On the representation of an inclined Gaussian beam

In most contemporary optics courses, Gaussian beams are demonstrated in the form of propagation along one coordinate axis. This is referred to as the conventional representation and is in fact a special form. In this paper, we derive the general representation of a Gaussian beam propagating obliquely to the coordinate axis, by performing a coordinate rotation transformation on the conventional representation. When doing so on the beam parameters, a restrictive condition has to be taken into account. Without this condition, the expressions for the beam parameters after the rotation are not consistent with the conventional ones.

Fast Haar Transform Based Feature Extraction for Face Representation and Recognition

Subspace learning is the process of finding a proper feature subspace and then projecting high-dimensional data onto the learned low-dimensional subspace. The projection operation requires many floating-point multiplications and additions, which makes the projection process computationally expensive. To tackle this problem, this paper proposes two simple-but-effective fast subspace learning and image projection methods, fast Haar transform (FHT) based principal component analysis and FHT based spectral regression discriminant analysis. The advantages of these two methods result from employing both the FHT for subspace learning and the integral vector for feature extraction. Experimental results on three face databases demonstrated their effectiveness and efficiency.

Graphical representation and the similarity of DNA primary sequences

In this article, graphical representations of DNA primary sequences were generated. Topological indices and molecular connectivity indices were calculated and used for the comparison of similarities among eight different DNA segments. The satisfactory results were achieved by this analysis.

Theoretical representation of shear and pressure influence on the phase separation behavior of PVME/PS mixture

In the framework of lattice fluid model, the Gibbs energy and equation of state are derived by introducing the energy (E-s) stored during flow for polymer blends under shear. From the calculation of the spinodal of poly(vinyl methyl ether) (PVME) and polystyrene (PS) mixtures, we have found the influence of E., an equation of state in pure component is inappreciable, but it is appreciable in the mixture. However, the effect of E, on phase separation behavior is extremely striking. In the calculation of spinodal for the PVME/PS system, a thin, long and banana miscibility gap generated by shear is seen beside the miscibility gap with lower critical solution temperature. Meanwhile, a binodal coalescence of upper and lower miscibility gaps is occurred. The three points of the three-phase equilibrium are forecasted. The shear rate dependence of cloud point temperature at a certain composition is discussed. The calculated results are acceptable compared with the experiment values obtained by Higgins et at. However, the maximum positive shift and the minimum negative shift of cloud point temperature guessed by Higgins are not obtained, Furthermore, the combining effects of pressure and shear on spinodal shift are predicted.

Estimation of gas hydrate saturation using constrained sparse spike inversion: Case study from the northern South China Sea

Bottom-simulating reflectors (BSRs) were observed beneath the seafloor in the northern continental margin of the South China Sea (SCS). Acoustic impedance profile was derived by Constrained Sparse Spike Inversion (CSSI) method to provide information on rock properties and to estimate gas hydrate or free gas saturations in the sediments where BSRs are present. In general, gas hydrate-bearing sediments have positive impedance anomalies and free gas-bearing sediments have negative impedance anomalies. Based on well log data and Archie's equation, gas hydrate saturation can be estimated. But in regions where well log data is not available, a quantitative estimate of gas hydrate or free gas saturation is inferred by fitting the theoretical acoustic impedance to sediment impedance obtained by CSSI. Our study suggests that gas hydrate saturation in the Taixinan Basin is about 10 - 20% of the pore space, with the highest value of 50%, and free gas saturation below BSR is about 2 - 3% of the pore space, that can rise to 8 - 10% at a topographic high. The free gas is non-continuous and has low content in the southeastern slope of the Dongsha Islands. Moreover, BSR in the northern continental margin of the SCS is related to the presence of free gas. BSR is strong where free gas occurs.

Representation of microscale ocean wavenumber spectrum correct to the second order

In this paper, the analytical representations of four wave source functions in high-frequency spectrum range are given on the basis of ocean wave theory and dimensional analysis, and the perturbation method is used to solve the governing equations of ocean wave high-frequency spectrum on the basis of the temporally stationary and locally homogeneous scale relations of microscale wave. The microscale ocean wavenumber spectrum correct to the second order has an explicit structure, its first order part represents the equilibrium between different source functions, and its second order part represents the contribution of microscale wave propagation.

