Cloaking of 2D particle geometries in a surface medium

We theoretically examine the cloaking condition for two-dimensional particles with varying geometry embedded inside a surface medium. General solutions are obtained for multi-layer particle configurations with either all positive or partially negative constitutive parameters respectively. Cloaking of particle geometries that are large relative to the incident wavelength is demonstrated. Theoretical predictions are compared to full-wave numerical simulations for arrays of particles consisting of different geometries.     

Trees and tensors on Kähler manifolds

We present an organized method to convert between partial derivatives of metrics (functions) and covariant derivatives of curvature tensors (functions) on Kähler manifolds. Basically, it reduces the highly recursive computation in tensor calculus to the enumeration of certain trees with external legs.     

Stereoconvergent,Redox‐Neutral Access to Tetrahydroquinoxalines through Relay Epoxide Opening/Amination of Alcohols

We present an economical catalytic procedure to convert readily available 1,2‐diaminobenzenes and terminal epoxides into valuable 1,2,3,4‐tetrahydroquinoxalines in a highly enantioselective fashion. This procedure operates through relay zinc and iridium catalysis, and achieves redox‐neutral and stereoconvergent production of valuable chiral heterocycles from racemic starting materials with water as the only side product. The use of commercially available reagents and catalysts and a convenient procedure also make this catalytic method attractive for practical application.     

Generalized projective chaos synchronization of gyroscope systems subjected to dead-zone nonlinear inputs

This Letter presents a robust control scheme to generalized projective synchronization between two identical two-degrees-of-freedom heavy symmetric gyroscopes with dead zone nonlinear inputs. Because of the nonlinear terms of the gyroscope system, the system exhibits complex and chaotic motions. By the Lyapunov stability theory with control terms, two suitable sliding surfaces are proposed to ensure the stability of the controlled closed-loop system in sliding mode. Then, two sliding mode controllers (SMC) are designed to guarantee the hitting of the sliding surfaces even when the control inputs contain dead-zone nonlinearity. This method allows us to arbitrarily direct the scaling factor onto a desired value. Numerical simulations show that this method works very well for the proposed controller.     

From Spherical to Leaf‐Like Morphologies: Tunable Supramolecular Assembly of Alkynylgold(I) Complexes through Variations of the Alkyl Chain Length

A series of luminescent polynuclear alkynylgold(I) complexes with different lengths of alkyl chains attached at the N‐heterocyclic carbene moieties has been synthesised and demonstrated to display intriguing self‐assembly behaviours through a cooperative growth mechanism. Variation of the alkyl chain length was found to cause drastic morphological differences in the aggregates and to strongly affect the thermodynamic parameters as revealed by the nucleation–elongation model.     

Maximal degeneracy points of GKZ systems

Motivated by mirror symmetry, we study certain integral representations of solutions to the Gel´fand-Kapranov-Zelevinsky (GKZ) hypergeometric system. Some of these solutions arise as period integrals for Calabi-Yau manifolds in mirror symmetry. We prove that for a suitable compactification of the parameter space, there exist certain special boundary points, which we called maximal degeneracy points, at which all solutions but one become singular.

     

Explicit construction of graph invariant for strongly pseudoconvex compact 3-dimensional rational CR manifolds

Let X be a strongly pseudoconvex compact 3-dimensional CR manifolds which bounds a complex variety with isolated singularities in some C^N. The weighted dual graph of the exceptional set of the minimal good resolution of V is a CR invariant of X; in case X has a tranversal holomorphic S¹ action, we show that it is a complete topological invariant of except for two special cases. When X is a rational CR manifolds, we give explicit algebraic algorithms to compute the graph invariant in terms of the ring structure of _k=0 m^k/m^k+1, where m is the maximal ideal of each singularity. An example is computed explicitly to demonstrate how the algorithms work.     

Anticancer Gold(III) Porphyrins Target Mitochondrial Chaperone Hsp60

Identification of the molecular target(s) of anticancer metal complexes is a formidable challenge since most of them are unstable toward ligand exchange reaction(s) or biological reduction under physiological conditions. Gold(III) meso‐tetraphenylporphyrin ( gold‐1 a ) is notable for its high stability in biological milieux and potent in vitro and in vivo anticancer activities. Herein, extensive chemical biology approaches employing photo‐affinity labeling, click chemistry, chemical proteomics, cellular thermal shift, saturation‐transfer difference NMR, protein fluorescence quenching, and protein chaperone assays were used to provide compelling evidence that heat‐shock protein 60 (Hsp60), a mitochondrial chaperone and potential anticancer target, is a direct target of gold‐1 a in vitro and in cells. Structure–activity studies with a panel of non‐porphyrin gold(III) complexes and other metalloporphyrins revealed that Hsp60 inhibition is specifically dependent on both the gold(III) ion and the porphyrin ligand.     

A sharp estimate of positive integral points in 6-dimensional polyhedra and a sharp estimate of smooth numbers

Inspired by Durfee Conjecture in singularity theory, Yau formulated the Yau number theoretic conjecture(see Conjecture 1.3) which gives a sharp polynomial upper bound of the number of positive integral points in an n-dimensional(n≥3) polyhedron. It is well known that getting the estimate of integral points in the polyhedron is equivalent to getting the estimate of the de Bruijn function ψ(x, y), which is important and has a number of applications to analytic number theory and cryptography. We prove the Yau number theoretic conjecture for n = 6. As an application, we give a sharper estimate of function ψ(x, y) for 5≤y 17, compared with the result obtained by Ennola.