Differential Equations Lecture: Non-Homogeneous Linear Differential Equationsbullardcr
A lecture I presented in Differential Equations, Spring 2006. This was supplemented with a hands-on solution to a random problem with variables designated by students in the class.
Differential Equations Lecture: Non-Homogeneous Linear Differential Equationsbullardcr
A lecture I presented in Differential Equations, Spring 2006. This was supplemented with a hands-on solution to a random problem with variables designated by students in the class.
These slides contain information about Euler method,Improved Euler and Runge-kutta's method.How these methods are helpful and applied to our questions are detailed discussed in the slides.
It is the adder used to eliminate the wastage of time occur at each stage of parallel binary adder.In this , by using only carry input signal , we can calculate the the carry output without going to calculate carry at each stage.it is commonly used only for 4 bit addition because further calculation will be more complex.
These slides contain information about Euler method,Improved Euler and Runge-kutta's method.How these methods are helpful and applied to our questions are detailed discussed in the slides.
It is the adder used to eliminate the wastage of time occur at each stage of parallel binary adder.In this , by using only carry input signal , we can calculate the the carry output without going to calculate carry at each stage.it is commonly used only for 4 bit addition because further calculation will be more complex.
AN ALTERNATIVE APPROACH FOR SELECTION OF PSEUDO RANDOM NUMBERS FOR ONLINE EXA...cscpconf
Fast and accurate selection of random pattern is needed for many scientific and commercial applications. One of the major applications is Online Examination system. In this paper, a sophisticated approach has been developed for the selection of uniform pseudo random pattern for Online Examination System. Three random integer generators have been compared for this
purpose. Most commonly used procedural language based pseudo random number; PHP random generator and atmospheric noise based true random number generator have been considered for easy generation of random patterns. The test result shows a varying degree of improvement in the quality of randomness of the generated patterns. The randomness quality of the generated pseudo random pattern has been assured by diehard test suite. An experimental
outcome for our recommended approach signifies that our approach selects a quality set of random pattern for Online Examination System
PPT on testing for randomness of numbers by using different tests like chi square test and chi autocorrelation test.
It aslo includes Komogrov Simrov test and other important topics of these.
It includes different methods to generate random numvers like
1. Mid square random number genetrator
2. Residue method
3. Arithmetic Congruetial Generator
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Parameter Estimation for Semiparametric Models with CMARS and Its ApplicationsSSA KPI
AACIMP 2010 Summer School lecture by Gerhard Wilhelm Weber. "Applied Mathematics" stream. "Modern Operational Research and Its Mathematical Methods with a Focus on Financial Mathematics" course. Part 11.
More info at http://summerschool.ssa.org.ua
Similar to MT6702 Unit 2 Random Number Generation (20)
Industrial Training at Shahjalal Fertilizer Company Limited (SFCL)MdTanvirMahtab2
This presentation is about the working procedure of Shahjalal Fertilizer Company Limited (SFCL). A Govt. owned Company of Bangladesh Chemical Industries Corporation under Ministry of Industries.
Final project report on grocery store management system..pdfKamal Acharya
In today’s fast-changing business environment, it’s extremely important to be able to respond to client needs in the most effective and timely manner. If your customers wish to see your business online and have instant access to your products or services.
Online Grocery Store is an e-commerce website, which retails various grocery products. This project allows viewing various products available enables registered users to purchase desired products instantly using Paytm, UPI payment processor (Instant Pay) and also can place order by using Cash on Delivery (Pay Later) option. This project provides an easy access to Administrators and Managers to view orders placed using Pay Later and Instant Pay options.
In order to develop an e-commerce website, a number of Technologies must be studied and understood. These include multi-tiered architecture, server and client-side scripting techniques, implementation technologies, programming language (such as PHP, HTML, CSS, JavaScript) and MySQL relational databases. This is a project with the objective to develop a basic website where a consumer is provided with a shopping cart website and also to know about the technologies used to develop such a website.
This document will discuss each of the underlying technologies to create and implement an e- commerce website.
