In this paper, we derive new differential Harnack estimates of Li–Yau type for positive smooth solutions to a class of nonlinear parabolic equations in the form

\[ {\mathscr L}_\phi^{\mathsf a} [w]:= \left[ \frac{\partial}{\partial t} - \mathsf{a}(x,t) - \Delta_\phi \right] w (x,t) = \mathscr G(t, x, w(x,t)), \quad t>0, \]

$({\mathsf k},\, m)$

This paper introduces type P web supercategories. They are defined as diagrammatic monoidal ${\mathbb {k}}$-linear supercategories via generators and relations. We study the structure of these categories and provide diagrammatic bases for their morphism spaces. We also prove these supercategories provide combinatorial models for the monoidal supercategory generated by the symmetric powers of the natural module and their duals for the Lie superalgebra of type P.

الملح في موريتانيا القيصرية و نوميديا. مصادره؟ استخداماته؟

تواتية عمراوي

هذا هو الملخص الأول للمناطق الوسطى من المغرب العربي (الجزائر) و الذي يظهر الدور الرئيسي الذي لعبه الملح محلياً و كجزء من شبكات تجارية أوسع، و على مدى فترة طويلة من الزمن . اعتمدت هذه الدراسة على مصادر قديمة وحديثة - جغرافية ومعدنية و إثنوغرافية - و تستخدم البيانات الأثرية التي أهمل تحليلها في السابق عن استغلال الملح واستخداماته في العصور القديمة في كل من موريتانيا القيصرية و نوميديا. إن إعادة التقييم هذه تكشف عن مدى توفر الموارد المحلية: حيث كان الملح وفيراً، ويمكن الوصول إليه بسهولة، و يسهل حصاده من البحيرات المالحة أو صخور الملح .

إن البقايا الأثرية التي يتم العثور عليها و بشكل منهجي بالقرب من مكامن الملح الموجودة داخل منطقة المقاطعة الرومانية أو على أطرافها، تؤكد أن السكان استخدموا هذه الموارد المحلية لاحتياجاتهم اليومية. وتظهر الدراسات الإثنوغرافية أن السكان أو القبائل العابرة كانوا - ولا يزالون - قادرين على الاستفادة من الملح المحلي كجزء من تجارتهم مع الشمال والجنوب . تشير أدلة العصور الوسطى إلى أن الملح الصخري من جبل ملح الوطاية (بسكرة) والملح من سبخة آرزيو كان يتم تصديرهما عن طريق البر و من ثم البحر، حيث يصدر الأول لتونس و الثاني لدول أوروبية مجاورة، ولا يوجد ما يتعارض مع حقيقة أن هذا النوع من الشبكات وغيرها كانت موجود بالفعل في العصور القديمة.

This article investigates the utility of a chaîne opératoire approach centered on technologies of ceramic production for identifying Inca mitmaqkuna archaeologically. Although early documents suggest that the Inca program of resettlement (mitmaq) was massive in scale, archaeologists have had minimal success in identifying such relocated populations. Here we test a novel approach that focuses on technologies of production and associated tool assemblages used within different communities of practice. Previous studies indicate that the ethnic Cañari of southern Ecuador used a distinctive method of pottery manufacture involving a specific chaîne opératoire and a unique set of production-related tools. According to early sources, the Inca deported Cañari peoples to various sectors of Tawantinsuyu. In this article, we investigate the contemporary manufacturing style of ceramics from the Ancash region of north-central Peru—an area where Cañari mitmaqkuna were purportedly resettled—to determine whether distinctive communities of practice potentially representing relocated communities might be visible. The results of this study suggest that it is possible to identify connections among distant communities of practice via a focus on craft production technologies that, in certain historical contexts, may be construed as evidence for the presence of resettled populations.

We view innovation investments as real options and explore the implications of risk (volatility) as well as a newly defined outcome independent measure of ambiguity (Knightian uncertainty) for innovation decisions. The empirical analysis uses stock returns to compute an implementable measure of ambiguity. We also control for risk and other determinants of innovation. We find a consistently significant negative effect of ambiguity on R&D, patents, and citations, as predicted. The effect of risk on R&D is positive and significant, but the corresponding effect on patents and citations is negative and significant. Ambiguity matters more for high-tech firms, consistent with intuition.

For any positive integers $k_1,k_2$ and any set $A\subseteq \mathbb {N}$, let $R_{k_1,k_2}(A,n)$ be the number of solutions of the equation $n=k_1a_1+k_2a_2$ with $a_1,a_2\in A$. Let g be a fixed integer. We prove that if $k_1$ and $k_2$ are two integers with $2\le k_1<k_2$ and $(k_1,k_2)=1$, then there does not exist any set $A\subseteq \mathbb {N}$ such that $R_{k_1,k_2}(A,n)-R_{k_1,k_2}(\mathbb {N}\setminus A,n)=g$ for all sufficiently large integers n, and if $1=k_1<k_2$, then there exists a set A such that $R_{k_1,k_2}(A,n)-R_{k_1,k_2}(\mathbb {N}\setminus A,n)=1$ for all positive integers n.

