作物垄作的数学模型

应用高等数学中对面积的曲面积分等方法,建立了垄作种植中半椭圆形、抛物线型和三角形垄的数学模型,比较了不同垄形、垄宽、垄高在增加单位土地表面积和突出地面垄体体积的效果.     

Automatic CAD model topology generation

Computer aided design (CAD) models often need to be processed due to the data translation issues and requirements of the downstream applications like computational field simulation, rapid prototyping, computer graphics, computational manufacturing, and real‐time rendering before they can be used. Automatic CAD model processing tools can significantly reduce the amount of time and cost associated with the manual processing. The topology generation algorithm, commonly known as CAD repairing/healing, is presented to detect commonly found geometrical and topological issues like cracks, gaps, overlaps, intersections, T‐connections, and no/invalid topology in the model, process them and build correct topological information. The present algorithm is based on the iterative vertex pair contraction and expansion operations called stitching and filling, respectively, to process the model accurately. Moreover, the topology generation algorithm can process manifold as well as non‐manifold models, which makes the procedure more general and flexible. In addition, a spatial data structure is used for searching and neighbour finding to process large models efficiently. In this way, the combination of generality, accuracy, and efficiency of this algorithm seems to be a significant improvement over existing techniques. Results are presented showing the effectiveness of the algorithm to process two‐ and three‐dimensional configurations. Copyright © 2006 John Wiley & Sons, Ltd.     

从圆内接三角形面积想到的

首先证明了正三角形的外接椭圆中面积最小的是一个圆.进而用初等方法证明了二维情形的F.John定理.     

Erds-Klamkin不等式的推广(英文)

Erds和Klamkin在1973年建立了如下命题:若A,B,C是一个三角形的内角,λ≥2且0≤μ≤λ,则存在以cos~μ(A/λ),cos~μ(B/λ),cos~μ(C/λ)为边的三角形。本文把μ的范围延拓成0≤μ≤λ~2/2后,证明原结论照样成立。     

Two-generator Discrete Subgroups of Isom(H2) Containing Orientation-reversing Elements

Let f and g be elements of the isometry group Isom(H²) of the hyperbolic plane H², and assume that one of them is orientation-reversing. We determine when the group (f,g) they generate is discrete; in particular, we obtain the classification of such groups. As an application to knot theory, we completely determine the tunnel number one Montesinos knots.     

More on a New Concept of Entropy and Information

An alternative notion of entropy called CRE is proposed in [Ra1] Rao et al. (IEEE Trans. Inf. Theory 50, 2004). This preserves many of the properties of Shannon Entropy and possesses mathematical properties, which we hope will be of use in statistical estimates. In this article, we develop some more mathematical properties of CRE, show its relation to the L log L class, and characterize among others the Weibull distribution.     

Real and spurious contributions for the Shannon, Rényi and Tsallis entropies

A two-parameter probability distribution is constructed by dilatation (or contraction) of the escort probability distribution. This transformation involves a physical probability distribution P associated with the system under study and an almost arbitrary reference probability distribution P^′. In contrast to the Shannon and Rényi entropies, the Tsallis entropy does not decompose as the sum of the physical contribution due to P and the reference or spurious part owing to P^′. For solving this problem, a slight modification to the relation between Tsallis and Rényi entropies must be introduced. The procedure in this paper gives rise to a nonconventional one-parameter Shannon entropy and to two-parameter Rényi and Tsallis entropies associated with P. It also contributes to clarify the meaning and role of the escort probabilities set.     

Info-quantifiers’ map-characterization revisited

We highlight the potentiality of a special Information Theory (IT) approach in order to unravel the intricacies of nonlinear dynamics, the methodology being illustrated with reference to the logistic map. A rather surprising dynamic feature→plane-topography map becomes available.     

Nature of Nonlocality in Triangle Network based on Elegant Joint Measurement

Defining nonlocality in a no-input closed quantum network scenario is a new area of interest nowadays. Gisin, in [Entropy 21, 325 (2019)], proposed a possible condition for non-tri-locality of the trivial no-input closed network scenario, triangle network, by introducing a new kind of joint measurement bases and a probability bound. In [npj Quantum Information (2020) 6:70] they found a shred of numerical evidence in support of Gisin's probability bound. Now based on that probability bound, it finds the nature of the correlation in a triangle network scenario. This study observes how far the probability lies from that Gisin's bound with every possible combination of entangled and local pure states distributed from three independent quantum sources. Here, it uses the generalized Elegant Joint Measurements bases for each party and find that there is a dependency of non-locality on the entanglement of these joint measurement bases. It also checks the probability bound for the polygon structure.     

Coloring triangle‐free graphs with local list sizes

We prove two distinct and natural refinements of a recent breakthrough result of Molloy (and a follow‐up work of Bernshteyn) on the (list) chromatic number of triangle‐free graphs. In both our results, we permit the amount of color made available to vertices of lower degree to be accordingly lower. One result concerns list coloring and correspondence coloring, while the other concerns fractional coloring. Our proof of the second illustrates the use of the hard‐core model to prove a Johansson‐type result, which may be of independent interest.