Let $G$ be a split reductive group over the ring of integers in a $p$-adic field with residue field $\mathbf {F}$. Fix a representation $\overline {\rho }$ of the absolute Galois group of an unramified extension of $\mathbf {Q}_p$, valued in $G(\mathbf {F})$. We study the crystalline deformation ring for $\overline {\rho }$ with a fixed $p$-adic Hodge type that satisfies an analog of the Fontaine–Laffaille condition for $G$-valued representations. In particular, we give a root theoretic condition on the $p$-adic Hodge type which ensures that the crystalline deformation ring is formally smooth. Our result improves on all known results for classical groups not of type A and provides the first such results for exceptional groups.

One of the most essential prerequisites in plant breeding is to have a maximum collection of germplasm materials with all sorts of variability. As a part of the programme under the All India Coordinated Research Projects on Spices, totally 196 germplasm accessions of small cardamom are being maintained as field gene bank repository at the Cardamom Research Station, Pampadumpara. Tropical evergreen forests of the Indian Western Ghats and Sri Lankan Central Highlands are recognized as the home of cardamom. The area and production of cardamom are maximum in Kerala followed by Karnataka and Tamil Nadu. Variations among the germplasm collections in morphological and biometrical characters as well as for yield have been studied and reported in this paper. Accessions with distinct morphological marker characters, such as compound panicle types, terminal panicle bearing, narrow leaf types, pink pseudostem types, dark green bold capsules with high-yield potential and biotic-stress tolerant types, are being evaluated and conserved in this repository. The assessment of genetic diversity is an essential prerequisite for undertaking crop breeding activities to evolve suitable area and region-specific variety. Sixty-seven cardamom accessions were studied for genetic diversity by evaluating 14 unique characters for 3 years (2016–2018). Almost all accessions have shown significant variability for most of the biometric and biotic stress characters. Results have indicated a greater magnitude of genetic diversity of small cardamom present among accessions representing whole evergreen tropical forest of the Western Ghats.

Let $k\ge 2$ be an integer and let A be a set of nonnegative integers. The representation function $R_{A,k}(n)$ for the set A is the number of representations of a nonnegative integer n as the sum of k terms from A. Let $A(n)$ denote the counting function of A. Bell and Shallit [‘Counterexamples to a conjecture of Dombi in additive number theory’, Acta Math. Hung., to appear] recently gave a counterexample for a conjecture of Dombi and proved that if $A(n)=o(n^{{(k-2)}/{k}-\epsilon })$ for some $\epsilon>0$, then $R_{\mathbb {N}\setminus A,k}(n)$ is eventually strictly increasing. We improve this result to $A(n)=O(n^{{(k-2)}/{(k-1)}})$. We also give an example to show that this bound is best possible.

Let $\mathcal {K}_u$ denote the class of all analytic functions f in the unit disk $\mathbb {D}:=\{z\in \mathbb {C}:|z|<1\}$, normalised by $f(0)=f'(0)-1=0$ and satisfying $|zf'(z)/g(z)-1|<1$ in $\mathbb {D}$ for some starlike function g. Allu, Sokól and Thomas [‘On a close-to-convex analogue of certain starlike functions’, Bull. Aust. Math. Soc. 108 (2020), 268–281] obtained a partial solution for the Fekete–Szegö problem and initial coefficient estimates for functions in $\mathcal {K}_u$, and posed a conjecture in this regard. We prove this conjecture regarding the sharp estimates of coefficients and solve the Fekete–Szegö problem completely for functions in the class $\mathcal {K}_u$.

In any healthy democracy, myriad policy issues compete for the public’s attention. Most remain on the periphery of politics, either because they achieve salience only in narrow communities of interest or because they grab headlines only for brief periods of time. But sometimes issues become what we term “durable attention items”—they capture public attention and sustain it over many years. Why? We focus on one such newly durable issue—gun control in the United States. Using an original dataset of roughly 4,500 letters to the editor over a 40-year period, we demonstrate that this once-episodic issue, long dominated by a narrow constituency of pro-gun advocates, has become a mainstay of mass politics. We show that the gun issue’s growing agenda status is due entirely to pro-regulation people mobilized by a combination of contextual factors, namely regularized mass shootings and efforts to relax gun policy, working in tandem with partisan polarization. Besides offering novel evidence of a fundamental shift in American gun politics, the study contributes to our theoretical understanding of how episodic issues come to command consistent political engagement over the long term.

Cryptic species in coral reefs, such as sea slugs, represent an important portion of their biodiversity, which is usually underestimated. Autonomous Reef Monitoring Structures (ARMS) have been implemented to estimate cryptic diversity in coral reefs. Therefore, this research aimed to contribute to the southern Gulf of Mexico (GM) and the Caribbean Sea (CAR) coral reefs’ sea slugs’ diversity and distribution using ARMS as a collection method. Fifty-eight ARMS were placed at three coral reefs in the GM and CAR, recovered after 1–2 years and then, disassembled at the laboratory. Plates were individually placed in trays with seawater, where we searched for sea slugs. A total of 242 organisms were found belonging to 31 species; 20 of them were identified to the species level, while 11 were determined up to genus or family. More than half of the species (19) were found in Bajo de 10 (GM), while 15 species were found in the CAR localities. Unlike previous studies, we assessed sea slugs’ diversity exclusively by an indirect sampling method. In this work, we found 9.4% of the sea slug diversity recorded in the Caribbean, and we report four determined species for the first time in the country. New records of species, and even one family for the GM stress the gap of information that we still need to fulfil in the area. We recognize ARMS as a useful tool to find juvenile, cryptic and rare species of sea slugs, as well as to standardize their quantification and record their diversity.

