On the rotational symmetry of 3-dimensional κ\kappa-solutions

In a recent paper, Brendle showed the uniqueness of the Bryant soliton among 3-dimensional $\kappa$-solutions. In this paper, we present an alternative proof for this fact and show that compact $\kappa$-solutions are rotational symmetric. Our proof arose from independent work relating to our Strong Stability Theorem for singular Ricci flows.Comment: 20 page

Uniqueness and stability of Ricci flow through singularities

We verify a conjecture of Perelman, which states that there exists a canonical Ricci flow through singularities starting from an arbitrary compact Riemannian 3-manifold. Our main result is a uniqueness theorem for such flows, which, together with an earlier existence theorem of Lott and the second named author, implies Perelman's conjecture. We also show that this flow through singularities depends continuously on its initial condition and that it may be obtained as a limit of Ricci flows with surgery. Our results have applications to the study of diffeomorphism groups of three manifolds --- in particular to the Generalized Smale Conjecture --- which will appear in a subsequent paper.Comment: 182 pages, 10 figures, minor correction

Ricci flow and diffeomorphism groups of 3-manifolds

We complete the proof of the Generalized Smale Conjecture, apart from the case of $RP^3$, and give a new proof of Gabai's theorem for hyperbolic 3-manifolds. We use an approach based on Ricci flow through singularities, which applies uniformly to spherical space forms other than $S^3$ and $RP^3$ and hyperbolic manifolds, to prove that the moduli space of metrics of constant sectional curvature is contractible. As a corollary, for such a 3-manifold $X$, the inclusion $\text{Isom} (X,g)\to \text{Diff}(X)$ is a homotopy equivalence for any Riemannian metric $g$ of constant sectional curvature.Comment: 29 pages, 1 figur

The design and construction of the CAD-1 airship

The background history, design philosophy and Computer application as related to the design of the envelope shape, stress calculations and flight trajectories of the CAD-1 airship, now under construction by Canadian Airship Development Corporation are reported. A three-phase proposal for future development of larger cargo carrying airships is included

Memory cell based on a φ\varphi Josephson junction

The $\varphi$ Josephson junction has a doubly degenerate ground state with the Josephson phases $\pm\varphi$. We demonstrate the use of such a $\varphi$ Josephson junction as a memory cell (classical bit), where writing is done by applying a magnetic field and reading by applying a bias current. In the "store" state, the junction does not require any bias or magnetic field, but just needs to stay cooled for permanent storage of the logical bit. Straightforward integration with Rapid Single Flux Quantum logic is possible.Comment: to be published in AP

Wiener splines

We describe an alternative way of constructing interpolating B-spline curves, surfaces or volumes in Fourier space which can be used for visualization. In our approach the interpolation problem is considered from a signal processing point of view and is reduced to finding an inverse B-spline filter sequence. The Fourier approach encompasses some advantageous features, such as successive approximation, compression, fast convolution and hardware support. In addition, optimal Wiener filtering can be applied to remove noise and distortions from the initial data points and to compute a smooth, least-squares fitting ‘Wiener spline’. Unlike traditional fitting methods, the described algorithm is simple and easy to implement. The performance of the presented method is illustrated by some examples showing the restoration of surfaces corrupted by various types of distortions

Personal Computing in the 1990s

Personal computers have changed the way that business is conducted in today\u27s office. Every position in a company is affected by the use of personal computers from secretaries to top level management. Tasks and job duties are performed more easily thereby increasing productivity. Personal computers in the 1990s will be networked via LANs to other personal computers, minicomputers and mainframes to enhance people\u27s abilities and allow them to perform their jobs better. With the increased use of LANs, many LAN productivity applications wUl be utilized that will also increase productivity. E-Mail and groupware software will allow people to interact with each other without leaving their offices. These systems will reduce the amount of needless paperwork and time spent in meetings. The 1990s will also see an increase in the use of portable computers because of the small size and increased expansion capabilities, making it easy for users to tap into the network. These portables will allow employees to work at home and transmit any data to the office. Also, these portables will increase the productivity of many field applications. With the new advancements in personal computing, managers in the 1990s will need to understand these PC-based systems and how they impact individuals in the workplace

Fluxon-semifluxon interaction in an annular long Josephson 0-pi-junction

We investigate theoretically the interaction between integer and half-integer Josephson vortices (fluxons and semifluxons) in an annular Josephson junction. Semifluxons usually appear at the 0-$\pi$-boundary where there is a $\pi$-discontinuity of the Josephson phase. We study the simplest, but the most interesting case of one $\pi$-discontinuity in a loop, which can be created only artificially. We show that measuring the current-voltage characteristic after injection of an integer fluxon, one can determine the polarity of a semifluxon. Depending on the relative polarity of fluxon and semifluxon the static configuration may be stable or unstable, but in the dynamic state both configurations are stable. We also calculate the depinning current of $N$ fluxons pinned by an arbitrary fractional vortex.Comment: 8pages, 6 figures, submitted to PR

Workforce Reduction Guidelines

Andrew Simone is senior financial analyst at Young\u27s Market Company, Orange CA 92834. Brian H. Kleiner is professor of human resource management, Department of Management, College of Business and Economics, California State University Fullerton, Fullerton, CA 99834