We derive some key extremal features for stationary kth-order Markov chains that can be used to understand how the process moves between an extreme state and the body of the process. The chains are studied given that there is an exceedance of a threshold, as the threshold tends to the upper endpoint of the distribution. Unlike previous studies with $k>1$, we consider processes where standard limit theory describes each extreme event as a single observation without any information about the transition to and from the body of the distribution. Our work uses different asymptotic theory which results in non-degenerate limit laws for such processes. We study the extremal properties of the initial distribution and the transition probability kernel of the Markov chain under weak assumptions for broad classes of extremal dependence structures that cover both asymptotically dependent and asymptotically independent Markov chains. For chains with $k>1$, the transition of the chain away from the exceedance involves novel functions of the k previous states, in comparison to just the single value, when $k=1$. This leads to an increase in the complexity of determining the form of this class of functions, their properties, and the method of their derivation in applications. We find that it is possible to derive an affine normalization, dependent on the threshold excess, such that non-degenerate limiting behaviour of the process, in the neighbourhood of the threshold excess, is assured for all lags. We find that these normalization functions have an attractive structure that has parallels to the Yule–Walker equations. Furthermore, the limiting process is always linear in the innovations. We illustrate the results with the study of kth-order stationary Markov chains with exponential margins based on widely studied families of copula dependence structures.

Strontioborite, which was first described in 1960 and later discredited by the then named Commission on New Minerals and Mineral Names of the International Mineralogical Association (IMA CNMMN), has been re-investigated (electron microprobe, single-crystal and powder X-ray diffraction, crystal structure determination and IR spectroscopy) on two specimens, including the holotype, and revalidated by the IMA Commission on New Minerals, Nomenclature and Classification (CNMNC). Strontioborite is known only at the Chelkar salt dome (North Caspian Region, Western Kazakhstan), in halite rocks with bischofite, magnesite, anhydrite, halurgite, boracite, ginorite and celestine. It forms colourless lamellar, scaly or tabular crystals up to 2 mm across. The chemical composition (wt.%, H2O is calculated for (OH)4 = 4 H apfu, according to structural data; holotype/neotype) is: CaO 1.42/0.27, SrO 23.10/23.79, B2O3 67.37/67.57, H2O 8.73/8.72, total 100.62/100.37. The empirical formulae [calculated based on 15 O apfu = O11(OH)4 pfu] of the holotype and neotype specimens are Sr0.92Ca0.10B7.98O11(OH)4 and Sr0.95Ca0.02B8.02O11(OH)4, respectively. The idealised formula is Sr[B8O11(OH)4]. Strontioborite is monoclinic, space group P21, a = 7.6192(3), b = 8.1867(2), c = 9.9164(3) Å, β = 108.357(4)°, V = 587.07(3) Å3 and Z = 2. The strongest reflections of the powder X-ray diffraction pattern [d,Å(I)(hkl)] are: 7.22(100)(100), 5.409(61)(110), 4.090(64)(020), 3.300(48)(210), 2.121(30)($\bar{1}$24) and 2.043(37)(040, 024, $\bar{2}$24). The crystal structure, solved from single-crystal X-ray diffraction data (R = 0.0372), is based upon the (100) layers of polymerised B–O–OH polyanions [B8O11(OH)4]2– and Sr-centred nine-fold polyhedra SrO6(OH)3. The B–O–OH polyanion is the cluster of three tetrahedra and three triangles; these clusters are decorated by the [B2O2(OH)3] pyro-group consisting of two triangles. The layers are linked via vertices of Sr-centred polyhedra, which share seven vertices with B-centred polyhedra of one layer and two vertices with B-centred polyhedra of the adjacent layer, and by the system of H bonds. The crystal chemistry of strontioborite is discussed in comparison with other natural and synthetic borates.

Consider a branching random walk on the real line with a random environment in time (BRWRE). A necessary and sufficient condition for the non-triviality of the limit of the derivative martingale is formulated. To this end, we investigate the random walk in a time-inhomogeneous random environment (RWRE), which is related to the BRWRE by the many-to-one formula. The key step is to figure out Tanaka’s decomposition for the RWRE conditioned to stay non-negative (or above a line), which is interesting in itself.

In Caspers et al. (Can. J. Math. 75[6] [2022], 1–18), transference results between multilinear Fourier and Schur multipliers on noncommutative $L_p$-spaces were shown for unimodular groups. We propose a suitable extension of the definition of multilinear Fourier multipliers for non-unimodular groups and show that the aforementioned transference results also hold in this more general setting.

To meet the specific education needs of ethics committee members (primarily full-time healthcare professionals), the Regional Ethics Department of Kaiser Permanente Northern California (KPNCAL) and Washington State University’s Elson Floyd School of Medicine have partnered to create a one-academic year Medical Ethics Certificate Program. The mission-driven nature of the KPNCAL-WSU’s Certificate Program was designed to be a low-cost, high-quality option for busy full-time practitioners who may not otherwise opt to pursue additional education.

