A Comparative Study of Laplacians and Schroedinger-Lichnerowicz-Weitzenboeck Identities in Riemannian and Antisymplectic Geometry

We introduce an antisymplectic Dirac operator and antisymplectic gamma matrices. We explore similarities between, on one hand, the Schroedinger-Lichnerowicz formula for spinor bundles in Riemannian spin geometry, which contains a zeroth-order term proportional to the Levi-Civita scalar curvature, and, on the other hand, the nilpotent, Grassmann-odd, second-order \Delta operator in antisymplectic geometry, which in general has a zeroth-order term proportional to the odd scalar curvature of an arbitrary antisymplectic and torsionfree connection that is compatible with the measure density. Finally, we discuss the close relationship with the two-loop scalar curvature term in the quantum Hamiltonian for a particle in a curved Riemannian space.Comment: 55 pages, LaTeX. v2: Subsection 3.10 expanded. v3: Reference added. v4: Published versio

EXISTING APPROACHES TO RISK ASSESSMENT OF REAL INVESTMENT PROJECTS: THEIR ADVANTAGES AND DISADVANTAGES

Risk management is impossible without a systematic assessment of the significance level of identified project risks. Within the scope of this article, features of the various qualitative and quantitative methods of risk assessment of real investment projects are highlighted. This article analyzes some of the methods from the aspect of their advantages and disadvantages in application with the aim to facilitate the selection of the most convenient method for the particular project

EXISTING APPROACHES TO RISK ASSESSMENT OF REAL INVESTMENT PROJECTS: THEIR ADVANTAGES AND DISADVANTAGES

Risk management is impossible without a systematic assessment of the significance level of identified project risks. Within the scope of this article, features of the various qualitative and quantitative methods of risk assessment of real investment projects are highlighted. This article analyzes some of the methods from the aspect of their advantages and disadvantages in application with the aim to facilitate the selection of the most convenient method for the particular project

Non-Commutative Batalin-Vilkovisky Algebras, Homotopy Lie Algebras and the Courant Bracket

We consider two different constructions of higher brackets. First, based on a Grassmann-odd, nilpotent \Delta operator, we define a non-commutative generalization of the higher Koszul brackets, which are used in a generalized Batalin-Vilkovisky algebra, and we show that they form a homotopy Lie algebra. Secondly, we investigate higher, so-called derived brackets built from symmetrized, nested Lie brackets with a fixed nilpotent Lie algebra element Q. We find the most general Jacobi-like identity that such a hierarchy satisfies. The numerical coefficients in front of each term in these generalized Jacobi identities are related to the Bernoulli numbers. We suggest that the definition of a homotopy Lie algebra should be enlarged to accommodate this important case. Finally, we consider the Courant bracket as an example of a derived bracket. We extend it to the "big bracket" of exterior forms and multi-vectors, and give closed formulas for the higher Courant brackets.Comment: 42 pages, LaTeX. v2: Added remarks in Section 5. v3: Added further explanation. v4: Minor adjustments. v5: Section 5 completely rewritten to include covariant construction. v6: Minor adjustments. v7: Added references and explanation to Section

Trigger, an active release experiment that stimulated auroral particle precipitation and wave emissions

The experiment design, including a description of the diagnostic and chemical release payload, and the general results are given for an auroral process simulation experiment. A drastic increase of the field aligned charged particle flux was observed over the approximate energy range 10 eV to more than 300 keV, starting about 150 ms after the release and lasting about one second. The is evidence of a second particle burst, starting one second after the release and lasting for tens of seconds, and evidence for a periodic train of particle bursts occurring with a 7.7 second period from 40 to 130 seconds after the release. A transient electric field pulse of 200 mv/m appeared just before the particle flux increase started. Electrostatic wave emissions around 2 kHz, as well as a delayed perturbation of the E-region below the plasma cloud were also observed. Some of the particle observations are interpreted in terms of field aligned electrostatic acceleration a few hundred kilometers above the injected plasma cloud. It is suggested that the acceleration electric field was created by an instability driven by field aligned currents originating in the plasma cloud

Quantum Open-Closed Homotopy Algebra and String Field Theory

We reformulate the algebraic structure of Zwiebach's quantum open-closed string field theory in terms of homotopy algebras. We call it the quantum open-closed homotopy algebra (QOCHA) which is the generalization of the open-closed homotopy algebra (OCHA) of Kajiura and Stasheff. The homotopy formulation reveals new insights about deformations of open string field theory by closed string backgrounds. In particular, deformations by Maurer Cartan elements of the quantum closed homotopy algebra define consistent quantum open string field theories.Comment: 36 pages, fixed typos and small clarifications adde

Absolute instruments and perfect imaging in geometrical optics

We investigate imaging by spherically symmetric absolute instruments that provide perfect imaging in the sense of geometrical optics. We derive a number of properties of such devices, present a general method for designing them and use this method to propose several new absolute instruments, in particular a lens providing a stigmatic image of an optically homogeneous region and having a moderate refractive index range.Comment: 20 pages, 9 image

Cosmological tachyon from cubic string field theory

The classical dynamics of the tachyon scalar field of cubic string field theory is considered on a cosmological background. Starting from a nonlocal action with arbitrary tachyon potential, which encodes the bosonic and several supersymmetric cases, we study the equations of motion in the Hamilton-Jacobi formalism and with a generalized Friedmann equation, appliable in braneworld or modified gravity models. The cases of cubic (bosonic) and quartic (supersymmetric) tachyon potential in general relativity are automatically included. We comment the validity of the slow-roll approximation, the stability of the cosmological perturbations, and the relation between this tachyon and the Dirac-Born-Infeld one.Comment: 20 pages JHEP style, 1 figure; v4: misprints corrected, matches the published versio

Investigation of a Light Gas Helicon Plasma Source for the VASIMR Space Propulsion System

An efficient plasma source producing a high-density (approx.10(exp 19/cu m) light gas (e.g. H, D, or He) flowing plasma with a high degree of ionization is a critical component of the Variable Specific Impulse Magnetoplasma Rocket (VASIMR) concept. We are developing an antenna to apply ICRF power near the fundamental ion cyclotron resonance to further accelerate the plasma ions to velocities appropriate for space propulsion applications. The high degree of ionization and a low vacuum background pressure are important to eliminate the problem of radial losses due to charge exchange. We have performed parametric (e.g. gas flow, power (0.5 - 3 kW), magnetic field , frequency (25 and 50 MHz)) studies of a helicon operating with gas (H2 D2, He, N2 and Ar) injected at one end with a high magnetic mirror downstream of the antenna. We have explored operation with a cusp and a mirror field upstream. Plasma flows into a low background vacuum (<10(exp -4) torr) at velocities higher than the ion sound speed. High densities (approx. 10(exp 19/cu m) have been achieved at the location where ICRF will be applied, just downstream of the magnetic mirror

Symplectic connections and Fedosov's quantization on supermanifolds

A (biased and incomplete) review of the status of the theory of symplectic connections on supermanifolds is presented. Also, some comments regarding Fedosov's technique of quantization are made.Comment: Submitted to J. of Phys. Conf. Se