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Questions related to Matrix
In 0° and 90° T300 carbon fiber cross-pressed fabric panels are considered as orthotropic anisotropic materials. How the Thomson anisotropy parameter can be used to derive the elasticity matrix of orthotropic anisotropic materials under the condition of phase velocity only.
Hi!
I´m currently trying to isolate Mitochondria from HCM cells. For my western blots I need an additional antibody against a mitochondrial protein which is bigger or smaller than 14/17 kDa.
I was thinking of a protein which is only present in mitochondria or in the matrix. Maybe transmembrane proteins (TOM or TIM) will work too, but I don't know if the membranes are still intact in my samples. Maybe proteins from the ß-oxidation? Does someone know which antibodies can be used to detect mitochondrial proteins in western blots? If possible only proteins/Abs that are located/synthesized in the mitochondria (matrix). Thanks a lot!
We suppose,
i- the starting point is to replace the complex PDE for the complex wave function Ψ (probability amplitude) by a real PDE for Ψ^2.
The PDE for Ψ^2 which is the probability density of finding the quantum particle in the volume element x-t dx dy dz dt is assumed exactly equal to the energy density of the quantum particles.
ii- Consequently, the solution of the Bmatrix chain follows the same procedure for solving the heat diffusion equation explained above in the last question:
How to invert a 2D and 3D Laplacian matrix without using MATLAB iteration or any other conventional mathematical method?
iii-The third and final step is to take the square root of the solution for Ψ^2 as the solution for Ψ itself.
As simple as that!
The importance of finding a powerful numerical solution for the Laplacian matrix A in the Laplace and Poisson partial differential equations is obvious.
The classical conventional numerical procedure for solving the Laplace partial differential equation is based on the discretization of the 1D, 2D, 3D geometric space into n equidistant free nodes and on the use of the finite difference method FDM supplemented by the Dirichlet boundary conditions (vector b) to obtain a system of algebraic equations of order n prime in the matrix form A,
A . U(x,y,z,t) = b
The solution to the above equation is U(x,y,z,t) = A^-1.b which is often quite complicated since the matrix A is singular.
It is worth mentioning that common numerical iteration methods such as Gaussian elimination and Gauss-Seidel methods are complicated and require the use of ready-made algorithms such as those in Matlab or Python..etc .
We assume that there exists another SIMPLE statistical numerical solution expressed by:
A^-1=(I-A)^-1=A^0+A+A+A^2+....+A^N
Where A^0=I and N is the number of iterations or time steps dt.
As simple as that!
I want to solve multi degree freedom system dynamic equation of motion in which the stiffness matrix is nonlinear .My system is 12 x 12 and for every displacement value , the stiffness matrix is changing .
Guys please help me out how to solve by using MATLAB.
Thanks
I am developing a SPE method as part of the sample preparation step in my analysis, but I’m not sure what is the best way to determine/calculate the matrix effect. I see a few different formulas online, can anyone help?
If we aim to compute the surface phonon lifetime of a Cu(111) surface, the second and third-order force constants are essential (to put in Boltzmann transport equation). However, to my knowledge, it seems that no one has performed such calculations before. Theoretically speaking, is it possible to compute the third-order force constant matrix of a slab using DFT?
Edit: It seems that calculations for 2D materials have already been performed by many people. From certain perspectives, 2D materials and surface systems (slabs) are quite similar in terms of DFT modelling. However, their phonon modes can be very different, for example, the Rayleigh mode exists only in surface systems.
I am wondering if it might be possible to apply the methods used for 2D materials to surface systems by simply adding a few more layers.
Hybrid composite
matrix -Aluminium Alloy
Reinforcement - Egg shell and SiC
Wikipedia mathematics suggests that the volume of a four-dimensional hypercube (tesseract) of side length "a" is 8 a^4.
On the other hand, the B matrix chains predict the volume of a four-dimensional hypercube with side length "a" (tesseract) as simply a^4.
The question arises which answer is true, if any?
Let us first discretize the simple geometry cube considered into 27 equidistant nodes as shown in Fig.1
Fig.1 A 3D cube discretized into 27 equally spaced nodes
It is clear that nodes 1,2,3. . ,. ,. 26.27
W1,W2,. . . . . . . . . . . . . . ,W26,W27
are located in Cartesian space like,
(0,0,0), (h,0,0), (2h,0,0), (0,h,0), (h,h,0), (2h,h,0), (0,2h,0),(h,2h,0),(2h,2h,0)
(0,0,h), (h,0,h), (2h,0,h), (0,h,h), (h,h,h), (2h,h,h) , (0,2h,h), (h,2h,h), (2h,2h,h),
(0,0,2h), (h,0,2h), (2h,0,2h), (0,h,2h), (h,h,2h), (2h,h,2h), (0,2h,2h), (h,2h,2h), (2h,2h,2h).
Now the values of the function W1,W2, . . . . ,W26,W27 for the case W=x+y+z are,
(0 , 1 , 2 , 1 , 2 , 3 , 2 , 3 , 4
(1 , 2 , 3 , 2 , 3, 4 , 3 , 4 , 5
(2 , 3 , 4 , 3 , 4 , 5 , 4 , 5 6 )
And the Statistical weights SW1,SW2, . . . . .SW26,SW27 are given by [1],
0.710215569 0.972846687 0.710215569 0.972846687 1.31404436 0.972846568 0.710215569 0.972846568 0.710215569
0.972846568 1.31404424 0.972846568 1.31404436 1.75985277 1.31404436 0.972846568 1.31404436 0.972846508
0.710215569 0.972846508 0.710215688 0.972846568 1.31404436 0.972846508 0.710215688 0.972846568 0.710215688
The numerical value of the triple integration I will be given by the simple formula,
I=∑ Wi . SWi . . . . . . (1)
Which is calculated as 3h^4.
Should be compared to the analytic form for I which is h^4(x^2+y^2+z^2)/2 . . . . . . (2)
Over the specified limits which is exactly 6 h^4,
back to the hypercube via Eq 1 with all Wi equal to 1, we arrive at,
I=1.0000 h^4
I am fighting my way through Axelrod and Hamilton (1981) on the Prisoners Dilemma.
this is the payoff matrix they present for the PD. But they only present the payoffs for player A. Normally, these matrices present the payoffs for both A and B. How do I modify this to present both . I’d like to really understand the math Later in the paper.
Often I need to transform several columns of data into rows of aligned values in a matrix, for multivariate analysis. So randomly ordered values in the same sample are arranged/aligned into the corresponding column. How can I conduct this automatically?
