Rate of convergence and bisection

Rate of convergence and bisection Rate of convergence estimate of the speed with which a given sequence or iteration approaches its limit, often measured by the number of terms or evaluations involved in obtaining a given accuracy. Although strictly speaking, a limit does not give information about any finite first part of the sequence, this concept is of practical importance if we deal with a sequence of successive approximations for an iterative method, as then typically fewer iterations are needed to yield a useful approximation if the rate of convergence is higher. This may even make the difference between needing ten or a million iterations. Rate of convergence is measured in terms of rate at which the relative error decreases between successive approximations. There are mainly two type of convergence: linear and quadratic. Convergence of a sequence subject to the condition, for p > 1, that as n increases is called pth-order convergence; for example, quadratic convergence when p = 2. One similarly speaks of logarithmic convergence or exponential convergence. The Bisection Method In mathematics, the bisection method is a root-finding algorithm which repeatedly bisects an interval then selects a subinterval in which a root must lie for further processing. It is a very simple and robust method, but it is also relatively slow. The bisection method is simple, robust, and straight-forward: take an interval [a, b] such that f(a) and f(b) have opposite signs, find the midpoint of [a, b], and then decide whether the root lies on [a, (a + b)/2] or [(a + b)/2, b]. Repeat until the interval is sufficiently small. The bisection method, suitable for implementation on a computer allows to find the roots of the equation f (x) = 0, based on the following theorem: Theorem: If f is continuous for x between a and b and if f (a) and f(b) have opposite signs, then there exists at least one real root of f (x) = 0 between a and b. Procedure: Suppose that a continuous function f is negative at x = a and positive at x = b, so that there is at least one real root between a and b. (As a rule, a and b may be found from a graph of f.) If we calculate f ((a +b)/2), which is the function value at the point of bisection of the interval a f ((a + b)/2) = 0, in which case (a + b)/2 is the root; f ((a + b)/2) f ((a + b)/2) > 0, in which case the root lies between a and (a + b)/2. Advantages and drawbacks of the bisection method Advantages of Bisection Method The bisection method is always convergent. Since the method brackets the root, the method is guaranteed to converge. As iterations are conducted, the interval gets halved. So one can guarantee the decrease in the error in the solution of the equation. Drawbacks of Bisection Method The convergence of bisection method is slow as it is simply based on halving the interval. If one of the initial guesses is closer to the root, it will take larger number of iterations to reach the root. If a function is such that it just touches the x-axis (Figure 3.8) such as it will be unable to find the lower guess, , and upper guess, , such that For functions where there is a singularity and it reverses sign at the singularity, bisection method may converge on the singularity (Figure 3.9). An example include and, are valid initial guesses which satisfy . However, the function is not continuous and the theorem that a root exists is also not applicable. Figure.3.8. Function has a single root at that cannot be bracketed. Figure.3.9. Function has no root but changes sign. False position method The false-position method is a modification on the bisection method. The false position method or regula falsi method is a root-finding algorithm that combines features from the bisection method and the secant method. If it is known that the root lies on [a,  b], then it is reasonable that we can approximate the function on the interval by interpolating the points (a, f(a)) and (b, f(b)).  The method of false position dates back to the ancient Egyptians. It remains an effective alternative to the bisection method for solving the equation f(x) = 0 for a real root between a and b, given that f (x) is continuous and f (a) and f(b) have opposite signs. The algorithm is suitable for automatic computation Procedure: The curve  y = f(x)  is not generally a straight line. However, one may join the points (a,f(a)) and (b,f(b)) by the straight line Thus straight line cuts the  x-axis at (X, 0) where so that Suppose that  f(a)  is negative and  f(b)  is positive. As in the bisection method, there are the three possibilities : f(X) = 0, when case  X  is the  root  ; f(X) f(X)>0, when the root lies between  X  and  a. Again, in Case  1, the process is terminated, in either Case  2  or Case  3, the process can be repeated until the root is obtained to the desired accuracy. Convergence of False Position Method and Bisection Method Source code for False Position Method: Example code of False-position method C code was written for clarity instead of efficiency. It was designed to solve the same problem as solved by the Newtons method and secant method code: to find the positive number x