Orthogonalization - Science topic

In an n-dimensional Euclidean space, what is the minimum number of rotations required to transform a given orthogonal coordinate system into an arbitrary orthogonal coordinate system? How can this be expressed mathematically, particularly using the language of linear algebra?

Please, could you give me some suggestions on how to solve this problem?

I am trying to simulate cavitation in a 2D venturi tube (in ANSYS FLUENT), however when I go from the meshing stage to the configuration stage, the console shows me the following message: "WARNING: 10000 cells with non-positive volume detected." I ignored this message and continued working, but when I try to initialize, the console shows me an error message and does not allow me to simulate.

I am attaching images of the errors that Ansys Fluent shows me, as well as my generated mesh. It should be noted that I tried to do the same job under the same boundary conditions in a 3D venturi tube and Ansys does not show me such an error. I tried to mesh with a tetra mesh, but the result is the same. In addition to that, I would like to comment that my mesh is hexa, conformal and with a minimum orthogonal quality of 0.94.

Einstein overcomplicated the theory of special and general relativity simply because he did not define time correctly.

A complete universal or physical space is a space where the Cartesian coordinates x, y, z are mutually orthogonal (independent) and time t is orthogonal to x, y, z.

Once found, this space would be able to solve almost all problems of classical and quantum physics as well as most of mathematics without discontinuities [A*].

Note that R^4 mathematical spaces such as Minkowski, Hilbert, Rieman. . . etc are all incomplete.

Schrödinger space may or may not be complete.

Heisenberg matrix space is neither statistical nor complete.

All the above mathematical constructions are not complete spaces in the sense that they do not satisfy the A* condition.

In conclusion, although Einstein pioneered the 4-dimensional unitary x-t space, he missed the correct definition of time.

Universal time t* must be redefined as an inseparable dimensionless integer woven into a 3D geometric space.

Here, universal time t* = Ndt* where N is the dimensionless integer of iterations or the number of steps/jumps dt*.

Finally, it should be clarified that the purpose of this article is not to underestimate Einstein's great achievements in theoretical physics such as the photoelectric effect equation, the Einstein Bose equation, the laser equation, etc. but only to discuss and explain the main aspects and flaws of his theory of relativity, if any.

Is there future for NOMA ( non orthogonal multiple access i need illustration with why ?

Why have changes in the North Atlantic Oscillation increased during the 20th century? Can climate change be predicted in the future?

The North Atlantic Oscillation explains a large part of the climate variability across the North Atlantic Ocean From the east coast of North America across Europe, many studies of the North Atlantic Oscillation in extreme weather conditions in this region, especially in Winter is relevant. It has motivated a significant study of this pattern. However, an overlooked feature is how the North Atlantic Oscillation has changed over time. There is a significant increase in the variance of the pattern. The North Atlantic Oscillation (NAO) increased during the 20th century from 32% in 1930 to 53% at the end of the 20th century. Whether this change is due to natural variation, a forced response to climate change, or a combination thereof is not yet clear. However, we found no evidence for a forced response from the Model Comparison Project Phase 6 (CMIP6) set of 50 pairwise models. All of these models showed significant internal variability in the strength of the North Atlantic Oscillation, but were biased toward it. In the region, this has direct implications for both long-term and short-term forecasting where regional climate changes are extreme. The North Atlantic Oscillation (NAO) is a pattern of variability associated with sea surface pressure over the North Atlantic Ocean with a subpolar low and subtropical high. The NAO is associated with large-scale changes in the position and intensity of both the storm track and the jet stream over the North Atlantic, and therefore plays a direct role in shaping the atmospheric transport of heat and moisture across the basin (Fasullo et al., 2020). ). It has also been shown that the NAO has a large effect on the Atlantic meridional overturning circulation and therefore the oceanic heat transfer, and this is the largest time scale of 20-30 years, which leads to changes in northern hemisphere temperatures of a few tenths. a degree (Delworth and Zeng, 2016). NAO has positive and negative. It shows significant interannual phase and changes. The positive phase of NAO shows between the two phases of pressure below the normal limit in the subpolar region and high pressure above the normal limit in the subtropics. It is often associated with a decrease in temperature and precipitation, an anomaly in southern Europe and an increase in precipitation, an anomaly in northern Europe, the effects of the NAO across the basin and the positive phase are also associated with it. Positive temperature anomaly in the eastern United States. The opposite pattern and its effects are observed during the period when the NAO is in its negative phase (Weisheimer et al., (2017). It has long been established that the NAO dominates climate variability over a large part of the Northern Hemisphere. The eastern coast of North America across Europe to the center of Russia and from the Arctic in the north to the subtropical Atlantic Ocean (Horrell et al., 2003) is one of the important components of winter variability and is related to the frequency and intensity of weather extremes. in Europe (Hilock and Goodes, 2004; Scaife et al., 2008; Fan et al., 2016). Therefore, it is necessary to understand the scale of natural variability in the NAO, how the NAO responds to changes in external forcing, and whether these If current climate models fail to account for natural variability or NAO forcing, this could lead to radical predictions of extreme climate change in Europe on time scales of decades to centuries.An index for the NAO is often identified in one of two

