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Why is the Danger Cylinder Dangerous in the P3P Problem? 被引量:5
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作者 ZHANG Cai-Xia HU Zhan-Yi 《自动化学报》 EI CSCD 北大核心 2006年第4期504-511,共8页
The PnP problem is a widely used technique for pose determination in computer vision community,and finding out geometric conditions of multiple solutions is the ultimate and most desirable goal of the multi-solution a... The PnP problem is a widely used technique for pose determination in computer vision community,and finding out geometric conditions of multiple solutions is the ultimate and most desirable goal of the multi-solution analysis,which is also a key research issue of the problem.In this paper,we prove that given 3 control points,if the camera's optical center lies on the so-called“danger cylinder”and is enough far from the supporting plane of control points,the corresponding P3P problem must have 3 positive solutions.This result can bring some new insights into a better understanding of the multi-solution problem.For example,it is shown in the literature that the solution of the P3P problem is instable if the optical center lies on this danger cylinder,we think such occurrence of triple-solution is the primary source of this instability. 展开更多
关键词 The p3p problem the danger cylinder instability of solution
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Three solutions to inequalities of Dirichlet problem driven by p(x)-Laplacian
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作者 葛斌 薛小平 郭梦舒 《Applied Mathematics and Mechanics(English Edition)》 SCIE EI 2010年第10期1283-1292,共10页
A class of nonlinear elliptic problems driven by p(x)-Laplacian with a nonsmooth locally Lipschitz potential is considered.By applying the version of the nonsmooth three-critical-point theorem,the existence of three... A class of nonlinear elliptic problems driven by p(x)-Laplacian with a nonsmooth locally Lipschitz potential is considered.By applying the version of the nonsmooth three-critical-point theorem,the existence of three solutions to the problems is proved. 展开更多
关键词 p(x)-Laplacian differential inclusion problem three-critical-point theorem
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The Simplest Possible Fully Correct Solution of the Clay Millennium Problem about P vs. NP. A Simple Proof That P ≠ NP = EXPTIME
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作者 Konstantinos E. Kyritsis 《Journal of Computer and Communications》 2023年第8期181-194,共14页
In the current paper, I present probably the simplest possible abstract formal proof that P ≠ NP, and NP = EXPTIME, in the context of the standard mathematical set theory of computational complexity and deterministic... In the current paper, I present probably the simplest possible abstract formal proof that P ≠ NP, and NP = EXPTIME, in the context of the standard mathematical set theory of computational complexity and deterministic Turing machines. My previous publications about the solution of the P vs. NP with the same result NP = EXPTIME, to be fully correct and understandable need the Lemma 4.1 and its proof of the current paper. The arguments of the current paper in order to prove NP = EXPTME are even simpler than in my previous publications. The strategy to solve the P vs. NP problem in the current paper (and in my previous publications) is by starting with an EXPTIME-complete language (problem) and proving that it has a re-formulation as an NP-class language, thus NP = EXPTIME. The main reason that the scientific community has missed so far such a simple proof, is because of two factors 1) It has been tried extensively but in vain to simplify the solutions of NP-complete problems from exponential time algorithms to polynomial time algorithms (which would be a good strategy only if P = NP) 2) It is believed that the complexity class NP is strictly a subclass to the complexity class EXPTIME (in spite the fact that any known solution to any of the NP-complete problems is not less than exponential). The simplicity of the current solution would have been missed if 2) was to be believed true. So far the majority of the relevant scientific community has considered this famous problem not yet solved. The present results definitely solve the 3rd Clay Millennium Problem about P versus NP in a simple, abstract and transparent way that the general scientific community, but also the experts of the area, can follow, understand and therefore become able to accept. 展开更多
关键词 3rd Clay Millennium problem EXPTIME-Complete problems NP-Complexity P-Complexity
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一类带p-Laplace算子的非线性二阶m点共振边值问题解的存在性
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作者 刘美玉 马锦然 裴明鹤 《北华大学学报(自然科学版)》 CAS 2024年第1期1-7,共7页
