Energy Decay for von Kármán-Gurtin-Pipkin System

This paper aims to prove the asymptotic behavior of the solution for the thermo-elastic von Karman system where the thermal conduction is given by Gurtin-Pipkins law. Existence and uniqueness of the solution are proved within the semigroup framework and stability is achieved thanks to a suitable Lyapunov functional.Therefore, the stability result clarified that the solutions energy functional decays exponentially at infinite time.     

Carathéodory-type Theorems à la Bárány

We generalise the famous Helly–Lovász theorem leading to a generalisation of the Bárány–Carathéodory theorem for oriented matroids in dimension ≤3. We also provide a non-metric proof of the latter colourful theorem for arbitrary dimensions and explore some generalisations in dimension 2.     

The von Kármán theory for incompressible elastic shells

We rigorously derive the von Kármán shell theory for incompressible materials, starting from the 3D nonlinear elasticity. In case of thin plates, the Euler-Lagrange equations of the limiting energy functional reduce to the incompressible version of the classical von Kármán equations, obtained formally in the limit of Poisson’s ratio ν → 1/2. More generally, the midsurface of the shell to which our analysis applies, is only assumed to have the following approximation property: ${\mathcal C^3}$ first order infinitesimal isometries are dense in the space of all W ^2,2 infinitesimal isometries. The class of surfaces with this property includes: subsets of ${\mathbb R^2}$ , convex surfaces, developable surfaces and rotationally invariant surfaces. Our analysis relies on the methods and extends the results of Conti and Dolzmann (Calc Var PDE 34:531–551, 2009, Lewicka et al. (Ann. Scuola Norm. Sup. Pisa Cl. Sci. (5) Vol. IX:253–295, 2010, Friesecke et al. (Comm. Pure. Appl. Math. 55, no. 2, 1461–1506, 2002).     

Small Chvátal Rank

We propose a variant of the Chvátal-Gomory procedure that will produce a sufficient set of facet normals for the integer hulls of all polyhedra {x : A x ≤ b} as b varies. The number of steps needed is called the small Chvátal rank (SCR) of A. We characterize matrices for which SCR is zero via the notion of supernormality which generalizes unimodularity. SCR is studied in the context of the stable set problem in a graph, and we show that many of the well-known facet normals of the stable set polytope appear in at most two rounds of our procedure. Our results reveal a uniform hypercyclic structure behind the normals of many complicated facet inequalities in the literature for the stable set polytope. Lower bounds for SCR are derived both in general and for polytopes in the unit cube.     

On a conjecture of Károly Bezdek and János Pach

Summary The following conjecture of K\'aroly Bezdek and J\'anos Pach is cited in~[1]. If <InlineEquation ID=IE"1"><EquationSource Format="TEX"><![CDATA[<InlineEquation ID=IE"2"><EquationSource Format="TEX"><![CDATA[<InlineEquation ID=IE"3"><EquationSource Format="TEX"><![CDATA[<InlineEquation ID=IE"4"><EquationSource Format="TEX"><![CDATA[<InlineEquation ID=IE"5"><EquationSource Format="TEX"><![CDATA[<InlineEquation ID=IE"6"><EquationSource Format="TEX"><![CDATA[$]]></EquationSource></InlineEquation>]]></EquationSource></InlineEquation>]]></EquationSource></InlineEquation>]]></EquationSource></InlineEquation>]]></EquationSource></InlineEquation>]]></EquationSource></InlineEquation>K\subset{\mathbb R}^d$ is a convex body then any packing of pairwise touching positive homothets of $K$ consists of at most $2^d$ copies of $K$. We prove a weaker bound, $2^{d+1}$.     

General páley problem

In the class of functionsu of finite lower order subharmonic in ? ^p+2,p ∈ ? we establish an exact upper bound for $$\mathop {\lim }\limits_{r \to \infty } \inf \frac{{m_q (r,u^ + )}}{{T(r,u)}}, 1< q \le \infty ,$$ whereT(r, u) is a Nevanlinna characteristic of the functionu andm _q (r, u ⁺) is the integralq-mean of the functionu ⁺,u ⁺ = max(u,0), on the sphere of radiusr.     

关于一阶剪切板的Kármán型精化理论

依据Mindlin_Reissner理论 ,着重研究一阶剪切板的K rm n型精化理论 ,并推导出仅以挠度和应力函数为未知变量的广义K rm n型大挠度方程 ,适用于复合材料上复合构造剪切板的非线性分析·　在当前板的精化理论中 ,消去的两个转角以隐含形式作用于板的整体变形·　这一工程理论适用于各种计及横向剪切复合材料板、正交各向异性中厚板和夹层板等的线性和非线性分析·　容易发现 ,针对具体的工程应用 ,由该方程可直接获得相应的退化形式 ,并且与文献所载的一致·     

关于Szász-Mirakjan算子

§1 前言设 C={f∶f∈C[0,∞),存在着 N>0,使得 f(x)=O(x~N)(x→ ∞)}.C~r={f;f~(t)∈C.i=0,1,2,…,r}.Szász-Mirakjan 算子是:S_n(,fx)=(?)f(k/n)P_(nk)(x),P_(nk)(x)=e~(-nx)((nx)~k)/(k!),f∈C设 C_0={f:f∈C[0,∞),(?)(?)类似地定义 C_0~r.在[1]中我们曾证明了:对于C_0 中的函数 f,‖S_n(f)-f‖_c=O(k(f,(?)).若0<α<1,则‖S_n(f)-f‖_e=O(n~(-α)与k(f,t)=O(t~(2α))等价。这里 k(f,t)=inf{‖f-g‖_c t~2‖xg〃‖c‖}.不难类似地证明此结     

Generalized Marguerre-von Kármán Equations for a Nonlinearly Elastic Shallow Shell

Using techniques from asymptotic analysis, we identify equations that generalize the classical Marguerre-von Kármán equations. These more general equations are justified by means of the leading term of a formal asymptotic expansion of the solution to the three-dimensional equations of nonlinear elasticity associated with a specific class of boundary conditions that characterizes "generalized Marguerre-von Kármán shallow shells".     

