Evolutionary Safe Padé Approximation Scheme for Dynamical Study of Nonlinear Cervical Human Papilloma Virus Infection Model

This study proposes a structure-preserving evolutionary framework to find a semi-analytical approximate solution for a nonlinear cervical cancer epidemic(CCE)model.The underlying CCE model lacks a closed-form exact solution.Numerical solutions obtained through traditional finite difference schemes do not ensure the preservation of the model’s necessary properties,such as positivity,boundedness,and feasibility.Therefore,the development of structure-preserving semi-analytical approaches is always necessary.This research introduces an intelligently supervised computational paradigm to solve the underlying CCE model’s physical properties by formulating an equivalent unconstrained optimization problem.Singularity-free safe Padérational functions approximate the mathematical shape of state variables,while the model’s physical requirements are treated as problem constraints.The primary model of the governing differential equations is imposed to minimize the error between approximate solutions.An evolutionary algorithm,the Genetic Algorithm with Multi-Parent Crossover(GA-MPC),executes the optimization task.The resulting method is the Evolutionary Safe PadéApproximation(ESPA)scheme.The proof of unconditional convergence of the ESPA scheme on the CCE model is supported by numerical simulations.The performance of the ESPA scheme on the CCE model is thoroughly investigated by considering various orders of non-singular Padéapproximants.

Determining Hubbard U of VO_(2) by the quasi-harmonic approximation

Vanadium dioxide VO_(2) is a strongly correlated material that undergoes a metal-to-insulator transition around 340 K.In order to describe the electron correlation effects in VO_(2), the DFT+U method is commonly employed in calculations.However, the choice of the Hubbard U parameter has been a subject of debate and its value has been reported over a wide range. In this paper, taking focus on the phase transition behavior of VO_(2), the Hubbard U parameter for vanadium oxide is determined by using the quasi-harmonic approximation(QHA). First-principles calculations demonstrate that the phase transition temperature can be modulated by varying the U values. The phase transition temperature can be well reproduced by the calculations using the Perdew–Burke–Ernzerhof functional combined with the U parameter of 1.5eV. Additionally,the calculated band structure, insulating or metallic properties, and phonon dispersion with this U value are in line with experimental observations. By employing the QHA to determine the Hubbard U parameter, this study provides valuable insights into the phase transition behavior of VO_(2). The findings highlight the importance of electron correlation effects in accurately describing the properties of this material. The agreement between the calculated results and experimental observations further validates the chosen U value and supports the use of the DFT+U method in studying VO_(2).

Saddlepoint Approximation Method in Reliability Analysis:A Review

The escalating need for reliability analysis(RA)and reliability-based design optimization(RBDO)within engineering challenges has prompted the advancement of saddlepoint approximationmethods(SAM)tailored for such problems.This article offers a detailed overview of the general SAM and summarizes the method characteristics first.Subsequently,recent enhancements in the SAM theoretical framework are assessed.Notably,the mean value first-order saddlepoint approximation(MVFOSA)bears resemblance to the conceptual framework of the mean value second-order saddlepoint approximation(MVSOSA);the latter serves as an auxiliary approach to the former.Their distinction is rooted in the varying expansion orders of the performance function as implemented through the Taylor method.Both the saddlepoint approximation and third-moment(SATM)and saddlepoint approximation and fourth-moment(SAFM)strategies model the cumulant generating function(CGF)by leveraging the initial random moments of the function.Although their optimal application domains diverge,each method consistently ensures superior relative precision,enhanced efficiency,and sustained stability.Every method elucidated is exemplified through pertinent RA or RBDO scenarios.By juxtaposing them against alternative strategies,the efficacy of these methods becomes evident.The outcomes proffered are subsequently employed as a foundation for contemplating prospective theoretical and practical research endeavors concerning SAMs.The main purpose and value of this article is to review the SAM and reliability-related issues,which can provide some reference and inspiration for future research scholars in this field.