基于信息重建技术的地震信号处理方法研究

The dissertation addressed the problems of signals reconstruction and data restoration in seismic data processing, which takes the representation methods of signal as the main clue, and take the seismic information reconstruction (signals separation and trace interpolation) as the core. On the natural bases signal representation, I present the ICA fundamentals, algorithms and its original applications to nature earth quake signals separation and survey seismic signals separation. On determinative bases signal representation, the paper proposed seismic dada reconstruction least square inversion regularization methods, sparseness constraints, pre-conditioned conjugate gradient methods, and their applications to seismic de-convolution, Radon transformation, et. al. The core contents are about de-alias uneven seismic data reconstruction algorithm and its application to seismic interpolation. Although the dissertation discussed two cases of signal representation, they can be integrated into one frame, because they both deal with the signals or information restoration, the former reconstructing original signals from mixed signals, the later reconstructing whole data from sparse or irregular data. The goal of them is same to provide pre-processing methods and post-processing method for seismic pre-stack depth migration. ICA can separate the original signals from mixed signals by them, or abstract the basic structure from analyzed data. I surveyed the fundamental, algorithms and applications of ICA. Compared with KL transformation, I proposed the independent components transformation concept (ICT). On basis of the ne-entropy measurement of independence, I implemented the FastICA and improved it by covariance matrix. By analyzing the characteristics of the seismic signals, I introduced ICA into seismic signal processing firstly in Geophysical community, and implemented the noise separation from seismic signal. Synthetic and real data examples show the usability of ICA to seismic signal processing and initial effects are achieved. The application of ICA to separation quake conversion wave from multiple in sedimentary area is made, which demonstrates good effects, so more reasonable interpretation of underground un-continuity is got. The results show the perspective of application of ICA to Geophysical signal processing. By virtue of the relationship between ICA and Blind Deconvolution , I surveyed the seismic blind deconvolution, and discussed the perspective of applying ICA to seismic blind deconvolution with two possible solutions. The relationship of PC A, ICA and wavelet transform is claimed. It is proved that reconstruction of wavelet prototype functions is Lie group representation. By the way, over-sampled wavelet transform is proposed to enhance the seismic data resolution, which is validated by numerical examples. The key of pre-stack depth migration is the regularization of pre-stack seismic data. As a main procedure, seismic interpolation and missing data reconstruction are necessary. Firstly, I review the seismic imaging methods in order to argue the critical effect of regularization. By review of the seismic interpolation algorithms, I acclaim that de-alias uneven data reconstruction is still a challenge. The fundamental of seismic reconstruction is discussed firstly. Then sparseness constraint on least square inversion and preconditioned conjugate gradient solver are studied and implemented. Choosing constraint item with Cauchy distribution, I programmed PCG algorithm and implement sparse seismic deconvolution, high resolution Radon Transformation by PCG, which is prepared for seismic data reconstruction. About seismic interpolation, dealias even data interpolation and uneven data reconstruction are very good respectively, however they can not be combined each other. In this paper, a novel Fourier transform based method and a algorithm have been proposed, which could reconstruct both uneven and alias seismic data. I formulated band-limited data reconstruction as minimum norm least squares inversion problem where an adaptive DFT-weighted norm regularization term is used. The inverse problem is solved by pre-conditional conjugate gradient method, which makes the solutions stable and convergent quickly. Based on the assumption that seismic data are consisted of finite linear events, from sampling theorem, alias events can be attenuated via LS weight predicted linearly from low frequency. Three application issues are discussed on even gap trace interpolation, uneven gap filling, high frequency trace reconstruction from low frequency data trace constrained by few high frequency traces. Both synthetic and real data numerical examples show the proposed method is valid, efficient and applicable. The research is valuable to seismic data regularization and cross well seismic. To meet 3D shot profile depth migration request for data, schemes must be taken to make the data even and fitting the velocity dataset. The methods of this paper are used to interpolate and extrapolate the shot gathers instead of simply embedding zero traces. So, the aperture of migration is enlarged and the migration effect is improved. The results show the effectiveness and the practicability.

