Peripheries of molecular projection in three-dimensional space and studies of quantitative structure-activity relationships

A new index, i.e., the periphery representation of the projection of a molecule from 3D space to a 2D plane is described. The results, correlation with toxicity of substituted nitrobenzenes, obtained by using periphery descriptors are much better than that obtained by using the areas (i.e., shadows) of projections of the compounds. Even better results were achieved by using the combination of periphery descriptors and the projections areas as well as the indicated variable K reflecting the action of group NO position on the benzene ring.

波前重建法射线追踪及走时表压缩

As a fast and effective method for approximate calculation of seismic numerical simulation, ray tracing method, which has important theory and practical application value, in terms of seismic theory and seismic simulation, inversion, migration, imaging, simplified from seismic theory according to geometric seismic, means that the main energy of seismic wave field propagates along ray paths in condition of high-frequency asymptotic approximation. Calculation of ray paths and traveltimes is one of key steps in seismic simulation, inversion, migration, and imaging. Integrated triangular grids layout on wavefront with wavefront reconstruction ray tracing method, the thesis puts forward wavefront reconstruction ray tracing method based on triangular grids layout on wavefront, achieves accurate and fast calculation of ray paths and traveltimes. This method has stable and reasonable ray distribution, and overcomes problems caused by shadows in conventional ray tracing methods. The application of triangular grids layout on wavefront, keeps all the triangular grids stable, and makes the division of grids and interpolation of a new ray convenient. This technology reduces grids and memory, and then improves calculation efficiency. It enhances calculation accuracy by accurate and effective description and division on wavefront. Ray tracing traveltime table, which shares the character of 2-D or 3-D scatter data, has great amount of data points in process of seismic simulation, inversion, migration, and imaging. Therefore the traveltime table file will be frequently read, and the calculation efficiency is very low. Due to these reasons, reasonable traveltime table compression will be very necessary. This thesis proposes surface fitting and scattered data compression with B-spline function method, applies to 2-D and 3-D traveltime table compression. In order to compress 2-D (3-D) traveltime table, first we need construct a smallest rectangular (cuboidal) region with regular grids to cover all the traveltime data points, through the coordinate range of them in 2-D surface (3-D space). Then the value of finite regular grids, which are stored in memory, can be calculated using least square method. The traveltime table can be decompressed when necessary, according to liner interpolation method of 2-D (3-D) B-spline function. In the above calculation, the coefficient matrix is stored using sparse method and the liner system equations are solved using LU decomposition based on the multi-frontal method according to the sparse character of the least square method matrix. This method is practiced successfully in several models, and the cubic B-spline function can be the best basal function for surface fitting. It make the construction surface smooth, has stable and effective compression with high approximate accuracy using regular grids. In this way, through constructing reasonable regular grids to insure the calculation efficiency and accuracy of compression and surface fitting, we achieved the aim of traveltime table compression. This greatly improves calculation efficiency in process of seismic simulation, inversion, migration, and imaging.

高斯束射线追踪

Using the approximate high-frequency asymptotic methods to solve the scalar wave equation, we can get the eikonal equation and transport equation. Solving the eikonal equation by the method of characteristics provides a mathematical derivation of ray tracing equations. So, the ray tracing system is folly based on the approximate high-frequency asymptotic methods. If the eikonal is complex, more strictly, the eikonal is real value at the rays and complex outside rays, we can derive the Gaussian beam. This article mainly concentrates on the theory of Gaussian beam. To classical ray tracing theory, the Gaussina beam method (GBM) has many advantages. First, rays are no longer required to stop at the exact position of the receivers; thus time-consuming two-point ray tracing can be avoided. Second, the GBM yields stable results in regions of the wavefield where the standard ray theory fails (e.g., caustics, shadows zones and critical distance). Third, unlike seismograms computed by conventional ray tracing techniques, the GBM synthetic data are less influenced by minor details in the model representation. Here, I realize kinematical and dynamical system, and based on this, realize the GBM. Also, I give some mathematical examples. From these examples, we can find the importance and feasibility of the ray tracing system. Besides, I've studied about the reflection coefficient of inhomogeneous S-electromagnetic wave at the interface of conductive media. Basing on the difference of directions of phase shift constant and attenuation constant when the electromagnetic wave propagates in conductive medium, and using the boundary conditions of electromagnetic wave at the interface of conductive media, we derive the reflection coefficient of inhomogeneous S-electromagnetic wave, and draw the curves of it. The curves show that the quasi total reflection will occur when the electromagnetic wave incident from the medium with greater conductivity to the medium with smaller conductivity. There are two peak, values at the points of the critical angles of phase shift constant and attenuation constant, and the reflection coefficient is smaller than 1. This conclusion is different from that of total reflection light obviously.