This article discusses the specific competency-focused methodologies and pedagogies adopted, as well as how the Certificate Program made permanent changes in response to the global pandemic. This article also discusses in detail one of the Program’s signature features, its Practicum—an extensive simulated clinical ethics consultation placing students in the role of ethics consultant, facilitating a conflict between family members played by paid professional actors. This article concludes with survey data responses from Program alumni gathered as part of a quality study.

After the political fragmentation of the “Five Dynasties and Ten Kingdoms” period, the Northern Song consolidated much of the lands under these regional states into a larger polity in a process often described as “reunification.” But this “reunification,” judged against the domain of the Tang dynasty, was incomplete. The “Sixteen Prefectures” to the northeast were ceded to the Liao, and this became a vexing issue for Song emperors and officials. But the northeast was not the only region once under Tang rule that did not enter the Song domain. In this article, I discuss the area to the northwest of the Song, much of which was eventually governed by the Tangut Xia state. This area, roughly the modern provinces of Ningxia and Gansu, featured prominently in Northern Song political discussions, national geographical treatises, and national and regional maps. By analyzing the treatment of the northwest in these diverse genres of representation, I demonstrate a spectrum in the perceptions of the northwest. It was sometimes seen as little different from areas under Song rule; in other cases, it was treated as “beyond the sphere of civilization” (huawai). Such ambiguity is visualized in many Song cartographers who placed this area between two segments of the Great Wall. For Song emperors and officials, the northwest sat uncomfortably in their imaginations of the world, not easily dismissed and forgotten, yet irrecoverable.

Modal panentheism claims that God encompasses all possible worlds and that a substantial number of possible worlds exist. This article defends a version of modal panentheism that is grounded in perfect-being theology, which maintains that God holds all great-making properties to the highest possible degree. In addition to goodness, modal panentheists consider encompassment to be a great-making property, and therefore, God (a maximally encompassing being) is said to encompass all possible worlds.

Nagasawa argues that modal panentheism faces a significant problem: the modal problem of evil. The argument states that if modal realism is true, then there exists a substantial number of possible evils that contradict God’s perfect goodness. Nagasawa proceeds to claim that modal evil poses a greater threat to modal panentheism than actual evil does to traditional theism.

This article develops two responses to the modal problem of evil. The first response (maximal-panentheism) argues that God need not be all-good or all-encompassing. The second response (no evil worlds) argues that worlds contradicting God’s perfect goodness are not possible worlds. In the light of these responses, I claim the modal problem of evil for modal panentheism is no more intractable than the problem of evil for traditional theism.

We investigate the relationship between lower bounds for the Mahler measure and splitting of primes, and prove various lower bounds for the Mahler measure of algebraic integers in terms of the least common multiples of all inertia degrees of primes. The results generalise work of the second author and Kumar [‘Lehmer’s problem and splitting of rational primes in number fields’, Acta Math. Hungar. 169(2) (2023), 349–358].

In this paper, we introduce topologically IGH-stable, IGH-persistent,average IGH-persistent and pointwise weakly topologically IGH-stable homeomorphisms of compact metric spaces. We prove that every topologically IGH-stable homeomorphism is topologically stable and every expansive topologically stable homeomorphism of a compact manifold is topologically IGH-stable. We further prove that every equicontinuous pointwise weakly topologically IGH-stable homeomorphism is IGH-persistent and every pointwise minimally expansive IGH-persistent homeomorphism is pointwise weakly topologically IGH-stable. Finally, we prove that every mean equicontinuous pointwise weakly topologically IGH-stable homeomorphism is average IGH-persistent.

We introduce a modification of the generalized Pólya urn model containing two urns, and we study the number of balls $B_j(n)$ of a given color $j\in\{1,\ldots,J\}$ added to the urns after n draws, where $J\in\mathbb{N}$. We provide sufficient conditions under which the random variables $(B_j(n))_{n\in\mathbb{N}}$, properly normalized and centered, converge weakly to a limiting random variable. The result reveals a similar trichotomy as in the classical case with one urn, one of the main differences being that in the scaling we encounter 1-periodic continuous functions. Another difference in our results compared to the classical urn models is that the phase transition of the second-order behavior occurs at $\sqrt{\rho}$ and not at $\rho/2$, where $\rho$ is the dominant eigenvalue of the mean replacement matrix.

Despite societal perceptions of older adults as vulnerable, literature on resilience suggests that exposure to adversity and resources gained with life experience contribute to adaptation. One way to explore the nature of resilience is to document assets supporting adaptation. Interviews were conducted with older adults living in Canada at two time points during the COVID-19 pandemic, September 2020–May 2021 (T1) and January–August 2022 (T2). Reflexive thematic analysis was completed to report on what older adults identified as assets and how they understood the value of those assets for resilience. Participants indicated that the potential value of their contributions went largely untapped at the level of the community but supported individual and household adaptation. In line with calls for an all-of-society approach to reduce disaster risk and support resilience, creating a culture of inclusivity that recognizes the potential contributions of older adults should be paired with opportunities for action.

