On quantization of singular varieties and applications to D-branes

We calculate the ring of differential operators on some singular affine varieties (intersecting stacks, a point on a singular curve or an orbifold). Our results support the proposed connection of the ring of differential operators with geometry of D-branes in (bosonic) string theory. In particular, the answer does know about the resolution of singularities in accordance with the string theory predictions.Comment: LaTeX2e, 17 pages, misprints correcte

Effect of proline-rich polypeptide on various lines of tumour cells, normal bone marrow and giantcell tumour stromal tissue

The aim of the study was to assess the effect of proline-rich polypeptide (PRP) on bone marrow stromal stem cells in vivo and in vitro and on tumour cell lines. Methods. Isolation of giant-cell tumour (GCT) stromal cells and obtaining these cell strains; obtaining normal bone marrow stromal cell strains; PRP administration to rats; bone marrow cell explantation into cultures; PRP addition to cell cultures. Results. Various routes and doses of PRP administration to rats increased the multipotent mesenchymal stromal cell (MMSC) concentration in the bone marrow. PRP addition to normal bone marrow MMSC cultures increased cell proliferation 1.5– 2.5-fold, whereas PRP addition to GCT MMSC cultures inhibited cell proliferation 1.5–2-fold. Both proliferation inhibition and no PRP effect on proliferation were observed in tumour cell cultures. Conclusions. PRP administration to rats increased MMSC concentration in the normal bone marrow, and PRP addition to tissue cultures revealed opposite effects of PRP on cell proliferation. Keywords: Proline-rich polypeptide (PRP), multipotent mesenchymal stromal cells (MMSC).Мета дослідження – вивчення впливу багатого на пролін поліпеп тиду (ПБП) на стовбурові клітини строми кісткового мозку in vivo та in vitro і лінії пухлинних клітин. Методи. Виділення стромальних клітин гігантоклітинної пухлнии (ГКП) і отримання штамів цих клітин, а також штамів стромальних клітин нормального кісткового мозку, введення ПБП щурам, експлантація в культуру кістковомозкових клітин, додавання ПБП у культури клітин. Результаты. Різні способи і дози введення ПБП щурам збільшують концентрацію мультипотентних мезенхімальних стромальних клітин (ММСК) у кістковому мозку. Додавання ПБП у культури ММСК нормального кісткового мозку призводить до зростання проліферативної активності клітин у 1,5–2,5 разу, внесення ПБП у культури ММСК ГКП інгібує проліферацію клітин у 1,5–2 разу. У культурах пухлинних клітин спостерігається як пригнічення пухлинних клітин, так і відсутність впливу поліпептиду на проліферацію. Висновки. Введення ПБП щурам підвищує концентрацію ММСК у нормальному кістковому мозку, а за додавання ПБП у культуру тканин виявлено його різноспрямовану дію на проліферацію клітин. Ключові слова: багатий на пролін поліпептид, мультипотентні мезенхімальні стромальні клітини.Цель исследования – изучение влияния богатого пролином полипептида (ПБП) на стволовые клетки стромы костного мозга in vivo и in vitro и линии опухолевых клеток. Методы. Выделение стромальных клеток гигантоклеточной опухоли (ГКО) и получение штаммов этих клеток, а также штаммов стромальных клеток нормального костного мозга, введение ПБП крысам, эксплантация в культуру костномозговых клеток, добавление ПБП в культуры клеток. Результаты. Различные способы и дозы введения ПБП крысам увеличивают концентрацию мультипотентных мезенхимальных стромальных клеток (ММСК) в костном мозге. Добавление ПБП в культуры ММСК нормального костного мозга приводит к возрастанию пролиферативной активности клеток в 1,5–2,5 раза, внесение ПБП в культуры ММСК ГКО ингибирует пролиферацию клеток в 1,5–2 раза. В культурах опухолевых клеток наблюдалось как угнетение, так и отсутствие влияния полипептида на пролиферацию. Выводы. Введение ПБП крысам повышает концентрацию ММСК в нормальном костном мозге, а при добавлении ПБП в культуру тканей выявлено его разнонаправленное действие на пролиферацию клеток. Ключевые слова: богатый пролином полипептид, мультипотентные мезенхимальные стромальные клетки

Rank rigidity for CAT(0) cube complexes

We prove that any group acting essentially without a fixed point at infinity on an irreducible finite-dimensional CAT(0) cube complex contains a rank one isometry. This implies that the Rank Rigidity Conjecture holds for CAT(0) cube complexes. We derive a number of other consequences for CAT(0) cube complexes, including a purely geometric proof of the Tits Alternative, an existence result for regular elements in (possibly non-uniform) lattices acting on cube complexes, and a characterization of products of trees in terms of bounded cohomology.Comment: 39 pages, 4 figures. Revised version according to referee repor

