text:
## owlet one year ago Find a scalar equation of the plane that contains the point P(2,4,1) and is parallel to the plane $$2x_1 + 3x_2 -5x_3 = 6$$.

1. Loser66

just plug the numbers in.

2. owlet

|dw:1443664554238:dw| simplifying that, I got 11, so d =11 will the answer be 2x1 + 3x2 - 5x3 = 11?

3. owlet

that's what i did, just wanted to make sure if I'm right

4. owlet

i usually have a mistake in vector and scalar equations.. I usually switch them

5. owlet

can we fin vector equation from this?

6. Loser66

|dw:1443664955587:dw|

7. Loser66

|dw:1443665007633:dw|

8. owlet

ok thanks for confirming it :) can we find vector equation from this scalar equation? is it possible?

9. Loser66

why not? @chris00 now your turn

10. owlet

wait is there even a vector equation for a plane? O.o

11. anonymous

haha nice to throw the ball to me

12. Loser66

it's not hard, right? all of us know how to do, right?

13. anonymous

there is a normal vector equation for the plane...

14. anonymous

you can simply read that off

15. anonymous

what this represents is

16. anonymous

|dw:1443665293308:dw|

17. Loser66

hey, guy, give him the easiest way, please.

18. anonymous

isn't that just $(r-r _{o})n=0$ jeez, its been so long

19. owlet

got it, nvm

20. anonymous

where n is the normal?

21. anonymous

yolo

22. anonymous

what did ya do?

23. owlet

i am already doing another prob

24. anonymous

oh, sorry mate

25. anonymous

probs need a refresher since its been like 4yrs ago since I've done this lel

26. owlet

try this then: Verify the triangle inequality and the CAuchy-Schwarz inequality if: |dw:1443665710601:dw|

27. Loser66

2x1+3x2-5x3=11 $$x_1= 11/2 - (3/2)x_2 +(5/2)x_3$$ Hence vector equation is $$\vec x= \left[\begin{matrix}(11/2)-(3/2)x_2 +(5/2)x_3\\x_2\\x_3\end {matrix}\right]$$ Now, turn to $$\vec x= \left[\begin{matrix}11/2\\0\\0\end{matrix}\right]+ x_2\left[\begin{matrix}(-3/2)\\1\\0\end{matrix}\right]+x_3\left[\begin{matrix}(5/2)\\0\\1\end{matrix}\right]$$

28. Loser66

That is the easiest way to find the vector equation from a scalar one.

29. Loser66

just replace x2 = lambda 1 and x3 = lambda2

30. anonymous

$|u.v|\le|u||v|$

31. anonymous

i think thats the Cauchy schwartz inequality theorem

32. anonymous

pretty straight forward if u apply this, i rekn

33. owlet

ok got it..i use the other one: |dw:1443666019926:dw|

34. owlet

thanks.

35. anonymous

the triangle inequality?

36. anonymous
37. anonymous

u don't need to verify anything if u just proof it using variables

38. anonymous

cause a proof applies it for all cases. but its easier with numbers cause you just plug and chug it into formulas

39. owlet

it says on the question "Verify the Triangle Inequality"

40. anonymous

yea, probs best to just verify then. i was just giving you a proof for you to understand that it word for any case. perhaps you can read that in your own time to familiarise it for yourself

41. owlet

i will do that for sure :) I'm studying it right now. Thanks for all your help. Really appreciate it

42. anonymous

no problem. good luck :)


text:
Solving Random Parity Games in Polynomial Time

Abstract

We consider the problem of solving random parity games. We prove that parity games exibit a phase transition threshold above $d_P$, so that when the degree of the graph that defines the game has a degree $d > d_P$ then there exists a polynomial time algorithm that solves the game with high probability when the number of nodes goes to infinity. We further propose the SWCP (Self-Winning Cycles Propagation) algorithm and show that, when the degree is large enough, SWCP solves the game with high probability. Furthermore, the complexity of SWCP is polynomial $O\Big(|{\cal V}|^2 + |{\cal V}||{\cal E}|\Big)$. The design of SWCP is based on the threshold for the appearance of particular types of cycles in the players' respective subgraphs. We further show that non-sparse games can be solved in time $O(|{\cal V}|)$ with high probability, and emit a conjecture concerning the hardness of the $d=2$ case.Comment: 23 page

Topics: Computer Science - Logic in Computer Science, Statistics - Machine Learning
Year: 2020
OAI identifier: oai:arXiv.org:2007.08387

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To submit an update or takedown request for this paper, please submit an Update/Correction/Removal Request.

format: plain


text:
# Journal of Nursing and Practice

ISSN: 2578-7071

### Article Outline

Research Article | Volume 4 | Issue 2 | DOI: 10.36959/545/405 Open Access

# Nurses Contributions to the Health Dimensions of the United Nation's Sustainable Development Goals

Philip Dekontee Davis RN, MSN Edu

• Philip Dekontee Davis 1*
• College of Nursing, University of Rhode Island, USA

Davis PD (2021) Nurses Contributions to the Health Dimensions of the United Nation's Sustainable Development Goals. J Nurs Pract 4(2):351-356.

Accepted: November 30, 2021 | Published Online: December 02, 2021

# Nurses Contributions to the Health Dimensions of the United Nation's Sustainable Development Goals

## Abstract

This paper aims to describe nurses' worldwide contributions to the health dimensions of the United Nation's Sustainable Development Goals. Valuable lesson learned from the Ebola Virus Disease (EVD) outbreak in Liberia are detailed to enhance the current COVID-19 mitigation strategy. An overview of EVD and the economic and political environment in Liberia are derived, followed by illustration of the eventually effective approach to EVD mitigation. Specifically, community-based contact tracing, social mobilization, refining EVD information, and rapid sample collection, testing, and reporting were tailored by the Ministry of Health in collaboration with nongovernmental organizations to involve nurses at every level. Nurse-led actions included health facilities settings as well as individuals, families, and community. This public health response model was antecedent to World Health Organization's declaring Liberia free from EVD and is thus offered for consideration by other organizations or nations who wish to more effectively mobilize nurses. Readiness for the demands of infectious disease mitigation and establishment of the global nursing workforce resilience is essential and requires sound preparation of nurses in the public health tenets of infectious disease. This knowledge must be matched with systemic capacity for mobilization, when necessary. To support a global response to disease outbreak, the model was developed to aid the process of responding to disease outbreak, emphasizing the need for strengthening the interconnections of health systems and the dissemination of clear and factual information to prevent and control diseases in relationship to the United Nation's Sustainability Goals are described.

## Keywords

Health system interfacing, Health dimensions, Global nursing workforce, Self-quarantine, Self-isolation

## Introduction

The Covid-19 pandemic has brought to light both the interconnections among the world's health care systems as well as the fragility. The oft-cited sentiment that the virus does not recognize political boundaries is clearly illustrated, as the limitation of any nation's health care system is now clearly recognized everyone's limitation. Moreover, unlike other recent novel viruses such as Middle East respiratory syndrome coronavirus (MERS-CoV) and Ebola Viral Disease (EVD), wealthy Western nations, for example, the U.S. and Great Britain, have not been spared widespread infection. Thus, perhaps this time, lessons learned in public health emergencies can finally be fully embedded in the very platform of world change. To that end, Liberia's struggle with the Ebola virus is detailed, as well as consequences and next steps. The aim is to foster nurses' worldwide contributions to the health dimensions of the United Nation's Sustainable Development Goals.

