Encapsulation of cyanometalates by a tris-macrocyclic ligand tricopper(II) complex: syntheses, structural variation, and magnetic exchange coupling pathways

The reaction of [M(CN)(6)](3-) (M = Cr(3+), Mn(3+), Fe(3+), Co(3+)) and [M(CN)(8)](4-/3-) (M = Mo(4+/5+), W(4+/5+)) with the trinuclear copper(II) complex of 1,3,5-triazine-2,4,6-triyltris[3-(1,3,5,8,12-pentaazacyclotetradecane)] ([Cu(3)(L)](6+)) leads to partially encapsulated cyanometalates. With hexacyanometalate(III) complexes, [Cu(3)(L)](6+) forms the isostructural host-guest complexes [[[Cu(3)(L)(OH(2))(2)][M(CN)(6)](2)][M(CN)(6)]][M(CN)(6)]30 H(2)O with one bridging, two partially encapsulated, and one isolated [M(CN)(6)](3-) unit. The octacyanometalates of Mo(4+/5+) and W(4+/5+) are encapsulated by two tris-macrocyclic host units. Due to the stability of the +IV oxidation state of Mo and W, only assemblies with [M(CN)(8)](4-) were obtained. The Mo(4+) and W(4+) complexes were crystallized in two different structural forms: [[Cu(3)(L)(OH(2))](2)[Mo(CN)(8)]](NO(3))(8)15 H(2)O with a structural motif that involves isolated spherical [[Cu(3)(L)(OH(2))](2)[M(CN)(8)]](8+) ions and a "string-of-pearls" type of structure [[[Cu(3)(L)](2)[M(CN)(8)]][M(CN)(8)]](NO(3))(4) 20 H(2)O, with [M(CN)(8)](4-) ions that bridge the encapsulated octacyanometalates in a two-dimensional network. The magnetic exchange coupling between the various paramagnetic centers is characterized by temperature-dependent magnetic susceptibility and field-dependent magnetization data. Exchange between the CuCu pairs in the [Cu(3)(L)](6+) "ligand" is weakly antiferromagnetic. Ferromagnetic interactions are observed in the cyanometalate assemblies with Cr(3+), exchange coupling of Mn(3+) and Fe(3+) is very small, and the octacoordinate Mo(4+) and W(4+) systems have a closed-shell ground state.     

Spectrum of Single-Photon Scattering in a Strong-Coupling Hybrid Optomechanical System

The single-photon excitation and transmission spectra of strong-coupling hybrid optomechanics are theoretically analyzed, where a two-level system (TLS) is coupled to a mechanical resonator (MR), generating Jaynes–Cummings-type polariton doublets. In this model, both the optomechanical coupling and the TLS-MR coupling are strong. In this parameter region, polaron-assisted excitation reemission processes can strongly affect the single-photon excitation and output spectra of the cavity. It is found that the fine structure around each sideband can be used to characterize the TLS-MR and the effective TLS-photon couplings, even at the single-quantum level. Thus, the spectrum structures may make it possible to sensitively probe the quantum nature of a macroscopic mechanical element. A possible approach for tomographic reconstruction of the state of a TLS, utilizing the single-photon transmission spectra, is further provided.     

Dirac on Gauges and Constraints

We examine the relevance of Dirac's view on the use of transformation theory and invariants in modern physics to current reflections on the meaning of physical symmetries, especially gauge symmetries.     

A landing theorem for periodic dynamic rays for transcendental entire maps with bounded post-singular set

In this article, we present a landing theorem for periodic dynamic rays for transcendental entire maps which have bounded post-singular sets, by using standard hyperbolic geometry results.     

