Reachable set bounding for nonlinear perturbed time-delay systems: The smallest bound

In this letter, we propose a new approach to obtain the smallest box which bounds all reachable sets of a class of nonlinear time-delay systems with bounded disturbances. A numerical example is studied to illustrate the obtained result.     

Spectrum is periodic for n-intervals

In this paper we study spectral sets which are unions of finitely many intervals in R. We show that any spectrum associated with such a spectral set Ω is periodic, with the period an integral multiple of the measure of Ω. As a consequence we get a structure theorem for such spectral sets and observe that the generic case is that of the equal interval case.     

Regular saturated graphs and sum-free sets

In a recent paper, Gerbner, Patkós, Tuza and Vizer studied regular F-saturated graphs. One of the essential questions is given F, for which n does a regular n-vertex F-saturated graph exist. They proved that for all sufficiently large n, there is a regular $K_3$-saturated graph with n vertices. We extend this result to both $K_4$ and $K_5$ and prove some partial results for larger complete graphs. Using a variation of sum-free sets from additive combinatorics, we prove that for all $k\ge 2$, there is a regular $C_{2k+1}$-saturated with n vertices for infinitely many n. Studying the sum-free sets that give rise to $C_{2k+1}$-saturated graphs is an interesting problem on its own and we state an open problem in this direction.     

Structural, electronic and optical properties of SrCl2 under hydrostatic stress

The results of first-principles theoretical study of the structural, electronic and optical properties of SrCl₂ in its cubic structure, have been performed using the full-potential linear augmented plane-wave method plus local orbitals (FP-APW+lo) as implemented in the WIEN2k code. In this approach both the local density approximation (LDA) and the generalized gradient approximation (GGA) are used for the exchange-correlation (XC) potential. Also we have used the Engel-Vosko GGA formalism, which optimizes the corresponding potential for band structure calculations. We performed these calculations with and without spin-orbit interactions. Including spin-orbit coupling cause to lifts the triple degeneracy at Γ point and a double degeneracy at X point. Results are given for structural properties. The pressure dependence of elastic constants and band gaps are investigated. The dielectric function, reflectivity spectra and refractive index are calculated up to 30 eV. Also we calculated the pressure and volume dependence of the static optical dielectric constant.     

Gradient control and synchronization of Julia sets

This paper firstly introduces the control methods to fractals and give the definition of synchronization of Julia sets between two different systems. Especially, the gradient control method is taken on the classic Julia sets of complex quadratic polynomial Zn＋1 = zn^2＋ c, which realizes its Julia sets control and synchronization. The simulations illustrate the effectiveness of the method.     

复系统Julia集的同步

非线性系统中的分形集——Julia集, 在工程技术中有着十分重要的应用,定义了不同系统间的Julia集同步的概念, 并引入一种非线性耦合的方法, 对同一系统不同参数的Julia集进行了有效的同步.并以多项式形式和三角函数形式的Julia集同步为例验证了该方法的有效性.     

基于粗糙集与小波变换的图像融合算法

粗糙集理论是处理不确定性问题的数学方法，本文提出了基于粗糙集与小波变换相结合的图像融合算法。该方法首先将粗糙集理论应用于图像滤波中，对含有椒盐噪声的图像进行粗糙中值滤波，然后对滤波后的图像进行小波融合。实验结果表明，粗糙中值滤波有较强的去噪能力，且较好地保持了图像的细节信息，在此基础上进行小波融合，使得融合结果图像具有良好的效果。     

Enveloppes convexes des processus gaussiens

Let X={X(t), t[0,1]} be a process on [0,1] and V_X=Conv{(t,x)t[0,1], x=X(t)} be the convex hull of its path.The structure of the set ext(V_X) of extreme points of V_X is studied. For a Gaussian process X with stationary increments it is proved that:

• The set ext(V_X) is negligible if X is non-differentiable.

• If X is absolutely continuous process and its derivative X′ is continuous but non-differentiable, then ext(V_X) is also negligible and moreover it is a Cantor set.

It is proved also that these properties are stable under the transformations of the type Y(t)=f(X(t)), if f is a sufficiently smooth function.     

On Clique-Transversals and Clique-Independent Sets

A clique-transversal of a graph G is a subset of vertices intersecting all the cliques of G. A clique-independent set is a subset of pairwise disjoint cliques of G. Denote by _C (G) and _C (G) the cardinalities of the minimum clique-transversal and maximum clique-independent set of G, respectively. Say that G is clique-perfect when _C (H)= _C (H), for every induced subgraph H of G. In this paper, we prove that every graph not containing a 4-wheel nor a 3-fan as induced subgraphs and such that every odd cycle of length greater than 3 has a short chord is clique-perfect. The proof leads to polynomial time algorithms for finding the parameters _C (G) and _C (G), for graphs belonging to this class. In addition, we prove that to decide whether or not a given subset of vertices of a graph is a clique-transversal is Co-NP-Complete. The complexity of this problem has been mentioned as unknown in the literature. Finally, we describe a family of highly clique-imperfect graphs, that is, a family of graphs G whose difference _C (G)– _C (G) is arbitrarily large.     

Stability of Julia sets for a quadratic random dynamical system

For a sequence (cⁿ) of complex numbers, the quadratic polynomials f_cn:= z² + C_n and the sequence (F_n) of iterates F_n: = f_cn ο ⋯ ο f_c1 are considered. The Fatou set F(C_n) is defined as the set of all such that (Fⁿ) is normal in some neighbourhood of z, while the complement J(C_n) of F(c_n) (in ) is called the Julia set. The aim of this paper is to study the stability of the Julia set J(C_n) in the case where (c_n) is bounded. A problem put forward by Brück is solved.