An extension of Buchberger's criteria for Groebner basis decision

Two fundamental questions in the theory of Groebner bases are decision ("Is a basis G of a polynomial ideal a Groebner basis?") and transformation ("If it is not, how do we transform it into a Groebner basis?") This paper considers the first question. It is well-known that G is a Groebner basis if and only if a certain set of polynomials (the S-polynomials) satisfy a certain property. In general there are m(m-1)/2 of these, where m is the number of polynomials in G, but criteria due to Buchberger and others often allow one to consider a smaller number. This paper presents two original results. The first is a new characterization theorem for Groebner bases that makes use of a new criterion that extends Buchberger's Criteria. The second is the identification of a class of polynomial systems G for which the new criterion has dramatic impact, reducing the worst-case scenario from m(m-1)/2 S-polynomials to m-1.Comment: 20 pages, 2 figure

The refined transfer, bundle structures and algebraic K-theory

We give new homotopy theoretic criteria for deciding when a fibration with homotopy finite fibers admits a reduction to a fiber bundle with compact topological manifold fibers. The criteria lead to a new and unexpected result about homeomorphism groups of manifolds. A tool used in the proof is a surjective splitting of the assembly map for Waldhausen's functor A(X). We also give concrete examples of fibrations having a reduction to a fiber bundle with compact topological manifold fibers but which fail to admit a compact fiber smoothing. The examples are detected by algebraic K-theory invariants. We consider a refinement of the Becker-Gottlieb transfer. We show that a version of the axioms described by Becker and Schultz uniquely determines the refined transfer for the class of fibrations admitting a reduction to a fiber bundle with compact topological manifold fibers. In an appendix, we sketch a theory of characteristic classes for fibrations. The classes are primary obstructions to finding a compact fiber smoothing.Comment: This version contains mostly minor revision

Relativistic and Radiative Corrections to the Mollow Spectrum

The incoherent, inelastic part of the resonance fluorescence spectrum of a laser-driven atom is known as the Mollow spectrum [B. R. Mollow, Phys. Rev. 188, 1969 (1969)]. Starting from this level of description, we discuss theoretical foundations of high-precision spectroscopy using the resonance fluorescence light of strongly laser-driven atoms. Specifically, we evaluate the leading relativistic and radiative corrections to the Mollow spectrum, up to the relative orders of (Z alpha)^2 and alpha(Z alpha)^2, respectively, and Bloch-Siegert shifts as well as stimulated radiative corrections involving off-resonant virtual states. Complete results are provided for the hydrogen 1S-2P_{1/2} and 1S-2P_{3/2} transitions; these include all relevant correction terms up to the specified order of approximation and could directly be compared to experimental data. As an application, the outcome of such experiments would allow for a sensitive test of the validity of the dressed-state basis as the natural description of the combined atom-laser system.Comment: 20 pages, 1 figure; RevTe

Closed-form expressions for correlated density matrices: application to dispersive interactions and example of (He)2

Empirically correlated density matrices of N-electron systems are investigated. Exact closed-form expressions are derived for the one- and two-electron reduced density matrices from a general pairwise correlated wave function. Approximate expressions are proposed which reflect dispersive interactions between closed-shell centro-symmetric subsystems. Said expressions clearly illustrate the consequences of second-order correlation effects on the reduced density matrices. Application is made to a simple example: the (He)2 system. Reduced density matrices are explicitly calculated, correct to second order in correlation, and compared with approximations of independent electrons and independent electron pairs. The models proposed allow for variational calculations of interaction energies and equilibrium distance as well as a clear interpretation of dispersive effects on electron distributions. Both exchange and second order correlation effects are shown to play a critical role on the quality of the results.Comment: 22 page

Strong-field approximation for intense-laser atom processes: the choice of gauge

The strong-field approximation can be and has been applied in both length gauge and velocity gauge with quantitatively conflicting answers. For ionization of negative ions with a ground state of odd parity, the predictions of the two gauges differ qualitatively: in the envelope of the angular-resolved energy spectrum, dips in one gauge correspond to humps in the other. We show that the length-gauge SFA matches the exact numerical solution of the time-dependent Schr\"odinger equation.Comment: 5 pages, 3 figures, revtex

Dollar Dominance, Euro Aspirations: Recipe for Discord?

