A High-Order Conservative Numerical Method for Gross-Pitaevskii Equation with Time-Varying Coefficients in Modeling BEC

We propose a high-order conservative method for the nonlinear Sehodinger/Gross-Pitaevskii equation with time- varying coefficients in modeling Bose Einstein condensation （BEC）. This scheme combined with the sixth-order compact finite difference method and the fourth-order average vector field method, finely describes the condensate wave function and physical characteristics in some small potential wells. Numerical experiments are presented to demonstrate that our numerical scheme is efficient by the comparison with the Fourier pseudo-spectral method. Moreover, it preserves several conservation laws well and even exactly under some specific conditions.

A Simulation Study on Comparing General Class of Semiparametric Transformation Models for Survival Outcome with Time-Varying Coefficients and Covariates

The consideration of the time-varying covariate and time-varying coefficient effect in survival models are plausible and robust techniques. Such kind of analysis can be carried out with a general class of semiparametric transformation models. The aim of this article is to develop modified estimating equations under semiparametric transformation models of survival time with time-varying coefficient effect and time-varying continuous covariates. For this, it is important to organize the data in a counting process style and transform the time with standard transformation classes which shall be applied in this article. In the situation when the effect of coefficient and covariates change over time, the widely used maximum likelihood estimation method becomes more complex and burdensome in estimating consistent estimates. To overcome this problem, alternatively, the modified estimating equations were applied to estimate the unknown parameters and unspecified monotone transformation functions. The estimating equations were modified to incorporate the time-varying effect in both coefficient and covariates. The performance of the proposed methods is tested through a simulation study. To sum up the study, the effect of possibly time-varying covariates and time-varying coefficients was evaluated in some special cases of semiparametric transformation models. Finally, the results have shown that the role of the time-varying covariate in the semiparametric transformation models was plausible and credible.

Comparison of Cox proportional hazards model,Cox proportional hazards with time-varying coefficients model,and lognormal accelerated failure time model:Application in time to event analysis of melioidosis patients

Objective:To compare the prognostic factors of mortality among melioidosis patients between lognormal accelerated failure time(AFT),Cox proportional hazards(PH),and Cox PH with time-varying coefficient(TVC)models.Methods:A retrospective study was conducted from 2014 to 2019 among 453 patients who were admitted to Hospital Sultanah Bahiyah,Kedah and Hospital Tuanku Fauziah,Perlis in Northern Malaysia due to confirmed-cultured melioidosis.The prognostic factors of mortality from melioidosis were obtained from AFT survival analysis,and Cox’s models and the findings were compared by using the goodness of fit methods.The analyses were done by using Stata SE version 14.0.Results:A total of 242 patients(53.4%)survived.In this study,the median survival time of melioidosis patients was 30.0 days(95%CI 0.0-60.9).Six significant prognostic factors were identified in the Cox PH model and Cox PH-TVC model.In AFT survival analysis,a total of seven significant prognostic factors were identified.The results were found to be only a slight difference between the identified prognostic factors among the models.AFT survival showed better results compared to Cox's models,with the lowest Akaike information criteria and best fitted Cox-snell residuals.Conclusions:AFT survival analysis provides more reliable results and can be used as an alternative statistical analysis for determining the prognostic factors of mortality in melioidosis patients in certain situations.

Molecular Dynamics, Diffusion Coefficients and Activation Energy of the Electrolyte (Anode) in Lithium (Li and Li+), Sodium (Na and Na+) and Potassium (K and K+)

This work is a simulation modelling with the LAMMPS calculation code of an electrode based on alkali metals (lithium, sodium and potassium) using the MEAM potential. For different multiplicities, two models were studied;with and without gap. In this work, we present the structural, physical and chemical properties of the lithium, sodium and potassium electrodes. For the structural properties, the cohesive energy and the mesh parameters were calculated, revealing that, whatever the chemical element selected, the compact hexagonal hcp structure is the most stable, followed by the face-centred cubic CFC structure, and finally the BCC structure. The most stable structure is lithium, with a cohesion energy of -6570 eV, and the lowest bcc-hcp transition energy of -0.553 eV/atom, followed by sodium. For physical properties, kinetic and potential energies were calculated for each of the sectioned chemical elements, with lithium achieving the highest value. Finally, for the chemical properties, we studied the diffusion coefficient and the activation energy. Only potassium followed an opposite order to the other two, with the quantities with lacunae being greater than those without lacunae, whatever the multiplicity. The order of magnitude of the diffusion coefficients is given by the relationship DLi > DNa > Dk for the multiplicity 6*6*6, while for the activation energy the order is reversed.

