76,721 research outputs found
On the imaginary parts of chromatic root
While much attention has been directed to the maximum modulus and maximum
real part of chromatic roots of graphs of order (that is, with
vertices), relatively little is known about the maximum imaginary part of such
graphs. We prove that the maximum imaginary part can grow linearly in the order
of the graph. We also show that for any fixed , almost every
random graph in the Erd\"os-R\'enyi model has a non-real root.Comment: 4 figure
Method and means for providing an absolute power measurement capability Patent
Input radio frequency circuit for switching type absolute temperature measuring radiometer for noise source
Interquark Potential in Schrodinger Representation
Static charges are introduced in Yang-Mills theory via coupling to heavy
fermions. The states containing static color charges are constructed using
integration over gauge transformations. A functional representation for
interquark potential is obtained. This representation provides a simple
criterion for confinement.Comment: 9pp., Late
On the accuracy of conservation of adiabatic invariants in slow-fast systems
Let the adiabatic invariant of action variable in slow-fast Hamiltonian
system with two degrees of freedom have two limiting values along the
trajectories as time tends to infinity. The difference of two limits is
exponentially small in analytic systems. An iso-energetic reduction and
canonical transformations are applied to transform the slow-fast systems to
form of systems depending on slowly varying parameters in a complexified phase
space. On the basis of this method an estimate for the accuracy of conservation
of adiabatic invariant is given for such systems.Comment: 27 pages, 14 figure
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