The metamorphosis of lambda-fold 4-wheel systems into lambda-fold 4-cycle systems

A 4-wheel is a simple graph on 5 vertices with 8 edges, formed by taking a 4-cycle and joining a fifth vertex (the centre of the 4-wheel) to each of the other four vertices. A lambda -fold 4-wheel system of order n is an edge-disjoint decomposition of the complete multigraph lambdaK(n) into 4-wheels. Here, with five isolated possible exceptions when lambda = 2, we give necessary and sufficient conditions for a lambda -fold 4-wheel system of order n to be transformed into a lambda -fold Ccyde system of order n by removing the centre vertex from each 4-wheel, and its four adjacent edges (retaining the 4-cycle wheel rim), and reassembling these edges adjacent to wheel centres into 4-cycles.

On the volume of 4-cycle trades

A 4-cycle trade of volume t corresponds to a simple graph G without isolated vertices, where the edge set can be partitioned into t 4-cycles in at least two different ways such that the two collections of 4-cycles have no 4-cycles in common. The foundation of the trade is v = \V(G)\. This paper determines for which values oft and a there exists a 4-cycle trade of volume t and foundation v.

Operator, organizational, direct and general support maintenance manual : delousing outfit, power driven; gasoline engine, 4-cycle, air-cooled, 3600 RPM, 4.7 HP; 10 dusting guns, (Curtis Automotive Devices, Inc. model CDR 70000), FSN 4230-078-5455, (Curtis Dyna-Products Corporation model CDR 70000B), FSN 4230-935-9361.

Includes index.

Organizational, direct, and general support maintenance repair parts and special tools list : delousing outfit, power driven, gasoline engine, 4 cycle, air cooled, 3600 rpm, 4.7 hp, 10 dusting guns (Curtis Automotive Devices, Inc model CDR 70,000), FSN 4230-078-5455 ....

"December 1970."

Common multiples of complete graphs and a 4-cycle

A graph G is a common multiple of two graphs H-1 and H-2 if there exists a decomposition of G into edge-disjoint copies of H-1 and also a decomposition of G into edge-disjoint copies of H-2. In this paper, we consider the case where H-1 is the 4-cycle C-4 and H-2 is the complete graph with n vertices K-n. We determine, for all positive integers n, the set of integers q for which there exists a common multiple of C-4 and K-n having precisely q edges. (C) 2003 Elsevier B.V. All rights reserved.

Configurations in 4-cycle systems

A 4-cycle system of order n, denoted by 4CS(n), exists if and only if nequivalent to1 (mod 8). There are four configurations which can be formed by two 4-cycles in a 4CS(n). Formulas connecting the number of occurrences of each such configuration in a 4CS(n) are given. The number of occurrences of each configuration is determined completely by the number d of occurrences of the configuration D consisting of two 4-cycles sharing a common diagonal. It is shown that for every nequivalent to1 (mod 8) there exists a 4CS(n) which avoids the configuration D, i.e. for which d=0. The exact upper bound for d in a 4CS(n) is also determined.

Embedding partial G-designs where G is a 4-cycle with a pendant edge

Let D denote the graph consisting of a cycle of length 4 with a pendant edge. In this paper, two very different small embeddings of partial D-designs are presented. (c) 2005 Elsevier B.V. All rights reserved.

Decomposition of complete tripartite graphs into gregarious 4-cycles

A 4-cycle in a tripartite graph with vertex partition {V-1, V-2, V-3} is said to be gregarious if it has at least one vertex in each V-i, 1 less than or equal to i less than or equal to 3. In this paper, necessary and sufficient conditions are given for the existence of an edge-disjoint decomposition of any complete tripartite graph into gregarious 4-cycles.

Packing lambda-fold complete multipartite graphs with 4-cycles

A maximum packing of any lambda-fold complete multipartite graph (where there are lambda edges between any two vertices in different parts) with edge-disjoint 4- cycles is obtained and the size of each minimum leave is given. Moreover, when lambda =2, maximum 4-cycle packings are found for all possible leaves.

Períodos críticos de défices hídricos em cultivares de cevada (Hordeum vulgare L.)

Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq)

Long-term outcome of ablative therapy of postoperative supraventricular tachycardias in patients with univentricular heart: a European multicenter study

BACKGROUND: Catheter ablation has evolved as a possible curative treatment modality for supraventricular tachycardias (SVT) in patients with univentricular heart. However, the long-term outcome of ablation procedures is unknown. We evaluated the procedural and long-term outcome of ablative therapy of late postoperative SVT in patients with univentricular heart. METHODS AND RESULTS: Patients with univentricular heart (n=19, 11 male; age, 29+/-9 years) referred for ablation of SVT were studied. Ablation was guided by 3D electroanatomic mapping in all but 2 procedures. A total of 41 SVT were diagnosed as intra-atrial reentrant tachycardia (n=30; cycle length, 310+/-68 ms), typical atrial flutter (n=4; cycle length, 288+/-42 ms), focal atrial tachycardia (n=6; cycle length, 400+/-60 ms), and atrial fibrillation (n=1). Ablation was successful in 73% of intra-atrial reentrant tachycardia, 75% of atrial flutter, and all focal atrial tachycardia and focal atrial fibrillation. During the follow-up period of 53+/-34 months, 2 patients were lost to follow-up, 3 died of heart failure, 2 underwent heart transplantation, and 1 underwent conduit replacement. Of the remaining group, 8 had sinus rhythm and 3 had SVT. CONCLUSIONS: Focal and reentrant mechanisms underlie postoperative SVT in patients with univentricular heart. Successive SVT developing over time may be caused by different mechanisms. Ablative therapy is potentially curative, with a procedural success rate of 78%. In patients who had multiple ablation procedures, the SVT originated from different atrial sites, suggesting that these new SVT were caused by progressive atrial disease. Despite recurrent SVT, sinus rhythm at the end of the follow-up period was achieved in 72%.

2-perfect directed m-cycle systems can be equationally defined for m=3,4, and 5 only

It is shown that quasigroups constructed using the standard construction from 2-perfect directed m-cycle systems are precisely the finite members of a variety if and only if m=3, 4 or 5.