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101.
In this paper, we investigate an original way to deal with the problems generated by the limitation process of high-order finite volume methods based on polynomial reconstructions. Multi-dimensional Optimal Order Detection (MOOD) breaks away from classical limitations employed in high-order methods. The proposed method consists of detecting problematic situations after each time update of the solution and of reducing the local polynomial degree before recomputing the solution. As multi-dimensional MUSCL methods, the concept is simple and independent of mesh structure. Moreover MOOD is able to take physical constraints such as density and pressure positivity into account through an “a posteriori” detection. Numerical results on classical and demanding test cases for advection and Euler system are presented on quadrangular meshes to support the promising potential of this approach. 相似文献
102.
103.
51.Introducti0nandMainResultlnthepaperL1J,Caffarelli,NirenbergandSpruckdiscussedtheDirichletproblemforthenonlinearellipticequationforunknownu=u(x):{':<;;>:,<";>:are,vxeD,(1-1)where0lsab0undedstrictlyconvexdomaininR"withsmoothboundaryare,K(u)=(K,(u),Kz(u),..',K"(u))denotestheprincipalcurvaturesofthegraph(x,u(x))andfisofaspecialnatureasinL2J'L3j.Typicalcasesoftheequationin(1.l),whichweretreatedaswellbyIvochkina[4J,isf=Sl/*(K),whereS*(K)arethee1ementarysymmetricfunctions,Recently,Ivochki… 相似文献
104.
综合国力的数学建模 总被引:2,自引:0,他引:2
王树禾 《高校应用数学学报(A辑)》1997,(1):29-36
本文考虑社会文明与社会导恶现象的制约机制,建立一个综合国力的非线性数学模型,从数学上讨论了相应的二次微分系统的Hopf分叉,中心与细焦点的判定,极限环的存在唯一性等问题,并对数学结论予以合理解释,把社会相平面划成社发展区域,社会动荡区域和社会崩溃区域,研讨社会走向,确定纳入社会发展区域的途径。 相似文献
105.
106.
For each sN define the constant θs with the following properties: if an entire function g(z) of type t(g)<θs satisfies then g is a polynomial; conversely, for any δ>0 there exists an entire transcendental function g(z) satisfying the display conditin and t(g)<θs+δ. The result θ1=log2 is known due to Hardy and Pólya. We provide the upper bound θsπs/3 and improve earlier lower bounds due to Gelfond (1929) and Selberg (1941). 相似文献
107.
Qifan Zhang 《Journal of Number Theory》2004,105(1):192-202
We extend some classical results on polynomial functions . We prove all results in algebraic methods avoiding any combinatorial calculation. As applications of our methods, we obtain some interesting new results on permutation polynomials in several variables over some finite commutative rings. 相似文献
108.
A.G. Kartsatos 《Journal of Mathematical Analysis and Applications》2004,290(1):76-85
The main purpose of this work is to obtain blow-up results for solutions of the inequality
109.
The stable set problem is to find in a simple graph a maximum subset of pairwise non-adjacent vertices. The problem is known to be NP-hard in general and can be solved in polynomial time on some special classes, like cographs or claw-free graphs. Usually, efficient algorithms assume membership of a given graph in a special class. Robust algorithms apply to any graph G and either solve the problem for G or find in it special forbidden configurations. In the present paper we describe several efficient robust algorithms, extending some known results. 相似文献
110.
We make a conjecture that the number of isolated local minimum points of a 2n-degree or (2n+1)-degree r-variable polynomial is not greater than n
r when n 2. We show that this conjecture is the minimal estimate, and is true in several cases. In particular, we show that a cubic polynomial of r variables may have at most one local minimum point though it may have 2r critical points. We then study the global minimization problem of an even-degree multivariate polynomial whose leading order coefficient tensor is positive definite. We call such a multivariate polynomial a normal multivariate polynomial. By giving a one-variable polynomial majored below a normal multivariate polynomial, we show the existence of a global minimum of a normal multivariate polynomial, and give an upper bound of the norm of the global minimum and a lower bound of the global minimization value. We show that the quartic multivariate polynomial arising from broad-band antenna array signal processing, is a normal polynomial, and give a computable upper bound of the norm of the global minimum and a computable lower bound of the global minimization value of this normal quartic multivariate polynomial. We give some sufficient and necessary conditions for an even order tensor to be positive definite. Several challenging questions remain open. 相似文献