Avocado is a delicious fruit crop having great economic importance. Understanding the extent of variability present in the existing germplasm is important to identify genotypes with specific traits and their utilization in crop improvement. The information on genetic variability with respect to morphological and biochemical traits in Indian avocados is limited and as it has hindered genetic improvement of the crop. In the current study, 83 avocado accessions from different regions of India were assessed for important 17 morphological and 8 biochemical traits. The results showed the existence of wide variability for traits such as fruit weight (75.88–934.12 g), pulp weight (48.08–736.19 g), seed weight (6.37–32.62 g), FRAP activity (27.65–119.81 mg AEAC/100 g), total carotenoids (0.96–7.17 mg/100 g), oil content (4.91–25.49%) and crude fibre (6.85–20.75%) in the studied accessions. The first three components of principal component analysis explained 54.79 per cent of total variance. Traits such as fruit weight, pulp weight, seed weight, moisture and oil content contributed more significantly towards total variance compared to other traits. The dendrogram constructed based on Euclidean distance wards minimum variance method divided 83 accessions into two major groups and nine sub clusters suggesting wide variability in the accessions with respect to studied traits. In this study, superior accessions for important traits such as fruit size (PA-102, PA-012), high pulp recovery (PA-036, PA-082,), thick peel (PA-084, PA-043, PA-011, PA-008), high carotenoids (PA-026, PA-096) and high oil content (PA-044, PA-043, PA-046, PA-045) were identified which have potential utility in further crop improvement programmes.

This paper discusses the syntactic behaviour of a small subset of object control verbs that have an implicative interpretation (e.g. obrigar ‘force’, impedir ‘prevent’) as well as the behaviour of superficially similar syntactic causatives in European Portuguese. By exploring different syntactic properties and giving special attention to inflected infinitives as complements to the two classes of verbs, we argue that implicative object control verbs are ambiguous between true control verbs (which are ditransitive) and syntactic causatives (which take a single, clausal, internal argument). To this extent, we present an argument defying Landau’s (2015) analysis of control under these verbs as predication. We also argue that the implicative interpretation of these verbs is not determined by the syntactic nature of their complement: This interpretation is maintained in both the causative and the control counterparts of the verb. By comparing implicative object control verbs and the understudied and superficially similar pôr a ‘put to / make’ and deixar a ‘put to / make’, and by highlighting the distribution and interpretation of inflected infinitives in their complements, we can argue that the latter are unambiguous syntactic causatives, which take as complement a small clause in which we internally observe control.

Ice-sheet volume during Marine Isotope Stage (MIS) 3 (57–29 ka) is controversial. Several recent studies have proposed that the Greenland Ice Sheet was smaller during MIS 3 than it is today based on radiocarbon ages of molluscan bivalve shells reworked into sedimentary deposits adjacent to the present ice margin. Such a result contrasts with available records of MIS 3 climate, ice volume, and sea level. We revisited a site previously interpreted as containing evidence for smaller than present ice during MIS 3. We collected marine bivalve shells and combined progressive acid dissolution in preparation for radiocarbon dating with new-generation amino acid analysis, which focuses on aspartic acid racemization. Our results suggest that contamination by young carbon yields finite radiocarbon ages despite bivalve shells likely dating to MIS 5e (∼125 ka) or even older. This result should be further tested, which could be accomplished with additional studies of this kind in combination with ice-sheet modeling and additional paleoclimate data generated from adjacent seas.

It is a theorem due to F. Haglund and D. Wise that reflection groups (aka Coxeter groups) virtually embed into right-angled reflection groups (aka right-angled Coxeter groups). In this article, we generalize this observation to rotation groups, which can be thought of as a common generalization of Coxeter groups and graph products of groups. More precisely, we prove that rotation groups (aka periagroups) virtually embed into right-angled rotation groups (aka graph products of groups).

We study optimal dimensionless inequalities

\begin{equation*} \|f\|_{\textrm{U}^k} \leqslant \|f\|_{\ell^{p_{k,n}}} \end{equation*}

that hold for all functions $f\colon\mathbb{Z}^d\to\mathbb{C}$ supported in $\{0,1,\ldots,n-1\}^d$ and estimates

\begin{equation*} \|\mathbb{1}_A\|_{\textrm{U}^k}^{2^k}\leqslant |A|^{t_{k,n}} \end{equation*}

that hold for all subsets A of the same discrete cubes. A general theory, analogous to the work of de Dios Pont, Greenfeld, Ivanisvili, and Madrid, is developed to show that the critical exponents are related by $p_{k,n} t_{k,n} = 2^k$. This is used to prove the three main results of the article:

• • an explicit formula for $t_{k,2}$, which generalizes a theorem by Kane and Tao,

• • two-sided asymptotic estimates for $t_{k,n}$ as $n\to\infty$ for a fixed $k\geqslant2$, which generalize a theorem by Shao, and

• • a precise asymptotic formula for $t_{k,n}$ as $k\to\infty$ for a fixed $n\geqslant2$.

We develop explicit bounds for the tail of the distribution of the all-time supremum of a random walk with negative drift, where the increments have a truncated heavy-tailed distribution. As an application, we consider a ruin problem in the presence of reinsurance.

This is the first report of Jurassic brachyurans and anomurans from the territory of Russia. These findings come from the Upper Jurassic (Oxfordian) reef limestones of the North Caucasus. The anomuran Gastrosacus wetzleri von Meyer, 1851 was collected from the locality near the Urup River and is the first find of this species outside of western Europe. The dromiacean crab, Goniodromites aliquantulus Schweitzer, Feldmann, and Lazăr, 2007, was discovered from another locality near the Kamennomostsky village. This species was first described from the Oxfordian of Romania. Findings of fossil remains of Goniodromites aliquantulus and Gastrosacus wetzleri from the Oxfordian of the North Caucasus indicate an interconnected paleobiogeographical community of decapod faunas in the Late Jurassic in the Tethys basins.

In the philosophy of religion, ‘de jure objections’ is an umbrella term that covers a wide variety of arguments for the conclusion that theistic belief is rationally impermissible, whether or not God exists. What we call ‘modal Calvinism’ counters these objections by proposing that ‘if God exists, God would ensure that theistic belief is rationally compelling on a global scale’, a modal conditional that is compatible with atheism. We respond to this modal Calvinist argument by examining it through the lenses of probability, modality, and logic – particularly, we apply analytical tools such as possible world semantics, Bayesian reasoning, and paraconsistent models. After examining various forms of the argument, we argue that none can compel atheists to believe that serious theistic possibilities worth considering would involve the purported divine measure.