Relaxed Stability Criteria for Time-Delay Systems:A Novel Quadratic Function Convex Approximation Approach

This paper develops a quadratic function convex approximation approach to deal with the negative definite problem of the quadratic function induced by stability analysis of linear systems with time-varying delays.By introducing two adjustable parameters and two free variables,a novel convex function greater than or equal to the quadratic function is constructed,regardless of the sign of the coefficient in the quadratic term.The developed lemma can also be degenerated into the existing quadratic function negative-determination(QFND)lemma and relaxed QFND lemma respectively,by setting two adjustable parameters and two free variables as some particular values.Moreover,for a linear system with time-varying delays,a relaxed stability criterion is established via our developed lemma,together with the quivalent reciprocal combination technique and the Bessel-Legendre inequality.As a result,the conservatism can be reduced via the proposed approach in the context of constructing Lyapunov-Krasovskii functionals for the stability analysis of linear time-varying delay systems.Finally,the superiority of our results is illustrated through three numerical examples.

An Overview of Sequential Approximation in Topology Optimization of Continuum Structure

This paper offers an extensive overview of the utilization of sequential approximate optimization approaches in the context of numerically simulated large-scale continuum structures.These structures,commonly encountered in engineering applications,often involve complex objective and constraint functions that cannot be readily expressed as explicit functions of the design variables.As a result,sequential approximation techniques have emerged as the preferred strategy for addressing a wide array of topology optimization challenges.Over the past several decades,topology optimization methods have been advanced remarkably and successfully applied to solve engineering problems incorporating diverse physical backgrounds.In comparison to the large-scale equation solution,sensitivity analysis,graphics post-processing,etc.,the progress of the sequential approximation functions and their corresponding optimizersmake sluggish progress.Researchers,particularly novices,pay special attention to their difficulties with a particular problem.Thus,this paper provides an overview of sequential approximation functions,related literature on topology optimization methods,and their applications.Starting from optimality criteria and sequential linear programming,the other sequential approximate optimizations are introduced by employing Taylor expansion and intervening variables.In addition,recent advancements have led to the emergence of approaches such as Augmented Lagrange,sequential approximate integer,and non-gradient approximation are also introduced.By highlighting real-world applications and case studies,the paper not only demonstrates the practical relevance of these methods but also underscores the need for continued exploration in this area.Furthermore,to provide a comprehensive overview,this paper offers several novel developments that aim to illuminate potential directions for future research.

Nonlinear Filtering With Sample-Based Approximation Under Constrained Communication:Progress, Insights and Trends

The nonlinear filtering problem has enduringly been an active research topic in both academia and industry due to its ever-growing theoretical importance and practical significance.The main objective of nonlinear filtering is to infer the states of a nonlinear dynamical system of interest based on the available noisy measurements. In recent years, the advance of network communication technology has not only popularized the networked systems with apparent advantages in terms of installation,cost and maintenance, but also brought about a series of challenges to the design of nonlinear filtering algorithms, among which the communication constraint has been recognized as a dominating concern. In this context, a great number of investigations have been launched towards the networked nonlinear filtering problem with communication constraints, and many samplebased nonlinear filters have been developed to deal with the highly nonlinear and/or non-Gaussian scenarios. The aim of this paper is to provide a timely survey about the recent advances on the sample-based networked nonlinear filtering problem from the perspective of communication constraints. More specifically, we first review three important families of sample-based filtering methods known as the unscented Kalman filter, particle filter,and maximum correntropy filter. Then, the latest developments are surveyed with stress on the topics regarding incomplete/imperfect information, limited resources and cyber security.Finally, several challenges and open problems are highlighted to shed some lights on the possible trends of future research in this realm.

Integrating a novel irrigation approximation method with a process-based remote sensing model to estimate multi-years'winter wheat yield over the North China Plain

