INVOLUTIONS WITH FIXED POINT SET RP(2m)∪P(2m, 2n + 1)

Let （M, T） be a smooth closed manifold with a smooth involution T whose fixed point set is a disjoint union of an even-dimensional real projective space and a Dold manifold. In some cases, the equivariant bordism classes of （M, T） are determined.

A Correntropy-based Affine Iterative Closest Point Algorithm for Robust Point Set Registration

The iterative closest point(ICP)algorithm has the advantages of high accuracy and fast speed for point set registration,but it performs poorly when the point set has a large number of noisy outliers.To solve this problem,we propose a new affine registration algorithm based on correntropy which works well in the affine registration of point sets with outliers.Firstly,we substitute the traditional measure of least squares with a maximum correntropy criterion to build a new registration model,which can avoid the influence of outliers.To maximize the objective function,we then propose a robust affine ICP algorithm.At each iteration of this new algorithm,we set up the index mapping of two point sets according to the known transformation,and then compute the closed-form solution of the new transformation according to the known index mapping.Similar to the traditional ICP algorithm,our algorithm converges to a local maximum monotonously for any given initial value.Finally,the robustness and high efficiency of affine ICP algorithm based on correntropy are demonstrated by 2D and 3D point set registration experiments.

Research on Algorithm of the Point Set in the Plane Based on Delaunay Triangulation

In the paper, an improved algorithm is presented for Delaunay triangulation of the point-set in the plain. Based on the original algorithm, we propose the notion of removing circle. During the process of triangulation, and the circle dynamically moves, the algorithm which is simple and practical, therefore evidently accelerates the process of searching a new point, while generating a new triangle. Then it shows the effect of the algorithm in the finite element mesh.

BLOW UP POINT SET OF POSITIVE SOLUTION FOR NONLINEAR HEAT EQUATION

In this paper we consider a class nonlinear heat cquation,with non-local ferm and study that the structure of blow up point set of positive solution of initial boundary value problem in nonsymmatric convex domain.

Commuting Involutions with Fixed Point Set of Constant Codimension

Special generators of the unoriented cobordism ring MO* are constructed to determine the groups Jn,kτ of n-dimensional cobordism classes in MOn containing a representative Mn admitting a （Z2）k -action with fixed point set of constant codimension.

(Z_2)~k-Actions with Fixed Point Set of Constant Codimension 2~k+2

Let J_(*,k)~r 2. denote the ideal in MO_* of cobordism classes containing arepresentative that admits (Z_2)~k-actions with a fixed point set of constant codimension r. Inthis paper we determine J_(*,k)^(2^k+2) and J_(*,3)^(2^3+1).

Improved HHO algorithm based on good point set and nonlinear convergence formula

Harris hawks optimization(HHO)algorithm is an efficient method of solving function optimization problems.However,it is still confronted with some limitations in terms of low precision,low convergence speed and stagnation to local optimum.To this end,an improved HHO(IHHO)algorithm based on good point set and nonlinear convergence formula is proposed.First,a good point set is used to initialize the positions of the population uniformly and randomly in the whole search area.Second,a nonlinear exponential convergence formula is designed to balance exploration stage and exploitation stage of IHHO algorithm,aiming to find all the areas containing the solutions more comprehensively and accurately.The proposed IHHO algorithm tests 17 functions and uses Wilcoxon test to verify the effectiveness.The results indicate that IHHO algorithm not only has faster convergence speed than other comparative algorithms,but also improves the accuracy of solution effectively and enhances its robustness under low dimensional and high dimensional conditions.

Commuting Involutions with Fixed Point Set of Variable Codimension

Special generators of the unoriented cobordism ring MO* are constructed to determine some groups Jn,kl1,l2,…,lm of cobordism classes in MOn containing a representative Mn admitting a （Z2）k-action with the fixed point set of（n-li）-dimensional submanifolds of Mn.

Curvature Estimation of Point Set Data Based on the Moving-Least Square Surface

Curvature estimation is a basic step in many point relative applications such as feature recognition, segmentation,shape analysis and simplification.This paper proposes a moving-least square(MLS) surface based method to evaluate curvatures for unorganized point cloud data.First a variation of the projection based MLS surface is adopted as the underlying representation of the input points.A set of equations for geometric analysis are derived from the implicit definition of the MLS surface.These equations are then used to compute curvatures of the surface.Moreover,an empirical formula for determining the appropriate Gaussian factor is presented to improve the accuracy of curvature estimation.The proposed method is tested on several sets of synthetic and real data.The results demonstrate that the MLS surface based method can faithfully and efficiently estimate curvatures and reflect subtle curvature variations.The comparisons with other curvature computation algorithms also show that the presented method performs well when handling noisy data and dense points with complex shapes.

Realization of Fixed Point Sets

Let f: X→X be a selfmap of a compact connected polyhedron, and A a nonempty closed subset of X. In this paper, we shall deal with the question whether or not there is a map g: X→X homotopic to f such that the fixed point set Fixg of g equals A. We introduce a necessary condition for the existence of such a map g. It is shown that this condition is easy to check, and hence some sufficient conditions are obtained.

