Selective Catalytic Isomerization of β-Pinene Oxide to Perillyl Alcohol Enhanced by Protic Tetraimidazolium Nitrate

A series of tetraimidazolium salts with different anions was prepared and applied in the isomerization of β-pinene oxide. After examining the activity of different catalysts, a remarkable enhancement of the selectivity of perillyl alcohol (47 %) was obtained over [PEimi][HNO₃]₄ under mild reaction conditions and using DMSO as the solvent. Furthermore, noncovalent interactions between solvent molecules and the catalyst were found by FT-IR spectroscopy and confirmed by computational chemistry. The homogeneous catalyst showed excellent stability and was reused up to six times without significant loss.     

Polyvinylpyrrolidone and graphene-modified hematite nanoparticles for efficient electrocatalytic oxidation of p-nitrophenol

Journal of Solid State Electrochemistry - Polyvinylpyrrolidone (PVP) and graphene (G)-modified iron oxides (Fe2O3-PVP-G) are prepared by a simple hydrothermal reaction. Their morphology and...     

The dual form of Beck type identities

The Ramanujan Journal - Inspired by Andrews and Merca’s recent work on the number of even parts over all partitions into distinct parts, we introduce a new kind of Beck type identities, which...     

GLOBAL WELL-POSEDNESS FOR FRACTIONAL NAVIER-STOKES EQUATIONS IN VARIABLE EXPONENT FOURIER-BESOV-MORREY SPACES

In this paper we study the Cauchy problem of the incompressible fractional Navier-Stokes equations in critical variable exponent Fourier-Besov-Morrey space F N^s(·)p(·),h(·),q(R³)with s(·)=4-2α-3/p(·).We prove global well-posedness result with small initial data belonging to FN^4-2α-3/p(·)p(·),h(·)q(R³).The result of this paper extends some recent work.     

Additive Hermitian idempotent preservers between operator algebras

Let L be an additive map between (real or complex) matrix algebras sending $n\times n$ Hermitian idempotent matrices to $m\times m$ Hermitian idempotent matrices. We show that there are nonnegative integers $p,q$ with $n(p+q)=r\le m$ and an $m\times m$ unitary matrix U such that$L(A)=U[(I_p?A)\oplus (I_q?A^t)\oplus 0_{m?r}]U^{?},\text{for any}n\times n\text{Hermitian}A\text{with rational trace}.$ We also extend this result to the (complex) von Neumann algebra setting, and provide a supplement to the Dye-Bunce-Wright Theorem asserting that every additive map of Hermitian idempotents extends to a Jordan ?-homomorphism.     

Three-weight linear codes from Weil sums

Journal of Algebraic Combinatorics - By appropriately choosing a defining set, we define a class of linear codes and establish their complete weight enumerators and weight enumerators using Weil...     

Generalized Jacobi spectral Galerkin method for fractional pantograph differential equation

This work is concerned with the extension of the Jacobi spectral Galerkin method to a class of nonlinear fractional pantograph differential equations. First, the fractional differential equation is converted to a nonlinear Volterra integral equation with weakly singular kernel. Second, we analyze the existence and uniqueness of solutions for the obtained integral equation. Then, the Galerkin method is used for solving the equivalent integral equation. The error estimates for the proposed method are also investigated. Finally, illustrative examples are presented to confirm our theoretical analysis.