The Density of Polynomials in a Special Space of Entire Functions of Exponential Type

The traditional approach to solving a specific problem of spectral synthesis in a complex domain involves reducing it to the problem of local description of closed submodules in a certain space of entire functions. The last problem is split into checking the stability and saturation of the submodule under study. This approach turned out to be very effective, for example, in the study of submodules of local rank 1 and in the study of submodules in topological modules associated with unbounded convex domains. Recent studies on spectral synthesis in the complex domain are based on a different scheme. This scheme involves reducing the problem of local description to checking the density of polynomials in a special module of entire functions of exponential type. Moreover, the space under study is a separable locally convex space of type (LN)*. Polynomial approximation in such a space is understood by us as sequential approximation, that is, we are talking about the approximation of space elements by ordinary (not generalized) sequences of polynomials. In this article, we study a special locally convex module of entire vector functions over the ring of polynomials in the degree of the independent variable. The theorem proved in the article can serve as a source of new results on spectral synthesis in the complex domain.

Comprehensive Analysis of Heat and Water Exchanges in the Human Lungs

This work presents a new mathematical model of the heat and water exchanges in the human lungs (newborn to adult). This model is based on a local description of the water and energy transports in both the lumen and the surrounding tissues, and is presented in a comprehensive, dimensionless framework with explicitly stated assumptions and a strong physiological background. The model is first used to analyze and quantify the key phenomena and dimensionless numbers governing these heat and water exchanges and then it is applied to an adult in various situations (varying atmospheric conditions, exercising…). The results highlight several interesting physiological elements. They show that the bronchial region of the lungs is able to condition the air in all the considered situations even if, sometimes, for instance when exercising, distal generations have to be involved. The model also shows that these distal generations are super-conditioners. Moreover, the results quantify the key role of the submucosal glands in mucus hydration. They also show that, during expiration, a significant cooling of the air and condensation of water occur along the respiratory tract as the vascularization of the tissues surrounding the airways is not able to maintain these tissues at body temperature during inspiration. Due to the interaction between several phenomena, it appears that the ratio of the amount of water returned to the mucosa during expiration to the amount extracted during inspiration is almost independent of the breathing conditions (around 33%). The results also show that, in acute situations, such as suffering from a pathology with airway dysfunction, when being intubated or when exercising above an intensity threshold, the heat and water exchanges in the lungs may be critical regarding mucus hydration. In proximal generations, the evaporation may overwhelm the ability of the submucosal glands to replenish the airway surface liquid with water. In some situations, the cooling of the mucosa may be very important; it can even become colder than the inspired air, due to evaporative cooling. Finally, the results show that breathing cold air can significantly increase the exchanges between the lungs and the environment, which can be critical regarding disease transmission.

The ABC of Deutsch–Hayden Descriptors

It has been more than 20 years since Deutsch and Hayden proved the locality of quantum theory, using the Heisenberg picture of quantum computational networks. Of course, locality holds even in the face of entanglement and Bell’s theorem. Today, most researchers in quantum foundations are still convinced not only that a local description of quantum systems has not yet been provided, but that it cannot exist. The main goal of this paper is to address this misconception by re-explaining the descriptor formalism in a hopefully accessible and self-contained way. It is a step-by-step guide to how and why descriptors work. Finally, superdense coding is revisited in the light of descriptors.

The cost of quantum locality

It has been more than 20 years since Deutsch and Hayden demonstrated that quantum systems can be completely described locally—notwithstanding Bell’s theorem. More recently, Raymond-Robichaud proposed two other approaches to the same conclusion. In this paper, all these means of describing quantum systems locally are proved formally equivalent. The cost of such descriptions is then quantified by the dimensionality of their underlining space. The number of degrees of freedom of a single qubit’s local description is shown to grow exponentially with the total number of qubits considered as a global system. This apparently unreasonable cost to describe such a small system in a large Universe is nonetheless shown to be expected. Finally, structures that supplement the universal wave function are investigated.

Drowning in the elderly in Paraíba-Brazil

Drowning is a global problem, and is among the main causes of death in the world, and the elderly are part of this new reality as a special group who also suffer submersion accidents. The aim of this study was to analyze deaths due to drowning in the elderly in the state of Paraíba from 2005 to 2015. This is a retrospective, descriptive study associated with spatial analysis of regions with a higher incidence of drowning in people aged 60 years or older in the state of Paraíba. Data were collected from the IML (Gemol and Numol) records from 2005 to 2015, totaling 80 cases of drowning. Sociodemographic characteristics such as age group, gender, spatiality and local description of the occurrence (rivers, dams, sea, waterfall, cacimbas, dams and domestic environments), care provider, file of the Legal Medical Institute of the Scientific Police, international code of diseases – ICD 10 (code W74), shift of occurrence. As results we located the region of Mari sector of the wild region of Paraíba – Açude Olho D’agua (Latitude 7.11º S and Longitude 35.2º ), was the place with the highest number of drownings, where dams/lakes (55%), male (91%), married (46%), aged between 60 and 69 years (60%), the local population made the first care (41%), 14h was of higher occurrence (11%), and on Sundays (29%). We can conclude that drowning occurs in several aquatic scenarios, and in this study occurred in fresh water, several factors were associated with drowning in the elderly, such as cognition deficits, polypharmaceuticals and physical limitations, such outcomes can help encourage protection policies for this group as well as family members guide in freshwater regions and accentuate care.

Evolution Equations for Quantum Semi-Markov Dynamics

Using a newly introduced connection between the local and non-local description of open quantum system dynamics, we investigate the relationship between these two characterisations in the case of quantum semi-Markov processes. This class of quantum evolutions, which is a direct generalisation of the corresponding classical concept, guarantees mathematically well-defined master equations, while accounting for a wide range of phenomena, possibly in the non-Markovian regime. In particular, we analyse the emergence of a dephasing term when moving from one type of master equation to the other, by means of several examples. We also investigate the corresponding Redfield-like approximated dynamics, which are obtained after a coarse graining in time. Relying on general properties of the associated classical random process, we conclude that such an approximation always leads to a Markovian evolution for the considered class of dynamics.

Symmetries, a Systematic Construction of Invariant Fields and AdS Backgrounds

We give a systematic local description of invariant metrics and other invariant fields on a spacetime under the action of a (non-abelian) group. This includes the invariant fields in a neighbourhood of a principal and a special orbit. The construction is illustrated with examples. We also apply the formalism to give the R-symmetry invariant metrics of some AdS backgrounds and comment on applications to Kaluza-Klein theory.