐DEM one, a field transfer method was required. In particular, a displacement field transfer method has been set‐up. The switching from a FEM subdomain to a DEM one is activated by a transition criterion. Each time a FEM subdomain is substituted by a DEM one, the DEM subdomain microscopic properties are set‐up with respect to the subdomain geometry and desired particle refinement. This is performed thanks to the linking to the so‐called "Cooker," a tool distributed along with the GranOO Workbench. Two subdomain remeshing cases were dealt with: that of an initially FEM subdomain that is converted to DEM, and that of DEM subdomains which coalesce. A numerical test case shows that the dynamic remeshing method behaves as expected: FEM subdomains are substituted by DEM ones when the transition criterion is met, and DEM subdomains coalesce when required. The final numerical test case shows a good agreement with a crack propagation experiment of the literature, while a speedup of about 20 was observed when compared to pure DEM computation. [ABSTRACT FROM AUTHOR]

In this work, we prove existence and multiplicity of solutions to a Kirchhoff elliptic problem in the whole space ℝN. More specifically, we consider the following nonlocal elliptic problem: − m(∥∇u∥22)Δu + V (x)u = λa(x)|u|q−2u − 휃b(x)|u|p−2uin ℝN,u ∈ H1(ℝN), where N ≥ 3, the parameters λ,휃 > 0, 2 < 2(σ + 1) < q < p < 2∗ := 2N/(N − 2), σ ∈ (0, 2/(N − 2)) and a,b ∈ L∞(ℝN) with a(x),b(x) > 0 almost everywhere in ℝN. This type of problem contains the function m : ℝ+ → ℝ+ known as the Kirchhoff function given by m(t) = α1 + α2tσ with α1,α2 > 0 and t ∈ ℝ+. Under our assumptions the potential V : ℝN → ℝ and the nonlinearities can be sign changing functions. Hence, our main objective is to prove that the above problem has at least two distinct nontrivial solutions, one of them being a ground state, whenever λ ∈ (λ∗, +∞) for some suitable λ∗ > 0. The main idea is to use the minimization method in the Nehari manifold together with the nonlinear Rayleigh quotient. In our setting, the main difficulty is ensuring the existence of nontrivial solutions by using the Nehari method considering the Lagrange Multipliers Theorem. In other words, we study the case where the fibering map admits inflections points with λ,휃 > 0. Furthermore, for each λ ∈ (−∞,λ∗], we show a nonexistence result for our main problem. It is important to emphasize that λ∗ > 0 is sharp in order to find the existence and multiplicity of nontrivial solutions for our main problem. [ABSTRACT FROM AUTHOR]

The width of natural fractures is an important parameter in the leak prevention and plugging operations for oil and gas drilling. To accurately predict the fracture width of the leaking formation when well leakage occurs during oilfield drilling, based on the mud logging data of adjacent oil wells during the loss process, the Spearman correlation analysis and data normalization methods were used to preprocess the data. A new method was then established to predict the natural fracture width based on FDCNN (Fluid Dynamics Constrained Neural Network), which is a neural network algorithm constrained by the prior knowledge of fluid dynamics. In this method, first, based on the fluid dynamics prior knowledge that there is a strict positive partial derivative relationship between the natural fracture width and the leakage volume and pressure difference in the fluid dynamics model, the constraint conditions of the neural network were optimized. Second, the augmented Lagrange multiplier method was used to establish the performance index of the neural network through a multiplier and a penalty factor. Finally, the model was trained using the backpropagation learning rule and gradient descent training methods. The results indicate that this method, utilizing FDCNN, can train the model with a small sample training set, demonstrating superior generalization ability and prediction accuracy compared to traditional fluid dynamics models and Data-Driven Neural Network (which refers to an algorithm training a neural network solely on data samples without using fluid dynamics prior knowledge). This approach can effectively reduce the prediction error of fracture width, providing valuable reference for the development of field plugging programs. [ABSTRACT FROM AUTHOR]