Accurate estimation of regional winter wheat yields is essential for understanding the food production status and ensuring national food security.However,using the existing remote sensing-based crop yield models to accurately reproduce the inter-annual and spatial variations in winter wheat yields remains challenging due to the limited ability to acquire irrigation information in water-limited regions.Thus,we proposed a new approach to approximating irrigations of winter wheat over the North China Plain(NCP),where irrigation occurs extensively during the winter wheat growing season.This approach used irrigation pattern parameters(IPPs)to define the irrigation frequency and timing.Then,they were incorporated into a newly-developed process-based and remote sensing-driven crop yield model for winter wheat(PRYM–Wheat),to improve the regional estimates of winter wheat over the NCP.The IPPs were determined using statistical yield data of reference years(2010–2015)over the NCP.Our findings showed that PRYM–Wheat with the optimal IPPs could improve the regional estimate of winter wheat yield,with an increase and decrease in the correlation coefficient(R)and root mean square error(RMSE)of 0.15(about 37%)and 0.90 t ha–1(about 41%),respectively.The data in validation years(2001–2009 and 2016–2019)were used to validate PRYM–Wheat.In addition,our findings also showed R(RMSE)of 0.80(0.62 t ha–1)on a site level,0.61(0.91 t ha–1)for Hebei Province on a county level,0.73(0.97 t ha–1)for Henan Province on a county level,and 0.55(0.75 t ha–1)for Shandong Province on a city level.Overall,PRYM–Wheat can offer a stable and robust approach to estimating regional winter wheat yield across multiple years,providing a scientific basis for ensuring regional food security.

Real scalar field scattering with polynomial approximation around Schwarzschild–de Sitter black-hole

As one of the fitting methods, the polynomial approximation is effective to process sophisticated problem. In this paper, we employ this approach to handle the scattering of scalar field around the Schwarzschild-de Sitter blackhole. The complicated relationship between tortoise coordinate and radial coordinate is replaced by the approximate polynomial. The Schroedinger-like equation, the real boundary conditions and the polynomial approximation construct a full Sturm Liouville type problem. Then this boundary value problem can be solved numerically for two limiting cases： the first one is the Nariai black-hole whose horizons are close to each other, the second one is the black-hole with the horizons widely separated. Compared with previous results （Brevik and Tian）, the field near the event horizon and cosmological horizon can have a better description.

POINTWISE CONVERGENCE RATE OF VANISHING VISCOSITY APPROXIMATIONS FOR SCALAR CONSERVATION LAWS WITH BOUNDARY

This article is concerned with the pointwise error estimates for vanishing vis- cosity approximations to scalar convex conservation laws with boundary.By the weighted error function and a bootstrap extrapolation technique introduced by Tadmor-Tang,an optimal pointwise convergence rate is derived for the vanishing viscosity approximations to the initial-boundary value problem for scalar convex conservation laws,whose weak entropy solution is piecewise C 2 -smooth with interaction of elementary waves and the ...

A Note on an Economic Lot-sizing Problem with Perishable Inventory and Economies of Scale Costs:Approximation Solutions and Worst Case Analysis

This paper presents an economic lot-sizing problem with perishable inventory and general economies of scale cost functions. For the case with backlogging allowed, a mathematical model is formulated, and several properties of the optimal solutions are explored. With the help of these optimality properties, a polynomial time approximation algorithm is developed by a new method. The new method adopts a shift technique to obtain a feasible solution of subproblem and takes the optimal solution of the subproblem as an approximation solution of our problem. The worst case performance for the approximation algorithm is proven to be （4√2 ＋ 5）/7. Finally, an instance illustrates that the bound is tight.

Nonlinear approximation of image based on monoscale orthonormal ridgelets frame

A new tight frame called as monoscale orthonormal ridgelet frame （MORF） is proposed. The localization principle and the orthonormal ridgelet constructed by Donoho are applied to construct the MORF, which are used to evaluate the order of nonlinear approximation for image with edge. Because the new tight frame not only has directionality but also bears orthonormality. It overcomes redundancy of Candes＇s monoscale ridgelets and provides many excellent properties in practical application. Theoretical analysis and experiments demonstrate that the new frame has remarkable potential for image compression, image reconstruction, and image denoising with the simple refinement for MORF.

Theoretical Approximation of Focusing-Wave Induced Load upon A Large-Scale Vertical Cylinder

Until now, most researches into the rogue-wave-structure interaction have relied on experimental measurement and numerical simulation. Owing to the complexity of the physical mechanism of rogue waves, theoretical study on the wave-structure issue still makes little progress. In this paper, the rogue wave flow around a vertical cylinder is analytically studied within the scope of the potential theory. The rogue wave is modeled by the Gauss envelope, which is one particular case of the well-known focusing theory. The formulae of the wave-induced horizontal force and bending moment are proposed. For the convenience of engineering application, the derived formulae are simplified appropriately, and verified against numerical results. In addition, the influence of wave parameters, such as the energy focusing degree and the wave focusing position, is thoroughly investigated.

