1,981 research outputs found
Quasigroups, Asymptotic Symmetries and Conservation Laws in General Relativity
A new quasigroup approach to conservation laws in general relativity is
applied to study asymptotically flat at future null infinity spacetime. The
infinite-parametric Newman-Unti group of asymptotic symmetries is reduced to
the Poincar\'e quasigroup and the Noether charge associated with any element of
the Poincar\'e quasialgebra is defined. The integral conserved quantities of
energy-momentum and angular momentum are linear on generators of Poincar\'e
quasigroup, free of the supertranslation ambiguity, posess the flux and
identically equal to zero in Minkowski spacetime.Comment: RevTeX4, 5 page
Mirror Descent and Convex Optimization Problems With Non-Smooth Inequality Constraints
We consider the problem of minimization of a convex function on a simple set
with convex non-smooth inequality constraint and describe first-order methods
to solve such problems in different situations: smooth or non-smooth objective
function; convex or strongly convex objective and constraint; deterministic or
randomized information about the objective and constraint. We hope that it is
convenient for a reader to have all the methods for different settings in one
place. Described methods are based on Mirror Descent algorithm and switching
subgradient scheme. One of our focus is to propose, for the listed different
settings, a Mirror Descent with adaptive stepsizes and adaptive stopping rule.
This means that neither stepsize nor stopping rule require to know the
Lipschitz constant of the objective or constraint. We also construct Mirror
Descent for problems with objective function, which is not Lipschitz
continuous, e.g. is a quadratic function. Besides that, we address the problem
of recovering the solution of the dual problem
Study of High Energy Gamma-Quanta Beyond the Atmosphere
Measurements of primary cosmic radiation gamma quanta from Proton I and II satellite
Nonlinear interfaces: intrinsically nonparaxial regimes and effects
The behaviour of optical solitons at planar nonlinear boundaries is a problem rich in intrinsically nonparaxial regimes that cannot be fully addressed by theories based on the nonlinear Schrödinger equation. For instance, large propagation angles are typically involved in external refraction at interfaces. Using a recently proposed generalized Snell's law for Helmholtz solitons, we analyse two such effects: nonlinear external refraction and total internal reflection at interfaces where internal and external refraction, respectively, would be found in the absence of nonlinearity. The solutions obtained from the full numerical integration of the nonlinear Helmholtz equation show excellent agreement with the theoretical predictions
Study of the nuclear component of primary cosmic rays aboard AES ''Proton-2''
Nuclear component of primary cosmic rays aboard Proton II satellite studied with aid of Cherenkov spectromete
Smooth Loops and Fiber Bundles: Theory of Principal Q-bundles
A nonassociative generalization of the principal fiber bundles with a smooth
loop mapping on the fiber is presented. Our approach allows us to construct a
new kind of gauge theories that involve higher ''nonassociative'' symmetries.Comment: 20 page
Use of computers to exclude the influence of radiometer instability upon measurement results
A radiometer, practically insensitive to great fluctuations in the equipment amplification coefficient, was developed by dividing the useful signal by a reference signal and modulating the two signals at different frequencies. The signals are simultaneously separated by corresponding synchronous detectors and recorded over two channels. The operation is simplified by replacing the continuous signals by a sampling of discrete values, and using a digital computer. The four steps involved in the process are described and a block diagram is included. This technique not only directly connects the radiometer with the computer, but also records all data provided by the control and signal channels
Separable Multipartite Mixed States - Operational Asymptotically Necessary and Sufficient Conditions
We introduce an operational procedure to determine, with arbitrary
probability and accuracy, optimal entanglement witness for every multipartite
entangled state. This method provides an operational criterion for separability
which is asymptotically necessary and sufficient. Our results are also
generalized to detect all different types of multipartite entanglement.Comment: 4 pages, 2 figures, submitted to Physical Review Letters. Revised
version with new calculation
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