高阶行列式的计算方法与技巧

行列式是数学中重要的计算工具之一,而高阶行列式的计算,其基本方法和技巧是"化零"和"降阶",本文主要对一些院校历年典型考研题的特征进行分析,说明其求解方法与技巧。

BLIND PARAFAC SIGNAL DETECTION FOR UNIFORM CIRCULAR ARRAY WITH POLARIZATION SENSITIVE ANTENNAS

The received signal of the polarization sensitive array is proved to have trilinear model characteristics. The blind parallel factor（PARAFAC） signal detection algorithm for the polarization sensitive array is proposed. The trilinear alternating least square （TALS） algorithm is used to abtain the source matrix, and then the matrix is judged. Simulation results show that the bit error rate （BER） of the detection algorithm is close to that of the non-blind decorrelating method and the algorithm works well under the array error condition. BER difference between the non-blind method and this algorithm is less than 2 dB under a high SNR. The algorithm is blind and robust. The channel fading, the direction of arrive（DOA） imformation and the polarization information are needless in the algorithm.

Determination of Melamine by Infrared Spectroscopy Based on Nonlinear Modeling

[Objective] The aim was to develop a nonlinear model of quantitative analysis of melamine content by infrared spectroscopy and provide theoretical basis for the nondestructive detection of melamine. [Method] According to dynamics,mathematical modeling and optimization theory,linear and nonlinear models were respectively set up by taking an absorption peak of 1 550 cm-1 as characteristic absorption peak. [Result] The correlation coefficient of nonlinear model was 0.922 7 and the recovery was 96%,which showed that the nonlinear model was more accurate than linearity model with correlation coefficient of 0.904 9 and recovery of 557%. [Conclusion] It is feasible to determine melamine content by using the nonlinear model quantitatively.

Applications of Lodrigues Matrix in 3D Coordinate Transformation

Three transformation models （Bursa-Wolf, Molodensky, and WTUSM） are generally used between two data systems transformation. The linear models are used when the rotation angles are small; however, when the rotation angles get bigger, model errors will be produced. In this paper, we present a method with three main terms：① the traditional rotation angles θ,φ,ψ are substituted with a,b,c which are three respective values in the anti-symmetrical or Lodrigues matrix; ② directly and accurately calculating the formula of seven parameters in any value of rotation angles; and ③ a corresponding adjustment model is established. This method does not use the triangle function. Instead it uses addition, subtraction, multiplication and division, and the complexity of the equation is reduced, making the calculation easy and quick.

Single Camera 3-D Coordinate Measuring System Based on Optical Probe Imaging

A new vision coordinate measuring system--single camera 3 D coordinate measuring system based on optical probe imaging is presented. A new idea in vision coordinate measurement is proposed. A linear model is deduced which can distinguish six freedom degrees of optical probe to realize coordinate measurement of the object surface. The effects of some factors on the resolution of the system are analyzed. The simulating experiments have shown that the system model is available.

Three-Dimensional Structure of Optimal Nonlinear Excitation for Decadal Variability of the Thermohaline Circulation

The decadal variability of the North Atlantic thermohaline circulation(THC) is investigated within a three-dimensional ocean circulation model using the conditional nonlinear optimal perturbation method. The results show that the optimal initial perturbations of temperature and salinity exciting the strongest decadal THC variations have similar structures: the perturbations are mainly in the northwestern basin at a depth ranging from 1500 to 3000 m. These temperature and salinity perturbations act as the optimal precursors for future modifications of the THC, highlighting the importance of observations in the northwestern basin to monitor the variations of temperature and salinity at depth. The decadal THC variation in the nonlinear model initialized by the optimal salinity perturbations is much stronger than that caused by the optimal temperature perturbations, indicating that salinity variations might play a relatively important role in exciting the decadal THC variability. Moreover, the decadal THC variations in the tangent linear and nonlinear models show remarkably different characteristics, suggesting the importance of nonlinear processes in the decadal variability of the THC.

