Additive Hermitian idempotent preservers between operator algebras

Let L be an additive map between (real or complex) matrix algebras sending $n\times n$ Hermitian idempotent matrices to $m\times m$ Hermitian idempotent matrices. We show that there are nonnegative integers $p,q$ with $n(p+q)=r\le m$ and an $m\times m$ unitary matrix U such that$L(A)=U[(I_p?A)\oplus (I_q?A^t)\oplus 0_{m?r}]U^{?},\text{for any}n\times n\text{Hermitian}A\text{with rational trace}.$ We also extend this result to the (complex) von Neumann algebra setting, and provide a supplement to the Dye-Bunce-Wright Theorem asserting that every additive map of Hermitian idempotents extends to a Jordan ?-homomorphism.     

Graphs are (1,Δ+1)-choosable

A graph $G$ is $(k,k^{\prime })$-choosable if the following holds: For any list assignment $L$ which assigns to each vertex $v$ a set $L\left(v\right)$ of $k$ real numbers, and assigns to each edge $e$ a set $L\left(e\right)$ of $k^{\prime }$ real numbers, there is a total weighting $?:V\left(G\right)\cup E\left(G\right)\to R$ such that $?\left(z\right)\in L\left(z\right)$ for $z\in V\cup E$, and ${\sum }_{e\in E\left(u\right)}?\left(e\right)+?\left(u\right)\ne {\sum }_{e\in E\left(v\right)}?\left(e\right)+?\left(v\right)$ for every edge $uv$. This paper proves that if $G$ is a connected graph of maximum degree $\Delta \ge 2$, then $G$ is $(1,\Delta +1)$-choosable.     

Solid-State NMR Spectroscopy: A Powerful Technique to Directly Study Small Gas Molecules Adsorbed in Metal–Organic Frameworks

Metal–organic frameworks (MOFs) have shown great potential in gas separation and storage, and the design of MOFs for these purposes is an on-going field of research. Solid-state nuclear magnetic resonance (SSNMR) spectroscopy is a valuable technique for characterizing these functional materials. It can provide a wide range of structural and motional insights that are complementary to and/or difficult to access with alternative methods. In this Concept article, the recent advances made in SSNMR investigations of small gas molecules (i.e., carbon dioxide, carbon monoxide, hydrogen gas and light hydrocarbons) adsorbed in MOFs are discussed. These studies demonstrate the breadth of information that can be obtained by SSNMR spectroscopy, such as the number and location of guest adsorption sites, host–guest binding strengths and guest mobility. The knowledge acquired from these experiments yields a powerful tool for progress in MOF development.     

Self-Healable Polyelectrolytes with Mechanical Enhancement for Flexible and Durable Supercapacitors

The practical application of advanced personalized electronics is inseparable from flexible, durable, and even self-healable energy storage devices. However, the mechanical and self-healing performance of supercapacitors is still limited at present. Herein, highly transparent, stretchable, and self-healable poly(2-acrylamido-2-methyl-1-propanesulfonic acid) (PAMPSA)/poly(vinyl alcohol) (PVA)/LiCl polyelectrolytes were facilely prepared by one-step radical polymerization. The cooperation of PAMPSA and PVA significantly increased the mechanical and self-healing capacity of the polyelectrolyte, which exhibited superior stretchability of 938 %, stress of 112.68 kPa, good electrical performance (ionic conductivity up to 20.6 mS cm⁻¹), and high healing efficiency of 92.68 % after 24 h. After assembly with polypyrrole-coated single-walled carbon nanotubes, the resulting as-prepared supercapacitor had excellent electrochemical properties with high areal capacitance of 297 mF cm⁻² at 0.5 mA cm⁻² and good rate capability (218 mF cm⁻² at 5 mA cm⁻²). Besides, after cutting in two the supercapacitor recovered 99.2 % of its original specific capacitance after healing for 24 h at room temperature. The results also showed negligible change in the interior contact resistance of the supercapacitor after ten cutting/healing cycles. The present work provides a possible solution for the development of smart and durable energy storage devices with low cost for next-generation intelligent electronics.     

Adaptive vehicle posture and height synchronization control of active air suspension systems with multiple uncertainties

This paper addresses the tasks of height and posture motion control for an electronically controlled active air suspension (AAS) system. A mathematical model of a vehicle body with AAS system is established to describe the dynamic characteristics and then formulated into a multi-input multi-output nonlinear system by considering parametric uncertainties and unmodelled dynamics. Based on this mathematical model, a synchronization control strategy is proposed to adjust the heights of adjacent AASs simultaneously, driving the pitch and roll angles closely to an arbitrarily neighborhood of zero, achieving global uniform ultimate boundedness. The proposed controller is robust to parametric uncertainties and external disturbances. A projection operator is utilized to limit the estimated parameters to their corresponding prescribed bounds in finite time. A co-simulation is conducted by combining a virtual vehicle plant with ASS system in AMEsim with the proposed synchronization controller in MATLAB/Simulink. Simulation results demonstrate that the proposed synchronization controller is effective and robust.     

