Hyperbolic Differential Polynomials: and their Singular Perturbations: Mathematics and Its Applications, cartea 3
Autor J. Chaillouen Limba Engleză Paperback – 19 oct 2011
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Specificații
ISBN-13: 9789400995086
ISBN-10: 9400995083
Pagini: 188
Dimensiuni: 152 x 223 x 10 mm
Greutate: 0 kg
Ediția:Softcover reprint of the original 1st ed. 1979
Editura: SPRINGER NETHERLANDS
Colecția Springer
Seria Mathematics and Its Applications
Locul publicării:Dordrecht, Netherlands
ISBN-10: 9400995083
Pagini: 188
Dimensiuni: 152 x 223 x 10 mm
Greutate: 0 kg
Ediția:Softcover reprint of the original 1st ed. 1979
Editura: SPRINGER NETHERLANDS
Colecția Springer
Seria Mathematics and Its Applications
Locul publicării:Dordrecht, Netherlands
Public țintă
ResearchDescriere
Approach
your
problems
from
It
isn't
that
they
can't
see
the
the
right
end
and
begin
with
the
solution.
It
is
that
they
can't
see
answers.
Then,
one
day,
perhaps
the
problem.
you
will
find
the
final
question.
'The
Hermit
Clad
in
Crane
Feathers'
G.
K.
Chesterton,
The
scandal
of
in
R.
Van
Gulik's
The
Chinese
Maze
Father
Brown
'The
point
of
a
Murders.
pin"
Growing
specialization
and
diversification
have
brought
a
host
of
monographs
and
textbooks
on
increasingly
specialized
topics.
However,
the
'tree'
of
knowledge
of
mathematics
and
related
fields
does
not
grow
only
by
putting
forth
new
branches.
It
also
happens,
quite
often
in
fact,
that
branches
which
were
thought
to
be
com
pletely
disparate
are
suddenly
seen
to
be
related.
Further,
the
kind
and
level
of
sophistication
of
mathematics
applied
in
various
sciences
has
changed
drastically
in
recent
years:
measure
theory
is
used
(non-trivially)
in
regional
and
theoretical
economics;
algebraic
geometry
interacts
with
physics;
the
Minkowsky
lemma,
coding
theory
and
the
structure
of
water
meet
one
another
in
packing
and
covering
theory;
quantum
fields,
crystal
defects
and
mathematical
programming
profit
from
homo
topy
theory;
Lie
algebras
are
relevant
to
filtering;
and
prediction
and
electrical
engineering
can
use
Stein
spaces.
Cuprins
I.
Generalities.-
I.1.
Emission
Cones.-
I.2.
The
Topological
Algebra
D?(?).-
I.3.
The
Set
U(?)
of
Polynomial
Distributions
with
Inverse
in
D?(?).-
I.4.
Bounded
Subsets
of
U(?)
with
Bounded
Inverse.-
I.5.
First
Consequences
of
U
being
Invertible
in
D?(?)with
Bounded
Inverse.-
1.6.
Remarks.-
II.
The
Semi-algebraic
Case.
Criterion
forUto
be
Invertible
with
Bounded
Inverse.-
II.1.
Semi-algebraic
Subsets
of
?n.-
II.2.
Polynomial
Mappings
of
?n
into
?m.
Theorem
of
Seidenberg.-
II.3.
Asymptotic
Behavior
of
Semi-algebraic
Subsets
of
?2.-
II.4.
If
U
is
Invertible
with
Bounded
Inverse,
then
the
Union
of
the
V(a)
can
be
Localized.-
II.5.
Hyperbolicity
of
A
or
of
$$\bigcup\limits_{a
\in
A}
{V\left(
a
\right)}$$
the
V(a).
Criterion
for
U
to
be
Invertible
with
Bounded
Inverse.-
II.6.
Differential
Polynomials
that
are
a
Polynomial
Function
of
a
Parameter
(?
?
?p).-
III.
A
Sufficient
Condition
thatUis
Invertible
with
Bounded
Inverse.
The
Cauchy
Problem
in
Hsloc.-
III.1.
Upper
Bounds
for
|a(?)|?1.-
III.2.
Laplace
Transforms
and
Supports
of
Distributions.-
III.3.
A
Sufficient
Condition
that
U
is
Invertible
with
Bounded
Inverse.-
III.4.
The
Cauchy
Problem
with
Data
in
Hsloc.-
IV.
Hyperbolic
Hypersurfaces
and
Polynomials.-
IV.0.
Preliminary
Notations
and
Definitions.-
IV.1.
First
Properties
of
0?-Hyperbolic
V(a).-
IV.2.
First
Properties
of
0?-Hyperbolic
Cones
V(am).-
IV.3.
0?-Hyperbolicity
and
?-Hyperbolicity.-
IV.4.
Polars
with
respect
to
?
?
0?
of
0?-Hyperbolic
V(a).-
IV.5.
Successive
Multiplicities
of
a
Series
in
?[[X]]
with
respect
to
a
Polynomial
with
Roots
in
?[[X]]..-
IV.6.
Relations
between
V(am?k)
and
V(am)
that
follow
from
Hyperbolicity
of
V(a).-
IV.7.
Relations
between
V(am?k)
and
the
Polars
of
V(am)
Implied
by
Hyperbolicity
of
V(a).-
IV.8.
Functions
Rm?k,
?
on
V(am(k),
?)
?
?n.
A
Sufficient
Condition
that
V(a)
is
Hyperbolic.-
IV.9.
Local
Properties
of
the
Functions
Rm?k,
?.-
IV.10.
Real
Ordered
Sheets
of
Hyperbolic
Cones.-
IV.11.
Locally
Constant
Multiplicity
on
V(am)*
?
?n.
A
Hyperbolicity
Criterion
for
V(a).-
IV.12.
n
=
3.
A
Criterion
for
Hyperbolicity.-
IV.13.
Hyperbolicity
and
Strength
of
Polynomials.-
IV.14.
The
Cauchy
Problem.-
V.
Examples.-
V.1.
Sets
of
Homogeneous
Polynomials
of
the
Same
Degree.-
V.2.
Sets
of
Polynomials
of
the
Same
Degree.-
V.3.
Lowering
the
Degree
by
One.-
V.4.
Lowering
the
Degree
by
Two.-
V.5.
An
Example
with
Arbitrary
Lowering
of
Degree.-
V.6.
Conclusion.-
Appendix
1.
On
a
Conjecture
of
Lars
Gårding
and
Lars
Hörmander.-
Appendix
2.
A
Necessary
and
Sufficient
Condition
For
Hyperbolicity.-
Name
Index.