997 research outputs found
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
of the pure 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 , can be realized exactly by
quantum circuits of size , 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 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
An Efficient Hybrid Algorithm for the Separable Convex Quadratic Knapsack Problem
This article considers the problem of minimizing a convex, separable quadratic function subject to a knapsack constraint and a box constraint. An algorithm called NAPHEAP has been developed to solve this problem. The algorithm solves the Karush-Kuhn-Tucker system using a starting guess to the optimal Lagrange multiplier and updating the guess monotonically in the direction of the solution. The starting guess is computed using the variable fixing method or is supplied by the user. A key innovation in our algorithm is the implementation of a heap data structure for storing the break points of the dual function and computing the solution of the dual problem. Also, a new version of the variable fixing algorithm is developed that is convergent even when the objective Hessian is not strictly positive definite. The hybrid algorithm NAPHEAP that uses a Newton-type method (variable fixing method, secant method, or Newton's method) to bracket a root, followed by a heap-based monotone break point search, can be faster than a Newton-type method by itself, as demonstrated in the numerical experiments
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
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