Homogeneous variable exponent Besov and Triebel–Lizorkin spaces

We introduce homogeneous Besov and Triebel–Lizorkin spaces with variable indexes. We show that their study reduces to the study of inhomogeneous variable exponent spaces and homogeneous constant exponent spaces. Corollaries include trace space characterizations and Sobolev embeddings.     

A survey on book-embedding of planar graphs

The book-embedding problem arises in several area, such as very large scale integration (VLSI) design and routing multilayer printed circuit boards (PCBs). It can be used into various practical application fields. A book embedding of a graph G is an embedding of its vertices along the spine of a book, and an embedding of its edges to the pages such that edges embedded on the same page do not intersect. The minimum number of pages in which a graph G can be embedded is called the pagenumber or book-thickness of the graph G. It is an important measure of the quality for book-embedding. It is NP-hard to research the pagenumber of book-embedding for a graph G. This paper summarizes the studies on the book-embedding of planar graphs in recent years.     

Corrigendum to “New algebraic properties of an amalgamated algebra along an ideal”

At some point, after publication, we realized that Proposition 4.1(2) and Theorem 4.4 in [2 D’Anna, M., Finocchiaro, C. A., Fontana, M. (2016). New algebraic properties of an amalgamated algebra along an ideal. Commun. Algebra 44(5):1836–1851.[Taylor & Francis Online], [Web of Science ®] , [Google Scholar]] hold under the assumption (not explicitly declared) that B = f(A)+J. Furthermore, we provide here the exact value for the embedding dimension of A?^fJ, also when B≠f(A)+J, under the hypothesis that J is finitely generated as an ideal of the ring f(A)+J.     

Quantum Bayesian computation

Quantum Bayesian computation is an emerging field that levers the computational gains available from quantum computers. They promise to provide an exponential speed-up in Bayesian computation. Our article adds to the literature in three ways. First, we describe how quantum von Neumann measurement provides quantum versions of popular machine learning algorithms such as Markov chain Monte Carlo and deep learning that are fundamental to Bayesian learning. Second, we describe quantum data encoding methods needed to implement quantum machine learning including the counterparts to traditional feature extraction and kernel embeddings methods. Third, we show how quantum algorithms naturally calculate Bayesian quantities of interest such as posterior distributions and marginal likelihoods. Our goal then is to show how quantum algorithms solve statistical machine learning problems. On the theoretical side, we provide quantum versions of high dimensional regression, Gaussian processes and stochastic gradient descent. On the empirical side, we apply a quantum FFT algorithm to Chicago house price data. Finally, we conclude with directions for future research.     

基于ZIF-8/PAN复合薄膜的柔性丙酮气体传感器

ZIF-8是一种Zn基金属有机骨架材料, 可以吸附丙酮气体从而作为电容式丙酮传感器的气敏材料, 然而ZIF-8的传统使用形式为粉末态, 这导致其不能成为具备柔性的整体, 从而限制了传感器的柔性. 结合包埋种子和二次生长法将ZIF-8与纳米纤维结合成纤维型柔性材料, 并将其作为气敏层制备了柔性电容式丙酮气体传感器. 该传感器在9种常见挥发性有机化合物中表现出良好的选择性, 对250~2000 cm³/m³的丙酮气体具有灵敏的响应、良好的循环响应及长期稳定性. 值得注意的是该柔性传感器不仅在室温下进行传感, 而且在弯折180°的状态下对丙酮气体的响应值与不弯折(0°)状态下几乎一致, 在200次以内的180°弯折-恢复后同样表现出了传感性能的稳定, 表明了其在柔性传感器方面的潜力.     

An explicit compact universal space for real flows

The Kakutani–Bebutov Theorem (1968) states that any compact metric real flow whose fixed point set is homeomorphic to a subset of $\mathbb{R}$ embeds into the Bebutov flow, the $\mathbb{R}$-shift on $C(\mathbb{R},[0,1])$. An interesting fact is that this universal space is a function space. However, it is not compact, nor locally compact. We construct an explicit countable product of compact subspaces of the Bebutov flow which is a universal space for all compact metric real flows, with no restriction; namely, into which any compact metric real flow embeds. The result is compared to previously known universal spaces.     

Uniqueness of isometric immersions with the same mean curvature

Motivated by the quasi-local mass problem in general relativity, we study the rigidity of isometric immersions with the same mean curvature into a warped product space. As a corollary of our main result, two star-shaped hypersurfaces in a spatial Schwarzschild or AdS-Schwarzschild manifold with nonzero mass differ only by a rotation if they are isometric and have the same mean curvature. We also prove similar results if the mean curvature condition is replaced by an ${\sigma }_2$-curvature condition.     

Hydrophobic cryogels for DNA adsorption: Effect of embedding of monosize microbeads into cryogel network on their adsorptive performances

As alternative hydrophobic adsorbent for DNA adsorption, supermacroporous cryogel disks were synthesized via free radical polymerization. In this study, we have prepared two kinds of cryogel disks: (i) poly(2‐hydroxyethyl methacrylate‐N‐methacryloyl‐l ‐tryptophan) [p(HEMA‐MATrp)] cryogel containing specific hydrophobic ligand MATrp; and (ii) monosize p(HEMA‐MATrp) particles synthesized via suspension polymerization embedded into p(HEMA) cryogel structure to obtain p(HEMA‐MATrp)/p(HEMA) composite cryogel disks. These cryogel disks containing hydrophobic functional group were characterized via swelling studies, Fourier transform infrared spectroscopy, elemental analysis, surface area measurements and scanning electron microscopy. DNA adsorption onto both p(HEMA‐MATrp) cryogel and p(HEMA‐MATrp)/p(HEMA) composite cryogels was investigated. Maximum adsorption of DNA on p(HEMA‐MATrp) cryogel was found to be 15 mg/g polymer. Otherwise, p(HEMA‐MATrp)/p(HEMA) composite cryogels significantly increased the DNA adsorption capacity to 38 mg/g polymer. Composite cryogels could be used repeatedly without significant loss on adsorption capacity after 10 repetitive adsorption–desorption cycles. Copyright © 2013 John Wiley & Sons, Ltd.