关于图中控制数γ_L,γ_t的关系

G(V,E)是一个图且D V,如果N[D]=V,则称D为图G的控制集.进一步,对任一个控制集D1而言均有γ(〈D〉)≤γ(〈D1〉)成立,则称D为图G的小控制集,且小控制数γL(G)=min{|D|:D V且D是G的一个小控制集}.如果点集S V, X∈V均有N(X)∩S≠ 或∪N(x)=V,则称S为图G的全控制集,且全控制数γt(G)=min{|S|:S是G的一个全控制集}.x∈S本文证明:在树T中如果阶n≥2,则有γL(T)≤32γt(T)-1.

On the Total Domination Number of Graphs with Minimum Degree at Least Three

Let G be a simple graph with no isolated vertices. A set S of vertices of G is a total dominating set if every vertex of G is adjacent to some vertex in S . The total domination number of G , denoted by γ t (G) , is the minimum cardinality of a total dominating set of G . It is shown that if G is a graph of order n with minimum degree at least 3, then γ t (G)≤n/2 . Thus a conjecture of Favaron, Henning, Mynhart and Puech is settled in the affirmative.

APPLICATION OF WAVE LETS TO OPTIMAL SHOCK AND IMPACT ISOLATION

The limiting performa nce analysis is used to study the optimal shock and impact isolation of mechanic al systems. The use of wavelets to approximate time-domain control functions is investigated. The formulation for numerical computation is developed. Numerical examples include the optimal shock isolation of a SDOF system and the optimal i mpact isolation of a MDOF system. Computational results show that compactly supp orted wavelets can represent abrupt changes in control functions better than tri gonometric series and considerably increase computational efficiency.

Numerical Minimum Time Control to a Class of Singular Integro-Differential Equations

This study presents a numerical method for determining the minimum time required for the states of one class of integro-differential equations of the first kind to reach its attainable region by assuming the forcing terms of the equations as controls. These equations consist of integro-differential parts containing weakly singular kernels. The feasibility of the numerical method is demonstrated by comparing the minimum time and corresponding possible time by using extreme controls to reach the attainable region under different initial conditions.

High-resolution anisotropy of magnetic susceptibility record in the central Chinese Loess Plateau and its paleoenvironment implications

We analyze high-resolution anisotropy of magnetic susceptibility (AMS) of the loess-paleosol successions at Luochuan, central Chinese Loess Plateau, in order to investigate the AMS characteristics and their climatic implications. Our results indicate a normal sedimentary magnetic fabric for almost of all samples, characterized by minimum susceptibility axes grouped in an almost vertical direction. Magnetic foliation and anisotropy degree show upwards decreasing trend due to decreasing post-depositional compaction. Magnetic lineations show no preferred directions and thus cannot indicate paleowind patterns. AMS parameters at Luochuan are controlled by particle size, pedogenesis, and sedimentary compaction. The high peaks of magnetic foliation and anisotropy degree of L2, L3, L6, L9, and L15 correspond to the coarse particle sizes of these loess beds, indicating the grain-size dependence of AMS.

Effect of Winglet Geometry Arrangement and Incidence on Tip Clearance Control in a Compressor Cascade

An experimental study is conducted to investigate the influences of blade tip winglet on the flow field of a compressor cascade. The tests are performed in a low speed linear cascade with stationary endwall, with three blade tip configurations, including the baseline tip, the suction-side winglet tip and the pressure-side winglet tip. The fiowfield downstream of the cascade is measured using five-hole probe, from which the three-dimensional velocity field, vorticity field and pressure field are obtained. Static pressure measurements are made on the endwall above the blade row using pressure taps embedded in the plywood endwall. All measurements are made at both design and off-design conditions for tip clearance level of about 2 percent of the blade chord. The results revealed the incidence variation significantly affects the secondary flow and the associated loss field downstream of the cascade, where the tip leakage vortex and passage vortex exist as the major contributors on the field. The winglet geometry arrangements can change the trajectory of the tip leakage vortex. The suction-side winglet tip blade provides a lower overall total pressure loss coefficient when compared to the baseline tip blade and pressure-side winglet tip blade at all incidence angles.