where cos(x) = x3. This problem is transformed into a root-finding problem of the form f(x) = cos(x) x3 = 0. #include #include double f(double x) { return cos(x) x*x*x; } double FalsiMethod(double s, double t, double e, int m) { int n,side=0; double r,fr,fs = f(s),ft = f(t); for (n = 1; n { r = (fs*t ft*s) / (fs ft); if (fabs(t-s) fr = f(r); if (fr * ft > 0) { t = r; ft = fr; if (side==-1) fs /= 2; side = -1; } else if (fs * fr > 0) { s = r; fs = fr; if (side==+1) ft /= 2; side = +1; } else break; } return r; } int main(void) { printf(%0.15fn, FalsiMethod(0, 1, 5E-15, 100)); return 0; } After running this code, the final answer is approximately 0.865474033101614 Example 1 Consider finding the root of f(x) = x2 3. Let ÃŽÂ µstep = 0.01, ÃŽÂ µabs = 0.01 and start with the interval [1, 2]. Table 1. False-position method applied to f(x)  =  x2 3. a b f(a) f(b) c f(c) Update Step Size 1.0 2.0 -2.00 1.00 1.6667 -0.2221 a = c 0.6667 1.6667 2.0 -0.2221 1.0 1.7273 -0.0164 a = c 0.0606 1.7273 2.0 -0.0164 1.0 1.7317 0.0012 a = c 0.0044 Thus, with the third iteration, we note that the last step 1.7273 à ¢Ã¢â‚¬  Ã¢â‚¬â„¢ 1.7317 is less than 0.01 and |f(1.7317)| Note that after three iterations of the false-position method, we have an acceptable answer (1.7317 where f(1.7317) = -0.0044) whereas with the bisection method, it took seven iterations to find a (notable less accurate) acceptable answer (1.71344 where f(1.73144) = 0.0082) Example 2 Consider finding the root of f(x) = e-x(3.2 sin(x) 0.5 cos(x)) on the interval [3, 4], this time with ÃŽÂ µstep = 0.001, ÃŽÂ µabs = 0.001. Table 2. False-position method applied to f(x)  = e-x(3.2 sin(x) 0.5 cos(x)). a b f(a) f(b) c f(c) Update Step Size 3.0 4.0 0.047127 -0.038372 3.5513 -0.023411 b = c 0.4487 3.0 3.5513 0.047127 -0.023411 3.3683 -0.0079940 b = c 0.1830 3.0 3.3683 0.047127 -0.0079940 3.3149 -0.0021548 b = c 0.0534 3.0 3.3149 0.047127 -0.0021548 3.3010 -0.00052616 b = c 0.0139 3.0 3.3010 0.047127 -0.00052616 3.2978 -0.00014453 b = c 0.0032 3.0 3.2978 0.047127 -0.00014453 3.2969 -0.000036998 b = c 0.0009 Thus, after the sixth iteration, we note that the final step, 3.2978 à ¢Ã¢â‚¬  Ã¢â‚¬â„¢ 3.2969 has a size less than 0.001 and |f(3.2969)| In this case, the solution we found was not as good as the solution we found using the bisection method (f(3.2963) = 0.000034799) however, we only used six instead of eleven iterations. Source code for Bisection method #include #include #define epsilon 1e-6 main() { double g1,g2,g,v,v1,v2,dx; int found,converged,i; found=0; printf( enter the first guessn); scanf(%lf,g1); v1=g1*g1*g1-15; printf(value 1 is %lfn,v1); while (found==0) { printf(enter the second guessn); scanf(%lf,g2); v2=g2*g2*g2-15; printf( value 2 is %lfn,v2); if (v1*v2>0) {found=0;} else found=1; } printf(right guessn); i=1; while (converged==0) { printf(n iteration=%dn,i); g=(g1+g2)/2; printf(new guess is %lfn,g); v=g*g*g-15; printf(new value is%lfn,v); if (v*v1>0) { g1=g; printf(the next guess is %lfn,g); dx=(g1-g2)/g1; } else { g2=g; printf(the next guess is %lfn,g); dx=(g1-g2)/g1; } if (fabs(dx)less than epsilon {converged=1;} i=i+1; } printf(nth calculated value is %lfn,v); } Example 1 Consider finding the root of f(x) = x2 3. Let ÃŽÂ µstep = 0.01, ÃŽÂ µabs = 0.01 and start with the interval [1, 2]. Table 1. Bisection method applied to f(x)  =  x2 3. a b f(a) f(b) c  =  (a  +  b)/2 f(c) Update new b à ¢Ã‹â€ Ã¢â‚¬â„¢ a 1.0 2.0 -2.0 1.0 1.5 -0.75 a = c 0.5 1.5 2.0 -0.75 1.0 1.75 0.062 b = c 0.25 1.5 1.75 -0.75 0.0625 1.625 -0.359 a = c 0.125 1.625 1.75 -0.3594 0.0625 1.6875 -0.1523 a = c 0.0625 1.6875 1.75 -0.1523 0.0625 1.7188 -0.0457 a = c 0.0313 1.7188 1.75 -0.0457 0.0625 1.7344 0.0081 b = c 0.0156 1.71988 1.7344 -0.0457 0.0081 1.7266 -0.0189 a = c 0.0078 Thus, with the seventh iteration, we note that the final interval, [1.7266, 1.7344], has a width less than 0.01 and |f(1.7344)| Example 2 Consider finding the root of f(x) = e-x(3.2 sin(x) 0.5 cos(x)) on the interval [3, 4], this time with ÃŽÂ µstep = 0.001, ÃŽÂ µabs = 0.001. Table 1. Bisection method applied to f(x)  = e-x(3.2 sin(x) 0.5 cos(x)). a b f(a) f(b) c  =  (a  +  b)/2 f(c) Update new b à ¢Ã‹â€ Ã¢â‚¬â„¢ a 3.0 4.0 0.047127 -0.038372 3.5 -0.019757 b = c 0.5 3.0 3.5 0.047127 -0.019757 3.25 0.0058479 a = c 0.25 3.25 3.5 0.0058479 -0.019757 3.375 -0.0086808 b = c 0.125 3.25 3.375 0.0058479 -0.0086808 3.3125 -0.0018773 b = c 0.0625 3.25 3.3125 0.0058479 -0.0018773 3.2812 0.0018739 a = c 0.0313 3.2812 3.3125 0.0018739 -0.0018773 3.2968 -0.000024791 b = c 0.0156 3.2812 3.2968 0.0018739 -0.000024791 3.289 0.00091736 a = c 0.0078 3.289 3.2968 0.00091736 -0.000024791 3.2929 0.00044352 a = c 0.0039 3.2929 3.2968 0.00044352 -0.000024791 3.2948 0.00021466 a = c 0.002 3.2948 3.2968 0.00021466 -0.000024791 3.2958 0.000094077 a = c 0.001 3.2958 3.2968 0.000094077 -0.000024791 3.2963 0.000034799 a = c 0.0005 Thus, after the 11th iteration, we note that the final interval, [3.2958, 3.2968] has a width less than 0.001 and |f(3.2968)| Comparison of rate of convergence for bisection and false-position method Like the bisection method, the method of false position has almost assured convergence, and it may converge