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(IME - 2020/2021 - 2 FASE) Text 3 Mathematical Modeling of Epidemic Diseases; A Case Study of the COVID-19 Coronavirus Reza Sameni Abstract The outbreak of the Coronavirus COVID-19 has taken the lives of several thousands worldwide and lockedout many countries and regions, with yet unpredictable global consequences. In this research we study the epidemic patterns of this virus, from a mathematical modeling perspective. The study is based on an extensions of the well-known susceptible-infected recovered (SIR) family of compartmental models. It is shown how social measures such as distancing, regional lockdowns, quarantine and global public health vigilance, influence the model parameters, which can eventually change the mortality rates and active contaminated cases over time, in the real world. As with all mathematical models, the predictive ability of the model is limited by the accuracy of the available data and to the so-called level of abstraction used for modeling the problem. In order to provide the broader audience of researchers a better understanding of spreading patterns of epidemic diseases, a short introduction on biological systems modeling is also presented and the Matlab source codes for the simulations are provided online. I. INTRODUCTION Since the outbreak of the Coronavirus COVID-19 in January 2020, the virus has affected most countries and taken the lives of several thousands of people worldwide. By March 2020, the World Health Organization (WHO) declared the situation a pandemic, the first of its kind in our generation. To date, many countries and regions have been locked-down and applied strict social distancing measures to stop the virus propagation. From a strategic and healthcare management perspective, the propagation pattern of the disease and the prediction of its spread over time is of great importance, to save lives and to minimize the social and economic consequences of the disease. Within the scientific community, the problem of interest has been studied in various communities including mathematical epidemiology, biological systems modeling, signal processing and control engineering. In this study, epidemic outbreaks are studied from an interdisciplinary perspective, by using an extension of the susceptible-exposed-infected-recovered (SEIR) model, which is a mathematical compartmental model based on the average behavior of a population under study. The objective is to provide researchers a better understanding of the significance of mathematical modeling for epidemic diseases. It is shown by simulation, how social measures such as distancing, regional lockdowns and public health vigilance, can influence the model parameters, which in turns change the mortality rates and active contaminated cases over time. It should be highlighted that mathematical models applied to real-world systems (social, biological, economical, etc.) are only valid under their assumptions and hypothesis. Therefore, this research and similar ones that address epidemic patterns, do not convey direct clinical information and dangers for the public, but should rather be used by healthcare strategists for better planning and decision making. Hence, the study of this work is only recommended for researchers familiar with the strength points and limitations of mathematical modeling of biological systems. The Matlab codes required for reproducing the results of this research are also online available in the Git repository of the project. In Section II, a brief introduction to mathematical modeling of biological systems is presented, to highlight the scope of the present study and to open perspectives for the interested researchers, who may be less familiar with the context. The proposed model for the outspread of the Coronavirus is presented in Section III. The article is concluded with some general remarks and future perspectives. Adapted from:Mathematical Modeling of Epidemic Diseases; A Case Study of the COVID-19 Coronavirus. Avaliable at: arxiv.org/abs/2003.11371 [Accessed 6th June 2020]. Text 4 Mathematical modeling of the spread of the coronavirus disease 2019 (COVID-19) taking into account the undetected infections. The case of China B. Ivorra, M.R. Ferrndez, M. Vela-Prez and A.M. Ramosa Abstract In this paper we develop a mathematical model for the spread of the coronavirus disease 2019 (COVID-19). It is a new -SEIHRD model (not a SIR, SEIR or other general purpose model), which takes into account the known special characteristics of this disease, as the existence of infectious undetected cases and the different sanitary and infectiousness conditions of hospitalized people. In particular, it includes a novel approach that considers the fraction of detected cases over the real total infected cases, which allows to study the importance of this ratio on the impact of COVID-19. The model is also able to estimate the needs of beds in hospitals. It is complex enough to capture the most important effects, but also simple enough to allow an affordable identification of its parameters, using the data that authorities report on this pandemic. We study the particular case of China (including Chinese Mainland, Macao, Hong-Kong and Taiwan, as done by the World Health Organization in its reports on COVID-19), the country spreading the disease, and use its reported data to identify the model parameters, which can be of interest for estimating the spread of COVID-19 in other countries. We show a good agreement between the reported data and the estimations given by our model. We also study the behavior of the outputs returned by our model when considering incomplete reported data (by truncating them at some dates before and after the peak of daily reported cases). By comparing those results, we can estimate the error produced by the model when identifying the parameters at early stages of the pandemic. Finally, taking into account the advantages of the novelties introduced by our model, we study different scenarios to show how different values of the percentage of detected cases would have changed the global magnitude of COVID-19 in China, which can be of interest for policy makers. Keywords: Mathematical model, -SEIHRD model, COVID-19, Coronavirus, SARS-CoV-2, Pandemic, Numerical simulation, Parameter estimation 1. Introduction Modeling and simulation are important decision tools that can be useful to control human and animal diseases. However, since each disease exhibits its own particular biological characteristics, the models need to be adapted to each specific case in order to be able to tackle real situations. Coronavirus disease 2019 (COVID-19) is an infectious disease emerging in China in December 2019 that has rapidly spread around China and many other countries. On 11 February 2020, the World Health Organization (WHO) renamed the epidemic disease caused by 2019-nCoV as strain severe acute respiratory syndrome coronavirus 2 (SARS-CoV-2) This is a new virus and a completely new situation. On 30 January 2020, WHO declared it to be a Public Health Emergency of International Concern. As of 11 March 2020, the disease was confirmed in more than 118,000 cases reported globally in 114 countries, more than 90 percent of cases are in just four countries (two of those China and the Republic of Korea - have significantly declining epidemics) and WHO declared it to be a pandemic, the first one caused by a coronavirus. On 1 April 2020 there are 872,481 and 43,275 official reported cases and deaths, respectively, and there is no vaccine specifically designed for this virus, with proven effectiveness. There are some mathematical models in the literature that try to describe the dynamics of the evolution of COVID-19. (...) Other works propose SEIR type models with little variations and some of them incorporate stochastic components. COVID-19 is a disease caused by a new virus, which is generating a worldwide emergency situation and needs a model taking into account its known specific characteristics. Adaptec from:Mathematical modeling of the spread of the coronavirus disease 2019 (COVID-19) taking into account the undetected infections. The case of China.In: Elsevier Public Health Emergency Colletion, 2020. Avaliable at: https://www.mcbi.nlm.nih.gov/pmc/articles/PMC7190554/ [Accessed 4th June 2020]. Choose the option in wich the meaning of to convey is the same as in (...) Therefore, this research and similar ones that address epidemic patterns, do not convey direct clinical information and dangers for the public, (.... (Text 3).