After nearly a century of dominance of the international monetary system, has the US dollar finally met its match in the euro? When Europe’s Economic and Monetary Union (EMU) came into existence in 1999, many observers predicted that the euro would soon join America’s greenback at the peak of global finance. Achievements, however, have fallen short of aspirations. After an initial spurt of enthusiasm, international use of the euro now actually appears to be levelling off, even stalling, and so far seems confined largely to a limited range of market sectors and regions. The euro has successfully attained a place second only to the greenback, but it remains, and is likely to remain, a quite distant second without a determined effort by EMU authorities to promote their money’s global role. The temptation will surely be great. In practical terms, it is difficult to imagine that EMU authorities will refrain entirely from trying to promote a greater role for the euro. But that, in turn, could be a recipe for discord with the US, which has never made any secret of its commitment to preserving the greenback’s world-wide dominance. A struggle for monetary leadership could become a source of sustained tensions in US-European relations. Fortunately, however, there seems relatively little risk of a destabilising escalation into outright geopolitical conflict

Regulation of CLL survival by hypoxia-inducible factor and its target genes

AbstractChronic lymphocytic leukemia (CLL), the most common adult leukemia in the Western world, is characterized by the progressive accumulation of small mature CD5+B lymphocytes in the peripheral blood, lymphoid organs, and bone marrow (BM). The main feature of the disease is decreased apoptosis, resulting in the pathologic accumulation of these malignant cells. Appropriate cellular responses to changes in oxygen tension during normal development or pathological processes, such as cardiovascular disease and cancer, are ultimately regulated by the transcription factor, hypoxia-inducible factor (HIF). Unlike their normal counterparts, CLL cells express HIF-1α even under normoxia. In addition, overexpression of HIF-1α has been observed in leukemic cells in BM specimens from CLL patients. The HIF transcription factor has been implicated in controlling the expression of a wide variety of genes implicated in apoptosis, angiogenesis, invasion, and metastasis. This review describes pathways regulating CLL survival with a focus on HIF-1α and its target genes, MIF and Midkine (MK), and the potential cross-talk between these factors

Duality and Pro-Spectra

Cofiltered diagrams of spectra, also called pro-spectra, have arisen in diverse areas, and to date have been treated in an ad hoc manner. The purpose of this paper is to systematically develop a homotopy theory of pro-spectra and to study its relation to the usual homotopy theory of spectra, as a foundation for future applications. The surprising result we find is that our homotopy theory of pro-spectra is Quillen equivalent to the opposite of the homotopy theory of spectra. This provides a convenient duality theory for all spectra, extending the classical notion of Spanier-Whitehead duality which works well only for finite spectra. Roughly speaking, the new duality functor takes a spectrum to the cofiltered diagram of the Spanier-Whitehead duals of its finite subcomplexes. In the other direction, the duality functor takes a cofiltered diagram of spectra to the filtered colimit of the Spanier-Whitehead duals of the spectra in the diagram. We prove the equivalence of homotopy theories by showing that both are equivalent to the category of ind-spectra (filtered diagrams of spectra). To construct our new homotopy theories, we prove a general existence theorem for colocalization model structures generalizing known results for cofibrantly generated model categories.Comment: Published by Algebraic and Geometric Topology at http://www.maths.warwick.ac.uk/agt/AGTVol4/agt-4-34.abs.htm

Scalar mesons: in search of the lightest glueball

According to the QCD expectations the lightest glueball should be a scalar particle (J^{PC}=0^{++}). Different scenarios have been considered for a classification of these states but -- despite considerable progress in recent years -- the experimental basis for various parameters is still rather weak. We present a new analysis of the elastic and charge exchange pi pi scattering between 1000 and 1800 MeV. A unique solution is selected which shows clear evidence for f_0(1500) and a broad state (\sigma or ``f_0(1000)''), but there is no evidence for f_0(1370) at a level of \gtrsim 10% branching ratio to pi pi. Arguments in favour of the broad state to be a glueball are summarized.Comment: talk presented at QCD06, Montpellier, France, July3-7, 200

Correlated electron emission in laser-induced nonsequence double ionization of Helium

In this paper, we have investigated the correlated electron emission of the nonsequence double ionization (NSDI) in an intense linearly polarized field. The theoretical model we employed is the semiclassical rescattering model, the model atom we used is the helium. We find a significant correlation between magnitude and direction of the momentum of two emission electrons, and give a good explanation for this striking phenomenon by observing the classical collisional trajectories. We argue that this correlation phenomenon is universal in NSDI process, as revealed by the recent experiment on the argon.Comment: 4 pages, 3 figures, accepted for publication in Phys. Rev.