Background: Chronic obstructive pulmonary disease (COPD) is a chronic, inflammatory respiratory disease that obstructs airflow and decreases lung function and is a leading cause death globally. In the United States (US), the prevalence among adults is 6.2%, but increases with age to 12.8% among those 65 years or older. Florida has one of the largest populations of older adults in the US, accounting for 4.5 million adults 65 years or older. This makes Florida an ideal geographic location for investigating COPD as disease prevalence increases with age. Understanding the geographic disparities in COPD and potential associations between its disparities and environmental factors as well as population characteristics is useful in guiding intervention strategies. Thus, the objectives of this study are to investigate county-level geographic disparities of COPD prevalence in Florida and identify county-level socio-demographic predictors of COPD prevalence. Methods: This ecological study was performed in Florida using data obtained from the US Census Bureau, Florida Health CHARTS, and County Health Rankings and Roadmaps. County-level COPD prevalence for 2019 was age-standardized using the direct method and 2020 US population as the standard population. High-prevalence spatial clusters of COPD were identified using Tango's flexible spatial scan statistics. Predictors of county-level COPD prevalence were investigated using multivariable ordinary least squares model built using backwards elimination approach. Multicollinearity of regression coefficients was assessed using variance inflation factor. Shapiro-Wilks, Breusch Pagan, and robust Lagrange Multiplier tests were used to assess for normality, homoskedasticity, and spatial autocorrelation of model residuals, respectively. Results: County-level age-adjusted COPD prevalence ranged from 4.7% (Miami-Dade) to 16.9% (Baker and Bradford) with a median prevalence of 9.6%. A total of 6 high-prevalence clusters with prevalence ratios >1.2 were identified. The primary cluster, which was also the largest geographic cluster that included 13 counties, stretched from Nassau County in north-central Florida to Charlotte County in south-central Florida. However, cluster 2 had the highest prevalence ratio (1.68) and included 10 counties in north-central Florida. Together, the primary cluster and cluster 2 covered most of the counties in north-central Florida. Significant predictors of county-level COPD prevalence were county-level percentage of residents with asthma and the percentage of current smokers. Conclusions: There is evidence of spatial clusters of COPD prevalence in Florida. These patterns are explained, in part, by differences in distribution of some health behaviors (smoking) and co-morbidities (asthma). This information is important for guiding intervention efforts to address the condition, reduce health disparities, and improve population health. [ABSTRACT FROM AUTHOR]

We consider the multiplicity of solutions for the following class of non-autonomous $ p $-Laplace equations:$ \begin{equation*} \begin{cases} -\Delta_p u = \lambda |u|^{p-2}u + h(\epsilon x)f(u), \quad x\in\mathbb{R}^N, \\ \int_{\mathbb{R}^N} |u|^pdx = a^p, \end{cases} \end{equation*} $where $ \epsilon, a>0 $, $ 1

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In this paper, a mathematical model is given that depicts the interactions between cancer cells and viruses in the setting of oncolytic virotherapy. The model is separated into three classes, namely, concentrations of uninfected tumor cells in the population “ U$$ \mathcal{U} $$”, free virus “ V$$ \mathcal{V} $$”, and cancerous cells infected “ I$$ \mathcal{I} $$”. Applying Caputo fractional derivative, the model is fractionalized, and using generalized Bessel polynomials, an optimal problem is solved utilizing Lagrange multipliers method. The results show that the presented method has high accuracy and is suitable for solving the nonlinear systems based on partial differential equations especially tumors models. [ABSTRACT FROM AUTHOR]

Summary In this paper, a novel strategy of video communication over a 5G platform of new radio (NR) is developed, and it is named ViNR. With the support of optimization on the ViNR quality of service (QoS) system design, we stretched the outdated R‐D optimization to a novel delay‐distortion‐rate optimization (DDRO) control method. The entire model is partitioned with two types of coding: source coding and channel coding. For source coding, we affianced the inter‐frame prediction method of independent predicted frames (IPPPP) with Lagrange multiplier optimization. Channel coding is intricate with the minimization of delay‐distortion and getting the most out of the rate using resource allocation optimization in terms of sub‐slice allocation. To perform this sub‐slice resource assignment with optimization of DDR, the isolation resource allocation is premeditated in this work to ensure the service level profile of various groups of resource slots or grids dealing with the subject of middling delay and rate. The widespread simulation results divulge that the proposed algorithm NR‐DDRO achieves better QoS parameters of delay, distortion, and rate with the metrics of end‐to‐end distortion, encoding Y‐PSNR, encoding bit rate, encoding time, end‐to‐end PSNR, optimization time, and complete computation time. [ABSTRACT FROM AUTHOR]

This paper points out the interval form deficiencies in the recent paper "An application of parametric approach for interval differential equation in inventory model for deteriorating items with selling-price-dependent demand" by Rehman et al. (Neural Comput Appl 32(17):14069–14085, 2020). The comments in this paper pertain mainly to the drawbacks of interval arithmetic (SIA) presented in Section 3 of Rehman et al. (2020) referencing the convention of converting an interval-valued model into a parametric form. Proposed corrections to the overestimation of the interval form through examples are presented. [ABSTRACT FROM AUTHOR]

