Continued Fraction Algorithm for Matrix Exponentials

A recursive rational algorithm for matrix exponentials was obtained by making use of the generalized inverse of a matrix in this paper. On the basis of the n th convergence of Thiele type continued fraction expansion, a new type of the generalized inverse matrix valued Padé approximant (GMPA) for matrix exponentials was defined and its remainder formula was proved. The results of this paper were illustrated by some examples.

GROWTH ESTIMATES FOR SINE-TYPE-FUNCTIONS AND APPLICATIONS TO RIESZ BASES OF EXPONENTIALS

We present explicit estimates for the growth of sine-type-functions as well as for the derivatives at their zero sets, thus obtaining explicit constants in a result of Levin. The estimates are then used to derive explicit lower bounds for exponential Riesz bases, as they arise in Avdonin's Theorem on 1/4 in the mean or in a Theorem, of Bogmtr, Horvath, Job and Seip. An application is discussed, where knowledge of explicit lower bounds of exponential Riese bases is desirable.

Efficiency of a Modular Cleanroom for Space Applications

A prototype cleanroom for hazardous testing and handling of satellites prior to launcher encapsulation,satisfying the ISO8 standard has been designed and analyzed in terms of performances.Unsteady Reynolds Averaged Navier-Stokes(URANS)models have been used to study the related flow field and particulate matter(PM)dispersion.The outcomes of the URANS models have been validated through comparison with equivalent large-eddy simulations.Special attention has been paid to the location and shape of the air intakes and their orientation in space,in order to balance the PM convection and diffusion inside the cleanroom.Forming a cyclone-type flow pattern inside the cleanroom is a key to maintaining a high ventilation efficiency.

Equivalence between the internal observability and equation

This paper is concerned with a third order in time linear Moore-Gibson-Thompson equation which describes the acoustic velocity potential in ultrasound wave program.Influenced by the work of Kaltenbacher,Lasiecka and Marchand(Control Cybernet.2011,40:971-988),we establish an observability inequality of the conservative problem,and then discuss the equivalence between the exponential stabilization of a dissipative system and the internal observational inequality of the corresponding conservative system.

Enhanced Differentiable Architecture Search Based on Asymptotic Regularization

In differentiable search architecture search methods,a more efficient search space design can significantly improve the performance of the searched architecture,thus requiring people to carefully define the search space with different complexity according to various operations.Meanwhile rationalizing the search strategies to explore the well-defined search space will further improve the speed and efficiency of architecture search.With this in mind,we propose a faster and more efficient differentiable architecture search method,AllegroNAS.Firstly,we introduce a more efficient search space enriched by the introduction of two redefined convolution modules.Secondly,we utilize a more efficient architectural parameter regularization method,mitigating the overfitting problem during the search process and reducing the error brought about by gradient approximation.Meanwhile,we introduce a natural exponential cosine annealing method to make the learning rate of the neural network training process more suitable for the search procedure.Moreover,group convolution and data augmentation are employed to reduce the computational cost.Finally,through extensive experiments on several public datasets,we demonstrate that our method can more swiftly search for better-performing neural network architectures in a more efficient search space,thus validating the effectiveness of our approach.

Influencing Factors and Prediction of Risk of Returning to Ecological Poverty in Liupan Mountain Region,China

China has resolved its overall regional poverty in 2020 by attaining moderate societal prosperity.The country has entered a new development stage designed to achieve its second centenary goal.However,ecological fragility and risk susceptibility have increased the risk of returning to ecological poverty.In this paper,the Liupan Mountain Region of China was used as a case study,and the counties were used as the scale to reveal the spatiotempora differentiation and influcing factors of the risk of returning to poverty in study area.The indicator data for returning to ecological poverty from 2011-2020 were collected and summarized in three dimensions:ecological,economic and social.The autoregressive integrated moving average model(ARIMA)time series and exponential smoothing method(ES)were used to predict the multidimensional indicators of returning to ecological poverty for 61 counties(districts)in the Liupan Mountain Region for 2021-2030.The back propagation neural network(BPNN)and geographic information system(GIS)were used to generate the spatial distribution and time variation for the index of the risk of returning to ecological poverty(RREP index).The results show that 1)ecological factors were the main factors in the risk of returning to ecological poverty in Liupan Mountain Region.2)The RREP index for the 61 counties(districts)exhibited a downward trend from 2021-2030.The RREP index declined more in medium-and high-risk areas than in low-risk areas.From 2021 to 2025,the RREP index exhibited a slight downward trend.From 2026 to2030,the RREP index was expected to decline faster,especially from 2029-2030.3)Based on the RREP index,it can be roughly divided into three types,namely,the high-risk areas,the medium-risk areas,and the low-risk areas.The natural resource conditions in lowrisk areas of returning to ecological poverty,were better than those in medium-and high-risk areas.

