First part of description of Matrix Calculus at Undergraduate in Science (Math, Physics, Engineering) level.
Please send comments and suggestions to solo.hermelin@gmail.com.
For more presentations please visit my website at
http://www.solohermelin.com.
Here we have included details about relaxation method and some examples .
Contribution - Parinda Rajapakha, Hashan Wanniarachchi, Sameera Horawalawithana, Thilina Gamalath, Samudra Herath and Pavithri Fernando.
In this presentation we will learn Del operator, Gradient of scalar function , Directional Derivative, Divergence of vector function, Curl of a vector function and after that solved some example related to above.
Gradient in math
Directional derivative in math
Divergence in math
Curl in math
Gradient , Directional Derivative , Divergence , Curl in mathematics
Gradient , Directional Derivative , Divergence , Curl in math
Gradient , Directional Derivative , Divergence , Curl
system of algebraic equation by Iteration methodAkhtar Kamal
solve the system of algebraic equation by Iteration method
classification of Iteration method:-
(1) Jacobi's method
(2) Gauss-Seidel method
each problem
Tensor Train (TT) decomposition [3] is a generalization of SVD decomposition from matrices to tensors (=multidimensional arrays).
It represents a tensor compactly in terms of factors and allows to work with the tensor via its factors without materializing the tensor itself.
For example, we can find the elementwise product of two TT-tensors of size 2^100 and get the result in the TT-format as well.
In the talk, we will show how Tensor Train decomposition can be used to represent parameters of neural networks [1] and polynomial models [2].
This parametrization allows exponentially many 'virtual' parameters while working only with small factors of the TT-format.
To train the model, i.e. optimize the objective subject to the constraint that the parameters are in the TT-format, [2] uses stochastic Riemannian optimization.
[1] Novikov, A., Podoprikhin, D., Osokin, A., & Vetrov, D. P. (2015). Tensorizing neural networks. In Advances in Neural Information Processing Systems.
[2] Novikov, A., Trofimov, M., & Oseledets, I. (2016). Tensor Train polynomial models via Riemannian optimization. arXiv:1605.03795.
[3] Oseledets, I. (2011). Tensor-train decomposition. SIAM Journal on Scientific Computing.
A very quick and easy to understand introduction to Gram-Schmidt Orthogonalization (Orthonormalization) and how to obtain QR decomposition of a matrix using it.
First part of description of Matrix Calculus at Undergraduate in Science (Math, Physics, Engineering) level.
Please send comments and suggestions to solo.hermelin@gmail.com.
For more presentations please visit my website at
http://www.solohermelin.com.
Here we have included details about relaxation method and some examples .
Contribution - Parinda Rajapakha, Hashan Wanniarachchi, Sameera Horawalawithana, Thilina Gamalath, Samudra Herath and Pavithri Fernando.
In this presentation we will learn Del operator, Gradient of scalar function , Directional Derivative, Divergence of vector function, Curl of a vector function and after that solved some example related to above.
Gradient in math
Directional derivative in math
Divergence in math
Curl in math
Gradient , Directional Derivative , Divergence , Curl in mathematics
Gradient , Directional Derivative , Divergence , Curl in math
Gradient , Directional Derivative , Divergence , Curl
system of algebraic equation by Iteration methodAkhtar Kamal
solve the system of algebraic equation by Iteration method
classification of Iteration method:-
(1) Jacobi's method
(2) Gauss-Seidel method
each problem
Tensor Train (TT) decomposition [3] is a generalization of SVD decomposition from matrices to tensors (=multidimensional arrays).
It represents a tensor compactly in terms of factors and allows to work with the tensor via its factors without materializing the tensor itself.
For example, we can find the elementwise product of two TT-tensors of size 2^100 and get the result in the TT-format as well.
In the talk, we will show how Tensor Train decomposition can be used to represent parameters of neural networks [1] and polynomial models [2].
This parametrization allows exponentially many 'virtual' parameters while working only with small factors of the TT-format.
To train the model, i.e. optimize the objective subject to the constraint that the parameters are in the TT-format, [2] uses stochastic Riemannian optimization.
[1] Novikov, A., Podoprikhin, D., Osokin, A., & Vetrov, D. P. (2015). Tensorizing neural networks. In Advances in Neural Information Processing Systems.
[2] Novikov, A., Trofimov, M., & Oseledets, I. (2016). Tensor Train polynomial models via Riemannian optimization. arXiv:1605.03795.
[3] Oseledets, I. (2011). Tensor-train decomposition. SIAM Journal on Scientific Computing.
A very quick and easy to understand introduction to Gram-Schmidt Orthogonalization (Orthonormalization) and how to obtain QR decomposition of a matrix using it.