This paper is devoted to a study of a history-dependent mixed hemivariational-variational inequality arising in contact mechanics. The contact problem concerns the deformation of a viscoelastic body with long memory, subject to a general friction law on one part of the boundary and a frictionless Signorini condition on another part of the boundary. The solution existence and uniqueness of the history-dependent mixed hemivariational-variational inequality based on a Lagrange multiplier approach are proved. Then, a fully discrete scheme is introduced and studied. The trapezoidal rule is used to approximate the integral in the history-dependent operator. For the spatial discretization, the linear finite elements are used to discretize the displacement field, and dual basis functions are used in the approximation of the Lagrange multiplier. Optimal order error estimates are derived for the displacement and the Lagrange multiplier under appropriate solution regularity assumptions. Numerical results are presented to illustrate the theoretical prediction of the convergence orders. [ABSTRACT FROM AUTHOR]

The integration of both sensing and communication functions is a crucial feature for future communication systems. This paper considers a novel scenario where a radar covers multiple small-cell base stations which operate in different spectra. Due to the limited spectra resource, the radar needs to reuse the spectra of one BS for tracking. To suppress interference and improve performance, we propose a framework including two stages and the corresponding communication and sensing algorithms. Specifically, at the detection stage, we aim to minimize the system transmit power while maintaining the performance of both radar and communication. At the tracking stage, our goal is to maximize the radar sensing performance under a given power budget, while ensuring communication quality. Due to the complexity of the original problem, we address it by introducing auxiliary variables and proposing a penalty dual decomposition-based algorithm, enabling us to solve a more tractable form of the problem. In the inner loop, we propose a concave–convex procedure-based algorithm to handle the optimization problem, while adopting the block coordinate descent algorithm to iteratively update the variables. In the outer loop, we update the penalty term or Lagrange multipliers. Furthermore, we propose a radar target parameter estimation algorithm based on successive interference cancellation, which aims to mitigate communication interference. Finally, numerical simulations demonstrate the effectiveness of the proposed system, and the superior performance of our proposed algorithms over benchmark algorithms. [ABSTRACT FROM AUTHOR]

Preconditioning of rock for drilling operations is a potential method to facilitate the mechanical breakage and mitigate the tool wear. This paper numerically investigates one such preconditioning technique, namely, the thermal jet assisted rock cutting. For this end, a numerical method for solving the governing thermo‐mechanical problem is developed and validated. The continuum approach is chosen to describe the rock failure, being based on a damage‐viscoplasticity model with the Drucker–Prager yield surface and the modified Rankine surface as the tensile cut‐off. In the damage part, separate scalar damage variables are employed for tension and compression. The cutters are modelled as rigid bodies and their interaction with the rock is modelled by imposing contact constraints by the forward increment Lagrange multiplier method, which is compatible with the chosen explicit time integration scheme. A damage‐based erosion criterion is applied to remove the contact nodes surrounded by heavily damaged elements. The thermal jets are modelled with a moving external heat flux boundary condition. The global thermo‐mechanical problem is solved with a staggered approach explicitly in time while applying mass scaling to increase the critical time step. The novel 3D numerical simulations involving two cutters demonstrate the capabilities of the method with a special emphasis on cutter‐thermal jet configurations. Therefore, the present method provides a potential tool for the bit design in thermal jet assisted drilling. [ABSTRACT FROM AUTHOR]

The purpose of this work is to propose and analyze a hybridized discontinuous Galerkin (HDG) method for the generalized Boussinesq equations with singular heat source. We use polynomials of order k, k − 1 and k to approximate the velocity, the pressure and the temperature. By introducing Lagrange multipliers for the pressure, the approximate velocity field obtained by the HDG method is shown to be exactly divergence-free and H(div)-conforming. Under a smallness assumption on the problem data and solutions, we prove by Brouwer's fixed point theorem that the discrete system has a solution in two dimensions. If the viscosity and thermal conductivity are further assumed to be positive constants, a priori error estimates with convergence rate O(h) and efficient and reliable a posteriori error estimates are derived. Finally numerical examples illustrate the theoretical analysis and show the performance of the obtained a posteriori error estimator. [ABSTRACT FROM AUTHOR]

