Extremal rank-one convex integrands and a conjecture of \v{S}ver\'ak

We show that in order to decide whether a given probability measure is laminate it is enough to verify Jensen's inequality in the class of extremal non-negative rank-one convex integrands. We also identify a subclass of these extremal integrands, consisting of truncated minors, thus proving a conjecture made by \v{S}ver\'ak in (Arch. Ration. Mech. Anal. 119 293-300, 1992)

Genome-scale metabolic network reconstruction of Polaromonas sp. strain JS666: analysis of cDCE degradation rates and design of experiments for bioremediation improvement

Release of chloroethene compounds into the environment often results in groundwater contamination, which puts people at risk of exposure by drinking contaminated water. cDCE (cis-1,2-dichloroethene) accumulation on subsurface environments is a common environmental problem due to stagnation and partial degradation of other precursor chloroethene species. Polaromonas sp. strain JS666 apparently requires no exotic growth factors to be used as a bioaugmentation agent for aerobic cDCE degradation. Although being the only suitable microorganism found capable of such, further studies are needed for improving the intrinsic bioremediation rates and fully comprehend the metabolic processes involved. In order to do so, a metabolic model, iJS666, was reconstructed from genome annotation and available bibliographic data. FVA (Flux Variability Analysis) and FBA (Flux Balance Analysis) techniques were used to satisfactory validate the predictive capabilities of the iJS666 model. The iJS666 model was able to predict biomass growth for different previously tested conditions, allowed to design key experiments which should be done for further model improvement and, also, produced viable predictions for the use of biostimulant metabolites in the cDCE biodegradation

Remarks on Ornstein's Non-Inequality in 2×2

We give a very concise proof of Ornstein's L1 non-inequality for first-and second-order operators in two dimensions. The proof just needs a two-dimensional laminate supported on three point

On the necessity of the constant rank condition for LpL^p estimates

We consider a generalization of the elliptic $L^p$-estimate suited for linear operators with non-trivial kernels. A classical result of Schulenberger and Wilcox (Ann. Mat. Pura Appl. (4) 88: 229-305, 1971) shows that if the operator has constant rank then the estimate holds. We prove necessity of the constant rank condition for such an estimate.Comment: 5 pages; weaker versions of the results here had previously appeared in arXiv:1909.0392

The internet of things : developing a sustainable competitive advantage in the hotel industry

The Internet of Things (IoT) is a technology that allows objects to be connected to the internet, enabling them with communication capabilities (with other objects and with people). By 2020 there will be over 50 billion things/objects connected to the internet, meaning this technology will completely revolutionize the world as we know it. This dissertation´s goal, is to analyze the strategic potential of the IoT in the hotel industry. In this view, the research problem this dissertation faces is to ascertain if a hotel may create value through the IoT, and if that value creation may lead to the development of a sustainable competitive advantage. In order to achieve this dissertation´s goal, a set of IoT´s functionalities are proposed and linked to a value activity, in a Hotel´s Value Chain. Then, through a survey, answered by 418 respondents from 44 nationalities, it is ascertained that IoT creates value and increases guest loyalty, and also, the most attractive IoT´s functionalities are identified. Then, through an analysis conducted to the most attractive IoT´s functionalities (identified in the survey), it is ascertained that these functionalities allow a hotel to develop two resources: 1) High Quality Customer Service, and 2) Guests´ Tacit Knowledge. Further on, by applying the RBV model, it is ascertained that Guests´ Tacit Knowledge is a resource that has value, it´s rare, imperfectly imitable and non-substitutable, which means that it may help a hotel developing and implementing value-creating strategies, that may last in time. It is concluded, then, that IoT has potential to help a hotel creating value, through the resource Guests´ Tacit Knowledge, and it may use that value creation to develop a sustainable competitive advantage.A Internet of Things (IoT) - ou a Internet das Coisas - é uma tecnologia que permite a conexão de objectos/coisas à internet, permitindo assim que os objectos/coisas possam comunicar entre si e com pessoas. Em 2020 vão existir mais de 50 biliões de objectos/coisas ligados à internet, o que significa que esta tecnologia vai revolucionar totalmente o mundo como o conhecemos. O objectivo desta dissertação é analisar o potencial estratégico da IoT na indústria hoteleira. Neste prisma, o problema de investigação, da presente dissertação, é aferir se um hotel consegue criar valor com a IoT, e se essa criação de valor pode levar ao desenvolvimento de uma vantagem competitiva sustentável. De modo a atingir o objectivo desta dissertação, são propostas algumas funcionalidades da IoT, e posteriormente ligadas a uma actividade, numa Cadeia de Valor de um hotel. De seguida, através de um questionário, respondido por 418 pessoas de 44 nacionalidades, é possível aferir que a IoT pode criar valor e aumentar a fidelização de clientes, por outro lado, assim, são também identificadas as funcionalidades da IoT mais atractivas. Através da análise das funcionalidades da IoT mais atractivas (identificadas através do questionário), é possível aferir que estas funcionalidades permitem que um hotel possa desenvolver dois recursos: 1) Serviço ao Cliente de Alta Qualidade, e 2) Conhecimento Tácito dos Hóspedes. Com o modelo RBV, é, então, possível analisar que o Conhecimento Tácito dos Hóspedes é um recurso valioso, raro, imperfeitamente imitável, e não substituível, pelo que pode ajudar um hotel a desenvolver e implementar estratégias de criação de valor, sutentáveis. É assim concluído que a IoT tem potencial para ajudar ajudar um hotel a criar valor, através do recurso Conhecimento Tácito dos Hóspedes, e essa criação de valor pode ser usada para desenvolver uma vantagem competitiva sustentável

Quasiconvexity, null Lagrangians, and Hardy space integrability under constant rank constraints

We present a systematic treatment of the theory of Compensated Compactness under Murat's constant rank assumption. We give a short proof of a sharp weak lower semicontinuity result for signed integrands, extending the results of Fonseca--M\"uller. The null Lagrangians are an important class of signed integrands, since they are the weakly continuous functions. We show that they are precisely the compensated compactness quantities with Hardy space integrability, thus proposing an answer to a question raised by Coifman-Lions-Meyer-Semmes. Finally we provide an effective way of computing the null Lagrangians associated with a given operator.Comment: Corrected typos and added an example in Section