17,128 research outputs found
On Sasaki-Einstein manifolds in dimension five
We prove the existence of Sasaki-Einstein metrics on certain simply connected
5-manifolds where until now existence was unknown. All of these manifolds have
non-trivial torsion classes. On several of these we show that there are a
countable infinity of deformation classes of Sasaki-Einstein structures.Comment: 18 pages, Exposition was expanded and a reference adde
Quantum Searching via Entanglement and Partial Diffusion
In this paper, we will define a quantum operator that performs the inversion
about the mean only on a subspace of the system (Partial Diffusion Operator).
This operator is used in a quantum search algorithm that runs in O(sqrt{N/M})
for searching an unstructured list of size N with M matches such that 1<= M<=N.
We will show that the performance of the algorithm is more reliable than known
{fixed operators quantum search algorithms} especially for multiple matches
where we can get a solution after a single iteration with probability over 90%
if the number of matches is approximately more than one-third of the search
space. We will show that the algorithm will be able to handle the case where
the number of matches M is unknown in advance such that 1<=M<=N in
O(sqrt{N/M}). A performance comparison with Grover's algorithm will be
provided.Comment: 19 pages. Submitted to IJQI. Please forward comments/enquires for the
first author to [email protected]
Scaling Symmetries of Scatterers of Classical Zero-Point Radiation
Classical radiation equilibrium (the blackbody problem) is investigated by
the use of an analogy. Scaling symmetries are noted for systems of classical
charged particles moving in circular orbits in central potentials V(r)=-k/r^n
when the particles are held in uniform circular motion against radiative
collapse by a circularly polarized incident plane wave. Only in the case of a
Coulomb potential n=1 with fixed charge e is there a unique scale-invariant
spectrum of radiation versus frequency (analogous to zero-point radiation)
obtained from the stable scattering arrangement. These results suggest that
non-electromagnetic potentials are not appropriate for discussions of classical
radiation equilibrium.Comment: 13 page
Darwin-Lagrangian Analysis for the Interaction of a Point Charge and a Magnet: Considerations Related to the Controversy Regarding the Aharonov-Bohm and Aharonov-Casher Phase Shifts
The classical electromagnetic interaction of a point charge and a magnet is
discussed by first calculating the interaction of point charge with a simple
model magnetic moment and then suggesting a multiparticle limit. The Darwin
Lagrangian is used to analyze the electromagnetic behavior of the model
magnetic moment (composed of two oppositely charged particles of different mass
in an initially circular orbit) interacting with a passing point charge. The
changing mangetic moment is found to put a force back on a passing charge; this
force is of order 1/c^2 and depends upon the magnitude of the magnetic moment.
It is suggested that in the limit of a multiparticle magnetic toroid, the
electric fields of the passing charge are screened out of the body of the
magnet while the magnetic fields penetrate into the magnet. This is consistent
with our understanding of the penetration of electromagnetic velocity fields
into ohmic conductors. Conservation laws are discussed. The work corresponds to
a classical electromagnetic analysis of the interaction which is basic to
understanding the controversy over the Aharonov-Bohm and Aharonov-Casher phase
shifts and represents a refutation of the suggestions of Aharonov, Pearle, and
Vaidman.Comment: 33 page
Some Heuristic Semiclassical Derivations of the Planck Length, the Hawking Effect and the Unruh Effect
The formulae for Planck length, Hawking temperature and Unruh-Davies
temperature are derived by using only laws of classical physics together with
the Heisenberg principle. Besides, it is shown how the Hawking relation can be
deduced from the Unruh relation by means of the principle of equivalence; the
deep link between Hawking effect and Unruh effect is in this way clarified.Comment: LaTex file, 6 pages, no figure
The Corrosion of Magnesium and of the Magnesium Aluminum Alloys Containing Manganese
The extensive use of magnesium and its alloys in aircraft has been seriously handicapped by the uncertainties surrounding their resistance to corrosion. This problem has been given intense study by the American Magnesium Corporation and at the request of the Subcommittee on Materials for Aircraft of the National Advisory Committee for Aeronautics this report was prepared on the corrosion of magnesium. The tentative conclusions drawn from the experimental facts of this investigation are as follows: the overvoltage of pure magnesium is quite high. On immersion in salt water the metal corrodes with the liberation of hydrogen until the film of corrosion product lowers the potential to a critical value. When the potential reaches this value it no longer exceeds the theoretical hydrogen potential plus the overvoltage of the metal. Rapid corrosion consequently ceases. When aluminum is added, especially when in large amounts, the overvoltage is decreased and hydrogen plates out at a much lower potential than with pure magnesium. The addition of small amount of manganese raises the overvoltage back to practically that of pure metal, and the film is again negative
Hydrodynamic reductions of the heavenly equation
We demonstrate that Pleba\'nski's first heavenly equation decouples in
infinitely many ways into a triple of commuting (1+1)-dimensional systems of
hydrodynamic type which satisfy the Egorov property. Solving these systems by
the generalized hodograph method, one can construct exact solutions of the
heavenly equation parametrized by arbitrary functions of a single variable. We
discuss explicit examples of hydrodynamic reductions associated with the
equations of one-dimensional nonlinear elasticity, linearly degenerate systems
and the equations of associativity.Comment: 14 page
Seeking Historical Truth: the International Commission of Inquiry into the 1932-33 Famine in Ukraine
In the 1980s the WCFU (World Congress of Free Ukrainians) undertook many initiatives to educate Western public opinion on the Ukrainian Famine of 1932- 33, claiming that the famine was a Soviet act of genocide against the Ukrainian people. The WCFU sponsored an international commission of enquiry, composed of seven eminent international jurists, and appeared before the commission as plaintiff. The Commission dealt with a number of controversial issues in international law, including the question of whether the charge of genocide could predate the 1948 convention. The Commission deliberations are examined in detail, frequently with the use of unpublished sources from the archives of one of the commissioners, John Peters Humphrey. The Final Report (1990) lacked unanimity and created very sharp divisions among the Commission\u27s members
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