to a root faster. Finally, note that bisection is rather slow; after  n  iterations the interval containing the root is of length  (b a)/2n. However, provided values of  f  can be generated readily, as when a computer is used, the rather large number of iterations which can be involved in the application of bisection is of relatively little consequence. The false position method would be better i.e. converges to the root more rapidly as it takes into account the relative magnitudes of f(b) and f(a) unlike bisection which just uses the midpoint of a and b, where [a,b] is the interval over which the root occurs. Following is the example of the convergence rate of bisection method and false position method for the similar equation which shows that rate of convergence of false position method is faster than that of the bisection method.

Malunggay as an Effective Cooking Oil

Commercial cooking oil is an enormous need of people nowadays. These days, cooking oil is becoming expensive. Commoners, or people with insufficient finance, can no longer afford this necessity. Instead, they opt for oil with lesser quality simply because it’s cheaper.It’s very ghastly to do this because for one; your health could be affected, two; you could harbour diseases, and three; on the worst case scenario, it could lead to your death. To think that they would go to extreme lengths, such as that, just to provide oil. Going back to the topic prior to this, we think that although it may be costly, most cooking oils are of unsatisfactory standards  especially in our nutrition. With that said, we all share the idea of wanting to solve this problem. We conducted a research about the effectivity of Moringa Olefeira, also known as â€Å"Malunggay†, when used as an ingredient for cooking oil. We chose Moringa Olefeira for a reason; gram for gram, â€Å"Malungga y† leaves contain: seven times the vitamin C in oranges, four times the Calcium in milk, four times the vitamin A in carrots, two times and the protein in milk and three times the Potassium in bananas.Using this so called â€Å"Wonder Vegetable† (according to the elderly), we could create a product that can be healthy and useful, and at the same time be sold in a reasonable price. Our main goal is aimed at the welfare of everyone. We hope that this experiment can be of great help to anyone who uses it. We gathered the data of this study from various references. We owe a massive and part of this study to literature and the internet; without them we wouldn’t have anything, even a problem, to begin with. 3Statement of the ProblemMain ProblemCan malunggay (Moringa Oleifera) leave extract be a potential material for formulating cheaper yet healthier commercial cooking oil?Specific Questions1. At which concentration of malunggay (Moringa Oleifera) leaves extract will i t be able to cook food?a. 10 mg/ml. b. 20 mg/ml. c. 25 mg/ml.2. How effective will it be on cooking safe and edible food? It can be inferred in terms of:a. Period or time of cooking. b. Taste of the food cooked. c. Nutrition facts or nutrients contained by the food.Significance of the StudyPeople living in the community. The study will help the people in the community to manufacture useful cooking oil that can be alternatively used  to cook food – which is a basic commodity. Malunggay is very common to the community so people can easily grow them and prepare it for extraction. In addition, unlike the commercial cooking oil we use, it is healthy and contains the nutrients of malunggay.The researchers. The researchers will benefit from the study because in would fulfil our curiosity. It will also encourage us to find other alternatives from malunggay -which is very abundant in our country- that can help us in our everyday lives.Environment. The environment profit from the stu dy in the fact that cooking oil that is already used by people will just be thrown away in the streams and it will cause water pollution. Not like with the cooking oil made from malunggay, its chemical components can be easily dissolved in water.Manufacturers of commercial cooking oil. This study would help big companies as it lessen the production cost of cooking oil because it only uses malunggay.Scopes and Limitations of the StudyThe study aims to produce budget-friendly and nutritious oil that can be used by people to cook their own food. In able to do this study, researchers must first collect Malunggay (Moringa Oleifera) around the community and prepare it for extraction in the laboratory or do it at home. After the extraction process, series of test must be done to prove and justify the effectivity of the product. It must cook food using stoves at normal cooking temperature that are normally used by households and the food must contain healthy nutrients that must be good to o ur body.This experiment also has its fair share of restrictions. And one of those restraints is when the researcher doesn’t have sufficient materials to create the said product, especially if they don’t have the main ingredient or, in this case, the malunggay. The person would have to plant or buy these  materials, thus spending much time and cash. Speaking about money, another problem may occur if the researcher has a weak budget. An extra problem is if the researcher does not have enough knowledge to create and research about the problem.Another limitation of the study is when the researcher doesn’t have a place to create the product or when his surrounding isn’t fit for the making of the substance. The researcher must remember to take into account even the smallest detail of this project. The researcher must have great dedication in doing this study. He should love what he is doing and he need to make it as one of he’s passion.

