412 research outputs found
Modified Paouris inequality
The Paouris inequality gives the large deviation estimate for Euclidean norms
of log-concave vectors. We present a modified version of it and show how the
new inequality may be applied to derive tail estimates of l_r-norms and suprema
of norms of coordinate projections of isotropic log-concave vectors.Comment: 14 page
Modelling water infiltration into macroporous hill slopes using special boundary conditions
The formulation of suitable boundary conditions is a very crucial task when
modeling water infiltration into macroporous hill slopes. The processes of water infiltration
and exfiltration vary in space and time and depend on the flow on the surface as well as in the
subsurface. In this contribution we have purposed special system process dependent boundary
conditions can be formulated for a two-phase dual-permeability model to simulate infiltration
and exfiltration processes. The presented formulation analyses the saturation conditions of the
dual-permeability model (e.g. saturation) at the boundary nodes and adopts the boundary
conditions depending on the processes at the soil surface such as rainfall intensity. Using a
simplified macroporous hill slope and a heavy rainfall event we demonstrate the functionality
of our formulation
An efficiency upper bound for inverse covariance estimation
We derive an upper bound for the efficiency of estimating entries in the
inverse covariance matrix of a high dimensional distribution. We show that in
order to approximate an off-diagonal entry of the density matrix of a
-dimensional Gaussian random vector, one needs at least a number of samples
proportional to . Furthermore, we show that with samples, the
hypothesis that two given coordinates are fully correlated, when all other
coordinates are conditioned to be zero, cannot be told apart from the
hypothesis that the two are uncorrelated.Comment: 7 Page
The LIL for -statistics in Hilbert spaces
We give necessary and sufficient conditions for the (bounded) law of the
iterated logarithm for -statistics in Hilbert spaces. As a tool we also
develop moment and tail estimates for canonical Hilbert-space valued
-statistics of arbitrary order, which are of independent interest
Muon Catalyzed Fusion in 3 K Solid Deuterium
Muon catalyzed fusion in deuterium has traditionally been studied in gaseous
and liquid targets. The TRIUMF solid-hydrogen-layer target system has been used
to study the fusion reaction rates in the solid phase of D_2 at a target
temperature of 3 K. Products of two distinct branches of the reaction were
observed; neutrons by a liquid organic scintillator, and protons by a silicon
detector located inside the target system. The effective molecular formation
rate from the upper hyperfine state of and the hyperfine transition
rate have been measured: , and .
The molecular formation rate is consistent with other recent measurements, but
not with the theory for isolated molecules. The discrepancy may be due to
incomplete thermalization, an effect which was investigated by Monte Carlo
calculations. Information on branching ratio parameters for the s and p wave
d+d nuclear interaction has been extracted.Comment: 19 pages, 11 figures, submitted to PRA Feb 20, 199
Measurement of the Resonant Molecular Formation Rate in Solid HD
Measurements of muon-catalyzed dt fusion () in solid
HD have been performed. The theory describing the energy dependent resonant
molecular formation rate for the reaction + HD is
compared to experimental results in a pure solid HD target. Constraints on the
rates are inferred through the use of a Monte Carlo model developed
specifically for the experiment. From the time-of- flight analysis of fusion
events in 16 and 37 targets, an average formation rate
consistent with 0.897(0.046) (0.166) times the
theoretical prediction was obtained.Comment: 4 pages, 5 figure
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