Tuning of Supramolecular Architectures of l‐Valine‐Containing Dicyanoplatinum(II) 2,2′‐Bipyridine Complexes by Metal–Metal, π–π Stacking,and Hydrogen‐Bonding Interactions

A series of newly synthesized dicyanoplatinum(II) 2,2′‐bipyridine complexes exhibits self‐assembly properties in solution after the incorporation of the l ‐valine amino units appended with various hydrophobic motifs. These l ‐valine‐derived substituents were found to have critical control over the aggregation behaviors of the complexes in the solution state. On one hand, one of the complexes was found to exhibit interesting circularly polarized luminescence (CPL) signals at low temperature due to the formation of chiral spherical aggregates in the temperature‐dependent studies. On the other hand, systematic transformation from less uniform aggregates to well‐defined fibrous and rod‐like structures via Pt???Pt and π–π stacking interactions has also been observed in the mixed‐solvent studies. These changes were monitored by UV/Vis absorption, emission, circular dichroism (CD), and CPL spectroscopies, and morphologies were studied by electron microscopy.     

Low band‐gap diketopyrrolopyrrole‐containing polymers for near infrared electrochromic and photovoltaic applications

Donor–acceptor type polymers bearing diketopyrrolopyrrole and 3,4‐ethylenedioxythiophene units are reported. The polymers are green and exhibit very low band‐gaps (1.19 eV) with strong and broad absorption (maxima of about 830 nm) in the near infrared (NIR) region in their neutral film states. The polymers display color changes between dark green and light blue with exceptional optical contrasts in the NIR regions of up to 78 and 63% as thin films and single‐layer electrochromic devices, respectively. Fast switching, good stabilities as well as high coloration efficiencies (743–901 cm² C^?1) were also observed. The polymers could also be potentially used as photovoltaic material, with a power conversion efficiency of up to 1.68%. © 2015 Wiley Periodicals, Inc. J. Polym. Sci., Part A: Polym. Chem. 2015 , 53, 1287–1295     

Air‐Stable Spirofluorene‐Containing Ladder‐Type Bis(alkynyl)borane Compounds with Readily Tunable Full Color Emission Properties

A series of air‐stable spiro‐fused ladder‐type boron(III) compounds has been designed, synthesized, and the electrochemistry and photophysical behavior have been characterized. By simply varying the substituents on the pyridine ring and extending the π‐conjugation of the spiro framework, the emission color of these compounds can be easily fine‐tuned spanning the visible spectrum from blue to red. All compounds exhibit a broad and structureless emission band across the entire visible region, assigned as an intramolecular charge‐transfer transition originating from the thiophene of the spiro framework to the pyridine‐borane moieties. In addition, these compounds demonstrate high photoluminescence quantum yields of up to 0.81 in dichloromethane solution and 0.86 in doped thin films. Some of the compounds have also been employed as emissive materials, in which solution‐processed organic light‐emitting devices (OLEDs) with tunable emission colors spanning the visible spectrum from blue, green to red have been realized, demonstrating the potential applications of these boron compounds in OLEDs.     

Solution-Based,Anion-Doping of Li4Ti5O12 Nanoflowers for Lithium-Ion Battery Applications

Solution-based, anionic doping represents a convenient strategy with which to improve upon the conductivity of candidate anode materials such as Li₄Ti₅O₁₂ (LTO). As such, novel synthetic hydrothermally-inspired protocols have primarily been devised herein, aimed at the large-scale production of unique halogen-doped, micron-scale, three-dimensional, hierarchical LTO flower-like motifs. Although fluorine (F) doping has been explored, the use of chlorine (Cl) dopants is the primary focus here. Several experimental variables, such as dopant amount, lithium hydroxide concentration, and titanium butoxide purity, were probed and perfected. Furthermore, the Cl doping process did not damage the intrinsic LTO morphology. The analysis, based on interpreting a compilation of SEM, XRD, XPS, and TEM-EDS results, was used to determine an optimized dopant concentration of Cl. Electrochemical tests demonstrated an increased capacity via cycling of 12 % for a Cl-doped sample as compared with pristine LTO. Moreover, the Cl-doped LTO sample described in this study exhibited the highest discharge capacity yet reported at an observed rate of 2C for this material at 143mAh g⁻¹. Overall, these data suggest that the Cl dopant likely enhances not only the ion transport capabilities, but also the overall electrical conductivity of our as-prepared structures. To help explain these favorable findings, theoretical DFT calculations were used to postulate that the electronic conductivity and Li diffusion were likely improved by the presence of increased Ti³⁺ ion concentration coupled with widening of the Li migration channel.     

Fundamental Groups of Graphs of Cyclic Subgroup Separable and Weakly Potent Groups

We give a characterization of the cyclic subgroup separability and weak potency of the fundamental group of a graph of polycyclic-by-finite groups and free-by-finite groups amalgamating edge subgroups of the form × D,where h has infinite order and D is finite.