Generalization of matching extensions in graphs (II)

Proposed as a general framework, Liu and Yu(Discrete Math. 231 (2001) 311-320) introduced $(n,k,d)$-graphs to unify the concepts of deficiency of matchings, $n$-factor-criticality and $k$-extendability. Let $G$ be a graph and let $n,k$ and $d$ be non-negative integers such that $n+2k+d\leq |V(G)|-2$ and $|V(G)|-n-d$ is even. If when deleting any $n$ vertices from $G$, the remaining subgraph $H$ of $G$ contains a $k$-matching and each such $k$- matching can be extended to a defect-$d$ matching in $H$, then $G$ is called an $(n,k,d)$-graph. In \cite{Liu}, the recursive relations for distinct parameters $n, k$ and $d$ were presented and the impact of adding or deleting an edge also was discussed for the case $d = 0$. In this paper, we continue the study begun in \cite{Liu} and obtain new recursive results for $(n,k,d)$-graphs in the general case $d \geq0$.Comment: 12 page

Research reports: 1985 NASA/ASEE Summer Faculty Fellowship Program

A compilation of 40 technical reports on research conducted by participants in the 1985 NASA/ASEE Summer Faculty Fellowship Program at Marshall Space Flight Center (MSFC) is given. Weibull density functions, reliability analysis, directional solidification, space stations, jet stream, fracture mechanics, composite materials, orbital maneuvering vehicles, stellar winds and gamma ray bursts are among the topics discussed

21st century manufacturing machines: Design, fabrication and controls

Advances in nanotechnology, microfabrication and new manufacturing processes, the revolution of open electronics, and the emerging internet of things will influence the design, manufacture, and control of manufacturing machines in the future. For instance, miniaturization will change manufacturing processes; additive and rapid prototyping will change the production of machine components; and open electronics offer a platform for new control architectures for manufacturing systems that are open, modular, and easy to reconfigure. Combined with the latest trends in cyber-physical systems and the internet of things, open architecture controllers for CNC systems can become platforms, oriented for numerical control as a service (NCaaS) and manufacturing as a service, tailored to the creation of cyber-manufacturing networks of shared resources and web applications. With this potential in mind, this research presents new design-for-fabrication methodologies and control strategies to facilitate the creation of next generation machine tools. It provides a discussion and examples of the opportunities that the present moment offers. The first portion of this dissertation focuses on the design of complex 3D MEMS machines realized from conventional 2.5D microfabrication processes. It presents an analysis of an example XYZ-MEMS parallel kinematics stage as well as of designs of the individual components of the manipulator, integrated into a design approach for PK-XYZ-MEMS stages. It seems likely that this design-for-fabrication methodology will enable higher functionality in MEMS micromachines and result in new devices that interact, in three full dimensions, with their surroundings. Novel and innovative research exemplifies the opportunities new and economical manufacturing technologies offer for the design and fabrication of modern machine tools. The second portion of this dissertation describes the demonstration of a new flexural joint designed with both traditional and additive manufacturing processes. It extrapolates principles based on the design of this joint that alleviate the effects of low accuracy and poor surface finishing, anisotropy, reductions in material properties of components, and small holding forces. Based on these results, the next section presents case examples of the construction of mesoscale devices and machine components using multilayered composites and hybrid flexures for precision engineering, medical training, and machine tools for reduced life applications and tests design-for-fabrication strategies. The results suggest the strategies effectively address existing problems, providing a repertory of creative solutions applicable to the design of devices with hybrid flexures. The implications for medical industry, micro robotics, soft robotics, flexible electronics, and metrology systems are positive. Chapter number five examines to positive impact of open architectures of control for CNC systems, given the current availability of micro-processing power and open-source electronics. It presents a new modular architecture controller based on open-source electronics. This component-based approach offers the possibility of adding micro-processing units and an axis of motion without modification of the control programs. This kind of software and hardware modularity is important for the reconfiguration of new manufacturing units. The flexibility of this architecture makes it a convenient testbed for the implementation of new control algorithms on different electromechanical systems. This research provides general purpose, open architecture for the design of a CNC system based on open electronics and detailed information to experiment with these platforms. This dissertation’s final chapter describes how applying the latest trends to the classical concepts of modular and open architecture controllers for CNC systems results in a control platform, oriented for numerical control as a service (NCaaS) and manufacturing as a service (MaaS), tailored to the creation of cyber-manufacturing networks of shared resources and web applications. Based on this technology, this chapter introduces new manufacturing network for numerical control (NC) infrastructure, provisioned and managed over the internet. The proposed network architecture has a hardware, a virtualization, an operating system, and a network layer. With a new operating system necessary to service and virtualize manufacturing resources, and a micro service architecture of manufacturing nodes and assets, this network is a new paradigm in cloud manufacturing

Binding Number, Toughness and General Matching Extendability in Graphs

A connected graph $G$ with at least $2m + 2n + 2$ vertices which contains aperfect matching is $E(m, n)$-{\it extendable}, if for any two sets of disjointindependent edges $M$ and $N$ with $|M| = m$ and $|N|= n$, there is a perfectmatching $F$ in $G$ such that $M\subseteq F$ and $N\cap F=\emptyset$.Similarly, a connected graph with at least $n+2k+2$ vertices is called$(n,k)$-{\it extendable} if for any vertex set $S$ of size $n$ and any matching$M$ of size $k$ of $G-S$, $G-S-V(M)$ contains a perfect matching. Let$\varepsilon$ be a small positive constant, $b(G)$ and $t(G)$ be the bindingnumber and toughness of a graph $G$. The two main theorems of this paper are:for every graph $G$ with sufficiently large order, 1) if $b(G)\geq4/3+\varepsilon$, then $G$ is $E(m,n)$-extendable and also $(n,k)$-extendable;2) if $t(G)\geq 1+\varepsilon$ and $G$ has a high connectivity, then $G$ is$E(m,n)$-extendable and also $(n,k)$-extendable. It is worth to point out thatthe binding number and toughness conditions for the existence of the generalmatching extension properties are almost same as that for the existence ofperfect matchings.Comment: 10 page

Research reports: 1987 NASA/ASEE Summer Faculty Fellowship Program

For the 23rd consecutive year, a NASA/ASEE Summer Faculty Fellowship Program was conducted at the Marshall Space Flight Center (MSFC). The program was conducted by the University of Alabama in Huntsville and MSFC during the period 1 June to 7 August 1987. Operated under the auspices of the American Society for Engineering Education, the MSFC program, as well as those at other NASA Centers, was sponsored by the Office of University Affairs, NASA Headquarters, Washington, D.C. The basic objectives of the program are: (1) to further the professional knowledge of qualified engineering and science faculty members; (2) to stimulate an exchange of ideas between participants and NASA; (3) to enrich and refresh the research and teaching activities of the participant's institutions; and (4) to contribute to the research objectives of the NASA Centers. This document is a compilation of Fellow's reports on their research during the Summer of 1987

Aeronautical Engineering: A continuing bibliography with indexes

This bibliography lists 725 reports, articles and other documents introduced into the NASA scientific and technical information system in April 1985