Imido-modified SiO2-supported Ti/Mg Ziegler-Natta catalysts for ethylene polymerization and ethylene/1-hexene copolymerization

A novel imido-modified SiO2-supported Ti/Mg Ziegler-Natta catalyst for ethylene and ethylene/1-hexene polymerization is investigated. The catalyst is prepared by modification of (SiO2/MgO/MgCl2)TiClx Ziegler-Natta catalysts via supporting vanadium species followed by reaction with p-tolyl isocyanate as imido agents, to get the merits from both the SiO2-supported imido vanadium catalyst and the (SiO2/MgO/MgCl2)TiClx Ziegler-Natta catalyst. The effects of cocatalyst amount, hydrogen and dosage of 1-hexene on polymerization behavior and the microstructures of their polymers are systematically investigated. Compared with (SiO2/MgO/MgCl2)TiClx Ziegler-Natta catalysts and vanadium-modified (SiO2/MgO/MgCl2)TiClx Ziegler-Natta catalysts, the imido-modified SiO2-supported Ti/Mg catalysts show lower but more stable activity including homopolymerization, polymerization with hydrogen and copolymerization owing to imido ligands, indicating that p-Tolyl isocyanate was unfavorable to improving catalytic activity but benefited the stability, and the products of all catalysts show lower 1-hexene incorporation but much higher molecular weight (MW) with medium molecular weight distribution (MWD). The most unique feature of the novel catalysts is the excellent hydrogen response without lowering the polymerization activity, showing great potential for industrial application

Varying Index Coefficient Model for Tail Index Regression

Investigating the causes of extreme events is crucial across various fields. However, existing asymptotic theoretical models often lack flexibility and fail to capture the complex dependency structures inherent in extreme events. Additionally, the scarcity of extreme event data and the challenge of fully nonparametric estimation with high-dimensional covariates lead to the “curse of dimensionality”, complicating the analysis of extreme events. Considering the nonlinear interactions among covariates, we propose a flexible model that combines varying index coefficient models with extreme value theory to address these issues. This approach effectively avoids the curse of dimensionality while providing robust explanatory power and high flexibility. Our model also includes a variable selection process, for which we have demonstrated the consistency of the estimators and the oracle property of the variable selection. Monte Carlo simulation results validate the finite sample properties of the estimators. Furthermore, an empirical analysis of tail risk in financial markets offers valuable insights into the drivers of risk

Lobatto-Milstein Numerical Method in Application of Uncertainty Investment of Solar Power Projects

Recently, there has been a growing interest in the production of electricity from renewable energy sources (RES). The RES investment is characterized by uncertainty, which is long-term, costly and depends on feed-in tariff and support schemes. In this paper, we address the real option valuation (ROV) of a solar power plant investment. The real option framework is investigated. This framework considers the renewable certificate price and, further, the cost of delay between establishing and operating the solar power plant. The optimal time of launching the project and assessing the value of the deferred option are discussed. The new three-stage numerical methods are constructed, the Lobatto3C-Milstein (L3CM) methods. The numerical methods are integrated with the concept of Black–Scholes option pricing theory and applied in option valuation for solar energy investment with uncertainty. The numerical results of the L3CM, finite difference and Monte Carlo methods are compared to show the efficiency of our methods. Our dataset refers to the Arab Republic of Egypt

Almost Sure Exponential Stability of Numerical Solutions for Stochastic Pantograph Differential Equations with Poisson Jumps

The stability analysis of the numerical solutions of stochastic models has gained great interest, but there is not much research about the stability of stochastic pantograph differential equations. This paper deals with the almost sure exponential stability of numerical solutions for stochastic pantograph differential equations interspersed with the Poisson jumps by using the discrete semimartingale convergence theorem. It is shown that the Euler–Maruyama method can reproduce the almost sure exponential stability under the linear growth condition. It is also shown that the backward Euler method can reproduce the almost sure exponential stability of the exact solution under the polynomial growth condition and the one-sided Lipschitz condition. Additionally, numerical examples are performed to validate our theoretical result

Modified Split-Step Theta Milstein Methods for M-Dimensional Stochastic Differential Equation With Respect To Poisson-Driven Jump

Recently, split-step techniques have been integrated with a Milstein scheme to improve the fundamental analysis of numerical solutions of stochastic differential equations (SDEs). Unfortunately, we note that stability conditions of these methods have restrictions on parameters and step-size to preserve mean-square stability and A-stability of SDEs. We construct new general modified spit-step theta Milstein (MSSTM) methods for using on multi-dimensional SDEs in order to overcome these restrictions. We investigate that the numerical methods are mean-square (MS) stable with no restrictions on parameters for all step-size h \u3e 0 when θ ∈ [1/2, 1] and it is proved that the methods with θ ≥ 1/2 are stochastically A-stable. Furthermore, there is a gap in discussing the split-step Milstein type methods for SDEs with Jump in the literature. Here, we extend the new general methods for SDEs with jump called compensated MSSTM (CMSSTM) methods. The unconditional MS-stability results of CMSSTM methods are proved for SDEs with Poisson-driven jump. Finally, several examples are given to show the effectiveness of the proposed method in approximation of one and two dimensional SDEs compared to some existing methods