ways. The first approach is to calculate the normalized difference in surface pressure between the subtropical high (Azores High) and subpolar low (Icelandic Low) over the North Atlantic sector. The second approach is to perform an Empirical orthogonal function (EOF) analysis on sea level pressure over the North Atlantic region. An EOF analysis separates the variability in the sea level pressure into orthogonal modes, with the first mode containing the largest proportion of the variability and each subsequent mode containing progressively less. When an EOF analysis is used to calculate the NAO, the first mode indicates the NAO index, while the second and third modes usually provide the North Atlantic ridge and Scandinavian blocking patterns (Cassou et al., 2004).

MIMO

Greetings and courtesy to the professors and students of mathematics. I wanted to know if there is a relationship between the curves and the orthogonal paths of the differential equation with the characteristics of its solution? If the answer is yes, please state the type of relation and relational formula. Thanks

I have been trying for a long time to get my 2-way FSI using a Mechanical and fluent model of an patient-specific carotid artery to work but it keeps crashing with errors before finishing the first time step. I cannot get even an extremely simplified model to work for any material softer than Young’s modulus of 50 MPa.

I have looked at all relevant tutorials (best practices for FSI, oscillating plate, etc). The model I am trying to solve is quite complex with linear elastic isotopic material and a coded time-dependent velocity inlet. It works completely fine when solving the individual solvers.  However, I can simply not solve a 2-way FSI simulation with this geometry no matter how much I simplify it, except when solving for structural steel material properties which are defaulted in engineering data.

Every time I get an “excessive deformation” error. In cases where the material is still pretty hard, it might not crash but it cannot converge. I have tried to correct the geometry and the geometry is perfectly good. but I can still not solve a 2-way FSI with a softness to human arterial tissue.

I have tried the following things (and checked if the individual solvers and 1-way FSI work):

-         GEOMETRY

-         Structural: idealized carotid artery. Internal diameter: 5.0.9 mm, thickness: 0.07 mm, length: 47 mm

-         Fluid:  same diameter as the internal diameter of the artery

-         I have checked the geometries and they completely match (no scaling issues during import)

-         MATERIALS

-         The only material I can solve the 2-way FSI simulation for is structural steel

-         I tried working with linearly elastic materials with different Young's Modulus. Since I am working with small pressures and velocities, the artery is not deforming visibly even for Young’s modulus of 100 MPa in the mechanical solver (deformation around e-8 m ).

-         Tring different Poisson Ratios, 0.49,0.45,0.42

-         MESHING

-         Working with fine meshes generated in Ansys Meshing (good values for min angle, quality, skewness, and orthogonality). Tetra or Hex. Homogenous or with inflation near the data transfer surface

-         Alternatively working with fine tetrahedral meshes. Smoothed to ensure good values for min angle, quality, skewness, and orthogonality.

-         BOUNDARY CONDITIONS

-         Pulsatile inlet velocity and 0 pressure at the outlet. Still crashes in the first timestep even though there are basically no forces applied to the system.

-         Various types of support (fixed on the ends or cylindrical or displacement or elastic etc)

-         SOLVER

-         Trying the “System Coupling” and “Fluid-Structure Interaction” interfaces

-         Using the Ramping option in System Coupling for the data transfers

-         Trying different Windows workstations

-         Building the model in different versions of Ansys (R2024 R1 and R2023 R2)

-         Trying out small timesteps of e-5 and less but stability is not improved and convergence is not accelerated

Many researchers are solving very complex FSI models with Fluent and Mechanical on patient-specific stented arteries with different pressure outlet boundary conditions. so I am very confused that even when following their tips and advice I cannot even get such a simple model to work. Any advice would be highly appreciated. Thank you!

1. All cell zones in Fluent may be automatically set to Fluid.

2. Inflation created stairstep mesh at some locations (regarding this problem I saw in some other platforms that it could be ignored if I have a minimum orthogonal mesh quality of 0.1, however I would like to solve this problem).

This is a case worked in Ansys fluent.