Znám-Newman结果的改进

本文主要结果如下:设正整数n_0是覆盖函数σ(x)=1周期。如果正整数d不整除n_0但整除某些n_i(1∈i∈r),则n_1…n_r中至少有(d/(d,n_)个是d的倍数,这儿记号(m,n)表示m和n的最大公因数。σ(x)≡1时它改进了著名的Znam—Newman结果,这个改进比Berger、Fellyenbaum和Fraenkel他们的结果要好。     

Two Turán type inequalities

Turán’s book [2], in Section 19.4, refers to the following result of Gábor Halász. Let a ₀, a ₁, ..., a _n−1 be complex numbers such that the roots α ₁, ⋯, α _n of the polynomial x ⁿ + a _n−1 x ⁿ⁻¹ + ⋯ + a ₁ x + a ₀ satisfy min _j Re α _j ≧ 0 and let function Y(t) be a solution of the linear differential equation Y ⁽ⁿ⁾ + a _n−1 Y ⁽ⁿ⁻¹⁾ + ⋯ + a ₁ Y′ + a ₀ Y = 0. Then

ON possible Turán densities

The Turán density π(F) of a family F of k-graphs is the limit as n → ∞ of the maximum edge density of an F-free k-graph on n vertices. Let Π _∞ ^(k) consist of all possible Turán densities and let Π _fin ^(k) ? Π _∞ ^(k) be the set of Turán densities of finite k-graph families. Here we prove that Π _fin ^(k) contains every density obtained from an arbitrary finite construction by optimally blowing it up and using recursion inside the specified set of parts. As an application, we show that Π _fin ^(k) contains an irrational number for each k ≥ 3. Also, we show that Π _∞ ^(k) has cardinality of the continuum. In particular, Π _∞ ^(k) ≠ Π _fin ^(k) .     

Supersaturation For Ramsey-Turán Problems

For an l-graph , the Turán number is the maximum number of edges in an n-vertex l-graph containing no copy of . The limit is known to exist [8]. The Ramsey–Turán density is defined similarly to except that we restrict to only those with independence number o(n). A result of Erdős and Sós [3] states that as long as for every edge E of there is another edge E′of for which |E∩E′|≥2. Therefore a natural question is whether there exists for which . Another variant proposed in [3] requires the stronger condition that every set of vertices of of size at least εn (0<ε<1) has density bounded below by some threshold. By definition, for every . However, even is not known for very many l-graphs when l>2. We prove the existence of a phenomenon similar to supersaturation for Turán problems for hypergraphs. As a consequence, we construct, for each l≥3, infinitely many l-graphs for which . We also prove that the 3-graph with triples 12a, 12b, 12c, 13a, 13b, 13c, 23a, 23b, 23c, abc, satisfies . The existence of a hypergraph satisfying was conjectured by Erdős and Sós [3], proved by Frankl and R?dl [6], and later by Sidorenko [14]. Our short proof is based on different ideas and is simpler than these earlier proofs. * Research supported in part by the National Science Foundation under grants DMS-9970325 and DMS-0400812, and an Alfred P. Sloan Research Fellowship. † Research supported in part by the National Science Foundation under grants DMS-0071261 and DMS-0300529.     

Vámos拟阵的直立

通过利用一个拟阵与它的直立之间的关系,特别是通过处理一个拟阵与一个特殊映射f之间的关系,具体分析了Vámos拟阵的直立问题,得到了除去平凡情形,Vámos拟阵没有直立的结论.从而回答了由Welsh提出"Vámos拟阵是否有直立?"的问题.     

Pták function and symmetry

We investigate subadditivity of Pták function as a sufficient and necessary condition for symmetry in the class of involutive spectrally bounded algebras. Among others it is proved an analogue of Raikov's criterion for complete lmc^*-algebras in which the hermitian elements have finite spectral radius. This paper is based on the author's Doctoral Thesis, University of Athens, written under the supervision of Professor M. Fragoulopoulou.     

Optimización robusta en aplicaciones aeronáuticas con la combinación de cálculo estocástico y algoritmos evolutivos

Uncertainties are a daily issue to deal with in aerospace engineering and applications. Robust optimization methods commonly use a random generation of the inputs and take advantage of multi-point criteria to look for robust solutions accounting with uncertainty definition. From the computational point of view, the application to coupled problems, like fluid-dynamics (CFD) or fluid-structure interaction (FSI), can be extremely expensive. This work presents a coupling between stochastic analysis techniques and evolutionary optimization algorithms for the definition of a stochastic robust optimization procedure. At first, a stochastic procedure is proposed to be applied into optimization problems. The proposed method has been applied to both CFD and FSI problems for the reduction of drag and flutter, respectively.     

Generalized Szász-Mirakjan Operator Approximation

In this paper we shall defin a kind of generahzed Szász-Mirakjan operator and discussits convergence and degree of approximation,extend some results got by J.Grof and Z.Ditzian.