We answer a question of Usuba by showing that the combinatorial principle $\mathrm {UB}_\lambda $ can fail at a singular cardinal. Furthermore, $\lambda $ can be taken to be $\aleph _\omega .$

Working in homotopy type theory, we introduce the notion of n-exactness for a short sequence $F\to E\to B$ of pointed types and show that any fiber sequence $F\hookrightarrow E \twoheadrightarrow B$ of arbitrary types induces a short sequence

that is n-exact at $\| E\|_{n-1}$. We explain how the indexing makes sense when interpreted in terms of n-groups, and we compare our definition to the existing definitions of an exact sequence of n-groups for $n=1,2$. As the main application, we obtain the long n-exact sequence of homotopy n-groups of a fiber sequence.

Forest raptor nest-site selection is mostly influenced by the quality of the habitat, food resources, and competition. Here, we identified common targets of trees selected as breeding sites and differences in selection traits, i.e. prey availability and intra- and interspecific competition, among Booted Eagle, Long-legged Buzzard, Black Kite, and Common Kestrel in a Mediterranean Cork Oak forest (private protected reserve of 25 km2). Using generalised linear mixed models we developed species-specific models describing nesting habitat selection. We tested the overlap in nesting habitat selection among species using environmental principal component analysis. The densities of forest raptor breeding pairs were high (3.1 pairs/km2) and the distance between occupied territories was short, strongly connected with food availability and competition. The results showed that all the species, with the exception of Common Kestrel, selected for nesting areas characterised by higher conspecific distance, highlighting the importance of conspecific competition. Booted Eagle and Black Kite selected areas with a high abundance of rabbits. The height of the nesting tree, the size and distance between surrounding trees, and the scrub cover were significant habitat characteristics for Booted Eagle and Long-legged Buzzard. Indeed, the environmental analyses showed a moderate nest site overlap between Black Kite and both Booted Eagle and Long-legged Buzzard, and a high overlap between Common Kestrel and both Booted Eagle and Long-legged Buzzard. Our study improves knowledge of the habitat requirements for nest selection and the potential competitive interactions between these raptor species in Mediterranean forests, and highlights the need for implementation of habitat management and conservation strategies.

The merits and means of accommodating non-binary populations into UK law is becoming an increasingly important issue for policymakers, judges, scholars and legal professionals. Following Elan-Cane's Supreme Court challenge to binary passport sex markers in 2021, the UK Government face another challenge this year concerning non-binary recognition on birth certificates. While an additional third sex option is perhaps the most well-known reform option for the current binary system, other options have been suggested, including additional multiple sex options and/or removing sex from the birth certificate. While scholars and policymakers debate the merits of these, little is known about non-binary people's own preferences towards these options. This paper therefore presents original empirical data on non-binary attitudes towards these options, demonstrating the various perceived opportunities and drawbacks of each, and reflecting on the possible consequences of reform.

The Attorney General for England and Wales is the Government's Senior Law Officer who, inter alia, initiates certain kinds of legal proceedings. She is also a politician: a member of the House of Commons or the House of Lords and appointed to Government by the Prime Minister. This paper considers the Attorney General's role in initiating contempt proceedings against fellow politicians. I detail a number of cases where politicians have been involved in potential contempts by publication. I argue that, in such cases, the Attorney General's position may amount to an actual or perceived conflict of interest and may breach the principle that justice should be seen to be done.

Reducing greenhouse gas emissions that are causing climate change requires the adoption of costly policies with often uncertain efficacy and distributional consequences. Because these emissions occur across sectors of the economy—electricity, transportation, and agriculture—and the built environment, and they require action at all levels of government—global, national, regional, and local—there is no single “silver-bullet” solution.

Ceramics play a central role in the debates around the relationship between the Viru and the Moche. A recent model considers Negative and Moche-decorated ceramics produced by potters affiliated with the elites to be the cultural markers of the Viru and Moche populations, respectively. Due to the similarity of Viru and Moche plain-wares and the presence of Castillo Decorated ceramics in Viru and Moche contexts, this model sees both types of ceramics as domestic traditions, produced by independent potters and sharing a common technique. The research we present here supports this recent model by reconsidering the social and cultural meaning associated with these ceramic types: it uses a novel approach for South America of reconstructing the chaîne opératoire by studying the traces visible on ceramics at a macroscopic and microscopic scale. The study demonstrates how these potters used their own traditions to produce decorated and undecorated ceramics. Furthermore, we found that Castillo Decorated is a type produced only by Viru potters, and we argue that its presence in Moche contexts is evidence of the numerous exchanges maintained by these two populations.

