Impacts of slip and mass transpiration on Newtonian liquid flow over a porous stretching sheet

This article focuses on analytic solutions for Newtonian fluid flow with slip and mass transpiration on a porous stretching sheet using the differential transform method and Pade approximants of an exceptionally nonlinear differential equation. The impacts of different parameters including mass transpiration (suction/injection), Navier's slip, and Darcy number parameters on the velocity of the liquid and tangential stress are discussed. A comprehensive comparison of our results with the previous one in the literature is made, and the results showed good agreement. An investigation is conducted of a combination of magnetic liquids that are conceivably pertinent for wound medicines, skin repair, and astute coatings for natural gadgets. It is found that there is a decrease in the velocity profiles and the boundary layer thickness for the case of suction.     

A globally convergent BFGS method for pseudo-monotone variational inequality problems

In this paper, we propose a globally convergent BFGS method to solve Variational Inequality Problems (VIPs). In fact, a globalization technique on the basis of the hyperplane projection method is applied to the BFGS method. The technique, which is independent of any merit function, is applicable for pseudo-monotone problems. The proposed method applies the BFGS direction and tries to reduce the distance of iterates to the solution set. This property, called Fejer monotonicity of iterates with respect to the solution set, is the basis of the convergence analysis. The method applied to pseudo-monotone VIP is globally convergent in the sense that subproblems always have unique solutions, and the sequence of iterates converges to a solution to the problem without any regularity assumption. Finally, some numerical simulations are included to evaluate the efficiency of the proposed algorithm.     

Multiple Empirical Kernel Learning with Majority Projection for imbalanced problems

Traditional Multiple Empirical Kernel Learning (MEKL) expands the expressions of the sample and brings better classification ability by using different empirical kernels to map the original data space into multiple kernel spaces. To make MEKL suit for the imbalanced problems, this paper introduces a weight matrix and a regularization term into MEKL. The weight matrix assigns high misclassification cost to the minority samples to balanced misclassification cost between minority and majority class. The regularization term named Majority Projection (MP) is used to make the classification hyperplane fit the distribution shape of majority samples and enlarge the between-class distance of minority and majority class. The contributions of this work are: (i) assigning high cost to minority samples to deal with imbalanced problems, (ii) introducing a new regularization term to concern the property of data distribution, (iii) and modifying the original PAC-Bayes bound to test the error upper bound of MEKL-MP. Through analyzing the experimental results, the proposed MEKL-MP is well suited to the imbalanced problems and has lower generalization risk in accordance with the value of PAC-Bayes bound.     

A new linearly constrained minimum variance beamformer for reconstructing EEG sparse sources

Brain source imaging based on EEG aims to reconstruct the neural activities producing the scalp potentials. This includes solving the forward and inverse problems. The aim of the inverse problem is to estimate the activity of the brain sources based on the measured data and leadfield matrix computed in the forward step. Spatial filtering, also known as beamforming, is an inverse method that reconstructs the time course of the source at a particular location by weighting and linearly combining the sensor data. In this paper, we considered a temporal assumption related to the time course of the source, namely sparsity, in the Linearly Constrained Minimum Variance (LCMV) beamformer. This assumption sounds reasonable since not all brain sources are active all the time such as epileptic spikes and also some experimental protocols such as electrical stimulations of a peripheral nerve can be sparse in time. Developing the sparse beamformer is done by incorporating L1-norm regularization of the beamformer output in the relevant cost function while obtaining the filter weights. We called this new beamformer SParse LCMV (SP-LCMV). We compared the performance of the SP-LCMV with that of LCMV for both superficial and deep sources with different amplitudes using synthetic EEG signals. Also, we compared them in localization and reconstruction of sources underlying electric median nerve stimulation. Results show that the proposed sparse beamformer can enhance reconstruction of sparse sources especially in the case of sources with high amplitude spikes.     

Semirigid inclusions in elastic bodies: Mechanical interplay and optimal control

The paper concerns an analysis of an equilibrium problem for 2D elastic body with two semirigid inclusions. It is assumed that inclusions have a joint point, and we investigate a junction problem for these inclusions. The existence of solutions is proved, and different equivalent formulations of the problem are proposed. We investigate a convergence to infinity of a rigidity parameter of the semirigid inclusion. It is proved that in the limit, we obtain an equilibrium problem for the elastic body with a rigid inclusion and a semirigid one. A parameter identification problem is investigated. In particular, the existence of a solution to a suitable optimal control problem is proved.     

Classic and inverse compositional Gauss-Newton in global DIC

Today, effective implementations of digital image correlation (DIC) are based on iterative algorithms with constant linear operators. A relevant idea of the classic finite element (or, more generally, global) DIC solver consists in replacing the gradient of the deformed state image with that of the reference image, so as to obtain a constant operator. Different arguments (small strains, small deformations, equality of the two gradients close to the solution, etc) have been given in the literature to justify this approximation, but none of them are fully accurate. Indeed, the convergence of the optimization algorithm has to be investigated from its ability to produce descent directions. Through such a study, this paper attempts to explain why this approximation works and what is its domain of validity. Then, an inverse compositional Gauss-Newton implementation of finite element DIC is proposed as a cost-effective and mathematically sound alternative to this approximation.     

An inverse problem for non-selfadjoint Sturm–Liouville operator with discontinuity conditions inside a finite interval

This paper is concerned with the inverse problem for non-selfadjoint Sturm–Liouville operator with discontinuity conditions inside a finite interval. Firstly, we give the definitions of generalized weight numbers for this operator which may have the multiple spectrum and then investigate the connections between the generalized weight numbers and other spectral characteristics. Secondly, we obtain the generalized spectral data, which consists of the generalized weight numbers and the spectrum. Then the operator is determined uniquely by the method of spectral mappings. Finally, we give an algorithm for reconstructing the potential function and the coefficients of the boundary conditions and the coefficients of the discontinuity conditions.