A Non-Perturbative Superpotential With E8E_8 Symmetry

We compute the non-perturbative superpotential in $F$-theory compactification to four dimensions on a complex three-fold $\P^1\times S$, where $S$ is a rational elliptic surface. In contrast to examples considered previously, the superpotential in this case has interesting modular properties; it is essentially an $E_8$ theta function.Comment: Additional references and clarifications. Latex, 10 page

Financing SMEs: a model for optimising the capital structure

This paper argues that the existing finance literature is inadequate with respect to its cov-erage of capital structure of small and medium sized enterprises (SMEs). In particular it is argued that the cost of equity (being both conceptually ill defined and empirically non quantifiable) is not applicable to the capital structure decisions for a large proportion of SMEs and the optimal capital structure depends only on the mix of short and long term debt. The paper then presents a model for optimising the debt mix and demonstrates its practical application using an Italian firm’s debt structure as a case study

The α+d→ 6Li+γ\alpha + d \rightarrow ~ ^6\mathrm{Li} + \gamma astrophysical SS-factor and its implications for Big Bang Nucleosynthesis

The \alpha+d\rightarrow\, ^6{\rm Li}+\gamma radiative capture is studied in order to predict the $^6$Li primordial abundance. Within a two-body framework, the $\alpha$ particle and the deuteron are considered the structureless constituents of $^6$Li. Five $\alpha+d$ potentials are used to solve the two-body problem: four of them are taken from the literature, only one having also a tensor component. A fifth model is here constructed in order to reproduce, besides the $^6$Li static properties as binding energy, magnetic dipole and electric quadrupole moments, also the $S$-state asymptotic normalization coefficient (ANC). The two-body bound and scattering problem is solved with different techniques, in order to minimize the numerical uncertainty of the present results. The long-wavelength approximation is used, and therefore only the electric dipole and quadrupole operators are retained. The astrophysical $S$-factor is found to be significantly sensitive to the ANC, but in all the cases in good agreement with the available experimental data. The theoretical uncertainty has been estimated of the order of few % when the potentials which reproduce the ANC are considered, but increases up to $\simeq 20$ % when all the five potential models are retained. The effect of this $S$-factor prediction on the $^6$Li primordial abundance is studied, using the public code PArthENoPE. For the five models considered here we find $^6{\rm Li}/$H$= (0.9 - 1.8) \times 10^{-14}$, with the baryon density parameter in the 3-$\sigma$ range of Planck 2015 analysis, $\Omega_b h^2= 0.02226 \pm 0.00023$.Comment: 26 pages, 9 figure

Equations of the reaction-diffusion type with a loop algebra structure

A system of equations of the reaction-diffusion type is studied in the framework of both the direct and the inverse prolongation structure. We find that this system allows an incomplete prolongation Lie algebra, which is used to find the spectral problem and a whole class of nonlinear field equations containing the original ones as a special case.Comment: 16 pages, LaTex. submitted to Inverse Problem

An Introduction to the Covariant Quantization of Superstrings

We give an introduction to a new approach to the covariant quantization of superstrings. After a brief review of the classical Green--Schwarz superstring and Berkovits' approach to its quantization based on pure spinors, we discuss our covariant formulation without pure spinor constraints. We discuss the relation between the concept of grading, which we introduced to define vertex operators, and homological perturbation theory, and we compare our work with recent work by others. In the appendices, we include some background material for the Green-Schwarz and Berkovits formulations, in order that this presentation be self contained.Comment: LaTex, 23 pp. Contribution to the Proceedings of the Workshop in String Theory, Leuven 2002, some references added and a comment on ref. [16

Relating Green-Schwarz and Extended Pure Spinor Formalisms by Similarity Transformation

In order to gain deeper understanding of pure-spinor-based formalisms of superstring, an explicit similarity transformation is constructed which provides operator mapping between the light-cone Green-Schwarz (LCGS) formalism and the extended pure spinor (EPS) formalism, a recently proposed generalization of the Berkovits' formalism in an enlarged space. By applying a systematic procedure developed in our previous work, we first construct an analogous mapping in the bosonic string relating the BRST and the light-cone formulations. This provides sufficient insights and allows us to construct the desired mapping in the more intricate case of superstring as well. The success of the construction owes much to the enlarged field space where pure spinor constraints are removed and to the existence of the ``B-ghost'' in the EPS formalism.Comment: 37pages, no figur

Towards Pure Spinor Type Covariant Description of Supermembrane -- An Approach from the Double Spinor Formalism --

In a previous work, we have constructed a reparametrization invariant worldsheet action from which one can derive the super-Poincare covariant pure spinor formalism for the superstring at the fully quantum level. The main idea was the doubling of the spinor degrees of freedom in the Green-Schwarz formulation together with the introduction of a new compensating local fermionic symmetry. In this paper, we extend this "double spinor" formalism to the case of the supermembrane in 11 dimensions at the classical level. The basic scheme works in parallel with the string case and we are able to construct the closed algebra of first class constraints which governs the entire dynamics of the system. A notable difference from the string case is that this algebra is first order reducible and the associated BRST operator must be constructed accordingly. The remaining problems which need to be solved for the quantization will also be discussed.Comment: 40 pages, no figure, uses wick.sty; v2: a reference added, published versio

Sonographic monitoring of gout

Objective: To assess the role of grayscale and power Doppler sonography in short-term monitoring of acute gouty synovitis. Methods: Clinical and sonographic assessments were performed in a patient with gout. Clinical and sonographic evaluations were performed within the first day of the acute onset of synovitis of the first metatarsophalangeal joint of the left foot and 7 and 14 days after the baseline assessments. The patient was treated only with colchicine. Results: At baseline, both grayscale and power Doppler sonography revealed clearly evident findings of acute synovitis (joint cavity widening, thickening of periarticular soft tissues and power Doppler signal). After seven days, a complete clinical remission occurred. Ultrasound examination revealed marked improvement with respect to the basic findings, even if all the sonographic features of joint inflammation were still detectable. Two weeks after the onset of the acute attack, clinical remission was maintained and all the sonographic features of synovitis disappeared. Conclusion: Sonography is a sensitive and reliable tool for assessing and short-term monitoring of acute gouty attack

Structure and dynamics of catalytically competent but labile paramagnetic metal-hydrides: The Ti(iii)-H in homogeneous olefin polymerization

Metal hydride complexes find widespread application in catalysis and their properties are often understood on the basis of the available crystal structures. However, some catalytically relevant metal hydrides are only spontaneously formed in situ, cannot be isolated in large quantities or crystallised and their structure is therefore ill defined. One such example is the paramagnetic Ti(iii)-hydride involved in homogeneous Ziegler–Natta catalysis, formed upon activation of CpTi(iv)Cl(3) with modified methylalumoxane (MMAO). In this contribution, through a combined use of electron paramagnetic resonance (EPR), electron-nuclear double resonance (ENDOR) and hyperfine sublevel correlation (HYSCORE) spectroscopies we identify the nature of the ligands, their bonding interaction and the extent of the spin distribution. From the data, an atomistic and electronic model is proposed, which supports the presence of a self-assembled ion pair between a cationic terminal Ti-hydride and an aluminate anion, with a hydrodynamic radius of ca. 16 Å

A New Renormalization Scheme of Fermion Fields in Electroweak Standard Model

This paper has been withdrawn by the author,due a immature idea.Comment: 6 page