ОРТОГОНАЛЬНАЯ КРИВОЛИНЕЙНАЯ СИСТЕМА КООРДИНАТ И ПОСТРОЕНИЕ ПОВЕРХНОСТЕЙ НА ТРАПЕЦИЕВИДНО-КРИВОЛИНЕЙНЫХ ПЛАНАХ

Thin space constructions on curved plans there are used at building of public structures, trade centers. Sport constructions. Working-out the methods of forming of the surfaces on the curved plans that is one of the modern task of the architecture and town building. The orthogonal coordinate system that is formed at the plane with some plane directrix curve and the system of the right lines orthogonal to the directrix curve there is regarded at the stat. The coordinate system forms some trapezium-curved segment. Taking some function of the vertical coordinate there is possible to receive different surfaces at the curved plans. Conjugating different directrix curves, it’s possible to receive the combined surfaces. The article presents a system of orthogonal coordinates of curvilinear-trapezoidal planes and methods for forming surfaces on these planes. Surfaces with a function of the vertical coordinate of a general view are considered, and surfaces on combined plans of segments of the same type are shown.Тонкостенные пространственные конструкции на криволинейных планах все более широко используются при строительстве общественных зданий, торговых центров, спортивных сооружений. Разработка методов формообразования поверхностей на криволинейных планах является одной из современных задач архитектуры и градостроительства. В статье рассматривается ортогональная система координат, образованная в плоскости с произвольной направляющей кривой и системой прямых линий, ортогональных направляющей кривой. Координатная система образует в плоскости криволинейно-трапециевидную область. Задание функции координаты ортогональной плоскости позволяет образовывать разнообразные поверхности на криволинейных планах. Сопрягая различные направляющие кривые в плоскости, можно формировать комбинированные поверхности. В статье приведена система ортогональных координат криволинейно-трапециевидных планов и способы формообразование поверхностей на этих планах. Рассмотрены поверхности с функцией вертикальной координаты общего вида, приведены поверхности на комбинированных планах из сегментов одного типа

New N=4 Superfields and Sigma-models

In this note, we construct new representations of D=2, N=4 supersymmetry which do not involve chiral or twisted chiral multiplets. These multiplets may make it possible to circumvent no-go theorems about N=4 superspace formulations of WZWN-models.Comment: 11 pages, late

Generalized Kahler manifolds and off-shell supersymmetry

We solve the long standing problem of finding an off-shell supersymmetric formulation for a general N = (2, 2) nonlinear two dimensional sigma model. Geometrically the problem is equivalent to proving the existence of special coordinates; these correspond to particular superfields that allow for a superspace description. We construct and explain the geometric significance of the generalized Kahler potential for any generalized Kahler manifold; this potential is the superspace Lagrangian.Comment: 21 pages; references clarified and added; theorem generalized; typos correcte

The spectrum features of UHECRs below and surrounding GZK

The energy spectrum of UHECRs is discussed on the basis of the Yakutsk array database analysis. In the region E=0.1 to 30 EeV the showers are detected under trigger-500, while at energies above 30 EeV the whole acceptance area for trigger-1000 is used in order to utilize all the data available in the region of GZK cutoff.Comment: Invited talk at CRIS2004: GZK and surroundings, Catania, Italy, 31.05.04. To appear in Nucl. Phys. B Proc. Supp

Monopoles and clusters

We define and study certain hyperkaehler manifolds which capture the asymptotic behaviour of the SU(2)-monopole metric in regions where monopoles break down into monopoles of lower charges. The rate at which these new metrics approximate the monopole metric is exponential, as for the Gibbons-Manton metric.Comment: v2.: relation to calorons mentioned; added explanation