Hybrid optimization of pumped hydro system and solar- Engr. Abdul-Azeez.pdffxintegritypublishin
Advancements in technology unveil a myriad of electrical and electronic breakthroughs geared towards efficiently harnessing limited resources to meet human energy demands. The optimization of hybrid solar PV panels and pumped hydro energy supply systems plays a pivotal role in utilizing natural resources effectively. This initiative not only benefits humanity but also fosters environmental sustainability. The study investigated the design optimization of these hybrid systems, focusing on understanding solar radiation patterns, identifying geographical influences on solar radiation, formulating a mathematical model for system optimization, and determining the optimal configuration of PV panels and pumped hydro storage. Through a comparative analysis approach and eight weeks of data collection, the study addressed key research questions related to solar radiation patterns and optimal system design. The findings highlighted regions with heightened solar radiation levels, showcasing substantial potential for power generation and emphasizing the system's efficiency. Optimizing system design significantly boosted power generation, promoted renewable energy utilization, and enhanced energy storage capacity. The study underscored the benefits of optimizing hybrid solar PV panels and pumped hydro energy supply systems for sustainable energy usage. Optimizing the design of solar PV panels and pumped hydro energy supply systems as examined across diverse climatic conditions in a developing country, not only enhances power generation but also improves the integration of renewable energy sources and boosts energy storage capacities, particularly beneficial for less economically prosperous regions. Additionally, the study provides valuable insights for advancing energy research in economically viable areas. Recommendations included conducting site-specific assessments, utilizing advanced modeling tools, implementing regular maintenance protocols, and enhancing communication among system components.
Saudi Arabia stands as a titan in the global energy landscape, renowned for its abundant oil and gas resources. It's the largest exporter of petroleum and holds some of the world's most significant reserves. Let's delve into the top 10 oil and gas projects shaping Saudi Arabia's energy future in 2024.
CFD Simulation of By-pass Flow in a HRSG module by R&R Consult.pptxR&R Consult
CFD analysis is incredibly effective at solving mysteries and improving the performance of complex systems!
Here's a great example: At a large natural gas-fired power plant, where they use waste heat to generate steam and energy, they were puzzled that their boiler wasn't producing as much steam as expected.
R&R and Tetra Engineering Group Inc. were asked to solve the issue with reduced steam production.
An inspection had shown that a significant amount of hot flue gas was bypassing the boiler tubes, where the heat was supposed to be transferred.
R&R Consult conducted a CFD analysis, which revealed that 6.3% of the flue gas was bypassing the boiler tubes without transferring heat. The analysis also showed that the flue gas was instead being directed along the sides of the boiler and between the modules that were supposed to capture the heat. This was the cause of the reduced performance.
Based on our results, Tetra Engineering installed covering plates to reduce the bypass flow. This improved the boiler's performance and increased electricity production.
It is always satisfying when we can help solve complex challenges like this. Do your systems also need a check-up or optimization? Give us a call!
Work done in cooperation with James Malloy and David Moelling from Tetra Engineering.
More examples of our work https://www.r-r-consult.dk/en/cases-en/
About
Indigenized remote control interface card suitable for MAFI system CCR equipment. Compatible for IDM8000 CCR. Backplane mounted serial and TCP/Ethernet communication module for CCR remote access. IDM 8000 CCR remote control on serial and TCP protocol.
• Remote control: Parallel or serial interface.
• Compatible with MAFI CCR system.
• Compatible with IDM8000 CCR.
• Compatible with Backplane mount serial communication.
• Compatible with commercial and Defence aviation CCR system.
• Remote control system for accessing CCR and allied system over serial or TCP.
• Indigenized local Support/presence in India.
• Easy in configuration using DIP switches.
Technical Specifications
Indigenized remote control interface card suitable for MAFI system CCR equipment. Compatible for IDM8000 CCR. Backplane mounted serial and TCP/Ethernet communication module for CCR remote access. IDM 8000 CCR remote control on serial and TCP protocol.
Key Features
Indigenized remote control interface card suitable for MAFI system CCR equipment. Compatible for IDM8000 CCR. Backplane mounted serial and TCP/Ethernet communication module for CCR remote access. IDM 8000 CCR remote control on serial and TCP protocol.
• Remote control: Parallel or serial interface
• Compatible with MAFI CCR system
• Copatiable with IDM8000 CCR
• Compatible with Backplane mount serial communication.
• Compatible with commercial and Defence aviation CCR system.
• Remote control system for accessing CCR and allied system over serial or TCP.
• Indigenized local Support/presence in India.
Application
• Remote control: Parallel or serial interface.
• Compatible with MAFI CCR system.
• Compatible with IDM8000 CCR.
• Compatible with Backplane mount serial communication.
• Compatible with commercial and Defence aviation CCR system.
• Remote control system for accessing CCR and allied system over serial or TCP.
• Indigenized local Support/presence in India.
• Easy in configuration using DIP switches.
Overview of the fundamental roles in Hydropower generation and the components involved in wider Electrical Engineering.
This paper presents the design and construction of hydroelectric dams from the hydrologist’s survey of the valley before construction, all aspects and involved disciplines, fluid dynamics, structural engineering, generation and mains frequency regulation to the very transmission of power through the network in the United Kingdom.
Author: Robbie Edward Sayers
Collaborators and co editors: Charlie Sims and Connor Healey.
(C) 2024 Robbie E. Sayers
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2. INTRODUCTION
• Random numbers are a necessary basic ingredient in
the simulation of almost all discrete systems.