Modeling of bistatic scattering from an underwater non-penetrable target using a Kirchhoff approximation method

A numerical triangulation and transformation into the time domain of a Kirchhoff approximation(KA)method is proposed for the modeling of bistatic scattering from an underwater non-penetrable target.The time domain solution in this approximation can be split up into two parts:the solution of reflected field,contributing around the specular direction,and the solution of shadow radiation,contributing around the forward direction.An average solution in the time domain satisfying the reciprocity principle is presented.The solution is expressed in terms of non-singular functions.The proposed method is validated against a normal mode method for bistatic scattering from a rigid sphere.Moreover,the reflected and shadow highlights on the surface of the sphere are shown to verify the integration surface of the reflected field and shadow radiation.It is also tested against a finite element method and an experiment involving a scaled Benchmark Target Strength Simulation Submarine model.The time-angle bistatic spectra for the model are evaluated by the direct and transformed average solutions of KA,and the former accelerates its speed of calculation.The results are good,and show that this method can be used to predict the bistatic scattered field of a non-penetrable target.

Electromagnetic scattering from two-layer rough interfaces in the Kirchhoff approximation

Electromagnetic wave scattering from multilayers consisting of two two-layer Caussian rough surfaces with lossless media is investigated in the Kirchhoff approximation （KA）, with consideration of the shadowing effects. The tapered incident wave is introduced into the classic KA, and the bistatic scattering coefficient is redetermined. The advantage of this method is that it is faster in computation than the exact numerical methods. The numerical results show that the bistatic scattering coefficient calculated in the KA is in good agreement with that obtained by using the method of moment （MOM） over a most angular range, which indicates the validity of the KA proposed in our paper. Finally, the effects of the relative permittivity, the root-mean-square （RMS） height, the correlative length, and the average height between the two interfaces on the bistatic scattering coefficient are discussed in detail.

Raman Scattering at Resonant or Near-Resonant Conditions： A Generalized Short-Time Approximation

We investigate the dynamics of resonant Raman scattering in the course of the frequency de- tuning. The dephasing in the time domain makes the scattering fast when the photon energy is tuned from the absorption resonance. This makes frequency detuning to act as a camera shutter with a regulated scattering duration and provides a practical tool of controlling the scattering time in ordinary stationary measurements. The theory is applied to resonant Raman spectra of a couple of few-mode model systems and to trans-1,3,5-hexatriene and guanine-cytosine （G-C） Watson-Crick base pairs （DNA） molecules. Besides some particular physical effects, the regime of fast scattering leads to a simplification of the spectrum as well as to the scattering theory itself. Strong overtones appear in the Raman spectra when the photon frequency is tuned in the resonant region, while in the mode of fast scattering, the overtones are gradually quenched when the photon frequency is tuned more than one vibra- tional quantum below the first absorption resonance. The detuning from the resonant region thus leads to a strong purification of the Raman spectrum from the contamination by higher overtones and soft modes and purifies the spectrum also in terms of avoidance of dissociation and interfering fluorescence decay of the resonant state. This makes frequency detuning a very useful practical tool in the analysis of the resonant Raman spectra of complex systems and considerably improves the prospects for using the Raman effect for detection of foreign substances at ultra-low concentrations.

Formalism of rotating-wave approximation in high-spin system with quadrupole interaction

We investigate the rotating wave approximation applied in the high-spin quantum system driven by a linearly polarized alternating magnetic field in the presence of quadrupole interactions.The conventional way to apply the rotating wave approximation in a driven high-spin system is to assume the dynamics being restricted in the reduced Hilbert space.However,when the driving strength is relatively strong or the driving is off resonant,the leakage from the target resonance subspace cannot be neglected for a multi-level quantum system.We propose the correct formalism to apply the rotating wave approximation in the full Hilbert space by taking this leakage into account.By estimating the operator fidelity of the time propagator,our formalism applied in the full Hilbert space unambiguously manifests great advantages over the conventional method applied in the reduced Hilbert space.

