Tail asymptotics of supremum of certain Gaussian processes over threshold dependent random intervals

Let {X(t),t ≥ 0} be a centered Gaussian process and let γ be a non-negative constant. In this paper we study the asymptotics of \(\mathbb {P} \left \{\underset {t\in [0,\mathcal {T}/u^{\gamma }]}\sup X(t)>u\right \}\) as \(u\rightarrow \infty \) , with \(\mathcal {T}\) an independent of X non-negative random variable. As an application, we derive the asymptotics of finite-time ruin probability of time-changed fractional Brownian motion risk processes.     

The defocusing energy-supercritical Hartree equation

In this paper,we study the global well-posedness and scattering problem for the energysupercritical Hartree equation iut+Δu.(|x|.γ.|u|2)u=0 with γ4 in dimension d γ.We prove that if the solution u is apriorily bounded in the critical Sobolev space,that is,u ∈Lt∞(I;Hxsc(Rd)) with sc:= γ/2.11,then u is global and scatters.The impetus to consider this problem stems from a series of recent works for the energy-supercritical nonlinear wave equation(NLW) and nonlinear Schrdinger equation(NLS).We utilize the strategy derived from concentration compactness ideas to show that the proof of the global well-posedness and scattering is reduced to disprove the existence of three scenarios:finite time blowup;soliton-like solution and low to high frequency cascade.Making use of the No-waste Duhamel formula,we deduce that the energy of the finite time blow-up solution is zero and so get a contradiction.Finally,we adopt the double Duhamel trick,the interaction Morawetz estimate and interpolation to kill the last two scenarios.     

Unrelated parallel-machine scheduling with deteriorating maintenance activities to minimize the total completion time

Wang et al. (J Operat Res Soc 62: 1898–1902, 2011) studied the m identical parallel-machine and unrelated parallel-machine scheduling with a deteriorating maintenance activity to minimize the total completion time. They showed that each problem can be solved in O(n ^2m+3) time, where n is the number of jobs. In this note, we discuss the unrelated parallel-machine setting and show that the problem can be optimally solved by a lower order algorithm.     

Effective semi-analytic integration for hypersingular Galerkin boundary integral equations for the Helmholtz equation in 3D

We deal with the Galerkin discretization of the boundary integral equations corresponding to problems with the Helmholtz equation in 3D. Our main result is the semi-analytic integration for the bilinear form induced by the hypersingular operator. Such computations have already been proposed for the bilinear forms induced by the single-layer and the double-layer potential operators in the monograph The Fast Solution of Boundary Integral Equations by O. Steinbach and S. Rjasanow and we base our computations on these results.     

Estimation of relative risk using a log-binomial model with constraints

The relative risk/prevalence ratio and odds ratio are very popular in medical research and epidemiological studies. The odds ratio is overused in practice due to its direct relation with the logistic regression. Interpreting the odds ratio in terms of “relative risk” may lead to incorrect inference on the prevalence of certain event. In this paper, we propose to estimate the relative risk using the log-binomial model by maximizing the likelihood with a linear constraint, which can be easily implemented by an existing function, such as “constrOptim” in R. Furthermore, we review other existing methods and compare their performance under a variety of settings using simulated data. We suggest the proposed and COPY methods in practice, based on its performance in the simulations. For illustration, we investigate the vigorous physical activity effects on obesity using data from the National Health and Nutrition Examination Survey, and the treatment effects on lung cancer mortality using data in R.     

利用有限域上的向量空间构作带仲裁的认证码

This paper is devoted to constructing an authentication code with arbitration using subspaces of vector spaces over finite fields.Moreover,if we choose the encoding rules of the transmitter and the decoding rules of the receiver according to a uniform probability distribution,then some parameters and the probabilities of successful attacks are computed.     

管线钢管局部屈曲应变分析与计算

针对基于应变的管线设计所使用的管线钢管进行变形能力评价,为基于应变设计地区用的钢管产品标准的指标制订提供技术基础。本文以精确建模的数值仿真计算作为钢管全尺寸弯曲变形试验的有效补充,对钢管进行了屈曲变形行为的研究;针对钢管产品试制中不同的材料性能进行了仿真计算,最终提出:两个与钢管临界屈曲应变相关的应力比指标Rt5.0/Rt1.0和Rt2.0/Rt1.0分别为1.04和1.08。该研究结果为基于应变设计地区使用的钢管标准的制订提供了技术支持。     

Hydrazone-based hydrogel hydrolytically degradable in acidic environment

We describe the synthesis of new crosslinker N′-{3-[2-(4-{2-[3-(methacryloylamino)propanoyl]hydrazono}cyclohexyliden)hydrazino]-3-oxopropyl}-2-methylacrylamide, which is stable at physiological pH, but is hydrolytically cleaved in acidic pH. Study of acid hydrolysis showed that the crosslinker is hydrolyzed into two N′-(3-hydrazino-3-oxopropyl)-2-methylacrylamide molecules and one 1,4-cyclohexanedione molecule. Hydrogels based on poly[N-(2-hydroxypropyl)methacrylamide] crosslinked with this crosslinker were prepared and their degradation rate was studied as a function of pH (in the range of pH 1.5-7.4). The hydrogel is cleaved within 8-27 days at pH between 1.5 and 6 and is stable at pH 7.4 making it promising for the construction of oesophageal stents.     

An efficient and convenient method for preparation of disulfides from thiols using air as oxidant catalyzed by Co-Salophen

Disulfides have been synthesized by oxidation of thiols using air as oxidant catalyzed by Co-Salophen with high yields,mild and neutral conditions,and easy procedures of the catalyst.The products were confirmed by ~1H NMR and IR.     

Miscible blends of nitro‐substituted polybenzimidazole and polyetherimide

A novel blend system was prepared by blending organosoluble nitro‐substituted polybenzimidazole (NO₂‐PBI) and polyetherimide (PEI) in a cosolvent at a moderate condition. It was shown that the NO₂‐PBI/PEI blends not only possess tractable processability owing to the enhanced solubility of NO₂‐PBI but also retain the desirable features of unmodified PBI/PEI blends. Apparent miscibility in the blends was observed and attributed to hydrogen‐bonding interactions between N? H groups in NO₂‐PBI and carbonyl groups in PEI. It was revealed that the NO₂‐PBI/PEI blends phase‐separate upon heating above the glass‐transition temperatures. The observed mixing of NO₂‐PBI and PEI in a molecular level, although sustainable only in the glassy region, was shown to lend synergy effects to the physical properties of the blends. © 2001 John Wiley & Sons, Inc. J Polym Sci Part B: Polym Phys 39: 1778–1783, 2001