Decomposition of singular large sparse matrix by adding dummy links and dummy degrees

Abstract

This paper proposes a simple scheme to decompose an n×n nonpositive definite matrix, A, associated with simultaneous equations, A X = B, into a triple‐factors (lower triangular, diagonal, and upper triangular matrices), i.e., Å = L D U, without interchanging rows or columns of A, but with A expanded with new rows and new columns to an m×m matrix Å. Whenever a near‐zero diagonal element, say ā_ii , is encountered and used as a pivoting element, an appropriate positive real number, say p, is added to this diagonal element, and a new term —px_k is also added to the i‐th equation, where x_k is a new variable called “dummy variable'’. If we also add a new equation —px_i + px_k = 0 to enforce the new added variable x_k equal to x_i then the modified i‐th equation has the same effect as the original equation. Therefore, the original solution X can be found directly from the expanded solution of the modified expanded equation. The method is very useful in solving the following problems: (1) nonlinear problems near the limit state, (2) postbuckling analysis, (3) system equations with constraint conditions, and (4) getting eigenvectors from eigenvalues.     

Shift and scale‐invariant correlation for pattern recognition based on the bidimensional empirical mode decomposition with noise robustness

Abstract

A novel filter is proposed to improve the noise robustness and discrimination capability for shift and scale invariant pattern recognition. This filter is a combination of mellin radial harmonic filter (RHF) and the bidimensional empirical mode decomposition. The basic principle of this method is to make use of partial reconstructions of the image by the relevant intrinsic mode functions corresponding to the most important structures of the image. A criterion is proposed to determine the proper number of intrinsic mode functions to be discarded for denoising by discussing the characteristic of the noise. The proposed filter provides a wider allowable scale change of the object. Within this range, the correlation peak intensity is relatively uniform even in the case of noise. This proposed filter has been tested experimentally to confirm the result from numerical simulations for cases with and without additive white Gaussian noise.     

Tailoring Materials for Mottronics: Excess Oxygen Doping of a Prototypical Mott Insulator

The Mott transistor is a paradigm for a new class of electronic devices—often referred to by the term Mottronics—which are based on charge correlations between the electrons. Since correlation‐induced insulating phases of most oxide compounds are usually very robust, new methods have to be developed to push such materials right to the boundary to the metallic phase in order to enable the metal–insulator transition to be switched by electric gating. Here, it is demonstrated that thin films of the prototypical Mott insulator LaTiO₃ grown by pulsed laser deposition under oxygen atmosphere are readily tuned by excess oxygen doping across the line of the band‐filling controlled Mott transition in the electronic phase diagram. The detected insulator to metal transition is characterized by a strong change in resistivity of several orders of magnitude. The use of suitable substrates and capping layers to inhibit oxygen diffusion facilitates full control of the oxygen content and renders the films stable against exposure to ambient conditions. These achievements represent a significant advancement in control and tuning of the electronic properties of LaTiO_3+x thin films making it a promising channel material in future Mottronic devices.     

In Situ Construction of Stable Tissue‐Directed/Reinforced Bifunctional Separator/Protection Film on Lithium Anode for Lithium–Oxygen Batteries

To achieve a high reversibility and long cycle life for Li–O₂ battery system, the stable tissue‐directed/reinforced bifunctional separator/protection film (TBF) is in situ fabricated on the surface of metallic lithium anode. It is shown that a Li–O₂ cell composed of the TBF‐modified lithium anodes exhibits an excellent anodic reversibility (300 cycles) and effectively improved cathodic long lifetime (106 cycles). The improvement is attributed to the ability of the TBF, which has chemical, electrochemical, and mechanical stability, to effectively prevent direct contact between the surface of the lithium anode and the highly reactive reduced oxygen species (Li₂O₂ or its intermediate LiO₂) in cell. It is believed that the protection strategy describes here can be easily extended to other next‐generation high energy density batteries using metal as anode including Li–S and Na–O₂ batteries.     

Significance of Nanomaterials in Wearables: A Review on Wearable Actuators and Sensors

Together with the evolution of digital health care, the wearable electronics field has evolved rapidly during the past few years and is expected to be expanded even further within the first few years of the next decade. As the next stage of wearables is predicted to move toward integrated wearables, nanomaterials and nanocomposites are in the spotlight of the search for novel concepts for integration. In addition, the conversion of current devices and attachment‐based wearables into integrated technology may involve a significant size reduction while retaining their functional capabilities. Nanomaterial‐based wearable sensors have already marked their presence with a significant distinction while nanomaterial‐based wearable actuators are still at their embryonic stage. This review looks into the contribution of nanomaterials and nanocomposites to wearable technology with a focus on wearable sensors and actuators.