Let G = (V,E) be an undirected d-regular graph, here, |V | = n, deg(u) = d for all u ∈ V . We will typically interpret the properties of expander graphs in an asymptotic sense. That is, there will be an infinite family of graphs G, with a growing number of vertices n. By “sparse”, we mean that the degree d of G should be very slowly growing as a function of n. When n goes to infinity (n → ∞), d...

The expander constructions based on algebraic methods can give expanders that are both explicit (i.e. we can quickly construct the graph, or even obtain neighborhood information without constructing the entire graph, and Ramanujan, meaning that the spectral gap is essentially as large as possible. It also follows from this spectral bound that the edge expansion of Ramanujan graphs is essentiall...

1. Schulman MR, Chun JK. The conjoined sternalispectoralis muscle flap in immediate tissue expander reconstruction after mastectomy. Ann Plast Surg 2005;55:672-5. 2. Barlow RN. The sternalis muscle in American whites and Negroes. Anat Rec 1934;61:416-26. 3. Alani HA, Balalaa N. Complete tissue expander coverage by musculo-fascial flaps in immediate breast mound reconstruction after mastectomy. ...

Sarday, O cber 7, 2017 the expander. Radiation oncologists and medical physicists will need to consider what effect the gas filled chamber and metal components within the expander have on their treatment planning and dosimetry. Breast air expanders require a wedged pair planning technique however, Saline expanders can be planned with a IMRT hybrid technique. It is critical to understand the con...

Since its application to the NGL process in 1964, the turbo-expander based demethanizer process has been the workhorse of many gas plants. The turbo-expander process isentropically expands the gas through a high speed turbine to create cryogenic temperatures facilitating the separation of ethane and heavier components from the methane. This process also uses significant heat integration to redu...

This paper proves that there exist infinite families of graphs which satisfy a uniform lower bound on their spectral gap. We first prove existence via a probabilistic method. The explicit construction involves various results from algebra and representation theory, which we explore at some length. It turns out that the expander family we construct achieves a maximal condition on expander famili...

AIM To show the use of an acrylic expander in the treatment of anterior open bite in patient with maxillary constriction and respiratory concern. Study design Clinical report. Setting "Fatebenefratelli" Hospital (Italy). MATERIAL AND METHOD The open bite treatment represents a challenge for orthodontists because it is determined by several complementary factors such as: adenoid reduction, ton...

A 13-month-old boy underwent placement of a tissue expander in the subgaleal plane in the forehead. The indication for skin expansion was a large congenital melanocytic nevus involving the forehead and glabella. Serial inflations of the expander were performed in the plastic surgery clinic using sterile equipment. Alcohol was used to prepare the skin overlying the injection port. Three months f...