798,903 research outputs found
Conditional symmetry and spectrum of the one-dimensional Schr\"odinger equation
We develop an algebraic approach to studying the spectral properties of the
stationary Schr\"odinger equation in one dimension based on its high order
conditional symmetries. This approach makes it possible to obtain in explicit
form representations of the Schr\"odinger operator by matrices for
any and, thus, to reduce a spectral problem to a purely
algebraic one of finding eigenvalues of constant matrices. The
connection to so called quasi exactly solvable models is discussed. It is
established, in particular, that the case, when conditional symmetries reduce
to high order Lie symmetries, corresponds to exactly solvable Schr\"odinger
equations. A symmetry classification of Sch\"odinger equation admitting
non-trivial high order Lie symmetries is carried out, which yields a hierarchy
of exactly solvable Schr\"odinger equations. Exact solutions of these are
constructed in explicit form. Possible applications of the technique developed
to multi-dimensional linear and one-dimensional nonlinear Schr\"odinger
equations is briefly discussed.Comment: LaTeX-file, 31 pages, to appear in J.Math.Phys., v.37, N7, 199
A portable absorbed dose measuring instrument with gamma discrimination
The characteristics of an electronic instrument for measuring the radiation dose absorbed by tissues are presented. The detector is a sphere of tissue-equivalent plastic with a single wire located on a diameter of the sphere. The electronic circuits and method of operation of the detector are described. Advantages are the small size and easy portability plus ability to selectively measure neutron and gamma plus neutron events
Remote measurement of the water content of snowpacks
Electronic equipment for sensing moisture content of snowpacks is described. Components of electronic test equipment are illustrated and methods of conducting tests are explained. Possibilities for airborne sensing are examined
Parity-violating DIS and the flavour dependence of the EMC effect
Isospin-dependent nuclear forces play a fundamental role in nuclear
structure. In relativistic models of nuclear structure constructed at the quark
level these isovector nuclear forces affect the u and d quarks differently,
leading to non-trivial flavour dependent modifications of the nuclear parton
distributions. We explore the effect of isospin dependent forces for
parity-violating deep inelastic scattering on nuclear targets and demonstrate
that the cross-sections for nuclei with N /= Z are sensitive to the flavour
dependence of the EMC effect. Indeed, for nuclei like lead and gold we find
that these flavour dependent effects are large.Comment: 4 pages, 2 figure
Cosmic Evolution and Primordial Black Hole Evaporation
A cosmological model in which primordial black holes (PBHs) are present in
the cosmic fluid at some instant t=t_0 is investigated. The time t_0 is
naturally identified with the end of the inflationary period. The PBHs are
assumed to be nonrelativistic in the comoving fluid, to have the same mass, and
may be subject to evaporation for t>t_0. Our present work is related to an
earlier paper of Zimdahl and Pavon [Phys. Rev. D {\bf 58}, 103506 (1998)], but
in contradistinction to these authors we assume that the (negative) production
rate of the PBHs is zero. This assumption appears to us to be more simple and
more physical. Consequences of the formalism are worked out. In particular, the
four-divergence of the entropy four-vector in combination with the second law
in thermodynamics show in a clear way how the the case of PBH evaporation
corresponds to a production of entropy. Accretion of radiation onto the black
holes is neglected. We consider both a model where two different sub-fluids
interact, and a model involving one single fluid only. In the latter case an
effective bulk viscosity naturally appears in the formalism.Comment: 18 pages, LaTeX, no figures. Extended discussion of the black hole
evaporation process. Version to appear in Phys. Rev.
Spin-dependent structure functions in nuclear matter and the polarized EMC effect
An excellent description of both spin-independent and spin-dependent quark
distributions and structure functions has been obtained with a modified
Nambu-Jona-Lasinio model, which is free of unphysical thresholds for nucleon
decay into quarks - hence incorporating an important aspect of confinement. We
utilize this model to investigate nuclear medium modifications to structure
functions and find that we are readily able to reproduce both nuclear matter
saturation and the experimental F^A_2N / F_2N ratio, that is, the EMC effect.
Applying this framework to determine g^A_1p, we find that the ratio g^A_1p /
g_1p differs significantly from 1, with the quenching caused by the nuclear
medium being about twice that of the spin-independent case. This represents an
exciting result, which if confirmed experimentally, will reveal much about the
quark structure of nuclear matter.Comment: 4 pages, 4 figure
Training a perceptron by a bit sequence: Storage capacity
A perceptron is trained by a random bit sequence. In comparison to the
corresponding classification problem, the storage capacity decreases to
alpha_c=1.70\pm 0.02 due to correlations between input and output bits. The
numerical results are supported by a signal to noise analysis of Hebbian
weights.Comment: LaTeX, 13 pages incl. 4 figures and 1 tabl
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