The <Emphasis Type="Italic">M</Emphasis>/<Emphasis Type="Italic">G</Emphasis>/∞ system revisited: finiteness,summability, long range dependence,and reverse engineering

We explore M/G/∞ systems ‘fed’ by Poissonian inflows with infinite arrival rates. Three processes – corresponding to the system's state, workload, and queue-size – are studied and analyzed. Closed form formulae characterizing the system's stationary structure and correlation structure are derived. And, the issues of queue finiteness, workload summability, and Long Range Dependence are investigated. We then turn to devise a ‘reverse engineering’ scheme for the design of the system's correlation structure. Namely: how to construct an M/G/∞ system with a pre-desired ‘target’ workload/queue auto-covariance function. The ‘reverse engineering’ scheme is applied to various examples, including ones with infinite queues and non-summable workloads. AMS Subject Classifications Primary: 60K25; Secondary: 60G55, 60G10     

GPS在无源多基地侦察系统中的应用

针对无源多基地侦察系统的高精度同步问题，提出了一种较为简单可行的方法-利用GPS进行校频和共视比对。     

Tensor logarithmic norm and its applications

Matrix logarithmic norm is an important quantity, which characterize the stability of linear dynamical systems. We propose the logarithmic norms for tensors and tensor pairs, and extend some classical results from the matrix case. Moreover, the explicit forms of several tensor logarithmic norms and semi‐norms are also derived. Employing the tensor logarithmic norms, we bound the real parts of all the eigenvalues of a complex tensor and study the stability of a class of nonlinear dynamical systems. Copyright © 2016 John Wiley & Sons, Ltd.     

Collaborative distributed decision making for large scale disaster relief operations: Drawing analogies from robust natural systems

One of the most ignored, but urgent and vital challenges confronting society today is the vulnerability of urban areas to extreme events. Current organization of response systems, predominantly based on a command and control model, limits their effectiveness and efficiency. Particularly, in decision‐making processes where a large number of actors may be involved. In this article, a new distributed collaborative decision‐making model is proposed to overcome command and control limitations encountered in stressful, hostile, chaotic, and large‐scale settings. This model was derived by borrowing concepts from the collective decision making of honeybees foraging, a successful process in solving complex tasks within complex settings. The model introduced in this article was evaluated through differential equations, i.e., continuous analysis, and difference equations, i.e., discrete analysis. The most important result found is that the best available option in any large‐scale decision‐making problem can be configured as an attractor, in a distributed and timely manner. We suggest that the proposed model has the potential to facilitate decision‐making processes in large‐scale settings. © 2005 Wiley Periodicals, Inc. Complexity 11:28–38, 2005     

Polling systems in heavy traffic: Exhaustiveness of service policies

We study the expected delay in cyclic polling models with general ‘branching-type’ service disciplines. For this class of models, which contains models with exhaustive and gated service as special cases, we obtain closed-form expressions for the expected delay under standard heavy-traffic scalings. We identify a single parameter associated with the service discipline at each queue, which we call the ‘exhaustiveness’. We show that the scaled expected delay figures depend on the service policies at the queues only through the exhaustiveness of each of the service disciplines. This implies that the influence of different service disciplines, but with the same exhaustiveness, on the expected delays at the queues becomes the same when the system reaches saturation. This observation leads to a new classification of the service disciplines. In addition, we show monotonicity of the scaled expected delays with respect to the exhaustiveness of the service disciplines. This induces a complete ordering in terms of efficiency of the service disciplines. The results also lead to new rules for optimization of the system performance with respect to the service disciplines at the queues. Further, the exact asymptotic results suggest simple expected waiting-time approximations for polling models in heavy traffic. Numerical experiments show that the accuracy of the approximations is excellent for practical heavy-traffic scenarios. This revised version was published online in June 2006 with corrections to the Cover Date.     

Two‐Component Supramolecular Gels Derived from Amphiphilic Shape‐Persistent Cyclo[6]aramides for Specific Recognition of Native Arginine

A unique supramolecular two‐component gelation system was constructed from amphiphilic shape‐persistent cyclo[6]aramides and diethylammonium chloride (or triethylammonium chloride). This system has the ability to discriminate native arginine from 19 other amino acids in a specific fashion. Cyclo[6]aramides show preferential binding for the guanidinium residue over ammonium groups. This specificity was confirmed by both experimental results and theoretical simulations. These results demonstrated a new modular displacement strategy, exploring the use of species‐binding hydrogen‐bonded macrocyclic foldamers for the construction of two‐component gelation systems for selective recognition of native amino acids by competitive host–guest interactions. This strategy may be amenable to developing a variety of functional two‐component gelators for specific recognition of various targeted organic molecular species.