Is there any normalization of the genus abundance matrix during enterotyping using the Dirichlet multinomial mixture (DMM) method? If so, what is it?
Thanks in advance.
What is the critical condition for a Laplacian Matrix representing the inter-agent communication graph of a networked dynamical system with delay in the information exchange between agents?
There has been recent interest in expanding the introduction of data science ideas in K-12 education. How often are these ideas connected to the linear/matrix algebra foundations of the subject?
EEG data a two-dimensional matrix as 868 by 16, when it details coefficients are calculated using Matlab code the matrix of D1, D2 and D3 are different from when similar data is decomposed using wavelet Analyzer. Can any one guide me what dimension of D1,D2 one can get when decomposed a 868 by 16 matrix with DB3 of level 6
I have created a data matrix from a CSV file In R. But whenever I try saving the data matrix in .RData format or CSV format and reload it again, the "is.numeric(data_matrix) returns FALSE. the argument returned TRUE before saving in CSV or RData format.
The commands i tried for saving are:
write.csv(data_matrix, file = "matrix.csv") #not numeric
write.csv(data_matrix, "data.csv", row.names = FALSE, col.names = FALSE) #matrix numeric but column names changed to 1,2,3,4.....
write.csv(data_matrix, "data.csv", row.names = TRUE) #not_numeric
The commands used for reloading are:
data <- read.csv("data.csv", header = FALSE, sep = "\t")
Please suggest something. The format of the data matrix is like the CSV file attached.
to find a research gap i want to mix mnagnetite and maghemite nanoparticle and mix them with silica as matrix does it considered as nanocomposite?
m=8
for i=1:m-1
for b=1:m
for c=1:m
F(b)=[E(1),E(2),E(3),E(4),E(5),E(6),E(7),E(8)]* matrix(:,i+1) - t_val *[E(1),E(2),E(3),E(4),E(5),E(6),E(7),E(8)]* matrix1* matrix(:,i+1) - delta +[E(1),E(2),E(3),E(4),E(5),E(6),E(7),E(8)]* matrix1 * matrix(:,i+1) + delta * [E(9),E(10),E(11),E(12),E(13),E(14),E(15),E(16)]* matrix1 * matrix(:,i+1) + Gamma
F(c)=[E(9),E(10),E(11),E(12),E(13),E(14),E(15),E(16)]* matrix(:,i+1) - [E(1),E(2),E(3),E(4),E(5),E(6),E(7),E(8)] * matrix1 * matrix(:,i+1) - delta* [E(9),E(10),E(11),E(12),E(13),E(14),E(15),E(16)]* matrix1 * matrix(:,i+1)- Gamma + t_val *[E(9),E(10),E(11),E(12),E(13),E(14),E(15),E(16)] * matrix1* matrix(:,i+1) + Gamma
iam solving this using matlab iam getting only E(1),E(2),E(3),E(4),E(5),E(6),E(9),E(10),E(11),E(12),E(13),E(14) these values the remaining values(E(7),E(8),E(15),E(16)) are not solved. Matlab gives initial guess instead of solution
Suppose I have a molecule for which I know the density matrix and overlap matrix. I can generate the Mulliken charge distribution in my system. Now I am interested in generating the electron and hole distribution in the molecule. Is it possible to generate such kind of distribution in the system? If possible, then How?
MALDI( Matrix Assisted Laser desorption Ionization)
Matrix use in MALDI in positive mode and negative mode
Dear colleagues,
I would like to use an Entropy method for calculation the weights of my criteria.
My problem:
1. matrix R, in which criteria are written in columns (j=1,2,3,..k) and variants in rows (i=1,2,3,..n)
2. one or more cases: rij = 0
One step of calculations is to calculate ln(rij), but in case that rij = 0, it cannot be calculated. How to solve it?
... I am thinking about replacing the zero with something else, e.g. 0.0000000001 (0=>0.0000000001). Can I do it? (I doubt that)
Thanks in advance for any help.
Roman
I'm currenty working on the antifungal activity of iron nanoparticles incorporated in a polymeric matrix. I've conducted the test against C.albicans and F.oxysporum but there is no antifungal activity. Is it due to the wall structure in fungi species?
Heisenberg matrix mechanics HMM is, in a way, a subset of Schrödinger mechanics SM.
HMM and SM are not adequate to describe sound energy density fields in audio rooms.
On the other hand, B matrix mechanics, [1,2] which is a product of Cairo techniques theory, can accurately predict the sound intensity in audio rooms and further rigorously proves the imperial formula of Sabines.
1- Theory and design of audio rooms -A statistical view
, IJISRT Review, Researchgate, July 2023.
2-Theory and design of audio rooms-Reformulation of Sabine's formula, IJISRT Review, Researchgate, October 2021.
We’ve got an LD laser matrix with 20 blue LDs (I attached the spec). We need to diffuse the beam to spread it over 20X20cm spot at 30-50mm. We need energy density variation <10% in the spot. I know how to do it by attaching fibers to emitters but it is not an option.
i make The confusion matrix for my model i want to know what is mean this matrix
Basically I have 40 subject and for each I collect
- coronary cannulation before TAVR as : selective, non selective e unsuccessfull.
Then i collected the same data after TAVR with the same 3 level of outcome.
This is a case of repeated measure with multilevel outcome. In addition my contingency table is not "square" due to the fact that there aren't "non selective" outcome in the group "before TAVR".
Here my dataset
AfterTAVR
BeforeTAVR 0 1 2
0 1 0 0
1 1 16 22
McNemar, Stuart-Maxwell’sTest and Cochran’sQTest due to the Not Binary Outcome and Non Square matrix (3x2) of the my dataset.
Can someone have some suggestions??? I will really appreciate it
We have a quantum system consists of quantum oscillators. Such system is described by its canonical position and momentum variables for each oscillators. The state of the system is described by the covariance matrix. How to define Bell inequality for such a system in terms of covariance matrix?
We assume that this is absolutely true because they tried to introduce and adjust matrix mechanics only to quantum particles when it should be applied to both classical physics situations as well as quantum physics particles of the the same way and via the same matrix.
Classical physics and quantum physics are two sides of the same coin (nature) and they simply arise and interpenetrate, as proposed and successfully solved by the B-matrix strings.
ref,
Fall and rise of matrix mechanics, Researchgate, IJISRT journal, January 2024.
Hello,
I greatly appreciate your help in my following statistic task. I need to reduce the number of financial ratios (FRs) - currently 20 - that best represent the firms' profitability in the technology sector. These 20 FRs were selected from 32 sources - practitioners and peer-reviewed articles.
