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## Homological algebra of semimodules and semicontramodules: Semi-infinite homological algebra of associative algebraic structures

Fonte: Universidade Cornell
Publicador: Universidade Cornell

Tipo: Artigo de Revista Científica

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We develop the basic constructions of homological algebra in the
(appropriately defined) unbounded derived categories of modules over algebras
over coalgebras over noncommutative rings (which we call semialgebras over
corings). We define double-sided derived functors SemiTor and SemiExt of the
functors of semitensor product and semihomomorphisms, and construct an
equivalence between the exotic derived categories of semimodules and
semicontramodules.
Certain (co)flatness and/or (co)projectivity conditions have to be imposed on
the coring and semialgebra to make the module categories abelian (and the
cotensor product associative). Besides, for a number of technical reasons we
mostly have to assume that the basic ring has a finite homological dimension
(no such assumptions about the coring and semialgebra are made).
In the final sections we construct model category structures on the
categories of complexes of semi(contra)modules, and develop relative
nonhomogeneous Koszul duality theory for filtered semialgebras and
quasi-differential corings.
Our motivating examples come from the semi-infinite cohomology theory.
Comparison with the semi-infinite (co)homology of Tate Lie algebras and graded
associative algebras is established in appendices...

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## Time and Entropy from Semi-classical Tunneling of the Cosmological Scale Function

Fonte: Universidade Cornell
Publicador: Universidade Cornell

Tipo: Artigo de Revista Científica

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Two major apparently unrelated problems, that of the origin of time in the
universe associated with quantum gravity and to the entropy in de Sitter
cosmological models, are found to have their origin in a single physical
phenomenon: the semi-classical tunneling through a classically forbidden region
of the cosmological scale function. In this region there is a mixing of the
states of quantum matter and those of the semi-classical gravity which produces
a thermal mixture of the matter states and hence an "entropy"; this same mixing
effect brings about the conversion of a parametric time variable into a
physical intrinsic time.; Comment: 17 pages;, no figure. latex 2e, To appear in Moscow Quantum Gravity
Seminar, June 12-19, 1995, latex correction!

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## On a series of Gorenstein cyclic quotient singularities admitting a unique projective crepant resolution

Fonte: Universidade Cornell
Publicador: Universidade Cornell

Tipo: Artigo de Revista Científica

Publicado em 20/03/1998
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In this paper we prove that the Gorenstein cyclic quotient singularities of
type \frac 1l (1,..., 1,l-(r-1)) with $l\geq r\geq 2$, have a
\textit{unique}torus-equivariant projective, crepant, partial resolution, which
is ``full'' iff either $l\equiv 0$ mod $% (r-1) $ or $l\equiv 1$ mod $(r-1) $.
As it turns out, if one of these two conditions is fulfilled, then the
exceptional locus of the full desingularization consists of $\lfloor
\frac{l}{r-1} \rfloor$ prime divisors, $\lfloor \frac{l}{r-1}\rfloor - 1$ of
which are isomorphic to the total spaces of $\Bbb{P}_{\Bbb{C}}^1$-bundles over
$\Bbb{P}_{\Bbb{C}%}^{r-2}$. Moreover, it is shown that intersection numbers are
computable explicitly and that the resolution morphism can be viewed as a
composite of successive (normalized) blow-ups. Obviously, the monoparametrized
singularity-series of the above type contains (as its ``first member'') the
well-known Gorenstein singularity defined by the origin of the affine cone
which lies over the $r$-tuple Veronese embedding of $\Bbb{P}_{\Bbb{C}}^{r-1}$.; Comment: 96 pages. 14 Figures. LaTeX 2e with AMS and epsfig macros. This is
the revised version of the ZIB preprint SC-97-39. To appear in the
DMV-Seminar-Volume "Combinatorial Convex Geometry and Toric Varieties"...

