Local Existence of an HP3H_P^3 Solution to the Hasegawa-Mima Plasma Equation

In this paper, we reformulate the non-linear Hasegawa-Mima initial-value plasma equation as a coupled system of two initial value linear PDEs, the first one being of hyperbolic type and the second of elliptic type, a solution of which is a pair $(u,w)$, with $w=(I-\Delta)u$. We then find several variational frames for obtaining weak solutions to the initial-value Hasegawa-Mima problem with periodic boundary conditions, and providing an efficient setting for Finite Element discretization models. For an initial data $u_0 \in H_P^3(\Omega)$ with $w_0:=(I-\Delta) u_0 \in L^\infty(\Omega)$, where $H_P^m(\Omega)$ are appropriately defined periodic Sobolev spaces on a rectangular domain $\Omega$, we prove the existence of a fixed-point Petrov-Galerkin sequence $\{(u_N,w_N)\}$ that converges weakly to a point-wise local solution $(u,w) \in [L^2(0,T;H_P^3(\Omega)) \cap C([0,T], H_P^2(\Omega))] \times [L^2(0,T;H_P^1(\Omega)) \cap C([0,T], L^2(\Omega))]$ with $(u_t,w_t) \in L^2(0,T;H_P^2(\Omega)) \times L^2(0,T;L^2(\Omega))$, of the coupled system. The existence interval $[0,T]$ appears to depend inversely on $||w_0||_{L^\infty}$ and $||w_0||_{H^1}$.Comment: 17 page

Direct Problem of Gas Diffusion in Polar Firn

Simultaneous use of partial differential equations in conjunction with data analysis has proven to be an efficient way to obtain the main parameters of various phenomena in different areas, such as medical, biological, and ecological. In the ecological field, the study of climate change (including global warming) over the past centuries requires estimating different gas concentrations in the atmosphere, mainly CO2. Antarctic and Greenland Polar snow and ice constitute a unique archive of past climates and atmospheres. The mathematical model of gas trapping in deep polar ice (firns) has been derived in [8, 11, 12, 13]. In this paper, we study the theoretical aspects of existence and uniqueness for the obtained, almost singular, parabolic partial differential equations

Quasi-Monte Carlo methods for Markov chains with continuous multi-dimensional state space

International audienceWe describe a quasi-Monte Carlo method for the simulation of discrete time Markov chains with continuous multi-dimensional state space. The method simulates copies of the chain in parallel. At each step the copies are reordered according to their successive coordinates. We prove the convergence of the method when the number of copies increases. We illustrate the method with numerical examples where the simulation accuracy is improved by large factors compared with Monte Carlo simulation

Data-Driven Models for studying the Dynamics of the COVID-19 Pandemics

This paper seeks to study the evolution of the COVID-19 pandemic based on daily published data from Worldometer website, using a time-dependent SIR model. Our findings indicate that this model fits well such data, for different chosen periods and different regions. This well-known model, consisting of three disjoint compartments, susceptible , infected , and removed , depends in our case on two time dependent parameters, the infection rate $\beta(t)$ and the removal rate $\rho(t)$. After deriving the model, we prove the local exponential behavior of the number of infected people, be it growth or decay. Furthermore, we extract a time dependent replacement factor $\sigma_s(t) ={\beta(t)}s(t)/{\rho(t) }$, where $s(t)$ is the ratio of susceptible people at time $t$. In addition, $i(t)$ and $r(t)$ are respectively the ratios of infected and removed people, based on a population of size $N$, usually assumed to be constant. Besides these theoretical results, the report provides simulations on the daily data obtained for Germany, Italy, and the entire World, as collected from Worldometer over the period stretching from April 2020 to June 2022. The computational model consists of the estimation of $\beta(t)$, $\rho(t)$ and $s(t)$ based on the time-dependent SIR model. The validation of our approach is demonstrated by comparing the profiles of the collected $i(t), r(t)$ data and those obtained from the SIR model with the approximated parameters. We also consider matching the data with a constant-coefficient SIR model, which seems to be working only for short periods. Thus, such model helps understanding and predicting the evolution of the pandemics for short periods of time where no radical change occurs.Comment: 59 page

Quasi-Monte Carlo methods for Markov chains with continuous multi-dimensional state space

