浅析以立体几何为载体的空间最值问题的求解策略

立体几何是高中数学的重要内容之一,在考试或者练习中常常会遇到,以立体几何为载体的空间最值问题,该问题的解决不仅需要具备识图、用图的能力,更要具备较高的空间想象能力.以立体几何为载体的空间最值问题,常常会找不到着手点,因此文中探究了几种策略,期望能够更好地解决“以立体几何为载体的空间最值问题”.

基于MC思想的布尔操作研究

为了提高布尔运算的执行效率及系统的鲁棒性,提出一种基于细胞元模型的布尔运算算法。该算法利用MC思想为每个特征实体的三角片建立cube,用最值空间和交互的充分性原理来快速检测发生相交的三角片,并根据每个cube顶点的颜色来判断三角片的内外关系、所属关系以及三角片的剖分方式,最后生成新的特征实体。该算法不仅提高了布尔运算的速度和性能,还避免了以往算法中出现孔洞的缺陷。实验表明,该算法具有更强的适应性和实用性。

Space-time spreading and space-time coding for correlated frequency-selective channel in the presence of interference

The space-time spreading （SIS）, superimposed training sequences and space-time coding （STC） are adopted to obtain a closed-form of average error probability upper bound and maximum likelihood esti- mation expression for multiple input and multiple output （MIMO） correlated frequency-selective channel in the presence of interference （colored interference）. Moreover, the correlation at both ends of the wire- less link that can be incorporated equivalently into correlation at the transmit end is derived. Finally, the mean square error （MSE） of the maximum likelihood estimate is also derived.

Experimental Evidence of the Formula of Saturation

There is more than one definition of the saturation ofcolour. In 2008, the author proposed a new formula for the saturation and in this presentation the experimental verification is shown by means of the Japanese Colour System PCCS, The distances in the lines of equal saturation have three maxima and three minima. A connection to neurology and to the colour sensation is possible. Making a new colour space with the saturation, the LSh-colour space, which is much more symmetrically than the LCh-colour space. This is of interest for calculating colour differences.

Upper tail probabilities of integrated Brownian motions

We obtain new upper tail probabilities of m-times integrated Brownian motions under the uniform norm and the Lp norm. For the uniform norm, Talagrand's approach is used, while for the Lp norm, Zolotare's approach together with suitable metric entropy and the associated small ball probabilities are used. This proposed method leads to an interesting and concrete connection between small ball probabilities and upper tail probabilities(large ball probabilities) for general Gaussian random variables in Banach spaces. As applications,explicit bounds are given for the largest eigenvalue of the covariance operator, and appropriate limiting behaviors of the Laplace transforms of m-times integrated Brownian motions are presented as well.

Improved Upper Bounds for the Largest Eigenvalue of Unicyclic Graphs

Let G（V, E） be a unicyclic graph, Cm be a cycle of length m and Cm G, and ui ∈ V（Cm）. The G - E（Cm） are m trees, denoted by Ti, i = 1, 2,..., m. For i = 1, 2,..., m, let eui be the excentricity of ui in Ti and ec = max{eui ： i = 1, 2 , m}. Let κ = ec＋1. Forj = 1,2,...,k- 1, let δij = max{dv ： dist（v, ui） = j,v ∈ Ti}, δj = max{δij ： i = 1, 2,..., m}, δ0 = max{dui ： ui ∈ V（Cm）}. Then λ1（G）≤max{max 2≤j≤k-2 （√δj-1-1＋√δj-1）,2＋√δ0-2,√δ0-2＋√δ1-1}. If G ≌ Cn, then the equality holds, where λ1 （G） is the largest eigenvalue of the adjacency matrix of G.

HASM-AD Algorithm Based on the Sequential Least Squares

The HASM(high accuracy surface modeling) technique is based on the fundamental theory of surfaces,which has been proved to improve the interpolation accuracy in surface fitting.However,the integral iterative solution in previous studies resulted in high temporal complexity in computation and huge memory usage so that it became difficult to put the technique into application,especially for large-scale datasets.In the study,an innovative model(HASM-AD) is developed according to the sequential least squares on the basis of data adjustment theory.Sequential division is adopted in the technique,so that linear equations can be divided into groups to be processed in sequence with the temporal complexity reduced greatly in computation.The experiment indicates that the HASM-AD technique surpasses the traditional spatial interpolation methods in accuracy.Also,the cross-validation result proves the same conclusion for the spatial interpolation of soil PH property with the data sampled in Jiangxi province.Moreover,it is demonstrated in the study that the HASM-AD technique significantly reduces the computational complexity and lessens memory usage in computation.

Visual tracking based on the sparse representation of the PCA subspace

We construct a collaborative model of the sparse representation and the subspace representation. First, we represent the tracking target in the principle component analysis(PCA) subspace, and then we employ an L_1 regularization to restrict the sparsity of the residual term, an L_2 regularization term to restrict the sparsity of the representation coefficients, and an L_2 norm to restrict the distance between the reconstruction and the target. Then we implement the algorithm in the particle filter framework. Furthermore, an iterative method is presented to get the global minimum of the residual and the coefficients. Finally, an alternative template update scheme is adopted to avoid the tracking drift which is caused by the inaccurate update. In the experiment, we test the algorithm on 9 sequences, and compare the results with 5 state-of-art methods. According to the results, we can conclude that our algorithm is more robust than the other methods.