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## Notes on the horizontal cohomology

Fonte: Universidade Cornell
Publicador: Universidade Cornell

Tipo: Artigo de Revista Científica

Publicado em 24/03/1998
Português

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#Mathematics - Differential Geometry#High Energy Physics - Theory#Mathematical Physics#Mathematics - Analysis of PDEs#Nonlinear Sciences - Exactly Solvable and Integrable Systems

This paper is devoted to the horizontal (``characteristic'') cohomology of
systems of differential equations. Recent results on computing the horizontal
cohomology via the compatibility complex are generalized. New results on the
Vinogradov C-spectral sequence and the Krasil'shchik C-cohomology are obtained.
As an application of general theory, the examples of an evolution equation and
a p-form gauge theory are explicitly worked out.; Comment: 21 pages, AMS-LaTeX 1.2 (based on LaTeX 2e), talk at the conference
``Secondary Calculus and Cohomological Physics'' in Moscow, 1997, to be
published in the proceedings of this conference (Contemporary Mathematics,
AMS)

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## On fibre bundle formulation of classical and statistical mechanics

Fonte: Universidade Cornell
Publicador: Universidade Cornell

Tipo: Artigo de Revista Científica

Publicado em 16/09/2001
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Some elements of classical mechanics and classical statistical mechanics are
formulated in terms of fibre bundles. In the bundle approach the dynamical and
distribution functions are replaced by liftings of paths in a suitably chosen
bundle. Their time evolution is described by appropriate linear transports
along paths in it or, equivalently, by corresponding invariant bundle equations
of motion. In particular, the bundle version of the Liouville equation is
derived.; Comment: 10 standard LaTeX 2e pages. The packages AMS-LaTeX and amsfonts are
required. For related works, concerning fibre bundle formulation of qunatum
physics, please visit the "publication" pages at
http://theo.inrne.bas.bg/~bozho/

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## Turbulent convection: comparing the moment equations to numerical simulations

Fonte: Universidade Cornell
Publicador: Universidade Cornell

Tipo: Artigo de Revista Científica

Publicado em 20/09/1999
Português

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The non-local hydrodynamic moment equations for compressible convection are
compared to numerical simulations. Convective and radiative flux typically
deviate less than 20% from the 3D simulations, while mean thermodynamic
quantities are accurate to at least 2% for the cases we have investigated. The
moment equations are solved in minutes rather than days on standard
workstations. We conclude that this convection model has the potential to
considerably improve the modelling of convection zones in stellar envelopes and
cores, in particular of A and F stars.; Comment: 10 pages (6 pages of text including figure captions + 4 figures),
Latex 2e with AAS Latex 5.0 macros, accepted for publication in ApJL

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## Fibre bundle formulation of nonrelativistic quantum mechanics. IV. Mixed states and evolution transport's curvature

Fonte: Universidade Cornell
Publicador: Universidade Cornell

Tipo: Artigo de Revista Científica

Português

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We propose a new systematic fibre bundle formulation of nonrelativistic
quantum mechanics. The new form of the theory is equivalent to the usual one
but it is in harmony with the modern trends in theoretical physics and
potentially admits new generalizations in different directions. In it a pure
state of some quantum system is described by a state section (along paths) of a
(Hilbert) fibre bundle. It's evolution is determined through the bundle
(analogue of the) Schr\"odinger equation. Now the dynamical variables and the
density operator are described via bundle morphisms (along paths). The
mentioned quantities are connected by a number of relations derived in this
work.
The present fourth part of this series is devoted mainly to the fibre bundle
description of mixed quantum states. We show that to the conventional density
operator there corresponds a unique density morphism (along paths) for which
the corresponding equations of motion are derived. It is also investigated the
bundle description of mixed quantum states in the different pictures of motion.
We calculate the curvature of the evolution transport and prove that it is
curvature free iff the values of the Hamiltonian operator at different moments
commute.; Comment: 14 standard (11pt...

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## Comments on: "Quantum mechanics as a gauge theory of metaplectic spinor fields" by M. Reuter [Int.J.Mod.Phys. A13 (1998), 3835-3884; hep-th/9804036]

Fonte: Universidade Cornell
Publicador: Universidade Cornell

Tipo: Artigo de Revista Científica

Publicado em 20/02/1999
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We point out how some mathematically incorrect passages in the paper of M.
Reuter can be formulated in a rigorous way. The fibre bundle approach to
quantum mechanics developed in quant-ph/9803083, quant-ph/9803084,
quant-ph/9804062, quant-ph/9806046, quant-ph/9901039, and quant-ph/9902068 is
compared with the one contained in loc. cit.; Comment: 11 standard (11pt, A4) LaTeX 2e pages. The packages AMS-LaTeX and
amsfonts are required. For related papers, view
http://www.inrne.bas.bg/mathmod/bozhome/

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## Fibre bundle formulation of nonrelativistic quantum mechanics. V. Theory's interpretation, summary and discussion

