Derived PD-Hirsch extensions of filtered crystalline complexes and filtered crysalline dga's

We construct a theory of the derived PD-Hirsch extension of the log crystalline complex of a log smooth scheme and we construct a fundamental filtered dga $(H_{{\rm zar},{\rm TW}},P)$ and a fundamental filtered complex $(H_{\rm zar},P)$ for a simple normal crossing log scheme $X$ over a family of log points by using the log crystalline method in order to overcome obstacles arising from the incompatibility of the p-adic Steenbrink complexes in [M] and [Nak4] with the cup product of the log crystalline complex of $X$. When the base log scheme is the log point of a perfect field of characteristic $p>0$, we prove that $(H_{{\rm zar},{\rm TW}},P)$ and $(H_{\rm zar},P)$ is canonically isomorphic to Kim and Hain's filtered dga and their filtered complex in [KH], respectively.Comment: 156 pages. arXiv admin note: text overlap with arXiv:1902.0018

Two commentaries on ‘Impact of tuberculosis preventive therapy on tuberculosis and mortality in HIV-infected children’

These are commentaries on a Cochrane review, published in this issue of EBCH, first published as: Gray DM, Young T, Cotton M, Zar H. Impact of tuberculosis preventive therapy on tuberculosis and mortality in HIV-infected children. Cochrane Database of Systematic Reviews 2009, Issue 1. Art. No.: CD006418. DOI:10.1002/14651858.CD006418.pub2

Kosher Olive Oil in Antiquity Reconsidered

Josephus attests several times to a Jewish aversion to the use of Gentile olive oil. In m. ‘Abod. Zar. 2:6, this practice is first advocated and then immediately reversed by Rabbi and his court. What is the rationale for this sudden leniency with regard to Gentile olive oil? In a well-known article entitled “Kosher Olive Oil in Antiquity,” Martin Goodman argues that Rabbi’s statement is the result of his inability to find a legal basis for the prohibition of Gentile olive oil. Goodman, however, accounts neither for the unique economic and dietary factors associated with olive oil, nor tannaitic legislation regarding other foodstuffs that may shed light on this case. In this article, I reconsider Jewish stances towards Gentile olive oil in antiquity from the time of Josephus to the Tannaitic period

Dichromacy: Color Vision Impairment and Consanguinity in Heterogenous Population of Pakistan

Background and Objectives: Dichromacy, an X-linked recessive disorder is identified worldwide, more in males than females. In European Caucasians, its incidence is 8% in males and 0.5% in females. In India, it is 8.73% in males and 1.69% in females, and in Iran, it is 8.18% in males and 0.43% in females. Population based epidemiological data about dichromacy in different ethnic groups in Pakistan is not available. The aim of this study was to find out the population prevalence of inherited red-green dichromacy in a heterogenous population of the district of Chiniot, Punjab, Pakistan, and to determine the impact of consanguinity and ethnicity. Methods: In this cross-sectional study, boys and girls of the higher secondary schools were examined in the three tehsils of district Chiniot. Pseudoisochromatic Ishihara Test has been employed for detection of dichromacy in the study population. The sample size was calculated statistically as 260, which was expanded to 705 and divided by population density of the three tehsils. Results: Screening of 359 males and 346 females revealed 19 (5.29%) dichromat males and only 2 (0.58%) females. The study population belonged to 23 castes / isonym groups. The consanguinity found in the district of Chiniot is 84.82% and in the dichromat families, it is 85.71%, of which 52.37% are first cousin. Interpretation & Conclusion: The study has shown that the incidence of dichromacy could be reduced through genetic counselin

Non-compact subsets of the Zariski space of an integral domain

Let $V$ be a minimal valuation overring of an integral domain $D$ and let $\mathrm{Zar}(D)$ be the Zariski space of the valuation overrings of $D$. Starting from a result in the theory of semistar operations, we prove a criterion under which the set $\mathrm{Zar}(D)\setminus\{V\}$ is not compact. We then use it to prove that, in many cases, $\mathrm{Zar}(D)$ is not a Noetherian space, and apply it to the study of the spaces of Kronecker function rings and of Noetherian overrings.Comment: To appear in the Illinois Journal of Mathematic

Some closure operations in Zariski-Riemann spaces of valuation domains: a survey

In this survey we present several results concerning various topologies that were introduced in recent years on spaces of valuation domains

On higher direct images of convergent isocrystals

Let k be a perfect field of characteristic p>0 and W the ring of Witt vectors of k. In this article, we give a new proof of the Frobenius descent for convergent isocrystals on a variety over k relative to W. This proof allows us to deduce an analogue of the de Rham complexes comparaison theorem of Berthelot without assuming a lifting of the Frobenius morphism. As an application, we prove a version of Berthelot's conjecture on the preservation of convergent isocrystals under the higher direct image by a smooth proper morphism of k-varieties.Comment: 35 page