Invertibility Properties Research Articles

A Fast Power Allocation Strategy for Multibeam Tracking Multiple Targets in Clutter

A collocated multiple-input–multiple-output (MIMO) radar has the ability to track multiple targets in the simultaneous multibeam working mode, where the defocused beams are transmitted to illuminate the whole space, and focused beams are received to extract target information. A fast power allocation (FPA) strategy is put forward in this mode. The predicted posterior Cramer–Rao lower bound (PCRLB) in the cluttered background is slighted relaxed and utilized as the optimization metric. The optimization model is then established as minimizing the worst case of PCRLB under the constraint of total power budget. By using the monotonic decreasing and invertible properties of the relaxed PCRLB, a fast sequential relaxation-based solver is proposed for this problem solving. At each iteration, the proposed solver tests the power allocation (PA) to one target whether should be set as the minimum level. Simulation results show the effectiveness and efficiency of the proposed solver, compared with convex optimization-based methods. The results also imply that the target distance and reflectivity are two main factors that influence the PA in our strategy.

Additive properties of central Drazin invertibility of elements in a ring

For two central Drazin invertible elements a and b of a ring, we first prove that a + b is central Drazin invertible under the condition ab = 0. Then we establish the relation between central Drazin invertibility of a + b and 1 + acb, when a2b = aba and b2a = bab hold, and also when ab = ba is valid. When a and b are two central group invertible elements, additive properties of central group inverses are studied under the condition ab = ba and also abbc = baac.

Double branched covers of knotoids

By using double branched covers, we prove that there is a 1-1 correspondence between the set of knotoids in the 2-sphere, up to orientation reversion and rotation, and knots with a strong inversion, up to conjugacy. This correspondence allows us to study knotoids through tools and invariants coming from knot theory. In particular, concepts from geometrisation generalise to knotoids, allowing us to characterise invertibility and other properties in the hyperbolic case. Moreover, with our construction we are able to detect both the trivial knotoid in the 2-sphere and the trivial planar knotoid.

Seismic Data Reconstruction via Wavelet-Based Residual Deep Learning

Seismic data reconstruction is one of the essential steps in the seismic data processing. Recently, the deep learning (DL) models have attracted huge attention in seismic exploration, which has been applied to seismic data reconstruction, especially the convolutional neural network (CNN)-based methods. However, the general CNN-based models only consider seismic features in the time domain and do not take into account the frequency features. Moreover, there are detailed features lost due to the downsampling scheme. We propose a wavelet-based residual DL (WRDL) network to reconstruct the incomplete seismic data. By selecting the U-Net as the backbone, we introduce the discrete wavelet transform (DWT) to replace the pooling operations, whose invertibility property benefits reserving the detailed features. Furthermore, the inverse wavelet transform (IWT) with the expansion convolutional layer is introduced to restore the feature maps. In addition, we adopt the residual blocks into the proposed model to promote the training accuracy and avoid the overfitting issue. To accurately and effectively reconstruct the missing seismic data, we propose a hybrid loss function based on the structural similarity (SSIM) loss and the Huber loss. Numerical experiments on synthetic data and field data show that the WRDL model reconstructs the missing seismic data more accurately than the U-Net and MWCNN models, including the irregularly missing seismic data and the consecutively missing seismic data with a big gap. Furthermore, the qualitative and quantitative results demonstrate the advantages of the proposed hybrid loss function over the commonly used traditional loss for seismic data reconstruction.

Construction of quasigroups with invertibility properties

Construction of quasigroups with invertibility properties

Retrieval of olive tree biophysical properties from Sentinel-2 time series based on physical modelling and machine learning technique

