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This document discusses differentiation and how it is used to find the derivative of a function. It explains that differentiation measures how rapidly a function is changing at a point and looks at the rate of change of a function based on one of its variables. It also provides an example of using differentiation to model population growth over time as an exponential function.
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Statistical Physics Assignment Help
I am Stacy W. I am a Statistical Physics Assignment Expert at statisticsassignmenthelp.com. I hold a Masters in Statistics from, University of McGill, Canada
I have been helping students with their homework for the past 7years. I solve assignments related to Statistical.
Visit statisticsassignmenthelp.com or email info@statisticsassignmenthelp.com.
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1979 Optimal diffusions in a random environment
This paper analyzes mathematical models of population growth and diffusion in a random environment. It presents both discrete and continuous models to determine the optimal rate of offspring dispersal to maximize population growth over time. Through analysis and examples, the paper shows that for many cases, having no dispersal (a diffusion rate of zero) is actually optimal, contrary to what numerical simulations may indicate. The optimal strategy is to not distribute the population but instead to allow it to remain concentrated, gambling on the small probability of extremely large growth.
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This document summarizes a basic science project on the applications of differential equations. It discusses how differentiation can be used to model population growth over time using exponential functions. As an example, it shows how to calculate the time needed for a population to triple if it is known to double every 30 years. The document concludes that differential equations have many applications in predicting real-world system behaviors over time.
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Write down the four (4) nonlinear regression models covered in class,.pdf
Write down the four (4) nonlinear regression models covered in class, i.e. both the name of the
model and their functional form showing their respective regression coefficients. A rapidly
growing bacteria has been discovered with a growth rate as shown in the table. Analyze this date
using a power law model. First linearize the data in the table based on the power law model, call
this new linearized data x and y. Next, determine the coefficients a_0 and a_1 of a linear
regression y = a_0 + a_1x for the linearized power law data x and y, and compute the correlation
coefficient for the liner regression. Note that you are not being asked to do a linear regression of
the data in the table but rather a linear regression of the linearized version of that data. Once you
compute a_0 and a_1 use these to determine the coefficients of the power law model. Write a
Matlab script that uses the polyfit function to determine the regression coefficients of a second
order polynomial fit to data in the table. In the same script, write down the code for using the
polyval command to determine the value of the regression curve at the observed times.
Solution
Nonlinear regression is a statistical technique that helps describe nonlinear relationships in
experimental data. A nonlinear regression model can be written Yn = f(xn, ) + Zn where f is the
expectation function and xn is a vector of associated regressor variables or independent variables
for the nth case.
A nonlinear model is one in which at least one of the parameters appears nonlinearly. More
formally, in a nonlinear model, at least one derivative with respect to a parameter should involve
that parameter. Examples of a nonlinear model are:
Y(t) = exp(at+bt2)
Y(t) = at + exp(-bt).
Important non linear growth models
1.Logistic Model
This model is represented by the differential equation
dN/dt = rN (1-N/K).
Integrating, we get
N(t) = K / [1+(K/No-1) exp(-rt)]
The graph of N(t) versus t is elongated S-shaped and the curve is symmetrical about its point of
inflexion.
2.Malthus Model
If N(t) denotes the population size or biomass at time t and r is the intrinsic growth rate, then the
rate of growth of population size is given by
dN/dt = rN.
Integrating, we get
N(t) = No exp (rt),
where No denotes the population size at t=0. Thus this law entails an exponential increase for
r>0. Furthermore, N(t) à as t à , which cannot happen in reality.
3. Monomolecular Model
This model describes the progress of a growth situation in which it is believed that the rate of
growth at any time is proportional to the resources yet to be achieved, i.e.
dN/dt = r(K-N),
where K is the carrying size of the system. Integrating (3.3), we get
N(t) = K-(K-No) exp (-rt).
4. Richards Model.
This model is given by dN/dt = rN (KN – Nm)/mKm which, on integration, gives N(t )=K N0 /[
N0+ (KN – N0m) exp (-rt)]1/m.
Unlike the earlier models, this model has four parameters
Hours (H)
10
20
40
50
No fo bacteria (N)
25
70
380
550
610
b)
N = b H m
Log10.
