39356858
Vertex-disjoint quadrilaterals in graphs
Let k be a positive integer and G a graph of order n. In (Discrete Math. 203 (1999) 229), we proved that if n=4k and @d(G)>=2k then G contains k-1 vertex-disjoint quadrilaterals. In this paper, we investigate vertex-disjoint quadrilaterals in G with n@?0(mod4), and we have found the best minimum degree condition @d(G)>=@?12n@? such that G contains @?14n@? vertex-disjoint quadrilaterals. As a result of our method, we have improved our previous result as follows: If n=4k and @d(G)>=2k-1 then G contains k-1 vertex-disjoint quadrilaterals.
206077177
Pentagons and cycle coverings
Let G be a graph of order n ≥ 5k + 2, where k is a positive integer. Suppose that the minimum degree of G is at least (n + k)/2 . We show that G contains k pentagons and a path such that they are vertexdisjoint and cover all the vertices of G. Moreover, if n ≥ 5k + 7, then G contains k + 1 vertex-disjoint cycles covering all the vertices of G such that k of them are pentagons. © 2006 Wiley Periodicals, Inc. J Graph Theory 54: 194–208, 2007
10626
All trees contain a large induced subgraph having all degrees 1 (mod k)
We prove that, for integers n ? 2 and k ? 2, every tree with n vertices contains an induced subgraph of order at least 2?(n + 2k ? 3)/(2k ? 1)? with all degrees congruent to 1 modulo k. This extends a result of Radcliffe and Scott, and answers a question of Caro et al.
36844780
Partition of a directed bipartite graph into two directed cycles
Abstract Let D = (V1, V2; A) be a directed bipartite graph with |V1| = |V2| = n ⩾ 2. Suppose that dD(x) + dD(y) ⩾ 3n + 1 for all x ϵ V1 and y ϵ V2. Then D contains two vertex-disjoint directed cycles of lengths 2n1 and 2n2, respectively, for any positive integer partition n = n1 + n2. Moreover, the condition is sharp for even n and nearly sharp for odd n.
36127171
Packing Three Copies of a Tree into a Complete Graph
Abstract A three T of order n is said to be 3-placeable if there are three edge-disjoint copies of T in Kn. In this paper we characterize all the trees T such that T is 3-placeable.
12358667
On Covering a Bipartite Graph with Cycles
We conjectured in [H. Wang, Australas. J. Combin., 19 (1999), pp. 115--121] that, for each integer $k\geq 2$, there exists N(k) such that if G=(V1,V2;E) is a bipartite graph with $|V_1|=|V_2|=n\geq N(k)$ and d(x)+d(y)\geq n+k$ for each pair of nonadjacent vertices x and y of G with $x\in V_1$ and $y\in V_2$, then for any k independent edges e1, . . ., ek of G, there exist k vertex-disjoint cycles C1, . . . ,Ck in G such that $e_i\in E(C_i)$ for all $i\in\{1,\ldots ,k\}$ and $V(C_1\cup\cdots \cup C_k)=V(G)$. This conjecture is also verified for k=2 in [H. Wang, Australas. J. Combin., 19 (1999), pp. 115--121]. We prove this conjecture for k=3 in this paper.
9557765
An ILC-Based Adaptive Control for General Stochastic Systems With Strictly Decreasing Entropy
In this paper, a new method for adaptive control of general nonlinear and non-Gaussian unknown stochastic systems has been proposed. The method applies the minimum entropy control scheme to decrease the closed-loop randomness of the output under an iterative learning control (ILC) basis. Both modeling and control of the plant are performed using dynamic neural networks. For this purpose, the whole control horizon is divided into a certain number of time domain subintervals called batches and a pseudo-D-type ILC law is employed to train the plant model and controller parameters so that the entropy of the closed-loop tracking error is made to decrease batch by batch. The method has the advantage of decreasing the output uncertainty versus the advances of batches along the time horizon. The analysis on the proposed ILC convergence is made and a set of demonstrable experiment results is also provided to show the effectiveness of the obtained control algorithm, where encouraging results have been obtained.
19553072
Direct solution of the parametric Stochastic Distribution Control problem
The Stochastic Distribution Control (SDC) problem is a generalised form of the minimum variance control problem where non-Gaussian noise distributions are encountered. The problem has been previously solved using two alternative approaches. When it is assumed that the output Probability Distribution Function (PDF) is measurable, then a parameterized controller is obtained. If on the other hand this assumption is removed (which corresponds to most practical cases), then the controller found is no longer parameterisable (i.e. it is a control action sequence). Both these approaches have thus far been solved using local Newtonian methods. In this paper a third alternative is presented which combines the desirable features of the previous two methods by finding a parameterized controller, without having to assume that the output PDF is directly measurable at the same time. In addition, global direct search algorithms are used to avoid convergence to local solutions. The approach is demonstrated on a SISO nonlinear system corrupted by non-Gaussian input noise.
7692886
Memory latency-tolerance approaches for Itanium processors: out-of-order execution vs. speculative precomputation
The performance of in-order execution Itanium/sup TM/ processors can suffer significantly due to cache misses. Two memory latency tolerance approaches can be applied for the Itanium processors. One uses an out-of-order (OOO) execution core; the other assumes multithreading support and exploits cache prefetching via speculative precomputation (SP). This paper evaluates and contrasts these two approaches. In addition, this paper assesses the effectiveness of combining the two approaches. For a select set of memory-intensive programs, an in-order SMT Itanium processor using speculative precomputation can achieve performance improvement (92%) comparable to that of an out-of-order design (87%). Applying both 000 and SP yields a total performance improvement of 141% over the baseline in-order machine. OOO tends to be effective in prefetching-for L1 misses; whereas SP is primarily good at covering L2 and L3 misses. Our analysis indicates that the two approaches can be redundant or complementary depending on the type of delinquent loads that each targets. Both approaches are effective on delinquent loads in the loop body; however only SP is effective on delinquent loads found in loop control code.
7007458
An Algorithm for Identification of Reduced-Order Dynamic Models of Gas Turbines
Model based approaches show a lot of advantages for fault detection and condition monitoring. Particularly, it is true in employing reduced order models for real-time parameter identification and output prediction of gas turbines. Many algorithms have been developed, but most of them focus on one-step-ahead prediction models and involve complex computation. These algorithms are not acceptable for long-term prediction and real-time condition monitoring. In this paper, an improved gradient method (dynamic gradient descent) is proposed. The idea is to take account of the dependency of prediction errors and calculate the gradient information recursively. Not only low computation expense is achieved, but the non-Gaussian errors can also be overcome when this approach is applied to estimate parameters of a reduced order gas turbine model and to improve long-term prediction
5894314
Sensor fault estimator and its application for linear multi-variable dynamic systems with delayed state and input
For systems with multiple time delays, a novel state and sensor noise observer is designed to estimate system states and sensor noises at the same time. In this design, descriptor system approach and linear matrix inequality technique are adopted. Unbounded sensor faults will make the system fail unavoidably, it is indispensable to derive a reliable control scheme against sensor failures. Using the estimated state and sensor fault, a fault-tolerant observer-based controller is proposed, which makes the system work well not matter whether sensor faults occur or not.