ABSTRACT The purpose of this work is to build a model that enables to estimate and monitor the biophysical properties of olive trees planted in super-intensive groves, using innovative forward/backward radiative transfer modelling. In the forward step, the Discrete Anisotropic Radiative Transfer (DART) model simulates a large dataset of satellite image (here, Sentinel-2, S2) reflectance values of realistic olive tree mock-ups with high accuracy. The backward model is composed by two successive regression neural networks trained with the DART simulated dataset. These networks are optimized respectively to estimate biophysical properties of the understory and of the olive trees from the reflectance images. To ensure accurate property retrieval, the dataset covers all possible biophysical and structural properties of the olive trees and understory in addition to the soil optical properties. Therefore, it is composed of trees with various sizes, leaf area index (LAI), tree covers, and leaf biophysical properties associated with ranges of chlorophyll content (Cab), carotenoid content (Ccar), leaf mesophyll structure (N), and leaf equivalent water thickness (EWT) that are compatible to standard properties of olive tree leaves. Particular attention is paid to soil signature estimation, as it is very bright and so greatly influences the canopy signature. Soil reflectance is estimated from the satellite images. Different soil classes with different moisture contents are considered. Inversion results from time series of S2 images are consistent with the olive tree phenological stages. For instance, Cab increases during winter and decreases during summer. The sharp decrease coincides to tree stress caused by lack of water and long-time exposure to the sun. Likewise, an increase in water content in winter is noted, especially in images taken after rainy events. Besides, olive tree sizes estimation in the areas crossed by water alleys shows the highest values. Furthermore, validation is done by comparing our inverted properties to in-situ measurements. For example, LAI, Cab, and EWT RMSE (Root Mean Squared Error) are 0.58 m2m−2, 2.5 µg cm−2 and 0.003 cm, respectively.

Invertibility of Generalized Space-Time Autoregressive Model with Random Weight

The generalized linear process accomplishes stationarity and invertibility properties. The invertibility property must be having a series of convergence conditions of the process parameter. The generalized Space-Time Autoregressive (GSTAR) model is one of the stationary linear models therefore it is necessary to reveal the invertibility through the convergence of the parameter series. This article studies the invertibility of model GSTAR(1;1) with kernel random weight. The result shows that the model GSTAR(1;1) under kernel random weight fulfills the invertibility property and obtains a finite order of Generalized Space-Time Moving Average (GSTMA) process. The other result obtained is the time order of the finite orde . On the Triangular kernel resulted in the relatively great value n, so that it does not apply to the kernel with a finite value n.

Classification of quasigroups according to directions of translations I

It is proved that every translation in a quasigroup has two independent parameters. One of them is a bijection of the carrier set. The second parameter is called a direction here. Properties of directions in a quasigroup are considered in the first part of the work. In particular, totally symmetric, semisymmetric, commutative, left and right symmetric and also asymmetric quasigroups are characterized within these concepts. The sets of translations of the same direction are under consideration in the second part of the work. Coincidence of these sets defines nine varieties, among them are varieties of $LIP$, $RIP$, $MIP$ and $CIP$ quasigroups. Quasigroups in other five varieties also have some invertibility properties.

Fast and feasible fabrication of zinc- and lithium-doped cobalt oxide layers as an emerging hole injection candidate for perovskite solar cells

Metal oxide-based hole injection layers inherent for stable third-generation methylammonium lead tri-iodide (CH3NH3PbI3) perovskite solar cells. Particularly for inverted types, their structural and optoelectronic properties determine the limit of the power conversion efficiencies. This work demonstrates a novel cobalt oxide-based hole injection layer (HIL) and metal doping effect on its performance. Using a fast and feasible solution-based route and employing Zn and Li as dopant sources, a systematic study is presented through photovoltaic performances. Structural and morphological properties and the effect of doping on the hole injection layers were examined through surface roughness, electrical and hole conductivity, bandgap, and crystalline structure analysis. In ambient air, glove-box free fabrication with a configuration of ITO/CoOx:ZnLi+/CH3NH3PbI3/PCBM/BCP/Ag boosted the efficiency up to 11.64 % from 3.99 % for pristine cobalt oxide employed devices. By employing optimum Zn and Li co-doping, open-circuit voltage, short-circuit current, fill factor of the pristine CoOx employed solar cell devices were changed from 882 to 925 mV, 8.6 to 19.7 mA/cm2 and 52.6 to 63.9, respectively. The enhancement of the photovoltaic performances linked to boosted hole mobility and electrical conductivity values for pristine and doped CoOx layers, from 0.55 × 10-6 cm2/Vs to 255 × 10-6 cm2/Vs and from 0.610 to 2.048 µS/cm, respectively. This report reveals the promising hole extraction capability of Zn and Li co-doped cobalt oxide layers for inverted CH3NH3PbI3-based perovskite solar cells.

Global Invertibility for Orientation-Preserving Sobolev Maps via Invertibility on or Near the Boundary

By a result of John Ball (1981), a locally orientation preserving Sobolev map is almost everywhere globally invertible whenever its boundary values admit a homeomorphic extension. As shown here for any dimension, the conclusions of Ball's theorem and related results can be reached while completely avoiding the problem of homeomorphic extension. For suitable domains, it is enough to know that the trace is invertible on the boundary or can be uniformly approximated by such maps. An application in Nonlinear Elasticity is the existence of homeomorphic minimizers with finite distortion whose boundary values are not fixed. As a tool in the proofs, strictly orientation-preserving maps and their global invertibility properties are studied from a purely topological point of view.

