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

Positselski, Leonid
Fonte: Universidade Cornell Publicador: Universidade Cornell
Tipo: Artigo de Revista Científica
Português
Relevância na Pesquisa
26%
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...

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

Horwitz, Gerald
Fonte: Universidade Cornell Publicador: Universidade Cornell
Tipo: Artigo de Revista Científica
Português
Relevância na Pesquisa
26%
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!

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

Dais, Dimitrios I.; Henk, Martin
Fonte: Universidade Cornell Publicador: Universidade Cornell
Tipo: Artigo de Revista Científica
Publicado em 20/03/1998 Português
Relevância na Pesquisa
26%
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"...

Notes on the horizontal cohomology

Verbovetsky, Alexander
Fonte: Universidade Cornell Publicador: Universidade Cornell
Tipo: Artigo de Revista Científica
Publicado em 24/03/1998 Português
Relevância na Pesquisa
26%
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)

On fibre bundle formulation of classical and statistical mechanics

Iliev, Bozhidar Z.
Fonte: Universidade Cornell Publicador: Universidade Cornell
Tipo: Artigo de Revista Científica
Publicado em 16/09/2001 Português
Relevância na Pesquisa
26%
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/

Turbulent convection: comparing the moment equations to numerical simulations

Kupka, F.
Fonte: Universidade Cornell Publicador: Universidade Cornell
Tipo: Artigo de Revista Científica
Publicado em 20/09/1999 Português
Relevância na Pesquisa
26%
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

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

Iliev, Bozhidar Z.
Fonte: Universidade Cornell Publicador: Universidade Cornell
Tipo: Artigo de Revista Científica
Português
Relevância na Pesquisa
26%
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...

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]

Iliev, Bozhidar Z.
Fonte: Universidade Cornell Publicador: Universidade Cornell
Tipo: Artigo de Revista Científica
Publicado em 20/02/1999 Português
Relevância na Pesquisa
26%
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/

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

Iliev, Bozhidar Z.
Fonte: Universidade Cornell Publicador: Universidade Cornell
Tipo: Artigo de Revista Científica
Publicado em 20/02/1999 Português
Relevância na Pesquisa
26%
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...

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

Vacaru, Sergiu I.
Fonte: Universidade Cornell Publicador: Universidade Cornell
Tipo: Artigo de Revista Científica
Português
Relevância na Pesquisa
26%
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

Fibre bundle formulation of relativistic quantum mechanics

Iliev, Bozhidar Z.
Fonte: Universidade Cornell Publicador: Universidade Cornell
Tipo: Artigo de Revista Científica
Português
Relevância na Pesquisa
26%
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...

AGNs with composite spectra II. Additional data

Goncalves, A. C.; Veron-Cetty, M. -P.; Veron, P.
Fonte: Universidade Cornell Publicador: Universidade Cornell
Tipo: Artigo de Revista Científica
Publicado em 20/11/1998 Português
Relevância na Pesquisa
26%
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...

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

Nieto, Michael Martin; Truax, D. Rodney
Fonte: Universidade Cornell Publicador: Universidade Cornell
Tipo: Artigo de Revista Científica
Português
Relevância na Pesquisa
26.08%
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

Homological Methods in Equations of Mathematical Physics

Krasil'shchik, Joseph; Verbovetsky, Alexander
Fonte: Universidade Cornell Publicador: Universidade Cornell
Tipo: Artigo de Revista Científica
Português
Relevância na Pesquisa
26.06%
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

Smoothness, Semistability, and Toroidal Geometry

Abramovich, Dan; de Jong, Johan
Fonte: Universidade Cornell Publicador: Universidade Cornell
Tipo: Artigo de Revista Científica
Publicado em 23/03/1996 Português
Relevância na Pesquisa
26%
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)

Desingularization of singular hyperkaehler varieties I

Verbitsky, Misha
Fonte: Universidade Cornell Publicador: Universidade Cornell
Tipo: Artigo de Revista Científica
Publicado em 12/11/1996 Português
Relevância na Pesquisa
26.2%
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

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

Mueller, U.; Braun, M.; Reichle, R.; Salzgeber, R. F.
Fonte: Universidade Cornell Publicador: Universidade Cornell
Tipo: Artigo de Revista Científica
Publicado em 18/12/1997 Português
Relevância na Pesquisa
26.08%
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

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

Pogorelov, Nikolai; Matsuda, Takuya
Fonte: Universidade Cornell Publicador: Universidade Cornell
Tipo: Artigo de Revista Científica
Publicado em 20/07/1998 Português
Relevância na Pesquisa
26%
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

On a class of three-dimensional integrable Lagrangians

Ferapontov, E. V.; Khusnutdinova, K. R.; Tsarev, S. P.
Fonte: Universidade Cornell Publicador: Universidade Cornell
Tipo: Artigo de Revista Científica
Português
Relevância na Pesquisa
26.08%
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...

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

Achasov, M. N.; Aulchenko, V. M.; Baru, S. E.; Beloborodov, K. I.; Berdyugin, A. V.; Bozhenok, A. V.; Bukin, A. D.; Bukin, D. A.; Burdin, S. V.; Dimova, T. V.; Dolinsky, S. I.; Druzhinin, V. P.; Dubrovin, M. S.; Gaponenko, I. A.; Golubev, V. B.; Ivanchenk
Fonte: Universidade Cornell Publicador: Universidade Cornell
Tipo: Artigo de Revista Científica
Publicado em 01/10/1999 Português
Relevância na Pesquisa
26.08%
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