Fonte: Universidade Cornell
Publicador: Universidade Cornell

Tipo: Artigo de Revista Científica

Publicado em 20/02/1999
Português

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We propose a new systematic fibre bundle formulation of nonrelativistic
quantum mechanics. The new form of the theory is equivalent to the usual one
but it is in harmony with the modern trends in theoretical physics and
potentially admits new generalizations in different directions. In it a pure
state of some quantum system is described by a state section (along paths) of a
(Hilbert) fibre bundle. It's evolution is determined through the bundle
(analogue of the) Schr\"odinger equation. Now the dynamical variables and the
density operator are described via bundle morphisms (along paths). The
mentioned quantities are connected by a number of relations derived in this
work.
This is the fifth closing part of our investigation. We briefly discuss the
observer's role in the theory and different realizations of the space-time
model used as a base space in the bundle approach to quantum mechanics. We
point the exact conditions for the equivalence of Hilbert bundle and Hilbert
space formulations of the theory. A comparison table between the both
description of nonrelativistic quantum mechanics is presented. We discuss some
principal moments of the Hilbert bundle description and show that it is more
general than the Hilbert space one. Different directions for further research
are pointed too.; Comment: 17 standard (11pt...

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## Loop Quantum Gravity in Ashtekar and Lagrange-Finsler Variables and Fedosov Quantization of General Relativity

Fonte: Universidade Cornell
Publicador: Universidade Cornell

Tipo: Artigo de Revista Científica

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We propose an unified approach to loop quantum gravity and Fedosov
quantization of gravity following the geometry of double spacetime fibrations
and their quantum deformations. There are considered pseudo-Riemannian
manifolds enabled with 1) a nonholonomic 2+2 distribution defining a nonlinear
connection (N-connection) structure and 2) an Arnowitt-Deser-Misner 3+1
decomposition. The Ashtekar-Barbero variables are generalized and adapted to
the N-connection structure which allows us to write the general relativity
theory equivalently in terms of Lagrange-Finsler variables and related
canonical almost symplectic forms and connections. The Fedosov results are
re-defined for gravitational gauge like connections and there are analyzed the
conditions when the star product for deformation quantization is computed in
terms of geometric objects in loop quantum gravity. We speculate on equivalence
of quantum gravity theories with 3+1 and 2+2 splitting and quantum analogs of
the Einstein equations.; Comment: latex 2e, 11pt, 48 pages, 1 latex figure, discussion added

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## Fibre bundle formulation of relativistic quantum mechanics

Fonte: Universidade Cornell
Publicador: Universidade Cornell

Tipo: Artigo de Revista Científica

Português

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We propose a fibre bundle formulation of the mathematical base of
relativistic quantum mechanics. At the present stage the bundle form of the
theory is equivalent to its conventional one, but it admits new types of
generalizations in different directions. In the bundle description the
wavefunctions are replaced with (state) sections (covariant approach) or
liftings of paths (equivalently: sections along paths) (time-dependent
approach) of a suitably chosen vector bundle over space-time whose (standard)
fibre is the space of the wavefunctions. Now the quantum evolution is described
as a linear transportation of the state sections/liftings in the (total) bundle
space. The equations of these transportations turn to be the bundle versions of
the corresponding relativistic wave equations. Connections between the
(retarded) Green functions of these equations and the evolution operators and
transports are found. Especially the Dirac and Klein-Gordon equations are
considered.; Comment: Essentially revised version in which an error in the previous one is
corrected. 24 LaTeX 2e pages. The packages AMS-LaTeX and amsfonts are
required. This is a unified and updated version of the papers
quant-ph/0105056 and quant-ph/0107002. For related works...

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## AGNs with composite spectra II. Additional data

Fonte: Universidade Cornell
Publicador: Universidade Cornell

Tipo: Artigo de Revista Científica

Publicado em 20/11/1998
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In a previous paper (Veron et al. 1997) we presented medium resolution (3.4 A
FWHM) spectroscopic observations of 15 "transition objects", selected for
having an ambiguous location in the Veilleux & Osterbrock (1987) diagnostic
diagrams, and showed that most of them were in fact "composite", this being due
to the simultaneous presence on the slit of both a Seyfert or Liner nucleus and
a HII region. Here, we report new spectroscopic observations of 53
emission-line galaxies with a "transition" spectrum, bringing up to 61 the
total number of observed objects in an unbiased sample of 88 "transition
objects". Almost all of the observed galaxies have a "composite" nature,
confirming the finding that true "transition" spectra may not exist at all. By
eliminating "composite objects" from the diagnostic diagrams, a clear
separation between the different classes of nuclear emission-line regions
(Seyfert 2s, Liners and HII regions) becomes apparent; by restricting the
volume occupied by the different line-emitting regions in the 3-dimensional
diagnostic diagrams, we are also restricting the range of possible physical
parameters in these regions. There seems to be no continuity between Seyfert 2s
and Liners, the two classes occupying distinct volumes in the 3-dimensional
space defined by [OIII]5007/Hbeta...