Mixed convectional and chemical reactive flow of nanofluid with slanted MHD on moving permeable stretching/shrinking sheet through nonlinear radiation,energy omission

Hybrid nanofluids are remarkable functioning liquids that are intended to reduce the energy loss while maximizing the heat transmission.In the involvement of suction and nonlinear thermal radiation effects,this study attempted to explore the energy transmission features of the inclined magnetohydrodynamic(MHD)stagnation flow of CNTs-hybrid nanofluid across the nonlinear permeable stretching or shrinking sheet.This work also included some noteworthy features like chemical reactions,variable molecular diffusivity,quadratic convection,viscous dissipation,velocity slip and heat omission assessment.Employing appropriate similarity components,the model equations were modified to ODEs and computed by using the HAM technique.The impact of various relevant flow characteristics on movement,heat and concentration profiles was investigated and plotted on a graph.Considering various model factors,the significance of drag friction,heat and mass transfer rate were also computed in tabular and graphical form.This leads to the conclusion that such factors have a considerable impact on the dynamics of fluid as well as other engineering measurements of interest.Furthermore,viscous forces are dominated by increasing the values ofλ_(p),δ_(m)andδ_(q),and as a result,F(ξ)accelerates while the opposite trend is observed for M andφ.The drag friction is boosted by the augmentation M,λ_(p)andφ,but the rate of heat transfer declined.According to our findings,hybrid nanoliquid effects dominate that of ordinary nanofluid in terms of F(ξ),Θ(ξ)andφ(ξ)profiles.The HAM and the numerical technique(shooting method)were found to be in good agreement.

Distance Sets Relating to Orthogonal Exponentials

The aim of this paper is to investigate the size properties of a planar set whose distance set has some prescribed arithmetic combinatorics. Such research is motivated by the conjecture that the disk has no more than 3 orthogonal exponentials. By proving a shifted version of ErdSs-Solymosi＇s theorem on the distance sets, we give some grounds on the conjecture. The results obtained here extend the corresponding results of Iosevich and Jaming in a simple manner.

Reviewing Stability Criteria for Positive Homogeneous Systems and Adding One for Discrete-Time Cases with Degree Less Than One

The article synthesizes and presents the results regarding the stability of positive homogeneous systems that have been researched and published in recent years. Next, we provide a sufficient condition for global exponential stability in the case of discrete-time positive homogeneous systems with an order less than one with time-varying delays.

The Maximum and Minimum Value of Exponential RandićIndices of Quasi-Tree Graph

The exponential Randić index has important applications in the fields of biology and chemistry. The exponential Randić index of a graph G is defined as the sum of the weights e 1 d( u )d( v ) of all edges uv of G, where d( u ) denotes the degree of a vertex u in G. The paper mainly provides the upper and lower bounds of the exponential Randić index in quasi-tree graphs, and characterizes the extremal graphs when the bounds are achieved.

Quantum Dynamics via a Hidden Liouville Space

The traditional simulations may occasionally turn out to be challenging for the quantum dynamics, particularly those governed by the nonlinear Hamiltonians. In this work, we introduce a nonstandard iterative technique where the Liouville space is briefly expanded with an additional (virtual) space only within ultrashort subintervals. This tremendously reduces the cost of time-consuming calculations. We implement our technique for an example of a charged particle in both harmonic and anharmonic potentials. The temporal evolutions of the probability for the particle being in the ground state are obtained numerically and compared to the analytical solutions. We further discuss the physics insight of this technique based on a thought-experiment. Successive processes intrinsically “hitchhiking” via virtual space in discrete ultrashort time duration, are the hallmark of our technique. We believe that this technique has potential for solving numerous problems which often pose a challenge when using the traditional approach based on time-ordered exponentials.

