text:
# Revision history [back]

### How to use external camera or webcam with cone_detectortf ?

Hello,

I'm relatively new to oOpenCVand I"m trying to use this GitHub code in python: https://github.com/fdiazgon/cone-detector-tf

Everything works fine with different video files, but when I try to use my webcam I get the following error :

Frames per second using video.get(cv2.CAP_PROP_FPS) : 29.97002997 Capturing 120 frames Time taken: 9.97166395187 seconds Estimated frames per second: 12.0340998833 Traceback (most recent call last): File "cone_detectorcam.py", line 169, in <module> main() File "cone_detectorcam.py", line 126, in main boxes = np.vstack(boxes) File "/Library/Frameworks/Python.framework/Versions/2.7/lib/python2.7/site-packages/numpy/core/shape_base.py", line 283, in vstack return _nx.concatenate([atleast_2d(_m) for _m in tup], 0) ValueError: need at least one array to concatenate

I maybe think it is a resolution problem but I'm not able to fix it, Hopely someone is able to help me :)

thanks in regards,

 2 None berak 32993 ●7 ●81 ●312

### How to use external camera or webcam with cone_detectortf ?

Hello,

I'm relatively new to oOpenCVand I"m trying to use this GitHub code in python: https://github.com/fdiazgon/cone-detector-tf

Everything works fine with different video files, but when I try to use my webcam I get the following error :

Frames per second using video.get(cv2.CAP_PROP_FPS) : 29.97002997
Capturing 120 frames
Time taken: 9.97166395187 seconds
Estimated frames per second: 12.0340998833
Traceback (most recent call last):
File "cone_detectorcam.py", line 169, in <module>
main()
File "cone_detectorcam.py", line 126, in main
boxes = np.vstack(boxes)
File "/Library/Frameworks/Python.framework/Versions/2.7/lib/python2.7/site-packages/numpy/core/shape_base.py", line 283, in vstack
return _nx.concatenate([atleast_2d(_m) for _m in tup], 0)
ValueError: need at least one array to concatenateconcatenate

I maybe think it is a resolution problem but I'm not able to fix it, Hopely someone is able to help me :)

thanks in regards,

format: plain


text:
# American Institute of Mathematical Sciences

December  2019, 24(12): 6553-6605. doi: 10.3934/dcdsb.2019155

## Nonlinear decomposition principle and fundamental matrix solutions for dynamic compartmental systems

 Department of Mathematics, University of Georgia, Athens, GA 30602, USA

* Corresponding author: Huseyin Coskun

Received  July 2018 Revised  November 2018 Published  December 2019 Early access  June 2019

A decomposition principle for nonlinear dynamic compartmental systems is introduced in the present paper. This theory is based on the mutually exclusive and exhaustive, analytical and dynamic, novel system and subsystem partitioning methodologies. A deterministic mathematical method is developed for the dynamic analysis of nonlinear compartmental systems based on the proposed theory. The dynamic method enables tracking the evolution of all initial stocks, external inputs, and arbitrary intercompartmental flows as well as the associated storages derived from these stocks, inputs, and flows individually and separately within the system. The transient and the dynamic direct, indirect, acyclic, cycling, and transfer ($\texttt{diact}$) flows and associated storages transmitted along a particular flow path or from one compartment-directly or indirectly-to any other are then analytically characterized, systematically classified, and mathematically formulated. Thus, the dynamic influence of one compartment, in terms of flow and storage transfer, directly or indirectly on any other compartment is ascertained. Consequently, new mathematical system analysis tools are formulated as quantitative system indicators. The proposed mathematical method is then applied to various models from literature to demonstrate its efficiency and wide applicability.

