涉及单形内一点和内外径的一类不等式

设 n维 Euclid空间 En(n≥ 2 )中单形 Ω(A)的顶点集为 A={ A0 ,A1,… ,An} .,Ω(A)内任一点 P至侧面 { A0 ,A1,… ,An} \{ Ai}的距离为 di(i=0 ,1,… ,n) ,Ω(A)的外接超球半径和内切超球半径分别为 R、r,记C( n,α) =(2 (n+ 1　 2 ) + (n+ 1) 2α- (n+ 1) α) / 4 (n+ 12 ) ) α(α≥ 1) ,本文建立了涉及Ω (A)内一点的不等式∑0≤ i相似文献   

Computing regions of interest for geometric features in digital images

We present an uncertainty model for geometric transformations based on polygonal uncertainty regions and transformation polytopes. The main contribution of this paper is a systematic approach for the computation of regions of interest for features by using the uncertainty model for affine and projective transformations. The focus is on the solution of transformation problems for geometric primitives, especially lines, so that regions of interest can be computed for corresponding geometric features in distinct images.     

A simple and efficient kinetic spanner

We present a new and simple (1+ε)-spanner of size O(n/ε²) for a set of n points in the plane, which can be maintained efficiently as the points move. Assuming the trajectories of the points can be described by polynomials whose degrees are at most s, the number of topological changes to the spanner is O((n/ε²)λ_s+2(n)), and at each event the spanner can be updated in O(1) time.     

String C-groups with real Schur index 2

We give examples of finite string C-groups (the automorphism groups of abstract regular polytopes) that have irreducible characters of real Schur index 2. This answers a problem of Monson concerning these groups.     

A simple method to compute economic order quantities

In this note, a simple method by using the arithmetic–geometric-mean-inequality theorem is proposed to computer the global minimum economic order quantities without taking complex differential calculus or using tedious algebraic manipulations. In contrast to (Minner, S., 2007. A note on how to compute economic order quantity without derivatives by cost comparisons. International Journal of Production Economics 105, 293–296; Wee, H.M., Wang, W.T., Chung, C.J., 2009. A modified method to computer economic order quantities without derivatives by cost-difference comparisons. European Journal of Operational Research) based on a local cost minimum initially to derive the solution and then proven it’s the global minimum, the proposed method yields the global minimum cost immediately and explicitly without using the cost comparisons and letting the time horizon to infinity.     

再论Pedoe不等式的高维推广及应用

本文对欧氏空间E~n中的两个n维单形,给出了著名的Pedoe不等式的一个实质性推广,并讨论了它的应用.     

A simple proof of the Markoff conjecture for prime powers

We give a simple and independent proof of the result of Jack Button and Paul Schmutz that the Markoff conjecture on the uniqueness of the Markoff triples (a, b, c) where a ≤ b ≤ c holds whenever c is a prime power. We also indicate some further directions for investigation.      

The desirability relation of simple games

We prove some properties of simple games with a complete desirability relation, and investigate the relationships between the desirability of a simple game G and that of some simple games that are derived from G. We also provide an example of a proper simple game that has a complete and acyclic desirability relation but is not a weighted majority game.     

A simple proof of logarithmic convexity of extended mean values

In the note, a simple proof is provided for the logarithmic convexity of extended mean values. The second author was partially supported by the China Scholarship Council.     

Polyhedra with simple dense geodesics

We characterize polyhedral surfaces admitting a simple dense geodesic ray and convex polyhedral surfaces with a simple geodesic ray.     

A relation-algebraic approach to simple games

Simple games are a powerful tool to analyze decision-making and coalition formation in social and political life. In this paper, we present relation-algebraic models of simple games and develop relational specifications for solving some basic problems of them. In particular, we test certain fundamental properties of simple games and compute specific players and coalitions. We also apply relation algebra to determine power indices. This leads to relation-algebraic specifications, which can be evaluated with the help of the BDD-based tool Rel View after a simple translation into the tool’s programming language. In order to demonstrate the visualization facilities of Rel View we consider an example of the Catalonian Parliament after the 2003 election.     

A simple four-unknown refined theory for bending analysis of functionally graded plates

In the present paper, a refined trigonometric higher-order plate theory is simply derived, which satisfies the free surface conditions. Moreover, the number of unknowns of this theory is the least one comparing with other shear theories. The effects of transverse shear strains as well as the transverse normal strain are taken into account. The number of unknown functions involved in the present theory is only four as against six or more in case of other shear and normal deformation theories. The bending response of FG rectangular plates is presented. A comparison with the corresponding results is made to check the accuracy and efficiency of the present theory. Additional results for all displacements and stresses are investigated through-the-thickness of the FG rectangular plate.     

Embeddings of simple directed triple systems

In this paper, we completely solve the embedding problem of simple directed triple systems by proving that the necessary conditions for the embeddings of directed triple systems are also sufficient. This project is supported by the Science and Technology Foundation of Shanghai Jiao Tong University     

On multiple simple recourse models

We consider multiple simple recourse (MSR) models, both continuous and integer versions, which generalize the corresponding simple recourse (SR) models by allowing for a refined penalty cost structure for individual shortages and surpluses. It will be shown that (convex approximations of) such MSR models can be represented as explicitly specified continuous SR models, and thus can be solved efficiently by existing algorithms. This research has been made possible by a fellowship of the Royal Netherlands Academy of Arts and Sciences.     

Adding Skolem functions to simple theories

We examine the conditions under which we can keep simplicity or categoricity after adding a Skolem function to the theory.Mathematics Subject Classification (2000): 03C45, 03C50     

Three problems about simple polygons

We give three related algorithmic results concerning a simple polygon P:

1. Improving a series of previous work, we show how to find a largest pair of disjoint congruent disks inside P in linear expected time.

2. As a subroutine for the above result, we show how to find the convex hull of any given subset of the vertices of P in linear worst-case time.

3. More generally, we show how to compute a triangulation of any given subset of the vertices or edges of P in almost linear time.