Stochastic Averaging Principle for Dynamical Systems with Fractional Brownian Motion

Stochastic averaging for a class of stochastic differential equations (SDEs) with fractional Brownian motion, of the Hurst parameter H in the interval (1/2, 1), is investigated. An averaged SDE for the original SDE is proposed, and their solutions are quantitatively compared. It is shown that the solution of the averaged SDE converges to that of the original SDE in the sense of mean square and also in probability. It is further demonstrated that a similar averaging principle holds for SDEs under stochastic integral of pathwise backward and forward types. Two examples are presented and numerical simulations are carried out to illustrate the averaging principle

Quantum correlation and classical correlation dynamics in the spin-boson model

We study the quantum correlation and classical correlation dynamics in a spin-boson model. For two different forms of spectral density, we obtain analytical results and show that the evolutions of both correlations depend closely on the form of the initial state. At the end of evolution, all correlations initially stored in the spin system transfer to reservoirs. It is found that for a large family of initial states, quantum correlation remains equal to the classical correlation during the course of evolution. In addition, there is no increase in the correlations during the course of evolution.Comment: 10 pages, 5 figure

Research Progress on Extraction Technology and Pharmacological Functions of Perilla Oil

Perilla (Perilla frutescens (L.) Britt.) is one of the traditional medicinal and edible plants in China.Perilla oil, extracted from the seed of perilla, contains the highest concentration of alpha-linolenic acid. It has huge market development potential in food, medicine and many other industries. With the continuous advancement and development of the big health industry, perilla oil byproducts have played an increasing role our lives. This paper comprehensively and systematically reviews the extraction process, chemical composition, pharmacological effects, development and application of perilla oil, to guide applications of perilla oil

Tuberostemoamide hemihydrate

In the crystal structure of the title compound {systematic name: (1′S,2R,2′R,3′S,6′R)-3′-ethyl-4-methyl-5H-5′-oxa-10′-aza­spiro­[furan-2,4′-tricyclo­[8.3.0.02,6]trideca­ne]-5,11′-dione hemihydrate}, C17H23NO4·0.5H2O, the asymmetric unit contains two mol­ecules of tuberostemoamide with similar conformations and one water mol­ecule. The tuberostemoamide mol­ecule is composed of one seven-membered ring (A) and three five-membered rings (B, C and D). Ring A exists in a chair conformation, both rings B and C exist in envelope conformations, and ring D is almost planar with a mean deviation of 0.0143 (4) Å in one molecule and 0.0095 (3) Å in the other.. The dihedral angles between the planes of rings C and D are 75.1 (3)° in one mol­ecule and 74.5 (3)° for the other. The solvent water mol­ecule links the tuberostemoamide mol­ecules through O—H⋯O(ketone) hydrogen bonds. Weak C—H⋯O inter­actions are also present, involving both the water mol­ecule and a heterocyclic ether O-atom acceptor