I plan to reduce the 20 financial ratios through diverse steps, starting with the "Intercorrelation Matrix Analysis" applied to the 20 FRs of 10 companies (random sample) over the past five years, using SPSS (29). It will eliminate FRs with weak inter-correlation – i.e., ≤ ± .5.
FRs data will be derived from the firms' annual reports.
PROBLEM: How do I build the intercorrelation matrix with the 20 financial ratios data (tabulated in Excel) from 10 firms over the past five years using SPSS (29)?
Should I perform a Matrix Correlation Analysis over the period by the single firm? If so, how do I interrelate the results of the five Correlation Matrixes - one for each firm - to eliminate those financial ratios with weak correlation?
Or,
Is it correct to create a single Excel table with 20 variables (FRs) columns and 25 Rows (5 firms x 5 years) and then export it to SPSS for the correlation analysis?
Is there any better approach for this first reduction step?
Thank you very much for your time and support!
I have created a 2d geometric model in order to investigate the fracture toughness of a reinforced composite using epoxy as a matrix.
I have inserted a predetermined crack, and defined it as a crack by inserting a cohesive team. I did this as it allowed me to assign a material to that crack section, as It was unsuitable to create a crack with defined thickness due to needing to see what becomes of the interaction between the particles and its matrix.
The problem I am facing is how to define the cohesive properties of this crack.
How do I define the three Nominal stresses, as well as the damage evolution?
I have been using cohesive element type within my mesh for the cohesive seam.
I have tried to troubleshoot to the best of my abilities but I am not sure where to start or where to get the necessary information from.
Any help would be incredibly appreciated.
Many thanks in advance.
edit: I have attached photos showing the cohesive properties ive assigned. if anybody could please highlight what is wrongly defined or what I may do instead to allow for my model to run accurately it would be greatly appreciated.
Concave upward structures in a fossiliferous laminated goethite-rich sedimentary rock (matrix is dominantly goethite with approx. 15% submicron silicate detritus e.g., clays and very sparse oxides).
We have considered stylolites, roots, ripples, burrows, or some sort of compaction feature.
The structures cross-cut bedding but don't demonstrably offset the bedding. They also appear to be slightly enriched in U and slightly depleted in Th relative to the matrix so perhaps some dissolution-reprecipitation has occurred.
Any ideas welcomed.
The problem is hot extrusion of Ti-6Al-4V from circular section to ellipse section the solver is coupled-temp-displacement 4 steps are defined first one is for diagnosing the contact from ABAQUS by moving the material 1mm down and second one for moving the material to complete the extrusion and third one is defined to deactivate the interaction between die and part and fourth is defined to apply convection and radiation to part for simulating the cooling I'm using ALE method for this problem. Please help me to resolve the error. The error occurs in the second step where the ALE is defined. I have modeled 1/4 of the whole model to reduce the elements number.
I am using Agilent 7000 series GC-MS/MS for the analysis of DTC pesticides such as Mancozeb and Zineb but the LOQ cannot be lowered up to 10 mg/Kg as there is matrix interference from the tea polyphenols. Please suggest some methods to do the same.
We assume that the chains of matrix B can introduce a numerical statistical solution for ψ(r)^2 (total quantum energy) in the same way that they present a numerical statistical solution for the heat diffusion energy density without go through the PDE heat itself. .
The question arises whether this solution exists, how important is it, and whether it is as accurate as the SE solution?
Hello everyone; I am doing a simple beam analysis in Abaqus and want to check the stiffness and mass matrix for that beam. I obtained the stiffness matrix in mtx format and want to see it as a matrix. Please anyone can suggest how to convert this mtx format file to the simple visual form of a matrix in Matlab. How to read these as well. I attached those files.
Thanks
Ram
Hi, I have a problem in calculating the mol ratio of ENR. This is required as I want to include additives in my compounding. But, the amount need to be in mol ratio to see equivalent amount of functional group that can react with other functional group of the additional additives. For your information, I use ENR with epoxidation level 50. ENR-50 has a very long chains since its polymer. My additive, for example is diacid. how For polymer, I basically used weight percent or volume percent to add fillers or anything into the matrix. I hope that someone could help me regarding this. Thank you in advance.
For example like this statement: "Mix compositions with different epoxide/diacid ratios: DA=dodecanedioic acid; phr= parts per hundred parts of rubber by weight; p=epoxide sites for 1 diacid molecule; M//DA= total monomer units/diacid"
the problem is: how i want know the calculation of the ratio of epoxide/diacid
Imaging the nanoparticles after drying the samples shows the samples like a matrix
I want to ask what is your prefered protocol to obtain a good image for your nanoparticles
Many Thanks
Dear all,
Can anybody help me to correctly write the Damper Location Matrix for a high rise building where dampers are provided at all floors.
Thanks in advance
From
Bhargav
Dear sirs,
I am working on high rise buildings. To determine the response (displacement, velocities, acceleration) State Space Method is used in MATLAB model.
Can anybody help me to properly positioned Location Matrix of damper ?. Means in matrix form. Presently in my model which I have kept diagonal as " 1 " and rest to be " 0". but not getting proper response quantity. So please someone help me to correctly write Location Matrix with size in MATALB model.
regards
from
Bhargav
Hi,
I did an exploratory factor analysis. Direct Oblimin and Principal Axis factoring. The 12 variables loaded on 2 factors. The factor loadings on factor 1 (column one in pattern matrix) and factor loadings on factor 2 (column two in pattern matrix) are highly negatively correlated (R2=0.991).
Is this normal or problematic? Thank you!
Hi every one. I want to use staggered grid to write MATLAB code about viscoelastic fluid. You suppose I have a 10×14 node at x and y direction. I have initial value for conformation tensor as A=[1 , 0 ;0 1]
I should allocate this value for all grids as matrix. Then It should calculate eigen values of A matrix and also its normalized vectors. Then put eigen values in matrix as diagonal matrix as "Lamda".
Then Z= RT *Lambda*R
Which RT is the transpose of normalazed matrix of A.
Now I do not know how should I define matrix (A) as the input , that the new one will replace with the previous in the loop.
I defined as this:
A (i,j)=eye(2)
Or
A11(i,j)=1, A12(i,j)0 , A21(i,j)=0 , A22(i,j)=1
But it gives error about dimension.
If I define A=eye(2), how MATLAB understand put this value in each node and in the next step replace it with new one which the value can be different from each grid to other one.
Because it just gives me a 2×2 matrix.