THE GROWTH OF SOLUTIONS TO HIGHER ORDER DIFFERENTIAL EQUATIONS WITH EXPONENTIAL POLYNOMIALS AS ITS COEFFICIENTS

By looking at the situation when the coefficients Pj(z)(j=1,2,…,n-1)(or most of them) are exponential polynomials,we investigate the fact that all nontrivial solutions to higher order differential equations f((n))+Pn-1(z)f((n-1))+…+P0(z)f=0 are of infinite order.An exponential polynomial coefficient plays a key role in these results.

A Numerical Investigation Based on Exponential Collocation Method for Nonlinear SITR Model of COVID-19

In this work,the exponential approximation is used for the numerical simulation of a nonlinear SITR model as a system of differential equations that shows the dynamics of the new coronavirus(COVID-19).The SITR mathematical model is divided into four classes using fractal parameters for COVID-19 dynamics,namely,susceptible(S),infected(I),treatment(T),and recovered(R).The main idea of the presented method is based on the matrix representations of the exponential functions and their derivatives using collocation points.To indicate the usefulness of this method,we employ it in some cases.For error analysis of the method,the residual of the solutions is reviewed.The reported examples show that the method is reasonably efficient and accurate.

Forecasting Stock Prices with an Integrated Approach Combining ARIMA and Machine Learning Techniques ARIMAML

Stock market prediction has long been an area of interest for investors, traders, and researchers alike. Accurate forecasting of stock prices is crucial for financial decision-making and risk management. This paper presents a novel approach to predict stock prices by integrating Autoregressive Integrated Moving Average (ARIMA) and Exponential smoothing and Machine Learning (ML) techniques. Our study aims to enhance the predictive accuracy of stock price forecasting, which can significantly impact investment strategies and economic growth in this research paper implement the ARIMAML proposed method to predict the stock prices for Investment Bank of Iraq.

Vertical deformation model on postseismic phase using exponential and logarithmic function based on InSAR

The Palu MW7.4 earthquake occurred on September 28, 2018, with the epicenter at 119.86°, 0.72°. The severe shaking caused severe damage in Central Sulawesi, especially in Palu. We conducted a postseismic deformation study to determine the deformation pattern and reduce future earthquakes’ impact.Interferometric Synthetic Aperture Radar(In SAR) data were processed using Li CSBAS to get the time series. The time series data were fitted to exponential and logarithmic functions to determine the mechanism of postseismic deformation. The exponential model identified the influence of the viscoelastic mechanism, and the logarithm identified the afterslip mechanism. The Palu earthquake was fitted to logarithmic and exponential, but the logarithmic was more significant than an exponential function.Afterslip mechanism predominates, and viscoelastic mechanisms play a minor role in this postseismic deformation.

Resonant Scattering of Gravitational Waves with Electromagnetic Waves

A certain class of exact solutions of Einstein Maxwell spacetime in general relativity is discussed to demonstrate that at the level of theory,when certain parametric resonance condition is met,the interaction of electromagnetic field with a gravitational wave will display certain Lyapunov instability and lead to exponential amplification of a gravitational wave train described by certain Newman-Penrose component of the Weyl curvature.In some way akin to a free electron laser in electromagnetic theory,by the conversion of electromagnetic energy into gravitational energy in a coherent way,the feasibility of generating a pulsed-laser-like intense beam of gravitational wave is displayed.

Improved population mean estimator with exponential function under non-response

In this article,we consider a new family of exponential type estimators for estimating the unknown population mean of the study variable.We propose estimators taking advantage of the auxiliary variable information under the first and second non-response cases separately.The required theoretical comparisons are obtained and the numerical studies are conducted.In conclusion,the results show that the proposed family of estimators is the most efficient estimator with respect to the estimators in literature under the obtained conditions for both cases.