Adaptive Random Effects/Coefficients Modeling

Adaptive fractional polynomial modeling of general correlated outcomes is formulated to address nonlinearity in means, variances/dispersions, and correlations. Means and variances/dispersions are modeled using generalized linear models in fixed effects/coefficients. Correlations are modeled using random effects/coefficients. Nonlinearity is addressed using power transforms of primary (untransformed) predictors. Parameter estimation is based on extended linear mixed modeling generalizing both generalized estimating equations and linear mixed modeling. Models are evaluated using likelihood cross-validation (LCV) scores and are generated adaptively using a heuristic search controlled by LCV scores. Cases covered include linear, Poisson, logistic, exponential, and discrete regression of correlated continuous, count/rate, dichotomous, positive continuous, and discrete numeric outcomes treated as normally, Poisson, Bernoulli, exponentially, and discrete numerically distributed, respectively. Example analyses are also generated for these five cases to compare adaptive random effects/coefficients modeling of correlated outcomes to previously developed adaptive modeling based on directly specified covariance structures. Adaptive random effects/coefficients modeling substantially outperforms direct covariance modeling in the linear, exponential, and discrete regression example analyses. It generates equivalent results in the logistic regression example analyses and it is substantially outperformed in the Poisson regression case. Random effects/coefficients modeling of correlated outcomes can provide substantial improvements in model selection compared to directly specified covariance modeling. However, directly specified covariance modeling can generate competitive or substantially better results in some cases while usually requiring less computation time.

Thermomechanical Dynamics (TMD) and Bifurcation-Integration Solutions in Nonlinear Differential Equations with Time-Dependent Coefficients

The new independent solutions of the nonlinear differential equation with time-dependent coefficients (NDE-TC) are discussed, for the first time, by employing experimental device called a drinking bird whose simple back-and-forth motion develops into water drinking motion. The solution to a drinking bird equation of motion manifests itself the transition from thermodynamic equilibrium to nonequilibrium irreversible states. The independent solution signifying a nonequilibrium thermal state seems to be constructed as if two independent bifurcation solutions are synthesized, and so, the solution is tentatively termed as the bifurcation-integration solution. The bifurcation-integration solution expresses the transition from mechanical and thermodynamic equilibrium to a nonequilibrium irreversible state, which is explicitly shown by the nonlinear differential equation with time-dependent coefficients (NDE-TC). The analysis established a new theoretical approach to nonequilibrium irreversible states, thermomechanical dynamics (TMD). The TMD method enables one to obtain thermodynamically consistent and time-dependent progresses of thermodynamic quantities, by employing the bifurcation-integration solutions of NDE-TC. We hope that the basic properties of bifurcation-integration solutions will be studied and investigated further in mathematics, physics, chemistry and nonlinear sciences in general.

Exponential convergence and stability of delayed fuzzy cellular neural networks with time-varying coefficients

In this paper, the dynamic behaviors of fuzzy cellular neural networks （FCNNs） with time-varying coefficients and delays are considered. Some criteria are established to ensure the exponential convergence or exponential stability of such neural networks. The effectiveness of obtained results is illustrated by a numerical example.

ADDITIVE HAZARDS MODEL WITH TIME-VARYING REGRESSION COEFFICIENTS

This article discusses regression analysis of failure time under the additive hazards model, when the regression coefficients are time-varying. The regression coefficients are estimated locally based on the pseudo-score function [12] in a window around each time point. The proposed method can be easily implemented, and the resulting estimators are shown to be consistent and asymptotically normal with easily estimated variances. The simulation studies show that our estimation procedure is reliable and useful.

GENERAL DECAY FOR A VISCOELASTIC EQUATION OF VARIABLE COEFFICIENTS WITH A TIME-VARYING DELAY IN THE BOUNDARY FEEDBACK AND ACOUSTIC BOUNDARY CONDITIONS

A variable coefficient viscoelastic equation with a time-varying delay in the boundary feedback and acoustic boundary conditions and nonlinear source term is considered.Under suitable assumptions, general decay results of the energy are established via suitable Lyapunov functionals and some properties of the convex functions. Our result is obtained without imposing any restrictive growth assumption on the damping term and the elements of the matrix A and the kernel function g.

Partial Time-Varying Coefficient Regression and Autoregressive Mixed Model

Regression and autoregressive mixed models are classical models used to analyze the relationship between time series response variable and other covariates. The coefficients in traditional regression and autoregressive mixed models are constants. However, for complicated data, the coefficients of covariates may change with time. In this article, we propose a kind of partial time-varying coefficient regression and autoregressive mixed model and obtain the local weighted least-square estimators of coefficient functions by the local polynomial technique. The asymptotic normality properties of estimators are derived under regularity conditions, and simulation studies are conducted to empirically examine the finite-sample performances of the proposed estimators. Finally, we use real data about Lake Shasta inflow to illustrate the application of the proposed model.