基于拓扑横截方法连同障碍带技巧,得到一类带p-Laplace算子的非线性二阶m点共振边值问题解的新的存在性结果,并给出应用举例。
关键词 P-LAPLACE算子 m点共振边值问题 存在性 拓扑横截方法 障碍带技巧
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Existence of Solutions for S-L Singular Boundary Value Problems with p-Laplacian Operators
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作者 郭彦平 葛渭高 单文锐 《Journal of Beijing Institute of Technology》 EI CAS 2002年第2期220-224,共5页
The existence of solutions for singular nonlinear two point boundary value problems subject to Sturm Liouville boundary conditions with p Laplacian operators is studied by the method of upper and lower solution... The existence of solutions for singular nonlinear two point boundary value problems subject to Sturm Liouville boundary conditions with p Laplacian operators is studied by the method of upper and lower solutions. The proof is based on an application of Schauder’s fixed point theorem to a modified problem whose solutions are that of the original one. At the same time, Arzela Ascoli theorem is used to prove that the defined operator N is a compact map. 展开更多
关键词 nonlinear boundary value problems p Laplacian operators fixed point upper solution lower solution
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Existence of Multiple Positive Solutions for Higher-Order p-Laplacian Boundary Value Problems
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作者 贺小明 葛渭高 《Journal of Beijing Institute of Technology》 EI CAS 2002年第2期212-216,共5页
The existence of multiple positive solutions for a class of higher order p Laplacian boundary value problem is studied. By means of the Leggett Williams fixed point theorem in cones, existence criteria which e... The existence of multiple positive solutions for a class of higher order p Laplacian boundary value problem is studied. By means of the Leggett Williams fixed point theorem in cones, existence criteria which ensure the existence of at least three positive solutions of the boundary value problem are established. 展开更多
关键词 positive solutions cone Leggett Williams fixed point theorem p Laplacian boundary value problems
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具p-Laplace算子的分数阶脉冲微分方程奇异边值问题的解
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作者 赵甜 胡卫敏 刘元彬 《吉林大学学报(理学版)》 CAS 北大核心 2024年第4期842-850,共9页
用Banach压缩映像原理和Krsnoasel’skii不动点定理证明一类具有p-Laplace算子的分数阶脉冲微分方程奇异边值问题解的唯一性和存在性.
关键词 分数阶微分方程 脉冲 不动点定理 奇异边值问题 P-LAPLACE算子
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SOLUTIONS TO DISCRETE MULTIPARAMETER PERIODIC BOUNDARY VALUE PROBLEMS INVOLVING THE p-LAPLACIAN VIA CRITICAL POINT THEORY 被引量:8
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作者 高承华 《Acta Mathematica Scientia》 SCIE CSCD 2014年第4期1225-1236,共12页
In this paper, we consider the existence of three nontrivial solutions for a discrete non-linear multiparameter periodic problem involving the p-Laplacian. By using the similar method for the Dirichlet boundary value ... In this paper, we consider the existence of three nontrivial solutions for a discrete non-linear multiparameter periodic problem involving the p-Laplacian. By using the similar method for the Dirichlet boundary value problems in [C. Bonanno and P. Candito, Appl. Anal., 88(4) (2009), pp. 605-616], we construct two new strong maximum principles and obtain that the boundary value problem has three positive solutions for λ and μ in some suitable intervals. The approaches we use are the critical point theory. 展开更多
关键词 discrete periodic boundary value problem P-LAPLACIAN MULTIPARAMETER three solutions critical point theory
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Multiple positive solutions for a class of nonlinear four-point boundary value problem with p-Laplacian 被引量:10
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作者 LI Xiang-feng 《Applied Mathematics(A Journal of Chinese Universities)》 SCIE CSCD 2008年第2期143-150,共8页
This paper deals with the existence of multiple positive solutions for a class of nonlinear singular four-point boundary value problem with p-Laplacian:{(φ(u′))′+a(t)f(u(t))=0, 0〈t〈1, αφ(u(... This paper deals with the existence of multiple positive solutions for a class of nonlinear singular four-point boundary value problem with p-Laplacian:{(φ(u′))′+a(t)f(u(t))=0, 0〈t〈1, αφ(u(0))-βφ(u′(ξ))=0,γφ(u(1))+δφ(u′(η))0,where φ(x) = |x|^p-2x,p 〉 1, a(t) may be singular at t = 0 and/or t = 1. By applying Leggett-Williams fixed point theorem and Schauder fixed point theorem, the sufficient conditions for the existence of multiple (at least three) positive solutions to the above four-point boundary value problem are provided. An example to illustrate the importance of the results obtained is also given. 展开更多
关键词 p-Laplacian operator multiple positive solution four-point singular boundary value problem fixed-point theorem.