We present new Dirichlet-Neumann and Neumann-Dirichlet algorithms with a time domain decomposition applied to unconstrained parabolic optimal control problems. After a spatial semidiscretization, we use the Lagrange multiplier approach to derive a coupled forward-backward optimality system, which can then be solved using a time domain decomposition. Due to the forwardbackward structure of the optimality system, three variants can be found for the Dirichlet-Neumann and Neumann-Dirichlet algorithms. We analyze their convergence behavior and determine the optimal relaxation parameter for each algorithm. Our analysis reveals that the most natural algorithms are actually only good smoothers, and there are better choices which lead to efficient solvers. We illustrate our analysis with numerical experiments. [ABSTRACT FROM AUTHOR]

In this paper, we consider solutions to the following nonlinear Schrödinger equation with competing Hartree‐type nonlinearities, −Δu+λu=|x|−γ1*|u|2u−|x|−γ2*|u|2uinRN,$$\begin{equation*} -\Delta u + \lambda u={\left(|x|^{-\gamma _1} \ast|u|^2\right)} u - {\left(|x|^{-\gamma _2} \ast|u|^2\right)} u\quad \mbox{in} \,\, \mathbb {R}^N, \end{equation*}$$under the L2$L^2$‐norm constraint ∫RN|u|2dx=c>0,$$\begin{equation*} \int _{\mathbb {R}^N}|u|^2 \, dx=c>0, \end{equation*}$$where N≥1$N \ge 1$, 0<γ2<γ1

Variational integrators play a pivotal role in the simulation and control of constrained mechanical systems. Current Lagrange multiplier-free variational integrators for such systems are concise but inevitably face issues with parameterization singularities, hindering global integration. To tackle this problem, this paper proposes a novel method for constructing variational integrators on manifolds without introducing Lagrange multipliers, offering the benefit of avoiding singularities. Our approach unfolds in three key steps: (1) the local parameterization of configuration space; (2) the formulation of forced discrete Euler-Lagrange equations on manifolds; and (3) the construction and implementation of high-order variational integrators. Numerical tests are conducted for both conservative and forced mechanical systems, demonstrating the excellent global energy behavior of the proposed variational integrators. [ABSTRACT FROM AUTHOR]

This paper proposes and establishes the iteration complexity of an inexact proximal accelerated augmented Lagrangian (IPAAL) method for solving linearly constrained smooth nonconvex composite optimization problems. Each IPAAL iteration consists of inexactly solving a proximal augmented Lagrangian subproblem by an accelerated composite gradient (ACG) method followed by a suitable Lagrange multiplier update. For any given (possibly infeasible) initial point and tolerance ρ > 0 , it is shown that IPAAL generates an approximate stationary solution in O (ρ - 3 log (ρ - 1)) ACG iterations, which can be improved to O (ρ - 2.5 log (ρ - 1)) if it is further assumed that a certain Slater condition holds. [ABSTRACT FROM AUTHOR]

In this paper, we propose and analyze two highly efficient compact finite difference schemes for coupled nonlinear wave equations containing coupled sine-Gordon equations and coupled Klein-Gordon equations. To construct energy-preserving, high-order accurate and linear numerical methods, we first utilize the scalar auxiliary variable (SAV) approach and introduce three auxiliary functions to rewrite the original problem as a new equivalent system. Then we make use of the compact finite difference method and the Crank-Nicolson method to propose an efficient fully-discrete scheme (SAV-CFD-CN). The modified energy conservation and the convergence of the SAV-CFD-CN scheme are proved in detail, which has fourth-order convergence in space and second-order convergence in time. In order to preserve the discrete energy of original system, we further combine Lagrange multiplier approach, compact finite difference method and the Crank-Nicolson method to propose the second fully-discrete scheme (LM-CFD-CN). The proposed two schemes are high-order accurate, linear and highly efficient, only four symmetric positive definite systems with constant coefficients are required to be solved at each time level. Numerical experiments for the coupled nonlinear wave equations are given to confirm theoretical findings. [ABSTRACT FROM AUTHOR]

