On Exact Tachyon Potential in Open String Field Theory

In these notes we revisit the tachyon lagrangian in the open string field theory using background independent approach of Witten from 1992. We claim that the tree level lagrangian (up to second order in derivatives and modulo some class of field redefinitions) is given by $L = e^{-T} (\partial T)^2 + (1+T)e^{-T}$. Upon obvious change of variables this leads to the potential energy $-\phi^2 \log {\phi^2 \over e}$ with canonical kinetic term. This lagrangian may be also obtained from the effective tachyon lagrangian of the p-adic strings in the limit $p\to 1$. Applications to the problem of tachyon condensation are discussed.Comment: 12pages, harvmac b mode, corrected some typo

On non-abelian structures in open string field theory

Multi-brane backgrounds are studied in the framework of the background independent open string field theory. A simple description of the non-abelian degrees of freedom is given. Algebra of the differential operators acting on the space of functions on the space-time provides a natural tool for the discussion of this phenomena.Comment: 16 pages, harvmac b mode, references adde

DECISION-SUPPORT SYSTEM FOR WOOD HARVESTING PLANNING IN RUSSIA

Abstract: Extraction of wood by cut-to-length harvesting method (CTL) is becoming a common practice in Russia. Logging companies are faced a large number of options for CTL planning, but they have limited knowledge of the potential in CTL logistics. Objective is to develop a decision support system (DSS) for CTL analyzing at a company level. DSS provides the comprehensive view on the benefits and limitations of different CTL options for making sound short and long term decisions. DSS has been constructed in MapInfo environment using C++ for coding/simulation. The system generates delivery plans, which reduce the CTL costs and rationalize the usage of machinery fleet

On Unification of RR Couplings

We consider the couplings of RR fields with open string sector for $Dp$-${\overline{Dp}}$ backgrounds of various $p$. Proposed approach, based on the approximation of the open string algebra by the algebra of differential operators, provides the unified description of these couplings and their interrelations.Comment: References added, Latex, 18 page

Normalizers of maximal tori and real forms of Lie groups

For a complex reductive Lie group $G$ Tits defined an extension $W_G^T$ of the corresponding Weyl group $W_G$. The extended group is supplied with an embedding into the normalizer $N_G(H)$ of the maximal torus $H\subset G$ such that $W_G^T$ together with $H$ generate $N_G(H)$. We give an interpretation of the Tits classical construction in terms of the maximal split real form $G(\mathbb{R})\subset G(\mathbb{C})$, leading to a simple topological description of $W^T_G$. We also propose a different extension $W_G^U$ of the Weyl group $W_G$ associated with the compact real form $U\subset G(\mathbb{C})$. This results into a presentation of the normalizer of maximal torus of the group extension $U\ltimes {\rm Gal}(\mathbb{C}/\mathbb{R})$ by the Galois group ${\rm Gal}(\mathbb{C}/\mathbb{R})$. We also describe explicitly the adjoint action of $W_G^T$ and $W^U_G$ on the Lie algebra of $G$.Comment: 17 page

On q-deformed gl(l+1)-Whittaker function II

A representation of a specialization of a q-deformed class one lattice gl(\ell+1}-Whittaker function in terms of cohomology groups of line bundles on the space QM_d(P^{\ell}) of quasi-maps P^1 to P^{\ell} of degree d is proposed. For \ell=1, this provides an interpretation of non-specialized q-deformed gl(2)-Whittaker function in terms of QM_d(\IP^1). In particular the (q-version of) Mellin-Barnes representation of gl(2)-Whittaker function is realized as a semi-infinite period map. The explicit form of the period map manifests an important role of q-version of Gamma-function as a substitute of topological genus in semi-infinite geometry. A relation with Givental-Lee universal solution (J-function) of q-deformed gl(2)-Toda chain is also discussed.Comment: Extended version submitted in Comm. Math. Phys., 24 page