Sums of products of Ramanujan sums

The Ramanujan sum $c_n(k)$ is defined as the sum of $k$-th powers of the primitive $n$-th roots of unity. We investigate arithmetic functions of $r$ variables defined as certain sums of the products $c_{m_1}(g_1(k))...c_{m_r}(g_r(k))$, where $g_1,..., g_r$ are polynomials with integer coefficients. A modified orthogonality relation of the Ramanujan sums is also derived.Comment: 13 pages, revise

Extended BRST invariance in topological Yang Mills theory revisited

Extended BRST invariance (BRST plus anti-BRST invariances) provides in principle a natural way of introducing the complete gauge fixing structure associated to a gauge field theory in the minimum representation of the algebra. However, as it happens in topological Yang Mills theory, not all gauge fixings can be obtained from a symmetrical extended BRST algebra, where antighosts belong to the same representation of the Lorentz group of the corresponding ghosts. We show here that, at non interacting level, a simple field redefinition makes it possible to start with an extended BRST algebra with symmetric ghost antighost spectrum and arrive at the gauge fixing action of topological Yang Mills theory.Comment: Interaction terms heve been included in all the calculations. Two references added. Version to be published in Phys. Rev. D. 7 pages, Latex, no figure

A spatial regression approach to FDI in Vietnam: province-level evidence

Foreign direct investment (FDI) flows into Vietnam have increased significantly in recent years and are distributed unequally between provinces. This paper aims to investigate the locational determinants of FDI in 62 Vietnamese provinces and whether spatial dependence is a significant factor that both researchers and policy-makers should take into account. We report that province-specific percapita income, secondary education enrolment, labor costs, openness to trade, and domestic investment affect FDI directly within the province itself and have indirect effects on FDI in neighboring provinces. The direct and indirect effects coexist with spill over effects and spatial dependence between provinces. Our findings indicate that FDI in Vietnam reflects a combination of complex vertical and export platform motivations on the part of foreign investors; and an agglomeration dynamics that may perpetuate the existing regional disparities in the distribution of FDI capital between provinces

Extending structures I: the level of groups

Let $H$ be a group and $E$ a set such that $H \subseteq E$. We shall describe and classify up to an isomorphism of groups that stabilizes $H$ the set of all group structures that can be defined on $E$ such that $H$ is a subgroup of $E$. A general product, which we call the unified product, is constructed such that both the crossed product and the bicrossed product of two groups are special cases of it. It is associated to $H$ and to a system $\bigl((S, 1_S,\ast), \triangleleft, \, \triangleright, \, f \bigl)$ called a group extending structure and we denote it by $H \ltimes S$. There exists a group structure on $E$ containing $H$ as a subgroup if and only if there exists an isomorphism of groups $(E, \cdot) \cong H \ltimes S$, for some group extending structure $\bigl((S, 1_S,\ast), \triangleleft, \, \triangleright, \, f \bigl)$. All such group structures on $E$ are classified up to an isomorphism of groups that stabilizes $H$ by a cohomological type set ${\mathcal K}^{2}_{\ltimes} (H, (S, 1_S))$. A Schreier type theorem is proved and an explicit example is given: it classifies up to an isomorphism that stabilizes $H$ all groups that contain $H$ as a subgroup of index 2.Comment: 17 pages; to appear in Algebras and Representation Theor

The time resolution of the St. Petersburg paradox

A resolution of the St. Petersburg paradox is presented. In contrast to the standard resolution, utility is not required. Instead, the time-average performance of the lottery is computed. The final result can be phrased mathematically identically to Daniel Bernoulli's resolution, which uses logarithmic utility, but is derived using a conceptually different argument. The advantage of the time resolution is the elimination of arbitrary utility functions.Comment: 20 pages, 1 figur

Bicrossed products for finite groups

We investigate one question regarding bicrossed products of finite groups which we believe has the potential of being approachable for other classes of algebraic objects (algebras, Hopf algebras). The problem is to classify the groups that can be written as bicrossed products between groups of fixed isomorphism types. The groups obtained as bicrossed products of two finite cyclic groups, one being of prime order, are described.Comment: Final version: to appear in Algebras and Representation Theor

