Dynamic Morse decompositions for semigroups of homeomorphisms and control systems

In this paper, we introduce the concept of dynamic Morse decomposition for an action of a semigroup of homeomorphisms. Conley has shown in [5, Sec. 7] that the concepts of Morse decomposition and dynamic Morse decompositions are equivalent for flows in metric spaces. Here, we show that a Morse decomposition for an action of a semigroup of homeomorphisms of a compact topological space is a dynamic Morse decomposition. We also define Morse decompositions and dynamic Morse decompositions for control systems on manifolds. Under certain condition, we show that the concept of dynamic Morse decomposition for control system is equivalent to the concept of Morse decomposition.

On the variations of the Betti numbers of regular levels of Morse flows

We generalize results in Cruz and de Rezende (1999) [7] by completely describing how the Beth numbers of the boundary of an orientable manifold vary after attaching a handle, when the homology coefficients are in Z, Q, R or Z/pZ with p prime. First we apply this result to the Conley index theory of Lyapunov graphs. Next we consider the Ogasa invariant associated with handle decompositions of manifolds. We make use of the above results in order to obtain upper bounds for the Ogasa invariant of product manifolds. (C) 2011 Elsevier B.V. All rights reserved.

3,5-cycle decompositions

For all odd integers n and all non-negative integers r and s satisfying 3r + 5s = n(n -1)/2 it is shown that the edge set of the complete graph on n vertices can be partitioned into r 3-cycles and s 5-cycles. For all even integers n and all non-negative integers r and s satisfying 3r + 5s = n(n-2)/2 it is shown that the edge set of the complete graph on n vertices with a 1-factor removed can be partitioned into r 3-cycles and s 5-cycles. (C) 1998 John Wiley & Sons, Inc.

Decompositions of complete multipartite graphs into cycles of even length

Necessary and sufficient conditions for the existence of an edge-disjoint decomposition of any complete multipartite graph into even length cycles are investigated. Necessary conditions are listed and sufficiency is shown for the cases when the cycle length is 4, 6 or 8. Further results concerning sufficiency, provided certain small decompositions exist, are also given for arbitrary even cycle lengths.

Phylogeny of Grumichellini Morse, 1981 (Trichoptera: Leptoceridae) with the description of a new genus from southeastern Peru

Osflintia manu, new genus, new species, of long-horned caddisfly (Leptoceridae: Triplectidinae: Grumichellini) is described and illustrated from southeastern Peru. The phylogeny of Grumichellini Morse (Leptoceridae: Triplectidinae) is revisited and hypotheses of homology of some morphological characters are reconsidered. The monophyly of the tribe is corroborated and the phylogenetic relationships of its included genera are inferred to be (Triplexa (Gracilipsodes ((Grumichella, Amazonatolica) (Atanatolica, Osflintia, n. gen.)))) from adult and larval characters. Diagnostic characters of the new genus include the following: reduced tibial spur formula (2, 2, 2), loss of forewing crossvein sc-r1, hind wing discoidal cell closed, hind wing fork IV present, pair of long setae on tergum IX of the male genitalia, and pair of processes on the apex of segment X.

d-cube decompositions of K-n/K-m

Necessary conditions on n, m and d are given for the existence of an edge-disjoint decomposition of K-n\K-m into copies of the graph of a d-dimensional cube. Sufficiency is shown when d = 3 and, in some cases, when d = 2(t). We settle the problem of embedding 3-cube decompositions of K-m into 3-cube decompositions of K-n; where n greater than or equal to m.

Star decompositions of cubes

Let Sk denote the complete bipartite graph K-1k and let e,, denote the ii-cube. We prove that the obvious necessary conditions for the existence of an S-k-decomposition of Q(n) are sufficient.