We investigate neighbourhood sizes in the enhanced power graph (also known as the cyclic graph) associated with a finite group. In particular, we characterise finite p-groups with the smallest maximum size for neighbourhoods of a nontrivial element in its enhanced power graph.

The impact of disasters on the health and wellbeing of children is well documented, with children identified as bellwethers of community recovery. It has also been demonstrated that building community-wide resilience benefits from being approached through a child-centric model of community participation. While much of this work has been focused on the USA, there is a need to develop models to adapt these approaches in international environments. Small Island Developing States (SIDS) are particularly at risk for disaster events. SIDS tend to have less diverse economies and a high dependence on climate-sensitive sectors that are vulnerable to disasters. The National Center for Disaster Preparedness at Columbia University along with Save the Children created The Resilient Children, Resilient Communities Initiative to build child-focused resilience within communities. The Initiative, which has already been applied to sites in the USA, is being adapted for the context of Dominica. The Initiative focuses on child-serving institutions and uses a Community Preparedness Index to quantify the current inventory of policies and practices related to children. The Initiative aims to implement strategies to improve the ability of the community to meet the needs of children in a disaster. This paper explores the application of these concepts surrounding the Initiative.

Panulirus stimpsoni is restricted to southern China, Vietnam, and Japan but has been rarely reported in tropical Gulf of Thailand. In Malaysia, only six species were previously reported. This study (1) reports the seventh Malaysian species – a new record of P. stimpsoni with morphological and genetic data; (2) establishes a checklist of Malaysian Panulirus species. Surveys from 2021 to 2022 sampled lobsters across Malaysia by SCUBA or from fishermen. Seven species were identified and a modified key of Malaysian species was constructed. The COI gene was used for genetic identification and phylogenetic tree reconstruction with maximum likelihood (ML). The best model was GTR + I + G. The ML tree comprised Clades I and II with sequences clustering by species and strong support. Most Peninsular Malaysian lobsters were P. polyphagus while P. versicolor dominated Sabah. Information on P. stimpsoni's full fishery potential, distribution, ecology, and biology is limited. Further research is needed to ensure conservation and management as data are only available for six previously reported species. Further studies are required to discover sustainable use approaches for all Panulirus species, particularly P. stimpsoni, given limited ecological understanding.

Insects experience variable temperature conditions in their natural environment, making constant temperature conditions in studies unrealistic. To address this, we investigated the effects of repeated short-term heat stress (STH) and short-term cold stress (STC) conditions on the pre-oviposition, oviposition, and post-oviposition periods, as well as on fecundity and egg viability of the parthenium beetle, Zygogramma bicolorata Pallister (Coleoptera: Chrysomelidae). We found that pre-oviposition periods were shortest under STH conditions and at the optimal temperature and longest under STC conditions. Conversely, oviposition and post-oviposition periods were longest at the optimal temperature. Oviposition periods were shortest under STH, whereas post-oviposition periods were shortest under both STH and STC conditions. Age-specific fecundity trends were triangular, and egg-viability trends were plateau-shaped at all temperatures. Females subjected to STH conditions experienced the highest oviposition peaks early in their adult life. Conversely, lifetime fecundity and longevity were highest at the optimal temperature, whereas egg viability was maximal under STH conditions. Regardless of the temperature they were maintained at, middle-aged females exhibited the highest fecundity and egg viability. Based on these results, despite reducing overall fecundity and longevity, STH conditions enhanced daily oviposition in females, with the peak occurring early in adult life. Additionally, both STH and STC conditions increased percentage egg viability in parthenium beetles.

In Oliveira, Schlomiuk, Travaglini, and Valls, Geometry, integrability and bifurcation diagrams of a family of quadratic differential systems as application of Darboux theory of integrability, Electron. J. Qual. Theory Differ. Equ. 45(2021), 1–90, the authors investigate about the integrability of the family QSH (the whole class of non-degenerate planar quadratic systems possessing at least one invariant hyperbola). However, some very difficult cases are left open in Oliveira, Schlomiuk, Travaglini, and Valls, Geometry, integrability and bifurcation diagrams of a family of quadratic differential systems as application of Darboux theory of integrability, Electron. J. Qual. Theory Differ. Equ. 45(2021), 1–90, and the main aim of this article is to study the Liouvillian integrability some of the systems that were left behind in Oliveira, Schlomiuk, Travaglini, and Valls, Geometry, integrability and bifurcation diagrams of a family of quadratic differential systems as application of Darboux theory of integrability, Electron. J. Qual. Theory Differ. Equ. 45(2021), 1–90.