## Liberia's Health and Health Care - A Brief Overview

Liberia is located on the west coast of Africa and has fifteen administrative counties, subdivided into 136 districts covering 111,369 square kilometers (Liberia Institute of Statistics & Geo-Information Services, 2017) [1]. The current population of Liberia is 5,059,005, based on projections of the latest United Nations 2019 data. The UN estimates the July 1, 2020 population at 5,057,681.

The world population review ranks Liberia as the poorest country in the world with $710 Gross National Income per capital (Harrington, 2020) [2]. The poverty of Liberians continues to slow down the improvement of access to health and basic social services. More than 83 percent of Liberia's population lives below the poverty line ($1.25 per day) and 94 percent of workers are poor (living on less than $2 per day) and the economy was projected to contract by 1.4% in 2019, following the modest growth of 1.2% in 2018 and inflation reached 31.3% by August 2019, up from 26.1% the previous year (World Bank Group, 2018) [3]. Covid-19 brings even more economic displacement. The national budget for fiscal year 2019/2020 submitted by the Ministry of Finance and Development Planning totals L$110,460,000,000 or US$526,000,000, provides for the expenditure or operational cost of the Government of Liberia. The National Budget accounts for three separate revenue envelopes, including Tax Revenue at US$378,000,000, Non-tax Revenue at US$87,200,000 as well as External Resources at US$60,800,000. Liberia revenue shortfalls have resulted to the recasting of the 2019/2020 national budget. The recast budget reduced allotment for spending entities across the health sector, except for the Ministry of Health itself whose budget was augmented as a result of the United States Agency for International.

Development (USAID) support of US$6.2 million and the Liberia Pharmacy Board with a budget increase of US$1,600. Spending entities affected by budget cut, include, but not limited to the John F. Kennedy Medical Center, Jackson Fiah Doe Memorial Hospital, Phebe Hospital, National Public Health Institute, Liberia Medical and Dental Council, Liberia Board of Nursing and Midwifery, National AIDS Commission, among others. There is a decline in Liberia's scores on key dimensions including, property rights, government integrity, fiscal health, and business freedom (Economic Freedom, 2020) [4]. Moreover, Liberia falls in the repressive zoon of the World's Economic Freedom ratings with a score of 49 and a rank of 165. Acceptable scores range from 80 - 100.

The major sector of the country including education, security, agriculture, and food security and the health systems are also struggling with post-war recovery - a fourteen-year war, and the impact of the EVD epidemic of 2014 proved that the Liberia healthcare delivery system was still inadequate. Ebola Viral Disease cumulative confirmed, probable, and suspected EVD cases in Guinea, Liberia, and Sierra Leone claimed the lives of 11,301 of which Liberia was hardest hit with 4,806 deaths (World Health Organization, 2016) [5]. However, the EVD crisis led to a devastation of the already fragile healthcare system in Liberia and severely constrained the Government of Liberia progress to deliver key social services, including basic and secondary health services, thereby leading to the outbreak of many preventable deaths. For example, measles vaccination rates dropped from about 78% in January 2014 to 45% in January 2015. Similarly, health facility deliveries decreased from 65% to 28%, while deliveries attended by skilled providers dropped from 61% to 31%. Maternal mortality rates are 1072 per 100,000 live births and chronic malnutrition is at 32% among the highest in the world (Ministry of Health, 2015) [6].

Study showed improvements and challenges in key health indicators (LISGIS, MOH, LDHS & ICFI, 2020) [7]. The study uncovered the disparities between the urban and rural populations in terms of delivery of basic social services which contribute to the socioeconomic determinants of health. The supply of safe drinking water in the urban areas is 83% compared to 63% in the rural areas. Sanitation provision is not impressive in urban areas 35% have basic sanitation service, as compared with 9% in the rural areas. Two in three children (66%) have their births registered with the civil authorities. Teenage pregnancy declined from 6.7% in 1986 to 4.2% in 2020. Under-5 years of age mortality also declined from 222 per l000 live birth in 1986 to 63 in 2020. Overall, the percentage of facility deliveries is higher in urban areas than in rural areas (83% and 76%, respectively). Birth attended by a skilled provider is 84%; 80% of birth occurred in a health facility.

The Liberian health system financing is heavily dependent on Non-Governmental Organizations (NGOs), but the scaling down of donors' funds and limited financial support for the government priority areas is facilitating a slow recovery of the health system, especially during the COVID-19 pandemic. In the national budgets for the fiscal years 2017-18 and 2018-19, the government of Liberia appropriated 14% and 13%, respectively, to the health sector. The full impact of COVID-19 is unclear at this time but given that wealthy nations are experiences a decrease in vaccination rates (Bramer et al., 2020) [8], and it is likely that Liberia will also see that rate slip.

The health sector is also constraint with weak supply chain management, particularly in terms of distribution and storage of pharmaceuticals and other supplies, limited pharmacists, laboratory technicians, and limited human resources for health particularly nurses, midwives, doctors. There is also limited essential medical equipment and pharmaceutical products, and there are frequently reported stock outages, especially in rural regions of the country.

It may same that these health system changes are unique to Liberia, but with certainty every health system share some proportion of these challenges but at different magnitude. The magnitude of health system challenges is evident in disease outbreaks, especially, during epidemic or pandemic.

## Sustainable Development Goals

In September 2015 world leaders developed the Sustainable Development Goals (SDGs) through the initiative of WHO to transform the world through measurable objectives with sustainability across the social, economic, and environmental dimensions to be achieved by 2030. The Declaration of the 17 SDGs, adopted by Member States of the UN General Assembly, articulated the world's "collective responsibility to uphold the principles of human dignity, equity at the global level" and to eradicate the world's most extreme and deplorable conditions, including poverty and destitution. The implementation of SDGs is based on the priority areas of each county and the strength of the health workforce, especially nurses.

Nurses play an enormous role in coordinating and delivering health care and they outnumber doctors by almost 3 to 1 (Myers, 2018) [9]. Nurses are constantly making enormous contributions to the coordinated approach to the attainment of SDGs. Globally, nurses continue to work within the public and private sectors providing health education that promotes behavior change to impact the health of the individual, family, the community, and improving access to health and health care especially among vulnerable populations. At each level of care, nurses continue to utilize the nursing process in gathering data that can be useful in the decision-making process in measuring the impact of SDGs strategies and the progress in improving the social determinants of health. The nursing process provides guidance for nurses to approach the situation of the individual, family, and the community as a client to achieve their full potentials.