I want to predict the beamforming matrix for BS (Base Station) and the phase shift matrix for RIS (Reconfigurable Intelligent Surface). How can I obtain a large number of past successful optimization results of beamforming matrices and phase shift matrices to use as labels for supervised pre-training?
matlab algorigrime, design an N*N matrix. target a fixed value on the main diagonal which repeats, from 2 to 2 or 4 to 4. other values can be between zero.
I'm currently working with a panel data set that has 6 cross-sections and 19 time periods. In the process, I've encountered issues related to endogeneity, as well as challenges with both stationary and non-stationary data. To address these, I decided to run a panel ARDL, but unfortunately, I faced a near-singular matrix issue. This led me to remove a few variables that I initially wanted to test.
I'm reaching out to seek your advice. Are there alternative methods or approaches I could consider for a data set of this nature? Your insights would be highly appreciated.
Dear All
I am trying to applying a phylogenetic correction to an MCMC model, but I have problems in making the inverse matrix. I can visualise the treeplot very well, but when I use the script:
inv.phylo<-inverseA(phylo_ultra,nodes="TIPS",scale=TRUE)
R tells me that there is an error:
Error in pedigree[, 2] : incorrect number of dimensions
In addition: Warning message:
In if (attr(pedigree, "class") == "phylo") { :
Do you have any experience with this? I couldn't find a solution so far
Thanks in advance
David
The strings in matrix B predict this statement.
As a numerical example, the sum of the entire series 0.99 + 0.99^2 + 0.99^3 + . . . . +0.99^N increases to 190 as N goes to infinity.
Additionally, B-matrix chains provide rigorous physical proof.
The question arises whether a pure mathematical proof can also be found?
Hello,
I performed doped structure in Vesta and i run the scf file for band calculation. But ı had an error as a following after scf.band calculation. what is it mean ? Thanks
task # 0
from cdiaghg : error # 170
S matrix not positive definite
If the eigenvalue of matrix A is λ1 and the eigenvalue of matrix B is λ2, the statistical chain of transition matrix B predicts that the eigenvalue of the sum A+B would be given by λ1 + λ2.
However, this rule does not constitute the general case and can only be applied under conditions.
The question arises: can we find these necessary conditions or, and above all, can we find the necessary and sufficient conditions for this rule?
Hello everyone,
I have applied 1D CNN on speech emotion recognition, when I shuffled columns I got diffrent results, for example, using matrix(:,[1 2 3]) gives different classification results than matrix(:,[2 3 1]) which should be the same, I have tried rng("default") but it hasn't resolved the issue. Can someone please assist me with this?
Thank you in advance!
Hello everyone,
I attempted to perform an orthogonality assessment on the Eigenmodes subsequent to conducting modal analysis on some structure.
The analysis was conducted using ANSYS 22R1 software. An example of an orthogonality check was performed using APDL commands. The check is deemed successful when the product of [(transpose) Phi M Phi] results in the identity matrix. In this equation, Phi represents the modal matrix of the specified (n) modes, and M denotes the mass matrix.
According to most textbooks, vectors are considered orthogonal when their dot products equal zero. Consequently, the dot product of each mode (vector) with the others in the Phi matrix should yield an identity matrix. I attempted to do the task by employing the
load Phi_MMF.txt
data = zeros(203490,1);
for r=1:203490
data(r,1)=Phi_MMF(r,1); %transforming from MMF form to common matrix form
end
size(data)
modes = reshape(data,5814, 35); %the modal matrix of first 35 modes
MODES=modes';
% Initialize a matrix to store the results
orthogonality_matrix = zeros(35, 35);
% Loop to check orthogonality for all pairs of columns
for i = 1:35
for j = i:35
% Calculate the dot product between column i and column j
dot_product = dot(MODES(:, i),MODES(:, j));
orthogonality_matrix(i, j) = dot_product;
end
end
% Display the orthogonality matrix
disp("Orthogonality Matrix:");
disp(orthogonality_matrix);
I am uncertain about the distinction between two rules and would appreciate insight from any fellow who have encountered the rule [(transpose) Phi M Phi ] as a means of verifying orthogonality in any academic literature.
Regards
Mohamed A M Salem Here you go. All you need is the free education edition of PERMAS. See https://www.intes.de/k_permas/overview/academic_license
in bio-fluid samples, we used to add mobile phase (mobile phase A, B, or mixture) to the sample after extraction and prior to LC-MS/MS
Wondering, it does not affect the analyte concentration?!!!. if yes how can I compensate for this loss?
I'm curious, if there's any way to estimate the two-qubit quantum state purity via direct measurements on quantum computer, without the need of full density matrix reconstruction?
I'd see some use of state purity in algorithms, but performing quantum state tomography seems really prohibitive, both runtime-wise and considering, that it's a huge decoherence source...
I'll be glad for any suggestions or paper recommendations.
need some articles based on seidal laplacian matrix
I have a large sparse matrix A which is column rank-defficient. Typical size of A is over 100000x100000. In my computation, I need the matrix W whose columns span the null space of A. But I do not know how to fastly compute all the columns of W.
If A is small-scale, I know there are several numerical methods based on matrix factorization, such as LU, QR, SVD. But for large-scale matrices, I can not find an efficient iterative method to do this.
Could you please give me some help?
I have a large sparse matrix A which is column rank-defficient. Typical size of A is over 100000x100000. In my computation, I need the matrix W whose columns span the null space of A. But I do not know how to fastly compute all the columns of W.
If A is small-scale, I know there are several numerical methods based on matrix factorization, such as LU, QR, SVD. But for large-scale matrices, I can not find an efficient iterative method to do this.
Could you please give me some help?
Hello,
I would like to compute de the stress tensor of a Timoshenko beam at its Gauss points, to be able to implement an elastoplastic law in my finite element calculations.
Firstly,I know the displacement field at any point of my beam thanks to the relation u(x) = N(x) U, where U is the matrix of degrees of freedom at the nodes of my beam tU = (ux1, uy1 , uz1, θx1, θy1, θz1, ux2, uy2, uz2, θx2, θy2, θz2)
Then, I took as an expression of N the form given in this article https://www.researchgate.net/publication/236659875_Shape_functions_of_three-dimensional_Timoshenko_beam_element#fullTextFileContent , which corresponds to a Timoshenko model.
I deduce the deformations for small strains with ε = 1/2 (grad(u) +tgrad(u)), I obtained the equation shown in the picture.
I then apply Hooke's law to find the stress.
I then obtain that for a traction test (ux2 = constant, the other components of U are zero), the displacement field and the strain tensor are constant on my beam in particular along a cross-section, with only εxx non-zero, on the other hand the stress tensor has non-zero components other than σxx.
