What is interpolation?
How to interpolate a polynomial through a given set of data?
General approach, Newton method, Lagrange method
#WikiCourses
https://wikicourses.wikispaces.com/Topic+Interpolation
In this lecture, we will discuss:
Functions of one variable
Functions of SeveraL VariabLes
Limits for Functions of Two Variables
Partial Derivatives of a Function of Two Variables
It introduces the reader to the basic concepts behind regression - a key advanced analytics theory. It describes simple and multiple linear regression in detail. It also talks about some limitations of linear regression as well. Logistic regression is just touched upon, but not delved deeper into this presentation.
This is the entrance exam paper for ISI MSQE Entrance Exam for the year 2006. Much more information on the ISI MSQE Entrance Exam and ISI MSQE Entrance preparation help available on http://crackdse.com
What is interpolation?
How to interpolate a polynomial through a given set of data?
General approach, Newton method, Lagrange method
#WikiCourses
https://wikicourses.wikispaces.com/Topic+Interpolation
In this lecture, we will discuss:
Functions of one variable
Functions of SeveraL VariabLes
Limits for Functions of Two Variables
Partial Derivatives of a Function of Two Variables
It introduces the reader to the basic concepts behind regression - a key advanced analytics theory. It describes simple and multiple linear regression in detail. It also talks about some limitations of linear regression as well. Logistic regression is just touched upon, but not delved deeper into this presentation.
This is the entrance exam paper for ISI MSQE Entrance Exam for the year 2006. Much more information on the ISI MSQE Entrance Exam and ISI MSQE Entrance preparation help available on http://crackdse.com
INDIAN STATISTICAL INSTITUTE OF ECONOMICS/ ME 2004 ECONOMICS DETAILED SOLUTIONS SERIES/ REQUIRES THOROUGH KNOWLEDGE/ LOGIC/ TRICKY QUESTIONS /WIDE RANGE OF VARIETY
Optimization: from mathematical tools to real applicationsPhilippe Laborie
The existence of powerful mathematical optimization engines is a necessary but not a sufficient condition for the pervasion of optimization technologies in the real world. This seminar, presented in 2013, explores some of the challenges related with the development of optimization applications as well as some general guidelines to avoid common pitfalls. It is illustrated with IBM ILOG optimization technologies and solutions.
MSC ENTRANCE IN ECONOMICS FOR ISI MSQE , JNU, DSE, IGIDR, MSE, TISS TUITION C...SOURAV DAS
MSC ENTRANCE IN ECONOMICS FOR ISI, JNU, DSE, IGIDR, MSE, TISS CLASS IN
REGULAR MOCK TESTS AND AFTER MOCK TESTS SOLUTIONS OF THE PAPERS WILL ALSO BE PROVIDED.
SPECIAL CLASSES FOR MATHEMATICS, MAMATHEMATICAL ECONOMICS , STATISTICS ECONOMETRICS AND MATHEMATICS.
SOLUTION OF ALL PREVIOUS YEAR QUESTION PAPERS OF RESPECTIVE EXAMINATIONS.
LIBRARY ACCESS. STUDY MATERIALS.
EXTRA DOUBT CLEARING CLASSES.
FOR ANY FURTHER DETAILS
*CONTACT:
SOURAV SIR'S CLASSES
Discuss and apply comprehensively the concepts, properties and theorems of functions, limits, continuity and the derivatives in determining the derivatives of algebraic functions
Principle of Definite Integra - Integral Calculus - by Arun Umraossuserd6b1fd
Definite integral notes. Best for quick preparation. Easy to understand and colored graphics. Step by step description. Suitable for CBSE board and State Board students in Class XI & XII
Integration Made Easy!
The derivative of a function can be geometrically interpreted as the slope of the curve of the mathematical function f(x) plotted as a function of x. But its implications for the modeling of nature go far deeper than this simple geometric application might imply. After all, you can see yourself drawing finite triangles to discover slope, so why is the derivative so important? Its importance lies in the fact that many physical entities such as velocity, acceleration, force and so on are defined as instantaneous rates of change of some other quantity. The derivative can give you a precise intantaneous value for that rate of change and lead to precise modeling of the desired quantity.
