Consider a reductive linear algebraic group G acting linearly on a polynomial ring S over an infinite field; key examples are the general linear group, the symplectic group, the orthogonal group, and the special linear group, with the classical representations as in Weyl’s book: For the general linear group, consider a direct sum of copies of the standard representation and copies of the dual; in the other cases, take copies of the standard representation. The invariant rings in the respective cases are determinantal rings, rings defined by Pfaffians of alternating matrices, symmetric determinantal rings and the Plücker coordinate rings of Grassmannians; these are the classical invariant rings of the title, with $S^G\subseteq S$ being the natural embedding.

Over a field of characteristic zero, a reductive group is linearly reductive, and it follows that the invariant ring $S^G$ is a pure subring of S, equivalently, $S^G$ is a direct summand of S as an $S^G$-module. Over fields of positive characteristic, reductive groups are typically no longer linearly reductive. We determine, in the positive characteristic case, precisely when the inclusion $S^G\subseteq S$ is pure. It turns out that if $S^G\subseteq S$ is pure, then either the invariant ring $S^G$ is regular or the group G is linearly reductive.

Maize is the primary staple crop cultivated during the monsoon season in eastern India. However, yield gaps are large because of multiple factors, including low adoption rates of good agronomic management practices. This study aimed to narrow the maize yield gap using diverse agronomic and varietal interventions through field experiments over 2 years (2013–2014) in the rainfed plateau region of Odisha. As a result, maize yield increased by 0.9, 0.74, and 0.17 Mg ha−1 under optimum plant population, fertilizer management, and herbicide-based weed management, respectively, over farmers’ current practices (Check). Moreover, when all three interventions were combined (‘best’ management practice), grain yields increased by 1.7 Mg ha−1 in conservation tillage and 2.2 Mg ha−1 in conventional tillage. We also observed that the combination of long-duration hybrids and best management practices (BMPs) increased grain yield by 4.0 Mg ha−1 and profitability by $888 ha−1 over farmers’ current practices. In addition, Nutrient Expert decision support tool-based fertilizer management along with BMPs increased grain yield by 1.7 Mg ha−1 and profitability by $314 ha−1 over farmers’ fertilizer practices (Check). These results suggest that the combination of maize hybrids and BMPs can improve the productivity and profitability of rainfed maize in the plateau region of Odisha. However, these entry points for intensification need to be placed in the context of varying investment requirements, input and output market conditions, and matched with farmer preferences and risk.

It is generally believed that the physiological consequences of stress could contribute to poor outcomes for patients being treated for cancer. However, despite preclinical and clinical evidence suggesting that stress promotes increased cancer-related mortality, a comprehensive understanding of the mechanisms involved in mediating these effects does not yet exist. We reviewed 47 clinical studies published between 2007 and 2020 to determine whether psychosocial stress affects clinical outcomes in cancer: 6.4% of studies showed a protective effect; 44.6% showed a harmful effect; 48.9% showed no association. These data suggest that psychosocial stress could affect cancer incidence and/or mortality, but the association is unclear. To shed light on this potentially important relationship, objective biomarkers of stress are needed to more accurately evaluate levels of stress and its downstream effects. As a potential candidate, the neuroendocrine signalling pathways initiated by stress are known to affect anti-tumour immune cells, and here we summarise how this may promote an immunosuppressive, pro-tumour microenvironment. Further research must be done to understand the relationships between stress and immunity to more accurately measure how stress affects cancer progression and outcome.

Polyphenols are naturally derived bioactive compounds with numerous reported health benefits. We have previously reported on the beneficial effect of a polyphenol-enriched apple extract in a murine model of food allergy. The objectives of the present study were to elucidate the class of bioactive polyphenols that exhibit a beneficial anti-allergic effect and to assess whether the protective effect matches the in vivo bioavailable metabolite concentrations. Female BALB/c mice were sensitised to ovalbumin (OVA) following the protocol of a well-established murine model of food allergy. They were fed diets containing polyphenol-enriched extracts or purified epicatechin for 8 d after the last sensitisation. The sensitised mice were orally challenged with OVA after the intervention. The allergy symptoms, in addition to allergen-specific serum Ig concentrations and gene expression profiles in the intestine, of the control and treated mice were compared. Plasma samples were collected to compare the concentrations of bioavailable epicatechin metabolites in the treatment groups. Polyphenol-enriched fruit extracts containing epicatechin exhibited a significant anti-allergic effect in vivo. This effect was unambiguously attributed to epicatechin, as oral administration of this purified polyphenol to sensitised mice by inclusion in their diet modulated allergy symptoms in a dose-dependent manner. Immune parameters were also affected by the administration of epicatechin. Bioavailability measurements in plasma indicated that the attenuation of allergy symptoms could be due to the higher concentrations of bioavailable epicatechin metabolites. In conclusion, epicatechin is a key bioactive polyphenol that has the ability to modulate allergy outcomes in sensitised mice.

