ISSDE: A Monte Carlo implicit simulation code based on Stratonovich SDE approach of Coulomb collision

A Monte Carlo implicit simulation program, Implicit Stratonovich Stochastic Differential Equations(ISSDE), is developed for solving stochastic differential equations(SDEs) that describe plasmas with Coulomb collision. The basic idea of the program is the stochastic equivalence between the Fokker–Planck equation and the Stratonovich SDEs. The splitting method is used to increase the numerical stability of the algorithm for dynamics of charged particles with Coulomb collision. The cases of Lorentzian plasma, Maxwellian plasma and arbitrary distribution function of background plasma have been considered. The adoption of the implicit midpoint method guarantees exactly the energy conservation for the diffusion term and thus improves the numerical stability compared with conventional Runge–Kutta methods. ISSDE is built with C++ and has standard interfaces and extensible modules. The slowing down processes of electron beams in unmagnetized plasma and relaxation process in magnetized plasma are studied using the ISSDE, which shows its correctness and reliability.     

Regularity of Nash payoffs of Markovian nonzero-sum stochastic differential games

In this paper we deal with the problem of existence of a smooth solution of the Hamilton–Jacobi–Bellman–Isaacs (HJBI for short) system of equations associated with nonzero-sum stochastic differential games. We consider the problem in unbounded domains either in the case of continuous generators or for discontinuous ones. In each case we show the existence of a smooth solution of the system. As a consequence, we show that the game has smooth Nash payoffs which are given by means of the solution of the HJBI system and the stochastic process which governs the dynamic of the controlled system.     

冠心苏合丸中挥发性组分的分析及主成分冰片的测定

采用同时蒸馏-萃取法提取冠心苏合丸中的挥发性组分,测得两种冠心苏合丸中的挥发性组分含量分别为14％和9．8％。利用GC-MS方法对两种冠心苏合丸所得的挥发性组分进行分析,通过检索NIST98谱图库,并结合标准谱图库和有关文献,从冠心苏合丸的挥发性组分中分别确定出14、19种化学成分,分别占挥发性组分总检出量的97．24％和98．76％。用峰面积归一化法,得出各化学成分在挥发性组分中的相对百分含量。主要挥发性组分是冰片。并采用气相色谱法对冠心苏合丸中冰片的含量进行了测定冰片质量浓度在1．0～5、0mg／mL范围内成良好的线性关系,冰片的平均回收率为98％～106％。     

Stochastic Komatu–Loewner evolutions and BMD domain constant

For Komatu–Loewner equation on a standard slit domain, we randomize the Jordan arc in a manner similar to that of Schramm (2000) to find the SDEs satisfied by the induced motion $\xi \left(t\right)$ on $?\mathbb{H}$ and the slit motion $\mathbf{s}\left(t\right)$. The diffusion coefficient $\alpha$ and drift coefficient $b$ of such SDEs are homogeneous functions.Next with solutions of such SDEs, we study the corresponding stochastic Komatu–Loewner evolution, denoted as ${\mathrm{SKLE}}_{\alpha ,b}$. We introduce a function $b_{\mathrm{BMD}}$ measuring the discrepancy of a standard slit domain from $\mathbb{H}$ relative to BMD. We show that ${\mathrm{SKLE}}_{\sqrt{6},?b_{\mathrm{BMD}}}$ enjoys a locality property.     

Analysis of terpenoic composition of conifer needle oils by steam distillation/extraction,gas chromatography and gas chromatography-mass spectrometry

Summary The essential oils of Estonian spruce and pine needles have been analysed by a combination of steam distillation/extraction, GC and GC-MS. According to their monoterpene composition Estonian pines belong to a high carene chemotype with monoterpenes representing up to 85% of total oil. Estonian spruce needle oil contains up to 70% of oxygenated terpenes and more limonene and 1,8-cineole than the same spruce species [Picea abies (L.) Karst.] from other localities.A total of 60 components were identified. Coefficients of variation describe the range of component contents in individual trees within the population.     

Regularity of strong solutions of one-dimensional SDE’s with discontinuous and unbounded drift

In this paper we develop a method for constructing strong solutions of one-dimensional Stochastic Differential Equations where the drift may be discontinuous and unbounded. The driving noise is the Brownian Motion and we show that the solution is Sobolev-differentiable in the initial condition and Malliavin differentiable. This method is not based on a pathwise uniqueness argument. We will apply these results to the stochastic transport equation. More specifically, we obtain a continuously differentiable solution of the stochastic transport equation when the driving function is a step function.     

Backward stochastic differential equations associated with the vorticity equations

In this paper we derive a non-linear version of the Feynman–Kac formula for the solutions of the vorticity equation in dimension 2 with space periodic boundary conditions. We prove the existence (global in time) and uniqueness for a stochastic terminal value problem associated with the vorticity equation in dimension 2. A particular class of terminal values provide, via these probabilistic methods, solutions for the vorticity equation.     

Characterization of the volatile fraction emitted by Pinus spp. by one- and two-dimensional chromatographic techniques with mass spectrometric detection

The chemical composition of the needles of P. pinea, P. pinaster, P. halepensis, P. nigra, P. brutia, P. patula, P. radiata, P. taeda, P. elliotti, P. kesiya, P. sylvestris and P. eldarica was investigated. Headspace solid-phase microextraction and steam distillation extraction were used to collect the volatile fractions. Samples were analyzed using one-dimensional gas chromatography (1D-GC) and comprehensive two-dimensional gas chromatography (GC × GC) associated with a quadrupole and a time-of-flight mass detectors. Results showed that the analytical capabilities of 1D-GC are partially limited by the separation power of the columns. The higher sensibility and the absence of peak skewing of the time-of-flight mass analyzer, with the use of automated peak finding and deconvolution algorithms, allowed for the detection of trace components with qualitative full spectra and the extraction of true mass spectra from coeluting compounds, promoting their reliable identification and thus significantly improving results obtained by 1D-GC/MS, when using a quadrupole mass analyzer. The use of GC × GC resulted in enhanced separation efficiency and increased signal to noise ratio (sensitivity) of the analytes, maximizing mass spectra quality and improving compound detection and identification. This work shows the use of 1D-GC/ToFMS for the analysis of pine needles volatiles, achieving the detection of 177 compounds, that is more than twice the number previously identified by standard 1D-GC/MS. The analysis by GC × GC for the same sample allowed the detection of 212 compounds. The enantioselective GC × GC analysis performed for all the Pinus spp. under study achieved the detection of 422 different compounds. Cross-over phenomena according to operational conditions are highlighted and discussed.