I conclude that my model shows that the cross sections are non-deformable, with therefore additional "virtual" forces, which prevent the beam subjected to traction along x, from being refined along y and z in accordance with the Poisson effect . On the other hand, I would like to have a "natural" behavior where the beam is refined according to y and z.
Do you have any articles for this?
Thanks a lot
Dear fellow researchers,
I am trying to simulate the temperature variation during a laser sintering of some metal powder. Material properties (density and conductivity) depend on temperature. I am using nonlinear FEM and writing my code.
I am using Newton-Raphson method. Now I want to know how to calculate the tangent matrix/jacobian matrix for nonlinear transient problem? could you please share some reference which has the complete derivation and some test cases to check my code? It would really be helpful.
best regards,
I am researching the Gridless Sparse Recovery for Space-Time Adaptive Processing(STAP) Based on Atomic Norm Minimization(ANM). In STAP, clutter plus noise covariance matrix is a PSD Hermitian block‐Toeplitz matrix.
The ANM-STAP problem can be equivalently transformed to a SDP problem, as shown in the attached image below.The problem Equation (11) can be efficiently implemented using any off‐the‐shelf SDP solvers HYPERLINK, but I don't know how to use MATLAB to build a block Toeplizte matrix, and how to use CVX toolbox to solve the SDP problem.
Hello.
We are writing a master thesis on microstructures of composite materials and we want to combine the cohesive zone model (CZM) for delamination of fibres and the phase-field model (PFM) for matrix/fibre failure in Abaqus.
I started off by constructing a CZM for a very simple 2D unit cell, where I defined cohesive contact between two separate parts in an assembly; e.g. fibre and matrix.
My partner has tried to implement phase-field modelling and has found a code she can implement. However, the description states that the only way to make the code work is to have an assembly as one merged part.
I have tried to research possibilities but had no success in implementing a CZ surface for the model as a merged part consisting of fibre and matrix material. Do you have any suggestions on how to do it?
We want to use a cohesive surface, not elements, to make the model as simple as possible.
We are also very new to Abaqus, so any help or reference is welcome :)
I want to solve an optimization problem with two vectors:
max ||yAx||^2
s.t. ||y||^2=1
||x||^2=1
where x and y are a vector. The A is a known matrix.
Are there any other solutions besides alternative optimization methods?
In applying this algorithm to the dynamic stiffness matrix of a structure, the number of negative terms on the main diagonal of the upper triangular matrix is counted. How can I apply this in the situation of for example a free-free beam? The matrix has finite number of diagonal elements while the beam has infinite number of natural frequencies.
Thank you.
Hello, I'm about to join a team working on auditory speech perception using iEEG. It is planned that I will use Temporal Response Function (TRF) to determine correlations between stimulus characteristics (variations in the acoustic signal envelope, for example) and characteristics of recorded neuronal activity.
I would therefore like to fully understand the different stages of data processing carried out, as well as the reasoning and hypotheses behind them.
I took a look at the article presenting the method
and I studied the matrix calculations
But several questions remain.
In particular, regarding this formula:
w = (ST S)-1 ST r
where S is a matrix of dimension (T*tau) presenting the characteristics of the stimulus over time (T) as a function of different temporal windows/shifts (tau) as :
S =
[ s(tmin-taumin) ... s(t) ... s(tmin-taumax) ]
[ ... ... ]
[ ... ... ]
[ s(tmax-taumin) ... s(t) ... s(tmax-taumax) ]
and where r is a matrix of dimension (T*N) presenting the recorded activity of each channel in time.
- Why do STS? What does the product of this operation represent?
- Why do (STS)-1? What does this operation bring?
- Why do (STS)-1ST? What is represented in this product?
- And finally w = (STS)-1STr. What does w of dimension tau * N really represent?
Hypothesis:
STS represents the "covariance" of each time window with the others (high covariance in the diagonal (because product of equal columns), high covariance for adjacent columns (because product of close time windows) and low covariance for distant columns whose time windows are very far apart (and therefore presenting little mutual information)).
Maybe that (STS)-1ST (of dimension T*tau) makes it possible to obtain a representation of the stimulus according to time windows and time, but with the abrogation of any correlations that may exist between windows? However, the representation of the stimulus in this product remains very unclear to me...
And finally, w may represents the weights (or correlations) of each N channel for the different time windows of the signal.
My incomprehension mainly concerns the representation of the stimulus by (STS)-1ST and I would like to better understand the reasoning behind these operations and the benefits they bring to the decoding of neural activity.
I'd like to thank anyone familiar with TRFs for any help he/she can give me. My reasoning may be wrong or incomplete, any contribution would be appreciated.
What do the stiffness matrix's eigenvalues tell about the finite element's quality? I have read similar answers on ResearchGate, but many refer to dynamic analysis.
Hello, everyone. I am Xing Ning.
I find in my Matlab program, when the location (x,y) is near the boundaries between two different regions, the analytical waveforms of Bx and By exist fluctuations. If y value of Path 1 of Region1 is 0.0995m, the analytical waveforms of Bx and By is calculated as shown in Attached file.
I can ensure that the parameters of matrixes are defined and calculated correctly. I can't figure the errors out.
Thank you for your time and effort.
Ning Xing, China
SWOT analysis, PESTEL analysis and IG ANSOFF matrix strategic planning for how reinsurance company can venture into business opportunities in Democratic Republic of Congo capitalising in the mining industry
Unbelievable is make believable in the world we connected prime number in matrix algebra form and I change history of math
Please see it
Hi!
I am trying to purchase the protease MMP21 but wasn't able to find a commercial source. Does anyone know of a distributor? I am located in the US.
Thank you!
Nadine
theoretical way for calculation of inverse of covariance matrix
Adjacency matrix represents the functional connectivity patterns of the human brain. In my opinion, thresholding of correlation matrix is one of the most important and ambiguous step to get the adjacency matrices. Reason behind my opinion is that thresholding is user dependent and can be chosen any value (i.e., from 0.051 to 0.999) above the 5% because above this level means there is no significant difference between two signals or there is coherence between both. User is open to select the strength of connectivity by its own.
I want to know your opinion that does this a fair way to move from correlation matrices to adjacency matrices? If yes, how results of two researchers can be compared when they use different thresholding values? If no, what should be a reasonable threshold value for correlation matrices?
Thanks in advance!
If a doped a material in a matrix. Its glass transition temperature and crystallization temperature decreases compared to the matrix but activation energy increases (Kissinger, Moynihan). Please give me the explanation for increased activation energy with decreased Tg and Tc.
