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This book presents original research results on pseudodifferential
operators. C*-algebras generated by pseudodifferential operators
with piecewise smooth symbols on a smooth manifold are considered.
For each algebra, all the equivalence classes of irreducible
representations are listed; as a consequence, a criterion for a
pseudodifferential operator to be Fredholm is stated, the topology
on the spectrum is described, and a solving series is constructed.
Pseudodifferential operators on manifolds with edges are
introduced, their properties are considered in details, and an
algebra generated by the operators is studied. An introductory
chapter includes all necessary preliminaries from the theory of
pseudodifferential operators and C*-algebras.
This book studies electron resonant tunneling in two- and
three-dimensional quantum waveguides of variable cross-sections in
the time-independent approach. Mathematical models are suggested
for the resonant tunneling and develop asymptotic and numerical
approaches for investigating the models. Also, schemes are
presented for several electronics devices based on the phenomenon
of resonant tunneling. Compared to its first edition, this book
includes four new chapters, redistributes the content between
chapters and modifies the estimates of the remainders in the
asymptotics of resonant tunneling characteristics. The book is
addressed to mathematicians, physicists, and engineers interested
in waveguide theory and its applications in electronics.
This book studies electron resonant tunneling in two- and
three-dimensional quantum waveguides of variable cross-sections in
the time-independent approach. Mathematical models are suggested
for the resonant tunneling and develop asymptotic and numerical
approaches for investigating the models. Also, schemes are
presented for several electronics devices based on the phenomenon
of resonant tunneling. Compared to its first edition, this book
includes four new chapters, redistributes the content between
chapters and modifies the estimates of the remainders in the
asymptotics of resonant tunneling characteristics. The book is
addressed to mathematicians, physicists, and engineers interested
in waveguide theory and its applications in electronics.
This volume studies electron resonant tunneling in two- and
three-dimensional quantum waveguides of variable cross-sections in
the time-independent approach. Mathematical models are suggested
for the resonant tunneling and develop asymptotic and numerical
approaches for investigating the models. Also, schemes are
presented for several electronics devices based on the phenomenon
of resonant tunneling. Devices based on the phenomenon of electron
resonant tunneling are widely used in electronics. Efforts are
directed towards refining properties of resonance structures. There
are prospects for building new nano size electronics elements based
on quantum dot systems. However, the role of resonance structure
can also be given to a quantum wire of variable cross-section.
Instead of an "electrode - quantum dot - electrode" system, one can
use a quantum wire with two narrows. A waveguide narrow is an
effective potential barrier for longitudinal electron motion along
a waveguide. The part of the waveguide between two narrows becomes
a "resonator" , where electron resonant tunneling can occur. This
phenomenon consists in the fact that, for an electron with energy
E, the probability T(E) to pass from one part of the waveguide to
the other part through the resonator has a sharp peak at E = Eres,
where Eres denotes a "resonant" energy. Such quantum resonators can
find applications as elements of nano electronics devices and
provide some advantages in regard to operation properties and
production technology. The book is addressed to mathematicians,
physicists, and engineers interested in waveguide theory and its
applications in electronics.
This book considers dynamic boundary value problems in domains with
singularities of two types. The first type consists of "edges" of
various dimensions on the boundary; in particular, polygons, cones,
lenses, polyhedra are domains of this type. Singularities of the
second type are "singularly perturbed edges" such as smoothed
corners and edges and small holes. A domain with singularities of
such type depends on a small parameter, whereas the boundary of the
limit domain (as the parameter tends to zero) has usual edges, i.e.
singularities of the first type. In the transition from the limit
domain to the perturbed one, the boundary near a conical point or
an edge becomes smooth, isolated singular points become small
cavities, and so on. In an "irregular" domain with such
singularities, problems of elastodynamics, electrodynamics and some
other dynamic problems are discussed. The purpose is to describe
the asymptotics of solutions near singularities of the boundary.
The presented results and methods have a wide range of applications
in mathematical physics and engineering. The book is addressed to
specialists in mathematical physics, partial differential
equations, and asymptotic methods.
This book considers dynamic boundary value problems in domains with
singularities of two types. The first type consists of "edges" of
various dimensions on the boundary; in particular, polygons, cones,
lenses, polyhedra are domains of this type. Singularities of the
second type are "singularly perturbed edges" such as smoothed
corners and edges and small holes. A domain with singularities of
such type depends on a small parameter, whereas the boundary of the
limit domain (as the parameter tends to zero) has usual edges, i.e.
singularities of the first type. In the transition from the limit
domain to the perturbed one, the boundary near a conical point or
an edge becomes smooth, isolated singular points become small
cavities, and so on. In an "irregular" domain with such
singularities, problems of elastodynamics, electrodynamics and some
other dynamic problems are discussed. The purpose is to describe
the asymptotics of solutions near singularities of the boundary.
The presented results and methods have a wide range of applications
in mathematical physics and engineering. The book is addressed to
specialists in mathematical physics, partial differential
equations, and asymptotic methods.
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