Multidimensional linear hyperbolic systems with constraints and delay are considered. The existence and uniqueness of solutions for rough data are established using Friedrichs method. With additional regularity and compatibility on the initial data and initial history, the stability of such systems are discussed. Under suitable assumptions on the coefficient matrices, we establish standard or regularity-loss type decay estimates. For data that are integrable, better decay rates are provided. The results are applied to the wave, Timoshenko, and linearized Euler–Maxwell systems with delay.

Although a subset of political scientists has been studying climate change for decades, the mainstream of the discipline lags behind. Journals such as Global Environmental Politics and even Nature and Science have long published political science research on climate, yet major disciplinary journals tend to marginalize climate and environmental politics more broadly (Green and Hale 2017). This trend has been changing slowly (as evidenced by this symposium), but mainstream political science still has much catching up to do.

In this paper, we study the dimension of planar self-affine sets, of which generating iterated function system (IFS) contains non-invertible affine mappings. We show that under a certain separation condition the dimension equals to the affinity dimension for a typical choice of the linear-parts of the non-invertible mappings, furthermore, we show that the dimension is strictly smaller than the affinity dimension for certain choices of parameters.

We consider the system of partial differential equations

\[ \begin{cases} \eta_t - \alpha u_{xxx} - \beta \eta_{xx} = 0 \\ u_t + \eta_x + \beta u_{xx} = 0 \end{cases} \]

\[ \varkappa=\alpha-\beta^2. \]

$\varkappa >0$

$\varkappa \leq 0$

The history of the sermon that Matthew Parker preached at the funeral of Martin Bucer is more complicated than has been thought. It is generally known that the first printing of 1551 was subsequently translated from English into Latin for a European audience in 1562 (printed in that year and again in 1577), and then published in English a second time, in a 1587 imprint that is thought to be a second edition. What is not generally known is that the second English printing was a translation of the 1562/1577 Latin version, and that in the process of translation and re-translation, Parker's original sermon was stripped of nearly 60 per cent of its content, as a eulogy that followed the sermon was misattributed to Walter Haddon at some point just prior to 1562. The present article seeks to explain how this came to pass, and argues that the 1551 imprint should replace the 1587 as the primary text for what Parker said of Bucer.

Separation commonly occurs in political science, usually when a binary explanatory variable perfectly predicts a binary outcome. In these situations, methodologists often recommend penalized maximum likelihood or Bayesian estimation. But researchers might struggle to identify an appropriate penalty or prior distribution. Fortunately, I show that researchers can easily test hypotheses about the model coefficients with standard frequentist tools. While the popular Wald test produces misleading (even nonsensical) p-values under separation, I show that likelihood ratio tests and score tests behave in the usual manner. Therefore, researchers can produce meaningful p-values with standard frequentist tools under separation without the use of penalties or prior information.

Assume $G\prec H$ are groups and ${\cal A}\subseteq {\cal P}(G),\ {\cal B}\subseteq {\cal P}(H)$ are algebras of sets closed under left group translation. Under some additional assumptions we find algebraic connections between the Ellis [semi]groups of the G-flow $S({\cal A})$ and the H-flow $S({\cal B})$. We apply these results in the model theoretic context. Namely, assume G is a group definable in a model M and $M\prec ^* N$. Using weak heirs and weak coheirs we point out some algebraic connections between the Ellis semigroups $S_{ext,G}(M)$ and $S_{ext,G}(N)$. Assuming every minimal left ideal in $S_{ext,G}(N)$ is a group we prove that the Ellis groups of $S_{ext,G}(M)$ are isomorphic to closed subgroups of the Ellis groups of $S_{ext,G}(N)$.

We continue investigating variants of the splitting and reaping numbers introduced in [4]. In particular, answering a question raised there, we prove the consistency of and of . Moreover, we discuss their natural generalisations $\mathfrak {s}_{\rho }$ and $\mathfrak {r}_{\rho }$ for $\rho \in (0,1)$, and show that $\mathfrak {r}_{\rho }$ does not depend on $\rho $.