This paper describes the airliner wing flutter sensitivity analysis. The sensitivity coefficients define the influence of the structural parameter changes to tthe structure eigenvalue and flutter stability characteristics. Evaluated structural parameters represent the possible changes of the structure due to the installation of the smart high-lift devices at the leading and trailing edge region. In general, we can suppose the increasing of the mass and mass moment of inertia around the elastic axis and decreasing of the stiffness. Described effects are ordinarily considered destabilizing regarding the flutter. The main aim of the presented work is to evaluate the impact of components to the stability and to define the most critical regions or parameters. and Obsahuje seznam literatury
The paper presents an iterative algorithm for computing the maximum cycle mean (or eigenvalue) of n×n triangular Toeplitz matrix in max-plus algebra. The problem is solved by an iterative algorithm which is applied to special cycles. These cycles of triangular Toeplitz matrices are characterized by sub-partitions of n−1.
We consider quasirandom properties for Cayley graphs of finite abelian groups. We show that having uniform edge-distribution (i.e., small discrepancy) and having large eigenvalue gap are equivalent properties for such Cayley graphs, even if they are sparse. This affirmatively answers a question of Chung and Graham (2002) for the particular case of Cayley graphs of abelian groups, while in general the answer is negative., Yoshiharu Kohayakawa, Vojtěch Rödl, Mathias Schacht., and Obsahuje seznam literatury
Let $G$ be a connected simple graph on $n$ vertices. The Laplacian index of $G$, namely, the greatest Laplacian eigenvalue of $G$, is well known to be bounded above by $n$. In this paper, we give structural characterizations for graphs $G$ with the largest Laplacian index $n$. Regular graphs, Hamiltonian graphs and planar graphs with the largest Laplacian index are investigated. We present a necessary and sufficient condition on $n$ and $k$ for the existence of a $k$-regular graph $G$ of order $n$ with the largest Laplacian index $n$. We prove that for a graph $G$ of order $n \geq 3$ with the largest Laplacian index $n$, $G$ is Hamiltonian if $G$ is regular or its maximum vertex degree is $\triangle (G)=n/2$. Moreover, we obtain some useful inequalities concerning the Laplacian index and the algebraic connectivity which produce miscellaneous related results.
We consider the Robin eigenvalue problem ∆u + λu = 0 in Ω, ∂u/∂ν + αu = 0 on ∂Ω where Ω ⊂ R n , n > 2 is a bounded domain and α is a real parameter. We investigate the behavior of the eigenvalues λk(α) of this problem as functions of the parameter α. We analyze the monotonicity and convexity properties of the eigenvalues and give a variational proof of the formula for the derivative λ ′ 1 (α). Assuming that the boundary ∂Ω is of class C 2 we obtain estimates to the difference λ D k −λk(α) between the k-th eigenvalue of the Laplace operator with Dirichlet boundary condition in Ω and the corresponding Robin eigenvalue for positive values of α for every k = 1, 2, . . ..
The He matrix, put forward by He and He in 1989, is designed as a means for uniquely representing the structure of a hexagonal system (= benzenoid graph). Observing that the He matrix is just the adjacency matrix of a pertinently weighted inner dual of the respective hexagonal system, we establish a number of its spectral properties. Afterwards, we discuss the number of eigenvalues equal to zero of the He matrix of a hexagonal system. Moreover, we obtain a relation between the number of triangles and the eigenvalues of the He matrix of a hexagonal system. Finally, we present an upper bound on the He energy of hexagonal systems.
Let $G$ be a finite graph with an eigenvalue $\mu $ of multiplicity $m$. A set $X$ of $m$ vertices in $G$ is called a star set for $\mu $ in $G$ if $\mu $ is not an eigenvalue of the star complement $G\setminus X$ which is the subgraph of $G$ induced by vertices not in $X$. A vertex subset of a graph is $(\kappa ,\tau )$-regular if it induces a $\kappa $-regular subgraph and every vertex not in the subset has $\tau $ neighbors in it. We investigate the graphs having a $(\kappa ,\tau )$-regular set which induces a star complement for some eigenvalue. A survey of known results is provided and new properties for these graphs are deduced. Several particular graphs where these properties stand out are presented as examples.
In this paper we derive new properties complementary to an $2n \times 2n$ Brualdi-Li tournament matrix $B_{2n}$. We show that $B_{2n}$ has exactly one positive real eigenvalue and one negative real eigenvalue and, as a by-product, reprove that every Brualdi-Li matrix has distinct eigenvalues. We then bound the partial sums of the real parts and the imaginary parts of its eigenvalues. The inverse of $B_{2n}$ is also determined. Related results obtained in previous articles are proven to be corollaries.
The distance Laplacian of a connected graph $G$ is defined by $\mathcal {L} = {\rm Diag(Tr)}- \mathcal {D}$, where $\mathcal {D}$ is the distance matrix of $G$, and ${\rm Diag(Tr)}$ is the diagonal matrix whose main entries are the vertex transmissions in $G$. The spectrum of $\mathcal {L}$ is called the distance Laplacian spectrum of $G$. In the present paper, we investigate some particular distance Laplacian eigenvalues. Among other results, we show that the complete graph is the unique graph with only two distinct distance Laplacian eigenvalues. We establish some properties of the distance Laplacian spectrum that enable us to derive the distance Laplacian characteristic polynomials for several classes of graphs.
The inertia of an $n$ by $n$ symmetric sign pattern is called maximal when it is not a proper subset of the inertia of another symmetric sign pattern of order $n$. In this note we classify all the maximal inertias for symmetric sign patterns of order $n$, and identify symmetric sign patterns with maximal inertias by using a rank-one perturbation.