Characteristic-free test ideals

Tight closure test ideals have been central to the classification of singularities in rings of characteristic p > 0 p>0 , and via reduction to characteristic p > 0 p>0 , in equal characteristic 0 as well. Their properties and applications have been described by Schwede and Tucker [Progress in commutative algebra 2, Walter de Gruyter, Berlin, 2012]. In this paper, we extend the notion of a test ideal to arbitrary closure operations, particularly those coming from big Cohen-Macaulay modules and algebras, and prove that it shares key properties of tight closure test ideals. Our main results show how these test ideals can be used to give a characteristic-free classification of singularities, including a few specific results on the mixed characteristic case. We also compute examples of these test ideals.

Quantitative properties of the non-properness set of a polynomial map, a positive characteristic case

Let [Formula: see text] be a generically finite polynomial map of degree [Formula: see text] between affine spaces. In [Z. Jelonek and M. Lasoń, Quantitative properties of the non-properness set of a polynomial map, Manuscripta Math. 156(3–4) (2018) 383–397] we proved that if [Formula: see text] is the field of complex or real numbers, then the set [Formula: see text] of points at which [Formula: see text] is not proper is covered by polynomial curves of degree at most [Formula: see text]. In this paper, we generalize this result to positive characteristic. We provide a geometric proof of an upper bound by [Formula: see text].

Refugee health and religion: Karenni Catholics in Omaha, United States

This article argues, based on the author’s research and years of engagement with resettled Karenni refugees in Omaha (U.S.) and illustrated by a characteristic case of a health emergency, that refugees’ religious beliefs and networks can increase access to resources needed to boost their resilience, improve their health, and advance their sense of wellbeing, and subsequently encourages agencies working with refugees and other migrants to pay attention to refugees’ religious beliefs and networks and closely collaborate with religious organizations. The author conceptualizes religious values and networks as social capital and calls for qualitative studies to explore the role of religion in improving resilience, health, and wellbeing of refugees and migrants.

Faith, Understanding, Proof

Faith and understanding are in a complex relationship with each other; they are living in their own way in the depths of every developed human consciousness. I believe in something and I understand something, but I do not understand everything I believe in, but sometimes I believe in something I don’t understand at all. Add the problem of proof to this. Not all that we believe in can be supported by proof. Relationship of faith, understanding and proof are designated as “intimate” by the author of the article because they are immersed in the depth of consciousness of each of the individual characters-personalities. Thus, it is proposed to call “faith” a certain directed state of the psyche, subordinate not to the dictatorship of external influences but to the internal intentions of the personality determining one of the directions of his inner world. “Understanding” is the ability, the skill of consciousness to establish a causal relationship placing the “phenomenon” in the frame of one of the existing pictures of the world or creating a new one. “Understanding” can also be attributed to the inner world of another person. Do you understand me…“Proof” is the ability to confirm something with certain constructions: arguments and theories, including axioms that do not require proof. The article expands on the content of the entire designated triad, but, most of all, the author pays attention to the questions of faith. Faith is mentioned in the article, above all, in connection with the theory and practice of religions, but faith, the author believes, is present even in the most rigorous sciences. The most common, characteristic case is the belief in the semantic ability of mathematics. One can also call the judgment of faith in a sufficiently finite number of expert checks to finally confirm the law relating to an infinite (in potency) number of cases. As a result of the movement on the topic, the author comes to the thought of immersing himself in the inner world of the individual. He immerses and imagines it both as an intimate property of the personality, and as the thing capable of covering outer space with the thought. My world is a gift from Heaven or Nature. Whose exactly is a matter of faith.

Language Comprehension, Inference, and Alternatives

This chapter discusses the importance of pragmatic inference involving alternatives for language comprehension, reviewing the problem of restricting the inferential hypothesis space. It presents a brief overview of theoretical and empirical work on adults and then turns to developmental evidence from two characteristic case studies: scalar implicature and quantifier spreading, where children struggle when interpreting sentences including quantifiers. The authors argue that in both cases, children’s problems are closely linked to difficulties in reducing the inferential hypothesis space, while matching what is said to what is meant. Children are argued to misidentify the Question Under Discussion (QUD), which leads them to consider irrelevant alternatives and make non-adult-like inferences. When relevant alternatives are made salient and the QUD is appropriately identified, children make inferences in an adult-like manner.

Ancient Egypt and the geological antiquity of man, 1847–1863

The 1850s through early 60s was a transformative period for nascent studies of the remote human past in Britain, across many disciplines. Naturalists and scholars with Egyptological knowledge fashioned themselves as authorities to contend with this divisive topic. In a characteristic case of long-distance fieldwork, British geologist Leonard Horner employed Turkish-born, English-educated, Cairo-based engineer Joseph Hekekyan to measure Nile silt deposits around pharaonic monuments in Egypt to address the chronological gap between the earliest historical and latest geological time. Their conclusion in 1858 that humans had existed in Egypt for exactly 13,371 years was the earliest attempt to apply geological stratigraphy to absolute human dates. The geochronology was particularly threatening to biblical orthodoxy, and the work raised private and public concerns about chronological expertise and methodology, scriptural and scientific authority, and the credibility of Egyptian informants. This essay traces these geo-archaeological investigations; including the movement of paper records, Hekekyan’s role as a go-between, and the publication’s reception in Britain. The diverse reactions to the Egyptian research reveal competing ways of knowing the prehistoric past and highlights mid-Victorian attempts to reshape the porous boundaries between scholarly studies of human antiquity.