(IME - 2020/2021- 2 FASE) Text 1 Materials Science in the time of Coronavirus Annela M Seddon Before 2020, phrases such as social distancing and lock down were not part of our normal vocabulary; however, it seems now that they are at the core of every conversation. We scientists naturally look to see where we ______(21)_____ be best placed to help as we start to piece together what this new normal means for us. ______(22)_____ a problem of the magnitude of a global pandemic cannot be undertaken by a single discipline. ______(23)_____ , while we are still in the early stages of this crisis, where emergency medical care and reducing pressure on health services are ______(24)_____, we look to our clinicians, epidemiologists, and experts in the biomedical sciences for frontline solutions. ______(25)_____, we must think more broadly about the role of materials science. Traditionally, when we think about viral infection our thoughts first turn to vaccines. After all, these ______(26)_____ one the most successful public health interventions in human history, rendering what were ______(27)_____ fatal or seriously debilitating diseases a thing of the past thanks to a simple ______(28)_____ of inoculations. They will always remain the heavy artillery in our fight against viruses; however, in the situation we face at present, a vaccine against COVID-19 ______(29)_____ some way into the future. What then of antiviral agents? Over the last 50years, more than 90 drugs have been approved as antivirals, ______(30)_____ these target only nine human infectious diseases. It is tempting to think that the development of new antiviral agents is beyond the scope of what we traditionally call materials science, Adapted from: Journal of Materials Science.Materials Science in the time of Coronavirus.Available at: http://link.springer.com/article/10.1007/s10853-020-04694-4 [Accessed 21st May 2020]. Fill the blank (30)

(IME - 2020/2021 - 2 FASE) Text 2 COVID-19s impact on mobile robotics growth The COVID 19 pandemic is creating the opportunity for mobile robots to be used for various markets and could lead to a reassessment of supply chains in the future. Gregory Hale Coronavirus has highlighted use cases for mobile robotics to successfully disinfect, monitor, look over, handle, and deliver materials to the point where the market will grow to $23 billion by 2021, new research showed. Crises shift perceptions on what is possible regarding investment and transformative action on the part of both private and government actors, said Rian Whitton, senior analyst at tech market advisory firm, ABI Research. By the time the COVID-19 pandemic has passed, robots will be mainstreamed across a range of applications and markets. Mobile robots on display The virus has been a good opportunity for companies to display robots for public applications. One of the more popular applications has been deploying mobile unmanned platforms with Ultraviolet (UV) light to disinfect facilities. Danish company UVD Robots is reaping the benefits of this opportunity and is scaling up deployments of robots to disinfect hospitals. U.S.-based Germ Falcon is offering a similar UV disinfection solution for aircraft, while Chinese TMiRob is deploying disinfection robots in Wuhan. Automating disinfection is a key part of maintaining health and safety and could be one of the major bright spots in the response to COVID-19, Whitton said. Drones have also been deployed to enforce curfews and surveil areas for security purposes. Short- and long-term opportunities This represents a big opportunity for aerospace and drone companies to increase sales to government agencies. ABI Research expects the small drone delivery market to reach $414 million by 2021 and $10.4 billion by 2030. In the short term, to enforce quarantine mandates, governments will need to increase their security apparatuses, as well as the productivity of their medical agencies. Robots will be key to achieving that through disinfection, monitoring, and surveillance. Furthermore, the shutting down of households and even ships represents a chance for robot delivery companies (for both land and air) to display their worth. The drone delivery market could take its experience with transporting supplies in the developing world and scale up their operations in the most affected countries. Long-term, COVID-19 is leading to a significant reassessment of the global manufacturing supply chain. Americas dependence on Chinese imports for basic equipment and medicines is becoming a contentious issue, and government representatives are already interpreting the crisis as a chance to revitalize the campaign to bring more manufacturing capacity to the domestic market. If this translates into more significant measures by governments to diversify or bringing back the manufacturing of key goods, this could bode very well for the robotics industry, as such changes would require big increases in CAPEX and productivity improvements within developed countries. COVID-19 represents a disaster for robotics vendors building solutions for developed markets in manufacturing, industry, and the supply chain. But for vendors targeting markets closer to government, such as health, security, and defense, it represents a big opportunity. Whitton said, Industrial players develop customized solutions for non-manufacturing use cases or look to build comprehensive solutions for enabling a scale-up in medical supply manufacturing. For mobile robotics vendors and software companies targeting more nascent markets, this represents a big chance to highlight the importance of robotics for dealing with national emergencies, as well as mitigating the economic shock. Available at: https://isssource.com/covid-19-and-growth-of-mobile-robotics/ Choose the correct option:

(IME - 2020/2021 - 2 FASE) Text 2 COVID-19s impact on mobile robotics growth The COVID 19 pandemic is creating the opportunity for mobile robots to be used for various markets and could lead to a reassessment of supply chains in the future. Gregory Hale Coronavirus has highlighted use cases for mobile robotics to successfully disinfect, monitor, look over, handle, and deliver materials to the point where the market will grow to $23 billion by 2021, new research showed. Crises shift perceptions on what is possible regarding investment and transformative action on the part of both private and government actors, said Rian Whitton, senior analyst at tech market advisory firm, ABI Research. By the time the COVID-19 pandemic has passed, robots will be mainstreamed across a range of applications and markets. Mobile robots on display The virus has been a good opportunity for companies to display robots for public applications. One of the more popular applications has been deploying mobile unmanned platforms with Ultraviolet (UV) light to disinfect facilities. Danish company UVD Robots is reaping the benefits of this opportunity and is scaling up deployments of robots to disinfect hospitals. U.S.