Citation: Huseyin Coskun. Nonlinear decomposition principle and fundamental matrix solutions for dynamic compartmental systems. Discrete and Continuous Dynamical Systems - B, 2019, 24 (12) : 6553-6605. doi: 10.3934/dcdsb.2019155
##### References:
 [1] D. Anderson, Compartmental Modeling and Tracer Kinetics, Lecture Notes in Biomathematics, 50. Springer-Verlag, Berlin, 1983. doi: 10.1007/978-3-642-51861-4. [2] R. M. Anderson and R. M. May, Population biology of infectious diseases: Part i, Nature, 280 (1979), 361-367.  doi: 10.1038/280361a0. [3] H. Coskun, Dynamic ecological system analysis, Heliyon, 5 (2019). Preprint: https://doi.org/10.31219/osf.io/35xkb. [4] H. Coskun, Dynamic ecological system measures, Results in Applied Mathematics, 2019. Preprint: https://doi.org/10.31219/osf.io/j2pd3. [5] H. Coskun, Static ecological system analysis, Theoretical Ecology, 2019, 1-36. Preprint: https://doi.org/10.31219/osf.io/zqxc5. [6] H. Coskun, Static ecological system measures, Theoretical Ecology, 2019, 1-26. Preprint: https://doi.org/10.31219/osf.io/g4xzt. [7] L. Edelstein-Keshet, Mathematical Models in Biology, Classics in Applied Mathematics, 46. Society for Industrial and Applied Mathematics (SIAM), Philadelphia, PA, 2005. doi: 10.1137/1.9780898719147. [8] B. Hannon, The structure of ecosystems, Journal of Theoretical Biology, 41 (1973), 535-546. [9] P. W. Hippe, Environ analysis of linear compartmental systems: The dynamic, time-invariant case, Ecological Modelling, 19 (1983), 1-26. [10] J. Jacquez and C. Simon, Qualitative theory of compartmental systems, SIAM Review, 35 (1993), 43-79.  doi: 10.1137/1035003. [11] W. O. Kermack and A. G. McKendrick, A contribution to the mathematical theory of epidemics, Proceedings of the Royal Society of London A: Mathematical, Physical and Engineering Sciences, 115 (1927), 700–721, http://rspa.royalsocietypublishing.org/content/115/772/700. [12] W. W. Leontief, Quantitative input and output relations in the economic systems of the united states, The Review of Economic Statistics, 18 (1936), 105-125. [13] W. W. Leontief, Input-output Economics, Oxford University Press on Demand, New York, 1986. [14] B. C. Patten, Systems approach to the concept of environment, Ohio Journal of Science, 78 (1978), 206-222. [15] J. Szyrmer and R. E. Ulanowicz, Total flows in ecosystems, Ecological Modelling, 35 (1987), 123-136. [16] L. J. Tilly, The structure and dynamics of Cone Spring, Ecological Monographs, 38 (1968), 169-197.