Hybrid configuration content of heavy S-wave mesons

We use the non-relativistic expansion of QCD (NRQCD) on the lattice to study the lowest hybrid configuration contribution to the ground state of heavy S-wave mesons. Using lowest-order lattice NRQCD to create the heavy-quark propagators, we form a basis of ``unperturbed'' S-wave and hybrid states. We then apply the lowest-order coupling of the quark spin and chromomagnetic field at an intermediate time slice to create ``mixed'' correlators between the S-wave and hybrid states. From the resulting amplitudes, we extract the off-diagonal element of our two-state Hamiltonian. Diagonalizing this Hamiltonian gives us the admixture of hybrid configuration within the meson ground state. The present effort represents a continuation of previous work: the analysis has been extended to include lattices of varying spacings, source operators having better overlap with the ground states, and the pseudoscalar (along with the vector) channel. Results are presented for bottomonium ($\Upsilon$, $\eta_b^{}$) using three different sets of quenched lattices. We also show results for charmonium ($J/\psi$, $\eta_c^{}$) from one lattice set, although we note that the non-relativistic approximation is not expected to be very good in this case.Comment: 9 pages, 7 figures, version to appear in Phys Rev

Families of N=2 Strings

In a given 4d spacetime bakcground, one can often construct not one but a family of distinct N=2 string theories. This is due to the multiple ways N=2 superconformal algebra can be embedded in a given worldsheet theory. We formulate the principle of obtaining different physical theories by gauging different embeddings of the same symmetry algebra in the same ``pre-theory.'' We then apply it to N=2 strings and formulate the recipe for finding the associated parameter spaces of gauging. Flat and curved target spaces of both (4,0) and (2,2) signatures are considered. We broadly divide the gauging choices into two classes, denoted by alpha and beta, and show them to be related by T-duality. The distinction between them is formulated topologically and hinges on some unique properties of 4d manifolds. We determine what their parameter spaces of gauging are under certain simplicity ansatz for generic flat spaces (R^4 and its toroidal compactifications) as well as some curved spaces. We briefly discuss the spectra of D-branes for both alpha and beta families.Comment: 66+1 pages, 2 tables, latex 2e, hyperref. ver2: typos corrected, reference adde

Properties of hyperkahler manifolds and their twistor spaces

We describe the relation between supersymmetric sigma-models on hyperkahler manifolds, projective superspace, and twistor space. We review the essential aspects and present a coherent picture with a number of new results.Comment: 26 pages. v2: Sign mistakes corrected; Kahler potential explicitly calculated in example; references added. v3: Published version--several small clarifications per referee's reques

Supersymmetric non-linear sigma-models with boundaries revisited

We study two-dimensional supersymmetric non-linear sigma-models with boundaries. We derive the most general family of boundary conditions in the non-supersymmetric case. Next we show that no further conditions arise when passing to the N=1 model. We present a manifest N=1 off-shell formulation. The analysis is greatly simplified compared to previous studies and there is no need to introduce non-local superspaces nor to go (partially) on-shell. Whether or not torsion is present does not modify the discussion. Subsequently, we determine under which conditions a second supersymmetry exists. As for the case without boundaries, two covariantly constant complex structures are needed. However, because of the presence of the boundary, one gets expressed in terms of the other one and the remainder of the geometric data. Finally we recast some of our results in N=2 superspace and discuss applications.Comment: LaTeX, 23 page

Superstrings on NS5 backgrounds, deformed AdS3 and holography

We study a non-standard decoupling limit of the D1/D5-brane system, which interpolates between the near-horizon geometry of the D1/D5 background and the near-horizon limit of the pure D5-brane geometry. The S-dual description of this background is actually an exactly solvable two-dimensional (worldsheet) conformal field theory: {null-deformed SL(2,R)} x SU(2) x T^4 or K3. This model is free of strong-coupling singularities. By a careful treatment of the SL(2,R), based on the better-understood SL(2,R) / U(1) coset, we obtain the full partition function for superstrings on SL(2,R) x SU(2) x K3. This allows us to compute the partition functions for the J^3 and J^2 current-current deformations, as well as the full line of supersymmetric null deformations, which links the SL(2,R) conformal field theory with linear dilaton theory. The holographic interpretation of this setup is a renormalization-group flow between the decoupled NS5-brane world-volume theory in the ultraviolet (Little String Theory), and the low-energy dynamics of super Yang--Mills string-like instantons in six dimensions.Comment: JHEP style, 59 pages, 1 figure; v2: minor changes, to appear in JHE