This review will provide an overview of the immune system and then describe the effects of frailty, obesity, specific micronutrients and the gut microbiota on immunity and susceptibility to infection including data from the severe acute respiratory syndrome coronavirus 2 (SARS-CoV-2) pandemic where relevant. A key role for the immune system is providing host defence against pathogens. Impaired immunity predisposes to infections and to more severe infections and weakens the response to vaccination. A range of nutrients, including many micronutrients, play important roles in supporting the immune system to function. The immune system can decline in later life and this is exaggerated by frailty. The immune system is also weakened with obesity, generalised undernutrition and micronutrient deficiencies, which all result in increased susceptibility to infection. Findings obtained during the SARS-CoV-2 pandemic support what was already known about the effects of ageing, frailty and obesity on immunity and susceptibility to infection. Observational studies conducted during the pandemic also support previous findings that multiple micronutrients including vitamins C, D and E, zinc and selenium and long-chain n-3 fatty acids are important for immune health, but whether these nutrients can be used to treat those already with coronavirus disease discovered in 2019 (COVID-19), particularly if already hospitalised, is uncertain from current inconsistent or scant evidence. There is gut dysbiosis in patients with COVID-19 and studies with probiotics report clinical improvements in such patients. There is an inverse association between adherence to a healthy diet and risk of SARS-CoV-2 infection and hospitalisation with COVID-19 which is consistent with the effects of individual nutrients and other dietary components. Addressing frailty, obesity and micronutrient insufficiency will be important to reduce the burden of future pandemics and nutritional considerations need to be a central part of the approach to preventing infections, optimising vaccine responses and promoting recovery from infection.

An individual’s birthweight, a marker of in utero exposures, was recently associated with certain psychiatric conditions. However, studies investigating the relationship between an individual’s preterm birth status and/or birthweight and risk for depression during adulthood are sparse; we used data from the Women’s Health Initiative (WHI) to investigate these potential associations. At study entry, 86,925 postmenopausal women reported their birthweight by category (<6 lbs., 6–7 lbs. 15 oz., 8–9 lbs. 15 oz., or ≥10 lbs.) and their preterm birth status (full-term or ≥4 weeks premature). Women also completed the Burnham screen for depression and were asked to self-report if: (a) they had ever been diagnosed with depression, or (b) if they were taking antidepressant medications. Linear and logistic regression models were used to estimate unadjusted and adjusted effect estimates. Compared to those born weighing between 6 and 7 lbs. 15 oz., individuals born weighing <6 lbs. (βadj = 0.007, P < 0.0001) and ≥10 lbs. (βadj = 0.006, P = 0.02) had significantly higher Burnam scores. Individuals born weighing <6 lbs. were also more likely to have depression (adjOR 1.21, 95% CI 1.11–1.31). Individuals born preterm were also more likely to have depression (adjOR 1.18, 95% CI 1.02–1.35); while attenuated, this association remained in analyses limited to only those reportedly born weighing <6 lbs. Our research supports the role of early life exposures on health risks across the life course. Individuals born at low or high birthweights and those born preterm may benefit from early evaluation and long-term follow-up for the prevention and treatment of mental health outcomes.

The Paris-trained, Japanese composer Michiko Toyama (1913–2006) was appointed as the earliest foreign-born visiting composer at the Columbia-Princeton Electronic Music Center (CPEMC), the first institutionally supported studio of its kind in the United States. Yet she remains virtually unknown to scholarship, despite a growing literature on women pioneers in electronic music. Drawing on interviews, archival research, and the interpretive study of music, this article studies the conditions under which Toyama has found little remembrance to date; and it conceptualizes Toyama's own ideas of modernity formulated over the massive cultural and geographical dislocations of her lifetime. Within an intensely lyrical compositional practice, Toyama thematized hallmarks of traditional modernism studies: self-reflexivity, estrangement, exile, and exoticism. Racist criticism during her lifetime dismissed her music as a belated mimicry of Western models. Yet the modernist qualities and themes of her work emerge as a consequence of her life lived in intercultural contact zones of uprooting – the very conditions that make ideas of the ‘modern’ possible.

A range of health effects are associated with debt burdens from ubiquitous access to expensive credit. These health effects are concerning, especially for women who owe multiple types of higher-cost debt simultaneously and experience significantly higher stress associated with their debt burdens when compared to men. While debt burdens have been shown to contribute to poor mental and physical health, the potential gendered and racialized effects are poorly understood. We conducted interviews between January and April 2021 with twenty-nine racially marginalized women who reported owing debt, and used theoretical concepts of predatory inclusion and intersectionality to understand their experiences. Women held many types of debt, most commonly from student loans, medical bills, and credit cards. Women described debt as a violent, abusive, and inescapable relationship that exacted consequential tolls on their health. Despite these, women found ways to resist the violence of debt, to care for themselves and others, and to experience joy in their daily lives.

Let $\pi$ be a discrete group, and let $G$ be a compact-connected Lie group. Then, there is a map $\Theta \colon \mathrm {Hom}(\pi,G)_0\to \mathrm {map}_*(B\pi,BG)_0$ between the null components of the spaces of homomorphisms and based maps, which sends a homomorphism to the induced map between classifying spaces. Atiyah and Bott studied this map for $\pi$ a surface group, and showed that it is surjective in rational cohomology. In this paper, we prove that the map $\Theta$ is surjective in rational cohomology for $\pi =\mathbb {Z}^m$ and the classical group $G$ except for $SO(2n)$, and that it is not surjective for $\pi =\mathbb {Z}^m$ with $m\ge 3$ and $G=SO(2n)$ with $n\ge 4$. As an application, we consider the surjectivity of the map $\Theta$ in rational cohomology for $\pi$ a finitely generated nilpotent group. We also consider the dimension of the cokernel of the map $\Theta$ in rational homotopy groups for $\pi =\mathbb {Z}^m$ and the classical groups $G$ except for $SO(2n)$.