Question bank Engineering Mathematics- ii Mohammad Imran
its a very short Revision of complete syllabus with theoretical as well Numerical problems which are related to AKTU SEMESTER QUESTIONS, UPTU PREVIOUS QUESTIONS,
constant strain triangular which is used in analysis of triangular in finite element method with the help of shape function and natural coordinate system.
Unix and Shell Programming,
Q P Code: 60305.
Additional Mathematics I
Q P Code: 60306
Computer Organization and Architecture
Q P Code: 62303
Data Structures Using C
Q P Code: 60303
Discrete Mathematical Structures
Q P Code: 60304
Engineering Mathematics - III
Q P Code: 60301
Soft Skill Development
Q P Code: 60307
Molecular dynamics simulation study of a polymer droplet motion over an array...Nikolai Priezjev
Anish Thomas and Nikolai V Priezjev
APS March Meeting 2021
YouTube talk https://youtu.be/cUkXYlXpW4E
https://meetings.aps.org/Meeting/MAR21/Session/J25.4
Lecture notes on Structure and Properties of Engineering Polymers
Course Objectives:
The main objective is to introduce polymers as an engineering material and emphasize the basic concepts of their nature, production and properties. Polymers are introduced at three levels; namely, the molecular level, the micro level, and macro-level. Through knowledge of all three levels, student can understand and predict the properties of various polymers and their performance in different products. The course also aims at introducing the students to the principles of polymer processing techniques and considerations of design using engineering polymers.
Lecture: Dynamics of Polymer Solutions and Melts Nikolai Priezjev
Lecture notes on Structure and Properties of Engineering Polymers
Course Objectives:
The main objective is to introduce polymers as an engineering material and emphasize the basic concepts of their nature, production and properties. Polymers are introduced at three levels; namely, the molecular level, the micro level, and macro-level. Through knowledge of all three levels, student can understand and predict the properties of various polymers and their performance in different products. The course also aims at introducing the students to the principles of polymer processing techniques and considerations of design using engineering polymers.
Lecture notes on Structure and Properties of Engineering Polymers
Course Objectives:
The main objective is to introduce polymers as an engineering material and emphasize the basic concepts of their nature, production and properties. Polymers are introduced at three levels; namely, the molecular level, the micro level, and macro-level. Through knowledge of all three levels, student can understand and predict the properties of various polymers and their performance in different products. The course also aims at introducing the students to the principles of polymer processing techniques and considerations of design using engineering polymers.
Lecture notes on Structure and Properties of Engineering Polymers
Course Objectives:
The main objective is to introduce polymers as an engineering material and emphasize the basic concepts of their nature, production and properties. Polymers are introduced at three levels; namely, the molecular level, the micro level, and macro-level. Through knowledge of all three levels, student can understand and predict the properties of various polymers and their performance in different products. The course also aims at introducing the students to the principles of polymer processing techniques and considerations of design using engineering polymers.
Lecture: Polymerization Reactions and TechniquesNikolai Priezjev
Lecture notes on Structure and Properties of Engineering Polymers
Course Objectives:
The main objective is to introduce polymers as an engineering material and emphasize the basic concepts of their nature, production and properties. Polymers are introduced at three levels; namely, the molecular level, the micro level, and macro-level. Through knowledge of all three levels, student can understand and predict the properties of various polymers and their performance in different products. The course also aims at introducing the students to the principles of polymer processing techniques and considerations of design using engineering polymers.
Lecture notes on Structure and Properties of Engineering Polymers
Course Objectives:
The main objective is to introduce polymers as an engineering material and emphasize the basic concepts of their nature, production and properties. Polymers are introduced at three levels; namely, the molecular level, the micro level, and macro-level. Through knowledge of all three levels, student can understand and predict the properties of various polymers and their performance in different products. The course also aims at introducing the students to the principles of polymer processing techniques and considerations of design using engineering polymers.
Molecular origin of surface tension at liquid-vapor interfacesNikolai Priezjev
In this presentation, the effect of surface tension at liquid-vapor interfaces will be discussed. We will consider a flat liquid-vapor interface at thermodynamic equilibrium and estimate the pressure-stress tensor in the interfacial layer. Further, the surface tension coefficient will be computed for monatomic liquid using the molecular dynamics simulation method. The dependence of the results will be examined as a function of the temperature, density, system size, and details of the interaction potential. Finally, a few examples where the surface tension forces are important will be considered; namely, soap bubbles, the shape of liquid droplets at solid surfaces, and survival of water striders.
Welcome to WIPAC Monthly the magazine brought to you by the LinkedIn Group Water Industry Process Automation & Control.
In this month's edition, along with this month's industry news to celebrate the 13 years since the group was created we have articles including
A case study of the used of Advanced Process Control at the Wastewater Treatment works at Lleida in Spain
A look back on an article on smart wastewater networks in order to see how the industry has measured up in the interim around the adoption of Digital Transformation in the Water Industry.
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.
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.
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.
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.
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.
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.
