Ellipsoidal optical reflectors reproduced by electroforming

An accurately dimensioned convex ellipsoidal surface, which will become a master after polishing, is fabricated from 316L stainless steel. When polishing of the master is completed, it is suspended in a modified watt bath for electroforming of nickel reflectors

Conforming polisher for aspheric surface of revolution Patent

Conforming polisher for aspheric surfaces of revolution with inflatable tub

Manufacturing and test procedures for Aerobee 350 burst diaphragms

Manufacturing and test procedures for fuel and oxidizer burst diaphragms for Aerobee 350 propellant start valve

On Protected Realizations of Quantum Information

There are two complementary approaches to realizing quantum information so that it is protected from a given set of error operators. Both involve encoding information by means of subsystems. One is initialization-based error protection, which involves a quantum operation that is applied before error events occur. The other is operator quantum error correction, which uses a recovery operation applied after the errors. Together, the two approaches make it clear how quantum information can be stored at all stages of a process involving alternating error and quantum operations. In particular, there is always a subsystem that faithfully represents the desired quantum information. We give a definition of faithful realization of quantum information and show that it always involves subsystems. This justifies the "subsystems principle" for realizing quantum information. In the presence of errors, one can make use of noiseless, (initialization) protectable, or error-correcting subsystems. We give an explicit algorithm for finding optimal noiseless subsystems. Finding optimal protectable or error-correcting subsystems is in general difficult. Verifying that a subsystem is error-correcting involves only linear algebra. We discuss the verification problem for protectable subsystems and reduce it to a simpler version of the problem of finding error-detecting codes.Comment: 17 page

Chiral Rings, Vacua and Gaugino Condensation of Supersymmetric Gauge Theories

We find the complete chiral ring relations of the supersymmetric U(N) gauge theories with matter in adjoint representation. We demonstrate exact correspondence between the solutions of the chiral ring and the supersymmetric vacua of the gauge theory. The chiral ring determines the expectation values of chiral operators and the low energy gauge group. All the vacua have nonzero gaugino condensation. We study the chiral ring relations obeyed by the gaugino condensate. These relations are generalizations of the formula $S^N=\Lambda^{3N}$ of the pure ${\cal N} =1$ gauge theory.Comment: 38 page

Large Fourier transforms never exactly realized by braiding conformal blocks

Fourier transform is an essential ingredient in Shor's factoring algorithm. In the standard quantum circuit model with the gate set \{\U(2), \textrm{CNOT}\}, the discrete Fourier transforms $F_N=(\omega^{ij})_{N\times N},i,j=0,1,..., N-1, \omega=e^{\frac{2\pi i}{N}}$, can be realized exactly by quantum circuits of size $O(n^2), n=\textrm{log}N$, and so can the discrete sine/cosine transforms. In topological quantum computing, the simplest universal topological quantum computer is based on the Fibonacci (2+1)-topological quantum field theory (TQFT), where the standard quantum circuits are replaced by unitary transformations realized by braiding conformal blocks. We report here that the large Fourier transforms $F_N$ and the discrete sine/cosine transforms can never be realized exactly by braiding conformal blocks for a fixed TQFT. It follows that approximation is unavoidable to implement the Fourier transforms by braiding conformal blocks

On the Invariants of Towers of Function Fields over Finite Fields

We consider a tower of function fields F=(F_n)_{n\geq 0} over a finite field F_q and a finite extension E/F_0 such that the sequence \mathcal{E):=(EF_n)_{n\goq 0} is a tower over the field F_q. Then we deal with the following: What can we say about the invariants of \mathcal{E}; i.e., the asymptotic number of places of degree r for any r\geq 1 in \mathcal{E}, if those of F are known? We give a method based on explicit extensions for constructing towers of function fields over F_q with finitely many prescribed invariants being positive, and towers of function fields over F_q, for q a square, with at least one positive invariant and certain prescribed invariants being zero. We show the existence of recursive towers attaining the Drinfeld-Vladut bound of order r, for any r\geq 1 with q^r a square. Moreover, we give some examples of recursive towers with all but one invariants equal to zero.Comment: 23 page

On Haagerup's list of potential principal graphs of subfactors

We show that any graph, in the sequence given by Haagerup in 1991 as that of candidates of principal graphs of subfactors, is not realized as a principal graph except for the smallest two. This settles the remaining case of a previous work of the first author.Comment: 19 page

Prospect of Studying Hard X- and Gamma-Rays from Type Ia Supernovae

We perform multi-dimensional, time-dependent radiation transfer simulations for hard X-ray and gamma-ray emissions, following radioactive decays of 56Ni and 56Co, for two-dimensional delayed detonation models of Type Ia supernovae (SNe Ia). The synthetic spectra and light curves are compared with the sensitivities of current and future observatories for an exposure time of 10^6 seconds. The non-detection of the gamma-ray signal from SN 2011fe at 6.4 Mpc by SPI on board INTEGRAL places an upper limit for the mass of 56Ni of \lesssim 1.0 Msun, independently from observations in any other wavelengths. Signals from the newly formed radioactive species have not been convincingly measured yet from any SN Ia, but the future X-ray and gamma-ray missions are expected to deepen the observable horizon to provide the high energy emission data for a significant SN Ia sample. We predict that the hard X-ray detectors on board NuStar (launched in 2012) or ASTRO-H (scheduled for launch in 2014) will reach to SNe Ia at \sim15 Mpc, i.e., one SN every few years. Furthermore, according to the present results, the soft gamma-ray detector on board ASTRO-H will be able to detect the 158 keV line emission up to \sim25 Mpc, i.e., a few SNe Ia per year. Proposed next generation gamma-ray missions, e.g., GRIPS, could reach to SNe Ia at \sim20 - 35 Mpc by MeV observations. Those would provide new diagnostics and strong constraints on explosion models, detecting rather directly the main energy source of supernova light.Comment: 14 pages, 7 figures, 1 table, accepted for publication in Ap