The call to global nursing varies each year as nurses celebrate International Nurses' Day. This year, the International Nurses' Day theme "Nursing the World to Health", focuses on the true value of nurses to the people of the world (International Council of Nurses, 2020) [10]. With this theme, nurses redefined their roles at the frontlines of disease outbreaks, disabilities, and natural disasters with the aims of prevention and providing holistic care for the population in need.

Although many countries have made significant progress towards the SDGs, the outbreak of the CODVID-19 pandemic has revealed the unpreparedness and weakness in many countries health systems to mitigate the spread of COVID-19.

## Comparing EVD Lessons for COVID-19

Although Liberia, Guinea, and Sierra Leone were hard hit during EVD outbreaks in 2014, the Democratic Republic of Congo is a county known for repeated EVD outbreaks. While many governments in Africa especially affected countries were still measuring the impact of EVD on the health systems, the outbreaks of COVID-19 revealed health system unpreparedness for disease prevention and control. Affected EVD countries are using EVD strategies to mitigate the spread of COVID-19. These EVD strategies include but are not limited to reorganizing disease mitigation from the level of the health facility to the individual, family and community, psychosocial support to affected individual and families, community-based contact tracing, and reporting strategies, information dissemination, cross countries networking, social mobilization, rapid sample collection and testing Table 1.

## Adopted from WHO & CDC

It is valuable to compare EVD and COVID-19 to assess the level of response by governments and the population to global strategies and compliance to mitigating the spread of COVID-19, especially breaking the mode of transmission, the weakest link in the chain of infection. First, the transmission of EVD and COVID-19 are similar except that EVD is not transmitted through respiratory droplets and care of the dead and safe burial play an important part in EVD prevention and control. Clear dissemination of information on the mode of transmission is essential to mitigate the disease, and this is enabled by the knowledge, attitude, and practice of the population. Second, the signs and symptoms of EVD are similar to malaria, creating a false sense among many Liberians that they were dealing with a familiar foe, like malaria. Study found an estimated 228 malaria cases worldwide with 93% of malaria cases in African regions and 94% of malaria deaths (World malaria report, 2019) [11]. World Health Organization 2016, recognized the difficulty distinguishing EVD from other infectious diseases like malaria, typhoid fever and identified this as one of the major reasons EVD infected people in Africa were constantly in a state of denial, a circumstance troublingly reoccurring in some areas of the U.S (Srikanth, 2020) [12].

## Declaration of Disease and Global Response

Globally, WHO in collaboration with affected countries may utilize two incubation periods of a disease to declare a country free from the disease. At the end of the two incubation periods, under effective surveillance and reporting strategies using the case definition of the disease with no suspected, probable, or confirmed cases, WHO declares a country free from the disease. In the case of EVD, 42 days defined this pronouncement while scientists are researching COVID-19 landmark.

On May 9, 2015, WHO declared Liberia free of EVD. Nearly two months later, Liberia confirmed 6 new cases. The resurgence of EVD is like the current COVID-19 pandemic because many countries are experiencing fluctuations in the incidence of the disease. With resilience in contact tracing, quarantine and isolation lead by nurses, Liberia was again declared EVD free on September 3, 2015.

Although disease response strategy many vary with the type of disease outbreak, it is important to accentuate that adequate and prompt infectious disease response strategies are essential to support governments, stakeholder's preparedness, and initiatives in exploring measures in preventing and controlling disease outbreaks. The readiness to prevent or control infectious diseases can be viewed from multiple perspectives. However, the four pillars of disease response strategy: global health system interfacing, conceptualizing diseases outbreak response measures, improving health system equity, quality improvement, and assurance, can enhance global health initiatives to better understand health systems strategies in preventing and controlling the spread of epidemic or pandemic-prone diseases.

There is an interplay of different COVID-19 strategies, especially in countries experiencing challenges in mitigating the spread of the disease. However, each COVID-19 strategy adopted, and implemented is based on the situational analysis of the country. The reality is that each strategy should be evaluated for quality improvement, and quality assurance, and reduction in COVID-19 morbidity and mortality Figure 1.

Diseases have no boundaries and as such health systems around the world need to redefine global strategies for surveillance and reporting public health events of international concerns. Epidemics or pandemics unites the health systems of the world, but sometimes the politics of infectious diseases underscore global response to diseases control and prevention. The political parameters of infectious diseases such are disease origin, global funding and approach, travel restrictions, approval of standardized treatment, development, and use of vaccines continue to slow down efforts in infectious disease control and prevention. Amidst these political scuffles on disease response and reporting, healthcare institutions are increasingly overwhelmed with cases, and yet again nurses, both current in practice and retired are called to action to improve the outcomes of patients' situations. It is important to emphasize that global nursing is achievable when nurses adequately prepared through their education to respond to epidemic or pandemic: Taking the frontline from institution-based nursing to community-based nursing.

The concept of building a resilient global nursing workforce implies that nurses should be educated to transcend professionalism that makes nursing practice approachable regardless of the health system. Meaning that nurses who are trained in other regions should have a foundation in global nursing practice to fit into other health systems. For example, a nurse educated in the US should work effectively in Africa and vice-versa. On the other hand, unfamiliar diseases may overwhelm nurses and expose them to a high risk of acquiring communicable diseases during outbreaks. The Board of Nursing in many African countries including Liberia has epidemic and pandemic-prone infectious in the curricula. For example, the Board for Nursing and Midwifery prototype competency-based curriculum has a course title: Tropical and Communicable Diseases. This course is equally weighted to non-communicable diseases or disorders on the RN licensure examination.

## Missed steps in information dissemination

Like the EVD, there are missed steps in the dissemination of information to prevent and control the spread of COVID-19. For example, during EVD outbreaks in west Africa, information dissemination on mitigating the spread of EVD resulted in the surged of EVD reproductive and mortality rates. During the earlier stage of EVD epidemic in 2014, the health system of Liberia, WHO in collaboration with other partners informed the world that EVD has no cure, and no standard treatment or vaccine to mitigate the spread of the disease, but the individual who was exposure or show signs and symptoms of the disease should seek healthcare. This message posed huge challenges to nurses serving as a bridge between individuals, families, communities, and the health system. Affected EVD individuals refused to seek health care because one of the reasons for seeking healthcare is to improve health outcomes, and if EVD has no cure, there was no reason for seeking healthcare at any level of care. At a glance of the missed steps in this message, nurses lead community-based outreach with a corrected version of the EVD message: although there is no standardized treatment or vaccine for EVD, early detection, and supportive management will increase the survivor rates. The modification of EVD message and the evidence of increase EVD patient's recovery rates, facilitated the change of mindset and improved public health compliance to disease mitigation measures.

