97 research outputs found
Root stacks and periodic decompositions
For an effective Cartier divisor D on a scheme X we may form an nth root
stack. Its derived category is known to have a semiorthogonal decomposition
with components given by D and X. We show that this decomposition is
2n-periodic. For n=2 this gives a purely triangulated proof of the existence of
a known spherical functor, namely the pushforward along the embedding of D. For
n>2 we find a higher spherical functor in the sense of recent work of
Dyckerhoff, Kapranov and Schechtman. We use a realization of the root stack
construction as a variation of GIT, which may be of independent interest.Comment: 21 pages. Revised introductio
Contraction algebra and invariants of singularities
In [7], Donovan and Wemyss introduced the contraction algebra of flop- ping
curves in 3-folds. When the flopping curve is smooth and irreducible, we prove
that the contraction algebra together with its A_\infty-structure recovers
various invariants associated to the underlying singularity and its small
resolution, including the derived category of singularities and the genus zero
Gopakuma-Vafa invariants
Introduction to management of drug hypersensitivity : guidelines of the Section of Drug Hypersensitivity of the Polish Society of Allergology
Hypersensitivity to iodine contrast media : guidelines of the Section of Drug Hypersensitivity of the Polish Society of Allergology
Application of the vibration test in the evaluation of the technical condition of shock absorbers built into the vehicle
The paper presents an assessment of the technical condition of the vehicle shock absorbers built into the vehicle on the basis of the signals recorded during the vibration test. The test was performed on a test stand with kinematic harmonic forcing. The test stand can enforce vibrations in the range of 0-21 Hz and amplitude of 6 mm. The shock absorbers with indicated technical condition were built into the vehicle (the new shock absorber and the one with oil leak). The research was conducted on the twin-tube hydraulic shock with a modified structure that allows to change the amount of the fluid. The study was conducted for the front suspension shock absorber of passenger car with an independent McPherson front suspension. Acceleration was measured using capacitive sensors of accelerations type ADXL. Acceleration was recorded on test stand platform and near the axis of the wheel and on the upper point of attachment of the McPherson strut. Registered acceleration diagrams were subject to further treatment consisting of filtration and analysis. The results were compared for selected technical states
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