Why Teachers Are Important

Why Teachers are Important Teachers are important because they educate the students by preparing them for a triumphant future. The number of human beings in the world is increasing every second of every day which is why it is not a surprise that teachers other than special education teachers hold about three point five million jobs (McKay, Dawn R. ). As each child grows older, he/she needs to learn in order to survive; teachers are the ones to instill knowledge (DeRoy). Every single person needs an education. To start most careers, a college degree is required.In order to get that college degree, an individual must complete grade school and high school and receive a high school diploma or GED, then complete college courses to learn the degree of choice. Children must be prepared for school and this starts with parents teaching them basic understandings of their alphabet and numbers (Archived: Early Childhood Education). If the students are not equipped with the basic knowledge, then they are bound to drop out of school (Shargel 19). Throughout the world, there are seventy two million children who are not getting the proper schooling they need (DeRoy).These children cannot better themselves through life without an education that can help them through the struggles of everyday life that only schooling can support. In those schools, teachers teach every single person how to write, how to read, how to do multiplication and addition facts, and how to write essays (McKay, Dawn R. ). Many people can think back and remember every teacher they have ever had, and if they cannot remember every one, then they at least remember their favorite one. Teachers are the ones who educate generations of people globally (DeRoy).There are many different teachers all over the world. There are teachers, who teach driving; there are teachers who teach art, and teachers who teach pupils how to construct machines. There are even teachers who teach teachers! All teachers however have to st art off somewhere, and that’s in a class room. Once schooling requirements have been met and some experience has been made, some teachers can become school administrators or can even get additional training and become a school librarian or a guidance counselor. Public school teachers in every state are required to have a achelor’s degree (Haugen, Lee). There are many states in the U. S. that even require a Master’s degree within a certain time frame. The future teacher must have fulfilled an official training program that includes earning a specific amount of educational credits. When it comes to teaching early education such as preschool, the requirements for training differ; some states require a bachelor’s degree while others accept just an associate’s degree (McKay, Dawn R. ). Absolutely all teachers, in every state, and the District of Columbia are required to be licensed.To get a teaching license, one must generally pass an exam that demonstr ates proficiency in basic skills and proficiency in the subject area that is desired. Licenses are normally issued by state boards or departments of educations (McKay, Dawn R. ). Since the world’s population is growing the teaching occupation is growing exceedingly as well. Employment of kindergarten through secondary school teachers alone will grow as quickly as all occupations through 2018. Location is key. Jobs are not meant to be everywhere in the world, if that was so then jobs would be given to anyone with a high school diploma.Also grade level and the subject specialty will have a great affect on job opportunity (McKay, Dawn R. ). In many schools today, students are required to have at least three years of a language course. People who have completed up to three years of a language are more likely to get a job over a competitor who has not had this extra information. Teachers are more likely to get a job over someone else if they indeed, can speak another language beca use they can help students who do not have English as their first language, which produces maximum learning efficiency (DeRoy).The most basic and most important teachers in the world, however, are grade school and high school teachers. Every single student must pass each grade in elementary school in order to go on to high school. Then in high school, the student must pass grades nine through twelve in order to receive one tiny piece of paper that gives individual opportunities in life. That piece of paper is called a diploma (McCourt). That one little piece of paper can make or break a person’s entire life. A diploma or equivalent, GED, is