-based Germ Falcon is offering a similar UV disinfection solution for aircraft, while Chinese TMiRob is deploying disinfection robots in Wuhan. Automating disinfection is a key part of maintaining health and safety and could be one of the major bright spots in the response to COVID-19, Whitton said. Drones have also been deployed to enforce curfews and surveil areas for security purposes. Short- and long-term opportunities This represents a big opportunity for aerospace and drone companies to increase sales to government agencies. ABI Research expects the small drone delivery market to reach $414 million by 2021 and $10.4 billion by 2030. In the short term, to enforce quarantine mandates, governments will need to increase their security apparatuses, as well as the productivity of their medical agencies. Robots will be key to achieving that through disinfection, monitoring, and surveillance. Furthermore, the shutting down of households and even ships represents a chance for robot delivery companies (for both land and air) to display their worth. The drone delivery market could take its experience with transporting supplies in the developing world and scale up their operations in the most affected countries. Long-term, COVID-19 is leading to a significant reassessment of the global manufacturing supply chain. Americas dependence on Chinese imports for basic equipment and medicines is becoming a contentious issue, and government representatives are already interpreting the crisis as a chance to revitalize the campaign to bring more manufacturing capacity to the domestic market. If this translates into more significant measures by governments to diversify or bringing back the manufacturing of key goods, this could bode very well for the robotics industry, as such changes would require big increases in CAPEX and productivity improvements within developed countries. COVID-19 represents a disaster for robotics vendors building solutions for developed markets in manufacturing, industry, and the supply chain. But for vendors targeting markets closer to government, such as health, security, and defense, it represents a big opportunity. Whitton said, Industrial players develop customized solutions for non-manufacturing use cases or look to build comprehensive solutions for enabling a scale-up in medical supply manufacturing. For mobile robotics vendors and software companies targeting more nascent markets, this represents a big chance to highlight the importance of robotics for dealing with national emergencies, as well as mitigating the economic shock. Available at: https://isssource.com/covid-19-and-growth-of-mobile-robotics/ Choose the correct option:

(IME - 2020/2021 - 2 FASE) Text 2 COVID-19s impact on mobile robotics growth The COVID 19 pandemic is creating the opportunity for mobile robots to be used for various markets and could lead to a reassessment of supply chains in the future. Gregory Hale Coronavirus has highlighted use cases for mobile robotics to successfully disinfect, monitor, look over, handle, and deliver materials to the point where the market will grow to $23 billion by 2021, new research showed. Crises shift perceptions on what is possible regarding investment and transformative action on the part of both private and government actors, said Rian Whitton, senior analyst at tech market advisory firm, ABI Research. By the time the COVID-19 pandemic has passed, robots will be mainstreamed across a range of applications and markets. Mobile robots on display The virus has been a good opportunity for companies to display robots for public applications. One of the more popular applications has been deploying mobile unmanned platforms with Ultraviolet (UV) light to disinfect facilities. Danish company UVD Robots is reaping the benefits of this opportunity and is scaling up deployments of robots to disinfect hospitals. U.S.-based Germ Falcon is offering a similar UV disinfection solution for aircraft, while Chinese TMiRob is deploying disinfection robots in Wuhan. Automating disinfection is a key part of maintaining health and safety and could be one of the major bright spots in the response to COVID-19, Whitton said. Drones have also been deployed to enforce curfews and surveil areas for security purposes. Short- and long-term opportunities This represents a big opportunity for aerospace and drone companies to increase sales to government agencies. ABI Research expects the small drone delivery market to reach $414 million by 2021 and $10.4 billion by 2030. In the short term, to enforce quarantine mandates, governments will need to increase their security apparatuses, as well as the productivity of their medical agencies. Robots will be key to achieving that through disinfection, monitoring, and surveillance. Furthermore, the shutting down of households and even ships represents a chance for robot delivery companies (for both land and air) to display their worth. The drone delivery market could take its experience with transporting supplies in the developing world and scale up their operations in the most affected countries. Long-term, COVID-19 is leading to a significant reassessment of the global manufacturing supply chain. Americas dependence on Chinese imports for basic equipment and medicines is becoming a contentious issue, and government representatives are already interpreting the crisis as a chance to revitalize the campaign to bring more manufacturing capacity to the domestic market. If this translates into more significant measures by governments to diversify or bringing back the manufacturing of key goods, this could bode very well for the robotics industry, as such changes would require big increases in CAPEX and productivity improvements within developed countries. COVID-19 represents a disaster for robotics vendors building solutions for developed markets in manufacturing, industry, and the supply chain. But for vendors targeting markets closer to government, such as health, security, and defense, it represents a big opportunity. Whitton said, Industrial players develop customized solutions for non-manufacturing use cases or look to build comprehensive solutions for enabling a scale-up in medical supply manufacturing. For mobile robotics vendors and software companies targeting more nascent markets, this represents a big chance to highlight the importance of robotics for dealing with national emergencies, as well as mitigating the economic shock. Available at: https://isssource.com/covid-19-and-growth-of-mobile-robotics/ Consider the following extract from Text 2 : In the short term, to enforce quarantine mandates, governments will need to increase their security apparatuses, as well as the productivity of their medical agencies. Robots will be key to achieving that through disinfection, monitoring, and surveillance. The word that refers to:

(IME - 2020/2021 - 2 FASE) Text 2 COVID-19s impact on mobile robotics growth The COVID 19 pandemic is creating the opportunity for mobile robots to be used for various markets and could lead to a reassessment of supply chains in the future. Gregory Hale Coronavirus has highlighted use cases for mobile robotics to successfully disinfect, monitor, look over, handle, and deliver materials to the point where the market will grow to $23 billion by 2021, new research showed. Crises shift perceptions on what is possible regarding investment and transformative action on the part of both private and government actors, said Rian Whitton, senior analyst at tech market advisory firm, ABI Research. By the time the COVID-19 pandemic has passed, robots will be mainstreamed across a range of applications and markets. Mobile robots on display The virus has been a good opportunity for companies to display robots for public applications. One of the more popular applications has been deploying mobile unmanned platforms with Ultraviolet (UV) light to disinfect facilities. Danish company UVD Robots is reaping the benefits of this opportunity and is scaling up deployments of robots to disinfect hospitals. U.S.