How do I orthogonalize a time series variable? Which software and analysis can be used for orthogonalization?

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

I am trying to do some harmonic analysis , I have to select the most effective natural modes. I have the modal matrix (natural modes eigen vectors), but I am confused between many techniques. some techniques depend on selection of modes based on orthogonality of modes. while some techniques depend on independency of the modes like (Modal Independence Factor (MIF), Modal Independence Index (MII), and Modal Assurance Criterion (MAC)).

Are there any other techniques ? and which of them consider the most effective and feasible technique ? and if it is possible to include a literature for such method ?

I uploaded 5 days ago has been completely updated.

It is intuitively understandable with three diagrams.

Read within 3 minutes and immediately know the Lorentz contraction is wrong.

Also you can find that the ultra speed of light are observed in your immediate daily life.

=============================================

Even if you are not a #physics expert, the content is understandable

Lorentzian contractions were recognized from two experiments 120 years ago.

The Michelson-Morley experiment and the Sagnac experiment.

I will review the experimental results to reveal the true nature of nature.

★Please see attached picture Fig2_San.jpg

Michelson Morley was an experiment confirming the existence of the aether.

A prism is used to split the light into two paths and finally join them together. Interference fringes of light are created when there is a speed difference between two light paths.

Result is

1. The interference fringes were small and aether could not be proved.

2. Earth's rotation and revolution do not affect the experiment

The Sagnac experiment was a set of Michelson-Morley experiments mounted on a rotating disk. expected the same result

★Please see attached picture Fig1_MM.jpg

However, for some reason, large interference fringes were observed.

Everyone didn't find the reason at the time

So the physics world accepted the Lorentz contraction hypothesis that the rotation speed of the disk shortens the distance, changes the speed of light, and creates interference fringes.

The real natural phenomenon shown by the Sagnac experiment is:

The revolution speed of the earth is added to the light emitted from the light source. As the disk rotates, the addition of the earth's revolution speed changes continuously. It is Doppler effect of light.

In particular, when the direction of light and the direction of revolution are orthogonal, the added speed becomes zero. Maximum interference fringes are produced.

★Please see attached picture Fig3_Evo.jpg

The speed which is added to the orinal light speed(3*10**8 m/sec) is :

1. The case of Revolution speed : 30000m/sec

2. The case of Rotation speed : 460m/ sec

3. Disk rotates speed of Sagnac experiment might be less than 10m /sec

The Lorentz contraction hypothesis cannot explain the large interference fringes in Sagnac's experimental results because of too slower speed.

Because

I did not find a mathematical formula to find or through which we can determine or choose the correspondences in the case of unequal sample sizes

I have read several papers on the same but I haven't yet succeeded in finding one with a script I can use on my data

I am a beginner with the use of SAS and Specially Orthogonal contrast. My experiment involve 4 rate of Nitrogen (23,46,69 and 92 kg N) at 3 time of application plus a control for bread wheat. The trail was at field by RCBD with three replication. The different responses are labeled as variables 1-39 as depicted in the SAS command I just prepared.

My treatments are:-

N-rates= 4

N application time =3

Control=1

Total treatments= 13

Thank you for your recommendation!

I want to do Polynomial orthogonal contrasts (quadratic and linear) analysis to analyze the appropriate replacement level of fish meal by a protein source.

Where is the Jade due to the throwing out of a brick and a paving stone?

A brand new conception of preferable probability and its evaluation were created, the book was entitled "Probability - based multi - objective optimization for material selection", and published by Springer, which opens a new way for multi-objective orthogonal experimental design, uniform experimental design, respose surface design, and robust design, discretization treatment and sequential optimization, etc.

It aims to provide a rational approch without personal or other subjective coefficients, which is available at https://link.springer.com/book/9789811933509,

DOI: 10.1007/978-981-19-3351-6.

Best regards.

Yours

M. Zheng

LoRaWAN Communication Field

Does a Reynolds Number always have to be defined with a length scale and velocity that are orthogonal to one another? Could the length scale and velocity be parallel?

OTFS, orthogonal time frequency & space, considers three dimensions and MIMO-OFDM also considers three dimensions. Is there any difference between the two concepts? Thanks!

Hi! I'm a chemical engineering undergraduate student, and I'm currently researching SLS bio-composites. I want to be able to optimize the laser processing parameters, and I've read various papers talking about multi-index synthetic weighted scoring method, but I'm still a bit confused on how this model works. I've read a bit about orthogonal experiments.

However, any detailed explanation, articles, videos, etc. would be greatly appreciated.