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changing. Ecologists use population models to study ecological systems, especially those where
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others. In human situations, it is normal to take intervals of 10 years as the census is taken every
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probably be appropriate. The survival fractions would then show the fraction of \"newborns\" (0-
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x(0) given with solution found iteratively to be (2) x(k) = Akx(0) (see Kolman for details of the
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which will form the basis for predicting school, transportation, housing, water, and electrical
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(the last census) is (3.1, 2.8, 2.0, 2.5, 2.0, 1.8, 2.9) (x105 ) and that the Leslie matrix,A, for this
model appears as Part One: Interpret carefully each of the nonzero terms in the matrix. In
addition, indicate what factors you think might change those numbers (they might be social,
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will look like in 2000, 2010, 2020 and 2030 what the total population will be in each of those
years by what fraction the total population changed each year Additionally, what does your
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Week 7
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Assignment Support Resources (ASR)
4. Diverse Cultures Resources
GENERAL RESOURCES
Public Broadcasting Service: Patterns of cultural differences
University of Colorado: Cultural barriers to Effective Communication
George Washington University: Differences affecting international teams
HOFSTEDE CONCEPTS
Boonghee, Y., Donthu, N., & Lenartowicz, T. (2011). Measuring Hofstede's five dimensions of
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International Consumer Marketing, 23(3/4), 193-210. doi:10.1080/08961530.2011.578059
Christley, J. (n.d.). Cultural dimensions for teaching diversity.
Hofstede, G. (2001). Culture's consequences: Comparing values, behaviors, institutions, and organizations across nations
(2nd ed.). Thousand Oaks, CA: SAGE. (classic resource available from academic libraries)
Powell, S., (2006) Geert Hofstede: challenges of cultural diversity, Human Resource
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Kirkman, B.L., Lowe, K.B., & Gibson, C.B. (2006). A quarter century of 'Culture's
Consequences': A review of empirical research incorporating Hofstede's cultural values
framework. Journal of International Business Studies, (3). 285.
http://www.pbs.org/ampu/crosscult.html
http://www.colorado.edu/conflict/peace/problem/cultrbar.htm
https://www.gwu.edu/~umpleby/recent_papers/2003_cross_cultural_differences_managin_international_projects_anbari_khilkhanova_romanova_umpleby.htm
http://vlib.excelsior.edu/login?url=http://search.ebscohost.com/login.aspx?direct=true&db=bth&AN=62668126&site=eds-live&scope=site
http://vlib.excelsior.edu/login?url=http://search.ebscohost.com/login.aspx?direct=true&db=bth&AN=62668126&site=eds-live&scope=site
https://vocationalcontent.com.au/using-hofstede-cultural-dimensions-teaching-diversity/
http://www.emeraldinsight.com/author/By+Sarah+Powell%2C+Interview
http://www.emeraldinsight.com/doi/abs/10.1108/09670730610663187
http://www.jstor.org.vlib.excelsior.edu/stable/3875261
http://www.jstor.org.vlib.excelsior.edu/stable/3875261
http://www.jstor.org.vlib.excelsior.edu/stable/3875261
IE 423 page 1 of 1
•••••••••••••••••••••••••••••••••••••••••
IE 423 Engineering OR II
Homework #2
••••••••••••••••••••••••••••••••••••••••
•
Part I. Read Sections #29.5 (Long-run properties of Markov Chains), #29.6 (First Passage
Times) of the attached, and write a summary report.
Note that the summary report has to be prepared on a word processor (e.g., MS Word), and it has
to be submitted through our class canvas system. Your report will be formatted with the
following traits:
The title page should include course title, student name, and the date.
There is no page limit but the article summary should be at least 2 pages long, single spaced
throughout.
Use a standard font (Times New Roman 12).
Use 1 inch margins for top, bottom, left, and right.
Use proper punctuation, spelling, and grammar.
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I am Stuart M. I am a Statistics Assignment Expert at statisticsassignmenthelp.com. I hold a Master in Statistics from, the University of Greenwich, UK. I have been helping students with their Assignments for the past 6 years. I solve assignments related to Statistics.
Visit statisticsassignmenthelp.com or email info@statisticsassignmenthelp.com.