without any exception, required for college. There is no way to skate around it and hope to get in without one.Teachers need to be able to handle students, and teach them the curriculum that is required for the grade level. What makes a great teacher so incredible is their personality. They capture the minds and attentions of their pupils and without realizing it, get the students to understand the topic and remember it. Many students become teachers themselves because they loved their teacher and wanted to follow in the footsteps of them (College Board). A man named Eric Hanushek says that â€Å"teacher’s quality matter so much that a student is likely better off in a bad school with a good teacher than a good school with a bad teacher. If the teacher is good at his or her job, then odds are that student is going to do well academically no matter what. An author and teacher William Sanders once wrote that : â€Å" although an effective teacher can facilitate excellent academic gain in students during the years in which they are assigned to them, the residual effects of ineffective teachers were measurable two years later, regardless of the effectiveness of teachers in later grade. † In simpler words Sanders is saying that if a pupil has one exceptional teacher, then their learning can become corrupt f or years to come.Teachers indeed have an impact. Those students whose guardians are poor may have a hard time in school, but if they were to receive excellent hard working teachers who are willing to teach them, that problem could very well disappear entirely (Hanuskek). There are many ways that a parent or guardian can put their child through schooling. The government is here to help everyone be the best that they can be in this world, for themselves and for the community as a whole (Archived Early Education). Many people sending their children to school worry about their food consumption.They worry that the kids will sit astray with no food while others have a plentiful lunch and snack. Proper schools will not let that happen. A child will not go hungry or thirsty while a teacher or administrator is in that building. These are formative years in children’s lives, and the education and attention that every student requires is very important in determining the future of those pupils (Teachers: Kindergarten, Elementary, Middle, and Secondary). College teachers and professors are more tough on their students than those who teach younger levels.This is because those teachers know what the real world is like (DeRoy). They have hands on experience. Each and every teacher knows how hard it is to get into college, get good grades, graduate, and get hired in a respectable school. They know that students need to get the degree of their choice in order to start a career. The individual needs to buckle down and get to work. Some students may have had bad study habits or bad learning habits in general and the college teacher will help to improve these abilities but will not however hold one’s hand while doing it (Haugen, Lee).College teachers typically teach about seven courses in their subject for example ranging from calculus, statistics, algebra and geometry. Not only may they teach graduates, but they could very well teach undergraduates as well. The tea chers in college do not necessarily teach pupils who have just gotten out of college and are not yet twenty years of age. They can teach all different ages that have no limit. A professor could be teaching someone that is the same age as their grandmother. Knowledge has no age limit and everyone is capable of retaining new material (Teachers—Postsecondary).Many teachers have very different and complicated schedules. Unlike grade school and high school classes that take place all day everyday Monday through Friday without change, these teachers have different obstacles. They may teach three classes a week and each class may be at different times every day. Many college teachers find the environment intellectually stimulating and rewarding because they are surrounded by others who enjoy the subject that they are teaching (Teachers Count). This is very different from younger grades and can be very stressful on students but teachers normally grow accustom to their hectic schedule . Teachers—Postsecondary) An impact that a teacher has on a student is extraordinary. Students spend more time with their teacher than they do with their parents or family while going to school. Teachers are no longer just training their pupils mind for an education but are affecting the intellectual, emotional, and social development of each student they meet (Teachers Count). Teachers are respected by others because they are viewed as knowledgeable about different subjects of school and because they take care of society’s children.Students look up to their teachers for guidance when they are most vulnerable (Rose, Mike). If a student is unsure about something they ask their teacher and trust that the answer given to them is the right response. A teacher spends an entire year with a handful of students. In that time they should have a pretty general idea about each and every pupil in