-based Germ Falcon is offering a similar UV disinfection solution for aircraft, while Chinese TMiRob is deploying disinfection robots in Wuhan. Automating disinfection is a key part of maintaining health and safety and could be one of the major bright spots in the response to COVID-19, Whitton said. Drones have also been deployed to enforce curfews and surveil areas for security purposes. Short- and long-term opportunities This represents a big opportunity for aerospace and drone companies to increase sales to government agencies. ABI Research expects the small drone delivery market to reach $414 million by 2021 and $10.4 billion by 2030. In the short term, to enforce quarantine mandates, governments will need to increase their security apparatuses, as well as the productivity of their medical agencies. Robots will be key to achieving that through disinfection, monitoring, and surveillance. Furthermore, the shutting down of households and even ships represents a chance for robot delivery companies (for both land and air) to display their worth. The drone delivery market could take its experience with transporting supplies in the developing world and scale up their operations in the most affected countries. Long-term, COVID-19 is leading to a significant reassessment of the global manufacturing supply chain. Americas dependence on Chinese imports for basic equipment and medicines is becoming a contentious issue, and government representatives are already interpreting the crisis as a chance to revitalize the campaign to bring more manufacturing capacity to the domestic market. If this translates into more significant measures by governments to diversify or bringing back the manufacturing of key goods, this could bode very well for the robotics industry, as such changes would require big increases in CAPEX and productivity improvements within developed countries. COVID-19 represents a disaster for robotics vendors building solutions for developed markets in manufacturing, industry, and the supply chain. But for vendors targeting markets closer to government, such as health, security, and defense, it represents a big opportunity. Whitton said, Industrial players develop customized solutions for non-manufacturing use cases or look to build comprehensive solutions for enabling a scale-up in medical supply manufacturing. For mobile robotics vendors and software companies targeting more nascent markets, this represents a big chance to highlight the importance of robotics for dealing with national emergencies, as well as mitigating the economic shock. Available at: https://isssource.com/covid-19-and-growth-of-mobile-robotics/ Choose the option that presents definition of the world curfews: as in Drones have also been deployed to enforce curfewsand surveil areas for security porposes:

(IME - 2020/2021 - 2 FASE) Text 2 COVID-19s impact on mobile robotics growth The COVID 19 pandemic is creating the opportunity for mobile robots to be used for various markets and could lead to a reassessment of supply chains in the future. Gregory Hale Coronavirus has highlighted use cases for mobile robotics to successfully disinfect, monitor, look over, handle, and deliver materials to the point where the market will grow to $23 billion by 2021, new research showed. Crises shift perceptions on what is possible regarding investment and transformative action on the part of both private and government actors, said Rian Whitton, senior analyst at tech market advisory firm, ABI Research. By the time the COVID-19 pandemic has passed, robots will be mainstreamed across a range of applications and markets. Mobile robots on display The virus has been a good opportunity for companies to display robots for public applications. One of the more popular applications has been deploying mobile unmanned platforms with Ultraviolet (UV) light to disinfect facilities. Danish company UVD Robots is reaping the benefits of this opportunity and is scaling up deployments of robots to disinfect hospitals. U.S.-based Germ Falcon is offering a similar UV disinfection solution for aircraft, while Chinese TMiRob is deploying disinfection robots in Wuhan. Automating disinfection is a key part of maintaining health and safety and could be one of the major bright spots in the response to COVID-19, Whitton said. Drones have also been deployed to enforce curfews and surveil areas for security purposes. Short- and long-term opportunities This represents a big opportunity for aerospace and drone companies to increase sales to government agencies. ABI Research expects the small drone delivery market to reach $414 million by 2021 and $10.4 billion by 2030. In the short term, to enforce quarantine mandates, governments will need to increase their security apparatuses, as well as the productivity of their medical agencies. Robots will be key to achieving that through disinfection, monitoring, and surveillance. Furthermore, the shutting down of households and even ships represents a chance for robot delivery companies (for both land and air) to display their worth. The drone delivery market could take its experience with transporting supplies in the developing world and scale up their operations in the most affected countries. Long-term, COVID-19 is leading to a significant reassessment of the global manufacturing supply chain. Americas dependence on Chinese imports for basic equipment and medicines is becoming a contentious issue, and government representatives are already interpreting the crisis as a chance to revitalize the campaign to bring more manufacturing capacity to the domestic market. If this translates into more significant measures by governments to diversify or bringing back the manufacturing of key goods, this could bode very well for the robotics industry, as such changes would require big increases in CAPEX and productivity improvements within developed countries. COVID-19 represents a disaster for robotics vendors building solutions for developed markets in manufacturing, industry, and the supply chain. But for vendors targeting markets closer to government, such as health, security, and defense, it represents a big opportunity. Whitton said, Industrial players develop customized solutions for non-manufacturing use cases or look to build comprehensive solutions for enabling a scale-up in medical supply manufacturing. For mobile robotics vendors and software companies targeting more nascent markets, this represents a big chance to highlight the importance of robotics for dealing with national emergencies, as well as mitigating the economic shock. Available at: https://isssource.com/covid-19-and-growth-of-mobile-robotics/ Choose the correct option.

(IME - 2020/2021 - 2 FASE) Text 2 COVID-19s impact on mobile robotics growth The COVID 19 pandemic is creating the opportunity for mobile robots to be used for various markets and could lead to a reassessment of supply chains in the future. Gregory Hale Coronavirus has highlighted use cases for mobile robotics to successfully disinfect, monitor, look over, handle, and deliver materials to the point where the market will grow to $23 billion by 2021, new research showed. Crises shift perceptions on what is possible regarding investment and transformative action on the part of both private and government actors, said Rian Whitton, senior analyst at tech market advisory firm, ABI Research. By the time the COVID-19 pandemic has passed, robots will be mainstreamed across a range of applications and markets. Mobile robots on display The virus has been a good opportunity for companies to display robots for public applications. One of the more popular applications has been deploying mobile unmanned platforms with Ultraviolet (UV) light to disinfect facilities. Danish company UVD Robots is reaping the benefits of this opportunity and is scaling up deployments of robots to disinfect hospitals. U.S.