Multiple Statistical models for simulation and prediction of nonlinear processes

The paper describes a parameterisation procedure for multiple nonlinear equations with intercepts. These equations may consist of numerous members with few practical limitations on their structure. Examples are given on the application of the procedure to simulation in the areas of chemical technology and hydrology. Advantages of the proposed method are simplicity of the fitting procedure, high accuracy of simulations and more reliable simulations beyond the calibration range     

Extrapolation of weights revisited: New proofs and sharp bounds

We use an appropriate factorization of the Ap weights to give another proof of the extrapolation theorem of Rubio de Francia. It provides sharp bounds in terms of the Ap-constant of the weights. Then we extend the result to more general settings including off-diagonal and partial range extrapolation. Among the applications, we prove by iteration a multivariable extrapolation theorem and give a sharp bound for Calderón-Zygmund operators on Lp(w) for weights in Aq (q<p).     

高维有噪频谱有限函数的外推

本文给出的定理既适合于一维与高维,又适合于有噪与无噪的频变有限函数的外推,是对Sanz-Huang两个猜想的改进,同时讨论了外推数与真函数的逼近关系。     

On a model of electromagnetic field propagation in ferroelectric media

The Maxwell system in an anisotropic, inhomogeneous medium with non-linear memory effect produced by a Maxwell type system for the polarization is investigated under low regularity assumptions on data and domain. The particular form of memory in the system is motivated by a model for electromagnetic wave propagation in ferromagnetic materials suggested by Greenberg, MacCamy and Coffman [J.M. Greenberg, R.C. MacCamy, C.V. Coffman, On the long-time behavior of ferroelectric systems, Phys. D 134 (1999) 362-383]. To avoid unnecessary regularity requirements the problem is approached as a system of space-time operator equation in the framework of extrapolation spaces (Sobolev lattices), a theoretical framework developed in [R. Picard, Evolution equations as space-time operator equations, Math. Anal. Appl. 173 (2) (1993) 436-458; R. Picard, Evolution equations as operator equations in lattices of Hilbert spaces, Glasnik Mat. 35 (2000) 111-136]. A solution theory for a large class of ferromagnetic materials confined to an arbitrary open set (with suitably generalized boundary conditions) is obtained.     

Nonlinear transformation methods for accelerating the convergence of Coulomb integrals over exponential type functions

It is well known that in any ab initio molecular orbital (MO) calculation, the major task involves the computation of molecular integrals, among which the computation of Coulomb integrals are the most frequently encountered. As the molecular system gets larger, computation of these integrals becomes one of the most laborious and time consuming steps in molecular systems calculation. Improvement of the computational methods of molecular integrals would be indispensable to a further development in computational studies of large molecular systems. The atomic orbital basis functions chosen in the present work are Slater type functions. These functions can be expressed as finite linear combinations of B functions which are suitable to apply the Fourier transform method. The difficulties of the numerical evaluation of the analytic expressions of the integrals of interest arise mainly from the presence of highly oscillatory semi-infinite integrals. In this work, we present a generalized algorithm based on the nonlinear transformation of Sidi, for a precise and fast numerical evaluation of molecular integrals over Slater type functions and over B functions. Numerical results obtained for the three-center two-electron Coulomb and hybrid integrals over B functions and over Slater type functions. Comparisons with numerical results obtained using alternatives approaches and an existing code are listed.     

Being uncertain in thin layer chromatography—Some thoughts about latent details in the retention estimation

This paper deals with some important (but often neglected) details about the uncertainty of retention measurement in thin layer chromatography, the propagation of uncertainty during computing simple and more complex values from the retention data, ending in influence of the retention uncertainty onto the regression estimates during extrapolation and lipophilicity estimation. Theoretical considerations are tested on data from previous study. It can be concluded that when TLC spots are broad and the retention uncertainty exceeds about 0.02 of R_F value, the uncertainty should be taken into the account in further computations.     

Extragradient and extrapolation methods with generalized Bregman distances for saddle point problems

In this paper, we introduce two Bregman-type algorithmic frameworks to generalize the extragradient and extrapolation methods. With the help of relative Lipschitzness and the Bregman distance tool, the iteration properties of the proposed frameworks are analyzed. As applied to smooth convex-concave saddle point problems, our theory rediscovers the main results in Mokhtari et al. (2020) [14] for wider frameworks under weaker assumptions via a conceptually different approach.     

Numerical methods and asymptotic error expansions for the Emden-Fowler equations

In the present paper we analyse a numerical method for computing the solution of some boundary-value problems for the Emden-Fowler equations. The differential equations are discretized by a finite-difference method and we derive asymptotic expansions for the discretization error. Based on these asymptotic expansions, we use an extrapolation algorithm to accelerate the convergence of the numerical method.     

Deconvolution with simple extrapolation for improved cerebral blood flow measurement in dynamic susceptibility contrast magnetic resonance imaging during acute ischemic stroke

Magnetic resonance (MR) perfusion imaging is a clinical technique for measuring brain blood flow parameters during stroke and other ischemic events. Ischemia in brain tissue can be difficult to accurately measure or visualize when using MR-derived cerebral blood flow (CBF) maps. The deconvolution techniques used to estimate flow can introduce a mean transit time-dependent bias following application of noise stabilization techniques. The underestimation of the CBF values, greatest in normal tissues, causes a decrease in the image contrast observed in CBF maps between normally perfused and ischemic tissues; resulting in ischemic areas becoming less conspicuous. Through application of the proposed simple extrapolation technique, CBF biases are reduced when missing high-frequency signal components in the MR data removed during deconvolution noise stabilization are restored. The extrapolation approach was compared with other methods and showed a statistically significant increase in image contrast in CBF maps between normal and ischemic tissues for white matter (P<.05) and performed better than most other methods for gray matter. Receiver operator characteristic curve analysis demonstrated that extrapolated CBF maps better-detected penumbral regions. Extrapolated CBF maps provided more accurate CBF estimates in simulations, suggesting that the approach may provide a better prediction of outcome in the absence of treatment.