International audienceWe describe a quasi-Monte Carlo method for the simulation of discrete time Markov chains with continuous multi-dimensional state space. The method simulates copies of the chain in parallel. At each step the copies are reordered according to their successive coordinates. We prove the convergence of the method when the number of copies increases. We illustrate the method with numerical examples where the simulation accuracy is improved by large factors compared with Monte Carlo simulation

Understanding the Entrepreneurial Process: a Dynamic Approach

There is considerable predominance in the adoption of perspectives based on characteristics in research into entrepreneurship. However, most studies describe the entrepreneur from a static or snapshot approach; very few adopt a dynamic perspective. The aim of this study is to contribute to the enhancement of knowledge concerning entrepreneurial process dynamics through an understanding of the values, characteristics and actions of the entrepreneur over time. By focusing on personal attributes, we have developed a framework that shows the importance of affective and cognitive aspects of entrepreneurs and the way that they evolve during the development of their business

Elective cancer surgery in COVID-19-free surgical pathways during the SARS-CoV-2 pandemic: An international, multicenter, comparative cohort study

PURPOSE As cancer surgery restarts after the first COVID-19 wave, health care providers urgently require data to determine where elective surgery is best performed. This study aimed to determine whether COVID-19–free surgical pathways were associated with lower postoperative pulmonary complication rates compared with hospitals with no defined pathway. PATIENTS AND METHODS This international, multicenter cohort study included patients who underwent elective surgery for 10 solid cancer types without preoperative suspicion of SARS-CoV-2. Participating hospitals included patients from local emergence of SARS-CoV-2 until April 19, 2020. At the time of surgery, hospitals were defined as having a COVID-19–free surgical pathway (complete segregation of the operating theater, critical care, and inpatient ward areas) or no defined pathway (incomplete or no segregation, areas shared with patients with COVID-19). The primary outcome was 30-day postoperative pulmonary complications (pneumonia, acute respiratory distress syndrome, unexpected ventilation). RESULTS Of 9,171 patients from 447 hospitals in 55 countries, 2,481 were operated on in COVID-19–free surgical pathways. Patients who underwent surgery within COVID-19–free surgical pathways were younger with fewer comorbidities than those in hospitals with no defined pathway but with similar proportions of major surgery. After adjustment, pulmonary complication rates were lower with COVID-19–free surgical pathways (2.2% v 4.9%; adjusted odds ratio [aOR], 0.62; 95% CI, 0.44 to 0.86). This was consistent in sensitivity analyses for low-risk patients (American Society of Anesthesiologists grade 1/2), propensity score–matched models, and patients with negative SARS-CoV-2 preoperative tests. The postoperative SARS-CoV-2 infection rate was also lower in COVID-19–free surgical pathways (2.1% v 3.6%; aOR, 0.53; 95% CI, 0.36 to 0.76). CONCLUSION Within available resources, dedicated COVID-19–free surgical pathways should be established to provide safe elective cancer surgery during current and before future SARS-CoV-2 outbreaks

Effects of hospital facilities on patient outcomes after cancer surgery: an international, prospective, observational study

Background Early death after cancer surgery is higher in low-income and middle-income countries (LMICs) compared with in high-income countries, yet the impact of facility characteristics on early postoperative outcomes is unknown. The aim of this study was to examine the association between hospital infrastructure, resource availability, and processes on early outcomes after cancer surgery worldwide.Methods A multimethods analysis was performed as part of the GlobalSurg 3 study-a multicentre, international, prospective cohort study of patients who had surgery for breast, colorectal, or gastric cancer. The primary outcomes were 30-day mortality and 30-day major complication rates. Potentially beneficial hospital facilities were identified by variable selection to select those associated with 30-day mortality. Adjusted outcomes were determined using generalised estimating equations to account for patient characteristics and country-income group, with population stratification by hospital.Findings Between April 1, 2018, and April 23, 2019, facility-level data were collected for 9685 patients across 238 hospitals in 66 countries (91 hospitals in 20 high-income countries; 57 hospitals in 19 upper-middle-income countries; and 90 hospitals in 27 low-income to lower-middle-income countries). The availability of five hospital facilities was inversely associated with mortality: ultrasound, CT scanner, critical care unit, opioid analgesia, and oncologist. After adjustment for case-mix and country income group, hospitals with three or fewer of these facilities (62 hospitals, 1294 patients) had higher mortality compared with those with four or five (adjusted odds ratio [OR] 3.85 [95% CI 2.58-5.75]; p<0.0001), with excess mortality predominantly explained by a limited capacity to rescue following the development of major complications (63.0% vs 82.7%; OR 0.35 [0.23-0.53]; p<0.0001). Across LMICs, improvements in hospital facilities would prevent one to three deaths for every 100 patients undergoing surgery for cancer.Interpretation Hospitals with higher levels of infrastructure and resources have better outcomes after cancer surgery, independent of country income. Without urgent strengthening of hospital infrastructure and resources, the reductions in cancer-associated mortality associated with improved access will not be realised