-based Germ Falcon is offering a similar UV disinfection solution for aircraft, while Chinese TMiRob is deploying disinfection robots in Wuhan. Automating disinfection is a key part of maintaining health and safety and could be one of the major bright spots in the response to COVID-19, Whitton said. Drones have also been deployed to enforce curfews and surveil areas for security purposes. Short- and long-term opportunities This represents a big opportunity for aerospace and drone companies to increase sales to government agencies. ABI Research expects the small drone delivery market to reach $414 million by 2021 and $10.4 billion by 2030. In the short term, to enforce quarantine mandates, governments will need to increase their security apparatuses, as well as the productivity of their medical agencies. Robots will be key to achieving that through disinfection, monitoring, and surveillance. Furthermore, the shutting down of households and even ships represents a chance for robot delivery companies (for both land and air) to display their worth. The drone delivery market could take its experience with transporting supplies in the developing world and scale up their operations in the most affected countries. Long-term, COVID-19 is leading to a significant reassessment of the global manufacturing supply chain. Americas dependence on Chinese imports for basic equipment and medicines is becoming a contentious issue, and government representatives are already interpreting the crisis as a chance to revitalize the campaign to bring more manufacturing capacity to the domestic market. If this translates into more significant measures by governments to diversify or bringing back the manufacturing of key goods, this could bode very well for the robotics industry, as such changes would require big increases in CAPEX and productivity improvements within developed countries. COVID-19 represents a disaster for robotics vendors building solutions for developed markets in manufacturing, industry, and the supply chain. But for vendors targeting markets closer to government, such as health, security, and defense, it represents a big opportunity. Whitton said, Industrial players develop customized solutions for non-manufacturing use cases or look to build comprehensive solutions for enabling a scale-up in medical supply manufacturing. For mobile robotics vendors and software companies targeting more nascent markets, this represents a big chance to highlight the importance of robotics for dealing with national emergencies, as well as mitigating the economic shock. Available at: https://isssource.com/covid-19-and-growth-of-mobile-robotics/ Choose the correct option

(IME - 2020/2021 - 2 FASE) Text 3 Mathematical Modeling of Epidemic Diseases; A Case Study of the COVID-19 Coronavirus Reza Sameni Abstract The outbreak of the Coronavirus COVID-19 has taken the lives of several thousands worldwide and lockedout many countries and regions, with yet unpredictable global consequences. In this research we study the epidemic patterns of this virus, from a mathematical modeling perspective. The study is based on an extensions of the well-known susceptible-infected recovered (SIR) family of compartmental models. It is shown how social measures such as distancing, regional lockdowns, quarantine and global public health vigilance, influence the model parameters, which can eventually change the mortality rates and active contaminated cases over time, in the real world. As with all mathematical models, the predictive ability of the model is limited by the accuracy of the available data and to the so-called level of abstraction used for modeling the problem. In order to provide the broader audience of researchers a better understanding of spreading patterns of epidemic diseases, a short introduction on biological systems modeling is also presented and the Matlab source codes for the simulations are provided online. I. INTRODUCTION Since the outbreak of the Coronavirus COVID-19 in January 2020, the virus has affected most countries and taken the lives of several thousands of people worldwide. By March 2020, the World Health Organization (WHO) declared the situation a pandemic, the first of its kind in our generation. To date, many countries and regions have been locked-down and applied strict social distancing measures to stop the virus propagation. From a strategic and healthcare management perspective, the propagation pattern of the disease and the prediction of its spread over time is of great importance, to save lives and to minimize the social and economic consequences of the disease. Within the scientific community, the problem of interest has been studied in various communities including mathematical epidemiology, biological systems modeling, signal processing and control engineering. In this study, epidemic outbreaks are studied from an interdisciplinary perspective, by using an extension of the susceptible-exposed-infected-recovered (SEIR) model, which is a mathematical compartmental model based on the average behavior of a population under study. The objective is to provide researchers a better understanding of the significance of mathematical modeling for epidemic diseases. It is shown by simulation, how social measures such as distancing, regional lockdowns and public health vigilance, can influence the model parameters, which in turns change the mortality rates and active contaminated cases over time. It should be highlighted that mathematical models applied to real-world systems (social, biological, economical, etc.) are only valid under their assumptions and hypothesis. Therefore, this research and similar ones that address epidemic patterns, do not convey direct clinical information and dangers for the public, but should rather be used by healthcare strategists for better planning and decision making. Hence, the study of this work is only recommended for researchers familiar with the strength points and limitations of mathematical modeling of biological systems. The Matlab codes required for reproducing the results of this research are also online available in the Git repository of the project. In Section II, a brief introduction to mathematical modeling of biological systems is presented, to highlight the scope of the present study and to open perspectives for the interested researchers, who may be less familiar with the context. The proposed model for the outspread of the Coronavirus is presented in Section III. The article is concluded with some general remarks and future perspectives. Adapted from: Mathematical Modeling of Epidemic Diseases; A Case Study of the COVID-19 Coronavirus. Avaliable at: arxiv.org/abs/2003.11371 [Accessed 6th June 2020]. Text 4 Mathematical modeling of the spread of the coronavirus disease 2019 (COVID-19) taking into account the undetected infections. The case of China B. Ivorra, M.R. Ferrndez, M. Vela-Prez and A.M. Ramosa Abstract In this paper we develop a mathematical model for the spread of the coronavirus disease 2019 (COVID-19). It is a new -SEIHRD model (not a SIR, SEIR or other general purpose model), which takes into account the known special characteristics of this disease, as the existence of infectious undetected cases and the different sanitary and infectiousness conditions of hospitalized people. In particular, it includes a novel approach that considers the fraction of detected cases over the real total infected cases, which allows to study the importance of this ratio on the impact of COVID-19. The model is also able to estimate the needs of beds in hospitals. It is complex enough to capture the most important effects, but also simple enough to allow an affordable identification of its parameters, using the data that authorities report on this pandemic. We study the particular case of China (including Chinese Mainland, Macao, Hong-Kong and Taiwan, as done by the World Health Organization in its reports on COVID-19), the country spreading the disease, and use its reported data to identify the model parameters, which can be of interest for estimating the spread of COVID-19 in other countries. We show a good agreement between the reported data and the estimations given by our model. We also study the behavior of the outputs returned by our model when considering incomplete reported data (by truncating them at some dates before and after the peak of daily reported cases). By comparing those results, we can estimate the error produced by the model when identifying the parameters at early stages of the pandemic. Finally, taking into account the advantages of the novelties introduced by our model, we study different scenarios to show how different values of the percentage of detected cases would have changed the global magnitude of COVID-19 in China, which can be of interest for policy makers. Keywords: Mathematical model, -SEIHRD model, COVID-19, Coronavirus, SARS-CoV-2, Pandemic, Numerical simulation, Parameter estimation 1. Introduction Modeling and simulation are important decision tools that can be useful to control human and animal diseases. However, since each disease exhibits its own