817 research outputs found
Action-Angle variables for the Gel'fand-Dikii flows
Using the scattering transform for order linear scalar operators,
the Poisson bracket found by Gel'fand and Dikii, which generalizes the Gardner
Poisson bracket for the KdV hierarchy, is computed on the scattering side.
Action-angle variables are then constructed. Using this, complete integrability
is demonstrated in the strong sense. Real action-angle variables are
constructed in the self-adjoint case
CETA truck and EVA restraint system
The Crew Equipment Translation Aid (CETA) experiment is an extravehicular activity (EVA) Space Transportation System (STS) based flight experiment which will explore various modes of transporting astronauts and light equipment for Space Station Freedom (SSF). The basic elements of CETA are: (1) two 25 foot long sections of monorail, which will be EVA assembled in the STS cargo bay to become a single 50 ft. rail called the track; (2) a wheeled baseplate called the truck which rolls along the track and can accept three cart concepts; and (3) the three carts which are designated manual, electric, and mechanical. The three carts serve as the astronaut restraint and locomotive interfaces with the track. The manual cart is powered by the astronaut grasping the track's handrail and pulling himself along. The electric cart is operated by an astronaut turning a generator which powers the electric motor and drives the cart. The mechanical cart is driven by a Bendix type transmission and is similar in concept to a man-propelled railroad cart. During launch and landing, the truck is attached to the deployable track by means of EVA removable restraint bolts and held in position by a system of retractable shims. These shims are positioned on the exterior of the rail for launch and landing and rotate out of the way for the duration of the experiment. The shims are held in position by strips of Velcro nap, which rub against the sides of the shim and exert a tailored force. The amount of force required to rotate the shims was a major EVA concern, along with operational repeatability and extreme temperature effects. The restraint system was tested in a thermal-vac and vibration environment and was shown to meet all of the initial design requirements. Using design inputs from the astronauts who will perform the EVA, CETA evolved through an iterative design process and represented a cooperative effort
Study of mechanical properties of uranium compounds
Study determines the mechanical properties, including brittleness and ductility of several uranium compounds. These include uranium dioxide, uranium sulfide, and uranium phosphide
Efficient Quantum Circuits for Schur and Clebsch-Gordan Transforms
The Schur basis on n d-dimensional quantum systems is a generalization of the
total angular momentum basis that is useful for exploiting symmetry under
permutations or collective unitary rotations. We present efficient (size
poly(n,d,log(1/\epsilon)) for accuracy \epsilon) quantum circuits for the Schur
transform, which is the change of basis between the computational and the Schur
bases. These circuits are based on efficient circuits for the Clebsch-Gordan
transformation. We also present an efficient circuit for a limited version of
the Schur transform in which one needs only to project onto different Schur
subspaces. This second circuit is based on a generalization of phase estimation
to any nonabelian finite group for which there exists a fast quantum Fourier
transform.Comment: 4 pages, 3 figure
The geometric sense of R. Sasaki connection
For the Riemannian manifold two special connections on the sum of the
tangent bundle and the trivial one-dimensional bundle are constructed.
These connections are flat if and only if the space has a constant
sectional curvature . The geometric explanation of this property is
given. This construction gives a coordinate free many-dimensional
generalization of the connection from the paper: R. Sasaki 1979 Soliton
equations and pseudospherical surfaces, Nuclear Phys., {\bf 154 B}, pp.
343-357. It is shown that these connections are in close relation with the
imbedding of into Euclidean or pseudoeuclidean -dimension
spaces.Comment: 7 pages, the key reference to the paper of Min-Oo is included in the
second versio
The Optimal Single Copy Measurement for the Hidden Subgroup Problem
The optimization of measurements for the state distinction problem has
recently been applied to the theory of quantum algorithms with considerable
successes, including efficient new quantum algorithms for the non-abelian
hidden subgroup problem. Previous work has identified the optimal single copy
measurement for the hidden subgroup problem over abelian groups as well as for
the non-abelian problem in the setting where the subgroups are restricted to be
all conjugate to each other. Here we describe the optimal single copy
measurement for the hidden subgroup problem when all of the subgroups of the
group are given with equal a priori probability. The optimal measurement is
seen to be a hybrid of the two previously discovered single copy optimal
measurements for the hidden subgroup problem.Comment: 8 pages. Error in main proof fixe
On an inverse problem for anisotropic conductivity in the plane
Let be a bounded domain with smooth
boundary and a smooth anisotropic conductivity on .
Starting from the Dirichlet-to-Neumann operator on
, we give an explicit procedure to find a unique domain
, an isotropic conductivity on and the boundary
values of a quasiconformal diffeomorphism which
transforms into .Comment: 9 pages, no figur
Constant-time solution to the Global Optimization Problem using Bruschweiler's ensemble search algorithm
A constant-time solution of the continuous Global Optimization Problem (GOP)
is obtained by using an ensemble algorithm. We show that under certain
assumptions, the solution can be guaranteed by mapping the GOP onto a discrete
unsorted search problem, whereupon Bruschweiler's ensemble search algorithm is
applied. For adequate sensitivities of the measurement technique, the query
complexity of the ensemble search algorithm depends linearly on the size of the
function's domain. Advantages and limitations of an eventual NMR implementation
are discussed.Comment: 14 pages, 0 figure
Efficient quantum algorithms for simulating sparse Hamiltonians
We present an efficient quantum algorithm for simulating the evolution of a
sparse Hamiltonian H for a given time t in terms of a procedure for computing
the matrix entries of H. In particular, when H acts on n qubits, has at most a
constant number of nonzero entries in each row/column, and |H| is bounded by a
constant, we may select any positive integer such that the simulation
requires O((\log^*n)t^{1+1/2k}) accesses to matrix entries of H. We show that
the temporal scaling cannot be significantly improved beyond this, because
sublinear time scaling is not possible.Comment: 9 pages, 2 figures, substantial revision
From Quantum Query Complexity to State Complexity
State complexity of quantum finite automata is one of the interesting topics
in studying the power of quantum finite automata. It is therefore of importance
to develop general methods how to show state succinctness results for quantum
finite automata. One such method is presented and demonstrated in this paper.
In particular, we show that state succinctness results can be derived out of
query complexity results.Comment: Some typos in references were fixed. To appear in Gruska Festschrift
(2014). Comments are welcome. arXiv admin note: substantial text overlap with
arXiv:1402.7254, arXiv:1309.773
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