Let R be a local ring of prime characteristic. We study the ring of Frobenius operators ${\mathcal F}(E)$, where E is the injective hull of the residue field of R. In particular, we examine the finite generation of ${\mathcal F}(E)$ over its degree zero component ${\mathcal F}^0(E)$, and show that ${\mathcal F}(E)$ need not be finitely generated when R is a determinantal ring; nonetheless, we obtain concrete descriptions of ${\mathcal F}(E)$ in good generality that we use, for example, to prove the discreteness of F-jumping numbers for arbitrary ideals in determinantal rings.

This study presents a reconstruction of the mass balance (MB) of Chhota Shigri glacier, Western Himalaya, India, and discusses the regional climatic drivers responsible for its evolution since 1969. The MB is reconstructed by a temperature-index and an accumulation model using daily air-temperature and precipitation records from the nearest meteorological station, at Bhuntar Observatory. The only adjusted parameter is the altitudinal precipitation gradient. The model is calibrated against 10 years of annual altitudinal MB measurements between 2002 and 2012 and decadal cumulative MBs between 1988 and 2010. Three periods were distinguished in the MB series. Periods I (1969-85) and III (2001-12) show significant mass loss at MB rates of -0.36±0.36 and -0.57±0.36mw.e.a-1 respectively, whereas period II (1986-2000) exhibits steady-state conditions with average MBs of -0.01 ±0.36mw.e.a–1. The comparison among these three periods suggests that winter precipitation and summer temperature are almost equally important drivers controlling the MB pattern of Chhota Shigri glacier at decadal scale. The sensitivity of the modelled glacier-wide MB to temperature is -0.52 m w.e. a–1 °C–1 whereas the sensitivity to precipitation is calculated as 0.16mw.e.a-1 for a 10% change.

Mass-balance and dynamic behaviour of Chhota Shigri glacier, western Himalaya, India, has been investigated between 2002 and 2010 and compared to data collected in 1987-89. During the period 2002-10, the glacier experienced a negative glacier-wide mass balance of -0.67 ± 0.40 m w.e. a-1. Between 2003 and 2010, elevation and ice-flow velocities slowly decreased in the ablation area, leading to a 24-37% reduction in ice fluxes, an expected response of the glacier dynamics to its recent negative mass balances. The reduced ice fluxes are still far larger than the balance fluxes calculated from the 2002-10 average surface mass balances. Therefore, further slowdown, thinning and terminus retreat of Chhota Shigri glacier are expected over the next few years. Conversely, the 2003/04 ice fluxes are in good agreement with ice fluxes calculated assuming that the glacier-wide mass balance is zero. Given the limited velocity change between 1987−89 and 2003/04 and the small terminus change between 1988 and 2010, we suggest that the glacier has experienced a period of near-zero or slightly positive mass balance in the 1990s, before shifting to a strong imbalance in the 21st century. This result challenges the generally accepted idea that glaciers in the Western Himalaya have been shrinking rapidly for the last few decades.

A Noetherian integral domain R is said to be a splinter if it is a direct summand, as an R-module, of every module-finite extension ring (see [Ma]). In the case that R contains the field of rational numbers, it is easily seen that R is splinter if and only if it is a normal ring, but the notion is more subtle for rings of characteristic p>0. It is known that F-regular rings of characteristic p are splinters and Hochster and Huneke showed that the converse is true for locally excellent Gorenstein rings [HH4]. In this paper we extend their result by showing that ℚ-Gorenstein splinters are F-regular. Our main theorem is:

THEOREM 1.1. Let R be a locally excellent ℚ-Gorenstein integral domain of characteristic p>0. Then R is F-regular if and only if it is a splinter.