show all references

##### References:
 [1] D. Anderson, Compartmental Modeling and Tracer Kinetics, Lecture Notes in Biomathematics, 50. Springer-Verlag, Berlin, 1983. doi: 10.1007/978-3-642-51861-4. [2] R. M. Anderson and R. M. May, Population biology of infectious diseases: Part i, Nature, 280 (1979), 361-367.  doi: 10.1038/280361a0. [3] H. Coskun, Dynamic ecological system analysis, Heliyon, 5 (2019). Preprint: https://doi.org/10.31219/osf.io/35xkb. [4] H. Coskun, Dynamic ecological system measures, Results in Applied Mathematics, 2019. Preprint: https://doi.org/10.31219/osf.io/j2pd3. [5] H. Coskun, Static ecological system analysis, Theoretical Ecology, 2019, 1-36. Preprint: https://doi.org/10.31219/osf.io/zqxc5. [6] H. Coskun, Static ecological system measures, Theoretical Ecology, 2019, 1-26. Preprint: https://doi.org/10.31219/osf.io/g4xzt. [7] L. Edelstein-Keshet, Mathematical Models in Biology, Classics in Applied Mathematics, 46. Society for Industrial and Applied Mathematics (SIAM), Philadelphia, PA, 2005. doi: 10.1137/1.9780898719147. [8] B. Hannon, The structure of ecosystems, Journal of Theoretical Biology, 41 (1973), 535-546. [9] P. W. Hippe, Environ analysis of linear compartmental systems: The dynamic, time-invariant case, Ecological Modelling, 19 (1983), 1-26. [10] J. Jacquez and C. Simon, Qualitative theory of compartmental systems, SIAM Review, 35 (1993), 43-79.  doi: 10.1137/1035003. [11] W. O. Kermack and A. G. McKendrick, A contribution to the mathematical theory of epidemics, Proceedings of the Royal Society of London A: Mathematical, Physical and Engineering Sciences, 115 (1927), 700–721, http://rspa.royalsocietypublishing.org/content/115/772/700. [12] W. W. Leontief, Quantitative input and output relations in the economic systems of the united states, The Review of Economic Statistics, 18 (1936), 105-125. [13] W. W. Leontief, Input-output Economics, Oxford University Press on Demand, New York, 1986. [14] B. C. Patten, Systems approach to the concept of environment, Ohio Journal of Science, 78 (1978), 206-222. [15] J. Szyrmer and R. E. Ulanowicz, Total flows in ecosystems, Ecological Modelling, 35 (1987), 123-136. [16] L. J. Tilly, The structure and dynamics of Cone Spring, Ecological Monographs, 38 (1968), 169-197.
Schematic representation of the dynamic subcompartmentalization in a three-compartment model system. Each subsystem is colored differently; the second subsystem ($k = 2$) is blue, for example. Only the subcompartments in the same subsystem ($x_{1_2}(t)$, $x_{2_2}(t)$, and $x_{3_2}(t)$ in the second subsystem, for example) interact with each other. Subsystem $k$ receives external input only at subcompartment ${k_k}$. The initial subsystem (gray) receives no external input. The dynamic flow decomposition is not represented in this figure. Compare this figure with Fig. 2, in which the subcompartmentalization and corresponding flow decomposition are illustrated for $x_1(t)$ only
Schematic representation of the dynamic flow decomposition in a three-compartment model system. The figure illustrates the subcompartmentalization of compartment $1$ and the corresponding flow decomposition of $f_{j1}(t,\mathit{\boldsymbol{ x}})$. The figure also illustrates further decomposition of initial subcompartment $1_0$ and the corresponding initial subflow function, $f_{j_0 1_0}(t,\bf{x})$ (both dark gray)
Schematic representation of the dynamic subsystem decomposition. The transient inflow and outflow rate functions, $f^w_{\ell_k j_k i_k}(t)$ and $f^w_{n_k \ell_k j_k}(t)$, at and associated transient substorage, $x^w_{n_k \ell_k j_k}(t)$, in subcompartment ${\ell_k}$ along subflow path $p^w_{n_k j_k} = i_k \mapsto j_k \to \ell_k \to n_k$