New double yield surface model for coarse granular materials incorporating nonlinear unified failure criterion

A new double-yield-sarface （DYS） model was developed to characterize the strength and deformation behaviors of coarse granular materials （CGMs）. Two kinds of deformation mechanisms, including the shear and compressive plastic deformation, were taken into account in this model, These two deformation mechanisms were described by the shear and compressive yield functions, respectively. The Lode angle dependent formulations of proposed model were deduced by incorporating a 3D nonlinear unified failure criterion. Some comparisons were presented between the numerical predictions of proposed model and test data of true triaxial tests on the modeled rockfills. The model predictions are in good agreement with the test data and capture the strain hardening and plastic volumetric dilation of CGMs. These findings verify the reasonability of current DYS model, and indicate that this model is well suited to reproduce the stress-strain-volume change behavior of CGMs in general.

Numerical simulation of tire/soil interaction using a verified 3D finite element model

The compaction and stress generation on terrain were always investigated based on empirical approaches or testing methods for tire/soil interaction.However,the analysis should be performed for various tires and at different soil strengths.With the increasing capacity of numerical computers and simulation software,finite element modeling of tire/terrain interaction seems a good approach for predicting the effect of change on the parameters.In this work,an elaborated 3D model fully complianning with the geometry of radial tire 115/60R13 was established,using commercial code Solidwork Simulation.The hyper-elastic and incompressible rubber as tire main material was analyzed by Moony-Rivlin model.The Drucker-Prager yield criterion was used to model the soil compaction.Results show that the model realistically predicts the laboratory tests outputs of the modeled tire on the soft soil.

Generalized 3D Scattering Channel Model with MIMO Antenna Systems

In this paper, a generalized three-dimensional(3D) scattering channel model for macrocellular land mobile environments is considered. This model simultaneously describes angular arrival of multi-path signals in the azimuth and elevation planes in an environment where uniformly distributed scatterers are assumed to be present in hemispheroids around the base station(BS) and mobile station(MS). Using this channel model, we first derive the closed-form expression for the joint and marginal probability density functions of the angle-of-arrival and time-of-arrival measured at the BS and the MS corresponding to the azimuth and elevation angles. Next, we derive an expression for the Doppler spectral distribution caused by motion of the MSs. Furthermore, we analyze the performance of multiple-input multiple-output antenna systems numerically. The results show that the proposed 3D scattering channel model performs better than previously proposed two-dimensional(2D) models for indoor and outdoor environments. We compare the results with previous scattering channel models and measurement results to validate the generalizability of our model.

A Computer Modeling of the China Central Television Headquarters in Beijing

This paper deals with the computer modeling of structures starting from a point cloud. The CCTV （China Central Television） tower headquarters is the case for study because the shape of this building is non-stellar, concave and multi-connected. It is composed of sowns and chains. The sown is the representation of a horizontal plane formed by dense points. The chain is a planar path modeled by rare points. The CCTV structure is defined only by the three orthogonal Cartesian coordinates of the points. The proposed computer modeling uses a sequence of procedures and the desired outputted 3D model is consistent. The first procedure is devoted to attributing points to their voxel and to estimating three values needed afterwards. The second procedure is devoted to analyzing clusters vertically and horizontally, to preliminarily distinguishing chains from sowns and to generating relational matching. The third procedure is devoted to building closed paths between all chains and all their projections on sowns. The fourth procedure is devoted to connecting points with triangles. The fifth procedure, still being implemented, is devoted to interpolating triangles with triangular splines. The results show it is possible to achieve the 3D model using the above mentioned procedures. These procedures are written, implemented and tested and they form a library of people＇s own software. The code is written using Matlab. It is not possible to obtain the required 3D model if the procedures are applied in the wrong order or one step is skipped. To conclude, it is possible to obtain the computer model of the CCTV using the provided sequence of procedures.

An initial study on left ventricular diastolic function in patients with hypertrophy cardiomyopathy using single-beat, real-time, three-dimensional echocardiography

Objectives To assess the regional diastolic function in patients with hypertrophic cardiomyopathy （HCM） by using single-beat, real-time, three-dimensional echocardiography （RT-3DE）. Methods Sixty-five patients with HCM in sinus rhythm together with fifty age- and gender-matched normal controls were studied by two dimensional echocardiography （2DE） and RT-3DE. The parameters analyzed by RT-3DE included： left ventrieular （LV） volumes, left ventricular ejection fraction （LVEF）, end diastolic sphericity index （EDSI）, diastolic dyssynchrony index （DDI）, dispersion end diastole （DISPED）, and normalized 17 segmental volume-time curves. Results Evaluated by RT-3DE, LVEF was slightly lower compared with 2DE （63.2 ± 6.8% vs. 59.1 ± 6.4%, P 〈 0.0001）. Normal subjects had relatively uniform volumetric curves for all LV segments. In HCM patients, the segmental volumetric curves were dyssynchronous. Increased DDI and DISPED in end diastole were observed in patients with HCM （9.95 ± 3.75, 41.76 ± 17.19, P 〈 0.0001）, and not all abnormal volumetric segments occurred in the hypertrophic regions. Conclusions Patients with HCM have presented regional diastolic dyssynchrony in the diastole phase, and this preclinical lesion can be recognized by single-beat RT-3DE.

