Stability analysis of fractional order fuzzy cellular neural networks with leakage delay and time varying delays

In this paper we investigated the stability of fractional order fuzzy cellular neural networks with leakage delay and time varying delays. Based on Lyapunov theory and applying bounded techniques of fractional calculation, sufficient criterion are established to guarantee the stability. Hybrid feedback control is applied to derive the proposed results. Finally, numerical examples with simulation results are given to illustrate the effectiveness of the proposed method.     

Microextraction sample preparation techniques in forensic analytical toxicology

Sample preparation is a critical step in forensic analytical toxicology. Different extraction techniques are employed with the goals of removing interferences from the biological samples, such as blood, tissues and hair, reducing matrix effects and concentrating the target analytes, among others. With the objective of developing faster and more ecological procedures, microextraction techniques have been expanding their applications in the recent years. This article reviews various microextraction methods, which include solid‐based microextraction, such as solid‐phase microextraction, microextraction by packed sorbent and stir‐bar sorptive extraction, and liquid‐based microextraction, such as single drop/hollow fiber‐based liquid‐phase microextraction and dispersive liquid–liquid microextraction, as well as their applications to forensic toxicology analysis. The development trend in future microextraction sample preparation is discussed.     

Template synthesis of ε-Fe2O3 nanoparticles in opal-like matrices

Nanoparticles of ε-Fe₂O₃ were obtained by template synthesis in the pores of opal-like matrices. The maximum content of ε-Fe₂O₃ is achieved upon calcination at 1000 °C for 2–4 h. The content of ε-Fe₂O₃ in a mixture of modifications of iron oxides reaches 80–90%, which is confirmed by the data of X-ray diffraction analysis, Mössbauer spectroscopy and magnetometry experiments.     

模糊支付合作博弈的可信性准核仁

合作博弈是处理局中人之间协同行为的数学理论。有诸如核心、稳定集、沙普利值、准核仁和核仁等不同的解概念。在很多情形,除了借助专家经验和主观直觉,没有恰当的方式来确定支付函数,由此产生了具有模糊支付的合作博弈模型。准核仁是一种重要的解概念,在模糊支付合作博弈中如何恰当定义准核仁是个重要的问题。本文在可信性理论的框架下研究了这个问题,定义了两类可信性准核仁概念并证明了它们的存在性和唯一性,同时研究了可信性核心、可信性核仁与它们之间的关系。     

Constructing sparse Davenport–Schinzel sequences

For any sequence $u$, the extremal function $Ex(u,j,n)$ is the maximum possible length of a $j$-sparse sequence with $n$ distinct letters that avoids $u$. We prove that if $u$ is an alternating sequence $abab\dots$ of length $s$, then $Ex(u,j,n)=\Theta \left(s{n}^2\right)$ for all $j\ge 2$ and $s\ge n$, answering a question of Wellman and Pettie (2018) and extending the result of Roselle and Stanton that $Ex(u,2,n)=\Theta \left(s{n}^2\right)$ for any alternation $u$ of length $s\ge n$ (Roselle and Stanton, 1971).Wellman and Pettie also asked how large must $s\left(n\right)$ be for there to exist $n$-block $DS(n,s\left(n\right))$ sequences of length $\Omega \left(n^{2-o\left(1\right)}\right)$. We answer this question by showing that the maximum possible length of an $n$-block $DS(n,s\left(n\right))$ sequence is $\Omega \left(n^{2-o\left(1\right)}\right)$ if and only if $s\left(n\right)=\Omega \left(n^{1-o\left(1\right)}\right)$. We also show related results for extremal functions of forbidden 0–1 matrices with any constant number of rows and extremal functions of forbidden sequences with any constant number of distinct letters.     

基于显示、生成偏好的序贯模糊选择函数的研究

本文分别在普通情况以及模糊情况下,对显示偏好、生成偏好合理化的序贯选择函数进行了一定的研究。首先,研究了该序贯合理的选择函数的选择结果与选择顺序无关的条件,其次,研究了选择函数与该序贯合理的选择函数之间的关系。     

Algebraic jump loci for rank and Betti numbers over Laurent polynomial rings

Let C be a chain complex of finitely generated free modules over a commutative Laurent polynomial ring $L_s$ in s indeterminates. Given a group homomorphism $p:{\mathbb{Z}}^s?{\mathbb{Z}}^t$ we let $p_{!}(C)=C{?}_{L_s}{L}_t$ denote the resulting induced complex over the Laurent polynomial ring $L_t$ in t indeterminates. We prove that the Betti number jump loci, that is, the sets of those homomorphisms p such that $b_k(p_{!}(C))>b_k(C)$, have a surprisingly simple structure. We allow non-unital commutative rings of coefficients, and work with a notion of Betti numbers that generalises both the usual one for integral domains, and the analogous concept involving McCoy ranks in case of unital commutative rings.     

关于具有Fuzzy约束的Fuzzy多目标规划非控解的存在性

本文对具有Fuzzy约束集的Fuzzy多目标规划引进Fuzzy非控点和Fuzzy非控解的概念,讨论了它们的一些基本性质和存在性。