You can also call on +1 678 648 4277 for any assistance with Statistics Assignments.
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All the talks are supported by script codes, in R language.
International Journal of Engineering Inventions (IJEI),
International Journal of Engineering Inventions (IJEI), International Journal of Engineering Inventions www.ijeijournal.com
call for papers, research paper publishing, where to publish research paper, journal publishing, how to publish research paper, Call For research paper, international journal, publishing a paper, IJEI, call for papers 2012,journal of science and technology, how to get a research paper published, publishing a paper, publishing of journal, research and review articles, engineering journal, International Journal of Engineering Inventions, hard copy of journal, hard copy of certificates, journal of engineering, online Submission, where to publish research paper, journal publishing, international journal, publishing a paper, hard copy journal, engineering journalMechanical Engineering Assignment Help
I am Keziah D. I am a Mechanical Engineering Assignment Expert at matlabassignmentexperts.com. I hold a Ph.D. Matlab, University of North Carolina, USA. I have been helping students with their homework for the past 8 years. I solve assignments related to Mechanical Engineering.
Visit matlabassignmentexperts.com or email info@matlabassignmentexperts.com.
You can also call on +1 678 648 4277 for any assistance with Mechanical Engineering Assignments.
International Refereed Journal of Engineering and Science (IRJES)
International Refereed Journal of Engineering and Science (IRJES) is a leading international journal for publication of new ideas, the state of the art research results and fundamental advances in all aspects of Engineering and Science. IRJES is a open access, peer reviewed international journal with a primary objective to provide the academic community and industry for the submission of half of original research and applications
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This document provides an overview of kinematics in one dimension, including graphical representations of motion, motion along a straight line, and motion with constant acceleration. It discusses topics like displacement, velocity, acceleration, and their relationships. Examples are provided to demonstrate calculating variables like position, velocity and acceleration from graphs or equations of motion. Kinematic formulas are also introduced for problems involving constant acceleration.
Problems and solutions statistical physics 1
This document is a physics problem set from MIT's 8.044 Statistical Physics I course in Spring 2004. It contains 5 problems related to statistical physics and probability distributions. Problem 1 considers the probability distribution and properties of the position of a particle undergoing simple harmonic motion. Problem 2 examines the probability distribution of the x-component of angular momentum for a quantum mechanical system. Problem 3 analyzes a mixed probability distribution describing the energy of an electron. Problem 4 involves finding and sketching the time-dependent probability distribution for the position of a particle given its wavefunction. Problem 5 concerns Bose-Einstein statistics and calculating properties of the distribution that describes the number of photons in a given mode.
The history of calculus first draft
- Calculus has its origins in ancient Greece, with mathematicians like Archimedes developing early concepts and methods related to integration through determining areas and volumes.
- In the 17th century, mathematicians like Pierre de Fermat and Isaac Newton independently developed foundational concepts and notations of calculus, such as derivatives, differentials, and rates of change.
- Gottfried Leibniz also made important contributions through developing standard notations and rules still used today, such as dx, dy/dx, and integral notations.
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- Life histories vary along an r-K continuum, with r-selected populations having high reproduction and mortality and K-selected having lower reproduction but higher survival and competition.
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Write down the four (4) nonlinear regression models covered in class,.pdf
Write down the four (4) nonlinear regression models covered in class, i.e. both the name of the
model and their functional form showing their respective regression coefficients. A rapidly
growing bacteria has been discovered with a growth rate as shown in the table. Analyze this date
using a power law model. First linearize the data in the table based on the power law model, call
this new linearized data x and y. Next, determine the coefficients a_0 and a_1 of a linear
regression y = a_0 + a_1x for the linearized power law data x and y, and compute the correlation
coefficient for the liner regression. Note that you are not being asked to do a linear regression of
the data in the table but rather a linear regression of the linearized version of that data. Once you
compute a_0 and a_1 use these to determine the coefficients of the power law model. Write a
Matlab script that uses the polyfit function to determine the regression coefficients of a second
order polynomial fit to data in the table. In the same script, write down the code for using the
polyval command to determine the value of the regression curve at the observed times.