particular biological characteristics, the models need to be adapted to each specific case in order to be able to tackle real situations. Coronavirus disease 2019 (COVID-19) is an infectious disease emerging in China in December 2019 that has rapidly spread around China and many other countries. On 11 February 2020, the World Health Organization (WHO) renamed the epidemic disease caused by 2019-nCoV as strain severe acute respiratory syndrome coronavirus 2 (SARS-CoV-2) This is a new virus and a completely new situation. On 30 January 2020, WHO declared it to be a Public Health Emergency of International Concern. As of 11 March 2020, the disease was confirmed in more than 118,000 cases reported globally in 114 countries, more than 90 percent of cases are in just four countries (two of those China and the Republic of Korea - have significantly declining epidemics) and WHO declared it to be a pandemic, the first one caused by a coronavirus. On 1 April 2020 there are 872,481 and 43,275 official reported cases and deaths, respectively, and there is no vaccine specifically designed for this virus, with proven effectiveness. There are some mathematical models in the literature that try to describe the dynamics of the evolution of COVID-19. (...) Other works propose SEIR type models with little variations and some of them incorporate stochastic components. COVID-19 is a disease caused by a new virus, which is generating a worldwide emergency situation and needs a model taking into account its known specific characteristics. Adaptec from: Mathematical modeling of the spread of the coronavirus disease 2019 (COVID-19) taking into account the undetected infections. The case of China. In: Elsevier Public Health Emergency Colletion, 2020. Avaliable at: https://www.mcbi.nlm.nih.gov/pmc/articles/PMC7190554/ [Accessed 4th June 2020]. Choose the correct option:

(IME - 2020/2021 - 2 FASE) Text 3 Mathematical Modeling of Epidemic Diseases; A Case Study of the COVID-19 Coronavirus Reza Sameni Abstract The outbreak of the Coronavirus COVID-19 has taken the lives of several thousands worldwide and lockedout many countries and regions, with yet unpredictable global consequences. In this research we study the epidemic patterns of this virus, from a mathematical modeling perspective. The study is based on an extensions of the well-known susceptible-infected recovered (SIR) family of compartmental models. It is shown how social measures such as distancing, regional lockdowns, quarantine and global public health vigilance, influence the model parameters, which can eventually change the mortality rates and active contaminated cases over time, in the real world. As with all mathematical models, the predictive ability of the model is limited by the accuracy of the available data and to the so-called level of abstraction used for modeling the problem. In order to provide the broader audience of researchers a better understanding of spreading patterns of epidemic diseases, a short introduction on biological systems modeling is also presented and the Matlab source codes for the simulations are provided online. I. INTRODUCTION Since the outbreak of the Coronavirus COVID-19 in January 2020, the virus has affected most countries and taken the lives of several thousands of people worldwide. By March 2020, the World Health Organization (WHO) declared the situation a pandemic, the first of its kind in our generation. To date, many countries and regions have been locked-down and applied strict social distancing measures to stop the virus propagation. From a strategic and healthcare management perspective, the propagation pattern of the disease and the prediction of its spread over time is of great importance, to save lives and to minimize the social and economic consequences of the disease. Within the scientific community, the problem of interest has been studied in various communities including mathematical epidemiology, biological systems modeling, signal processing and control engineering. In this study, epidemic outbreaks are studied from an interdisciplinary perspective, by using an extension of the susceptible-exposed-infected-recovered (SEIR) model, which is a mathematical compartmental model based on the average behavior of a population under study. The objective is to provide researchers a better understanding of the significance of mathematical modeling for epidemic diseases. It is shown by simulation, how social measures such as distancing, regional lockdowns and public health vigilance, can influence the model parameters, which in turns change the mortality rates and active contaminated cases over time. It should be highlighted that mathematical models applied to real-world systems (social, biological, economical, etc.) are only valid under their assumptions and hypothesis. Therefore, this research and similar ones that address epidemic patterns, do not convey direct clinical information and dangers for the public, but should rather be used by healthcare strategists for better planning and decision making. Hence, the study of this work is only recommended for researchers familiar with the strength points and limitations of mathematical modeling of biological systems. The Matlab codes required for reproducing the results of this research are also online available in the Git repository of the project. In Section II, a brief introduction to mathematical modeling of biological systems is presented, to highlight the scope of the present study and to open perspectives for the interested researchers, who may be less familiar with the context. The proposed model for the outspread of the Coronavirus is presented in Section III. The article is concluded with some general remarks and future perspectives. Adapted from:Mathematical Modeling of Epidemic Diseases; A Case Study of the COVID-19 Coronavirus. Avaliable at: arxiv.org/abs/2003.11371 [Accessed 6th June 2020]. Text 4 Mathematical modeling of the spread of the coronavirus disease 2019 (COVID-19) taking into account the undetected infections. The case of China B. Ivorra, M.R. Ferrndez, M. Vela-Prez and A.M. Ramosa Abstract In this paper we develop a mathematical model for the spread of the coronavirus disease 2019 (COVID-19). It is a new -SEIHRD model (not a SIR, SEIR or other general purpose model), which takes into account the known special characteristics of this disease, as the existence of infectious undetected cases and the different sanitary and infectiousness conditions of hospitalized people. In particular, it includes a novel approach that considers the fraction of detected cases over the real total infected cases, which allows to study the importance of this ratio on the impact of COVID-19. The model is also able to estimate the needs of beds in hospitals. It is complex enough to capture the most important effects, but also simple enough to allow an affordable identification of its parameters, using the data that authorities report on this pandemic. We study the particular case of China (including Chinese Mainland, Macao, Hong-Kong and Taiwan, as done by the World Health Organization in its reports on COVID-19), the country spreading the disease, and use its reported data to identify the model parameters, which can be of interest for estimating the spread of COVID-19 in other countries. We show a good agreement between the reported data and the estimations given by our model. We also study the behavior of the outputs returned by our model when considering incomplete reported data (by truncating them at some dates before and after the peak of daily reported cases). By comparing those results, we can estimate the error produced by the model when identifying the parameters at early stages of the pandemic. Finally, taking into account the advantages of the novelties introduced by our model, we study different scenarios to show how different values of the percentage of detected cases would have changed the global magnitude of COVID-19 in China, which can be of interest for policy