Mathematics Without Calculations – It’s a Beautiful Thing!

All students should have the opportunity to do mathematics in a meaningful way for the sheer fun of it. Such experiences, if well designed, improve students’ effective thinking skills, increase their appreciation of the beauty and utility of mathematics, and prepare them to be mathematically-literate members of society. This session invites talks on how we can engage the liberal arts student through courses specifically designed for them. We welcome presentations on innovative course design, pedagogy, projects, or activities, as well as talks on tools used to assess such courses. Presentations should include a research basis for the design or pedagogical choices, a report on outcomes in student learning or attitude, or other evidence of success. Papers about programs demonstrating success engaging students who enter the course reluctant to engage in mathematics are especially encouraged. We also welcome talks on first year seminars or other experiences that engage first year students in doing mathematics as well as Honors courses in mathematics that incorporate the liberal arts

Is Mathematics Created by Humans or is it Discovered by Humans? A Catholic Intellectual Perspective

In this essay, Dr. Molitierno intends to show that not only is it appropriate to discuss the Catholic Intellectual Tradition in light of mathematics, the CIT can actually be exemplified in mathematics

Tight Bounds on the Algebraic Connectivity of a Balanced Binary Tree

In this paper, quite tight lower and upper bounds are obtained on the algebraic connectivity, namely, the second-smallest eigenvalue of the Laplacian matrix, of an unweighted balanced binary tree with k levels and hence n = 2k - 1 vertices. This is accomplished by considering the inverse of a matrix of order k - 1 readily obtained from the Laplacian matrix. It is shown that the algebraic connectivity is 1/(2k - 2k + 3) + 0(1/22k)

Seismic retrofit of an existing reinforced concrete building with buckling-restrained braces

Background: The seismic retrofitting of frame structures using hysteretic dampers is a very effective strategy to mitigate earthquake-induced risks. However, its application in current practice is rather limited since simple and efficient design methods are still lacking, and the more accurate time-history analysis is time-consuming and computationally demanding. Aims: This paper develops and applies a seismic retrofit design method to a complex real case study: An eight-story reinforced concrete residential building equipped with buckling-restrained braces. Methods: The design method permits the peak seismic response to be predicted, as well as the dampers to be added in the structure to obtain a uniform distribution of the ductility demand. For that purpose, a pushover analysis with the first mode load pattern is carried out. The corresponding story pushover curves are first idealized using a degrading trilinear model and then used to define the SDOF (Single Degree-of-Freedom) system equivalent to the RC frame. The SDOF system, equivalent to the damped braces, is designed to meet performance criteria based on a target drift angle. An optimal damper distribution rule is used to distribute the damped braces along the elevation to maximize the use of all dampers and obtain a uniform distribution of the ductility demand. Results: The effectiveness of the seismic retrofit is finally demonstrated by non-linear time-history analysis using a set of earthquake ground motions with various hazard levels. Conclusion: The results proved the design procedure is feasible and effective since it achieves the performance objectives of damage control in structural members and uniform ductility demand in dampers

Failure Propagation Controlling for Frangible Composite Canister Design

The complexity in predicting the damage initiation and failure propagation controlling in composite structures is challenging. The focus of this paper is to design a potential component for new ship gunnels to make the composite canister affordable in structural applications by using a damage tolerant design approach. The design of a new tailgate configuration was investigated, taking into account the correct fragmentation of the structure to ensure a clear ejection while reducing the weight of the panels by exploiting the properties of the composite material. The complex geometry of the tailgate, the high impulse load, the energy transferred to the tailgate during missile impact, and how to safely break large panel flaps are elements that characterize the sizing of the composite component to meet the stringent ejection requirements in the life cycle of a missile during takeoff. The numerical simulations were performed using the LS/Dyna code and its explicit formulation was contemplated to take into account the geometrical, contact, and material non linearities

On the Fiedler value of large planar graphs

The Fiedler value $\lambda_2$, also known as algebraic connectivity, is the second smallest Laplacian eigenvalue of a graph. We study the maximum Fiedler value among all planar graphs $G$ with $n$ vertices, denoted by $\lambda_{2\max}$, and we show the bounds $2+\Theta(\frac{1}{n^2}) \leq \lambda_{2\max} \leq 2+O(\frac{1}{n})$. We also provide bounds on the maximum Fiedler value for the following classes of planar graphs: Bipartite planar graphs, bipartite planar graphs with minimum vertex degree~3, and outerplanar graphs. Furthermore, we derive almost tight bounds on $\lambda_{2\max}$ for two more classes of graphs, those of bounded genus and $K_h$-minor-free graphs.Comment: 21 pages, 4 figures, 1 table. Version accepted in Linear Algebra and Its Application

Endoscopic treatment of vesicoureteral reflux in pediatric patients

Endoscopic treatment is a minimally invasive treatment for managing patients with vesicoureteral reflux (VUR). Although several bulking agents have been used for endoscopic treatment, dextranomer/hyaluronic acid is the only bulking agent currently approved by the U.S. Food and Drug Administration for treating VUR. Endoscopic treatment of VUR has gained great popularity owing to several obvious benefits, including short operative time, short hospital stay, minimal invasiveness, high efficacy, low complication rate, and reduced cost. Initially, the success rates of endoscopic treatment have been lower than that of open antireflux surgery. However, because injection techniques have been developed, a recent study showed higher success rates of endoscopic treatment than open surgery in the treatment of patients with intermediate- and high-grade VUR. Despite the controversy surrounding its effectiveness, endoscopic treatment is considered a valuable treatment option and viable alternative to long-term antibiotic prophylaxis

On some properties of the Laplacian matrix revealed by the RCM algorithm

In this paper we present some theoretical results about the irreducibility of the Laplacian matrix ordered by the Reverse Cuthill-McKee (RCM) algorithm. We consider undirected graphs with no loops consisting of some connected components. RCM is a well-known scheme for numbering the nodes of a network in such a way that the corresponding adjacency matrix has a narrow bandwidth. Inspired by some properties of the eigenvectors of a Laplacian matrix, we derive some properties based on row sums of a Laplacian matrix that was reordered by the RCM algorithm. One of the theoretical results serves as a basis for writing an easy MATLAB code to detect connected components, by using the function “symrcm” of MATLAB. Some examples illustrate the theoretical results.The research has been supported by Spanish DGI grant MTM2010-18674, Consolider Ingenio CSD2007-00022, PROMETEO 2008/051, OVAMAH TIN2009-13839-C03-01, and PAID-06-11-2084.Pedroche Sánchez, F.; Rebollo Pedruelo, M.; Carrascosa Casamayor, C.; Palomares Chust, A. (2016). On some properties of the Laplacian matrix revealed by the RCM algorithm. Czechoslovak Mathematical Journal. 66(3):603-620. doi:10.1007/s10587-016-0281-yS60362066

The Spectral Radius of Submatrices of Laplacian Matrices for Trees and Its Comparison to the Fiedler Vector

We consider the effects on the spectral radius of submatrices of the Laplacian matrix for graphs by deleting the row and column corresponding to various vertices of the graph. We focus most of our attention on trees and determine which vertices v will yield the maximum and minimum spectral radius of the Laplacian when row v and column v are deleted. At this point, comparisons are made between these results and results concerning the Fiedler vector of the tree

A Tight Upper Bound on the Spectral Radius of Bottleneck Matrices for Graphs

In this paper, we find a tight upper bound on the spectral radius of bottleneck matrices for graphs. We use this upper bound to find a tight lower bound on the algebraic connectivity of graphs in terms of the radius of the graph. We show that these lower bounds are an improvement on those found in[9]