Partial Time-Varying Coefficient Regression and Autoregressive Mixed Model

Regression and autoregressive mixed models are classical models used to analyze the relationship between time series response variable and other covariates. The coefficients in traditional regression and autoregressive mixed models are constants. However, for complicated data, the coefficients of covariates may change with time. In this article, we propose a kind of partial time-varying coefficient regression and autoregressive mixed model and obtain the local weighted least-square estimators of coefficient functions by the local polynomial technique. The asymptotic normality properties of estimators are derived under regularity conditions, and simulation studies are conducted to empirically examine the finite-sample performances of the proposed estimators. Finally, we use real data about Lake Shasta inflow to illustrate the application of the proposed model.

Impacts of Surface Exchange Coefficients on Simulations of Super Typhoon Megi(2010)Using a Coupled Ocean-Atmosphere-Wave Model

In this study,the effects of surface exchange coefficients on simulations of Super Typhoon Megi(2010)are investigated using a fully coupled ocean-atmosphere-wave model.Several experiments are conducted using different parameterization schemes for the drag(C_(D))and enthalpy exchange(C_(K))coefficients.For the selected case,considering only the leveling-off of C_(D)at high wind speeds does not effectively improve the simulated typhoon track,intensity,or size.We found that increasing C_(K)monotonically with wind speed(Komori et al.,2018)yields stronger winds and deeper pressures by enhancing latent and sensible heat fluxes,but typhoon intensity remains underestimated.We propose a new higher C_(K)than that from Komori et al.(2018)based on the theory of Emanuel(1995).This approach produces a greater modeled typhoon intensity that is in good agreement with the best track data and effectively improves the track error for the simulation.Improved accuracy for modeled typhoon intensity is achieved with the new coefficient because C_(K)/C_(D)reaches the threshold of about 0.75 predicted by Emanuel(1995).The new proposed C_(K)also results in a reasonably accurate modeled sea surface temperature.However,typhoon size and surface wave height are overestimated.This finding implies that more numerical tests for tropical cyclones of different nature(such as strong,weak,dissipating,rapidly intensifying,or weakening tropical cyclones)should be studied,and more physical processes should be explored in future coupled models.

THE FEKETE-SZEG?INEQUALITY AND SUCCESSIVE COEFFICIENTS DIFFERENCE FOR A SUBCLASS OF CLOSE-TO-STARLIKE MAPPINGS IN COMPLEX BANACH SPACES

Let C be the familiar class of normalized close-to-convex functions in the unit disk.In[17],Koepf demonstrated that,as to a function■in the class C,■By applying this inequality,it can be proven that‖a3|-|a2‖≤1 for close-to-convex functions.Now we generalized the above conclusions to a subclass of close-to-starlike mappings defined on the unit ball of a complex Banach space.

Theoretical calculations on Landé g-factors and quadratic Zeeman shift coefficients of nsnp ^(3)P_(0)^(o) clock states in Mg and Cd optical lattice clocks

The study of magnetic field effects on the clock transition of Mg and Cd optical lattice clocks is scarce.In this work,the hyperfine-induced Landég-factors and quadratic Zeeman shift coefficients of the nsnp ^(3)P_(0)^(o) clock states for ^(111,113)Cd and ^(25)Mg were calculated by using the multi-configuration Dirac–Hartree–Fock theory.To obtain accurate values of these parameters,the impact of electron correlations and furthermore the Breit interaction and quantum electrodynamical effects on the Zeeman and hyperfine interaction matrix elements,and energy separations were investigated in detail.We also estimated the contributions from perturbing states to the Landég-factors and quadratic Zeeman shift coefficients concerned so as to truncate the summation over the perturbing states without loss of accuracy.Our calculations provide important data for estimating the first-and second-order Zeeman shifts of the clock transition for the Cd and Mg optical lattice clocks.

Darboux transformation,infinite conservation laws,and exact solutions for the nonlocal Hirota equation with variable coefficients

This article presents the construction of a nonlocal Hirota equation with variable coefficients and its Darboux transformation.Using zero-seed solutions,1-soliton and 2-soliton solutions of the equation are constructed through the Darboux transformation,along with the expression for N-soliton solutions.Influence of coefficients that are taken as a function of time instead of a constant,i.e.,coefficient functionδ(t),on the solutions is investigated by choosing the coefficient functionδ(t),and the dynamics of the solutions are analyzed.This article utilizes the Lax pair to construct infinite conservation laws and extends it to nonlocal equations.The study of infinite conservation laws for nonlocal equations holds significant implications for the integrability of nonlocal equations.