By coding the messages xi (i=1,2,…, N) of a finite information source X having the probabilities pi = p(xi) with letters yj (j=1, 2, …, D) of a finite coding alphabet Y, we obtain a new information source Y. I need to characterize Y as an information source with memory, in order to verify the relation H(Y) = LH(X), where L is the average length of the codewords and H(X) and H(Y) are the entropies of X and Y respectively. My questions: how we can obtain the stady-states of the information source Y? How the matrix containing the transition probabilities between the states of Y can be determined? How the probabilities of the stady-states of the information source Y are obtained? Does anyone have some results on this topic?
Please guide me on how to perform an NMF analysis in any software. If anyone has any available tips, please guide us on implementing the NMF analysis for FTIR data.
I haven't fully grasped the function of the 3-parameter U gate in quantum mechanics. What is its purpose? Where is it employed? Additionally, I haven't been able to derive its proof. What do I need to utilize to establish this proof? (Why are the elements inside the matrix in exponential and trigonometric function forms?)
Many people may think that an irrational such as 2^1/2 is mathematical, not physical, and has no direct connection to quantum mechanics (QM).
On the other hand, we guess that's a great question even though no one really knows the exact answer.
We offer the following:
For the interpretation of probabilities in QM to make sense, the wave function Ψ must satisfy certain conditions.
An extremely important and yet rarely mentioned condition is,
Ψ squared = Ψ* squared=Ψ.Ψ* must always be positive and real.
This is the required answer.
Matrix transition chains B (solving the heat diffusion/conduction equation as a function of time) suggests finding an adequate alternative complex transition matrix to solve the Schrödinger equation as a function of time.
what is quite striking is that 2^1/2 should appear explicitly and be expressed numerically as 1.142... in order to construct the required complex transition matrix.
Hello,
I’m having trouble finding all eigenvectors from complex eigenvalues for 3.6.1 bii . The complete eigenvectors format is a 4x8 matrix. I’m able to find the last row, but the rest I’m struggling with. The last row was found with this equation;
(u/)-1 = (kc)/(m*s2+kt)
Kc = 75kN
m = 122.68kg
s= any of the eigenvalues (
Kt = 2.3M\N/m
The next rows are dependent on the modes, whirl rotation, and natural frequency. The answer is the matrix in the eigenvectors picture file. The other page files are background info.
+1
I am trying to generate the Haar wavelet operational matrix of integration of order one, that is P(1, i). For example, where the maximum level of resolution, J=3. Implies, 2M is equal to 16. Hence, the operational matrix is going to be a 2M square matrix.
Hello everyone, I am currently using COMSOL to simulate the piezoelectric behavior of zinc oxide (ZnO) nanowires. I would like to add either PMMA or PDMS as the surrounding polymer material.
However, I have noticed that there are different types of PMMA and PDMS available. I would like to know the differences between them.
My second question is regarding the selection of PMMA and PDMS from the MEMS branch in COMSOL. COMSOL requires me to provide the coupling matrix, elastic matrix, and relative permittivity for these materials.Where can I find this information?
I think it could be easier getting first the image.
I need to do a matrix and without the image (really complex) I think it's near impossible.
Hi all, I have scRNA data generated from Rapsody platform and analysed in seven bridges platform. Now could you please give me an idea how to deal with seven bridges platform output files for seurat R scRNA analysis. Mainly i need Filtered Feature, Barcodes, and Matrix files for analysis.
Dear friends, there is an error says "A singular matrix occurred during the estimation of the final path coefficients. Using a large number of datasets could solve the problem" when I run the Bootstrapping Algorithm, but when I set the cases and samples from 2000 to 20000 and tried many other numbers between 2000 and 20000, it still didn't work. I'm wondering is this problem about the number of samples or there are other problems, thanks very much for your answering!
Dear colleagues. I need to build a matrix A100x100,where are some values and a lot of zero with a shift.
Example of code:
b<-c(0.08,0.18, 0.28, 0.35 , 0.46, 0.61, 0.75 , 0.89 , 1, 0.89, 0.75, 0.61, 0.46, 0.35, 0.28, 0.18, 0.08)
a14<-c(rep(0,4),b,rep(0,79))
a15<-c(rep(0,5),b,rep(0,78))
a16<-c(rep(0,6),b,rep(0,77))
a17<-c(rep(0,7),b,rep(0,76))
a18<-c(rep(0,8),b,rep(0,75))
a19<-c(rep(0,9),b,rep(0,74))
a20<-c(rep(0,10),b,rep(0,73))
a21<-c(rep(0,11),b,rep(0,72))
a22<-c(rep(0,12),b,rep(0,71))
a23<-c(rep(0,13),b,rep(0,70))
I ask you help.how is it possible to write loop in order to build a 100-by-100 matrix ,where a are rows of the matrix until a99?
Dear colleagues. I need to build a matrix A,where are some values and a lot of zero.
Thanks a lot for your help
There are the elements ,matrix rows:
a_1=1 0,89 0,75 0,61 0,46 0,35 0,28 0,18 0,08 and after 91 zeros
a_2=0,89 1 0,89 0,75 0,61 0,46 0,35 0,28 0,18 0,08 after 90 zeros
a_3=0,75 0,89 1 0,89 0,75 0,61 0,46 0,35 0,28 0,18 0,08 89 zeros
a_4=0,61 0,75 0,89 1 0,89 0,75 0,61 0,46 0,35 0,28 0,18 0,08 88 z
a_5=0,46 0,61 0,75 0,89 1 0,89 0,75 0,61 0,46 0,35 0,28 0,18 0,08 87 z
a_6=0,35 0,46 0,61 0,75 0,89 1 0,89 0,75 0,61 0,46 0,35 0,28 0,18 0,08 86 z
a_7=0,28 0,35 0,46 0,61 0,75 0,89 1 0,89 0,75 0,61 0,46 0,35 0,28 0,18 0,08 85 z
a_8=0,18 0,28 0,35 0,46 0,61 0,75 0,89 1 0,89 0,75 0,61 0,46 0,35 0,28 0,18 0,08 84 zeros
a_9=0,08 0,18 0,28 0,35 0,46 0,61 0,75 0,89 1 0,89 0,75 0,61 0,46 0,35 0,28 0,18 0,08 83 zeros
Is there any way to convert molecular orbital (MO) to NO or NLMO and have them output in matrix format? Please let me know if there is a way to do this in Gaussian16.