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Picard Boundary Value Problems of Second Order p-Laplacian Differential Equations 被引量:8
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作者 LIU Yu-ji 《Chinese Quarterly Journal of Mathematics》 CSCD 2011年第1期77-84,共8页
Suffcient conditions for the existence of at least one solution of two-point boundary value problems for second order nonlinear differential equations [φ(x(t))] + kx(t) + g(t,x(t)) = p(t),t ∈(0,π) x(0) = x(π) = 0 ... Suffcient conditions for the existence of at least one solution of two-point boundary value problems for second order nonlinear differential equations [φ(x(t))] + kx(t) + g(t,x(t)) = p(t),t ∈(0,π) x(0) = x(π) = 0 are established,where [φ(x)] =(|x |p-2x) with p > 1.Our result is new even when [φ(x)] = x in above problem,i.e.p = 2.Examples are presented to illustrate the effciency of the theorem in this paper. 展开更多
关键词 solutions second order p-Laplacian differential equation two-point boundary value problem fixed-point theorem
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EXISTENCE OF POSITIVE SOLUTIONS FOR p-LAPLACIAN SINGULAR BOUNDARY VALUE PROBLEMS OF FUNCTIONAL DIFFERENTIAL EQUATION 被引量:5
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作者 SongChangxiu WengPeixuan 《Applied Mathematics(A Journal of Chinese Universities)》 SCIE CSCD 2005年第1期51-58,共8页
In this paper,the boundary value problems of p-Laplacian functional differential equation are studied.By using a fixed point theorem in cones,some criteria for the existence of positive solutions are given.
关键词 p-Laplacian operator functional differential equation boundary value problem positive solution fixed point theorem in cones.
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Existence of Positive Solutions for Higher-Order Four-Point Boundary Value Problems with a p-Laplacian Operator
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作者 路月峰 葛渭高 《Journal of Beijing Institute of Technology》 EI CAS 2009年第1期98-100,共3页
A class of higher-order four-point boundary value problems with a p-Laplacian operator is studied. By use of a fixed point theorem in cones, sufficient conditions for the existence of positive solutions for the bounda... A class of higher-order four-point boundary value problems with a p-Laplacian operator is studied. By use of a fixed point theorem in cones, sufficient conditions for the existence of positive solutions for the boundary value problems are obtained. 展开更多
关键词 positive solutions four-point boundary value problem P-LAPLACIAN fixed point theorem CONE
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A Potential-Reduction Algorithm for Linear Complementarity Problems
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作者 WangYan-jin FeiPu-sheng YanZi-zong 《Wuhan University Journal of Natural Sciences》 CAS 2004年第2期144-148,共5页
Feasible-interior-point algorithms start from a strictly feasible interior point, but infeassible-interior-point algorithms just need to start from an arbitrary positive point, we give a potential reduction algorithm ... Feasible-interior-point algorithms start from a strictly feasible interior point, but infeassible-interior-point algorithms just need to start from an arbitrary positive point, we give a potential reduction algorithm from an infeasible-starting-point for a class of non-monotone linear complementarity problem. Its polynomial complexity is analyzed. After finite iterations the algorithm produces an approximate solution of the problem or shows that there is no feasible optimal solution in a large region. Key words linear complementarity problems - infeasible-starting-point - P-matrix - potential function CLC number O 221 Foundation item: Supported by the National Natural Science Foundation of China (70371032) and the Doctoral Educational Foundation of China of the Ministry of Education (20020486035)Biography: Wang Yan-jin (1976-), male, Ph. D candidate, research direction: optimal theory and method. 展开更多
关键词 linear complementarity problems infeasible-starting-point P-MATRIX potential function
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Positive Solutions for a Boundary Value Problem with a Derivative Argument
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作者 Bo Sun 《Journal of Applied Mathematics and Physics》 2013年第4期73-77,共5页
In this paper, several existence results of multiple positive solutions are obtained for a boundary value problem with p-Laplacian, by applying a fixed point theorem in cones. The interesting point is that the nonline... In this paper, several existence results of multiple positive solutions are obtained for a boundary value problem with p-Laplacian, by applying a fixed point theorem in cones. The interesting point is that the nonlinear term f is involved with the first-order derivative explicitly. 展开更多
关键词 Positive Solutions Fixed Point THEOREM CONE Boundary Value problem P-LAPLACIAN
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P∗(κ)-线性权互补问题的一种全牛顿步可行内点算法
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作者 迟晓妮 张璐 +1 位作者 刘三阳 张所滨 《应用数学》 北大核心 2023年第2期540-549,共10页
本文提出一种求解P∗(κ)-线性权互补问题(LWCP)的新全牛顿步可行内点算法.首先基于一个连续可微的核函数,构造新代数等价变换,得到光滑中心路径的等价形式.然后沿着搜索方向使用全牛顿步,无需进行线搜索,节省运行内存.最后分析算法的可... 本文提出一种求解P∗(κ)-线性权互补问题(LWCP)的新全牛顿步可行内点算法.首先基于一个连续可微的核函数,构造新代数等价变换,得到光滑中心路径的等价形式.然后沿着搜索方向使用全牛顿步,无需进行线搜索,节省运行内存.最后分析算法的可行性及收敛性,并通过数值算例验证算法的有效性. 展开更多
关键词 P∗(κ)-线性权互补问题 全牛顿步 可行内点算法 代数等价变换
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带p(t)-Laplace算子的分数阶Langevin方程参数型反周期边值问题解的存在性 被引量:1
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作者 倪晋波 陈港 董蝴蝶 《吉林大学学报(理学版)》 CAS 北大核心 2023年第3期490-496,共7页
利用Schaefer不动点定理,讨论一类带有p(t)-Laplace算子的分数阶Langevin方程参数型反周期边值问题,通过给出非线性项合理的假设条件得到了其解的存在性结果,并举例说明主要结果的应用.
