A lower bound for the modulus of the Dirichlet eta function on partition P\mathcal{P} from 2-D principal component analysis

The present manuscript aims to derive an expression for the lower bound of the modulus of the Dirichlet eta function on vertical lines $\Re(s)=\alpha$. An approach based on a two-dimensional principal component analysis matching the dimensionality of the complex plane, which is built on a parametric ellipsoidal shape, has been undertaken to achieve this result. This lower bound, which is expressed as $\forall s \in \, \mathbb{C}$ s.t. $\Re(s) \in \mathcal{P}(s)$, $|\eta(s)| \geq |1- \frac{\sqrt{2}}{2^{\alpha}}|$, where $\eta$ is the Dirichlet eta function, has implications for the Riemann hypothesis as $|\eta(s)| >0$ for any such $s \in \mathcal{P}$, where $\mathcal{P}$ is a partition spanning one half of the critical strip on either sides of the critical line $\Re(s) = 1/2$ depending upon a variable delimiting regions, complementary by mirror symmetry with respect to $\Re(s) = 1/2$.Comment: 13 page

An investigation of the non-trivial zeros of the Riemann zeta function

The zeros of the Riemann zeta function outside the critical strip are the so-called trivial zeros. While many zeros of the Riemann zeta function are located on the critical line $\Re(s)=1/2$, the non-existence of zeros in the remaining part of the critical strip $\Re(s) \in \, ]0,1[$ remains to be proven. The Riemann zeta functional leads to a relationship between the zeros of the Riemann zeta function on either sides of the critical line. Given $s$ a complex number and $\bar{s}$ its complex conjugate, if $s$ is a zero of the Riemann zeta function in the critical strip $\Re(s) \in \, ]0,1[$, then we have $\zeta(s) = \zeta(1-\bar{s})$. As the Riemann hypothesis states that all non-trivial zeros lie on the critical line $\Re(s) = 1/2$, it is enough to show there are no zeros on either sides of the critical line within the critical strip $\Re(s) \in \, ]0,1[$, to say the Riemann hypothesis is true.Comment: 16 page

On the origin of the canyon diablo no. 2 and no. 3 meteorites

Measurements of helium-3, neon-21, and argon-38 in Canyon Diablo meteorites indicated origin of Canyon Diablo-

Rare gas evidence for two paired meteorite falls

Mass spectroscopic analysis of rare gas contents of two paired meteorite fall

The extent of community and public support available to families caring for orphans in Malawi.

There are an estimated 15 million AIDS orphans worldwide. Families play an important role in safeguarding orphans, but they may be increasingly compromised by the HIV/AIDS epidemic. The international aid community has recognized the need to help families continue caring for orphaned children by strengthening their safety nets. Before we build new structures, however, we need to know the extent to which community and public safety nets already provide support to families with orphans. To address this gap, we analyzed nationally representative data from 27,495 children in the 2004-2005 Malawi Integrated Household Survey. We found that communities commonly assisted orphan households through private transfers; organized responses to the orphan crisis were far less frequent. Friends and relatives provided assistance to over 75% of orphan households through private gifts, but the value of such support was relatively low. Over 40% of orphans lived in a community with support groups for the chronically ill and approximately a third of these communities provided services specifically for orphans and other vulnerable children. Public programs, which form a final safety net for vulnerable households, were more widespread. Free/subsidized agricultural inputs and food were the most commonly used public safety nets by children's households in the past year (44 and 13%, respectively), and households with orphans were more likely to be beneficiaries. Malawi is poised to drastically expand safety nets to orphans and their families, and these findings provide an important foundation for this process

An algebra of discrete event processes

This report deals with an algebraic framework for modeling and control of discrete event processes. The report consists of two parts. The first part is introductory, and consists of a tutorial survey of the theory of concurrency in the spirit of Hoare's CSP, and an examination of the suitability of such an algebraic framework for dealing with various aspects of discrete event control. To this end a new concurrency operator is introduced and it is shown how the resulting framework can be applied. It is further shown that a suitable theory that deals with the new concurrency operator must be developed. In the second part of the report the formal algebra of discrete event control is developed. At the present time the second part of the report is still an incomplete and occasionally tentative working paper

Land-Rich Economies, Education and Economic Development

We analyze the emergence of large-scale education systems in a setup where growth is associated with changes in the configuration of the economy. The model is based on three central elements: first, individual preferences over consumption goods generate changes in the composition of individual spending as income grows, embodied in Engel curves. Second, the production of sophisticated services is intensive in human capital. Third, investment in human capital by individual households faces borrowing constraints. Our model uses an overlapping generation framework similar to the one in Galor and Moav (2003). As that paper does, we also model the incentives that the economic ´elite may have (collectively) to accept taxation destined to finance the education of credit-constrained workers. In our model this incentive does not necessarily arise from a complementarity between physical and human capital in manufacturing. Rather, we emphasize the demand for human-capital-intensive services by high-income groups. The argument model seems capable to account for salient features of the development of Latin America in the 19th century, where, in particular, land-rich countries such as Argentina established an extensive public education system and a sophisticated service sector before developing significant manufacturing activities.

Self-consistent 2-phase AGN torus models: SED library for observers

We assume that dust near active galactic nuclei (AGN) is distributed in a torus-like geometry, which may be described by a clumpy medium or a homogeneous disk or as a combination of the two (i.e. a 2-phase medium). The dust particles considered are fluffy and have higher submillimeter emissivities than grains in the diffuse ISM. The dust-photon interaction is treated in a fully self-consistent three dimensional radiative transfer code. We provide an AGN library of spectral energy distributions (SEDs). Its purpose is to quickly obtain estimates of the basic parameters of the AGN, such as the intrinsic luminosity of the central source, the viewing angle, the inner radius, the volume filling factor and optical depth of the clouds, and the optical depth of the disk midplane, and to predict the flux at yet unobserved wavelengths. The procedure is simple and consists of finding an element in the library that matches the observations. We discuss the general properties of the models and in particular the 10mic. silicate band. The AGN library accounts well for the observed scatter of the feature strengths and wavelengths of the peak emission. AGN extinction curves are discussed and we find that there is no direct one-to-one link between the observed extinction and the wavelength dependence of the dust cross sections. We show that objects of the library cover the observed range of mid IR colors of known AGN. The validity of the approach is demonstrated by matching the SEDs of a number of representative objects: Four Seyferts and two quasars for which we present new Herschel photometry, two radio galaxies, and one hyperluminous infrared galaxy. Strikingly, for the five luminous objects we find pure AGN models fit the SED without a need to postulate starburst activity.Comment: A&A accepted by referee, AGN library available at http://www.eso.org/~rsiebenm/agn_models/index.htm