Most current methods to value healthcare treatments only incorporate measures such as quality-adjusted life-years, combining gains in health-related quality of life and life expectancy in specific ways. Failure of these methods to recognize other dimensions of value has led to calls for methods to include additional values that are associated with the healthcare treatments but not captured directly by quality-adjusted life-years. This article seeks to provide methodologically sound ways to incorporate additional health-related outcomes, focusing on budget-constrained healthcare systems, in which using standard welfare economics methods are often eschewed. The analysis develops standard extra-welfarist approaches to maximizing aggregate health, subject to fixed-budget constraints, using Lagrange multiplier methods. Then, additional valuable health-related outcomes, eg, reduced caregiver burden, real option value, and market- and non-market productivity are introduced. The article also introduces a social welfare function approach to illuminate how disability, disease severity and other equity-related issues can be incorporated into complete welfare measures. Resulting analysis, fully developed in an Appendix in Supplemental Materials found at https://doi.org/10.1016/j.jval.2024.02.005 and summarized in the main text, show that understanding how average and marginal healthcare costs increase with output and how health augments "additional values" provides ways to assess willingness to pay for them in these fixed-budget situations. In budget-constrained healthcare systems, only from actual budget allocations can values both of health itself and "additional values" be inferred. These methods, combined with methodologically sound social welfare functions, demonstrate how to move from "health" to "welfare" in measuring the value of increased healthcare use. • Most analyses using extra-welfarist approaches rely solely on "health" as the measure of value. Methods to assess and use "additional values" beyond health have been sporadic, with no unifying methods available. Few existing analyses of healthcare values have incorporated formal social welfare functions to assess aggregate benefit from health gains, relying instead on ad hoc approaches to adjust for disease severity, disability, and other ethical issues. • Specific formulations are developed to show how to combine values of health improvements and "additional values." This requires that decision makers understand the incremental costs of increasing health levels, the processes by which health adds to "extra values," and the values themselves for health and each "additional value" incorporated into overall value measures. Measuring "additional values" can also be combined with formal social welfare functions to truly move from "health" to "welfare." • In systems with centralized budgets, value is inferred from budget allocations to provide both healthcare services and additional budget augmentations to further gain desired "extra values." In fixed-budget systems, ambiguity may exist as to which funding body should augment healthcare systems' budgets to appropriately increase health output to properly capture "added values." Full social welfare analysis requires knowing not only how much health and "other values" are produced but also who receives them. [ABSTRACT FROM AUTHOR]

This study is a response to a paper on group decision problems in a linguistic environment. We show that their M1 model can be directly solved by Schwarz inequality to avoid using the Lagrange multiplier methods. Moreover, their M2 model can also be solved by our modification of applying Schwarz inequality to avoid referring to soft ware of MatLab with Lingo or Lindo soft ware package or optimization toolbox. The same numerical examples are provided to illustrate our findings. [ABSTRACT FROM AUTHOR]

This work is devoted to the mathematical and numerical study of a framework handling a system of coupled variational inequalities. We prove both the existence and the uniqueness of a weak solution to the problem. Then, we introduce a convergent iterative scheme. Using this latter, we decouple the problem into further subproblems and derive their corresponding minimization problems. As a practical application of this class of coupled abstract variational inequalities, we consider a class of problems that model an electroelastic body coming into frictional contact with a rigid electrically conductive foundation. Both electrical and mechanical contacts are of Signorini type. In other words, our model prescribes the mechanical response produced by the foundation and the outflow of the free charges across the contact zone. The last part of this paper is mainly reserved for the numerical resolution of the problem at hand. For this purpose, we have developed an alternating direction method of multipliers and convex dualities to compute and illustrate the solutions. [ABSTRACT FROM AUTHOR]

Constrained least mean square (CLMS) algorithm is the most popular constrained adaptive filtering algorithm due to its simple structure and easy implementation. However, its convergence slows down when the input signal is colored. To address this issue, this paper firstly introduces the normalized subband adaptive filter (NSAF) into the constrained filtering problem and derives a constrained NSAF (CNSAF) algorithm using the Lagrange multiplier method. Benefiting from the good decorrelation capability of the NSAF, the proposed CNSAF algorithm significantly improves the convergence performance of the CLMS algorithm under colored inputs. Then, the mean and mean-square stability of the CNSAF algorithm is analyzed, and the theoretical models to characterize the transient and steady-state mean square deviation (MSD) behaviors of the CNSAF algorithm are derived utilizing the Kronecker product property and vectorization method. Further to extend the CNSAF algorithm to the problem of sparse system identification, a sparse version of the CNSAF algorithm (S-CNSAF) is derived. Finally, the validity of the derived theoretical MSD prediction models and the superiority of the proposed algorithms are confirmed by extensive computer simulations on system identification with colored inputs. [ABSTRACT FROM AUTHOR]