Mathematics (from Greek μάθημα máthēma, “knowledge, study, learning”) is the study of topics such as quantity (numbers), structure, space, and change. There is a range of views among mathematicians and philosophers as to the exact scope and definition of mathematics
Hierarchical Digital Twin of a Naval Power SystemKerry Sado
A hierarchical digital twin of a Naval DC power system has been developed and experimentally verified. Similar to other state-of-the-art digital twins, this technology creates a digital replica of the physical system executed in real-time or faster, which can modify hardware controls. However, its advantage stems from distributing computational efforts by utilizing a hierarchical structure composed of lower-level digital twin blocks and a higher-level system digital twin. Each digital twin block is associated with a physical subsystem of the hardware and communicates with a singular system digital twin, which creates a system-level response. By extracting information from each level of the hierarchy, power system controls of the hardware were reconfigured autonomously. This hierarchical digital twin development offers several advantages over other digital twins, particularly in the field of naval power systems. The hierarchical structure allows for greater computational efficiency and scalability while the ability to autonomously reconfigure hardware controls offers increased flexibility and responsiveness. The hierarchical decomposition and models utilized were well aligned with the physical twin, as indicated by the maximum deviations between the developed digital twin hierarchy and the hardware.
Sachpazis:Terzaghi Bearing Capacity Estimation in simple terms with Calculati...Dr.Costas Sachpazis
Terzaghi's soil bearing capacity theory, developed by Karl Terzaghi, is a fundamental principle in geotechnical engineering used to determine the bearing capacity of shallow foundations. This theory provides a method to calculate the ultimate bearing capacity of soil, which is the maximum load per unit area that the soil can support without undergoing shear failure. The Calculation HTML Code included.
Cosmetic shop management system project report.pdfKamal Acharya
Buying new cosmetic products is difficult. It can even be scary for those who have sensitive skin and are prone to skin trouble. The information needed to alleviate this problem is on the back of each product, but it's thought to interpret those ingredient lists unless you have a background in chemistry.
Instead of buying and hoping for the best, we can use data science to help us predict which products may be good fits for us. It includes various function programs to do the above mentioned tasks.
Data file handling has been effectively used in the program.
The automated cosmetic shop management system should deal with the automation of general workflow and administration process of the shop. The main processes of the system focus on customer's request where the system is able to search the most appropriate products and deliver it to the customers. It should help the employees to quickly identify the list of cosmetic product that have reached the minimum quantity and also keep a track of expired date for each cosmetic product. It should help the employees to find the rack number in which the product is placed.It is also Faster and more efficient way.
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.
Immunizing Image Classifiers Against Localized Adversary Attacksgerogepatton
This paper addresses the vulnerability of deep learning models, particularly convolutional neural networks
(CNN)s, to adversarial attacks and presents a proactive training technique designed to counter them. We
introduce a novel volumization algorithm, which transforms 2D images into 3D volumetric representations.
When combined with 3D convolution and deep curriculum learning optimization (CLO), itsignificantly improves
the immunity of models against localized universal attacks by up to 40%. We evaluate our proposed approach
using contemporary CNN architectures and the modified Canadian Institute for Advanced Research (CIFAR-10
and CIFAR-100) and ImageNet Large Scale Visual Recognition Challenge (ILSVRC12) datasets, showcasing
accuracy improvements over previous techniques. The results indicate that the combination of the volumetric
input and curriculum learning holds significant promise for mitigating adversarial attacks without necessitating
adversary training.
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.
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
Water scarcity is the lack of fresh water resources to meet the standard water demand. There are two type of water scarcity. One is physical. The other is economic water scarcity.
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.
Top 10 Oil and Gas Projects in Saudi Arabia 2024.pdf
Numerical analysis convexity, concavity
1. D Nagesh Kumar, IISc Optimization Methods: M2L21
Optimization using Calculus
Convexity and Concavity
of Functions of One and
Two Variables
2. D Nagesh Kumar, IISc Optimization Methods: M2L22
Objective
To determine the convexity and concavity of functions
3. D Nagesh Kumar, IISc Optimization Methods: M2L23
Convex Function (Function of one variable)
A real-valued function f defined on an interval (or on any convex subset
C of some vector space) is called convex, if for any two points x and y in
its domain C and any t in [0,1], we have
In other words, a function is convex if and only if its epigraph (the set of
points lying on or above the graph) is a convex set. A function is also said
to be strictly convex if
for any t in (0,1) and a line connecting any two points on the function lies
completely above the function.
( (1 ) ) ( ) (1 ) ( ))f ta t b tf a t f b+ − ≤ + −
( (1 ) ) ( ) (1 ) ( )f ta t b tf a t f b+ − < + −
4. D Nagesh Kumar, IISc Optimization Methods: M2L24
A convex function
5. D Nagesh Kumar, IISc Optimization Methods: M2L25
Testing for convexity of a single variable
function
A function is convex if its slope is non decreasing or
0. It is strictly convex if its slope is continually
increasing or 0 throughout the function.
2 2
/f x∂ ∂ ≥
2 2
/f x∂ ∂ >
6. D Nagesh Kumar, IISc Optimization Methods: M2L26
Properties of convex functions
A convex function f, defined on some convex open interval C, is
continuous on C and differentiable at all or at many points. If C is
closed, then f may fail to be continuous at the end points of C.
A continuous function on an interval C is convex if and only if
for all a and b in C.