Tachyon Kinks on Unstable Dp-branes

In the context of tachyon effective theory coupled to Born-Infeld electromagnetic fields, we obtain all possible singularity-free static flat configurations of codimension one on unstable Dp-branes. Computed tension and string charge density suggest that the obtained kinks are D(p-1) or D(p-1)F1-branes.Comment: 22pages, LaTeX2e, 7figure

Progress in QCD next-to-leading order calculations

I review progress related to the calculation of QCD jet cross sections at the NLO accuracy. After a short introduction into the theory of NLO calculations, I discuss two recent developments: the calculation of two- and three-jet leptoproduction at the NLO accuracy and the extension of the dipole subtraction method for computing NLO corrections for processes involving massive partons.Comment: 5 pages, 4 figures, LaTeX using JHEP3.cls, Invited talk at the International Europhysics Conference on High-Energy Physics (HEP 2001

On open superstring partition function in inhomogeneous rolling tachyon background

We consider open superstring partition function Z on the disc in time-dependent tachyon background T= f(x_i) e^{m x_0} where the profile function f depends on spatial coordinates. We compute Z to second order in derivatives of f and compare the result with some previously suggested effective actions depending only on the first derivatives of the tachyon field. We also compute the target-space stress-energy tensor in this background and demonstrate its conservation in the ``on-shell'' case of the linear profile f= f_0 + q_i x_i corresponding to a marginal perturbation. We comment on the role of the rolling tachyon with linear spatial profile in the decay of an unstable D-brane.Comment: 32p, latex, v2: introduction revised to expand and correct comments on the paper by Kutasov and Niarchos, v3: corrected typos and formulas in section 4, final version to appear in JHE

Decay of Unstable D-branes with Electric Field

Using the techniques of two dimensional conformal field theory we construct time dependent classical solutions in open string theory describing the decay of an unstable D-brane in the presence of background electric field, and explicitly evaluate the time dependence of the energy momentum tensor and the fundamental string charge density associated with this solution. The final decay product can be interpreted as a combination of stretched fundamental strings and tachyon matter.Comment: 35 pages, LaTe

Noncommutativity and Tachyon Condensation

We study the fuzzy or noncommutative Dp-branes in terms of infinitely many unstable D0-branes, from which we can construct any Dp-branes. We show that the tachyon condensation of the unstable D0-branes induces the noncommutativity. In the infinite tachyon condensation limit, most of the unstable D0-branes disappear and remaining D0-branes are actually the BPS D0-branes with the correct noncommutative coordinates. For the fuzzy S^2 case, we explicitly show only the D0-branes corresponding to the lowest Landau level survive in the limit. We also show that a boundary state for a Dp-brane satisfying the Dirichlet boundary condition on a curved submanifold embedded in the flat space is not localized on the submanifold. This implies that the Dp-brane on it is ambiguous at the string scale and solves the problem for a spherical D2-brane with a unit flux on the world volume which should be equivalent to one D0-brane. We also discuss the diffeomorphism in the D0-brane picture.Comment: 30 pages, references added, minor corrections and clarifications, version to appear in JHE

Tachyon Tube and Supertube

We search for tubular solutions in unstable D3-brane. With critical electric field E=1, solutions representing supertubes, which are supersymmetric bound states of fundamental strings, D0-branes, and a cylindrical D2-brane, are found and shown to exhibit BPS-like property. We also point out that boosting such a {\it tachyon tube} solution generates string flux winding around the tube, resulting in helical electric fluxes on the D2-brane. We also discuss issues related to fundamental string, absence of magnetic monopole, and finally more tachyon tubes with noncritical electric field.Comment: 21 pages, 3 figure

Tachyon Dynamics and the Effective Action Approximation

Recently effective actions have been extensively used to describe tachyon condensation in string theory. While the various effective actions which have appeared in the literature have very similar properties for static configurations, they differ for time-dependent tachyons. In this paper we discuss general properties of non-linear effective Lagrangians which are first order in derivatives. In particular we show that some observed properties, such as asymptotically vanishing pressure, are rather generic features, although the quantative features differ. On the other hand we argue that certain features of marginal tachyon profiles are beyond the reach of any first order Lagrangian description. We also point out that an effective action, proposed earlier, captures the dynamics of tachyons well.Comment: References added and confusing reference clarifie