Geometry of spacelike generalized constant ratio surfaces in Minkowski 3-space

Generalized constant ratio surfaces are defined by the property that the tangential component of the position vector is a principal direction on the surfaces. In this work, we study these class of surfaces in the 3-dimensional Minkowski space L³. We achieve a complete classification of spacelike generalized constant ratio surfaces in L³.     

Multi-recurrence and van der Waerden systems

We explore recurrence properties arising from dynamical approach to the van der Waerden theorem and similar combinatorial problems. We describe relations between these properties and study their consequences for dynamics. In particular, we present a measure-theoretical analog of a result of Glasner on multi-transitivity of topologically weakly mixing minimal maps. We also obtain a dynamical proof of the existence of a C-set with zero Banach density.     

Synthesis,characterization of new bisphenol-based benzoxazines and the thermal properties of their polymers

Journal of Thermal Analysis and Calorimetry - New bisphenol-based benzoxazines (BBA-a and BBA-bra) were synthesized from bisphenol containing trityl group, paraformaldehyde, aniline and...     

A facile chemical reduction method for synthesis of platinum–iron catalysts on carbon fiber papers for methanol oxidation

To enhance catalytic activity and durability for methanol oxidation reaction (MOR), we have fabricated bimetallic Pt–Fe catalysts on carbon fiber papers (denoted as Pt–Fe@CFP) by a facile chemical reduction method using iron as the precursor, ascorbic acid and sodium hypophosphite as the reductants, respectively. When ascorbic acid is using as the reductant, the Pt–Fe@CFP catalysts are composed of platinum and disordered Pt–Fe phases. The atomic ratio between Pt and Fe can be adjusted by altering deposition conditions. The Pt–Fe@CFP catalysts with Pt/Fe ratio of 1.1, which deposited with surfactant CTAB in bath at room temperature, exhibit excellent catalytic activity and stability in MOR. However, when sodium hypophosphite is employed as the reductant, the co-deposition of phosphorus would lead to a decreased catalytic performance in MOR.     

Lanthanide-organic frameworks based on terphenyl-tetracarboxylate ligands: syntheses,structures, optical properties and selective sensing of nitro explosives

Three isostructural three-dimensional(3D) lanthanide-based metal-organic frameworks [Ln_2L(H_2L)(NMP)_2].H_2O(Ln=Sm(1), Eu(2), Gd(3); H_4L=1,1′:4′,1″-terphenyl-2′,4,4″,5′-tetracarboxylic acid; NMP=N-methyl-2-pyrrolidone) have been synthesized and structurally characterized. In 1–3, two Ln3+ ions are doubly-bridged by two oxygen atoms of two carboxylate groups to form the dinuclear Ln_2(OCOO–)_2 unit. Each Ln_2(OCOO–)_2 unit links with four H_2L~(2-) ligands and four L4. ligands to lead to the 3D framework,which can be rationalized as a new trinodal 4,4,8-connected(44.62)(45.6)(412.616) topological network by considering the dinuclear Ln_2(OCOO–)_2 units as 8-connected nodes and L~4./H_2L~(2-) ligands as planar 4-connected nodes, respectively. 1 and 3 exhibit blue emission originated from the ligand with the emission maximum at 384 nm, while 2 shows intense characteristic red emission of Eu~(3+) ions and weak ligand-centered emission. Moreover, 2 has fluorescent quenching response towards the aromatic nitro compounds, especially for the 3,4-dinitrotoluene(3,4-DNT) with the linear Stern-Volmer relationship in the concentration range of 0–1 mM and the quenching constant(Ksv) of 2.084×10~3 M~(-1).     

On input-to-state stability for stochastic multi-group models with multi-dispersal

This paper focuses on the input-to-state stability for a general class of stochastic multi-group models with multi-dispersal. By incorporating graph theory with Lyapunov method as well as stochastic analysis techniques, novel sufficient criteria are derived, which are in the form of Lyapunov-type theorem and coefficient-type criterion, respectively. Moreover, to show the applicability of our findings, we employ coefficient-type criterion to analyze the input-to-state stability for stochastic coupled oscillators. Finally, a numerical example and its simulations are offered to demonstrate the validity and feasibility of the theoretic results.     

Strict comparison theorems under sublinear expectations

In this paper, we consider strict comparison theorems in the framework of G-expectation, which is a type of sublinear expectation associated with fully nonlinear parabolic partial differential equations. In particular, we first apply Krylov–Safonov estimates to establish the strict comparison theorem for functions from the Lipschitz class \(Lip(\Omega )\). Then we prove generalized strict comparison theorems on the enlarged space \(L_G^1(\Omega )\), which is the Banach completion of \(Lip(\Omega )\) under the G-expectation.     

Gröbner–Shirshov bases for some Lie algebras

Siberian Mathematical Journal - We give Gröbner–Shirshov bases for the Drinfeld–Kohno Lie algebra L n in [1] and the Kukin Lie algebra A P in [2], where P is a semigroup. By way of...