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A. Isaev

Publications and source records attributed to A. Isaev.

7 recordsLinked to original sources
arXiv2020

The Cesium Source Calibration and Monitoring System of the ATLAS Tile Calorimeter: Design, Construction and Results

This article describes the design, construction and use of a calibration and monitoring system, based on movable 137Cs gamma-ray sources, for the ATLAS Tile Calorimeter (TileCal). The sources, propelled by a water-based liquid through tubes that traverse all the calorimeter's cells, produce signals that precisely characterise the response of each tile, thereby providing very granular and accurate data on the response of TileCal to particles. The system has been used to guide and control the quality of the optical instrumentation of all TileCal modules, to set and equalise the dynamic range of the response to physics data, and to set the energy scale of the readout system. In the ATLAS cavern, periodic measurements of the whole detector's response to 137Cs sources allow monitoring the uniformity and stability of all the calorimeter's cells as well as maintaining precise knowledge of its energy calibration. The design of the source hydraulic drive system's hardware and software, the data acquisition system and the data processing algorithms are described. Finally, the results of this two-decade program are shown.

physics.ins-det↗
arXiv2010

Isolated hypersurface singularities and polynomial realizations of affine quadrics

Let $V$, $\tilde V$ be hypersurface germs in $\CC^m$, each having a quasi-homogeneous isolated singularity at the origin. We show that the biholomorphic equivalence problem for $V$, $\tilde V$ reduces to the linear equivalence problem for certain polynomials $P$, $\tilde P$ arising from the moduli algebras of $V$, $\tilde V$. The polynomials $P$, $\tilde P$ are completely determined by their quadratic and cubic terms, hence the biholomorphic equivalence problem for $V$, $\tilde V$ in fact reduces to the linear equivalence problem for pairs of quadratic and cubic forms.

math.CV↗
arXiv2008

Spectral extension of the quantum group cotangent bundle

The structure of a cotangent bundle is investigated for quantum linear groups GLq(n) and SLq(n). Using a q-version of the Cayley-Hamilton theorem we construct an extension of the algebra of differential operators on SLq(n) (otherwise called the Heisenberg double) by spectral values of the matrix of right invariant vector fields. We consider two applications for the spectral extension. First, we describe the extended Heisenberg double in terms of a new set of generators -- the Weyl partners of the spectral variables. Calculating defining relations in terms of these generators allows us to derive SLq(n) type dynamical R-matrices in a surprisingly simple way. Second, we calculate an evolution operator for the model of q-deformed isotropic top introduced by A.Alekseev and L.Faddeev. The evolution operator is not uniquely defined and we present two possible expressions for it. The first one is a Riemann theta function in the spectral variables. The second one is an almost free motion evolution operator in terms of logarithms of the spectral variables. Relation between the two operators is given by a modular functional equation for Riemann theta function.

math.QA↗
arXiv2005

The SPHINX spectrometer

The paper describes the SPHINX facility which includes a wide-aperture magnetic spectrometer with scintillation counters and hodoscopes, proportional chambers and drift tubes, multichannel electromagnetic and hadron calorimeters, a guard system, a RICH velocity spectrometer and a hodoscopical threshold Cherenkov detector for the identification of charged secondary particles. The SPHINX spectrometer, in its last modification, had the possibility to record 3000-4000 trigger events per an accelerator burst. The spectrometer was used during the last decade in experiments with the 70GeV proton beam of the IHEP accelerator U-70.

physics.ins-det↗
arXiv1999

Q-multilinear Algebra

The Cayley-Hamilton-Newton theorem - which underlies the Newton identities and the Cayley-Hamilton identity - is reviewed, first, for the classical matrices with commuting entries, second, for two q-matrix algebras, the RTT-algebra and the RLRL-algebra. The Cayley-Hamilton-Newton identities for these q-algebras are related by the factorization map. A class of algebras M(R,F) is presented. The algebras M(R,F) include the RTT-algebra and the RLRL-algebra as particular cases. The algebra M(R,F) is defined by a pair of compatible matrices R and F. The Cayley-Hamilton-Newton theorem for the algebras M(R,F) is stated. A nontrivial example of a compatible pair is given.

math.QA↗
arXiv1998

Generalized Cayley-Hamilton-Newton identities

The q-generalizations of the two fundamental statements of matrix algebra -- the Cayley-Hamilton theorem and the Newton relations -- to the cases of quantum matrix algebras of an "RTT-" and of a "Reflection equation" types have been obtained in [2]-[6]. We construct a family of matrix identities which we call Cayley-Hamilton-Newton identities and which underlie the characteristic identity as well as the Newton relations for the RTT- and Reflection equation algebras, in the sence that both the characteristic identity and the Newton relations are direct consequences of the Cayley-Hamilton-Newton identities.

math.QA↗