6,740 research outputs found
Codimension 3 Arithmetically Gorenstein Subschemes of projective -space
We study the lowest dimensional open case of the question whether every
arithmetically Cohen--Macaulay subscheme of is glicci, that is,
whether every zero-scheme in is glicci. We show that a set of points in general position in \PP^3 admits no strictly descending
Gorenstein liaison or biliaison. In order to prove this theorem, we establish a
number of important results about arithmetically Gorenstein zero-schemes in
.Comment: to appear in Annales de l'Institut Fourie
Deformations of Fuchsian Systems of Linear Differential Equations and the Schlesinger System
We consider holomorphic deformations of Fuchsian systems parameterized by the
pole loci. It is well known that, in the case when the residue matrices are
non-resonant, such a deformation is isomonodromic if and only if the residue
matrices satisfy the Schlesinger system with respect to the parameter. Without
the non-resonance condition this result fails: there exist non-Schlesinger
isomonodromic deformations. In the present article we introduce the class of
the so-called isoprincipal deformations of Fuchsian systems. Every isoprincipal
deformation is also an isomonodromic one. In general, the class of the
isomonodromic deformations is much richer than the class of the isoprincipal
deformations, but in the non-resonant case these classes coincide. We prove
that a deformation is isoprincipal if and only if the residue matrices satisfy
the Schlesinger system. This theorem holds in the general case, without any
assumptions on the spectra of the residue matrices of the deformation. An
explicit example illustrating isomonodromic deformations, which are neither
isoprincipal nor meromorphic with respect to the parameter, is also given
The Edge Electric Field of a Pyroelectric and its Applications
Following a change of temperature of a pyroelectric (PE), a depolarizing
electric field appears both inside the PE, as well as outside its edges, the
edge depolarizing electric field (EDEF). The EDEF extends outwards up to a
distance of the order of magnitude of the PE width. The mapping and the
strength of the EDEF have been calculated and analyzed for the case of a
semi-infinite pyroelectric plate. This strong EDEF (104-105 V/cm), when
penetrating into the surrounding medium, creates a variety of physical effects:
inducing electrical current in a semiconductor and affecting its resistance,
accelerating charged and neutral particles in vacuum or in a gas, generating
electromagnetic waves, modifying optical characteristics by electrooptical and
photoelasic effects, generating piezoelectric deformation and more. We show
that these EDEF induced effects could serve as a basis for the development of
various applications and devices.Comment: 27 pages including 13 figure
Optical alignment system Patent
Electro-optical/computer system for aligning large structural members and maintaining correct positio
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