Thank you!

please suggest me a software used for the orthogonal regression.

Hi

I am trying to find technique to improve isolation between ports of a multiple feed slot ring antenna.

Generally there are dual feed which are orthogonal and the port isolation between them is well below -30 dB.

I tried to make annular slot ring antenna with slant polarization and also vertical or horizontal polarization. However the non orthogonal feeds have port isolation below -10dB.

O would really apprecitate if anyone can comment on suitable technique usuagea in this scenerio to put myself in right direction.

Thank you

I want to reproject ERA5-Land data from orthogonal projection to 9km Ease-Grid v2 in MATLAB or R. Any leads are much appreciated. Thanks in advance.

Dear Researchers,

I am looking for methods to mesh a twisted blade in order to get more structure mesh.

I tried several mesh size yet the quality metric are a bit bad.

I am analyzing regarding the skewness and the orthogonal quality.

My objective will be performing modal and harmonic in order to determine the stress distribution adequate to the natural frequencies.

Thanks in advance for your advise.

Hi, I have a matrix A of size 50 X 6 and I have a vector x of size 50 X 1. Assume that all columns of A are orthogonal to each other. I have 2 questions:

Thank you for your attention.

A(A^T)=(A^T)A =I(Identity Matrix)

Then A always have real enteries.

Is it true?

Hi my dynamic model is

Gender Inequality Index(GII) = a+GIIt-1+bFDI+ (ControlV)+U

My control variables are 7. I have used all the control variables and my main explanatory variable as the strictly exogenous ivstyle instruments. Is this correct. I have read somewhere that we can treat all the regressors in ivstyle but i still don't understand why?

xtabond2 GII lag_GII log_FDIinflowreal NaturalresourceRent Generalgovernmentexpenditure GDPGrowth Schoolsecondaryfemale UrbanPopulationControl polity2 Fertilityrate Y*, gmm(GII, lag (0 5) collapse) iv( log_FDIinflowreal NaturalresourceRent Generalgovernmentexpenditure GDPGrowth Schoolsecondaryfemale UrbanPopulationControl polity2 Fertilityrate Y*, equation(level)) nodiffsargan two

> step robust orthogonal small

Dynamic panel-data estimation, two-step system GMM

------------------------------------------------------------------------------

Group variable: countrycode Number of obs = 239

Time variable : Year Number of groups = 49

Number of instruments = 24 Obs per group: min = 1

F(17, 48) = 22.88 avg = 4.88

Prob > F = 0.000 max = 9

----------------------------------------------------------------------------------------------

| Corrected

GII | Coef. Std. Err. t P>|t| [95% Conf. Interval]

-----------------------------+----------------------------------------------------------------

lag_GII | .4063319 .1660706 2.45 0.018 .0724247 .7402392

log_FDIinflowreal | .0052016 .004571 1.14 0.261 -.0039891 .0143923

NaturalresourceRent | .0001336 .0007056 0.19 0.851 -.0012852 .0015523

Generalgovernmentexpenditure | -.0011517 .0027406 -0.42 0.676 -.0066621 .0043588

GDPGrowth | .0000538 .0011326 0.05 0.962 -.0022235 .0023311

Schoolsecondaryfemale | -.0015661 .0005599 -2.80 0.007 -.0026918 -.0004405

UrbanPopulationControl | .0002386 .000501 0.48 0.636 -.0007687 .0012459

polity2 | .0029176 .00107 2.73 0.009 .0007662 .005069

Fertilityrate | .0172748 .0121555 1.42 0.162 -.0071655 .0417151

Year | -.0002603 .0066672 -0.04 0.969 -.0136656 .013145

Yeardummy1 | .1047832 .1552767 0.67 0.503 -.2074215 .4169879

Yeardummy17 | -.006658 .0432925 -0.15 0.878 -.0937034 .0803874

Yeardummy18 | -.0006796 .0359611 -0.02 0.985 -.0729842 .071625

Yeardummy19 | -.0071339 .0330241 -0.22 0.830 -.0735332 .0592655

Yeardummy20 | -.0066488 .0261336 -0.25 0.800 -.0591938 .0458963

Yeardummy21 | .0021421 .0180578 0.12 0.906 -.0341655 .0384498

Yeardummy22 | .0005937 .0097345 0.06 0.952 -.0189789 .0201663

_cons | .8149224 13.41294 0.06 0.952 -26.15361 27.78345

----------------------------------------------------------------------------------------------

Instruments for orthogonal deviations equation

GMM-type (missing=0, separate instruments for each period unless collapsed)