Exact solutions are constructed for a class of nonlinear hyperbolic reaction-diffusion equations in two-space dimensions. Reduction of variables and subsequent solutions follow from a special nonclassical symmetry that uncovers a conditionally integrable system, equivalent to the linear Helmholtz equation. The hyperbolicity is commonly associated with a speed limit due to a delay, $\tau $, between gradients and fluxes. With lethal boundary conditions on a circular domain wherein a species population exhibits logistic growth of Fisher–KPP type with equal time lag, the critical domain size for avoidance of extinction does not depend on $\tau $. A diminishing exact solution within a circular domain is also constructed, when the reaction represents a weak Allee effect of Huxley type. For a combustion reaction of Arrhenius type, the only known exact solution that is finite but unbounded is extended to allow for a positive $\tau $.

In this paper, the design and experimental validation of a knee exoskeleton are presented. The exoskeleton can capture the negative work from the wearer’s knee motion while decreasing the muscle activities of the wearer. First, the human knee biomechanics during the normal walking is described. Then, the design of the exoskeleton is presented. The exoskeleton mainly includes a left one-way transmission mechanism, a right one-way transmission mechanism, and a front transmission mechanism. The left and right one-way transmission mechanisms are designed to capture the negative work from the wearer’s knee motion in the stance and swing phases, respectively. The front transmission mechanism is designed to transform the bidirectional rotation of the wearer’s knee joint into the generator unidirectional rotation. Additionally, the modeling and analysis of the energy harvesting of the exoskeleton is described. Finally, walking experiments are performed to validate the effectiveness of the proposed knee exoskeleton. The testing results verify that the developed knee exoskeleton can output a maximum power of 5.68 ± 0.23 W and an average power of 1.45 ± 0.13 W at a speed of 4.5 km/h in a gait cycle. The average rectus femoris and semitendinosus activities of the wearers in a gait cycle are decreased by 3.68% and 3.40%, respectively.

This piece analyses the recent judgment from the Makhanda High Court in Sustaining the Wild Coast NPC v Minister of Mineral Resources and Energy setting aside the decision to grant Shell and Impact Africa an exploratory right. Shell and Impact Africa intended to conduct a seismic survey along South Africa’s Wild Coast. Such a survey stood to have a substantial impact on the rights and interests of several local communities residing along the coastline. Because Shell, Impact Africa and the Director-General of the Department of Mineral Resources and Energy failed to consider these rights and interests, the court decided to overturn the decision granting the companies their exploratory right. To this end, the judgment provides a powerful vindication of the rights of local communities, illustrating what is possible when regulatory schemes are applied purposively and not as a mere box-ticking exercise.

Diminished skeletal muscle strength and size, termed sarcopenia, contributes substantially to physical disability, falls, dependence and reduced quality of life among older people. Physical activity and nutrition are the cornerstones of sarcopenia prevention and treatment. The optimal daily protein intake required to preserve muscle mass and function among older adults is a topic of intense scientific debate. Older adults require protein intakes about 67 % higher than their younger counterparts to maximally stimulate postprandial muscle protein synthesis rates. In addition, evidence suggests a possible benefit of increasing protein intake above the population reference intake (0⋅83 g/kg/d) on lean mass and, when combined with exercise training, muscle strength. In addition to protein quantity, protein quality, the pattern of protein intake over the day and specific amino acids (i.e. leucine) represent key considerations. Long-chain n-3 PUFA (LC n-3 PUFA) supplementation has been shown to enhance muscle protein synthesis rates, increase muscle mass and function and augment adaptations to resistance training in older adults. Yet, these effects are not consistent across all studies. Emerging evidence indicates that an older person's dietary, phenotypic and behavioural characteristics may modulate the efficacy of protein and LC n-3 PUFA interventions for promoting improvements in muscle mass and function, highlighting the potential inadequacy of a ‘one-size-fits-all’ approach. The application of personalised or precision nutrition to sarcopenia represents an exciting and highly novel field of research with the potential to help resolve inconsistencies in the literature and improve the efficacy of dietary interventions for sarcopenia.

Let K be an imaginary quadratic field and $p\geq 5$ a rational prime inert in K. For a $\mathbb {Q}$-curve E with complex multiplication by $\mathcal {O}_K$ and good reduction at p, K. Rubin introduced a p-adic L-function $\mathscr {L}_{E}$ which interpolates special values of L-functions of E twisted by anticyclotomic characters of K. In this paper, we prove a formula which links certain values of $\mathscr {L}_{E}$ outside its defining range of interpolation with rational points on E. Arithmetic consequences include p-converse to the Gross–Zagier and Kolyvagin theorem for E.

A key tool of the proof is the recent resolution of Rubin’s conjecture on the structure of local units in the anticyclotomic ${\mathbb {Z}}_p$-extension $\Psi _\infty $ of the unramified quadratic extension of ${\mathbb {Q}}_p$. Along the way, we present a theory of local points over $\Psi _\infty $ of the Lubin–Tate formal group of height $2$ for the uniformizing parameter $-p$.