Hamiltonian BRST-anti-BRST Theory

The hamiltonian BRST-anti-BRST theory is developed in the general case of arbitrary reducible first class systems. This is done by extending the methods of homological perturbation theory, originally based on the use of a single resolution, to the case of a biresolution. The BRST and the anti-BRST generators are shown to exist. The respective links with the ordinary BRST formulation and with the $sp(2)$-covariant formalism are also established.Comment: 34 pages, Latex fil

Composition of KBO (50000) Quaoar

Aims. The objective of this work is to investigate the physical properties of objects beyond Neptune-the new frontiers of the Solar System-and in particular to study the surface composition of (50 000) Quaoar, a classical Transneptunian (or Kuiper Belt) object. Because of its distance from the Sun, Quaoar is expected to have preserved, to a degree, its original composition. Our goals are to determine to what degree this is true and to shed light on the chemical evolution of this icy body. Methods. We present new near-infrared (3.6 and 4.5 mu m) photometric data obtained with the Spitzer Space Telescope. These data complement high resolution, low signal-to-noise spectroscopic and photometric data obtained in the visible and near-infrared (0.4-2.3 mu m) at VLT-ESO and provide an excellent set of constraints in the model calculation process. We perform spectral modeling of the entire wavelength range-from 0.3 to 4.5 mu m by means of a code based on the Shkuratov radiative transfer formulation of the slab model. We also attempt to determine the temperature of H(2)O ice making use of the crystalline feature at 1.65 mu m. Results. We present a model confirming previous results regarding the presence of crystalline H(2)O and CH(4) ice, as well as C(2)H(6) and organic materials, on the surface of this distant icy body. We attempt a measurement of the temperature and find that stronger constraints on the composition are needed to obtain a precise determination. Conclusions. Model fits indicate that N(2) may be a significant component, along with a component that is bright at lambda > 3.3 mu m, which we suggest at this time could be amorphous H(2)O ice in tiny grains or thin grain coatings. Irradiated crystalline H(2)O could be the source of small-grained amorphous H(2)O ice. The albedo and composition of Quaoar, in particular the presence of N(2), if confirmed, make this TNO quite similar to Triton and Pluto

Amorphous and Crystalline H20 Ice at Rhea's Inktomi Crater

We present the analysis of Cassini spectral data from spectral mapping of Saturnian icy moons Dione and Rhea, to investigate possible effects of impact crater formation on the relative abundances of crystalline and amorphous water ice in the moons' ice crusts. Both moons display morphologically young ray craters as well as older craters. Possible changes in ice properties due to crater formation are conjectured to be more visible in younger craters, and as such Rhea's well imaged ray crater Inktomi is analysed, as are older craters for comparison. We used data from Cassini's Visual and Infrared Mapping Spectrometer (VIMS). For each pixel in the VIMS maps, spectral data were extracted in the near-infrared range (1.75 micrometers less than lambda less than 2.45 micrometers). Analysis was begun by fitting a single Gaussian to the peak in absorption at 2.0 micrometers, which was then subtracted from the data, leaving residuals with a minimum on either side of the original 2.0-micrometers band. The spectra of the individual spatial pixels were then clustered by the differences between these minima, which are sensitive to changes in both ice grain size and crystallinity. This yielded preliminary maps which approximated the physical characteristics of the landscape and were used to identify candidates for further analysis. Spectra were then clustered by the properties of the 1.5-micrometers band, to divide the map into regions based on inferred grain size. For each region, the predicted differences in minima from the Gaussian residuals, over a range of crystallinities, were calculated based on the found grain sizes. This model was used to find the crystallinity of each pixel via grain size and characteristics of the residual function. Preliminary results show a greater degree of crystallization of young crater interiors, particularly in Rhea's ray crater Inktomi, where ice showed crystalline ice abundances between 33 percent and 61 percent. These patterns in ice crystallization are possibly attributable to increased heat generated during crater formation