Solution
Nonlinear regression is a statistical technique that helps describe nonlinear relationships in
experimental data. A nonlinear regression model can be written Yn = f(xn, ) + Zn where f is the
expectation function and xn is a vector of associated regressor variables or independent variables
for the nth case.
A nonlinear model is one in which at least one of the parameters appears nonlinearly. More
formally, in a nonlinear model, at least one derivative with respect to a parameter should involve
that parameter. Examples of a nonlinear model are:
Y(t) = exp(at+bt2)
Y(t) = at + exp(-bt).
Important non linear growth models
1.Logistic Model
This model is represented by the differential equation
dN/dt = rN (1-N/K).
Integrating, we get
N(t) = K / [1+(K/No-1) exp(-rt)]
The graph of N(t) versus t is elongated S-shaped and the curve is symmetrical about its point of
inflexion.
2.Malthus Model
If N(t) denotes the population size or biomass at time t and r is the intrinsic growth rate, then the
rate of growth of population size is given by
dN/dt = rN.
Integrating, we get
N(t) = No exp (rt),
where No denotes the population size at t=0. Thus this law entails an exponential increase for
r>0. Furthermore, N(t) à as t à , which cannot happen in reality.
3. Monomolecular Model
This model describes the progress of a growth situation in which it is believed that the rate of
growth at any time is proportional to the resources yet to be achieved, i.e.
dN/dt = r(K-N),
where K is the carrying size of the system. Integrating (3.3), we get
N(t) = K-(K-No) exp (-rt).
4. Richards Model.
This model is given by dN/dt = rN (KN – Nm)/mKm which, on integration, gives N(t )=K N0 /[
N0+ (KN – N0m) exp (-rt)]1/m.
Unlike the earlier models, this model has four parameters
Hours (H)
10
20
40
50
No fo bacteria (N)
25
70
380
550
610
b)
N = b H m
Log10.
probability assignment help (2)
I am Ben R. I am a Statistics Assignment Expert at statisticshomeworkhelper.com. I hold a Ph.D. in Statistics, from University of Denver, USA. I have been helping students with their homework for the past 5 years. I solve assignments related to Statistics.
Visit statisticshomeworkhelper.com or email info@statisticshomeworkhelper.com.
You can also call on +1 678 648 4277 for any assistance with Statistics Assignment.
Phase-Type Distributions for Finite Interacting Particle Systems
Master's Thesis presentation on Phase-Type Distributions for Finite Interacting Particle Systems. Presented June 9, 2020. Gothenburg University.
Project #4 Urban Population Dynamics This project will acquaint y.pdf
Project #4: Urban Population Dynamics This project will acquaint you with population
modeling and how linear algebra tools may be used to study it. Background Kolman, pages
305-307. Population modeling is useful from many different perspectives: planners at the city,
state, and national level who look at human populations and need forecasts of populations in
order to do planning for future needs. These future needs include housing, schools, care for the
elderly, jobs, and utilities such as electricity,water and transportation. businesses do population
planning so as to predict how the portions of the population that use their product will be
changing. Ecologists use population models to study ecological systems, especially those where
endangered species are involved so as to try to find measures that will restore the population.
medical researchers treat microorganisms and viruses as populations and seek to understand the
dynamics of their populations; especially why some thrive in certain environments but don\'t in
others. In human situations, it is normal to take intervals of 10 years as the census is taken every
10 years. Thus the age groups would be 0-9,10-19,11-20 etc , so 8 or 9 age categories would
probably be appropriate. The survival fractions would then show the fraction of \"newborns\" (0-
9) who survive to age 10, the fraction of 10 to 19 year olds who survive to 20 etc. This type of
data is compiled, for example, by actuaries working for insurance companies for life and medical
insurance purposes. The basic equations we begin with are (1) x(k+1) = Ax(k) k=0,1,2,. . . and
x(0) given with solution found iteratively to be (2) x(k) = Akx(0) (see Kolman for details of the
structure of A, which is 7 x 7 in this case). Your Project Suppose we are studying the
population dynamics of Los Angeles for the purpose of making a planning proposal to the city
which will form the basis for predicting school, transportation, housing, water, and electrical
needs for the years from 2000 on. As above, we take the unit of time to be 10 years, and take 7
age groups: 0-9,10-19,...,50-59,60+. Suppose further that the population distribution as of 1990
(the last census) is (3.1, 2.8, 2.0, 2.5, 2.0, 1.8, 2.9) (x105 ) and that the Leslie matrix,A, for this
model appears as Part One: Interpret carefully each of the nonzero terms in the matrix. In
addition, indicate what factors you think might change those numbers (they might be social,
economical, political or environmental). Part Two: Predict: what the population distribution
will look like in 2000, 2010, 2020 and 2030 what the total population will be in each of those
years by what fraction the total population changed each year Additionally, what does your
software tell you the largest, positive eigenvalue of A is? Part Three: Decide if you believe the
population is going to zero, becoming stable, or is unstable in the long run. Be sure and describe
in your write up how you arrived at your conclusion. If.