Schematic representation of the simple and composite $\texttt{diact}$ flows. Solid arrows represent direct flows, and dashed arrows represent indirect flows through other compartments (not shown). The composite $\texttt{diact}$ flows (black) generated by outward throughflow $\hat{\tau}_{j}(t,\mathit{\boldsymbol{x}}) - \hat{\tau}_{j_0}(t,{\bf x})$ (i.e. derived from all external inputs): direct flow, $\tau^\texttt{d}_{i j}(t)$, indirect flow, $\tau^\texttt{i}_{ij}(t)$, acyclic flow, $\tau^\texttt{a}_{ij}(t) = \tau^\texttt{t}_{ij}(t) - \tau^\texttt{c}_{ij}(t)$, cycling flow, $\tau^\texttt{c}_{ij}(t)$, and transfer flow, $\tau^\texttt{t}_{ij}(t)$. The simple $\texttt{diact}$ flows (blue) generated by outward subthroughflow $\hat{\tau}_{i_i}(t,{\bf x})$ (i.e. derived from single external input $z_{i}(t)$): direct flow, ${\tau}^\texttt{d}_{j_i}(t) = {\tau}^\texttt{d}_{j_i i_i}(t)$, indirect flow, ${\tau}^\texttt{i}_{j_i}(t) = \tau^\texttt{i}_{j_i i_i}(t)$, acyclic flow, ${\tau}^\texttt{a}_{j_i}(t) = \tau^\texttt{a}_{j_i i_i}(t) = {\tau}^\texttt{t}_{j_i}(t) - {\tau}^\texttt{c}_{j_i}(t)$, cycling flow, ${\tau}^\texttt{c}_{j_i}(t) = \tau^\texttt{c}_{j_i i_i}(t)$, and transfer flow, $\tau^{\texttt{t}}_{j_i}(t) = \tilde{\tau}_{j_i}(t,{\bf x}) = \check{\tau}_{j_i}(t,{\bf x}) - z_{j_i}(t)$. Note that the cycling flows at the terminal (sub)compartment may include the segments of the direct and/or indirect flows at that (sub)compartment, if the cycling flows indirectly pass through the corresponding initial (sub)compartment (see Fig. 10). Therefore, the acyclic flows are composed of the segments of the direct and/or indirect flows
Schematic representation of the model network. Arrows are labeled by the corresponding rate constants. Subflow paths $p^2_{0_1 1_1}$ and $p^3_{0_1 1_1}$ along which the transient external outputs are computed are red (subsystems are not shown) (Case study 3.1)
Numerical results for the evolution of the initial populations, $\underline {\mathit{\boldsymbol{x}}} \left( t \right)$, and state variables, $\mathit{\boldsymbol{x}}(t)$. The populations generated by external inputs alone, $\bar{\mathit{\boldsymbol{x}}}(t)$, are presented in Fig. 7 (Case study 3.1)
The graphical representations of the initial substate and substate functions ${\underline x _{{i_k}}}\left( t \right)$ and ${x}_{i_k}(t) = \bar{x}_{i}(t)$ for all $i,k$. The substates that are equal to zero are not labeled. (Case study 3.1)
The graphical representations of the transient substorage functions at subcompartment $2_1$, $x^{1,m}_{3_1 2_1 1_1}(t)$, along path $p^1_{2_1 1_1}$, and the transient output rates $f^{2}_{0_1 2_1 1_1}(t)$ and $f^{3}_{0_1 2_1 1_1}(t)$ along paths $p^2_{0_1 1_1}$ and $p^3_{0_1 1_1}$, respectively (Case study 3.1)
The graphical representation for the indirect storages from compartment $1$ to $3$ through $2$ within both the subsystems and initial subsystems, $x^\texttt{i}_{31}(t)$ and $x^\texttt{i}_{31}(t)$, respectively, and the residence times, $r_i(t)$ (Case study 3.1)
Schematic representation for the complementary nature of the simple indirect and cycling flows within the $k^{th}$ subsystem. The composite direct subflow, $f_{k_k i_k}(t,{\bf x})$, is represented by solid arrow. This subflow also contributes to the simple cycling flow at subcompartment $k_k$. The simple indirect subflow, ${\tau}^\texttt{i}_{i_k k_k}(t)$, is represented by dashed arrow
Schematic representation of the model network. Subflow path $p^1_{1_1}$, along which the cycling flow and storage functions are computed, is red (subsystems are not shown) (Case study E.1)
The graphical representation of the substorage and inward subthroughflow matrices, $X(t)$ and $\check{T}(t)$, for time dependent input $z(t) = \left[ 3+\operatorname{sin}(t), 3+\operatorname{sin}(2 \, t) \right]^T$, and composite cycling flows and storages, $\tau^c_{i_0i_0}(t)+\tau^c_i(t)$ and $x^c_{i_0i_0}(t)+x^c_i(t)$ (Case study E.1)