Photoelastic Stress Analysis of Different Designs of Cement-Retained Fixed Partial Dentures on Morse Taper Oral Implants

There is no consensus in literature regarding the best plan for prosthetic rehabilitation with partial multiple adjacent implants to minimize stress generated in the bone-implant interface. The aim of this study was to evaluate the biomechanical behavior of cemented fixed partial dentures, splinted and nonsplinted, on Morse taper implants and with different types of coating material (ceramic and resin), using photoelastic stress analysis. A photoelastic model of an interposed edentulous space, missing a second premolar and a first molar, and rehabilitated with 4 different types of cemented crowns and supported by 2 adjacent implants was used. Groups were as follows: UC, splinted ceramic crowns; IC, nonsplinted ceramic crowns; UR, splinted resin crowns; and IR, nonsplinted resin crowns. Different vertical static loading conditions were performed: balanced occlusal load, 10 kgf; simultaneous punctiform load on the implanted premolar and molar, 10 kgf; and alternate punctiform load on the implanted premolar and molar, 5 kgf. Changes in stress distribution were analyzed in a polariscope, and digital photographs were taken of each condition to allow comparison of stress pattern distribution around the implants. Cementation of the fixed partial dentures generated stresses between implants. Splinted restorations distributed the stresses more evenly between the implants than nonsplinted when force was applied. Ceramic restorations presented better distribution of stresses than resin restorations. Based on the results obtained, it was concluded that splinted ceramic restorations promote better stress distribution around osseointegrated implants when compared with nonsplinted crowns; metal-ceramic restorations present less stress concentration and magnitude than metal-plastic restorations.

Influence of interimplant distances and placement depth on peri-implant bone remodeling of adjacent and immediately loaded Morse cone connection implants: a histomorphometric study in dogs

Objectives The aim of this study was to histomorphometrically evaluate the influence of interimplant distances (ID) and implant placement depth on bone remodeling around contiguous Morse cone connection implants with `platform-shifting` in a dog model. Material and methods Bilateral mandibular premolars of six dogs were extracted, and after 12 weeks, each dog received 8 implants, four placed 1.5 mm subcrestally (SCL) on one side of the mandible and four placed equicrestally (ECL) on the other side, alternating the ID of 2 and 3 mm. The experimental groups were SCL with IDs of 2 mm (2 SCL) and 3 mm (3 SCL) and ECL with IDs of 2 mm (2 ECL) and 3 mm (3 ECL). Metallic crowns were immediately installed. After 8 weeks, the animals were euthanized and histomorphometric analyses were performed to compare bone remodeling in the groups. Results The SCL groups` indices of crestal bone resorption were significantly lower than those of ECL groups. In addition, the vertical bone resorption around the implants was also numerically inferior in the SCL groups, but without statistical significance. No differences were obtained between the different IDs. All the groups presented similar good levels of bone-to-implant contact and histological bone density. Conclusion The subcrestal placement of contiguous Morse cone connection implants with `platform shifting` was more efficient in preserving the interimplant crestal bone. The IDs of 2 and 3 mm did not affect the bone remodeling significantly under the present conditions. To cite this article:Barros RRM, Novaes AB Jr., Muglia VA, Iezzi G, Piattelli A. Influence of interimplant distances and placement depth on peri-implant bone remodeling of adjacent and immediately loaded Morse cone connection implants: a histomorphometric study in dogs.Clin. Oral Impl. Res. 21, 2010; 371-378.doi: 10.1111/j.1600-0501.2009.01860.x.

Further decompositions of complete tripartite graphs into 5-cycles

Let K(r,s,t) denote the complete tripartite graph with partite sets of sizes r, s and t, where r less than or equal to s less than or equal to t. Necessary and sufficient conditions are given for decomposability of K(r, s, t) into 5-cycles whenever r, s and t are all even. This extends work done by Mahmoodian and Mirza-khani (Decomposition of complete tripartite graphs into 5-cycles, in: Combinatorics Advances, Kluwer Academic Publishers, Netherlands, 1995, pp. 235-241) and Cavenagh and Billington. (C) 2002 Elsevier Science B.V. All rights reserved.

Decompositions of complete graphs into theta graphs with fewer than ten edges

A theta graph is a graph consisting of three pairwise internally disjoint paths with common end points. Methods for decomposing the complete graph K-nu into theta graphs with fewer than ten edges are given.

Bilateral semidirect product decompositions of transformation monoids

In this paper we consider the monoid OR(n) of all full transformations on a chain with n elements that preserve or reverse the orientation, as well as its submonoids OD(n) of all order-preserving or order-reversing elements, OP(n) of all orientation-preserving elements and O(n) of all order-preserving elements. By making use of some well known presentations, we show that each of these four monoids is a quotient of a bilateral semidirectproduct of two of its remarkable submonoids.