On the other hand, the common global COVID-19 message calls on people who were exposed to a case or have a fever, cough other symptoms should self-isolate because most people with mild illness may self-recover at home. These messages also required individuals experiencing emergency warning sign (difficulty breathing), to get emergency medical care immediately. First, these messages is one of the factors leading to the increase in COVID-19 morbidity because if the individual who has pre-existing conditions will seek emergency medical care at the moderate or chronic state of the disease rather than the acute stage, may lower the individual chances of recovery. Second, during the latent phase of the disease, standardized mitigation measures at home may be bridged and exposure to household will be eminent. Third, it is important to clarify the difference between self-isolation and self-quarantine. Arguably, the vertical use of self-isolation during exposure and disease state is unacceptable. In an event that the individual is exposed to a disease, but does not show signs and symptoms, self-quarantine is the preferred phrase. During quarantine, the individual movement is restricted and observed through the incubation period of the disease. An individual who shows signs and symptoms of the disease cannot self-quarantine, but rather self-isolate. Therefore, the phrase "self-isolate" does not balance the response to exposure and case.

Key messages and actions for COVID-19 prevention and control for schools to slow down or prevent the spread of COVID-19 include staying home when sick; covering mouth and nose with flexed elbow or tissue when coughing or sneezing; dispose of used tissue immediately; washing hands often with soap and water, and cleaning frequently tough surfaces and objects ( UNICEF, WHO & CIFRC, 2020) [12]. To add to this message, staying home when sick and seeking immediate testing for COVID-19 especially when the individuals shows presumptive or probable signs of COVID-19. During EVD outbreaks, frequent hand washing and taking a bath upon returning from work, school, or other outings that involve interaction with people and disinfecting clothes were emphasized. These measures should also be considered for COVID-19 since the mode of transmission and length of time the virus stays on materials and other surfaces are still under study.

## Lessons Moving Forward

Clearly, the role of accurate and effective transmission of factual information is essential to prevent the spread of infectious disease. Moreover, the nursing workforce in all nations should be systematically prepared in the public health tenets of infectious disease and be prepared to be mobilized when necessary. The advancement of systematic preparations of nurses and factual information dissemination during response to infectious disease outbreaks can be tailored through the interconnection among health systems of the world. The disease response model developed can aid in the coordination of global health response. The strategy to control the spread of infectious diseases like COVID-19 can be modified because of the variability of the disease. The modification of current infectious diseases response and reporting is based on the mode of transmission, political, social, and cultural barriers. However, the response to disease outbreak can yield a measurable impact based on global health system interfacing, conceptualizing response strategy, improving health systems equity, and quality improvement and assurance. These strategies show the interconnections of disease response measures for assessing, identifying the nature of the disease, planning, implementation, evaluation, and recognizing key stakeholders for the global health approach.

Given the substantial proportion of the overall health workforce represented by nurses, it is clear that resilience in global health coverage is attainable through interdisciplinary and inter-sectoral collaboration. The disease response team consists of a cohort of multidisciplinary professionals and government health systems in collaboration with major stakeholders in health and healthcare delivery. These stakeholders like NGOs are crucial for the argumentation of health system financing, especially in low-income countries. Stakeholders assist governments to implement health plans that are aimed at improving the social determinants of health and wellbeing of individuals, families, and communities.

An important point in initiating planning for global health response to disease outbreak is conceptualizing the strategy. During the process conceptualization, key stakeholders including nurses assume collaborative responsibility at every level to achieve a set goal of controlling outbreaks or the spread of diseases. Exclusion or scaling down the importance of any key stakeholder, especially nurses will pose huge challenges to the attainment of set goals. Conceptualizing disease response strategy is associated with resources and resources is associated with health attainment. However, it is also important to emphasize the active engagement and mobilization of the community for action. Each community response should be coordinated by health workers and influential members of the community to monitor community engagement and compliance to health promotion and disease prevention measures. Mitigating the spread of disease without or limited community involvement and key stakeholders like nurses will result to prolong occurrence or reoccurrence of the disease. The effectiveness of these measures can be determined through the application of reflective reasoning in evaluating and strategizing to measure the quality and sustainability of disease response. Quality assurance measures compliance against certain necessary standards typically focusing on the individual while quality improvement is a continuous improvement process focuses on processes, and systems (Health Resources and Service Administration, 2011) [14]. This description can be modified to include the family and community in disease response strategy for health system equity. Health system equity provides for the strengthening of the health system to meet the health needs of the population at all levels of care. Health system equity can be measured by evidence-informed, evidence-based strategies and health resources allocations. The development of policy at the national or global level can have a positive or negative impact on the level of care provided by nurses or other health cadres at the three levels of care: Individual, family, and community, especially when resources are not available or limited to meet the health needs of the population.

## Acknowledgment

The author acknowledges the suggestions of Betty Rambur, PhD, RN, FAAN on an earlier version of this manuscript.

## Abstract

This paper aims to describe nurses' worldwide contributions to the health dimensions of the United Nation's Sustainable Development Goals. Valuable lesson learned from the Ebola Virus Disease (EVD) outbreak in Liberia are detailed to enhance the current COVID-19 mitigation strategy. An overview of EVD and the economic and political environment in Liberia are derived, followed by illustration of the eventually effective approach to EVD mitigation. Specifically, community-based contact tracing, social mobilization, refining EVD information, and rapid sample collection, testing, and reporting were tailored by the Ministry of Health in collaboration with nongovernmental organizations to involve nurses at every level. Nurse-led actions included health facilities settings as well as individuals, families, and community. This public health response model was antecedent to World Health Organization's declaring Liberia free from EVD and is thus offered for consideration by other organizations or nations who wish to more effectively mobilize nurses. Readiness for the demands of infectious disease mitigation and establishment of the global nursing workforce resilience is essential and requires sound preparation of nurses in the public health tenets of infectious disease. This knowledge must be matched with systemic capacity for mobilization, when necessary. To support a global response to disease outbreak, the model was developed to aid the process of responding to disease outbreak, emphasizing the need for strengthening the interconnections of health systems and the dissemination of clear and factual information to prevent and control diseases in relationship to the United Nation's Sustainability Goals are described.


text:
# How do you simplify ((3^-2 x^5 y^-5)^10 (3^3 x^-5 y^2)^3)/((3^5 x^-3 y^4)^2)?

Mar 27, 2018

( x^41 )/(3^21 y^52

#### Explanation:

Simplify

((3^-2 x^5 y^-5)^10  (3^3 x^-5 y^2)^3)/((3^5 x^-3  y^4)^2)

This problem isn't hard conceptually; it's just painstaking.

1) Clear the parentheses by raising all the powers inside the parentheses by the powers outside.
To raise a power to a power, you multiply.