the seats before him or her. Through the teacher’s words and through their act ions, they are being a role model to a student. The teacher provides a special window for the student on a possible future (Adviser, Teacher, Role Model, Friend).Teachers make the world go round. Teachers have the ability to shape and mold the attitudes and values that their pupils possess. This possession can be beneficial with extraordinary outcomes. The society needs decent human beings who know right from wrong and who know how to help the community so the world can be a better place. By teachers enlightening students with more in-depth attitudes they are shaping the world with a strong society (Adviser, Teacher, Role Model, Friend) Teachers are the foundation of this world.They bestow knowledge to all people of every age. Teachers do not just instruct math skills or English skills. They teach moral lessons to everyone willing to learn. When it comes to knowledge, the poorest person in the world could be rich, rich with knowledge. A teacher cannot just stand in front of a room a nd teach. The material in which they preach must be accurate and the students must understand it. One cannot call himself or herself a teacher if the students are not learning the material. The opinions of society can be very influential.If teachers are being viewed negatively than the students are not going to take the teachers seriously and will not respect them not soak up the information that they need (Shargel 19). A proper and positive learning environment is not all that is needed to educate students. Teachers need to radiate positive attitudes and let their students know that they are in charge and that they are there to help the students for a triumphant future that they will need to survive in the world full of seven billion people (McKay, Dawn R. ).

Examples Of Position Of Officer - 967 Words

I am pleased to submit my application for the position of Officer. It is exciting to consider a position with the global leader in consulting and technology services. In this letter, I provide some background about my education and credentials relevant to this position. I believe I have the required qualifications for this position. I earned my MD from Kabul Medical University specializing in Family Medicine. I then earned an Executive MBA in Health Management and Administration from Preston University Pakistan. Subsequently, I earned my Dual MPH degree in Epidemiology and Global Health, and my PhD in Epidemiology at the University of South Florida, College of Public Health. Here, I would like to briefly address the critical†¦show more content†¦As a member of the program development team, we secured several million USD in funding from World Bank and European Commission (EC) to offer primary healthcare services in three provinces including sexually transmitted infections (STIs) prevention. I am a subject matter expert in a number of public health areas, including STIs (HIV, HPV and other STIs), and have working experience in global health security and humanitarian aid. During my work at SCA, I led an evaluation to examine the effectiveness of HIV awareness campaign and HIV Voluntary Counseling and Treatment (VCT) program. Together with the HIV Department, we also piloted a number of community-based HIV prevention interventions, such as training of local barbers, and needle-exchange program. We implemented our projects in close coordination with UNAIDS and UN Office on Drugs and Crime (UNODC). During my work with the SCA and the UN, I led the design and implementation of a number of projects that were focused on improving access to development aid, community participation, and the assessment of cultural and religious barriers in accessing healthcare services for women and children. Furthermore, during my PhD, I worked with the Center for Infection Research on Cancer (CI RC) at Moffitt Cancer Center in the United States to study the role of STIs in the development of cancer,Show MoreRelated2000 Word Essay on Being a Team Leader1073 Words   |  5 PagesNon Commissioned officers are a vital part of the United States Army which is why they are often referred to as the â€Å"back bone of the Army†. Non Commissioned officers play several key roles in the army, everywhere from the lowest Sergeant or Corporal as a team leader to the First Sergeant working as advisory and counter part to a Captain in charge of a Company, to a Command Sergeant Major, responsible for anything fro a battalion to an entire post. Regardless of which position a non commissionedRead MoreFire Service Personnel Management Officer879 Words   |  4 Pages FIRE SERVICE PERSONNEL MANAGEMENT OFFICER JOB ANALYSIS BY COREY SCOTT CLASS SPECIFICATION Firefighter Personnel Management Officer DEFINITION OF CLASS A personal manager officer is a supervisor and managerial position within the fire department. Under general direction it is their job to lead, plan, organize, and direct the personnel management program of the fire department. The position’s main focus should be on staffing, retention, development, adjustment, and managing change. 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