• A differentiable function of one variable is convex on an interval if
and only if its derivative is monotonically non-decreasing on that
interval.
( ) ( )
2 2
a b f a f b
f
+ +⎛ ⎞
≤⎜ ⎟
⎝ ⎠
7. D Nagesh Kumar, IISc Optimization Methods: M2L27
Properties of convex functions (contd.)
A continuously differentiable function of one variable is convex on an
interval if and only if the function lies above all of its tangents: for all a
and b in the interval.
A twice differentiable function of one variable is convex on an interval if
and only if its second derivative is non-negative in that interval; this
gives a practical test for convexity.
More generally, a continuous, twice differentiable function of several
variables is convex on a convex set if and only if its Hessian matrix is
positive semi definite on the interior of the convex set.
If two functions f and g are convex, then so is any weighted combination
af + b g with non-negative coefficients a and b. Likewise, if f and g are
convex, then the function max{f, g} is convex.
8. D Nagesh Kumar, IISc Optimization Methods: M2L28
Concave function (function of one variable)
A differentiable function f is concave on an interval if its derivative
function f ′ is decreasing on that interval: a concave function has a
decreasing slope.
A function f(x) is said to be concave on an interval if, for all a and b
in that interval,
Additionally, f(x) is strictly concave if
[0,1], ( (1 ) ) ( ) (1 ) ( )t f ta t b tf a t f b∀ ∈ + − ≥ + −
[0,1], ( (1 ) ) ( ) (1 ) ( )t f ta t b tf a t f b∀ ∈ + − > + −
9. D Nagesh Kumar, IISc Optimization Methods: M2L29
A concave function
10. D Nagesh Kumar, IISc Optimization Methods: M2L210
Testing for concavity of a single variable
function
A function is convex if its slope is non increasing or
0. It is strictly concave if its slope is continually
decreasing or 0 throughout the function.
2 2
/f x∂ ∂ ≤
2 2
/f x∂ ∂ <
11. D Nagesh Kumar, IISc Optimization Methods: M2L211
Properties of concave functions
A continuous function on C is concave if and only if
for any a and b in C.
• Equivalently, f(x) is concave on [a, b] if and only if the function −f(x)
is convex on every subinterval of [a, b].
• If f(x) is twice-differentiable, then f(x) is concave if and only if
f ′′(x) is non-positive. If its second derivative is negative then it is
strictly concave, but the opposite is not true, as shown by f(x) = -x4.
( ) ( )
2 2
a b f a f b
f
+ +⎛ ⎞
≥⎜ ⎟
⎝ ⎠
12. D Nagesh Kumar, IISc Optimization Methods: M2L212
Example
Consider the example in lecture notes 1 for a function of two variables.
Locate the stationary points of
and find out if the function is convex, concave or neither at the points of
optima based on the testing rules discussed above.
5 4 3
( ) 12 45 40 5f x x x x= − + +
13. D Nagesh Kumar, IISc Optimization Methods: M2L213
Example …contd.
14. D Nagesh Kumar, IISc Optimization Methods: M2L214
Example …contd.
15. D Nagesh Kumar, IISc Optimization Methods: M2L215
Functions of two variables
A function of two variables, f(X) where X is a vector = [x1,x2], is
strictly convex if
where X1 and X2 are points located by the coordinates given in their
respective vectors. Similarly a two variable function is strictly
concave if
1 2 1 2( (1 ) ) ( ) (1 ) ( )f t t tf t fΧ + − Χ < Χ + − Χ
1 2 1 2( (1 ) ) ( ) (1 ) ( )f t t tf t fΧ + − Χ > Χ + − Χ
16. D Nagesh Kumar, IISc Optimization Methods: M2L216
Contour plot of a convex function
17. D Nagesh Kumar, IISc Optimization Methods: M2L217
Contour plot of a concave function
18. D Nagesh Kumar, IISc Optimization Methods: M2L218
Sufficient conditions
To determine convexity or concavity of a function of
multiple variables, the eigen values of its Hessian matrix
is examined and the following rules apply.
– If all eigen values of the Hessian are positive the function is
strictly convex.
– If all eigen values of the Hessian are negative the function is
strictly concave.
– If some eigen values are positive and some are negative, or if
some are zero, the function is neither strictly concave nor strictly
convex.
19. D Nagesh Kumar, IISc Optimization Methods: M2L219
Example
Consider the example in lecture notes 1 for a function of two
variables. Locate the stationary points of f(X) and find out if the
function is convex, concave or neither at the points of optima based
on the rules discussed in this lecture.
3 2
1 1 2 1 2 2( ) 2 /3 2 5 2 4 5f x x x x x x= − − + + +X
20.
21. D Nagesh Kumar, IISc Optimization Methods: M2L221
Example (contd..)