Hi, for my graduate research, I need to analyze a simple bolted connection on ABAQUS. The bolted connection consists of 3 bolts that connects 3 plates (see the picture attached for reference). The top and the bottom plates, is fixed at the end of the plate. The middle plate is loaded with uniform loading on the other end. I've tried to run it, however I get these kind of error
***WARNING: THE SYSTEM MATRIX HAS 3 NEGATIVE EIGENVALUES.
***WARNING: DISPLACEMENT INCREMENT FOR CONTACT IS TOO BIG.
I have tried to make the surface contacts each other in the beginning of the analysis, however it still doesn't works.
Hello,
I am applying a Logit Model on heart disease data (400k instances) which are imbalanced (90% negative and 10% positive classifier). Does anyone know how one has to proceed in this context? My approach is the following:
A. Doing logistic regression with the original imbalanced dataset
1. I split data into train and test data (80%,20%)
2. What do I have to do afterwards? Then fit a LR classifier on training data and making predictions on test set? Does it mean to make a prediction based on the training model and compare it with the test data --> which results in the Confusion Matrix (CM).
3. Based on this I calculate the Recall and Precision metrics
4. As performance measure I chose the Area under the Precision - Recall Curve.
--> This results in an AUC of under 0.5 which is worse then guessing!!
B. Applying a SMOTE (synthetic oversampling) AND random oversampling to correct the imbalance in the dataset
1. I split data into train and test data (80%,20%)
2. Then applying Random oversampling or SMOTE
3. Then again fit a LR classifier on training data and making predictions on test set? And Confusion Matrix (CM).
3. Based on this I calculate the Recall and Precision metrics
4. As performance measure I chose the Area under the Precision - Recall Curve.
Further Questions:
- Can I and if yes how can I apply threshold tuning in case A and B? Does it make sense in a balanced dataset in case B? Do I generate the best threshold value by applying the PR curve or the ROC?
-Do I calculate the Precision and Recall metrics after thershold tuning?
- Are Pseudo R2 necessary to be checked for the coefficients?
Thank you very much!!!
I am working on multi species occupancy modelling and I stumbled upon creating residual covariance matrix which has a range of -1 to +1. I need to get a very basic understanding of what a residual covariance matrix is showing me? Is it as simple as showing relation between each species? So, if the value comes to be negative between two species, does it mean they have a negative relation? I am confused because of the term "residual covariance". I would appreciate guidance on this.
Hello! I need to extract the mass and stiffness matrices for a model with the following problem size:
P R O B L E M S I Z E
NUMBER OF ELEMENTS IS 249191
153326 linear line elements of type T3D2
84141 linear hexahedral elements of type C3D8R
102 linear line elements of type B31
11613 linear quadrilateral elements of type S4R
NUMBER OF NODES IS 267444
NUMBER OF NODES DEFINED BY THE USER 267240
NUMBER OF INTERNAL NODES GENERATED BY THE PROGRAM 204
TOTAL NUMBER OF VARIABLES IN THE MODEL 837207 (DEGREES OF FREEDOM PLUS MAX NO. OF ANY LAGRANGE MULTIPLIER VARIABLES. INCLUDE *PRINT,SOLVE=YES TO GET THE ACTUAL NUMBER.)
The properties are input as mass density, and I believe they will be used to generate a consistent mass matrix.
Here's the input file code I used: ** Global Mass and Stiffness matrix *Step, name=Export matrix *MATRIX GENERATE, STIFFNESS, MASS, VISCOUS DAMPING, STRUCTURAL DAMPING *MATRIX OUTPUT, STIFFNESS, MASS, VISCOUS DAMPING, STRUCTURAL DAMPING, FORMAT=coordinate
I have the following questions regarding my problem:
- Dimensions of M and K matrices As indicated above, the number of degrees of freedom is 837,207, but the matrix dimensions are reduced to 354,231*354,231. Shouldn't the number of degrees of freedom match the matrix dimensions?
- Node numbering The model consists of 8 parts, and the nodes start from 1 for each part. However, when I extract the matrices using the FORMAT=matrix input option, a different node numbering system (1 to 241,751) is applied, making it difficult to match the entries to the actual model locations. How can I find the correspondence between the entries in the M and K matrices and the nodes in the model?
- In the coordinate format, I get 5,620,189 rows of data, while in the matrix input format, I get 2,987,210 rows of data. Shouldn't the number of data entries be the same in both cases?
- When using the matrix input format, the entries are extracted in the following format: 241751,3, 241751,3, 9.038200770026704e+00 Can I interpret the corresponding data as follows? 1: X (translational) 2: Y (translational) 3: Z (translational) 4: RX (rotational) 5: RY (rotational) 6: RZ (rotational)
- The modes obtained from modal analysis in ABAQUS CAE GUI and the eigenanalysis results obtained from extracting the M and K matrices and performing the Lanczos method in MATLAB do not match. Is there any way to reconcile them?
Do i have to revalidate the method using some blank matrix or this matrix effect is acceptable?
I performed matrix base calibration(linearity) for validation.
All the parameters are well within acceptable limits.
I am just not so sure about matrix effect
Please guide.
Hello to everyone,
I would like some clarifications regarding the PRM technique. I have always used this technique for the Orbirtrap Q Exactive Focus for quantification analyzes on food matrices. By doing some tests on a matrix, I realize that the full scan spectrum for a given molecule has a decidedly better quality, as well as being more intense (but I think this is normal), for quantification compared to the PRM spectrum.
What I can't quite understand is why in PRM, a more specific and selective method, the peak is of low quality. I used a method already tested for other analyses:
Resolution 35,000 ; N(CE) 20.40, 70 eV; Insulation width: 1.5m/z; Target AGC 1e5.
What could it be related to?
Thank you,
Francersco
I want to find eigen frequencies of a cantilever beam. The beam has random elastic modulus. The stiffness matrix is obtained using kosambi karhunen loeve method as A_0+A_i. where A_o is mean stifness matrix and A_i is fuction of normal random variable. The egien values are expanded in terms of polynomial chaos expansion. The final equation is obtained after galerkin projection. The equation is attached in the files. I want a matlab code to obtain the the eigen frequencies,
Dear amazing researchers,
I am working on a nonlinear FEM problem and using Python for coding.
To get the nodal values of the field variable, I have to solve a system of linear equation. In matrix notation, [A]{x}={b}, where [A] is a sparse-matrix (a lot of zeros away from main diagonal), {b} is the right hand side vector.
One trivial solution is {x}={b}/[A], but it is computationally heavy when needs to be done many times and [A] is large.
Lets take a simple example:
A = [[5, 2, -1, 0, 0],
[1, 4, 2, -1, 0],
[0, 1, 3, 2, -1],
[0, 0, 1, 2, 2],
[0, 0, 0, 1, 1]]
and b = [ [0],
[1],
[2],
[2],
[3]]
To store the complete sparse-matrix is waste of memory when a large number of element values are zero, so I wrote a code to store the matrix in a compact form, which stores the non-zero diagonals in every row.