L(0/5).GII collapsed

Instruments for levels equation

Standard

log_FDIinflowreal NaturalresourceRent Generalgovernmentexpenditure

GDPGrowth Schoolsecondaryfemale UrbanPopulationControl polity2

Fertilityrate Year Yeardummy1 Yeardummy2 Yeardummy3 Yeardummy4 Yeardummy5

Yeardummy6 Yeardummy7 Yeardummy8 Yeardummy9 Yeardummy10 Yeardummy11

Yeardummy12 Yeardummy13 Yeardummy14 Yeardummy15 Yeardummy16 Yeardummy17

Yeardummy18 Yeardummy19 Yeardummy20 Yeardummy21 Yeardummy22 Yeardummy23

Yeardummy24

_cons

GMM-type (missing=0, separate instruments for each period unless collapsed)

DL.GII collapsed

------------------------------------------------------------------------------

Arellano-Bond test for AR(1) in first differences: z = -1.70 Pr > z = 0.090

Arellano-Bond test for AR(2) in first differences: z = 0.43 Pr > z = 0.669

------------------------------------------------------------------------------

Sargan test of overid. restrictions: chi2(6) = 18.25 Prob > chi2 = 0.006

(Not robust, but not weakened by many instruments.)

Hansen test of overid. restrictions: chi2(6) = 5.55 Prob > chi2 = 0.475

(Robust, but weakened by many instruments.)

.

Maxwell four Equations.

I am using Gamma-Re theta transition model for an asymmetrical airfoil. For the academic Ansys Fluent version, the maximum allowable cell limit is 512000 cells. Is it possible to have a good mesh quality in the academic version for transition modelling? If yes, what can i do to improve my mesh quality? Thank you very much.

Maximum aspect ratio = 438.08

Maximum skewness = 0.84746

Minimum orthogonal quality = 0.10908

Y+ < 1

Total cell number = 504400

It is well-known that for an ordinary matrix G, its orthogonal projection matrix is I--G^T (GG^T)^-1G. But when G is sparse, (GG^T) in the above expression is noninvertible, such that the determination of orthogonal projection is difficult.

By the way, my final goal is to obtain the null space of a sparse matrix G. That is to say, I hope to get a matrix formed by eigenvectors having non-zero eigenvalues of the eigen-decomposition of the orthogonal projection matrix about G.

Dear Researchers,

The overall cost of "my algorithm" is dominated by finding orthogonal basis, which costs (M p.^2) where p is less than M , for the input matrix. My concern is: is there nay alternative method (or low-cost QR decomposition) to find the orthogonal basis with lower cost, please?

Thank you so much for your consideration in advance

Best regards,

Bakhtiar

How does Offset-QAM ensure orthogonality of subcarriers in FBMC?

Please elaborate, how to design an experiment for better yield optimization with minimum experiments. I have four variables, mole ratio, temp, time, catalyst loading, and sometimes instead of a cat. loading I use microwave watt power

I may recall that,possibly they are orthogonal with respect to a Gaussian.,What other weights,if any

Hello,

In our process, we first need to polish and AR treat two faces of a polygonal TeO2 cristal. Then, we have to treat another orthogonal face. I wanted to know if you can propose some easy put and remove protection to apply on this optical faces?

Thank you

I have two IDTs (interdigitated transducers) orthogonal to each other o a piezoelectric substrate. I want to know what happens when an RF signal is applied to both the IDTs at the same time. how to find out the orthogonal interference of two acoustic waves?

Hello,

I have to do a fluid simulation in Ansys Fluent. I have the problem that the orthogonal quality of the mesh is under 0.1. In the picture you can see the problem zone. What can I do to improve this?

Dear colleagues,

recently I had performed some confirmatory bifactor analyzes which the factors were orthogonal. For my surprise all factor scores estimators in lavaan and in mirt have produced factor scores from these analyzes with considerable correlation. I know that it is possible that factor scores can correlate even in bifactor analysis. However, I did not know that the correlations among the factor scores could be so large (.40), while the factors are orthogonal in the confirmatory solution. This problem occurred in all estimators of lavaan and mirt. However, I tried to use Ten Berger estimator of the psych R package and it produced satisfactory factor scores. I run Ten Berger estimator in other confirmatory models which the factors are correlated and this estimator have produced factor scores correlations very similar to the confirmatory solutions, indicating that this estimator is suitable to achieve good results to correlated factors, which it did not occur to default factor scores in mirt and lavaan.

Have you experienced anything like that?

Best regards,

Cristiano

I'm trying to determine the lift and drag coefficient of airfoil DAE-11 for laminar flow using Ansys Fluent laminar model.