Convective flow of Jeffrey nanofluid along an upright microchannel with Hall current and Buongiorno model:an irreversibility analysis

The thermal properties and irreversibility of the Jeffrey nanofluid through an upright permeable microchannel are analyzed by means of the Buongiorno model.The effects of the Hall current,exponential space coefficient,nonlinear radiation,and convective and slip boundary conditions on the Jeffrey fluid flow are explored by deliberating the buoyant force and viscous dissipation.The non-dimensionalized equations are obtained by employing a non-dimensional system,and are further resolved by utilizing the shooting approach and the 4th-and 5th-order Runge-Kutta-Fehlberg approaches.The obtained upshots conclude that the amplified Hall parameter will enhance the secondary flow profile.The improvement in the temperature parameter directly affects the thermal profile,and hence the thermal field declines.A comparative analysis of the Newtonian fluid and non-Newtonian fluid(Jeffrey fluid)is carried out with the flow across a porous channel.In the Bejan number,thermal field,and entropy generation,the Jeffrey nanofluid is more highly supported than the Newtonian fluid.

A Comparative Study on Kinematic Calibration for a 3-DOF Parallel Manipulator Using the Complete-Minimal,Inverse-Kinematic and Geometric-Constraint Error Models

Kinematic calibration is a reliable way to improve the accuracy of parallel manipulators, while the error model dramatically afects the accuracy, reliability, and stability of identifcation results. In this paper, a comparison study on kinematic calibration for a 3-DOF parallel manipulator with three error models is presented to investigate the relative merits of diferent error modeling methods. The study takes into consideration the inverse-kinematic error model, which ignores all passive joint errors, the geometric-constraint error model, which is derived by special geometric constraints of the studied RPR-equivalent parallel manipulator, and the complete-minimal error model, which meets the complete, minimal, and continuous criteria. This comparison focuses on aspects such as modeling complexity, identifcation accuracy, the impact of noise uncertainty, and parameter identifability. To facilitate a more intuitive comparison, simulations are conducted to draw conclusions in certain aspects, including accuracy, the infuence of the S joint, identifcation with noises, and sensitivity indices. The simulations indicate that the complete-minimal error model exhibits the lowest residual values, and all error models demonstrate stability considering noises. Hereafter, an experiment is conducted on a prototype using a laser tracker, providing further insights into the diferences among the three error models. The results show that the residual errors of this machine tool are signifcantly improved according to the identifed parameters, and the complete-minimal error model can approach the measurements by nearly 90% compared to the inverse-kinematic error model. The fndings pertaining to the model process, complexity, and limitations are also instructive for other parallel manipulators.

The Class of Atomic Exponential Basis Functions EFup_(n)(x,ω)-Development and Application

The purpose of this paper is to present the class of atomic basis functions(ABFs)which are of exponential type and are denoted by EFupn(x,ω).While ABFs of the algebraic type are already represented in the numerical modeling of various problems inmathematical physics and computationalmechanics,ABFs of the exponential type have not yet been sufficiently researched.These functions,unlike the ABFs of the algebraic type Fupn(x),contain the tension parameterω,which gives them additional approximation properties.Exponential monomials up to the nth degree can be described exactly by the linear combination of the functions EFupn(x,ω).The function EFupn for n=0 is called the“mother”ABF of the exponential type,i.e.,EFup0(x,ω)≡Eup(x,ω).In other words,the functions EFupn(x,ω)are elements of the linear vector space EUPn and retain all the properties of their“mother”function Eup(x,ω).Thus,this paper,in terms of its content and purpose,can be understood as a sequel of the article by Brajcic Kurbasa et al.,which shows the basic properties and application of the basis function Eup(x,ω).This paper presents,in an analogous way,the development and application of the exponential basis functions EFupn(x,ω).Here,for the first time,expressions for calculating the values of the functions EFupn(x,ω)and their derivatives are given in a form suitable for application in numerical analyses,which is shown in the verification examples of the approximations of known functions.