关键词 Schaefer不动点定理 p(t)-Laplace算子 分数阶Langevin方程 参数型反周期边值问题
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带p-Laplace算子的离散混合边值问题负凸解的存在性
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作者 赵亚丽 陈天兰 《中山大学学报(自然科学版)(中英文)》 CAS CSCD 北大核心 2023年第6期171-176,共6页
运用锥上的不动点定理讨论带p-Laplace算子的离散混合边值问题△[φ_(p)(△u(t-1))]=f(t,-u(t)),t∈[2,T-1]_(Z),△u(1)=0,u(T)=0负凸解的存在性,其中φ_(p)(s)=|s|^(p-2)s,p>1,f:[2,T-1]_(Z)×[0,+∞)→[0,+∞)连续.
关键词 P-LAPLACE算子 离散混合边值问题 负凸解 不动点定理
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New Algorithms for the Perspective-Three-Point Problem
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作者 高小山 陈航飞 《Journal of Computer Science & Technology》 SCIE EI CSCD 2001年第3期194-207,共14页
In this paper, two approaches are used to solve the PerspectiveThree-Point Problem (P3P): the symbolic computation approach and the geometric approach. In the symbolic computation approach, we use Wu-Ritt's zero ... In this paper, two approaches are used to solve the PerspectiveThree-Point Problem (P3P): the symbolic computation approach and the geometric approach. In the symbolic computation approach, we use Wu-Ritt's zero decomposition algorithm to give a complete triangular decomposition for the P3P equation system. This decomposition provides the first complete analytical solution to the P3P problem. In the geometric approach, we give some pure geometric criteria for the number of real physical solutions. The complete solution classification for two special cases with three and four parameters is also given. 展开更多
关键词 camera calibration pose determination perspective-three-point problem (p3p) analytical solution geometric criterion symbolic computation
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SOLUTION CLASSIFICATION FOR THE NONPERSPECTIVE-THREE-POINT PROBLEM
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作者 Jianliang TANG Wensheng CHEN 《Journal of Systems Science & Complexity》 SCIE EI CSCD 2006年第2期219-226,共8页
In the PnP problem,the imaging devices follow the perspective rule and the imaging rays pass through a common point. However,there are many new imaging devices being developed for robot navigation or other fields with... In the PnP problem,the imaging devices follow the perspective rule and the imaging rays pass through a common point. However,there are many new imaging devices being developed for robot navigation or other fields with the advance in imaging technologies for machine vision. These devise are not necessarily being designed to follow the perspective rule in order to satisfy some design criterion and,thus, the imaging rays may not pass through a common point.Such generalized imaging devices may not be perspective and, therefore, their poses cannot be estimated with traditional perspective technique.Using the Wu-Ritt's zero decomposition method,the main component for the nonperspective-three-point problem is given. We prove that there are at most eight solutions in the general case and give the solution classification for the NP3P problem. 展开更多
关键词 Complete discrimination system Nonperspective-three-Point perspective-three-Point problem p3p revised sign lists Solution classification.
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p-Laplace算子方程三点边值问题单调正解的存在性 被引量:10
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作者 刘锡平 贾梅 葛渭高 《吉林大学学报(理学版)》 CAS CSCD 北大核心 2007年第1期49-55,共7页
利用锥拉伸与锥压缩不动点定理,研究一类具p-Laplace算子的二阶微分方程的三点边值问题单调正解的存在性,给出了单调正解存在的充分条件,并确定了解曲线的凹凸性.
关键词 P-LAPLACE算子 三点边值问题 锥拉伸与锥压缩不动点定理 单调正解
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