Final project report on grocery store management system..pdf
Numerical Methods: Solution of system of equations
1. ME4010 Computational Methods for
Mechanical Engineering
Chapter 4 Solution of system of equations
Instructor: Nikolai V. Priezjev
Office: 430 Russ Engineering Center
Phone: 937-775-3214
Email: nikolai.priezjev@wright.edu
The course is adopted from Prof. Huang at WSU
3. Statics
R1 + T1 cos 60 + T2 = 0
R2 + T1 sin 60 = 0
-T2 -T3 cos 60 + T4 cos 60 + T5 = 0
T3 sin 60 + T4 sin 60 = 0
-T5 - T6 cos 60 = 0
T6 sin 60 + R3 = 0
-T1 cos 60 + T3 cos 60 + T7 - F1 cos = 0
-T1 sin 60 - T3 sin 60 - F1 sin= 0
-T4 cos 60 - T7 + T6 cos 60 - F2 cos = 0
-T4 sin 60 - T6 sin 60 - F2 sin = 0
6. Method
[A] = [L][U]
where
[L] = lower triangular matrix
[U] = upper triangular matrix
LU Decomposition
Given [A][X] = [B]
1. Decompose [A] into [L] and [U]
2. Solve [L][Z] = [B] for [Z]
3. Solve [U][X] = [Z] for [X]
7. Method: [A] Decomposes to [L] and [U]
33
2322
131211
3231
21
00
0
1
01
001
u
uu
uuu
ULA
[U] is the same as the coefficient matrix at the end of the forward elimination step.
[L] is obtained using the multipliers that were used in the forward elimination process
21. Module LU_solver
Contains
! SUBROUTINE TO PERFORM DOLITTLE FACTORIZATION: A=LU
SUBROUTINE LU(N,A,B,X)
integer::N,I,j,k
double precision:: A(N,N),L(N,N),U(N,N),B(N),Z(N),X(N)
double precision:: S,S1,S2,SS,S3,S4
DO I = 1,N
L(I,I)=1.
ENDDO
U(1,1)=A(1,1)
IF(U(1,1).EQ.0.)THEN
WRITE(1,*)'LU FACTORIZATION IS IMPOSSIBLE'
RETURN
ENDIF
DO J =2,N
U(1,J)=A(1,J) ! DETERMINE THE FIRST ROW OF U
L(J,1)=A(J,1)/U(1,1) ! DETERMINE THE FIRST COLUMN OF XL
ENDDO
DO I = 2, N-1
S=0.
DO K = 1, I-1
S=S+L(I,K)*U(K,I)
ENDDO
U(I,I)= A(I,I)-S
IF(U(I,I).EQ.0.)THEN
WRITE(1,*)'LU FACTORIZATION IS IMPOSSIBLE'
RETURN
ENDIF
DO J = I+1, N
S1=0.
S2=0.
DO K = 1, I-1
S1=S1+L(I,K)*U(K,J) ! DETERMINE THE (ith) ROWS OF U
S2=S2+L(J,K)*U(K,I) ! DETERMINE THE (ith) COLUMN OF XL
U(I,J)=A(I,J)-S1
L(J,I)=(A(J,I)-S2)/U(I,I)
ENDDO
ENDDO
ENDDO
SS=0
DO K = 1,N-1
SS=SS+L(N,K)*U(K,N)
U(N,N)=A(N,N)-SS
ENDDO
IF(U(N,N).EQ.0) THEN
WRITE(1,*)' THE MATRIX A IS SINQULAR'
ENDIF
! SUBROUTINE TO SOLVE LZ=B USING FORWARD SUBSTITUTION
Z(1)=B(1)
DO I =2,N
S3=0.
DO J =1,I-1
S3=S3+L(I,J)*Z(J)
ENDDO
Z(I)=B(I)-S3
ENDDO
X(N)=Z(N)/U(N,N)
DO K = N-1,1,-1 ! SOLVING UX=Z
S4=0.
DO J=K+1,N
S4=S4+U(K,J)*X(J)
ENDDO
X(K)=(Z(K)-S4)/U(K,K)
ENDDO
RETURN
END subroutine LU
end module solver
22. program main
use LU_solver
double precision, dimension(4,4)::A
double precision, dimension (4)::B,X
integer::i,j,N=4
open (1, file='matrix.dat')
do i=1,n
read(1,*)(a(i,j),J=1,N)
enddo
read(1,*)B
call LU(N,A,B,X)
print *,x
stop
end program main 4. -2. -3. 6.
-6. 7. 6.5 -6.
1. 7.5 6.25 5.5
-12. 22. 15.5 -1.
12. -6.5 16. 17.
matrix.dat file
1
2
3
4
4 2 3 6 12
6 7 6.5 6 6.5
1 7.5 6.25 5.5 16
12 22 15.5 1 17
x
x
x
x