中国北方典型生态区表土孢粉组合特征及其与现代植被和气候的关系

Surface pollen assemblages and their relationhips with the modern vegetation and climate provide a foundation for investigating palaeo-environment conditions by fossil pollen analysis. A promising trend of palynology is to link pollen data more closely with ecology. In this study, I summarized the characteristics of surface pollen assemblages and their quantitative relation with the vegetation and climate of the typical ecological regions in northern China, based on surface pollen analysis of 205 sites and investigating of modern vegetation and climate. The primary conclusions are as follows:The differences in surface pollen assemblages for different vegetation regions are obvious. In the forest communities, the arboreal pollen percentages are more than 30%, herbs less than 50% and shrubs less than 10%; total pollen concentrations are more than 106 grains/g. In the steppe communities, arboreal pollen percentages are generally less than 5%; herb pollen percentages are more than 90%, and Artemisia and Chenopodiaceae are dominant in the pollen assemblages; total pollen concentrations range from 103 to 106 grains/g. In the desert communities, arboreal pollen percentages are less than 5%. Although Chenopodiaceae and Artemisia still dominate the pollen assemblages, Ephedra, Tamaricaceae and Nitraria are also significant important in the pollen assemblages; total pollen concentrations are mostly less than 104grains/g. In the sub-alpine or high and cold meadow communities, arboreal pollen percentages are less than 30%. and Cyperaceae is one of the most significant-taxa in the pollen assemblages. In the shrub communities, the pollen assemblages are consistent with the zonal vegetation; shrub pollen percentages are mostly less than 20%, except for Artemisia and Hippophae rhamnoides communities.There are obvious trends for the pollen percentage ratios of Artemisia to Chenopodiaceae (A/C), Pinus to Artemisia (P/A) and arbor to non-arbor (AP/NAP) in the different ecological regions. In the temperate deciduous broad-leaved forest region, the P/A ratios are generally higher than 0.1, the A/C ratios higher than 2 and the AP/NAP ratios higher than 0.3. In the temperate steppe regions, the P/A ratios are generally less than 0.1, the A/C ratios higher than 1 and the AP/NAP ratios less than 0.1. In the temperate desert regions, the P/A ratios are generally less than 0.1, the A/C ratios less than 1, and the AP/NAP ratios less than 0.1.The study on the representation and indication of pollen to vegetation shows that Pinus, Artemisia, Betula, Chenopodiaceae, Ephedra, Selaginella sinensis etc. are over-representative in the pollen assemblages and can only indicate the regional vegetation. Some pollen types, such as Quercus, Carpinus, Picea, Abies, Elaeagus, Larix, Salix, Pterocelis, Juglans, Ulmus, Gleditsia, Cotinus, Oleaceae, Spiraea, Corylus, Ostryopsis, Vites, Tetraena, Caragana, Tamaricaceae, Zygophyllum, Nitraria, Cyperaceae, Sanguisorba etc. are under-representative in the pollen assemblages, and can indicate the plant communities well. Populus, Rosaceae, Saxifranaceae, Gramineae, Leguminosae, Compositae, Caprifoliaceae etc. can not be used as significant indicators to the plants.The study on the relation of pollen percentages with plant covers shows that Pinus pollen percentages are more than 30% where pine trees exist in the surrounding region. The Picea+Abies pollen percentages are higher than 20% where the Picea+Abies trees are dominant in the communities, but less than 5% where the parent plants are sparse or absent. Larix pollen percentages vary from 5% to 20% where the Larix trees are dominant in the communities, but less than 5% where the parent plants are sparse or absent. Betula pollen percentages are higher than 40% where the Betula trees are dominant in the communities" but less than 5% where the parent plants are sparse or absent. Quercus pollen percentages are higher than 10% where the Quercus trees are dominant in the communities, but less than 1% where the parent plants sparse or absent. Carpinus pollen percentages vary from 5% to 15% where the Carpinus trees are dominant in the communities, but less than 1% where the parent plants are sparse or absent. Populus pollen percentages are about 0-5% at pure Populus communities, but cannot be recorded easily where the Populus plants mixed with other trees in the communities. Juglans pollen accounts for 25% to 35% in the forest of Juglans mandshurica, but less than 1% where the parent plants are sparse or absent. Pterocelis pollen percentages are less than 15% where the Pterocelis trees are dominant in the communities, but cannot be recorded easily where the parent plants are sparse or absent. Ulmus pollen percentages are more than 8% at Ulmus communities, but less than 1% where the Ulmus plants mixed with other trees in the communities. Vitex pollen percentages increase along with increasing of parent plant covers, but the maximum values are less than 10 %. Caragana pollen percentages are less than 20 % where the Caragana plant are dominant in the communities, and cannot be recorded easily where the parent plants are sparse or absent. Spiraea pollen percentages are less than 16 % where the Spiraea plant are dominant in the communities, and cannot be recorded easily where the parent plants are sparse or absent.The study on the relation of surface pollen assemblages with the modern climate shows that, in the axis 1 of DCA, surface samples scores have significant correlation with the average annual precipitations, and the highest determination coefficient (R2) is 0.8 for the fitting result of the third degree polynomial functions. In the axis 2 of DCA, the samples scores have significant correlation with the average annual temperatures, average July temperatures and average January temperatures, and the determination coefficient falls in 0.13-0.29 for the fitting result of the third degree polynomial functions with the highest determination coefficient for the average July temperature.The sensitivity of the different pollen taxa to climate change shows that some pollen taxa such as Pinus, Quercus, Carpinus, Juglans, Spiraea, Oleaceae, Gramineae, Tamariaceae and Ephedra are only sensitive to the change in precipitation.