On a Class of Uniformly Distributed Sequences of Point Sets

In this note we construct certain sequences of finite point sets in [0, 1) s (s ≥ 1) and give the upper bounds of their discrepancy. Furthermore we prove that these sequences are uniformly distrbuted in [0, 1) s .

A Method for Exact Calculation of the Discrepancy of Low-Dimensional Finite Point Sets(II)

In the present paper a general formula for exact calculation of the discrepancy of an arbitrary finite point set of dimension d≥2 is explicitly given only in terms of the components of the points.

Novel 3D point set registration method based on regionalized Gaussian process map reconstruction

Point set registration has been a topic of significant research interest in the field of mobile intelligent unmanned systems.In this paper,we present a novel approach for a three-dimensional scan-to-map point set registration.Using Gaussian process(GP)regression,we propose a new type of map representation,based on a regionalized GP map reconstruction algorithm.We combine the predictions and the test locations derived from the GP as the predictive points.In our approach,the correspondence relationships between predictive point pairs are set up naturally,and a rigid transformation is calculated iteratively.The proposed method is implemented and tested on three standard point set datasets.Experimental results show that our method achieves stable performance with regard to accuracy and efficiency,on a par with two standard methods,the iterative closest point algorithm and the normal distribution transform.Our mapping method also provides a compact point-cloud-like map and exhibits low memory consumption.

Formulas of exact calculation of discrepancy of low-dimensionalfinite point sets (Ⅱ)

This letter is a continuation of refs.[1] and [2]. Let d≥2, Sd={uk（1≤k≤n）} be a finiteset of points in the d-dimensional unit cube [0, 1)d, where uk=(u1,k, u2,k,…,ud,k)

m-degree Center-connecting Line of Finite Points Set and Its Properties

In this paper, we first give the concept of m-degree center-connecting line in n-dimensional Euclidean space Enand investigate its several properties, then we obtain the length of m-degree center-connecting line formula in finite points set. As its application,we extend the Leibniz formula and length of medians formula in n-dimensional simplex to polytope.

MANIFOLDS WITH INVOLUTIONS WHOSE FIXED POINT SET HAS CONSTANT CODIMENSION

Let (M^n, T) be a smooth involution T on a closed manifold M^n. The fixed point set of T has a constant codimension k. Let J_n^k be the set of n-dimensional cobordism class in MO_n (unoriented cobordism group), which has such a representative. In this paper, we obtain a necessary and sufficient condition of α∈J_n^(2k), α∈J_n^(2l+1) for 2k≤40, 2t+1≤19.

A Divide-and-Conquer Strategy for Embedding a Distance-Net Point Set Into E^n and Its Application

A divide-and-conquer strategy is given for embedding a distance-net point set into Euclidean space En, and the problem of embedding a bounded distance-net point set into E3 and its application to the macromolecular conformation with Nuclear Magnetic Resonance data are discussed.

Environmental Risk Factors for Stomach Cancer in an African Setting about 193 Cases at the CHU Point G in Bamako/Mali

CHU (University Hospital Center) Point G: The department of surgery B is a surgical department of CHU Point G. The department is par excellence a reference department for cases of visceral surgery, cancer surgery, cardiovascular surgery, plastic and endocrinology surgery. As a reminder, the CHU Point G is the largest 3rd level referral hospital in Mali. Aim: To study the environmental risk factors of stomach cancer in the B surgery department of the Point G University Hospital in Bamako. Patients and Methods: We performed a cross-sectional study with retrospective collection from January 2008 to June 2018 (126 months). Results: We have identified 380 cases of digestive cancer, including 193 cases of stomach cancer or 50.79% of digestive cancers. The mean age of the patients was 57.21 ± 13 years. Male sex represented 55% (n = 106). Eating habits were dominated by the consumption of tô with potash (cereal paste) with 64.76% (n = 185). The main methods of preserving meat and fish were curing and smoking with 57.51% (n = 111). Chronic smoking was found in 24.35% (n = 47), alcohol + tobacco consumption in 2.59% (n = 5). The low socio-economic class represented 126 cases or 65.38%. Housewives and cultivators were respectively 37.82% (n = 73) and 227.97% (n = 54). 20.20% (n = 39) had a history of epigastric pain. Epigastralgia was the most common functional sign with 84.5% of cases (n = 169). An epigastric mass was found in 72 patients or 37.3%. Adenocarcinoma represented 97.4% (n = 188). Palliative surgery concerned the majority of our patients with 64.8% of patients (n = 79). The postoperative consequences were simple in 28.57% of cases (n = 28), the postoperative morbidity and mortality were respectively 33.61% (n = 41), and 23.77% (n = 29). The overall survival rate after surgery was 10.81% at 2 years and 2.94% at 5 years. This rate was 58.83% at 2 years and 28.50% at 5 years after curative surgery. Conclusion: The risk factors for stomach cancer are many and varied. Some are particularly present in Africa. Delay in diagnosis due to a belief in traditional healers is common in our community.

Finite Type Transcendental Entire Functions Whose Buried Points Set Contains Unbounded Positive Real Interval

Let fμ(z)=z·ep(z)+μ with p(z) being real coefficient polynomial and it's leading coefficient be positive, μ∈R+, when p(z) and μ satisfy two certain conditions, buried point set of fμ(z) contains unbounded positive real interval.