This paper concerns and presents new improved beam and plate finite elements for analysing sandwich structures from the structural and modal points of view. In this study, the material behaviour is supposed to be linear elastic and orthotropic, but the method could be extended for nonlinear problems as well. The current models are able to treat the compressibility of the soft core materials, besides the interlaminar continuity conditions and the zero shear stresses on the shear-free surfaces are granted by the Lagrange multiplier method. In order to provide stress continuity along the element boundaries, the Hermite interpolation is employed for the elementary formulations that yields subparametric finite elements. On the contrary, the semi-analytical solutions of these enhanced beam and plate models are also discussed here for particular boundary conditions. The verification of the new finite elements is carried out by two case studies. The test examples are modelled and solved in commercial finite element software (ANSYS) with general shell and solid elements, too. The results derived from different models are subjected to a comprehensive comparison. Also, the structural and modal analyses of the test examples are presented during the case studies. The structural analysis of an overconstrained sandwich panel is also discussed to point out the significance of the proper shear stress distributions. Finally, the advantages and disadvantages of the newly developed elements and semi-analytical solutions are revealed in detail. [ABSTRACT FROM AUTHOR]

The purpose of this study is to introduce a computational method for solving the two-dimensional optimal control problem of the large membrane vibration equation of fractional order. Our proposed approach utilizes Chebyshev cardinal functions in two dimensions to obtain a finite dimensional optimal control problem. This problem is then solved using the Lagrange multipliers method by substituting the expansions of the state and control variables in terms of two-dimensional Chebyshev cardinal functions into the objective function, dynamical system, and initial conditions. The utilization of Chebyshev nodes offers a distinct advantage by effectively mitigating the Runge phenomenon, characterized by the undesirable oscillation and divergence of high-degree polynomial interpolants in close proximity to the interval's endpoints. We extensively discuss the convergence of our method and evaluate its accuracy using three test problems. Our results demonstrate that this technique provides highly accurate numerical solutions for these types of problems. [ABSTRACT FROM AUTHOR]

Full-waveform inversion (FWI) is an effective method for imaging subsurface properties using sparsely recorded data. It involves solving a wave propagation problem to estimate model parameters that accurately reproduce the data. Recent trends in FWI have seen a renewed interest in extended methodologies, among which source extension methods leveraging reconstructed wavefields to solve penalty or augmented Lagrangian (AL) formulations have emerged as robust algorithms, even for inaccurate initial models. Despite their demonstrated robustness on synthetic data, challenges remain, such as the lack of a clear physical interpretation and reliance on difficult-to-compute least-squares (LS) wavefields. Moreover, the literature lacks a general and through comparison of these source extension methods with each other and with the standard FWI. This paper is divided into three critical parts. In the first, a novel formulation of these methods is explored within a unified Lagrangian framework. This novel perspective permits the introduction of alternative algorithms that use LS multipliers instead of wavefields. These multiplier-oriented variants appear as regularizations of the standard FWI, are suitable to the time domain, offer tangible physical interpretations, and foster enhanced convergence efficiency. The second part of the paper delves into understanding the underlying mechanisms of these techniques. This is achieved by solving the associated non-linear equations using iterative linearization and inverse scattering methods. The paper provides insight into the role and significance of Lagrange multipliers in enhancing the linearization of the equations. It explains how different methods estimate multipliers or make approximations to increase computing efficiency. Additionally, it presents a new physical understanding of the Lagrange multiplier used in the AL method, highlighting how important it is for improving algorithm performance when compared to penalty methods. In the final section, the paper presents numerical examples that compare different methods within a unified iterative algorithm, utilizing benchmark Marmousi and 2004 BP salt models. [ABSTRACT FROM AUTHOR]

Shear wave velocity (Vs) is a fundamental property of elastic media whose estimation from PS converted waves is challenging and requires modelling the boundary where P to S conversion occurs. This paper presents a PS tomography where seismic wave conversion/reflection points correspond to reflectors modelled with the level-set function set to zero [ ϕ (x, z) = 0]. The proposed method aims for stable Vs inversion in a seismic acquisition setting using multicomponent receivers. Synthetic models simulating true Vs , Vp and the location of the geological reflector are used in the study. The inversion starts by locating a flat reflector, ϕ (x, z) = 0, which defines the zone Ω1 between the surface and the reflector, where the initial Vs and Vp fields are also set. To calculate the traveltimes of incident PT (P wave that propagates in Ω1 from source to the reflector), converted PS and reflected PP waves, for both observed and modelled data (forward problem), the methodology proposed by Rawlinson and Sambridge is adopted. This method uses the arrival times of the P waves, Tpt , from the seismic source at each reflector point as secondary sources generating the times Tps and Tpp. These times are calculated as a solution to the eikonal equation by using the Fast Marching method. The PS and PP residual times are minimized by updating Vs , Vp and ϕ (x, z) = 0 through adjoint variables designed from a formulation using Lagrange Multipliers in a variational context. The performance of the algorithm is evaluated for models with synclinal, sinusoidal and monoclinal reflector geometries using numerical tests considering the inversion of: (1) ϕ , given the true values of Vs and Vp ; (2) ϕ and Vs , given the true value of Vp ; (3) ϕ and Vp , given the true value of Vs and (4) the three parameters ϕ, Vs and Vp , simultaneously. Good results are obtained by inverting Vs and ϕ , given the true value of Vp. The simultaneous inversion of the three parameters exhibits promising results, despite the illumination problems caused by the different distribution of the PS, PP and PT time gradients due to the geometry of the reflectors and the acquisition setting (sources–receivers in the same plane). The proposed tomography estimates Vs and reflector positions which could help in statics corrections and improve the lithological characterization of near surface. [ABSTRACT FROM AUTHOR]