Week 7
This document discusses implicit differentiation and exponential growth and decay models. It contains:
1) An example of using implicit differentiation to find the derivative of a circle equation and the equation of the tangent line.
2) An explanation of how exponential growth and decay models take the form of y' = ky, leading to solutions of y = Ce^kt where k is the constant relative growth or decay rate.
3) An example modeling world population growth from 1950-2020 using an exponential growth model that estimates the 1993 population and predicts the 2020 population.
Ss important questions
1. The document provides a list of 2 mark questions and answers related to the Signals and Systems subject for the 3rd semester IT students.
2. It includes definitions of key terms like signal, system, different types of signals and their classifications. Properties of Fourier series and Fourier transforms are also covered.
3. The questions address topics ranging from periodic/aperiodic signals, even/odd signals, unit step and impulse functions, Fourier series, Fourier transforms, Laplace transforms, linear and time invariant systems.
Assignment Support Resources (ASR) 4. Diverse Cultures Res.docx
Assignment Support Resources (ASR)
4. Diverse Cultures Resources
GENERAL RESOURCES
Public Broadcasting Service: Patterns of cultural differences
University of Colorado: Cultural barriers to Effective Communication
George Washington University: Differences affecting international teams
HOFSTEDE CONCEPTS
Boonghee, Y., Donthu, N., & Lenartowicz, T. (2011). Measuring Hofstede's five dimensions of
cultural values at the individual level: Development and validation of CVSCALE. Journal Of
International Consumer Marketing, 23(3/4), 193-210. doi:10.1080/08961530.2011.578059
Christley, J. (n.d.). Cultural dimensions for teaching diversity.
Hofstede, G. (2001). Culture's consequences: Comparing values, behaviors, institutions, and organizations across nations
(2nd ed.). Thousand Oaks, CA: SAGE. (classic resource available from academic libraries)
Powell, S., (2006) Geert Hofstede: challenges of cultural diversity, Human Resource
Management International Digest, 14(3), 12 – 15. (interview)
Kirkman, B.L., Lowe, K.B., & Gibson, C.B. (2006). A quarter century of 'Culture's
Consequences': A review of empirical research incorporating Hofstede's cultural values
framework. Journal of International Business Studies, (3). 285.
http://www.pbs.org/ampu/crosscult.html
http://www.colorado.edu/conflict/peace/problem/cultrbar.htm
https://www.gwu.edu/~umpleby/recent_papers/2003_cross_cultural_differences_managin_international_projects_anbari_khilkhanova_romanova_umpleby.htm
http://vlib.excelsior.edu/login?url=http://search.ebscohost.com/login.aspx?direct=true&db=bth&AN=62668126&site=eds-live&scope=site
http://vlib.excelsior.edu/login?url=http://search.ebscohost.com/login.aspx?direct=true&db=bth&AN=62668126&site=eds-live&scope=site
https://vocationalcontent.com.au/using-hofstede-cultural-dimensions-teaching-diversity/
http://www.emeraldinsight.com/author/By+Sarah+Powell%2C+Interview
http://www.emeraldinsight.com/doi/abs/10.1108/09670730610663187
http://www.jstor.org.vlib.excelsior.edu/stable/3875261
http://www.jstor.org.vlib.excelsior.edu/stable/3875261
http://www.jstor.org.vlib.excelsior.edu/stable/3875261
IE 423 page 1 of 1
•••••••••••••••••••••••••••••••••••••••••
IE 423 Engineering OR II
Homework #2
••••••••••••••••••••••••••••••••••••••••
•
Part I. Read Sections #29.5 (Long-run properties of Markov Chains), #29.6 (First Passage
Times) of the attached, and write a summary report.