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## The Schr\"odinger system H=-{1/2}e^{\Upsilon(t-t_o)}\partial_{xx} +\lfrac{1}{2}\omega^2e^{-\Upsilon(t-t_o)}x^2

Fonte: Universidade Cornell
Publicador: Universidade Cornell

Tipo: Artigo de Revista Científica

Português

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In this paper, we attack the specific time-dependent Hamiltonian problem
H=-{1/2}e^{\Upsilon(t-t_o)}\partial_{xx}
+\lfrac{1}{2}\omega^2e^{-\Upsilon(t-t_o)}x^2. This corresponds to a
time-dependent mass (TM) Schr\"odinger equation. We give the specific
transformations to i) the more general quadratic (TQ) Schr\"odinger equation
and to ii) a different time-dependent oscillator (TO) equation. For each
Schr\"odinger system, we give the Lie algebra of space-time symmetries, the
number states, the coherent states, the squeezed-states and the time-dependent
,

, (\Delta x)^2, (\Delta p)^2, and uncertainty product.; Comment: Latex, 24 pages, including 3 figures and 8 tables. New title and format for journal. Conclusion added

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## Homological Methods in Equations of Mathematical Physics

Fonte: Universidade Cornell
Publicador: Universidade Cornell

Tipo: Artigo de Revista Científica

Português

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#Mathematics - Differential Geometry#High Energy Physics - Theory#Mathematical Physics#Mathematics - Analysis of PDEs#Nonlinear Sciences - Exactly Solvable and Integrable Systems

These lecture notes are a systematic and self-contained exposition of the
cohomological theories naturally related to partial differential equations: the
Vinogradov C-spectral sequence and the C-cohomology, including the formulation
in terms of the horizontal (characteristic) cohomology. Applications to
computing invariants of differential equations are discussed. The lectures
contain necessary introductory material on the geometric theory of differential
equations and homological algebra.; Comment: 150 pages, AmS-LaTeX 1.2 (based on LaTeX 2e), needs to run through
LaTeX four times, no figures, Lectures given in August 1998 at the
International Summer School in Levoca, Slovakia. Revised version 2 (Mon, 21
Dec 1998): misprints corrected, Definition 4.3 on page 70 changed

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## Smoothness, Semistability, and Toroidal Geometry

Fonte: Universidade Cornell
Publicador: Universidade Cornell

Tipo: Artigo de Revista Científica

Publicado em 23/03/1996
Português

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We provide a new proof of the following result:
Let $X$ be a variety of finite type over an algebraically closed field $k$ of
characteristic 0, let $Z\subset X$ be a proper closed subset. There exists a
modification $f:X_1 \rar X$, such that $X_1$ is a quasi-projective nonsingular
variety and $Z_1 = f^{-1}(Z)_\red$ is a strict divisor of normal crossings.
Needless to say, this theorem is a weak version of Hironaka's well known
theorem on resolution of singularities. Our proof has the feature that it
builds on two standard techniques of algebraic geometry: semistable reduction
for curves, and toric geometry.
Another proof of the same result was discovered independently by F. Bogomolov
and T. Pantev. The two proofs are similar in spirit but quite different in
detail.; Comment: 12 pages (in large font)., LATEX 2e (in latex 2.09 compatibility
mode)

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## Desingularization of singular hyperkaehler varieties I

Fonte: Universidade Cornell
Publicador: Universidade Cornell

Tipo: Artigo de Revista Científica

Publicado em 12/11/1996
Português

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Let $M$ be a singular hyperkaehler variety, obtained as a moduli space of
stable holomorphic bundles on a compact hyperkaehler manifold
(alg-geom/9307008). Consider $M$ as a complex variety in one of the complex
structures induced by the hyperkaehler structure. We show that normalization of
$M$ is smooth, hyperkaehler and does not depend on the choice of induced
complex structure.; Comment: 13 pages, LaTeX 2e LaTeX 2e

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## Vibrational Frequencies of the 2p^2A^"_2 and 3d^2E^" States of the Triatomic Deuterium Molecule