Schematic representation of the model network. (subsystems are not shown) (Case study E.2)
The dynamic $\texttt{diact}$ flow distribution and the simple and composite $\texttt{diact}$ (sub)flow matrices. The superscript ($^\texttt{*}$) in each equation represents any of the $\texttt{diact}$ symbols. For the sake of readability, the function arguments are dropped
 $\texttt{diact}$ flow distribution matrix flows $\texttt{d}$ $N^\texttt{d} = F \, \mathcal{T}^{-1}$ $\texttt{i}$ $N^\texttt{i}= {N}^\texttt{*} \, (\mathcal{T} - \mathcal{\hat T}_0)$ ${T^*} = {N^*}\left( {{\cal T} - {{\widehat {\cal T}}_0}} \right)$ $\texttt{a}$ ${N}^\texttt{a} = \tilde{T} \, \hat{\mathsf{T}}^{-1} - \tilde{\mathsf{T}} \, \hat{\mathsf{T}}^{-1} \, \hat{T} \, \hat{\mathsf{T}}^{-1}$ ${T}^\texttt{*}_\ell= {N}^\texttt{*} \, \mathcal{\hat T}_\ell$ $\texttt{c}$ ${N}^\texttt{c} = \tilde{\mathsf{T}} \, \hat{\mathsf{T}}^{-1} \, \hat{T} \, \hat{\mathsf{T}}^{-1}$ ${\tilde T^*} = {N^*}{\mkern 1mu} \mathsf{\hat T}$ $\texttt{t}$ $N^\texttt{t} = \tilde{T} \, \hat{\mathsf{T}}^{-1}$
 $\texttt{diact}$ flow distribution matrix flows $\texttt{d}$ $N^\texttt{d} = F \, \mathcal{T}^{-1}$ $\texttt{i}$ $N^\texttt{i}= {N}^\texttt{*} \, (\mathcal{T} - \mathcal{\hat T}_0)$ ${T^*} = {N^*}\left( {{\cal T} - {{\widehat {\cal T}}_0}} \right)$ $\texttt{a}$ ${N}^\texttt{a} = \tilde{T} \, \hat{\mathsf{T}}^{-1} - \tilde{\mathsf{T}} \, \hat{\mathsf{T}}^{-1} \, \hat{T} \, \hat{\mathsf{T}}^{-1}$ ${T}^\texttt{*}_\ell= {N}^\texttt{*} \, \mathcal{\hat T}_\ell$ $\texttt{c}$ ${N}^\texttt{c} = \tilde{\mathsf{T}} \, \hat{\mathsf{T}}^{-1} \, \hat{T} \, \hat{\mathsf{T}}^{-1}$ ${\tilde T^*} = {N^*}{\mkern 1mu} \mathsf{\hat T}$ $\texttt{t}$ $N^\texttt{t} = \tilde{T} \, \hat{\mathsf{T}}^{-1}$
The $\texttt{diact}$ flow and storage distribution and the simple and composite $\texttt{diact}$ (sub)flow and (sub)storage matrices. The superscript ($^\texttt{*}$) in each equation represents any of the $\texttt{diact}$ symbols
 $\texttt{diact}$ flow and storage distribution matrices flows storages $\texttt{d}$ $N^\texttt{d} = F \, \mathcal{T}^{-1}$ ${S}^\texttt{*} = \mathcal{R} \, {N}^\texttt{*}$ $\texttt{i}$ $N^\texttt{i} = (N-I) \, \mathcal{N}^{-1} - F \,\mathcal{T}^{-1}$ ${T}^\texttt{*} = {N}^\texttt{*} \, \mathcal{T}$ ${X}^\texttt{*} = {S}^\texttt{*} \, \mathcal{T}$ $\texttt{a}$ ${N}^\texttt{a} = (\mathcal{N}^{-1} \, N - I) \, \mathcal{N}^{-1}$ ${T}^\texttt{*}_\ell = {N}^\texttt{*} \, \mathcal{T}_\ell$ ${X}^\texttt{*}_\ell = {S}^\texttt{*} \, \mathcal{T}_\ell$ $\texttt{c}$ ${N}^\texttt{c} = (N - \mathcal{N}^{-1} N) \, \mathcal{N}^{-1}$ $\tilde{T}^\texttt{*} = {N}^\texttt{*} \, \mathsf{T}$ $\tilde{X}^\texttt{*} = {S}^\texttt{*} \, \mathsf{T}$ } $\texttt{t}$ $N^\texttt{t} = (N-I) \, \mathcal{N}^{-1}$
 $\texttt{diact}$ flow and storage distribution matrices flows storages $\texttt{d}$ $N^\texttt{d} = F \, \mathcal{T}^{-1}$ ${S}^\texttt{*} = \mathcal{R} \, {N}^\texttt{*}$ $\texttt{i}$ $N^\texttt{i} = (N-I) \, \mathcal{N}^{-1} - F \,\mathcal{T}^{-1}$ ${T}^\texttt{*} = {N}^\texttt{*} \, \mathcal{T}$ ${X}^\texttt{*} = {S}^\texttt{*} \, \mathcal{T}$ $\texttt{a}$ ${N}^\texttt{a} = (\mathcal{N}^{-1} \, N - I) \, \mathcal{N}^{-1}$ ${T}^\texttt{*}_\ell = {N}^\texttt{*} \, \mathcal{T}_\ell$ ${X}^\texttt{*}_\ell = {S}^\texttt{*} \, \mathcal{T}_\ell$ $\texttt{c}$ ${N}^\texttt{c} = (N - \mathcal{N}^{-1} N) \, \mathcal{N}^{-1}$ $\tilde{T}^\texttt{*} = {N}^\texttt{*} \, \mathsf{T}$ $\tilde{X}^\texttt{*} = {S}^\texttt{*} \, \mathsf{T}$ } $\texttt{t}$ $N^\texttt{t} = (N-I) \, \mathcal{N}^{-1}$
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# wshShell.Exec Error 80070002 "The system cannot find the file specified"