In this paper, a second‐order time discretizing block‐centered finite difference method is introduced to solve the compressible wormhole propagation. The optimal second‐order error estimates for the porosity, pressure, velocity, concentration and its flux are established carefully in different discrete norms on non‐uniform grids. Then by introducing Lagrange multiplier, a novel bound‐preserving scheme for concentration is constructed. Finally, numerical experiments are carried out to demonstrate the correctness of theoretical analysis and capability for simulations of compressible wormhole propagation. [ABSTRACT FROM AUTHOR]

Memristor crossbars offer promising low-power and parallel processing capabilities, making them efficient for implementing convolutional neural networks (CNNs) in terms of delay time, area, etc. However, mapping large CNN models like ResNet-18, ResNet-34, VGG-Net, etc., onto memristor crossbars is challenging due to the line resistance problem limiting crossbar size. This necessitates partitioning full-image convolution into sub-image convolution. To do so, an optimized mapping of memristor crossbars should be considered to divide full-image convolution into multiple crossbars. With limited crossbar resources, especially in edge devices, it is crucial to optimize the crossbar allocation per layer to minimize the hardware resource in term of crossbar area, delay time, and area–delay product. This paper explores three optimization scenarios: (1) optimizing total delay time under a crossbar's area constraint, (2) optimizing total crossbar area with a crossbar's delay time constraint, and (3) optimizing a crossbar's area–delay-time product without constraints. The Lagrange multiplier method is employed for the constrained cases 1 and 2. For the unconstrained case 3, a genetic algorithm (GA) is used to optimize the area–delay-time product. Simulation results demonstrate that the optimization can have significant improvements over the unoptimized results. When VGG-Net is simulated, the optimization can show about 20% reduction in delay time for case 1 and 22% area reduction for case 2. Case 3 highlights the benefits of optimizing the crossbar utilization ratio for minimizing the area–delay-time product. The proposed optimization strategies can substantially enhance the neural network's performance of memristor crossbar-based processing-in-memory architectures, especially for resource-constrained edge computing platforms. [ABSTRACT FROM AUTHOR]

The article presents a methodology for determining the hydraulic resistance multiplier, used for a rapid estimation of linear losses in pipes with non-circular cross-sections. The numerical approach was applied using the Finite Volume Method and the ANSYS Fluent software. The research was conducted under turbulent flow conditions, covering two Reynolds number ranges: 10,000 to 100,000 (10 cases) and 100,000 to 1,000,000 (5 cases). The first section of the article presents calculations of losses for a circular pipe, accompanied by a mesh test and error estimation. The second section includes calculations conducted for a series of pipes with various selected cross-sectional shapes: half-circle, quarter-circle, square, rectangles with aspect ratios of 2:1 and 3:1, isosceles triangle, and equilateral triangle. The last section of the article discusses the calculation of linear losses and the hydraulic resistance multiplier for each tested shape. It was found that this coefficient ranged from 1.33 to 2.2, depending on the shape, with the influence of the Reynolds number being relatively insignificant. [ABSTRACT FROM AUTHOR]

This article is dedicated to studying a class of frictional contact problems involving the p(x)-Laplacian-like operator, on a bounded domain Ω ⊆ R². Using an abstract Lagrange multiplier technique and the Schauder fixed point theorem we establish the existence of a weak solution. Furthermore, we also obtain the uniqueness of the solution assuming that the datum f1 satisfies a suitable monotonicity condition. The results here extend earlier theorems due to Cojocaru- Matei to the quasilinear case, with semilinearity f1. [ABSTRACT FROM AUTHOR]