(3^-20  x^50  y^-50  3^9  x^-15  y^6)/(3^10  x^-6  y^8

2) Clear the negative exponents by flipping them to the opposite side of the fraction bar and reversing the negative signs to positive

( x^50   3^9   y^6   x^6)/(3^10   y^8  3^20   y^50   x^15

3) Group like bases to make it easier to multiply them

(3^9    x^50 x^6    y^6 )/(3^10 3^20    x^15    y^8 y^50

4) Multiply like bases

(3^9  x^56  y^6 )/(3^30  x^15  y^58

5) Reduce by cancelling
To divide exponents, you subtract

( x^(56-15) )/(3^(30-9)  y^(58-6)

same as

( x^41 )/(3^21  y^52 $\leftarrow$ answer


text:
# American Institute of Mathematical Sciences

December  2009, 25(4): 1209-1217. doi: 10.3934/dcds.2009.25.1209

## On the regularity of global attractors

 1 Politecnico di Milano - Dipartimento di Matematica "F. Brioschi", Via Bonardi 9, 20133 Milano

Received  January 2009 Revised  June 2009 Published  September 2009

This note is focused on a novel technique to establish the boundedness in more regular spaces for global attractors of dissipative dynamical systems, without appealing to uniform-in-time estimates. As an application, we consider the semigroup generated by the strongly damped wave equation with critical nonlinearity, whose attractor is shown to possess the optimal regularity.
Citation: Monica Conti, Vittorino Pata. On the regularity of global attractors. Discrete & Continuous Dynamical Systems - A, 2009, 25 (4) : 1209-1217. doi: 10.3934/dcds.2009.25.1209
 [1] Zhijian Yang, Zhiming Liu. Global attractor for a strongly damped wave equation with fully supercritical nonlinearities. Discrete & Continuous Dynamical Systems - A, 2017, 37 (4) : 2181-2205. doi: 10.3934/dcds.2017094 [2] Zhiming Liu, Zhijian Yang. Global attractor of multi-valued operators with applications to a strongly damped nonlinear wave equation without uniqueness. Discrete & Continuous Dynamical Systems - B, 2017, 22 (11) : 1-18. doi: 10.3934/dcdsb.2019179 [3] Cedric Galusinski, Serguei Zelik. Uniform Gevrey regularity for the attractor of a damped wave equation. Conference Publications, 2003, 2003 (Special) : 305-312. doi: 10.3934/proc.2003.2003.305 [4] Piotr Kokocki. Homotopy invariants methods in the global dynamics of strongly damped wave equation. Discrete & Continuous Dynamical Systems - A, 2016, 36 (6) : 3227-3250. doi: 10.3934/dcds.2016.36.3227 [5] Nicholas J. Kass, Mohammad A. Rammaha. Local and global existence of solutions to a strongly damped wave equation of the $p$-Laplacian type. Communications on Pure & Applied Analysis, 2018, 17 (4) : 1449-1478. doi: 10.3934/cpaa.2018070 [6] Fengjuan Meng, Chengkui Zhong. Multiple equilibrium points in global attractor for the weakly damped wave equation with critical exponent. Discrete & Continuous Dynamical Systems - B, 2014, 19 (1) : 217-230. doi: 10.3934/dcdsb.2014.19.217 [7] Filippo Dell'Oro. Global attractors for strongly damped wave equations with subcritical-critical nonlinearities. Communications on Pure & Applied Analysis, 2013, 12 (2) : 1015-1027. doi: 10.3934/cpaa.2013.12.1015 [8] Út V. Lê. Regularity of the solution of a nonlinear wave equation. Communications on Pure & Applied Analysis, 2010, 9 (4) : 1099-1115. doi: 10.3934/cpaa.2010.9.1099 [9] Fabrizio Colombo, Davide Guidetti. Identification of the memory kernel in the strongly damped wave equation by a flux condition. Communications on Pure & Applied Analysis, 2009, 8 (2) : 601-620. doi: 10.3934/cpaa.2009.8.601 [10] Pengyan Ding, Zhijian Yang. Attractors of the strongly damped Kirchhoff wave equation on $\mathbb{R}^{N}$. Communications on Pure & Applied Analysis, 2019, 18 (2) : 825-843. doi: 10.3934/cpaa.2019040 [11] Abdelghafour Atlas. Regularity of the attractor for symmetric regularized wave equation. Communications on Pure & Applied Analysis, 2005, 4 (4) : 695-704. doi: 10.3934/cpaa.2005.4.695 [12] Milena Stanislavova. On the global attractor for the damped Benjamin-Bona-Mahony equation. Conference Publications, 2005, 2005 (Special) : 824-832. doi: 10.3934/proc.2005.2005.824 [13] Guy V. Norton, Robert D. Purrington. The Westervelt equation with a causal propagation operator coupled to the bioheat equation.. Evolution Equations & Control Theory, 2016, 5 (3) : 449-461. doi: 10.3934/eect.2016013 [14] Sergey Zelik. Asymptotic regularity of solutions of a nonautonomous damped wave equation with a critical growth exponent. Communications on Pure & Applied Analysis, 2004, 3 (4) : 921-934. doi: 10.3934/cpaa.2004.3.921 [15] A. Kh. Khanmamedov. Global attractors for strongly damped wave equations with displacement dependent damping and nonlinear source term of critical exponent. Discrete & Continuous Dynamical Systems - A, 2011, 31 (1) : 119-138. doi: 10.3934/dcds.2011.31.119 [16] Shaoyong Lai, Yong Hong Wu, Xu Yang. The global solution of an initial boundary value problem for the damped Boussinesq equation. Communications on Pure & Applied Analysis, 2004, 3 (2) : 319-328. doi: 10.3934/cpaa.2004.3.319 [17] Zhaojuan Wang, Shengfan Zhou. Existence and upper semicontinuity of random attractors for non-autonomous stochastic strongly damped wave equation with multiplicative noise. Discrete & Continuous Dynamical Systems - A, 2017, 37 (5) : 2787-2812. doi: 10.3934/dcds.2017120 [18] Yanbing Yang, Runzhang Xu. Nonlinear wave equation with both strongly and weakly damped terms: Supercritical initial energy finite time blow up. Communications on Pure & Applied Analysis, 2019, 18 (3) : 1351-1358. doi: 10.3934/cpaa.2019065 [19] Tomás Caraballo, Marta Herrera-Cobos, Pedro Marín-Rubio. Global attractor for a nonlocal p-Laplacian equation without uniqueness of solution. Discrete & Continuous Dynamical Systems - B, 2017, 22 (5) : 1801-1816. doi: 10.3934/dcdsb.2017107 [20] Wided Kechiche. Regularity of the global attractor for a nonlinear Schrödinger equation with a point defect. Communications on Pure & Applied Analysis, 2017, 16 (4) : 1233-1252. doi: 10.3934/cpaa.2017060

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text:
# FAQ overflow

#### QUESTION

I want to know about the setter and getter. I know that it is a properties of declaring variable but some time I get confused. Presently I am using a sample of code that is below:

public with sharing class hello
{
public String temp{set;get;}
public hello(){
temp = 'first' ;
}

public String gettemp(){
return 'second' ;
}
}

So I want to know that when I use temp on VFP than what value will show on page, what is reason for that, and what is the difference between temp and gettemp?

Thanks Ashlekh Gera

You might want to read about getters, setters and VF page order of execution (that's a very long read with lots of examples though). There's also an interesting (if a bit hidden) topic in Apex Reference on how names (of variables and methods) are resolved

Your temp variable gets assigned a value in the constructor because constructor is the first thing that fires. Since you've defined the automatic getter and setter. the gettemp() is now redundant - actually I have no idea how to "force call" this method from Visualforce (not counting action methods etc).

I'd say decide on one convention and stick to it? Either

• shortcut with writing {get;set;} (with variations like {get;private set;} or
• full getVariable/setVariable methods?