Nondegenerate solitons of the(2+1)-dimensional coupled nonlinear Schrodinger equations with variable coefficients in nonlinear optical fibers

We derive the multi-hump nondegenerate solitons for the(2+1)-dimensional coupled nonlinear Schrodinger equations with propagation distance dependent diffraction,nonlinearity and gain(loss)using the developing Hirota bilinear method,and analyze the dynamical behaviors of these nondegenerate solitons.The results show that the shapes of the nondegenerate solitons are controllable by selecting different wave numbers,varying diffraction and nonlinearity parameters.In addition,when all the variable coefficients are chosen to be constant,the solutions obtained in this study reduce to the shape-preserving nondegenerate solitons.Finally,it is found that the nondegenerate two-soliton solutions can be bounded to form a double-hump two-soliton molecule after making the velocity of one double-hump soliton resonate with that of the other one.

Review of All Possible Conversion Equations of Influence Coefficients with Different Formats on Two-Plane Balancing

This article lists all possible conversion equations of influence coefficients(ICs)with different formats when some of these are known to handle two-plane balancing tasks with no or less trial weight runs.There are two approaches for two-plane balancing.One can treat it as a multi-plane balance problem involving a 2×2 matrix of complex ICs where two direct ICs along with two cross-effect ICs are generated so that correction weights at one or two balance planes can be determined.One can also apply a static pare(in-phase)and/or couple pair(180 degrees out-of-phase)weights for balancing.The latter approach has been used quite often in the field,especially on steam turbine and generator rotors.Dependent on vibration mode shapes and combinations as well as balance plane accessibility,sometimes applying static or couple pair weights can be a wise choice;other times weights at one or two end planes are needed.There are totally 4 possible sets of IC data due to weights at plane 1,plane 2,static pair,and couple pair.IC data would typically be obtained by applying trial weights followed by trial weight runs.It is found,however,that all these IC data can be converted easily without trial weight runs once any two of 4 sets are known.The above findings and conversion equations have been obtained analytically and verified by experimental results.Real cases are given to demonstratetheirapplications.

Complementary-Label Adversarial Domain Adaptation Fault Diagnosis Network under Time-Varying Rotational Speed and Weakly-Supervised Conditions

Recent research in cross-domain intelligence fault diagnosis of machinery still has some problems,such as relatively ideal speed conditions and sample conditions.In engineering practice,the rotational speed of the machine is often transient and time-varying,which makes the sample annotation increasingly expensive.Meanwhile,the number of samples collected from different health states is often unbalanced.To deal with the above challenges,a complementary-label(CL)adversarial domain adaptation fault diagnosis network(CLADAN)is proposed under time-varying rotational speed and weakly-supervised conditions.In the weakly supervised learning condition,machine prior information is used for sample annotation via cost-friendly complementary label learning.A diagnosticmodel learning strategywith discretized category probabilities is designed to avoidmulti-peak distribution of prediction results.In adversarial training process,we developed virtual adversarial regularization(VAR)strategy,which further enhances the robustness of the model by adding adversarial perturbations in the target domain.Comparative experiments on two case studies validated the superior performance of the proposed method.

On the Application of Mixed Models of Probability and Convex Set for Time-Variant Reliability Analysis

In time-variant reliability problems,there are a lot of uncertain variables from different sources.Therefore,it is important to consider these uncertainties in engineering.In addition,time-variant reliability problems typically involve a complexmultilevel nested optimization problem,which can result in an enormous amount of computation.To this end,this paper studies the time-variant reliability evaluation of structures with stochastic and bounded uncertainties using a mixed probability and convex set model.In this method,the stochastic process of a limit-state function with mixed uncertain parameters is first discretized and then converted into a timeindependent reliability problem.Further,to solve the double nested optimization problem in hybrid reliability calculation,an efficient iterative scheme is designed in standard uncertainty space to determine the most probable point(MPP).The limit state function is linearized at these points,and an innovative random variable is defined to solve the equivalent static reliability analysis model.The effectiveness of the proposed method is verified by two benchmark numerical examples and a practical engineering problem.

Finite-time Prescribed Performance Time-Varying Formation Control for Second-Order Multi-Agent Systems With Non-Strict Feedback Based on a Neural Network Observer

This paper studies the problem of time-varying formation control with finite-time prescribed performance for nonstrict feedback second-order multi-agent systems with unmeasured states and unknown nonlinearities.To eliminate nonlinearities,neural networks are applied to approximate the inherent dynamics of the system.In addition,due to the limitations of the actual working conditions,each follower agent can only obtain the locally measurable partial state information of the leader agent.To address this problem,a neural network state observer based on the leader state information is designed.Then,a finite-time prescribed performance adaptive output feedback control strategy is proposed by restricting the sliding mode surface to a prescribed region,which ensures that the closed-loop system has practical finite-time stability and that formation errors of the multi-agent systems converge to the prescribed performance bound in finite time.Finally,a numerical simulation is provided to demonstrate the practicality and effectiveness of the developed algorithm.