makers. Keywords: Mathematical model, -SEIHRD model, COVID-19, Coronavirus, SARS-CoV-2, Pandemic, Numerical simulation, Parameter estimation 1. Introduction Modeling and simulation are important decision tools that can be useful to control human and animal diseases. However, since each disease exhibits its own particular biological characteristics, the models need to be adapted to each specific case in order to be able to tackle real situations. Coronavirus disease 2019 (COVID-19) is an infectious disease emerging in China in December 2019 that has rapidly spread around China and many other countries. On 11 February 2020, the World Health Organization (WHO) renamed the epidemic disease caused by 2019-nCoV as strain severe acute respiratory syndrome coronavirus 2 (SARS-CoV-2) This is a new virus and a completely new situation. On 30 January 2020, WHO declared it to be a Public Health Emergency of International Concern. As of 11 March 2020, the disease was confirmed in more than 118,000 cases reported globally in 114 countries, more than 90 percent of cases are in just four countries (two of those China and the Republic of Korea - have significantly declining epidemics) and WHO declared it to be a pandemic, the first one caused by a coronavirus. On 1 April 2020 there are 872,481 and 43,275 official reported cases and deaths, respectively, and there is no vaccine specifically designed for this virus, with proven effectiveness. There are some mathematical models in the literature that try to describe the dynamics of the evolution of COVID-19. (...) Other works propose SEIR type models with little variations and some of them incorporate stochastic components. COVID-19 is a disease caused by a new virus, which is generating a worldwide emergency situation and needs a model taking into account its known specific characteristics. Adaptec from:Mathematical modeling of the spread of the coronavirus disease 2019 (COVID-19) taking into account the undetected infections. The case of China.In: Elsevier Public Health Emergency Colletion, 2020. Avaliable at: https://www.mcbi.nlm.nih.gov/pmc/articles/PMC7190554/ [Accessed 4th June 2020]. Choose the correct option:

(IME - 2020/2021 - 2 FASE) Text 3 Mathematical Modeling of Epidemic Diseases; A Case Study of the COVID-19 Coronavirus Reza Sameni Abstract The outbreak of the Coronavirus COVID-19 has taken the lives of several thousands worldwide and lockedout many countries and regions, with yet unpredictable global consequences. In this research we study the epidemic patterns of this virus, from a mathematical modeling perspective. The study is based on an extensions of the well-known susceptible-infected recovered (SIR) family of compartmental models. It is shown how social measures such as distancing, regional lockdowns, quarantine and global public health vigilance, influence the model parameters, which can eventually change the mortality rates and active contaminated cases over time, in the real world. As with all mathematical models, the predictive ability of the model is limited by the accuracy of the available data and to the so-called level of abstraction used for modeling the problem. In order to provide the broader audience of researchers a better understanding of spreading patterns of epidemic diseases, a short introduction on biological systems modeling is also presented and the Matlab source codes for the simulations are provided online. I. INTRODUCTION Since the outbreak of the Coronavirus COVID-19 in January 2020, the virus has affected most countries and taken the lives of several thousands of people worldwide. By March 2020, the World Health Organization (WHO) declared the situation a pandemic, the first of its kind in our generation. To date, many countries and regions have been locked-down and applied strict social distancing measures to stop the virus propagation. From a strategic and healthcare management perspective, the propagation pattern of the disease and the prediction of its spread over time is of great importance, to save lives and to minimize the social and economic consequences of the disease. Within the scientific community, the problem of interest has been studied in various communities including mathematical epidemiology, biological systems modeling, signal processing and control engineering. In this study, epidemic outbreaks are studied from an interdisciplinary perspective, by using an extension of the susceptible-exposed-infected-recovered (SEIR) model, which is a mathematical compartmental model based on the average behavior of a population under study. The objective is to provide researchers a better understanding of the significance of mathematical modeling for epidemic diseases. It is shown by simulation, how social measures such as distancing, regional lockdowns and public health vigilance, can influence the model parameters, which in turns change the mortality rates and active contaminated cases over time. It should be highlighted that mathematical models applied to real-world systems (social, biological, economical, etc.) are only valid under their assumptions and hypothesis. Therefore, this research and similar ones that address epidemic patterns, do not convey direct clinical information and dangers for the public, but should rather be used by healthcare strategists for better planning and decision making. Hence, the study of this work is only recommended for researchers familiar with the strength points and limitations of mathematical modeling of biological systems. The Matlab codes required for reproducing the results of this research are also online available in the Git repository of the project. In Section II, a brief introduction to mathematical modeling of biological systems is presented, to highlight the scope of the present study and to open perspectives for the interested researchers, who may be less familiar with the context. The proposed model for the outspread of the Coronavirus is presented in Section III. The article is concluded with some general remarks and future perspectives. Adapted from:Mathematical Modeling of Epidemic Diseases; A Case Study of the COVID-19 Coronavirus. Avaliable at: arxiv.org/abs/2003.11371 [Accessed 6th June 2020]. Text 4 Mathematical modeling of the spread of the coronavirus disease 2019 (COVID-19) taking into account the undetected infections. The case of China B. Ivorra, M.R. Ferrndez, M. Vela-Prez and A.M. Ramosa Abstract In this paper we develop a mathematical model for the spread of the coronavirus disease 2019 (COVID-19). It is a new -SEIHRD model (not a SIR, SEIR or other general purpose model), which takes into account the known special characteristics of this disease, as the existence of infectious undetected cases and the different sanitary and infectiousness conditions of hospitalized people. In particular, it includes a novel approach that considers the fraction of detected cases over the real total infected cases, which allows to study the importance of this ratio on the impact of COVID-19. The model is also able to estimate the needs of beds in hospitals. It is complex enough to capture the most important effects, but also simple enough to allow an affordable identification of its parameters, using the data that authorities report on this pandemic. We study the particular case of China (including Chinese Mainland, Macao, Hong-Kong and Taiwan, as done by the World Health Organization in its reports on COVID-19), the country spreading the disease, and use its reported data to identify the model parameters, which can be of interest for estimating the spread of COVID-19 in other countries. We show a good agreement between the reported data and the estimations given by our model. We also study the behavior of the outputs returned by our model when considering incomplete reported data (by truncating them at some dates before and after the peak of daily reported cases). By comparing those results, we can estimate the error produced by the model when identifying the parameters at early stages