Fonte: Universidade Cornell
Publicador: Universidade Cornell

Tipo: Artigo de Revista Científica

Publicado em 18/12/1997
Português

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We investigated the vibrational energies in the 2p^2A^"_2 and 3d^2E^" states
of the triatomic deuterium molecule D_3. The experiments were performed using a
fast neutral beam photoionization spectrometer recently developed at Freiburg.
A depletion type optical double-resonance scheme using two pulsed dye lasers
was applied. The measured vibrational frequencies of the 2p^2A^"_2 state of D_3
are compared to those of H_3 and to theoretical values calculated from an ab
initio potential energy surface. The data give insight into the importance of
the coupling between the valence electron and the ion core.; Comment: 24 pages of LaTeX including 8 Figures

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## Application of numerical methods to modeling the stellar wind and interstellar medium interaction

Fonte: Universidade Cornell
Publicador: Universidade Cornell

Tipo: Artigo de Revista Científica

Publicado em 20/07/1998
Português

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We present a review of the application of numerical methods to solve the
problem of the stellar/solar wind with the local interstellar medium. Most of
approaches described are developed by the authors. They include both purely gas
dynamic and magnetohydrodynamic methods. Some attention is given to the
influence of the neutral component of the interstellar medium on the flow
structure. Far-field boundary conditions are formulated which are usually
required in astrophyscal application owing to the extremely large length scale
of these problems. Results are presented of the stationary and nonstationary,
axisymmetric and geniunly three-dimensional calculations. Newly developed
high-resolution numerical methods are discussed which can be applied to a large
variety of astrophysical problems. The bibliography includes 113 references.
The review will be published in ``CFD Review 97'' by John Wiley.; Comment: 27 pages, 25 figures, TeX files, can be used only in LaTeX 2.09,
LaTeX 2e in 2.09 compatibility mode cannot compile style files

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## On a class of three-dimensional integrable Lagrangians

Fonte: Universidade Cornell
Publicador: Universidade Cornell

Tipo: Artigo de Revista Científica

Português

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We characterize non-degenerate Lagrangians of the form $ \int f(u_x, u_y,
u_t) dx dy dt $ such that the corresponding Euler-Lagrange equations $
(f_{u_x})_x+ (f_{u_y})_y+ (f_{u_t})_t=0 $ are integrable by the method of
hydrodynamic reductions. The integrability conditions constitute an
over-determined system of fourth order PDEs for the Lagrangian density $f$,
which is in involution and possess interesting differential-geometric
properties. The moduli space of integrable Lagrangians, factorized by the
action of a natural equivalence group, is three-dimensional. Familiar examples
include the dispersionless Kadomtsev-Petviashvili (dKP) and the Boyer-Finley
Lagrangians, $f=u_x^3/3+u_y^2-u_xu_t$ and $f=u_x^2+u_y^2-2e^{u_t}$,
respectively. A complete description of integrable cubic and quartic
Lagrangians is obtained. Up to the equivalence transformations, the list of
integrable cubic Lagrangians reduces to three examples, $ f=u_xu_yu_t,
f=u_x^2u_y+u_yu_t, and f=u_x^3/3+u_y^2-u_xu_t ({\rm dKP}).$ There exists a
unique integrable quartic Lagrangian, $ f=u_x^4+2u_x^2u_t-u_xu_y-u_t^2.$ We
conjecture that these examples exhaust the list of integrable polynomial
Lagrangians which are essentially three-dimensional (it was verified that there
exist no polynomial integrable Lagrangians of degree five). We prove that the
Euler-Lagrange equations are integrable by the method of hydrodynamic
reductions if and only if they possess a scalar pseudopotential playing the
role of a dispersionless `Lax pair'. MSC: 35Q58...

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## The process $e^+e^-\to\pi^+\pi^-\pi^0$ in the energy range 2E_0=1.04 - 1.38 GeV

Fonte: Universidade Cornell
Publicador: Universidade Cornell

Tipo: Artigo de Revista Científica

Publicado em 01/10/1999
Português

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In the experiment with the SND detector at VEPP-2M e^+e^- collider the
process $e^+e^-\to\pi^+\pi^-\pi^0$ was studied in the energy range 2E_0 from
1.04 to 1.38 GeV. A broad peak was observed with the visible mass
$M_{vis}=1220\pm 20$ MeV and cross section in the maximum $\sigma_0\simeq 4$
nb. The peak can be interpreted as a $\omega$-like resonance $\omega (1200)$.; Comment: 10 pages LATEX and 5 figures

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