RE = 260941.0492

Number of cells = 495700

Maximum mesh skewness = 0.84481

Minimum orthogonal quality = 0.11398

Maximum aspect ratio = 163.72

Wind speed = 4.075 m/s

I had tried playing around with SIMPLE, SIMPLEC and Coupled as well as skewness correction, courant number and relaxation factors. Lift coefficient, drag coefficient and residuals for 10AoA are included in the attachment. Both coefficients never stop fluctuating. Am I doing something wrong?

It might be worth mentioning that for 0-3 AoA, both lift and drag coefficients managed to settle down around 600-700 iterations with continuity residual of about 1e-3.

When researchers create wealth indexes, it seems that standard practice involves using a varimax rotation of the data within a series of principal component analyses. This seems anomalous because the variables under consideration are usually claimed to be correlated with each other - even strongly so according to some researchers. I have trouble seeing why variables that are regarded as correlated would be subjected to an orthogonal rotation. Wouldn't it be more consonant to use an oblique rotation?

Hello every one.

I am PhD candidate in finance. I using this command in stata. The sample is compose by N = 88 country and T= 37 years

xtabond2 Index L1.Index L2.Index Savings private Value FDI MO invest Governst PowerD Individ mas Uncert Longter , gmm(L1.Index L2.Index, laglimits(2 .) collapse) iv( PowerD Individ mas Uncert Longter, equation(level)) twostep orthogonal small

Arellano-Bond test for AR(1) in first differences: z = -0.99 Pr > z = 0.323

Arellano-Bond test for AR(2) in first differences: z = -1.03 Pr > z = 0.304

------------------------------------------------------------------------------

Sargan test of overid. restrictions: chi2(27) = 2.83 Prob > chi2 = 1.000

(Not robust, but not weakened by many instruments.)

Hansen test of overid. restrictions: chi2(27) = 36.62 Prob > chi2 = 0.102

(Robust, but weakened by many instruments.)

Difference-in-Hansen tests of exogeneity of instrument subsets:

GMM instruments for levels

Hansen test excluding group: chi2(25) = 27.78 Prob > chi2 = 0.318

Difference (null H = exogenous): chi2(2) = 8.84 Prob > chi2 = 0.012

wait for usefull help

Is there any MATLAB package for performing orthogonal collocation for differential equations?

I am trying to solve Population Balance Equations for Dynamic optimization of Batch Crystallizer. For ease of simulation, I want to use the orthogonal collocation technique to discretize in both space and time.

How can one find the following integral using the orthogonality relations of the spherical Bessel functions

Dear Colleagues,

The polarisability matrix in orthogonal x-y coordinate system is symmetric.

But, as I transform the matrix to an oblique co-ordinate system, the matrix is no longer symmetric. I can't explain it physically.

Can anyone please help me to understand the physics of this. Why the matrix is no more symmetric in oblique co-ordinate system.

Thanks and Regards

N Das

Let H be an infinite dimensional non-separable real Hilbert space and T:H->H be a linear and bounded operator. Let s be an eigenvalue of T. The set E_s(T)={x/T(x)=sx} is a closed subspace of H.

In the above situation, how can be represented the orthogonal complement of a subspace of the form E_s(T), using only other subspaces of the form E_s(T)?

What happens if T is self-adjoint or compact? Or self-adjoint and compact simultaneous? What happens in case of linear integral operators from L² to L²?

Remark It is known that: If T is self-adjoint and a and b are different eigenvalues of T, then E_a(T) and E_b(T) are orthogonal.

Dear all,

I created mesh in Numeca Hexpress for Multiphase simulations of a ship (snapshot attached).

When I check the mesh quality, in this regard orthogonality in specific, the minimum orthogonality is 21.89 degrees. It shall be above 5 degrees for a good mesh. So considering this my mesh is good.

However, when I check the mesh quality with regard to Ansys Fluent, the minimum orthogonality is now 0.02678. As we know that for a good mesh in Fluent, orthogonality shall be above 0.1. So this mesh is not considered very good with regards to Fluent.

I used this mesh in Ansys Fluent and the solution was always diverging.

So my question is why the mesh has good quality in Hexpress but when I use it in Ansys Fluent, the mesh quality becomes very low?

Is there any compatibility issue with Hexpress and Fluent?

Let ABC be a triangle with angle BAC<90^o . Let M on AC and N on AB be two points so that MA=MC and CN is orthogonal to AB. Let P be the intersection point of BM and CN. We suppose that BM=CN. Prove that BP=2PN.

Hello all!

I am designing a 2x2 patch antenna array with circular polarization for 24GHz.