There's also this crazy syntax of getters that initialize the variable first time they're used - it has some uses (especially when you want to make constructor "thin" and not fire off queries that might not be used on the page. Still - I prefer making explicit getVariable methods in such situations anyway. That's more of philosophical matter about getters/setters in general ;)

public Account acc {
set;
get {
if (acc == null) acc = [SELECT Id FROM Account LIMIT 1];
return acc;
}
}

As you can see from the last link - the {get; set;} thing is "new" ;) It was introduced to Visualforce in 2008. There might be still some ancient VF pages with version 14 or something that can't use it unless their version is upgraded. Before Summer '08 you had to explicitly write out getter/setter for each variable you planned to use on VF page.


text:
# How to recognize a digit

The first task is to train a model so that it can recognize 5 x 5 LCD digits, shown in Fig 1.

Fig 1. Images of ten LCD digits

To do this we use a linear regression, which is sufficiently powerful for a task of this complexity.

Each digit is represented as a 5 x 5 array of 0s and 1s. We flatten each one of the arrays into a vector of 25 floats. We stack all vectors forming a 2D array $X_{\mbox{flat}}$. Next, we compute $X_{\mbox{flat}} W + b$, where $W$ is a 25 by 10 matrix and $b$ is a vector of size 10.

$\left[ \begin{array}{ccccccc} 1 & 1 & 1 & \cdots & 1 & 1 & 1 \\ 0 & 0 & 0 & \cdots & 0 & 0 & 1 \\ 1 & 1 & 1 & \cdots & 1 & 1 & 1 \\ & & & \ddots & & & \\ 1 & 1 & 1 & \cdots & 1 & 1 & 1 \\ 1 & 1 & 1 & \cdots & 0 & 0 & 1 \end{array} \right] \times \left[ \begin{array}{cccc} w_{0,0} & w_{0,1} & \cdots & w_{0,9} \\ w_{1,0} & w_{1,1} & \cdots & w_{1,9} \\ w_{2,0} & w_{2,1} & \cdots & w_{2,9} \\ & & \ddots & \\ w_{23,0} & w_{23,1} & \cdots & w_{23,9} \\ w_{24,0} & w_{24,1} & \cdots & w_{24,9} \end{array} \right] + \left[ \begin{array}{c} b_0 \\ b_1 \\ \vdots \\ b_9 \end{array} \right]$

The above expression gives us, for each row of $X_{\mbox{flat}}$, a vector of ten numbers, $y$ referred to as logits. $y_i$ is proportional to the likelihood that the row represents digit $i$. When training a model, we use gradient descent to nudge the model so that if a row represents, say, a 0, then $y_0$ is greater than $y_1$$y_9$.

We cannot treat $y_i$ as probability, as there is no guarantee that each $y_i$ is between 0 and 1 and the sum of all $y_i$‘s adds to 1. However, this can be remedied by using softmax function. A value $h_i$ is expressed as

$\displaystyle h_i = {e^{y_i} \over \sum_{j} e^{y_j}}$

Using softmax converts values y to probabilities h. The goal of training a model is to make sure that when we see an image for, say, 0, the resulting vector $h$ is as close as possible to $[1, 0, 0, 0, 0, 0, 0, 0, 0, 0]$. This requirement is captured with the help of cross entropy function:

$\displaystyle -\frac{1}{10} \sum_{i = 0}^{10} t_i \lg h_i + (1 - t_i) \lg(1 - h_i)$

Where $t_i$ is the true (desired) value, taking either 1 or 0. Let us express the above using Tensorflow:

img_size = 5
shape_size = 5
kind_count = 10
learning_rate = 0.03
pixel_count = img_size * img_size

x = tf.placeholder(tf.float32,
shape=[None, img_size, img_size])
x_flat = tf.reshape(x, [-1, pixel_count])
y_true = tf.placeholder(tf.float32,
shape=[None, kind_count])
W = tf.Variable(tf.zeros([pixel_count, kind_count]))
b = tf.Variable(tf.zeros([kind_count]))
y_pred = tf.matmul(x_flat, W) + b
loss_op = tf.reduce_mean(
tf.nn.softmax_cross_entropy_with_logits(
labels=y_true, logits=y_pred))
learning_rate)
train_op = optimizer.minimize(loss_op)
correct_prediction = tf.equal(tf.argmax(y_pred, 1),
tf.argmax(y_true, 1))
accuracy_op = tf.reduce_mean(
tf.cast(correct_prediction, tf.float32))

First we set up a few parameters. Initially image size and shape size are going to be the same. This means that the shape completely fills the image. We set the number of kinds of images to 10, so that all ten digits are present. The learning rate defines how fast we follow the slope of the loss function. In our case we chose a conservative 0.03. Choosing a larger value can lead to a faster convergence, but it can also cause us to overshoot the minimum, once we are near it. Lines 7, 8 and 9 create placeholders for input data. Both x and y_true are going to be repeatedly fed batches of images and correct labels for those images. In line 12 we set up the weight matrix. In order to compute $X_{\mbox{flat}} W$, W must have pixel_count = 25 rows. It has 10 columns (or kind_count) to produce a vector of size 10. The i-th element of that vector is proportional to the likelihood that the given image represents digit i. Line 15 sets up the loss function. It is set as the mean value of softmax expression computed by taking predictions and true labels. Line 18 uses a gradient descent optimizer and line 20 uses it to create a training operation that minimizes the loss function by descending along the gradient of the mean value of the softmax expression. Line 21 computes, for each batch, how many predictions for that batch were correct. Finally, in line 23 we express accuracy as the sum of the correct predictions divided by the total number of predictions. Next comes the training of the model:

sess = tf.InteractiveSession()
sess.run(tf.global_variables_initializer())
batch_maker = BatchMaker(img_data, true_kind, batch_size)
step_nbr = 0
while step_nbr < 5:
img_batch, label_batch = batch_maker.next()
train_op.run(feed_dict={x: img_batch, y_true: label_batch})
step_nbr += 1

We first train the model for five steps. After five steps we print a selection of images. As LCD digits are very regular and fit exactly inside each image, just 5 steps is sufficient to get 60% accuracy:

Fig 2. Predictions made by the model after five steps.

The model cannot distinguish between 1, 4, 7 and 9 and between 2 and 3. We continue training until accuracy is 1.

The final matrix W is shown in Fig 3. To better visualize W, we reshape each column of W into a 5 x 5 matrix. Then we normalize each value between -1 and 1. Finally, we plot 1 as red, -1 as blue, 0 as white, and intermediate values as shades of blue or red.

Fig 3. Matrix W at 100% accuracy.

The red color indicates positive interaction between the matrix and the image, while blue colors indicate negative interaction. Looking at 0, we can see that the model learned to distinguish between 0 and 8 by using negative weights for the line in the middle. For 1, the matrix strongly selects for a vertical line on the left, penalizing at the same time parts that would make the image look like 4, 7 or 9. 3 has positive interaction with almost all but 2 pixels, which would turn 3 into 8. The model did not learn the cleanest features, but it learned enough to tell each digit apart.