Self-Identification Deep Learning ARIMA

The aspiration to predict the future values as close to the actual values as possible leads to the invention of time series models, the autoregressive integrated moving average (ARIMA) model which requires appropriate parameters of model identification, the ARIMA order, prior to fit coefficients of the models using the Box-Jenkins method. Statisticians for a decade identified the order via the sample autocorrelation function (ACF) and the sample partial autocorrelation function (PACF) which were very challenging for a human eye. To circumvent this issue, the recent model identification development uses a likelihood based-method that automatically generates orders and fits coefficients by varying the ARIMA order and pick the best one having the smallest Akaike information criterion (AIC) or Bayesian information criterion (BIC). The acquired ARIMA model may fail residual diagnostics. Consequently, this paper proposes the convolution neural network model, called the self-identification deep learning (SID) model, to automatically identify the ARIMA order via sample ACF/PACF. Accordingly, randomly simulated time series data with stationary and invertibility properties are generated by ARIMA model. Next, the time series data are converted into ACF/PACF graphs in order to feed into the SID model. The derived ARIMA order will be passed to determine the best fit coefficients of the ARIMA model via the Box-Jenkin methods for forecasting future values. The complete algorithm is called the self-identification deep learning ARIMA (SIDA) algorithm. The performance of identifying the ARIMA order from the SID model outperforms the likelihood based-method and ResNET50 which accepts the time series data directly in terms of precision, recall and F1-scores. Moreover, the SIDA algorithm applying to the real world dataset shows a better performance over the likelihood-based method via the mean absolute percentage error, the symmetric mean absolute percentage error, the mean absolute error and the root mean square error.

Probabilistic inversion for compressional modulus and shear modulus based on QA-MCMC algorithm with joint probability distribution

Compressional modulus and shear modulus play an important role in the reservoir prediction and fluid identification. Based on an optimized Markov chain Monte Carlo (MCMC) method in the Bayesian framework, we propose a probabilistic approach of utilizing seismic aptitudes to estimate compressional modulus and shear modulus. Conventional MCMC method is not efficient for prestack inversion due to the complex model parameter space. In order to accelerating the running speed of MCMC and improving the stability of Markov chain, we have developed a novel algorithm called “Quantum Annealing- Markov chain Monte Carlo algorithm (QA-MCMC) with joint probability distribution”. We derive an improved acceptance probability expression to reduce unnecessary model update in burn-in phase, and utilize joint probability distribution (JPD) to reduce the sampling space of inverted properties. Following a Bayesian framework, we generate the posterior probability distribution function and employ the improved MCMC algorithm to solve the inversion problem to estimate compressional modulus and shear modulus from prestack or angle stack gathers. The method is validated through the tests on the 1D model, 2D model and real data.

Self-Identification ResNet-ARIMA Forecasting Model

The challenging endeavor of a time series forecast model is to predict the future time series data accurately. Traditionally, the fundamental forecasting model in time series analysis is the autoregressive integrated moving average model or the ARIMA model requiring a model identification of a three-component vector which are the autoregressive order, the differencing order, and the moving average order before fitting coefficients of the model via the Box-Jenkins method. A model identification is analyzed via the sample autocorrelation function and the sample partial autocorrelation function which are effective tools for identifying the ARMA order but it is quite difficult for analysts. Even though a likelihood based-method is presented to automate this process by varying the ARIMA order and choosing the best one with the smallest criteria, such as Akaike information criterion. Nevertheless the obtained ARIMA model may not pass the residual diagnostic test. This paper presents the residual neural network model, called the self-identification ResNet-ARIMA order model to automatically learn the ARIMA order from known ARIMA time series data via sample autocorrelation function, the sample partial autocorrelation function and differencing time series images. In this work, the training time series data are randomly simulated and checked for stationary and invertibility properties before they are used. The result order from the model is used to generate and fit the ARIMA model by the Box-Jenkins method for predicting future values. The whole process of the forecasting time series algorithm is called the self-identification ResNet-ARIMA algorithm. The performance of the residual neural network model is evaluated by Precision, Recall and F1-score and is compared with the likelihood basedmethod and ResNET50. In addition, the performance of the forecasting time series algorithm is applied to the real world datasets to ensure the reliability by mean absolute percentage error, symmetric mean absolute percentage error, mean absolute error and root mean square error and this algorithm is confirmed with the residual diagnostic checks by the Ljung-Box test. From the experimental results, the new methodologies of this research outperforms other models in terms of identifying the order and predicting the future values.