Initially, I begun with designing single element. In order to achieve circular polarization, I intended to go ahead with trimmed square patch. However, after analytical calculations, the length of the patch was estimated to be around 4 millimeters and truncation around 0.5 millimeters. I suppose it is not possible to achieve this accurate truncation at all during fabrication. It is also the same case with slots such as diagonal slots, since they too will be extremely narrow (less than 1 millimeter).

I have also considered the possibility of using 2 orthogonal feed to rectangular patch. However, I am not entirely sure how to build an array for the same.

Is there any other way to achieve circular polarization for this small patch antenna keeping the fabrication errors in mind ?

Regards

What is the best and bad values of mesh-quality variables such as skewness, Orthogonal Quality, maximum cell size or others parameters using Fluent CFD for pumps?

Which modulation technique is best for the 5G ( MIMO based antenna system) wifi application ? usually OFDM is recommended for this application. Since there is some disadvantages of OFDM.

I placed a camera in front of 3D shape and capture an image. I have saved camera intrinsic and extrinsic matrices - that are used for capturing the image from 3D shape. Now, I want to use these camera matrices for transforming (rotating) the 3D shape, such that its looks similar to the captured image.

Hello. I have a skewed elliptical coordinate system (I use alternative elliptical coordinates). And I need to determine connections between coordinates in order to fetch a covariance matrix of those coordinates. How can I do it?

And one more question: if I will do QR- decomposition of the metric tensor matrix it will produce an orthogonal system of bases vectors. But what does it mean? And what the matrix R mean if Q provides a new orthogonal basis? I confused a little.

For now, I just can put a minimum number of choice sets (scenarios) with spss. For example I want 8 choice sets and I put minimum number of choice sets to 8. But SPSS gave me 16 scenarios. But I want to fix the number of choice sets to one value ( 8).

Hello, I was wondering the best way to build an orthogonal box filled with a defined crystal structure in ASE. I know it could be easily done in LAMMPS, but I guess it is also doable in ASE. The question is how....happy to learn from you guys.....

Is there any straightforward way to avoid the kinetic singularity associated with the inertia matrix when Newton-Euler equations are described using Euler parameters? I have learned that applying the coordinate-partitioning method and using the augmented form of equations of motion can bypass this issue, and using the orthogonal projection of mass matrix can somehow circumvent this problem. However, the former technique may lead to a large system, and implementing the latter method to the code requires an extra expense of numerical implementation and not quite straightforward (to me). If anyone shed some light on this besides the above methods, it is much appreciated.

I have used a Pin-on-disc tribometer to find the friction coefficient. However, now I am getting feedback from some seniors that I need to get a friction coefficient from orthogonal milling. There is a relationship of "u=Friction force/normal force" (Friction Force=FcSina+FtCosa), and (Normal Force=FcCosa-FtCosa); and ''a'' is rake angle. However, the dynamometer provides us Fx, Fy, and Fz components of force. Which force components will be used as Fc, and Ft in orthogonal milling to find the friction coefficient?

Hye all;

Hope all of you doing fine today.. I want to ask related with meshing technique. First i manage to do all the mesh using hexa mesh and get the good quality mesh value which Minimum Orthogonal Quality is >0.1, then i need to study the combination of tetra and hexa mesh.Using same equipment then i change the hexa part as you can see in the picture with tetra mesh. Unfortunately, this time i cannot get the mesh quality of Minimum Orthogonal Quality >0.1. The value is to small. Any idea on any technique to combine this hexa and tetra mesh so i can get the good quality mesh value. I use ANSYS FLUENT software. Thanks in advance.

I am trying to have a c-grid with airfoil unit cell extension through Z for LES, when I assemble special domain along with airfoil upper lower and c curve the cells are not orthogonal near the boundary.

Hye all;

Hope all of you doing fine today.. I want to ask related with meshing technique. First i manage to do all the mesh using hexa mesh and get the good quality mesh value which Minimum Orthogonal Quality is >0.1, then i need to study the combination of tetra and hexa mesh.Using same equipment then i change the hexa part as you can see in the picture with tetra mesh. Unfortunately, this time i cannot get the mesh quality of Minimum Orthogonal Quality >0.1. The value is to small. Any idea on any technique to combine this hexa and tetra mesh so i can get the good quality mesh value. I use ANSYS FLUENT software. Thanks in advance.

Hi,

I have done a research and to developed my conjoint profiles, I used SPSS Orthogonal Design.

One of the reviewers came back to us and questioned the efficiency of the Orthogonal design.