Clearly, linear regression can learn a number of features, given a well behaved problem. In the following posts we are going to show how a small change in the problem’s complexity causes linear regression to struggle. The change is to increase the image size, while keeping the digits sizes at 5. Deep neural networks are able to cope with this situation, at the expense of much longer training and much larger models. The final solution, that uses a convolutional neural network, can achieve fast training, 100% accuracy and small model size.

### Resources

A Jupyter Notebook with the above code can be found at GitHub’s LCD repository.


text:
Problem Involving The Conservation Of Energy

I have another problem I need some help with.

Here's the problem :

A 51.1 kg child slides down a water slide with a velocity of 0.9 m/sec at the top. At the bottom of the slide, she is moving horizontally, y=2.5 meters above the water. She splashes into the water d=3 meters to the left of the bottom of the slide.
--------------------------------------------------------------------------------
a) Assuming potential energy to be zero at the water level, what is the mechanical energy of the child at the top of the slide?
MEo= J
1704 J
--------------------------------------------------------------------------------
b) How high is the top of the slide above the bottom of the slide?

As shown I was able to find out the mechanical energy of the child at the top of the slide (1704J) but I can't seem to figure out how to solve for the height of the slide.

I would have thought that you just set KE + PE = 1704 and solve for h, which I did and got 3.36m, but it isn't the right answer :(

So I did .5(51.1kg)(.9m/s)^2 + 51.1kg(9.81m/s^2)h = 1704J

I'm stumped as I don't see any other way of solved for the height. Any help would be appriciated. :)

Related Introductory Physics Homework Help News on Phys.org
alphysicist
Homework Helper
Hi Pat2666,

The potential energy is zero at the water's surface, so that's where h=0 at. So when you found that h=3.36m, that means the slide is that far above the water's surface.

However, although that will help to answer part b, that's not quite what part b was asking for.

Well it's not really asking for the total height is it? Just the height of the top of the slide to the end of it no? I tried adding 3.36m to the 2.5m above water just to see if I misread the question, but it was still wrong.

alphysicist
Homework Helper
The top of the slide is 3.36 m above the water, the bottom of the slide is 2.5 meters above the water. The question is asking for how far the top of the slide is above the bottom of the slide. What would that be?

OMG I'm so dumb! Thank you lol

I kept thinking that what I was solving for was h, rather than h + the additional height.

Thanks so much! I've been working on this problem forever!

alphysicist
Homework Helper


text:
# When 3 is added to the denominator and 2 is subtracted from the numerator a fraction becomes 1/4.

Question:

When 3 is added to the denominator and 2 is subtracted from the numerator a fraction becomes 1/4. And when 6 is added to numerator and the denominator is multiplied by 3, it becomes 2/3. Find the fraction.

Solution:

Let the numerator and denominator of the fraction be $x$ and $y$ respectively. Then the fraction is $\frac{x}{y}$

If 3 is added to the denominator and 2 is subtracted from the numerator, the fraction becomes $\frac{1}{4}$. Thus, we have

$\frac{x-2}{y+3}=\frac{1}{4}$

$\Rightarrow 4(x-2)=y+3$

$\Rightarrow 4 x-8=y+3$

$\Rightarrow 4 x-y-11=0$

If 6 is added to the numerator and the denominator is multiplied by 3 , the fraction becomes $\frac{2}{3}$. Thus, we have

$\frac{x+6}{3 y}=\frac{2}{3}$

$\Rightarrow 3(x+6)=6 y$

$\Rightarrow 3 x+18=6 y$

$\Rightarrow 3 x-6 y+18=0$

$\Rightarrow 3(x-2 y+6)=0$

$\Rightarrow x-2 y+6=0$

So, we have two equations

$4 x-y-11=0$

$x-2 y+6=0$

Here x and y are unknowns. We have to solve the above equations for x and y.

By using cross-multiplication, we have

$\frac{x}{(-1) \times 6-(-2) \times(-11)}=\frac{-y}{4 \times 6-1 \times(-11)}=\frac{1}{4 \times(-2)-1 \times(-1)}$

$\Rightarrow \frac{x}{-6-22}=\frac{-y}{24+11}=\frac{1}{-8+1}$

$\Rightarrow \frac{x}{-28}=\frac{-y}{25}=\frac{1}{-7}$

$\Rightarrow \frac{x}{28}=\frac{y}{35}=\frac{1}{7}$

$\Rightarrow x=\frac{28}{7}, y=\frac{35}{7}$

$\Rightarrow x=4, y=5$

Hence, the fraction is $\frac{4}{5}$.


text:
# Graphing proportional relationships

### Problem

Graph the line that represents a proportional relationship between y and x where the unit rate of change of y with respect to x is space, start fraction, 3, divided by, 8, end fraction . In other words, a change of 1 unit in x corresponds to a change of space, start fraction, 3, divided by, 8, end fraction units in y.
Graph the line and write the equation of the line.
The equation is
.
Get 5 answers correct in a row


text:
Question
As a woman walks, her entire weight is momentarily placed on one heel of her high-heeled shoes. Calculate the pressure exerted on the floor by the heel if it has an area of $1.50 \textrm{ cm}^2$ and the woman's mass is 55.0 kg. Express the pressure in Pa. (In the early days of commercial flight, women were not allowed to wear high-heeled shoes because aircraft floors were too thin to withstand such large pressures.)

$3.59 \times 10^6 \textrm{ Pa}$

Solution Video

# OpenStax College Physics Solution, Chapter 11, Problem 11 (Problems & Exercises) (1:03)

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Video Transcript
This is College Physics Answers with Shaun Dychko. The pressure exerted by the heel of a woman’s high heel shoe is going to equal the force that it exerts divided by its area. So assuming she has only one heel on the floor at a time, that would mean her entire weight which is mg will be on that heel, and this is just before her toe touches the ground, so just the heel. And that’s going to be mg divided by the area of the heel, so that’s 55 kilograms times 9.8 Newtons per kilogram divided by 1.8 squared centimeters of area converted into meters in order to have our units in Pascal in the end. We need to have Newtons on the top divided by meters squared on the bottom in order to have units in Pascals, because a Pascal is a Newton per meter squared. So we have 1.5 centimeters squared times one over 100 centimeters squared, and this works out to 3.59 times ten to the six Pascal.


text:
Definition of L-function attached to automorphic representation - MathOverflow most recent 30 from http://mathoverflow.net 2013-06-19T08:14:14Z http://mathoverflow.net/feeds/question/19586 http://www.creativecommons.org/licenses/by-nc/2.5/rdf http://mathoverflow.net/questions/19586/definition-of-l-function-attached-to-automorphic-representation Definition of L-function attached to automorphic representation unknown (google) 2010-03-28T04:47:44Z 2011-01-20T03:49:58Z
Suppose $\pi$ is an irreducible automorphic representation of a reductive connected algebraic group $G$ over $\mathbb{A}_K$, here $K$ is a number field, $\mathbb{A}_K$ denotes its adeles. We have a restricted tensor product decomposition of $\pi=\otimes\pi_v$, where $\pi_v$ is an irreducible admissible representation for $G(K_v)$, and for all but finitely many $v$, $\pi_v$ is unramified.

