Estimating the segregation strength of microphase‐separated diblock copolymers from the interfacial width

The ever‐growing catalog of monomers being incorporated into block polymers affords exceptional control over phase behavior and nanoscale structure. The segregation strength, χN, is the fundamental link between the molecular‐level detail and the thermodynamics. However, predicting phase behavior mandates at least one experimental measurement of χN for each pair of blocks. This typically requires access to the disordered state. We describe a method for estimating χN from small‐angle X‐ray scattering measurements of the interfacial width between lamellar microdomains, t_x, in the microphase‐separated melt. The segregation strength is determined by comparing t_x to self‐consistent field theory calculations of the intrinsic interfacial width, t_i, as a function of the mean‐field χN. The method is validated using a series of independent experimental measurements of t_x and χN, measured via the order–disorder transition temperature, T_ODT. The average absolute relative difference between χN calculated from t_x and the value calculated from T_ODT is a modest 11%. Corrections for nonplanarity of the interfaces are investigated but do not improve the agreement between the experiments and theory. Published 2019. This article is a U.S. Government work and is in the public domain in the USA. J. Polym. Sci., Part B: Polym. Phys. 2019 © 2019 Wiley Periodicals, Inc. J. Polym. Sci., Part B: Polym. Phys. 2019 , 57, 932–940     

Consistent Quantum Realism: A Reply to Bassi and Ghirardi

A recent claim by Bassi and Ghirardi that the consistent (decoherent) histories approach cannot provide a realistic interpretation of quantum theory is shown to be based upon a misunderstanding of the single-framework rule: they have replaced the correct rule with a principle which directly contradicts it. It is their assumptions, not those of the consistent histories approach, which lead to a logical contradiction.     

Interactions Between Solitons and Cnoidal Periodic Waves of the(2+1)-Dimensional Konopelchenko–Dubrovsky Equation

The(2+1)-dimensional Konopelchenko–Dubrovsky equation is an important prototypic model in nonlinear physics, which can be applied to many fields. Various nonlinear excitations of the(2+1)-dimensional Konopelchenko–Dubrovsky equation have been found by many methods. However, it is very difficult to find interaction solutions among different types of nonlinear excitations. In this paper, with the help of the Riccati equation, the(2+1)-dimensional Konopelchenko–Dubrovsky equation is solved by the consistent Riccati expansion(CRE). Furthermore, we obtain the soliton-cnoidal wave interaction solution of the(2+1)-dimensional Konopelchenko–Dubrovsky equation.     

Electronic confinement effects on the reaction field type calculations of solvent effects

We analyze some procedures to introduce the effect of confining the electrons of the hydrogen atoms in cavitation spheres like those used in the self‐consistent reaction field models for studying the solvent influence on molecular properties [as polarizable continuum model (PCM), or conductor screening model (COSMO)]. We have found that the boundary conditions to be applied have an important effect on the system energy that by no means should be neglected in this type of calculations. We have found as well that “‐nG” expansion technique could be applicable in this kind of calculations (even at the very simple “‐3G” level) and lead us to a relatively simple form of applying the theory. Moreover, we have found a way to define the cavitation radius of PCM calculations, by minimizing the system energy with respect to this parameter, which could be a more satisfactory procedure—at least from a theoretical point of view—than the use of empirical values characteristic of most of the PCM or COSMO standard calculations. © 2013 Wiley Periodicals, Inc.     

半参数回归模型独立情形的分离法估计

对半参数回归模型,用L2最佳逼近加矩估计的方法,推出其非参数部分的依L2与强相合联合收敛意义下的估计,及参数部分的强相合与相合渐近正态估计,并设计实行了一个模拟实验.     

Consistent interpolation of equidistantly sampled data

Let u₁, u₂, …, u_N with u_n∈? denote the values of a function recorded or computed at N real and equidistant abscissa values t_n=nΔt+t₀ for n=1, …, N. A consistent interpolation operator L , as defined in this paper, interpolates these function values for N new abscissas t_n = (n+½)Δt+t₀, the first N?1 of which are halfway between those originally given while the last one is outside of the original abscissa range. Application of L to these interpolated function values produces the last N?1 samples u₂, u₃, …, u_N of the original data plus one extrapolated function value u_N+1. Hence, L ² is essentially a shift operator, but with a prediction component. The difference between various interpolation methods (e.g. polynomials, Fourier series) is now reduced to the way in which u_N+1 is determined. This concept not only permits a uniform view at interpolation by quite different classes of functions but also allows the creation of more general interpolation, differentiation, and integration formulas, which can be tailored to particular problems. Copyright © 2008 John Wiley & Sons, Ltd.     

T分布族对数似然方程根的大样本性质

对一类具体的分布族——T分布族中的参数θ,证明了存在θ的一个强相合且最优渐近正态估计θn*,它以概率1当n充分大时是对数似然方程的根.     

Time series with Birnbaum‐Saunders marginal distributions

A stationary sequence of random variables with Birnbaum‐Saunders marginal distribution is constructed using a Gaussian autoregressive moving average sequence. The parameters of the model are then estimated by the maximum likelihood method, and the resulting estimators are shown to be consistent and asymptotically normal. A simulation study is carried out to assess the performance of the estimators. The proposed model is finally used to analyze 2 real data sets.     

Lyapunov direct method for investigating stability of nonstandard finite difference schemes for metapopulation models

In this paper nonstandard finite difference (NSFD) schemes of two metapopulation models are constructed. The stability properties of the discrete models are investigated by the use of the Lyapunov stability theorem. As a result of this we have proved that the NSFD schemes preserve essential properties of the metapopulation models (positivity, boundedness and monotone convergence of the solutions, equilibria and their stability properties). Especially, the basic reproduction number of the continuous models is also preserved. Numerical examples confirm the obtained theoretical results of the properties of the constructed difference schemes. The method of Lyapunov functions proves to be much simpler than the standard method for studying stability of the discrete metapopulation model in our very recent paper.     

Recovery of periodicities hidden in heavy‐tailed noise

We address a parametric joint detection‐estimation problem for discrete signals of the form , , with an additive noise represented by independent centered complex random variables . The distributions of are assumed to be unknown, but satisfying various sets of conditions. We prove that in the case of a heavy‐tailed noise it is possible to construct asymptotically strongly consistent estimators for the unknown parameters of the signal, i.e., frequencies , their number N, and complex coefficients . For example, one of considered classes of noise is the following: are independent identically distributed random variables with and . The construction of estimators is based on detection of singularities of anti‐derivatives for Z‐transforms and on a two‐level selection procedure for special discretized versions of superlevel sets. The consistency proof relies on the convergence theory for random Fourier series.