This article is concerned with a class of nonsmooth semi-infinite programming problems on Hadamard manifolds (abbreviated as, (NSIP)). We introduce the Guignard constraint qualification (abbreviated as, (GCQ)) for (NSIP). Subsequently, by employing (GCQ), we establish the Karush-Kuhn-Tucker (abbreviated as, KKT) type necessary optimality conditions for (NSIP). Further, we derive that the Lagrangian function associated with a fixed Lagrange multiplier, corresponding to a known solution, remains constant on the solution set of (NSIP) under geodesic pseudoconvexity assumptions. Moreover, we derive certain characterizations of the solution set of the considered problem (NSIP) in the framework of Hadamard manifolds. We provide illustrative examples that highlight the importance of our established results. To the best of our knowledge, characterizations of the solution set of (NSIP) using Clarke subdifferentials on Hadamard manifolds have not been investigated before. [ABSTRACT FROM AUTHOR]

We present a method for the numerical approximation of distributed optimal control problems constrained by parabolic partial differential equations. We complement the first-order optimality condition by a recently developed space-time variational formulation of parabolic equations which is coercive in the energy norm, and a Lagrange multiplier. Our final formulation fulfills the Babuška–Brezzi conditions on the continuous as well as discrete level, without restrictions. Consequently, we can allow for final-time desired states, and obtain an a posteriori error estimator which is efficient and reliable up to an additional discretization error of the adjoint problem. Numerical experiments confirm our theoretical findings. [ABSTRACT FROM AUTHOR]

In this paper we will investigate the existence of multiple normalized solutions to the logarithmic Schrödinger equation given by - ϵ 2 Δ u + V (x) u = λ u + u log u 2 , in R N , ∫ R N | u | 2 d x = a 2 ϵ N , where N ≥ 1 , a , ϵ > 0 , λ ∈ R is an unknown parameter that appears as a Lagrange multiplier and V : R N → (- 1 , + ∞) is a continuous function. Our analysis demonstrates that the number of normalized solutions of the equation is associated with the topology of the set where the potential function V attains its minimum value. To prove the main result, we employ minimization techniques and use the Lusternik-Schnirelmann category. Additionally, we introduce a new function space where the energy functional associated with the problem is of class C 1 . [ABSTRACT FROM AUTHOR]

Due to assembling, manufacturing errors, and wear, irregular rough surfaces inevitably exist in joints, which will increase the contact stiffness nonlinearity at the joint of the spatial developable mechanism, and the traditional contact force model is difficult to accurately predict the contact force change of irregular rough surface clearance. Aiming at the difficulty of accurately predicting the dynamic behavior of the spatial developable mechanism caused by rough joint clearance, an improved clearance contact force modeling method based on an uncoordinated contact model is proposed in this paper. The influence of rough peak distribution on the contact area is analyzed. The stiffness of the traditional Hertz model is modified based on the probability distribution density function of the rough peak, and an improved contact force model based on dynamic contact stiffness is established. Based on the Lagrange multiplier method, the dynamics model of spatial developable mechanism is constructed. Based on the model, the dynamic analysis of the spatial expansion mechanism is carried out, and the influence of the roughness of the contact surface and the size of the clearance on the dynamic characteristics of the system are explored; as well, the influence of different clearance parameters on the dynamic characteristics of the development mechanism is revealed. Through the analysis, this paper provides a theoretical basis for predicting the effect of a spatial revolute clearance joint on the dynamic characteristics of the mechanism and lays a good foundation for the manufacture and application of the mechanism. [ABSTRACT FROM AUTHOR]

Distributed inference tasks could be performed by adaptive filtering techniques. Several enhancement strategies for such techniques were proposed, such as sparsity-aware algorithms, coefficients reuse and correntropy-based cost functions in the case of impulsive noise. In this paper, a general framework based on Lagrange multipliers for the derivation of sophisticated algorithms that incorporate most of these improvements is described. A new general identification algorithm is derived as an example of the proposed approach and its performance is assessed in a distributed setting. [ABSTRACT FROM AUTHOR]

The variational iteration method, a powerful tool for solving nonlinear oscillators with initial conditions, has been expanded to accommodate two-point boundary conditions. In this modification, two Lagrange multipliers are introduced, and their identification process mirrors that of the conventional approach. A generalized equation is provided for a category of highly nonlinear mechanical systems, followed by three illustrative examples derived from this generalized equation. These examples serve to demonstrate the effectiveness of the method. The solutions produced by this modified approach not only show remarkable agreement with numerical results but also exhibit superior accuracy when compared to outcomes obtained through other established methods. [ABSTRACT FROM AUTHOR]