16-Moment Approximation for Ion Velocity Distribution and its Application in Calculations of Incoherent Scatter Spectra

A sixteen moment approximation based on a bi-Maxwellian that contains the stress tensor and the heat flow vector is applied to describe the ion velocity distribution which influences the incoherent scatter spectra. A discussion is made about the effects on the incoherent scatter spectra caused by different values of the normalized perpendicular drift velocity D, aspect angle Φ between the magnetic field and the line-of-sight direction, and the ratio α of the ion-neutral collision to ion cyclotron frequency. Numerical results show that the shifting and asymmetry of incoherent scatter spectra appear parallel to E × B and E as the normalized perpendicular drift velocity D increases due to the ion drift velocity, the stress tensor and the heat flow vector respectively. However, the spectrum is always typically double-humped Maxwellian parallel to B. The ion velocity distribution is more distorted from the Maxwellian as the aspect angle Φ increases from 0° to 90°, and consequently the incoherent scatter spectra is no longer typically double-humped Maxwellian. Asαincreases, the ion velocity distribution becomes Maxwellian and the incoherent scatter spectra become typically double-humped Maxwellian even with a large value of the normalized perpendicular drift velocity D. It is reasonable to use the sixteen-moment approximation to describe the non-Maxwellian plasma characterized by the large temperature anisotropy.

Light Propagation in the Second post-Newtonian Approximation of Scalar-Tensor Theory of Gravity

In this paper, we use the metric coefficients and the equation of motion obtained in the second post- Newtonian approximation of scalar-tensor theory to derive the second-order light propagation equation and the light deflection angle and compare it with previous works. These results are useful for precision astrometry missions like ASTROD, GALA, Darwin and SIM which aim at astrometry with micro-arcsecond and nano-aresecond accuracies, and need for the second post-Newtonian framework and ephemeris for observations to determine the stellar and spacecraft positions.

A novel method for simulating nuclear explosion with chemical explosion to form an approximate plane wave: Field test and numerical simulation

A nuclear explosion in the rock mass medium can produce strong shock waves,seismic shocks,and other destructive effects,which can cause extreme damage to the underground protection infrastructures.With the increase in nuclear explosion power,underground protection engineering enabled by explosion-proof impact theory and technology ushered in a new challenge.This paper proposes to simulate nuclear explosion tests with on-site chemical explosion tests in the form of multi-hole explosions.First,the mechanism of using multi-hole simultaneous blasting to simulate a nuclear explosion to generate approximate plane waves was analyzed.The plane pressure curve at the vault of the underground protective tunnel under the action of the multi-hole simultaneous blasting was then obtained using the impact test in the rock mass at the site.According to the peak pressure at the vault plane,it was divided into three regions:the stress superposition region,the superposition region after surface reflection,and the approximate plane stress wave zone.A numerical simulation approach was developed using PFC and FLAC to study the peak particle velocity in the surrounding rock of the underground protective cave under the action of multi-hole blasting.The time-history curves of pressure and peak pressure partition obtained by the on-site multi-hole simultaneous blasting test and numerical simulation were compared and analyzed,to verify the correctness and rationality of the formation of an approximate plane wave in the simulated nuclear explosion.This comparison and analysis also provided a theoretical foundation and some research ideas for the ensuing study on the impact of a nuclear explosion.

Cyclic Solution and Optimal Approximation of the Quaternion Stein Equation

In this paper, two different methods are used to study the cyclic structure solution and the optimal approximation of the quaternion Stein equation AXB - X = F . Firstly, the matrix equation equivalent to the target structure matrix is constructed by using the complex decomposition of the quaternion matrix, to obtain the necessary and sufficient conditions for the existence of the cyclic solution of the equation and the expression of the general solution. Secondly, the Stein equation is converted into the Sylvester equation by adding the necessary parameters, and the condition for the existence of a cyclic solution and the expression of the equation’s solution are then obtained by using the real decomposition of the quaternion matrix and the Kronecker product of the matrix. At the same time, under the condition that the solution set is non-empty, the optimal approximation solution to the given quaternion circulant matrix is obtained by using the property of Frobenius norm property. Numerical examples are given to verify the correctness of the theoretical results and the feasibility of the proposed method. .