Convergence and Almost Sure Polynomial Stability of Partially Truncated Split-Step Theta Method for Stochastic Pantograph Models with Lévy Jumps

This paper addresses a stochastic pantograph model with Lévy leaps where non-jump coefficients exceed linearity. The partially truncated split-step theta method is introduced and applied to the proposed model. The finite time Lϱ^(ϱ^≥2) convergence rate of the numerical scheme is obtained. Furthermore, the almost sure polynomial stability of the numerical scheme is investigated and numerical examples are presented to endorse the addressed theorems

流溪河水库的盔形滔和舌状叶镖水蚤对浮游植物的牧食影响研究

盔形涵Daphnia galeata和舌状叶镖Phyllodiaptomus tunguidus是流溪河水库的两种大型的滤食物性的浮游动物，Ptunguidus也是中国特有种，他们的牧食直接影响浮游植物种类组成和群落结构。为了解这两种浮游动物在自然水体中对浮游植物牧食的作用及营养盐水平对牧食作用的影响，将D．galeata和Ptunguidus以4．4ind．L^-1的密度，分别在两个营养水平（不添加与添加营养盐）中用4．5L的透明塑料瓶培养10天（2008年3月28-4月8日）。在不添加营养盐的实验中，水样为用64um孔径的筛绢过滤后的水库水，在添加营养盐的实验中，为过滤后的水样再加入KH2P04和NaNO3，使TN：TP=16：1（TN=34．86μmol·L^-1，TP=2．18μmol·L^-1）。10天后，计数和分析浮游植物四个粒径级别（〈20μm，20—30μm，30．50μm，〉50μm）和各门类及优势种类的生物量组成，比较两组动物在两种营养状态中对浮游植物生物量的影响。在不添加营养盐的实验中，两种浮游动物对浮游植物总生物量的抑制均不明显，但〈30μm的浮游植物生物量均下降，且D．galeata处理组中，小于20μm的浮游植物生物量低于Ptunguidus处理组，Ptunguidus处理组中20-30μm的浮游植物生物量低于D．galeata组，说明两种浮游动物对〈30Ixm的浮游植物均有抑制作用，但D．galeata对〈20μm的浮游植物抑制强于Ptunguidus而Ptunguidus对20．30μm的浮游植物抑制强于D．galeata。在添加营养盐的实验中，营养盐对浮游植物生物量，尤其对〈20μm的浮游植物生物量的促进作用明显。但两种浮游动物对浮游植物的抑制作用在不同种类之间产生差异。Dgaleataa处理组的浮游植物总生物量明显高于Ptunguidus组，表明Ptunguidus对浮游植物的抑制作用强于Dgaleata。Dgaleata处理组中，蓝藻生物量比例（15％）远低于绿藻（41％）和硅藻（37％），但在Ptunguidus组蓝藻生物量比例（36％）远高于绿藻（18％）和硅藻（32％），与不添加营养盐实验的t检验表明Dgaleata对绿藻和蓝藻抑制明显，而Ptunguidus对绿藻和硅藻的抑制明显（t-test,p〉0．05）。Dgaleata对衣藻chlamydomonassp．，绿球藻chlorococcumsp．，单细胞蓝藻抑制作用明显，而Ptunguidus对小球藻chlorellasp．，衣藻chlamydomonassp．，绿球藻chlorococcumsp．，小环藻cyclotellasp．，曲壳藻achnanthessp．，针杆藻Synedrasp．的抑制明显。实验结果表明两种浮游动物影响不同的浮游植物种类，对浮游植物的群落结构的影响具有差异

Function Spaces with a Random Variable Exponent

The spaces with a random variable exponent ()(×Ω) and ,()(×Ω) are introduced. After discussing the properties of the spaces ()(×Ω) and ,()(×Ω), we give an application of these spaces to the stochastic partial differential equations with random variable growth

Malliavin Derivatives in Spaces with Variable Exponents

Spaces with variable exponents Lpx(H,μ) and Lpx(H,μ;H) are introduced. After discussing some approximation results of Lpx(H,μ), Sobolev spaces on H with variable exponents are introduced. At last, we define Malliavin derivatives in Lpx(H,μ) and discuss some properties of Malliavin derivatives in Lpx(H,μ)