Global Affinities: The Natural Method and Anomalous Plants in the Nineteenth Century

Approaching from an analysis of the work of Robert Brown (1773-1858) and Friedrich Welwitsch (1806–1872) on Rafflesia and Welwitschia, this article explores how the “natural method” became a tool for understanding extra-European flora in the nineteenth century. As botanists worked to detect “hidden affinities” between plants that would enable them to identify the so-called natural families to which even anomalous species belonged, they relied on comparison as their basic methodological procedure, making it essential for them to have access to collections. In their scientific writings, professional botanists tended to steer clear of any emphasis on plant exoticism. While botany engaged in dialogue with various types of approaches, the field essentially normalized the exotic. The article’s exploration of the hermetic style of scientific texts and the way botanists incorporated illustrators’ work sheds light on the complexity of the spaces where natural history was done, in a context where plants were circulating from around the globe.

Averages and higher moments for the $$\ell $$-torsion in class groups

We prove upper bounds for the average size of the $$\ell $$ ℓ -torsion $${{\,\mathrm{Cl}\,}}_K[\ell ]$$ Cl K [ ℓ ] of the class group of K, as K runs through certain natural families of number fields and $$\ell $$ ℓ is a positive integer. We refine a key argument, used in almost all results of this type, which links upper bounds for $${{\,\mathrm{Cl}\,}}_K[\ell ]$$ Cl K [ ℓ ] to the existence of many primes splitting completely in K that are small compared to the discriminant of K. Our improvements are achieved through the introduction of a new family of specialised invariants of number fields to replace the discriminant in this argument, in conjunction with new counting results for these invariants. This leads to significantly improved upper bounds for the average and sometimes even higher moments of $${{\,\mathrm{Cl}\,}}_K[\ell ]$$ Cl K [ ℓ ] for many families of number fields K considered in the literature, for example, for the families of all degree-d-fields for $$d\in \{2,3,4,5\}$$ d ∈ { 2 , 3 , 4 , 5 } (and non-$$D_4$$ D 4 if $$d=4$$ d = 4 ). As an application of the case $$d=2$$ d = 2 we obtain the best upper bounds for the number of $$D_p$$ D p -fields of bounded discriminant, for primes $$p>3$$ p > 3 .

ORGANIZERS AND COORDINATORS OF FAMILY FOSTER CARE

Family is an environment that contributes to child development in the best benefi cial way. The State should support families through its entities and institutions and it should ensure that a child shall not be separated from their parents if it is not necessary. However, there are situations when it is necessary to place a child in a foster family for the child’s best interest. There reasons why a child should be separated from his family, although sometimes diff erent, must always be serious. Foster upbringing environment, especially a foster family, requires organization and co-ordination, but these problems have not been fully or separately raised in existing literature concerning foster care. That is why the study aims at analyzing legal regulations concerning organizers and coordinators of family foster care and at presenting statistical data that show organization and coordination of family foster care in practice. Support of organizers and coordinators of family foster care contributes to ensuring the highest standard of care for children who are brought up outside their natural families and in this way it contributes to realizing the best interest of the child.

Smooth Compactness for Spaces of Asymptotically Conical Self-Expanders of Mean Curvature Flow

We show compactness in the locally smooth topology for certain natural families of asymptotically conical self-expanding solutions of mean curvature flow. Specifically, we show such compactness for the set of all 2D self-expanders of a fixed topological type and, in all dimensions, for the set of self-expanders of low entropy and for the set of mean convex self-expanders with strictly mean convex asymptotic cones. From this we deduce that the natural projection map from the space of parameterizations of asymptotically conical self-expanders to the space of parameterizations of the asymptotic cones is proper for these classes.

The Algebraic de Rham Cohomology of Representation Varieties

The SL(2, ℂ)-representation varieties of punctured surfaces form natural families parameterized by monodromies at the punctures. In this paper, we compute the loci where these varieties are singular for the cases of one-holed and two-holed tori and the four-holed sphere. We then compute the de Rham cohomologies of these varieties of the one-holed torus and the four-holed sphere when the varieties are smooth via the Grothendieck theorem. Furthermore, we produce the explicit Gauß-Manin connection on the natural family of the smooth SL(2, ℂ)-representation varieties of the one-holed torus.

A Tale of Two Families

During military deployment, soldiers can become part of a system of people and experiences in their assigned military unit that may rival the importance of relationships and experiences within their natural families at home. Following deployment, returning soldiers may face the challenges of managing membership in two complex and powerful family systems, each with its own unique priorities, rules of engagement, and demands for the soldier’s attention and participation that may not always be compatible. Achieving a mutual understanding of the system of close relationships formed around military deployment and incorporating this new “unit family” system into a couple’s marital relationship and natural family system becomes a task that is important and, possibly, essential to successful family reintegration after deployment.

On p-adic L-series, p-adic cohomology and class field theory

We establish several close links between the Galois structures of a range of arithmetic modules including certain natural families of ray class groups, the values at strictly positive integers of p-adic Artin L-series, the Shafarevich–Weil Theorem and the conjectural surjectivity of certain norm maps in cyclotomic {\mathbb{Z}_{p}} -extensions. Non-commutative Iwasawa theory and the theory of organising matrices play a key role in our approach.