The Exit Problem from a Neighborhood of the Global Attractor for Dynamical Systems Perturbed by Heavy-Tailed Lévy Processes

The concept of filtered counting process is used to model several stochastic problems in manufacturing systems. Through a judicious selection of an appropriate response function, several system characteristics are evaluated under distribution-free condition. Applications include a machine shop problem, a machine sequencing problem, a flexible manufacturing problem, a job sequencing problem, a maintenance problem and an inventory problem. The methodology provides a unique, original and simple way to solve a large array of problems     

On weak uniqueness and distributional properties of a solution to an SDE with α-stable noise

For an SDE driven by a rotationally invariant $\alpha$-stable noise we prove weak uniqueness of the solution under the balance condition $\alpha +\gamma >1$, where $\gamma$ denotes the Hölder index of the drift coefficient. We prove the existence and continuity of the transition probability density of the corresponding Markov process and give a representation of this density with an explicitly given “principal part”, and a “residual part” which possesses an upper bound. Similar representation is also provided for the derivative of the transition probability density w.r.t. the time variable.     

Analysis of volatile compounds of wild gilthead sea bream (Sparus aurata) by simultaneous distillation–extraction (SDE) and GC–MS

The volatile compounds of wild gilthead sea bream (Sparus aurata) were analyzed by sensory and instrumental analyses. Simultaneous distillation and extraction (SDE) with dichloromethane were used for extraction of volatile components. According to sensory analysis, the aromatic extract obtained by SDE was representative of sea bream odour. A total of 46 compounds were identified and quantified in sea bream. Aldehydes and alcohols were the most dominant volatiles in sea bream, as they accounted for the largest proportion. Hexanal, heptanal, nonanal, (Z)-4-heptenal, octanal, (E)-2-nonenal, decanal, benzenacetaldehyde, (E,E)-2,4-decadienal, 1-octen-3-ol and (E)-1,5-octadien-3-ol were potent aroma compounds on the basis of odour activity values (OAVs). Within these, decanal (OAV: 1110) and (E)-2-nonenal (OAV: 447.5) were the most powerful contributors to the aroma of the sea bream.     

On a type of stochastic differential equations driven by countably many Brownian motions

Consider the one-dimensional SDE , where Wⁱ is an infinite sequence of independent standard Brownian motions, i=1,2,3,…. We prove two theorems on the existence and uniqueness of solutions with non-Lipschitz coefficients, and give a non-contact property and a strong comparison theorem for solutions.     

Recommended Tests for the Self-Disproportionation of Enantiomers (SDE) to Ensure Accurate Reporting of the Stereochemical Outcome of Enantioselective Reactions

The purpose of this review is to highlight the necessity of conducting tests to gauge the magnitude of the self-disproportionation of enantiomers (SDE) phenomenon to ensure the veracity of reported enantiomeric excess (ee) values for scalemic samples obtained from enantioselective reactions, natural products isolation, etc. The SDE always occurs to some degree whenever any scalemic sample is subjected to physicochemical processes concomitant with the fractionation of the sample, thus leading to erroneous reporting of the true ee of the sample if due care is not taken to either preclude the effects of the SDE by measurement of the ee prior to the application of physicochemical processes, suppressing the SDE, or evaluating all obtained fractions of the sample. Or even avoiding fractionation altogether if possible. There is a clear necessity to conduct tests to assess the magnitude of the SDE for the processes applied to samples and the updated and improved recommendations described herein cover chromatography and processes involving gas-phase transformations such as evaporation or sublimation.     

香樟树叶挥发油的化学成分研究

用同时蒸馏萃取法(SDE)和气相色谱-质谱连用技术(GC-MS)对香樟树叶挥发油成分进行了分离分析,共鉴定出98种化合物。其中主要成分为樟脑与β-芳樟醇(24.099%)、桉油醇(15.723%)、α-松油醇(11.204%)、石竹烯(4.957%)、蛇床-6-烯-4-醇(5.724%)、β-水芹烯(3.394%)等。     

香格里拉产小叶杜鹃花挥发性成分的GC-MS分析

研讨香格里拉县小叶杜鹃花的挥发油化学成分,为进一步合理开发利用其药用资源提供试验依据。利用水蒸汽同时蒸馏萃取法(SDE)提取小叶杜鹃花的挥发性化学成分,通过气相色谱-质谱联用技术(GC-MS)对各个色谱峰定性,并采用色谱峰面积归一法获得各个化合物的相对含量。从小叶杜鹃花挥发油中共分离鉴定了73个色谱峰,占挥发油总量的85.53%。小叶杜鹃花挥发油主要成分有α-蒎烯(14.00%)、正二十三烷(9.51%)、7-甲氧基-2,2-二甲基-3-色烯(6.26%)、正二十烷(6.11%)、苯乙醇(5.10%)、1-Heneicosyl formate(4.60%)等。     

QUASI-SURE CONVERGENCE RATE OF EULER SCHEME FOR STOCHASTIC DIFFERENTIAL EQUATIONS

Let Xt(x) be the solution of stochastic dierential equations with smooth and bounded derivatives coeffcients. Let Xnt(x) be the Euler discretization scheme of SDEs with step 2-n. In this note, we prove that for any R 0 and γ∈(0, 1/2), supt∈[0,1],|x|≤R |Xnt(x, ω)- Xt(x, ω)|≤ξR,γ(ω)2-nγ, n≥1, q.e., where ξR,γ(ω) is quasi-everywhere finite.