Multidimensional singular integrals and integral equations in fractional spaces I

The boundedness, invertibility and smoothness properties of multidimensional singular integral operators and solvability of the corresponding singular integral equations are investigated in Besov spaces.

Analysis of boundary-domain integral equations based on a new parametrix for the mixed diffusion BVP with variable coefficient in an interior Lipschitz domain

A mixed boundary value problem for the partial differential equation of diffusion in an inhomogeneous medium in a Lipschitz domain is reduced to a system of direct segregated parametrix-based Boundary-Domain Integral Equations (BDIEs). We use a parametrix different from the one employed in the papers by Mikhailov (2002, 2006) and Chkadua, Mikhailov, Natroshvili (2009). We prove the equivalence between the original BVP and the corresponding BDIE system. The invertibility and Fredholm properties of the boundary-domain integral operators are also analysed.

From ℋ∞ to 𝒩. Pointwise properties and algebraic structure in the Nevanlinna class

Abstract This survey shows how, for the Nevanlinna class 𝒩 of the unit disc, one can define and often characterize the analogues of well-known objects and properties related to the algebra of bounded analytic functions ℋ∞: interpolating sequences, Corona theorem, sets of determination, stable rank, as well as the more recent notions of Weak Embedding Property and threshold of invertibility for quotient algebras. The general rule we observe is that a given result for ℋ∞ can be transposed to 𝒩 by replacing uniform bounds by a suitable control by positive harmonic functions. We show several instances where this rule applies, as well as some exceptions. We also briefly discuss the situation for the related Smirnov class.

Linear Operators and Equations with Partial Integrals

We consider linear operators and equations with partial integrals in Banach ideal spaces, spaces of vector functions, and spaces of continuous functions. We study the action, regularity, duality, algebras, Fredholm properties, invertibility, and spectral properties of such operators. We describe principal properties of linear equations with partial integrals. We show that such equations are essentially different compared to usual integral equations. We obtain conditions for the Fredholm alternative, conditions for zero spectral radius of the Volterra operator with partial integrals, and construct resolvents of invertible equations. We discuss Volterra-Fredholm equations with partial integrals and consider problems leading to linear equations with partial integrals.

Invertibility and spectral properties of dual Toeplitz operators

In this paper, we consider dual Toeplitz operators with continuous symbols and bounded harmonic symbols on the orthogonal complement of the Bergman space over the open unit disk. We construct a dual Toeplitz operator with continuous symbol such that its spectrum is disconnected. On the other hand, we show that the spectra of dual Toeplitz operators with certain class of bounded harmonic symbols are connected, which leads to some partial answers to the open question posed by Stroethoff and Zheng [18] in 2002. We obtain a complete characterization for the hyponormality of dual Toeplitz operators with bounded harmonic symbols. Moreover, we establish some sufficient conditions that are convenient to check for dual Toeplitz operators with continuous symbols and bounded harmonic symbols to be invertible, respectively.

An Efficient Upgradation of STATCOM to PV-STATCOM and Result Estimation using SIMULINK

Power generation is a much discussed topic in research works recently. Power production from different renewable source were the most processed topic. There are large number of solar farms which produce heavy electricity throughout the world but the overall efficiency of those solar farms remain unutilized especially in morning and evening when the sunlight is at its minimum the power production is too low. The series of Photovoltaic Cells (PV) are responsible for power production which are connected with the grid. The solar power output is D.C which can be transformed into A.C by inverter injection in the production line. STATCOM is proposed system which is a device is coming from the sub categorization of FACTS. STATCOM is concentrated on voltage source transformer. It operates in accordance as rectifier and inverter is used to increase power transmission limits. It also has the feature of damping control. The overall gist of the system is we propose a PV-STATCOM control concept. We use MATLAB 2013a to develop a Simulink simulation of PV-STATCOM system. It will be a solar inverter which is voltage controlled and it has overall inverter properties too.

Analogues of Gluskin–Hosszú and Malyshev theorems for strongly dependent n-ary operations

Abstract The paper contains an extension of Malyshev theorem for n-ary quasigroups with a right or left weak invertibility property to the case of strongly dependent n-ary operations. As a corollary a new proof of Gluskin–Hosszú theorem for strongly dependent n-ary semigroups is obtained.