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.     

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.     

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.     

Facile synthesis of high-molecular-weight acid-labile polypeptides using urethane derivatives

Polypeptides have received noticeable attention in the biomedical field due to their structural versatility and biomimetic properties. Particularly, polypeptides that are responsive to biological stimuli, such as mildly acidic extracellular and intracellular conditions, have great potential as delivery carriers for therapeutics. However, synthesis of high-molecular-weight acid-labile peptides is often daunting due to highly restrictive polymerization conditions and limitations in preserving acid-degradable functional groups. For instance, the popular N-carboxyanhydride (NCA) ring-opening polymerization (ROP) is efficient, but acid-labile NCA monomers are difficult to synthesize and store. In this study, acid-labile polypeptides with high molecular weights were synthesized under mild, permissive conditions using carboxylated urethane derivative monomers which are stable for ease of handling. The polymerization was successful in various organic solvents at room temperature, and did not require additional energy or initiation to drive the formation of NCA intermediates. The polymerization was also rapid enough to be independent of inert atmosphere. The strategy explored here to synthesize high-molecular-weight acid-labile polypeptides offers significant advantages including facile synthesis of acid-labile urethane derivative monomers that are stable, even in contact with moisture, and fast polymerization under easily achievable conditions. © 2014 Wiley Periodicals, Inc. J. Polym. Sci., Part A: Polym. Chem. 2015 , 53, 280–286     

Cycloelimination of Imidazolidin‐2‐ylidene N‐Heterocyclic Carbenes: Mechanism and Insights into the Synthesis of Stable “NHC‐CDI” Amidinates

We report the discovery that 1,3‐bis(aryl)imidazolidin‐2‐ylidenes, one of the most widely studied classes of N‐heterocyclic carbenes (NHCs), undergo quantitative conversion to zwitterionic “NHC‐CDI” amidinates upon heating to ≈100 °C in solution. The mechanism of this novel NHC decomposition process is studied in detail. These studies enabled the rational synthesis of a new class of bench stable amidinates from a panel of NHCs and carbodiimides. We expect these constructs to find utility in a variety of applications.