• Most computer languages have a subroutine, object,
or function that will generate a random number.
• Random numbers that are used to generate event
times and other random variables.
3. Properties of Random Numbers
• A sequence of random numbers, R1, R2... must
have two important statistical properties,
uniformity and independence.
• Each random number Ri, is an independent
sample drawn from a continuous uniform
distribution between 0 and 1.
4. Properties of Random Numbers
• That is, the pdf is given by
• The density function is shown below:
5. Properties of Random Numbers
• Some consequences of the uniformity and independence
properties are :
1. If the interval (0, 1) is divided into n classes, or
subintervals of equal length, the expected number of
observations m each interval is N/n where N is the total
number of observations.
2. The probability of observing a value in a particular
interval is independent of the previous values drawn.
6. Generation of Pseudo-Random Numbers
• Pseudo means false, so false random numbers
are being generated.
• The goal of any generation scheme, is to produce
a sequence of numbers between zero and 1
• Which simulates, or initiates, the ideal properties
of uniform distribution and independence as
closely as possible.
7. Generation of Pseudo-Random Numbers
• When generating pseudo-random numbers,
certain problems or errors can occur.
• These errors, or departures from ideal
randomness, are all related to the properties
stated previously.
• Some examples include the following
8. Generation of Pseudo-Random Numbers
1) The generated numbers may not be uniformly
distributed.
2) The generated numbers may be discrete -valued instead
continuous valued.
3) The mean of the generated numbers may be too high or
too low.
4) The variance of the generated numbers may be too high
or low.
9. Considerations in RN routine
• The routine should be fast
• The routine should be portable
• The routine should have a sufficiently long cycle
• The random numbers should be replicable.
• Random numbers should closely approximate the
ideal statistical properties of uniformity and
independences
10. Techniques for Generating Random Numbers
The linear congruential method
• It widely used technique, initially proposed by
Lehmer [1951]
• It produces a sequence of integers, X1, X2,...
Between zero and m — 1 according to the following
recursive relationship:
Xi+1 = (aXi + c) mod m, i = 0, 1, 2....
11. The linear congruential method
• If c ≠ 0then the form is called mixed congruential
method.
• When c = 0, the form is known as the multiplicative
congruential method.
• The selection of the values for a, c, m and X0
drastically affects the statistical properties and the
cycle length.
12. Multiplicative Congruential Method:
• Most natural choice for m is one that equals to the
capacity of a computer word.
• m = 2b (binary machine), where b is the number of bits in
the computer word.
• m = 10d (decimal machine), where d is the number of
digits in the computer word.
Xi+1 = a Xi (mod m), where a ≥ 0 and m ≥ 0 …
13. Tests For Random Numbers
1. Frequency test. Uses the Kolmogorov-Smirnov or the
chi-square test to compare the distribution of the set
of numbers generated to a uniform distribution.
2. Runs test. Tests the runs up and down or the runs
above and below the mean by comparing the actual
values to expected values. The statistic for
comparison is the chi-square.
14. Tests For Random Numbers
3. Autocorrelation test. Tests the correlation between
numbers and compares the sample correlation to the
expected correlation of zero.
4. Gap test. Counts the number of digits that appear
between repetitions of a particular digit and then
uses the Kolmogorov-Smirnov test to compare with
the expected number of gaps.
15. Tests For Random Numbers
5. Poker test. Treats numbers grouped together as a
poker hand. Then the hands obtained are compared
to what is expected using the chi-square test.
• In testing for uniformity, the hypotheses are as
follows:
H0: Ri ~ U[0,1]
H1: Ri ɫ U[0,1]
16. Tests For Random Numbers
• The null hypothesis, H0, reads that the numbers are
distributed uniformly on the interval [0, 1].
• In testing for independence, the hypotheses are as
follows
H0: Ri ~ independently
H1: Ri ɫ independently
17. Frequency Tests
• To validate a new generator is the test of uniformity.
• Two types - Kolmogorov-Smirnov and Chi-square test.
• Both measure the degree of agreement between the
distribution of a sample of generated random numbers and
the theoretical uniform distribution.
• Both tests are on the null hypothesis of no significant
difference between the sample distribution and the
theoretical distribution.
19. The Kolmogorov-Smirnov test
• Suppose that the five numbers 0.44, 0.81,
0.14, 0.05, 0.93 were generated, and it is
desired to perform a test for uniformity using
the Kolmogorov-Smirnov test with a level of
significance of 0.05.
20. Chi-Square Test
Use the chi-square test with level of significance 0.05 to
test whether the data shown below are uniformly
distributed. The test uses n = 10 intervals of equal length
23. Run Test
Based on runs up and runs down, determine whether the
following sequence of 40 numbers is such that the hypothesis
of independence can be rejected where a = 0.05.