Two-and Three-Dimensional Urban Core Determinants of the Urban Heat Island： A Statistical Approach

There is no doubt that the UHI （urban heat island） is a mounting problem in built-up environments, due to the energy retention by surface dense building materials, leading to increased temperatures, air pollution, and energy consumption. Much of the earlier research on the UHI has used two-dimensional （2-D） information, such as land uses and the distribution of vegetation. In the case of homogeneous land uses, it is possible to predict surface temperatures with reasonable accuracy with 2-D information. However, three-dimensional （3-D） information is necessary to analyze more complex sites, including dense building clusters. In this research, 3-D building geometry information is combined with 2-D urban surface information to examine the relationship between urban characteristics and temperature. The research includes the following stages： （1） estimating urban temperature; （2） developing a 3-D city model; （3） generating geometric parameters; and （4） conducting statistical analyses using both linear and non-linear regression models. The implications of the results are discussed, providing guidelines for policies aiming to reduce the UHI.

Super-resolution amplification of bitmap images based on 3D modeling theory

As a general format of the image,bitmap(BMP)image has wide applications,and consequently it is an important part of image processing.By segmenting the bitmap and combining the three-dimesional(3D)model of the discrete algorithm with the scanning line compensation algorithm,a mathematical model is built.According to the topological relations between several control points on the model surface,the surface of the model is discretized,and a planar triangle sequence is used to describe 3D objects.Finally,the bitmap is enlarged by combining the borrowing compensation based on 3D modeling principle of discrete algorithm with the scanning line compensation algorithm of binary lattice image,thus getting a relatively clear enlarged BMP image.

Stress-strain relationship of unsaturated cohesive soil

A moisture-content based constitutive model was proposed based on the hyperbolic model as an attempt to move towards the implementation of unsaturated soil mechanics into routine geotechnical engineering practice. The stress-strain behavior of in-situ soil at a depth of 5 m was investigated by conducting undrained triaxial compression tests using the remolded soil samples. The test results show that the stress-strain relationship of unsaturated cohesive soil is still hyperbolic. The values of parameters a and b given in the model decrease with increasing the confining pressure for soil samples with the same moisture content and increase with increasing the moisture content for soil samples under the same confining pressure. The relationships between parameters a, b and moisture content were studied for confining pressures of 100, 150, 200 and 250 kPa. The comparison between the measured and predicted stress-strain curves for an additional group of soil samples, having a moisture content of 25.4%, shows that the proposed moisture content-dependent hyperbolic model provides a good prediction of stress-strain behavior of unsaturated cohesive soil.

Combined back-analysis method of ground stress based on refined geological modeling

A new back-analysis method of ground stress is proposed with comprehensive consideration of influence of topography, geology and nonlinear physical mechanical properties of rock on ground stress. This method based on non-uniform rational B-spline (NURBS) technology provides the means to build a refined three-dimensional finite element model with more accurate meshing under complex terrain and geological conditions. Meanwhile, this method is a back-analysis of ground stress with combination of multivariable linear regression model and neural network (ANN) model. Firstly, the regression model is used to fit approximately boundary loads. Regarding the regressed loads as mean value, some sets of boundary loads with the same interval are constructed according to the principle of orthogonal design, to calculate the corresponding ground stress at the observation positions using finite element method. The results (boundary loads and the corresponding ground stress) are added to the samples for ANN training. And on this basis, an ANN model is established to implement higher precise back-analysis of initial ground stress. A practical application case shows that the relative error between the inversed ground stress and observed value is mostly less than 10 %, which can meet the need of engineering design and construction requirements.

