Random sets of finite perimeter

An approach to modelling random sets with locally finite perimeter as random elements in the corresponding subspace of L¹ functions is suggested. A Crofton formula for flat sections of the perimeter is shown. Finally, random processes of particles with finite perimeter are introduced and it is shown that their union sets are random sets with locally finite perimeter.     

Double‐step block division plant‐wide fault detection and diagnosis based on variable distributions and relevant features

Large‐scale process data in plant‐wide process monitoring are characterized by two features: complex distributions and complex relevance. This study proposes a double‐step block division plant‐wide process monitoring method based on variable distributions and relevant features to overcome this limitation. First, the data distribution is considered, and the normality test method called the D‐test is applied to classify the variables with the same distribution (i.e., Gaussian distribution or non‐Gaussian distribution) in a block. Thus, the second block division is implemented on both blocks obtained in the previous step. The mutual information shared between two variables is used to generate relevant matrixes of the Gaussian and non‐Gaussian blocks. The K‐means method clusters the vectors of the relevant matrix. Principal component analysis is conducted to monitor each Gaussian subblock, whereas independent component analysis is conducted to monitor each non‐Gaussian subblock. A composite statistic is eventually derived through Bayesian inference. The proposed method is applied to a numerical system and the Tennessee Eastman process data set. The monitoring performance shows the superiority of the proposed method. Copyright © 2015 John Wiley & Sons, Ltd.     

Recent hypertopologies and continuity of the value function and of the constrained level sets

Given a continuous function f: X→R, sufficient conditions are offered for the continuity of the value function v(A):=inf{f{x): x ε A} and of the level set multifunction Lev(A, α) := {x ε A: f(x)?α}, with respect to recently defined topologies on the closed sets of a metric space.     

Topologies related to the prox map and the restricted center map

In this paper we review some of the recently introduced hypertopologies on collections of nonempty closed subsets of a metrizable space in the context of continuity properties of the prox map and the restricted center map. We identify here suitable families A, B of nonempty closed sets equipped with natural topologies, as coordinate spaces for the gap functional and the restricted radius functional, with a view to explore bivariate continuity of these functionals. This leads us to sharpenings of many known results as well as to some new results for upper semicontinuity of the prox map and the restricted center map. This, in turn, also leads us to improvements of certain best approximation results for convex-valued multifunctions and fixed point theorems for such multifunctions.     

Spaces of Ideal Convergent Sequences of Bounded Linear Operators

Abstract

The notation of I–convergence was introduced and studied by Kostyrko, Macaj, Salat, and Wilczynski. Recently, the concept of I–convergent for a sequence of bounded linear operators has been studied by Khan and Shafiq. This has motivated us to introduce and study some new spaces of double sequences of bounded linear operators and their basic topological and algebraic properties of these spaces. And we study some of their basic topological and algebraic properties of these spaces. We prove some inclusion relations on these spaces.     

关于常系数非齐次线性微分方程通解的注释

给出了二、三阶常系数非齐次线性微分方程的通解的表达式,并且对于任意阶常系数非齐次线性微分方程的某些类别也给出了通解的表达式.     

Improved electrical and interfacial properties of RF-sputtered HfAlOx on n-GaAs with effective Si passivation

In this paper, we present the effects of ultrathin Si interfacial layer on the physical and electrical properties of GaAs MOS capacitors fabricated using RF-sputtered HfAlO_x gate dielectric. It is found that HfAlO_x/Si/n-GaAs stack exhibits excellent electrical properties with low frequency dispersion (∼4.8%), hysteresis voltage (0.27 V) and interface trap density (1.3 × 10¹² eV⁻¹ cm⁻²). The current density of 3.7 × 10⁻⁵ A/cm² is achieved with an equivalent-oxide-thickness of 1.8 nm at V_FB + 1 V for Si-passivated HfAlO_x films on n-GaAs. X-ray photoelectron spectroscopy (XPS) analysis shows that the suppression of low-k interfacial layer formation is accomplished with the introduction of ultrathin Si interface control layer (ICL). Thus the introduction of thin layer of Si between HfAlO_x dielectrics and GaAs substrate is an effective way to improve the interface quality such as low frequency dispersion, hysteresis voltage and leakage current. Additionally, current conduction mechanism has been studied and the dominant conduction mechanisms are found to be Schottky emission at low to medium electric fields and Poole-Frenkel at high fields and high temperatures under substrate injection. In case of gate injection, the main current conduction at low field is found to be the Schottky emission at high temperatures.     

Extension of Fourier algebra homomorphisms to duals of algebras of uniformly continuous functionals

For a locally compact group G, let XG be one of the following introverted subspaces of VN(G): , the C^∗-algebra of uniformly continuous functionals on A(G); , the space of weakly almost periodic functionals on A(G); or , the C^∗-algebra generated by the left regular representation on the measure algebra of G. We discuss the extension of homomorphisms of (reduced) Fourier-Stieltjes algebras on G and H to cb-norm preserving, weak^∗-weak^∗-continuous homomorphisms of into , where (XG,XH) is one of the pairs , , or . When G is amenable, these extensions are characterized in terms of piecewise affine maps.