[Ac]= [[ 0, 0, -1, -1, -1],
[ 0, 2, 2, 2, 2],
[ 5, 4, 3, 2, 1],
[ 1, 1, 1, 1, 0]]
There is a function in "scipy" library. It is scipy.solve_banded(), which takes the "Ac", and "b" as arguments and return the solution {x}.
Could anyone help me to find out the algorithm behind scipy.solve_banded() function?
I will be very thankful for your help.
Reservoir Compressibility: Useful only in land subsidence?
Feasible to deduce the compressibility of a petroleum reservoir (sandstone) as a function of fluid-pressure drop in a reservoir?
How difficult would it remain
to deduce the ‘relative changes in reservoir thickness’
in order to estimate the above sandstone’s rock-matrix compressibility?
Feasible to deduce the role of individual contributions:
(a) deformation of the solid-grain matrix of the reservoir;
(b) expansion of brine, oil and gas –
upon hydrocarbon production from a confined reservoir?
How useful would it remain,
if we deduce the value of ‘Storativity’
(S: a dimensionless property) of a petroleum reservoir
as a function of
(a) drop in piezometric-head;
(b) surface area of the reservoir being produced from; and
(c) volume of fluids withdrawn from stored reservoir
(S = ab/c)?
Could the estimation of ‘specific storage (SS)’ of a reservoir
also remain useful in reservoir engineering,
(estimated as a function of Storativity over reservoir thickness’
(SS = S/thickness)?
OR
Whether the correlation between ‘specific-storage’
as a function of rock-compressibility (RC), fluid compressibility (FC), reservoir porosity (P) and specific-weight of the fluid (SWF)
has any vital information associated
with the draining principle of reservoir engineering
{SS = (SWF*RC)+(P*FC)}?
OR
The concept of ‘Storativity’ would remain useful -
only in the estimation of ‘reservoir compaction’
and its associated ‘land subsidence’?
How do we ensure whether a reservoir undergoes
a ‘normal compaction’ upon hydrocarbon production?
How do we know that the deformation of the solid-grains
of a sandstone reservoir
remains concurrent with the fluid expulsion?
Or
How do we know that the ‘rate of loading’
remains larger than the ‘rate of fluid expulsion’
so that we could conclude that
there is a ‘disequilibrium compaction’ of the concerned reservoir?
And, in such cases,
how do we estimate
the ‘enhanced fluid-pressure’
resulting from the fact that
‘the fluid temporarily carries part of the load,
which remains ultimately transferred
to the solid-grain matrix of the reservoir’?
Dear all,
I am evaluating vegetation recovery 1 year after wildfires in Mediterranean forest ecosystems. I have selected two factors: 1) previous (or not) silviculture treatment to wildfire and 2) exposition (south and north-facing slopes). I consider both factors as fixed factors, right?
Secondly, I have measured vegetation cover at different plots by combining two factors (treatment x facing slope). In the end, I have a matrix containing vegetation cover (in cm) for each plant species measured in the combination of factors (treatment (yesxno); facing slope (NxS)). Shall a first transform the matrix using square root and then build the resemblance matrix? What is best for my analyses ANOSIM or PERMANOVA?
Thirdly, Shall I make any previous analyses like checking the variability of variance or homogeneity of my data?
I am using Primer software.
Thanks in advance
Size of polymer matrix is near about 500 nm and size of filler used is 1000 nm. Can it be called as nanocomposites? Please discuss.
Are there conditions (constraints) that the elements of the correlation matrix must meet? (For example, the linear correlation coefficient of X1 and X2 is 0.99, and it is the same between X2 and X3. Then between X1 and X3, it can be any low, or must it be greater than a given value?) If there are such constraints, what are they?
I want to check the effect of DDSDDE in UMAT on the element stiffness matrix. So, is it possible to output the element stiffness matrix in each iteration in Abaqus/Standard?
Dear: Jean Dezert , Albena Tchamovag, Deqiang Han, Jean-Marc Tacne
Reference is made to your paper :
The SPOTIS Rank Reversal Free Method for Multi-Criteria Decision-Making Support
My comments as follows:
It is a very good news to have a method without Rank Reversal (RR)
1- In my opinion you use the phrased ‘score matrix’ to indicate what in reality is the initial matrix, composed by performance values. This induces to confusion to readers for who score matrix is a matrix with different scores or results derived from applying a MCDM method.
2- You say in page 3 “The score matrix S = [Sij ] is sometimes also called benefit or payoff matrix in the literature.”
What happens if the matrix, as is most usual, also calls for minimization, using ‘cost’ values?
3- I don’t think that an initial decision matrix (IDM) can be considered incomplete because it does not have bounds for criteria. A matrix is incomplete when there is no indications of the quantity of resources for each criterion, procedure unfortunately followed by most MCDM methods, except PROMETHEE and those working with Linear Programming.
4- I agree with what you say about validations.
5 – You say “Classical MCDM problem becomes a well-defined MCDM one, where all scores values for each criterion are between its bounds”
6- “SPOTIS method will provide the best multi-criteria decision-making solution with preference ordering of all alternatives.”
Are you sure it is the best? On what grounds do you assert that?
7- In page 3: You consider criteria independent from each other. This s is a serious drawback, since in most projects criteria are interrelated. According to this, if you have two criteria like ‘Sped’ and ‘Fuel consumption’, that are interrelated, you can’ use SPOTIS? Why not?
8- How do you determine an ideal solution a priori? Based on what? Of course, if this solution is say very high, is does not matter what alternative you add, because it will be always above the maximum.
I grant you that it is a very elegant procedure.
9- I don’t think is correct to work with difference types of distances in the same problem?
10 - Where does weights come from? Are they subjective or objective?
11 – In page 5 “Once the MCDM is well-defined thanks to the specification of the bounds values of each criteria, the SPOTIS method does not suffer from rank reversal because the evaluation of each alternative is done independently of the others”
I agree 100% with this statement, because I also believe that the only way to avoid RR is evaluate each alternative independently. There is another method that applies this same principle and does not produce RR, but is not based on distances to a fixed point.
12- In page 7 “It could be argued that the SPOTIS method is more difficult (or risky) to use because of the freedom left in the choice of min and max bounds of the criteria”:
More difficult, risky? I don’t think so. It looks as a transparent method and very easy to understand. In my opinion its only drawback is using subjective weights.
Do you have a software for SPOTIS?
I hope my comments may be useful to your paper.
Nolberto Munier
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