The reviewer gave two comments:

"1. Read about orthogonality versus confounding. For example, Plackett Burma designs are not always orthogonal but still permit the estimation of main effects. 2. What software was used to generate the design? This does not sound like a fractional factorial design. It sounds like an Optimal design (D- or A- or maybe G-?) What was the efficiency of this design?"

I don't know what I should reply to him/her. Orthogonal design for conjoining analysis in the Marketing field is a very common technique. It seems SPSS does not use D-, A- or G- method, does it? where can I get the efficiency?

I have written, "In this study we used SPSS - Orthogonal Design procedure (ORTHOPLAN) - automatically generates main-effects orthogonal fractional factorial plans, known as orthogonal arrays (Kuzmanovic, Martic, Vujosevic, & Panic, 2011).”

Any help would be greatly appreciated.

For the numerous use of IV regression in economics, Ii come across this question?

for example, if we take Y=bX+u(1), a possible causal relationship with possible endogeneity problem, and also an opposite possible causal relationship X=b*Y+u*(2). and to estimate b or b* we probably may use IV approach, for example, z1 in the model(1) and z2 in the model(2). and here is my question: what is the statistical analytical relationship between z1 and z2? is it causal ? do they come from an opposite base of eigenvectors (meaning orthogonal bases), whats the cov(z1,z2)? a common example of that in economics is the relationship between health and in income or health and education, many types of research used many instruments to prove both-ways causal effects.

that is my question I hope it was clear enough, please any related work or paper would be of great help? or any answer would be amazing. Thank you

I have purified a transporter membrane protein and want to perform a CPM assay to assess its melting temperature as apo- and with ligands. The melt scan results in steadily dropping curve while my control protein melts fine (still a blue shift). My target melts with an orthogonal method (tryptophan DSF) but gives a broad transition and therefore wanted to try CPM as well.

My target protein has an abundance of cysteines while it seems the control has much less and has them located in TMs instead of solvent exposed loops (no wonder it worked for control and not for my target).

I thought about alkylating the solvent exposed cysteines with reagents like iodoacetamide and derivatives. Is this possible for an already purified membrane protein? Most protocol suggest to add to membranes before purification. What about side reactions? What is the best setup to selectively alkylate solvent exposed cysteines?

From research into cross-laminated timber (CLT) elements, it has become clear that the resistance of the panel to deformation and, most crucially, rolling shear (RS) resistance is heavily dependent on two key things: the thickness of the layers (with much research showing thinner layers resisting RS much better than thicker) and the number of layers present (more layers being better, at least as far as can be told). My question is this: engineered wood comprised of numerous thin layers bonded together already exists, in the form of laminated veneer lumber (LVL), but this material has the grain of each layer running parallel, rather than orthogonal. This makes LVL a great alternative to Glulam for beams etc but not very useful for slabs and shear walls. Is there any reason that a version of LVL with alternating orthogonal layers, similar to CLT cannot be produced? And, if not, could it be produced in sizes large enough to use as slabs, as with CLT? Has this been tried anywhere and if so can anyone point me to the research? Thank you for your help.

Hi all,

I am specifically looking for commercial and/or lab-made wet etchants options for etching specifically glass substrate and/or SiO2 with the underneath Si substrate. In my device, I have metal electrodes that are separated by micron gaps on top of the glass or SiO2/Si substrate. I would like to etch the underneath substrate wherever the micron gap exists and leaving the metal electrodes intact.

Is there any suggestions, I appreciate your valuable suggestions in advance.

I want to introduce a functional group (e.g. Carboxyl, amine) to the benzene ring of PETG (2-phenylethyl β-D-thiogalactoside), does anyone have some suggestions on the synthetic route? Btw, The functional groups should be tethered to the benzene ring with a rigid linker, the replacement is preferred at an orthogonal position.

Thanks!

I'm an undergrad psychology student writing a paper on personality and I have come across the concept of orthogonality numerous times. I understand that it refers to the statistical independence of each variable, my question is what is the importance of this? Is orthogonality needed for analysis or is there another reason?

Hi everyone,

Based on the results of PCA using rainwater data, it is possible to determine the relative contributions of the sources using the PCA orthogonal basis?

I would appreciate your help!

I am simulating a turbulent flow through an obstacle via fluent Ansys, I was able to validate my results with a mesh quality (min orthogonality = 0.8011) but when I changed the obstacle despite having obtained a better mesh quality (min orthogonality = 0.84234) the solution did not want to converge. could you advise me please

I am looking for the application of operational matrix method(with any type of orthogonal polynomails) for 1D, 2D and 3D PDEs.