The Bertini irreducibility theorem for higher codimensional slices

In [3], Poonen and Slavov recently developed a novel approach to Bertini irreducibility theorems over an arbitrary field, based on random hyperplane slicing. In this paper, we extend their work by proving an analogous bound for the dimension of the exceptional locus in the setting of linear subspaces of higher codimensions.     

次线性期望下的一般中心极限定理

受Peng-中心极限定理的启发,本文主要应用G-正态分布的概念,放宽Peng-中心极限定理的条件,在次线性期望下得到形式更为一般的中心极限定理.首先,将均值条件E[X_n]=ε[X_n]=0放宽为|E[X_n]|+|ε[X_n]|=O(1/n);其次,应用随机变量截断的方法,放宽随机变量的2阶矩与2+δ阶矩条件;最后,将该定理的Peng-独立性条件进行放宽,得到卷积独立随机变量的中心极限定理.     

Differential equations driven by rough paths with jumps

We develop the rough path counterpart of Itô stochastic integration and differential equations driven by general semimartingales. This significantly enlarges the classes of (Itô/forward) stochastic differential equations treatable with pathwise methods. A number of applications are discussed.     

On the global dynamic behaviour for a generalized haematopoiesis model with almost periodic coefficients and oscillating circulation loss rate

A generalized non‐linear nonautonomous model for the haematopoiesis (cell production) with several delays and an oscillating circulation loss rate is studied. We prove a fixed point theorem in abstract cones, from which different results on existence and uniqueness of positive almost periodic solutions are deduced. Moreover, some criteria are given to guarantee that the obtained positive almost periodic solution is globally exponentially stable.     

Mechanism of Insertion Reactions between Silylenoid H2SiLiF and GeH3R (R =F,OH, NH2): a Theoretical Study

Theoretical investigations on the insertion reaction mechanisms of three- membered-ring silylenoid H2 Si Li F with GeH 3R(R = F, OH, NH2) have been systematically carried out by combined density functional theory(DFT) and ab initio quantum chemical calculations. The geometries of all stationary points for these reactions were optimized using the B3 LYP method and then the QCISD method was used to calculate the single-point energies. The calculated results indicate that, there are one precursor complex(Q), one transition state(TS), and one intermediate(IM) which connect the reactants and the products along the potential energy surface. The insertion reactions of three-membered-ring silylenoid with Ge H3 R proceed in a concerted manner, forming H2RSi-Ge H3 and Li F. The calculated potential energy barriers of the three reactions are 29.17, 30.90, and 54.07 k J/mol, and the reaction energies for the three reactions are –127.05, –116.91, and –103.31 k J/mol, respectively. The insertion reactions in solvents are similar to those in vacuum. Under the same situation, the insertion reactions should occur easily in the following order: GeH 3-F GeH 3-OH GeH 3-NH2. The elucidations of the mechanism of these insertion reactions provided a new mode of silicon-germanium bond formation.     

Counterion-Trapped-Molecules: From High Polarity and Enriched IR Spectra to Induced Isomerization

We report extensive computational studies of some novel intermolecular systems and their properties. Recombination of alkali-halide counterions separated by a noncovalently trapped hydrocarbon molecule is prevented by significant potential energy barriers, resulting in unusual metastable insertion complexes. These systems are extremely polar, while the inserted molecule is strongly counter-polarized, leading to significant cooperative nonadditivity effects. The compression and electric field produced by the counterions favours isomerization of the trapped molecule via a significant reduction of the barriers to bond rearrangement, in a field-induced mechanochemical process. The predicted IR intensity spectra clearly reflect (1) formation of the insertion complex, rather than simple attachment of alkali halide, and (2) isomerization of the trapped molecule, thus allowing experimental access to these events.     

Stereoselectivity and nonmigratory insertion mechanism of dimethylacetylene dicarboxylate into metallocene-hydride of Cp2M(L)H [Cp = η5-C5H5; M = Nb,V; L = CO,P (OMe)3]: A DFT study

The insertion of an alkyne into transition metal–hydrogen bonds is a key elementary step in catalytic polymerization and hydrogenation processes. It was found that a (Z)- or (E)-type alkyenyl complex can be formed through trans/cis stereospecific processes. In this work, the reaction mechanism of Cp₂M(L)H [Cp = η⁵-C₅H₅; M = Nb, V; L = CO, P (OMe)₃] with dimethylacetylene dicarboxylate (DMAD), and the factors influencing the stereoselectivity have been investigated based on density functional theory calculations. The calculated results show that all of the reactions are exothermic. For L = CO, the Z-isomer product forms first even at low temperatures because of the low Gibbs free energy barrier (ΔG^#). Then the Z-pro converts to E-pro , while for L = P (OMe)₃, the exclusive product is the E-isomer. For different metal centers, the reaction mechanisms of the Cp₂M(CO)H + DMAD (M = Nb and V) reaction are similar, while their products are different at room temperature. For M = Nb, because the energy barrier of the isomerization from Z-pro to E-pro is low and the relative free energies of Z-pro and E-pro are almost equal, both Z-pro and E-pro can be obtained. While for the Cp₂V(CO)H + DMAD reaction, only the Z-pro can be obtained under mild conditions, E-pro can be obtained only at high temperatures. For the Cp₂M(CO)H+DMAD(M=V and Nb) reactions, the formation of E-isomer products proceeds via two five-membered ring transition states. The calculated results provide an reasonable explanation for the experimental results and predict a new insertion reaction.     

Enzymatic Insertion of Lipids Increases Membrane Tension for Inhibiting Drug Resistant Cancer Cells

Although lipids contribute to cancer drug resistance, it is challenging to target diverse range of lipids. Here, we show enzymatically inserting exceedingly simple synthetic lipids into membranes for increasing membrane tension and selectively inhibiting drug resistant cancer cells. The lipid, formed by conjugating dodecylamine to d -phosphotyrosine, self-assembles to form micelles. Enzymatic dephosphorylation of the micelles inserts the lipids into membranes and increases membrane tension. The micelles effectively inhibit a drug resistant glioblastoma cell (T98G) or a triple-negative breast cancer cell (HCC1937), without inducing acquired drug resistance. Moreover, the enzymatic reaction of the micelles promotes the accumulation of the lipids in the membranes of subcellular organelles (e.g., endoplasmic reticulum (ER), Golgi, and mitochondria), thus activating multiple regulated cell death pathways. This work, in which for the first time membrane tension is increased to inhibit cancer cells, illustrates a new and powerful supramolecular approach for antagonizing difficult drug targets.