Elective Cancer Surgery in COVID-19-Free Surgical Pathways During the SARS-CoV-2 Pandemic: An International, Multicenter, Comparative Cohort Study.

PURPOSE: As cancer surgery restarts after the first COVID-19 wave, health care providers urgently require data to determine where elective surgery is best performed. This study aimed to determine whether COVID-19-free surgical pathways were associated with lower postoperative pulmonary complication rates compared with hospitals with no defined pathway. PATIENTS AND METHODS: This international, multicenter cohort study included patients who underwent elective surgery for 10 solid cancer types without preoperative suspicion of SARS-CoV-2. Participating hospitals included patients from local emergence of SARS-CoV-2 until April 19, 2020. At the time of surgery, hospitals were defined as having a COVID-19-free surgical pathway (complete segregation of the operating theater, critical care, and inpatient ward areas) or no defined pathway (incomplete or no segregation, areas shared with patients with COVID-19). The primary outcome was 30-day postoperative pulmonary complications (pneumonia, acute respiratory distress syndrome, unexpected ventilation). RESULTS: Of 9,171 patients from 447 hospitals in 55 countries, 2,481 were operated on in COVID-19-free surgical pathways. Patients who underwent surgery within COVID-19-free surgical pathways were younger with fewer comorbidities than those in hospitals with no defined pathway but with similar proportions of major surgery. After adjustment, pulmonary complication rates were lower with COVID-19-free surgical pathways (2.2% v 4.9%; adjusted odds ratio [aOR], 0.62; 95% CI, 0.44 to 0.86). This was consistent in sensitivity analyses for low-risk patients (American Society of Anesthesiologists grade 1/2), propensity score-matched models, and patients with negative SARS-CoV-2 preoperative tests. The postoperative SARS-CoV-2 infection rate was also lower in COVID-19-free surgical pathways (2.1% v 3.6%; aOR, 0.53; 95% CI, 0.36 to 0.76). CONCLUSION: Within available resources, dedicated COVID-19-free surgical pathways should be established to provide safe elective cancer surgery during current and before future SARS-CoV-2 outbreaks

Performance Analysis Of Supply And Return Fans For Hvac Systems Under Different Operating Strategies Of Economizer Dampers

HVAC systems and associated equipment consume a relatively large fraction of total building energy consumption, a significant portion of which is attributed to fan operation. The operation of economizer dampers when installed can cause high energy consumption in fans if they are not functioning in proper and optimal manner. This will mainly be due to the potential high pressure drops through those dampers and associated high total pressures that should be developed by supply and/or return fans. It is then necessary to ensure that a proper strategy to operate optimally the economizer dampers is implemented with minimum fan energy use. The paper examines several operation strategies of the economizer dampers and investigates their effects on the performance of both the supply and return fans in HVAC system. It also discusses a new operating strategy for economizer dampers that can lead to lower fan energy use. The strategies are evaluated by simulations for a typically existing HVAC system. Several factors such as the building locations, system characteristics, resistance in the duct where the dampers are installed, supply air temperature and economizer control, and minimum ventilation requirements are also considered during the evaluations. The results show that the way of the economizer dampers been controlled has a significant effect on fan performance and its energy use. The proposed strategy if properly implemented can provide fan energy saving in the range of 5-30%, depending mainly on the number of hours when the system operates in the free cooling mode, damper characteristics, and minimum outdoor air. © 2010 Elsevier B.V. All rights reserved