of the pandemic. Finally, taking into account the advantages of the novelties introduced by our model, we study different scenarios to show how different values of the percentage of detected cases would have changed the global magnitude of COVID-19 in China, which can be of interest for policy makers. Keywords: Mathematical model, -SEIHRD model, COVID-19, Coronavirus, SARS-CoV-2, Pandemic, Numerical simulation, Parameter estimation 1. Introduction Modeling and simulation are important decision tools that can be useful to control human and animal diseases. However, since each disease exhibits its own particular biological characteristics, the models need to be adapted to each specific case in order to be able to tackle real situations. Coronavirus disease 2019 (COVID-19) is an infectious disease emerging in China in December 2019 that has rapidly spread around China and many other countries. On 11 February 2020, the World Health Organization (WHO) renamed the epidemic disease caused by 2019-nCoV as strain severe acute respiratory syndrome coronavirus 2 (SARS-CoV-2) This is a new virus and a completely new situation. On 30 January 2020, WHO declared it to be a Public Health Emergency of International Concern. As of 11 March 2020, the disease was confirmed in more than 118,000 cases reported globally in 114 countries, more than 90 percent of cases are in just four countries (two of those China and the Republic of Korea - have significantly declining epidemics) and WHO declared it to be a pandemic, the first one caused by a coronavirus. On 1 April 2020 there are 872,481 and 43,275 official reported cases and deaths, respectively, and there is no vaccine specifically designed for this virus, with proven effectiveness. There are some mathematical models in the literature that try to describe the dynamics of the evolution of COVID-19. (...) Other works propose SEIR type models with little variations and some of them incorporate stochastic components. COVID-19 is a disease caused by a new virus, which is generating a worldwide emergency situation and needs a model taking into account its known specific characteristics. Adaptec from:Mathematical modeling of the spread of the coronavirus disease 2019 (COVID-19) taking into account the undetected infections. The case of China.In: Elsevier Public Health Emergency Colletion, 2020. Avaliable at: https://www.mcbi.nlm.nih.gov/pmc/articles/PMC7190554/ [Accessed 4th June 2020]. Choose the correct option

(IME - 2020 - Questo 21) Um corpo de gelo esta dispostona extremidade de uma gangorra que possui uma barra de comprimento C, cuja massa e uniformemente distribuda. Inicialmente, o sistema est em repouso, conforme mostra a figura acima. Em t = 0, o gelo e aquecido por um resistor de resistncia R, percorrido por uma corrente eltrica contnua i. Dados: calor latente de fuso do gelo = Lf; massa da barra da gangorra: m; e massa inicial do bloco de gelo: 4m. Considerando que a gua proveniente do gelo no se acumula na gangorra e que todo o calor proveniente do aquecimento da resistncia e empregado para aquecer o gelo, o instante de tempot em que a barra iniciara seu movimento ser:

[IME - 2020/2021 - 2 fase - REDAO] PRODUO DE TEXTO Na trama visvel, dilacerada das grandes guerras contemporneas, reconhecem-se apenas a paisagem cultural da guerra, as nervuras de sua representao dominante. No se veem mais,e tanto melhor, colunas de soldados em centenas de milhares chegando ao futuro campo de batalha, dispondo-se em ordem para a batalha decisiva. (GROS, Frdric.Estados de violncia: ensaio sobre o fim da guerra.Traduo de Jos Augusto da Silva. Aparecida, SP. Editora Ideias Letras, 2009. p. 227. Texto adaptado). No est completamente fora de contexto fazermos uma comparao entre uma zona de guerra, aquela onde ocorrem combates, com reas atingidas por pandemias como a do Coronavrus ou COVID-19. Em uma guerra, os combatentes esto a merc de serem atingidos, a qualquer momento, por disparos de um franco atirador, de morteiros, do fogo da artilharia inimiga, de bombardeios areos e de seus prprios companheiros, quer por erro de clculo ou acidente. (Woloszyn, Andr Lus.O que guerras e pandemias tm em comum. Disponvel em:https://www.defesanet.com.br/pw/noticia/36136/Woloszyn---O-Que-Guerras-e-Pandemias-tem-em-Comum/. Acesso em 16/04/2020) Os flagelos, na verdade, so uma coisa comum, mas difcil acreditar neles quando se abatem sobre ns. Houve no mundo tantas pestes quanto guerras. E contudo, as pestes, como as guerras, encontram sempre as pessoas igualmente desprevenidas (...)nossos concidados, a esse respeito, eram como todo mundo (...) no acreditavam nos flagelos. O flagelo no est altura do homem (...).Continuavam a fazer negcios, preparavam viagens e tinham opinies. Como poderiam ter pensado na peste, que suprime o futuro, os deslocamentos e as discusses? Julgavam-se livres, e nunca algum ser livre enquanto houver flagelos. (CAMUS, Albert.A peste. Traduo de Valerie Rumjanek. Rio de Janeiro: Editora Record, 2017, p. 41) Sabe-se que o mundo tem enfrentado graves problemas devido propagao do novo coronavrus, o que tem evocado a memria dos flagelos da humanidade, que pareciam ter sido erradicados para sempre. Imersas em uma vida cotidiana marcada pela hiperatividade, excitao permanente e autopromoo digital, as pessoas foram obrigadas a suportar o isolamento, o medo da doena e do desemprego, a perda dos entes queridos, a interrupo drstica e prolongada de suas rotinas, de forma similar ao que aconteceria em um conflito armado de grandes propores. Considerando a radicalidade da experincia da peste e da guerra, abordada nos excertos transcritos nesta prova, redija um texto dissertativo-argumentativo sobre o seguinte tema:A luta contra a COVID-19: a pandemia vivida como guerra na sociedade contempornea. Em sua escrita, atente para as seguintes consideraes: 1. Privilegie a norma culta da lngua portuguesa. Eventuais equvocos morfossintticos, erros de regncia, concordncia, coeso e coerncia, bem como desviosda grafia vigente e a no observncia das regras de acentuao sero penalizados. 2. Seu texto dever ter entre 25 (vinte e cinco) a 30(trinta) linhas escritas tinta azul ou preta. A produo de texto DEVER ser realizada no CADERNO DE SOLUES. 3. No copie nem faa parfrase de nenhuma parte dos textos apresentados neste exame, seja da prova de portugus ou da prova de ingls.

(IME - 2019/2020 - 2 FASE) A figura mostra um sistema usado em um laboratrio de fsica para demonstrar a difrao de luz por uma fenda. A luz de um laser de comprimento de onda passa por uma fenda de largura , formada pelo espao entre as extremidades de duas barras de comprimento . A outra extremidade de cada barra mantida fixa. Depois de passar pela fenda, a luz incide em uma tela distante, na qual observado um padro de difrao formado por regies claras e escuras. a) Dado que na tela so observados exatamente 3 mnimos de intensidade luminosa em cada lado do mximo central de intensidade, determine o intervalo de valores da largura da fenda que so compatveis com essa observao. b) A temperatura do laboratrio normalmente mantida em 24,0 C por um aparelho de ar condicionado. Em um dia no qual o experimento foi realizado com o aparelho de ar condicionado desligado, observou-se na tela apenas 1 mnimo de intensidade luminosa em cada lado do mximo central de intensidade, o que foi atribudo dilatao trmica das barras. Sabendo que o coeficiente de dilatao linear das barras , determine o intervalo de temperaturas do laboratrio, no dia em que o aparelho de ar condicionado foi desligado, que so compatveis com essa observao. Dados: comprimento de onda do laser: ; comprimento de cada barra a ; coeficiente de dilatao linear de cada barra: .

(IME - 2019/2020 - 1 FASE) Considere que a superfcie da Lua seja bombardeada a cada segundo por cerca de 100 bilhes de tomos de hidrognio por cm2 em funo da ao do vento solar. Supondo que esse fluxo se mantenha constante, a massa aproximada de hidrognio, que atingir 1 cm2da Lua nos prximos 5 milhes de anos ser: (Dado: NA = 6,0 x 1023)