We know how to define local L-factors at $v$ is $\pi_v$ is unramified, and we also know how to define local L-factors at archimedean places because of Langlands classification. So the question is how to define L-factors at ramified places?

As far as I know, at least for $GL_n$, we can define it as the gcd of some family of integrals via integral representation of L-function.
 http://mathoverflow.net/questions/19586/definition-of-l-function-attached-to-automorphic-representation/19601#19601 Answer by Kevin Buzzard for Definition of L-function attached to automorphic representation Kevin Buzzard 2010-03-28T08:29:57Z 2010-03-28T08:29:57Z
I think you're slightly misled. $\pi$ doesn't have an $L$-function "in abstracta". An unramified $\pi_v$ at a finite place $v$ gives rise, by Langlands' interpretation of the Satake isomorphism, to a semi-simple conjugacy class in the local $L$-group (or, more fancily, to an unramified representation of the local Weil[-Deligne] group [with N=0]), and that's not enough for an Euler factor. So what one does is also fixes a representation $r:{}^LG\to GL_n(\mathbf{C})$. Now one has an $L$-function $L(\pi,r,s)$, it depends on both $\pi$ and $r$ though. For example, if you choose a modular elliptic curve over the rationals, but let $r$ be the bazillion'th tensor power of the standard 2-dimensional representation of $GL_2$, you have an $L$-function which no-one knows how to analytically continue.

But the real answer to your question is that this is an open problem. One would like to say that by functoriality there is a representation $r_*(\pi)$ on $GL_n$ and you use standard definitions of $L$-functions on $GL_n$. However the existence of $r_*(\pi)$ is a fundamental open problem: Langlands functoriality. Defining local $L$-functions at the ramified places is a tiny tiny piece of this open problem, but as far as I know it's also open.
 http://mathoverflow.net/questions/19586/definition-of-l-function-attached-to-automorphic-representation/19664#19664 Answer by Dipramit Majumdar for Definition of L-function attached to automorphic representation Dipramit Majumdar 2010-03-28T20:44:48Z 2010-03-28T20:44:48Z
As far as I understand, attaching an $L$-function to an automorphic representation attached to a general reductive group $G$ is conjectural and still open.

The way one attaches $L$-function depends on a representation $r$ of ${^L}G$ and partitioning the set of irreducible admissible representation of $G(k_v)$ in to $L$-packets (which is conjectural in general and known in very few cases). Assuming one can define local $L$-packets, Borel and Tate's article in Corvalis explains how to attach $L$-function to it. But still this $L$-function depends on the chosen representation $r$.

If $\pi$ is an irreducible admissible representation of $G_A$ then $\pi= \otimes_v \pi_v$, where $\pi_v$ is an irreducible admissible representation of $G(k_v)$. So assuming we can partition the set of irreducible admissible representation of $G(k_v)$ in to $L$-packets, $\pi_v$ belongs to $L$-packet $\Pi_{\phi_v}$ corresponding to some admissible homomorphism $\phi_v$ of Weil-Deligne group to ${^L}G/k_v$ . The repesenation $r$ defines a representation $r_v$ of ${^L}G/k_v$.

Then the $L$-function attached to $\pi$ and $r$ is defined as: $L(s,\pi,r) = \prod_v L(s,\pi_v,r_v)$, $L(s,\pi_v,r_v)=L(s, r_v \circ \phi_v)$

Now $r_v \circ \phi_v$ is a represenatation Wiel-Deilgne group, so by Tate's article in Corvalis, we know local $L$-factor.
 http://mathoverflow.net/questions/19586/definition-of-l-function-attached-to-automorphic-representation/52575#52575 Answer by Ramin for Definition of L-function attached to automorphic representation Ramin 2011-01-20T03:49:58Z 2011-01-20T03:49:58Z
This question was posted a while back but I just saw it. Here are some thoughts. In practice there are a couple of methods to construct L functions for local ramified representations. The first one is the Langlands-Shahidi method which works for "generic representations" of quasi-split groups and the second one is the method of integral representations (Rankin-Selberg method, Shimura's integral and the doubling method, etc). It is probably a bit painful to give a meaningful description of these two methodologies in such a limited space, so instead let me refer you to a couple of places where you can see accessible accounts of the two approaches. A good reference for the basics of the Langlands-Shahidi method is the beautiful monograph "Analytic properties of automorphic L functions" by Gelbart and Shahidi. The same reference has a nice introduction to the method of integral representations. Dan Bump has written two very informative survey papers on the Rankin-Selberg method. Cogdell's ICTP lectures on the Rankin-Selberg method are lovely. Another good book to look at is the AMS book by Cogdell, Kim, Murty.

As it stands there is no Langlands-Shahidi method for non-generic representations. What is missing from the picture is a good supply of easy to use unique models, like the Whittaker model in the generic setting. For orthogonal groups, however, recent progress by Waldspurger and others on the Gross-Prasad conjectures gives one the hope that maybe one can now develop a Langlands-Shahidi method, although there are serious obstacles to deal with.

Most of the integral representations known to mankind too are closely linked with unique models (Whittaker, Bessel, etc). Sakellaridis has a theory that "explains" (some) integral representations in terms of spherical subgroups of reductive groups.


text:
# Given f(t) = \sum_k C_k exp(2 pi i w_k t ) + noise. Need to estimate C_k and w_k .

## Simpliefied setup.

Assume I am given some function f(t). I know that it is constructed as $f(t) = \sum_{k=1...M} C_k exp(2 \pi~ i~ w_k t ) + noise(t)$. where $noise(t)$ is some random set of numbers depending on $t$ (white noise if you like). I need to estimate $C_k$ and $w_k$.

Solution: I will make Fourier Transform $\hat f(\lambda)$ and will pick up those $\lambda= w_k$ such that $\hat f(\lambda) > threshold$. How should I choose this threshold ? (The question is probably not 100% well-posed, but hope idea is clear).

## True setup.

Now assume that $t$ is discrete e.g. $t= l/N$, for some $N$ and $l=1...N$.

And the problem is that $w_k$ are do not of the form $l/N$.

Difficulty So the functions $exp(2 \pi~ i~ w_k t )$ are NOT orthogonal on the discrete set $t=l/N$.

So there are some problems with making Fourier transform approach.

-
Shouldn't that be tagged statistics rather than functional analysis? – Vincent Beffara Mar 28 '12 at 20:53

Looks like could take a look at Prony's method.

-

You have what's called a 'predictable' process (sum of shifted diracs) and a simple regular process (white noise in this case). You can just average out signal as much as you like, the harmonies will stay the same and the noise will diminish. You can actually get as low a noise as you like.

If you just want to threshold the coefficients, you can try it by seeing the FFT (white noise has a constant frequency response and the exponents will be peaks), you will immediately see the threshold. You can also calculate it via the power (or variance) of the noise, but this also relies on you knowing the amplitude of the C's.

-