Note that the summary report has to be prepared on a word processor (e.g., MS Word), and it has
to be submitted through our class canvas system. Your report will be formatted with the
following traits:
The title page should include course title, student name, and the date.
There is no page limit but the article summary should be at least 2 pages long, single spaced
throughout.
Use a standard font (Times New Roman 12).
Use 1 inch margins for top, bottom, left, and right.
Use proper punctuation, spelling, and grammar.
Statistics Assignment Help
I am Stuart M. I am a Statistics Assignment Expert at statisticsassignmenthelp.com. I hold a Master in Statistics from, the University of Greenwich, UK. I have been helping students with their Assignments for the past 6 years. I solve assignments related to Statistics.
Visit statisticsassignmenthelp.com or email info@statisticsassignmenthelp.com.
You can also call on +1 678 648 4277 for any assistance with Statistics Assignments.
Talk 5
This 10 hours class is intended to give students the basis to empirically solve statistical problems. Talk 1 serves as an introduction to the statistical software R, and presents how to calculate basic measures such as mean, variance, correlation and gini index. Talk 2 shows how the central limit theorem and the law of the large numbers work empirically. Talk 3 presents the point estimate, the confidence interval and the hypothesis test for the most important parameters. Talk 4 introduces to the linear regression model and Talk 5 to the bootstrap world. Talk 5 also presents an easy example of a markov chains.
All the talks are supported by script codes, in R language.
International Journal of Engineering Inventions (IJEI),
International Journal of Engineering Inventions (IJEI), International Journal of Engineering Inventions www.ijeijournal.com
call for papers, research paper publishing, where to publish research paper, journal publishing, how to publish research paper, Call For research paper, international journal, publishing a paper, IJEI, call for papers 2012,journal of science and technology, how to get a research paper published, publishing a paper, publishing of journal, research and review articles, engineering journal, International Journal of Engineering Inventions, hard copy of journal, hard copy of certificates, journal of engineering, online Submission, where to publish research paper, journal publishing, international journal, publishing a paper, hard copy journal, engineering journalMechanical Engineering Assignment Help
I am Keziah D. I am a Mechanical Engineering Assignment Expert at matlabassignmentexperts.com. I hold a Ph.D. Matlab, University of North Carolina, USA. I have been helping students with their homework for the past 8 years. I solve assignments related to Mechanical Engineering.
Visit matlabassignmentexperts.com or email info@matlabassignmentexperts.com.
You can also call on +1 678 648 4277 for any assistance with Mechanical Engineering Assignments.
International Refereed Journal of Engineering and Science (IRJES)
International Refereed Journal of Engineering and Science (IRJES) is a leading international journal for publication of new ideas, the state of the art research results and fundamental advances in all aspects of Engineering and Science. IRJES is a open access, peer reviewed international journal with a primary objective to provide the academic community and industry for the submission of half of original research and applications
GEN PHYSICS 1 WEEK 2 KINEMATICS IN ONE DIMENSION.pptx
This document provides an overview of kinematics in one dimension, including graphical representations of motion, motion along a straight line, and motion with constant acceleration. It discusses topics like displacement, velocity, acceleration, and their relationships. Examples are provided to demonstrate calculating variables like position, velocity and acceleration from graphs or equations of motion. Kinematic formulas are also introduced for problems involving constant acceleration.
Problems and solutions statistical physics 1
This document is a physics problem set from MIT's 8.044 Statistical Physics I course in Spring 2004. It contains 5 problems related to statistical physics and probability distributions. Problem 1 considers the probability distribution and properties of the position of a particle undergoing simple harmonic motion. Problem 2 examines the probability distribution of the x-component of angular momentum for a quantum mechanical system. Problem 3 analyzes a mixed probability distribution describing the energy of an electron. Problem 4 involves finding and sketching the time-dependent probability distribution for the position of a particle given its wavefunction. Problem 5 concerns Bose-Einstein statistics and calculating properties of the distribution that describes the number of photons in a given mode.
