一个系数两次变号的二阶两点边值问题的正解存在性

对于二阶两点非线性边值问题W” k(t)f(ω)=0，ω(0)=ω(1)=0，建立了一个正解存在定理，其中系数k(t)在[0，1]上两次变号．     

A Simplified Proof of the 0–1 Law for Existential Second-Order Ackermann Sentences

Recently we gave a finitistic proof of the 0–1 law for ∑₁¹ (Ackermann) sentences, which relied as much as possible on the original argument of Kolaitis and Vardi. Here we present another version of our proof which, on the contrary, is self-contained. Finitism allows us to use the beautiful probabilistic argument of Kolaitis and Vardi in a simple and intuitive way. Consequently, we obtain a shorter proof.     

A symmetry completeness criterion for second-order differential equations

A simple criterion for the completeness of an infinitesimal automorphism of a second-order differential equation is given.

     

Propagation invariants of twisted Gaussian Schell-model beams

The second-order moments method is used to study the M² factor and intrinsic astigmatism of twisted Gaussian Schell-model (GSM) beams. It is shown that the M² factor of twisted GSM beams defined by the determinate of the 4×4 variance matrix is a propagation invariant and is independent of the beam twist, whereas the twist affects the intrinsic astigmatism of twisted GSM beams.     

The effect of information in separable Bayesian semi-Markov control models and its application to investment planning

We consider a separable Bayesian semi-Markov control model to describe economic decisions under uncertainty. Our main interest is to examine the influence of the possibility of learning on the economic decisions and on the total expected return in a multi-period framework. We make use of the concept of Blackwell-sufficiency and apply the results to multi-period investment planing under uncertainty.     

On the ratio integral formula for the likelihood ratio of a maximal invariant

The usual ratio of an integral formula for the likelihood ratio of a maximal invariant in a group model is shown to be correct under assumption that the denominator integral is finite almost everywhere. The limitation of this assumption is discussed, and an application to invariant suffciency is given.     

Global solutions of initial value problems for nonlinear second-order integro-differential equations of mixed type in Banach spaces

In this paper, the global solutions of initial value problems for nonlinear second-order integro-differential equations of mixed type in Banach spaces are investigated. The existence and uniqueness of solutions and their iterative approximation are obtained by using Mönch fixed point theorem and new comparison results. The results presented here essentially improve, generalize and unify many well-known results.     

Non-standard Analysis in WKL0

Within a weak subsystem of second-order arithmetic WKL₀, we develop basic part of non-standard analysis up to the Peano existence theorem.     

Special functions as solutions to discrete Painlevé equations

We present results on special solutions of discrete Painlevé equations. These solutions exist only when one constraint among the parameters of the equation is satisfied and are obtained through the solutions of linear second-order (discrete) equations. These linear equations define the discrete analogues of special functions.     

The application to wastewaters of chemometric approaches to handling problems of highly complex matrices

This overview covers current chemometric methodologies using second-order advantage to solve problems of analyzing highly complex matrices. Among the existing algorithms, it focuses on those most frequently used (e.g., the standard for second-order approaches to data analysis, PARAFAC (parallel factor analysis), and MCR-ALS (multivariate curve resolution alternating least squares), as well as the most recently implemented BLLS (bilinear least-squares), and U-PLS/RBL (unfolded partial least squares/residual bilinearization)). All of these are based on linear models. The overview also covers ANN/RBL (artificial neural networks followed by residual bilinearization), which achieves the second-order advantage in systems involving non-linear behavior. In addition, the overview deals with the drawbacks of these approaches, as well as other drawbacks that are inherent in the analytical techniques to question.