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.     

Water and oil signal assignment in low-moisture mozzarella as determined by time-domain NMR T2 relaxometry

A time-domain ¹H nuclear magnetic resonance relaxometry method was elaborated for the rapid microstructural characterization of mozzarella cheese. For this purpose, there is a strong need to know how the experimentally determined T₂ relaxation time distribution can be related to specific constituents in mozzarella. In this study, a detailed investigation is offered for fresh and aged low-moisture mozzarella cheese, often applied as a pizza cheese, by application of both a conventional Carr–Purcell–Meiboom–Gill (CPMG) sequence and a free-induction decay CPMG (FID-CPMG) sequence. The relaxation behavior was further elucidated by addition of deuterium oxide and by mild heat treatment of samples. The relaxation times of water protons in mozzarella were found to range from a few microseconds to some tens of milliseconds (in aged mozzarella) or to about hundred milliseconds (in fresh mozzarella). The upper limit of the T₂ distribution can even be extended to the seconds range upon releasing water protons from the mozzarella matrix using a mild heat treatment or upon addition of deuterated water. Both stimuli also provided evidence for the absorption of water into the cheese matrix. The potential release and uptake of water demonstrated that mozzarella acts as a very dynamic system during production and storage. The detected differences in the behavior of the water fraction between fresh and aged low-moisture mozzarella might be utilized to study the influence of either production and/or storage conditions on the cheese ripening process.     

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.     

Airy Equation for the Topological String Partition Function in a Scaling Limit

We use the polynomial formulation of the holomorphic anomaly equations governing perturbative topological string theory to derive the free energies in a scaling limit to all orders in perturbation theory for any Calabi–Yau threefold. The partition function in this limit satisfies an Airy differential equation in a rescaled topological string coupling. One of the two solutions of this equation gives the perturbative expansion and the other solution provides geometric hints of the non-perturbative structure of topological string theory. Both solutions can be expanded naturally around strong coupling.