The history of calculus first draft
- Calculus has its origins in ancient Greece, with mathematicians like Archimedes developing early concepts and methods related to integration through determining areas and volumes.
- In the 17th century, mathematicians like Pierre de Fermat and Isaac Newton independently developed foundational concepts and notations of calculus, such as derivatives, differentials, and rates of change.
- Gottfried Leibniz also made important contributions through developing standard notations and rules still used today, such as dx, dy/dx, and integral notations.
14 (2013).pptx
Population ecology studies how organism numbers change over time and space and the factors influencing these changes. Key concepts include:
- Populations are groups of the same species in a defined area, with measures including population density and dispersion patterns.
- Populations can grow exponentially if birth and death rates remain constant, but density dependence causes logistic/sigmoidal growth towards an equilibrium carrying capacity K.
- Life histories vary along an r-K continuum, with r-selected populations having high reproduction and mortality and K-selected having lower reproduction but higher survival and competition.
- Capture-recapture methods can estimate unknown population sizes using marked and recaptured individuals.
Lesson 5: Tangents, Velocity, the Derivative
Many problems in science are about rates of change. They boil down to the mathematical question of finding the slope of a line tangent to a curve. We state this quantity as a limit and give it a name: the derivative
Stochastic Processes - part 5
"stochastic Processes" graduate course.
Lecture notes of Prof. H.Amindavar.
Professor of Electrical engineering at Amirkabir university of technology.
Introduction to Bootstrap and elements of Markov Chains
This document provides an introduction to bootstrap methods and Markov chains. It discusses how bootstrap can be used to estimate properties of a statistic like mean or variance when the sample is small and assumptions of the central limit theorem may not apply. The basic bootstrap approach resamples the original sample with replacement to create new bootstrap samples and estimates the statistic for each. Markov chains are defined as stochastic processes where the next state only depends on the current state. An example of a 2-state Markov chain is provided along with notation for transition probabilities and computing unconditional probabilities. The document also discusses stationary distributions for Markov chains.
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roex.pptx
- 1. Mathematical functions : Differentiation is a process of looking at the way of function changes from one point to another. In particular ,it measures how rapidly a function is changing at an point. Differentiation is a method of finding the derivative of a function. Differentiation is a process in maths ,where we find one instantaneous rate of change in function based on one of it’s variabels. values of particular functions
- 2. ANALYSIS : We consider the growth of a population (for example, human, an animal, or a bacteria colony) as a function of time t. Let x (t) be the size of the population at any time t . Assume that population grows at a rate directly proportional to the amount of population present at that time. Then, we obtain dx/dt = k(x), Solution of the differential equation is x(t)=Ce^kt, where C is a constant of integration. The values of C and k are determined with the help of initial conditions. Thus, the population increases exponentially with time.
- 3. CALCULATION : The growth of a population is proportional to the number present. If the population of a colony doubles in 30 years, in how many years will the population become triple? Solution : Let x(t) be the population at time t . Then dx/dt = kx. By separating the variables, we obtain dx/x = kdt. Integrating on both sides, we get, log |x| = kt + log |C| or x = Ce^kt, where C is an arbitrary constant. Let x0 be the population when t = 0 and obtain C = x0 . Thus, we get x = x0e^kt Now x = 2x0 , when t = 30 and thus, k = 1/30(log 2). Hence, x = x0 2^(t/30) is the population at any time t. Assume that the population is tripled in t1 years. That is, x = 3x0 , when t = t1 . Thus, t1= 30 (log3/log2). Therefore, the population is tripled in 30 (log3/log2) year. (or) 47.5 years.
- 4. RESULT AND DISCUSSION: The subject of differential equations has vast applications in solving real world problems. The solutions of the differential equations are used to predict the behaviours of the system at a future time, or at an unknown location. So differentiation is use to predict the future population of particular area.
- 5. ADVANTAGES Able to predict the future population our country using python program and determine the time of death. This project can help to measure and manage population growth in the current world setup. DISADVANTAGES It is only for the prediction not for exact solution.It is hard to predict the future population and time consuming.
- 6. CONCLUSION : Using the techniques above I have been able to predict the population size of our country. some of the method displayed above to improve their social and economic status.