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Unified Field Theories
In physics, a set of theories that seeks to relate
all the known, basic forces that exist in nature.
Scientists generally agree upon the existence of four basic
forces. Two of these Electro magnetism and Gravitation are long-range
forces, and the other two, the Weak Interaction
and Strong Interaction, are short-range forces,
effective only at the scale of the atomic nucleus. Early field
theories, such as James Clerk Maxwell's electromagnetic theory,
were extended by quantum field theory.
The first modern theory was the ElectroWeak Theory,
which succeeded in unifying electromagnetism and the weak
interaction. Grand unification theories (GUT's) unify the electroweak
interactions with the strong interaction. No GUT
has as yet been verified. A new class of unified
field theories called supergravity theories propose to unify
gravitation with the other basic forces; like the GUT's, these are
unverified. Weak Interaction force that is associated
with radioactivity and particle decay and is mediated,
or carried, by the W and Z Particles. The weak
interaction is one of four fundamental forces of nature; the others
are Gravitation, electromagnetism, and Strong
Interaction.
Gell-Mann, Murray
1929-, American theoretical physicist; b. N.Y.C.
In 1953 he and, independently, the Japanese team
of T. Nakano and Kazuhiko Nishijima proposed the
concept of strangeness to account for certain particle-decay patterns.
In 1961 Gell-Mann and Yuval Ne'eman independently introduced the
eightfold way, or SU (3) symmetry, a tablelike
ordering of all subatomic particles. The 1964
discovery of the omega-minus particle, which filled a gap in
this ordering, brought the theory wide acceptance and led to Gell-Mann's
being awarded the 1969 Nobel Prize for physics.
In 1963 Gell-Mann and George Zweig independently
postulated the existence of the Quark an even more
fundamental particle with a fractional electric charge.
Zeno of Elea
c.490-c.430 BC, Greek philosopher of the Eleatic
school founded by Parmenides. Zeno's only known
work, extant in fragmented form, uses a series
of paradoxes to show the error of commonsense notions of time and
space, thereby demonstrating Parmenides' doctrine
that motion and multiplicity are logically impossible.
Contemporary thinkers have shown renewed interest
in the problems Zeno raised.
Quantum Optics
Quantum Optics is the study of radiation and matter
in the optical wavelength domain, where sophisticated
advances in laser technology enable tests of fundamental
physical questions with unprecedented precision. Optical probes
of coherent states of atoms and photons permit new insights into
questions about the basic foundations of quantum
mechanics and are leading to concrete realization
of futuristic applications such as quantum computing, cryptography
and even teleportation. They are also permitting exciting advances
in laser cooling and trapping (CAT) techniques that were highlighted
by the 1997 Nobel Prize in Physics, which was shared by UR alumnus
Steven Chu (BS 1970). These are being extended to create Bose- Einstein
condensates (BEC) in ultra-cold (nano-°K) atomic gases, to explore
the new field of nonlinear atom-optics, and to achieve potentially
reversible control of single-molecule bond formation
for the first time.
Stochastic Process
In probability theory, a family of random variables
indexed by some other set and having the property
that for each finite subset of the index set, the collection
of random variables thus indexed has a joint probability distribution;
it is one of the most general objects of study
in probability. These distributions are compatible
with each other; a property that ensures that there
exists some probability space and some family of random variables
defined on the space that realizes the original
stochastic process. Examples of stochastic processes
include Markov processes, Poisson processes, and time
series, with the index family originally thought of as referring
to time. This indexing is either discrete or continuous,
the interest being in the nature of changes of
the variables with respect to time.
Commonly, spectral value sets or pseudospectra
are defined via complex perturbations of a given
matrix. In contrast, real spectral value sets focus on the
variability of the spectrum subject to real structured perturbations.
In this talk we review some recent results on
the structure theory of real spectral value sets.
We discuss semi-algebraicity, continuous dependence on parameters
and show some numerical examples. In particular, we discuss the
difference between real and complex spectral value
sets of normal matrices. While the normal case
is trivial if complex perturbations are considered, the problem
turns out to be more complicated in the real case.
A further topic of the talk is a quantification
of the often remarked phenomenon, that spectral
value sets tend to be large for matrices with great
departure from normality. We discuss a bound for spectral value
sets based on the departure from normality in
Henrici's sense. Finally, the relation of departure
from normality and the transient behavior of dynamic systems will
be considered. In particular, we introduce the notion of stability
with normal transient behavior and give a sufficient
condition for this property in terms of departure
from normality.
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