Linking solutions for p-Laplace equations with nonlinear boundary conditions and indefinite weight

We apply the linking method for cones in normed spaces to p-Laplace equations with various nonlinear boundary conditions. Some existence results are obtained.     

带树枝状侧链聚苯乙炔的合成与结构表征

合成了带树枝状聚苯甲醚修饰基团的苯乙炔单体,在Rh[(nbd)Cl2]2催化剂的作用下得到了侧链带聚苯甲醚树枝的新型聚苯乙炔衍生物,用红外吸收光谱、核磁共振谱、紫外可见吸收光谱和凝胶渗透色谱表征了聚合物的结构.发现聚合物的重均分子量达到了57300,在氯仿、N,N-二甲基甲酰胺、四氢呋喃等有机溶剂中有良好的溶解性能.由于侧链上聚苯甲醚树枝体积庞大,聚合物主链采取立构规整的顺-顺式构象,紫外可见吸收光谱在440nm附近出现了显著的共轭主链的吸收肩峰;立构规整的顺-顺式构象使树枝状侧链形成了对主链保护的"夹套效应",聚合物热分解温度从聚苯乙炔母体的225℃提高到295℃.     

The Ground State Solutions for Kirchhoff-Schr¨odinger Type Equations with Singular Exponential Nonlinearities in RN*

In this paper, the authors consider the following singular Kirchhoff-Schr¨odinger problem M Z RN |u|N + V (x)|u|N dx (N u + V (x)|u|N?2u) = f(x, u) |x|η in RN , (Pη) where 0 < η < N, M is a Kirchhoff-type function and V (x) is a continuous function with positive lower bound, f(x, t) has a critical exponential growth behavior at infinity.Combining variational techniques with some estimates, they get the existence of ground state solution for (Pη). Moreover, they also get the same result without the A-R condition.     

"Triplet-excited region" in polyene oligomers revisited: Pariser-Parr-Pople model studied with the density matrix renormalization group method

We have carried out density matrix renormalization group calculations on the T1 state of linear polyenes applying the Pariser-Parr-Pople (PPP) Model. The geometry optimization for the polyene oligomers C(2n)H(2n+2) (n = 4,5,6,...,15) shows that the S0 to T1 excitation region is composed of a soliton-antisoliton pair located symmetrically away from the center of the chain and leads to single- and double-bond interconversions in between. The distance between the soliton and antisoliton centers in T1 state changes with the length of the chain, contradictory to earlier conclusions obtained with PPP-SDCI or ab initio SCI methods. The inconsistency most possibly comes from the insufficient consideration of the electron correlations in small-scale CI methods.     

Nontrivial Solutions of Superquadratic Hamiltonian systems with Lagrangian Boundary Conditions and the L-index Theory

In this paper, the authors study the existence of nontrivial solutions for the Hamiltonian systems z（t） = J△↓H（t, z（t）） with Lagrangian boundary conditions, where ^H（t,z）=1/2（^B（t）z, z） ＋ ^H（t, z）,^B（t） is a semipositive symmetric continuous matrix and ^H（t, z） = satisfies a superquadratic condition at infinity. We also obtain a result about the L-index.     

Theoretical study of very high spin organic pi-conjugated polyradicals

Different forms of pi-conjugated polyarylmethyl systems, such as diradicals, polyradicals, spin clusters, and polymers, were studied with valence bond (VB) calculations within the density matrix renormalization group (DMRG) framework. For these systems, the energy gap between the high-spin ground state and the lowest low-spin excited state (DeltaE(L-H)) was computed and found to correlate well with their stability. On the basis of our analysis, medium-sized polyarylmethyl cycles are suggested to be potential key building blocks of very high spin spin clusters and polymers.     

Toward a synthetically useful stereoselective C-H amination of hydrocarbons

Reaction between a sulfur(VI) compound and an iodine(III) oxidant in the presence of a catalytic quantity (<=3 mol %) of a rhodium(II) catalyst leads to the formation of a chiral metallanitrene of unprecedented reactivity. The latter allows intermolecular C-H amination to proceed in very high yields up to 92% and excellent diastereoselectivities up to 99% with C-H bond containing starting materials as the limiting component. The scope of this C-H functionalization includes benzylic and allylic substrates as well as alkanes. Secondary positions react preferentially, but insertion into activated primary C-H bonds or sterically accessible tertiary sites is also possible. Cooperative effects between the nitrene precursor and the chiral catalyst at the origin of these good results have also been applied to kinetic resolution of racemic sulfonimidamide. This methodology paves the way to the use of Csp3-H bonds as synthetic precursors for the introduction of a nitrogen functionality into selected positions.     

On the Range of the Pseudomonotone Second-Order Cone Linear Complementarity Problem

In this paper, we provide a complete characterization of the range of the pseudomonotone second-order cone linear complementarity problem. In particular, by answering the three questions that under what conditions the range is the whole space, convex and closed, respectively, we explicitly characterize and formulate the range of the pseudomonotone second-order cone linear complementarity problem.     

壬基酚对三角帆蚌的毒性效应

利用壬基酚对三角帆蚌进行急性毒性试验,获得三角帆蚌在壬基酚溶液中的安全浓度;在安全浓度范围内设定了2个浓度的实验组进行慢性毒性试验,并取蚌的鳃、肝脏、性腺进行石蜡切片观察。结果表明壬基酚对三角帆蚌的急性毒性24、48、72、96h的LC50分别为65.924、45.182、27.374和16.226mg·L-1,安全浓度为1.623mg·L-1。利用0.5和1.0mg·L-1壬基酚浓度进行慢性毒性试验21d后,三角帆蚌鳃和肝组织的损伤随壬基酚浓度增加而加深;而2种浓度壬基酚处理的精巢症状基本相似,表现为精原细胞破裂,精子外泄且大多数死亡,精子细胞数目减少,细胞排列紊乱,说明NP对三角帆蚌精巢的损伤比其它组织严重。 更多还原