New results for the Liebau phenomenon via fixed point index

We prove new results regarding the existence of positive solutions for a nonlinear periodic boundary value problem related to the Liebau phenomenon. As a consequence we obtain new sufficient conditions for the existence of a pump in a simple model. Our methodology relies on the use of classical fixed point index. Some examples are provided to illustrate our theory. We improve and complement previous results in the literature.     

One‐dimensional q‐Dirac equation

In this paper, we introduce a q‐analog of 1‐dimensional Dirac equation. We investigate the existence and uniqueness of the solution of this equation. Later, we discuss some spectral properties of the problem, such as formally self‐adjointness, the case that the eigenvalues are real, orthogonality of eigenfunctions, Green function, existence of a countable sequence of eigenvalues, and eigenfunctions forming an orthonormal basis of . Finally, we give some examples.     

The pointwise estimates of solutions for a nonlinear convection diffusion reaction equation

This paper studies the time asymptotic behavior of solutions for a nonlinear convection diffusion reaction equation in one dimension.First,the pointwise estimates of solutions are obtained,furthermore,we obtain the optimal L~p,1≤ p ≤ +∞,convergence rate of solutions for small initial data.Then we establish the local existence of solutions,the blow up criterion and the sufficient condition to ensure the nonnegativity of solutions for large initial data.Our approach is based on the detailed analysis of the Green function of the linearized equation and some energy estimates.     

Candidates for nonzero Betti numbers of monomial ideals

Let I be a monomial ideal in the polynomial ring S generated by elements of degree at most d. In this paper, it is shown that, if the i-th syzygy of I has no elements of degrees j,…,j+(d?1) (where j≥i+d), then (i+1)-th syzygy of I does not have any element of degree j+d. Then we give several applications of this result, including an alternative proof for Green–Lazarsfeld index of the edge ideals of graphs as well as an alternative proof for Fröberg’s theorem on classification of square-free monomial ideals generated in degree 2 with linear resolution. Among all, we deduce a partial result on subadditivity of the syzygies for monomial ideals.     

弹性力学问题的虚边界元-配点法

本文提出虚边界方法,建立了离散化虚边界元-配点法,给出了离散化求系数的积分解析式。本文方法完全避免了边界奇异积分及其复杂耗时的运算,成功地提高了普通边界元法(以下简称边界元法)中边界附近区域内包括边界上解的精度,保留了边界元法的优点并扬弃了其弱点。边界元间接法是本文方法中的一个特例。数值算例表明,程序可靠,节省机时,计算精度较高。     

An efficient and novel synthesis of chromonyl chalcones using recyclable Zn(l-proline)2 catalyst in water

A novel approach was adopted for the synthesis of a series of chromonyl chalcones (3a-o) from 3-formylchromones (1a-c) and different cyclic active methyl compounds (2a-e), employing Zn(l-proline)₂ as a recyclable Lewis acid catalyst in water. In each conversion, the catalyst was successfully recovered and reused several times without significant loss in yield and selectivity. All the newly synthesized compounds were characterized using elemental analysis and spectral data (IR, ¹H NMR, ¹³C NMR and mass spectrometry).     

Palladium-catalyzed oxidation of vinyl ether to acetate with hydrogen peroxide

The selective hydrogen peroxide oxidation of vinyl ethers to give acetates was developed using triphenylphosphine palladium and triethyl amine catalysts under mild reaction conditions.     

离子液体与微波协同促进有机合成反应

介绍了离子液体作溶剂、助溶剂、催化剂和反应试剂与微波协同促进有机合成的研究进展。离子液体与微波协同促进有机合成反应,缩短了反应时间,提高了反应的选择性和产率,对环境更加友好。