Interactions of delta shock waves for the relativistic Chaplygin Euler equations with split delta functions

In this article, we are concerned with the interactions of delta shock waves with contact discontinuities for the relativistic Euler equations for Chaplygin gas by using split delta functions method. The solutions are obtained constructively and globally when the initial data consists of three piecewise constant states. The global structure and large time‐asymptotic behaviors of the solutions are analyzed case by case. During the process of the interaction, the strengths of delta shock waves are computed completely. Moreover, it can be found that the Riemann solutions are stable for such small perturbations with special initial data by letting perturbed parameter ε tends to zero. Copyright © 2014 John Wiley & Sons, Ltd.     

On Gradient Solitons of the Ricci–Harmonic Flow

In this paper, we study gradient solitons to the Ricci flow coupled with harmonic map heat flow. We derive new identities on solitons similar to those on gradient solitons of the Ricci flow. When the soliton is compact, we get a classification result. We also discuss the relation with quasi-Einstein manifolds.     

Hausdorff operators on the Heisenberg group

This paper is devoted to the high-dimensional and multilinear Hausdorff operators on the Heisenberg group H n. The sharp bounds for the strong type(p, p)(1 ≤ p ≤∞) estimates of n-dimensional Hausdorff operators on H n are obtained. The sharp bounds for strong(p, p) estimates are further extended to multilinear cases. As an application, we derive the sharp constant for the multilinear Hardy operator on H n. The weak type(p, p)(1 ≤ p ≤∞) estimates are also obtained.     

Amarusine A,a new dioxaspiro[4.4]nonane derivative with a butyrolactone ring from Pleioblastus amarus

Amarusine A (1), a new polyketide derivative possessing an unusual dioxaspiro[4.4]nonane derivative with a butyrolactone ring, was isolated from the leaves of Pleioblastus amarus. The structure and absolute stereochemistry of compound 1 were rigorously determined using UV, IR, HRESIMS, and 1D and 2D NMR techniques and by comparing experimental and calculated electronic circular dichroism (ECD) spectra. Amarusine A (1) exhibits a good antioxidant activity for scavenging the DPPH radical. A possible biosynthetic pathway was postulated.     

Tuning Structural Topologies of Two Cadmium(II) Coordination Polymers via Isomeric Dipyridyl Ligands: Syntheses,Crystal Structures,and Luminescent Properties

Abstract. Two new coordination polymers {[Cd₂(BDC)₂(3‐bpmp)(H₂O)₂] · 2H₂O}_n ( 1 ) and [Cd₂(BDC)₂(4‐bpmp)]_n ( 2 ) [H₂BDC = 5‐hydroxy‐isophthalic acid, 3‐bpmp = 1,4‐bis(3‐pyridylmethy)piperazine, and 4‐bpmp = 1,4‐bis(4‐pyridylmethy) piperazine] were synthesized via hydrothermal synthesis, and further characterized by IR spectroscopy, elemental analysis, XRD, and X‐ray crystallography. Complex 1 shows a two‐dimensional (4,4) sql topology and complex 2 features an 8‐connected hex topology. Moreover, the luminescent properties of complexes 1 and 2 were investigated in the solid state at room temperature.     

A New Tricarboxylate‐Terbium(III) Compound: Synthesis,Structure, and Luminescent Property

The Tb^III compound [Tb(tci)(H₂O)]_n · n(DMF) ( 1 ) [H₃tci = tri(2‐carboxythyl)isocyanurate, DMF = N,N′‐dimethylformamide] was synthesized by the reaction of terbium oxide, H₃tci, and two drops of concentrated nitric acid in the presence of DMF and H₂O. Single crystal X‐ray analysis reveals that it features a three‐dimensional (3D) framework based on infinite –Tb–COO–Tb– chains. The tci ligand in 1 links six different Tb^III ions with its two carboxylate groups in μ₂‐κ¹O;κ²O,O′ mode and the third in μ₂‐κ¹O;κ¹O′ mode. Thermal analysis reveals that it remains high thermal stability until 390 °C. Luminescence investigation shows that it emits characteristic green light of Tb^III ions.     

Synthesis,Structure, Photoluminescence,and Theoretical ­Calculation of an rtl‐type Zinc(II) Compound with Linear Trinuclear [Zn3(COO)4(μ2‐H2O)2] Subunits

The zinc(II) coordination polymer [Zn₃(BPT)₂(μ₂‐H₂O)₂(H₂O)₂]_n · n(DMA) ( 1 ) (H₃BPT = biphenyl‐3,4′,5‐tricarboxylic acid, DMA = N,N′‐dimethylactamide) was obtained by the solvothermal reaction of H₃BPT with Zn(NO₃)₂ in DMA/H₂O mixed solvent. Single crystal X‐ray analysis reveals that compound 1 has a complicated 3D framework containing linear trinuclear [Zn₃(COO)₄(μ₂‐H₂O)₂] clusters as building subunits, which can be simplified into a (3,6)‐connected rtl topological network with the Schläfli symbol {4.6²}₂{4².6¹⁰.8³}. The calculated results of total and partial density of states (DOS) indicate that the luminescence of 1 mainly originates from intraligand charge transfer.     

Synthesis,Structure, and Properties of O6‐Corona[3]arene[3]tetrazines

O₆‐Corona[3]arene[3]tetraazines, a new class of macrocyclic compounds, were synthesized efficiently in a one‐pot reaction from the nucleophilic aromatic substitution reaction between 1,4‐dihydroxybenzene derivatives and 3,6‐dichlorotetrazine in warm acetonitrile. In the crystalline structure, the resulting macrocycles adopt highly symmetric structures of a regular hexagonal cavity with all bridging oxygen atoms and tetrazine rings located on the same plane with phenylene units orthogonally orientated. The constitutional aromatic rings are able to rotate around the macrocyclic annulus, depending on the steric effect of the substituents and temperature, in solution. The electron‐deficient nature revealed by cyclic voltammetry, differential pulse voltammetry, and characteristic absorbances at a visible region show the O₆‐corona[3]arene[3]tetrazines to be suitable macrocyclic receptors for electron‐rich guests.     

Easily Accessible Auxiliary for Palladium‐Catalyzed Intramolecular Amination of C(sp2)?H and C(sp3)?H Bonds at δ‐ and ε‐Positions

An easily synthesized and accessible N,O‐bidentate auxiliary has been developed for selective C H activation under palladium catalysis. The novel auxiliary showed its first powerful application in C H functionalization of remote positions. Both C(sp²) H and C(sp³) H bonds at δ‐ and ε‐positions were effectively activated, thus giving tetrahydroquinolines, benzomorpholines, pyrrolidines, and indolines in moderate to excellent yields by palladium‐catalyzed intramolecular C H amination.