Multistage seismic damage constitutive model and parameter calibration of reinforced concrete columns

The road traffic network contains a large number of bridges,and calculating bridge damage using refined models demands significant time and resources.Therefore,developing a rapid evaluation method for the seismic capacity of regular bridges has become a crucial scientific challenge.This study presents an approach in which the ductile column is represented by a single degree-of-freedom model with elastic-plastic constitutive characteristics.Utilizing an uncoupled multivariate power function model and a plastic hinge model,a multidimensional power function model for section hierarchical curvature is constructed.Subsequently,the seismic multistage damage constitutive model(SMSD-CM)of member hierarchy is deduced and calibrated through theoretical methods.This model efficiently derives the trilinear constitutive model of components by inputting several crucial parameters.The SMSD-CM accurately simulates the hysteretic curve and displacement time-history under actual seismic conditions and aligns well with pushover analysis results from tests.The efficiency,ease of operation,and accuracy make the model suitable for rapid evaluation of the seismic capacity of regular bridges within the road traffic network.

The seamless model for three-dimensional datum transformation

With extensive applications of space geodesy, three-dimensional datum transformation model has been necessarily used to transform the coordinates in the different coordinate systems.Its essence is to predict the coordinates of non-common points in the second coordinate system based on their coordinates in the first coordinate system and the coordinates of common points in two coordinate systems.Traditionally, the computation of seven transformation parameters and the transformation of noncommon points are individually implemented, in which the errors of coordinates are taken into account only in the second system although the coordinates in both two systems are inevitably contaminated by the random errors.Moreover, the coordinate errors of non-common points are disregarded when they are transformed using the solved transformation parameters.Here we propose the seamless (rigorous) datum transformation model to compute the transformation parameters and transform the non-common points integratively, considering the errors of all coordinates in both coordinate systems.As a result, a nonlinear coordinate transformation model is formulated.Based on the Gauss-Newton algorithm and the numerical characteristics of transformation parameters, two linear versions of the established nonlinear model are individually derived.Then the least-squares collocation (prediction) method is employed to trivially solve these linear models.Finally, the simulation experiment is carried out to demonstrate the performance and benefits of the presented method.The results show that the presented method can significantly improve the precision of the coordinate transformation, especially when the non-common points are strongly correlated with the common points used to compute the transformation parameters.

NON-DEGENERATE INVARIANT BILINEAR FORMS ON NONASSOCIATIVE TRIPLE SYSTEMS

A bilinear form f on a nonassociative triple system T is said to be invariant if and only if f( abc ,d) = f(a, dcb ) = f(c, bad ) for all a,b,c,d ∈ T . (T ,f) is called a pseudo-metric triple system if f is non-degenerate and invariant. A decomposition theory for triple systems and pseudo-metric triple systems is established. Moreover, the ?nite-dimensional metric Lie triple systems are characterized in terms of the structure of the non-degenerate, invariant and symmetric bilinear forms on them.

DYNAMICAL ANALYSIS OF A 3-D CHAOTIC SYSTEM WITH ONLY TWO QUADRATIC NONLINEARITIES

The paper reports the dynamical study of a three-dimensional quadratic autonomous chaotic system with only two quadratic nonlinearities, which is a special case of the so-called conjugate Lue system. Basic properties of this system are analyzed by means of Lyapunov exponent spectrum and bifurcation diagram. The analysis shows that the system has complex dynamics with some interesting characteristics in which there are several periodic regions, but each of them has quite different periodic orbits.

Study on seismic response control of a single-tower self-anchored suspension bridge with elastic-plastic steel damper

Elastic-plastic steel damper(EPSD) is a new device controlling seismic responses.The mechanical principle of EPSD was presented and a comparison was conducted between the theoretical formulas and finite element(FE) simulation of damper units.The verified force-displacement hysteretic curve of the damper system was obtained with reference to tests.The Nanjing Jiangxinzhou Bridge(NJB) was subsequently taken as the case to investigate the seismic response control effect of EPSDs on single-tower self-anchored suspension bridges.A 3-dimensional FE model of the bridge was established in ANSYS and the dynamic and static analyses of the bridge were conducted,the control effect of EPSDs under different seismic waves was further investigated through nonlinear time-history analysis based on the validated model.Results showed that both the simplified theoretical and FE simulation methods can preferable reflect the mechanical performance of EPSD,and that seismic responses of NJB with EPSDs are better than those with elastic connection device or fluid viscous damper.However,the control effect of EPSDs is influenced by seismic wave characteristics.