13,725

Shell.Run returns an integer, so you can't call a method (Terminate) on its return value. You also can't Set it since it's not an object.

You can call your shutdown script by just running it. Give it the full path, however, not a relative path. Scripts launched from Task Scheduler often have different "starting folders" than those launched manually so don't rely on your script finding the other one relatively. Also, you'll have to add Chr(34) before and after your path to account for any spaces.

strForceShutdown = "c:\path\to\ForceShutdown.vbs"
wshShell.Run Chr(34) & strForceShutdown & Chr(34)

Finally, why launch the script and then ask whether to shutdown? Why not just launch your script after the user has responded and then you don't have to worry about terminating a running process.

Share:
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Author by

System and Network Admin at Vancouver Bolt and Supply B.A. Physics and B.A. Mathematics, Lewis & Clark College

Updated on June 04, 2022

I'm trying to use either wshShell.Exec or wshShell.Run to run a script through another script. I have tried both methods, and both methods give me the same error. I've Googled the issue and can't find anything that seems to fix the issue. The only suggestion that really was very relevant was to try using wshShell.Run instead of Exec.

Here's the relevant part of my script:

strScriptPath = "T:\IT resources\Scripts\Shutdown Scripts"
strForceShutdown = "ForceShutdown.vbs"

For j = 0 to 99
Set objActive = wshShell.Run(strForceShutdown)
' In case I ever need to get this working to run it from another folder.
' Set objActive = wshShell.Exec("cd " & strScriptPath & "")
' Set objActive = wshShell.Exec("wscript " & strForceShutdown & "")
constConf = MsgBox("Automatic shutdown initializing. Continue?" & chr(10) & "Y=Shutdown N=Postpone 30 minutes",4,"Automatic Shutdown Notification")

If constConf = 7 Then
objActive.Terminate
Wscript.Sleep(1800000)

Else
objActive.Terminate
Exit For
End If
Next

Thanks for any help!

• Adam Harvey over 8 years
Yep. Looks like I just read something wrong and thought it returned an object. Anyway, I'm running it this way so that I can get the computer to shutdown if no option has been selected after 30 minutes. Otherwise, if no one is at the computer, it will get stuck on the MsgBox line. Anyway, thanks for the help!
• Adam Harvey over 8 years
Actually, I needed the process to be terminateable. It looks like the only way to do that is with the Exec method. I got it working by adding "CMD" to the commands. The Terminate method only works with an object set by Exec. So it seems like Exec does return an object? Because it is working when I treat it as such. And I have seen it suggested elsewhere, after looking for some info on Terminate. Anyway, my script is working now with Exec, at least.
• Bond over 8 years
You can have a message box that disappears and performs a default action. See the Popup method of the Shell class. If it returns -1, it means the timer elapsed.
• Bond over 8 years
So if the user clicks Yes to shutdown or if the Popup times-out after 30 minutes, use Shell.Run to launch your shutdown script. If intResult = vbYes Or intResult = -1 Then wshShell.Run ...
• Adam Harvey over 8 years
That would definitely help simplify my script a bit. Thanks for the info!


text:
# Dielectric constants and conductivity

Discussion in 'General Electronics Chat' started by rperea, Apr 13, 2009.

1. ### rperea Thread Starter Member

Apr 7, 2009
15
0
Is there a simple relation between dielectric constants and conductivity one? I know conductivity is the reciprocal of resistivity but what about dielectrics. Also, I am aware that dielectric constants are use for insulator while conductivity for conductors but still I would like to know any relation.
Regards.

2. ### Ron H AAC Fanatic!

Apr 14, 2005
7,050
655
There is no relationship between the conductivity and dielectric constant of a material. The capacitance between two conductors will be proportional to the dielectric constant of the material between the conductors, assuming the spacing and area are fixed.

3. ### Dave Retired Moderator

Nov 17, 2003
6,960
144
In dielectrics, the permittivity can be expressed as a complex number:

ε = ε' - jε''

ε' is the dielectric constant

ε'' is the dielectric loss factor

The dielectric loss factor is a function of conductivity and frequency:

ε'' = σ/(2∏f)

Where: ω = 2∏f

So the permittivity can be expressed as a function of the dielectric constant and the conductivity:

ε = ε' - jσ/ω

The concept of conductivity in a dielectric manifests itself in a description of how lossy the dielectric material is - that how well does the dielectric material convert the energy in the E-field at a certain frequency into heat; in fact this is a fundamental concept underpinning how a microwave oven cooks food.

Dave

4. ### steveb Senior Member

Jul 3, 2008
2,433
469
Adding to the ideas above. RonH is talking about the general case, for which there is no relationship between those values. Dave is talking about the complex permitivity and how it is related to the dielectric constant and the conductivity. This concept is generally used for linear media.

In the restricted case of linear media, there are the Kramers-Kronig relations which expresses conductivity as an integral of dielectric constant over all frequencies, and also expresses dielectric constant as an integral of conductivity over all frequencies.

The following reference gives the basic expressions, but you will need a good reference to come to grips with the concepts since it is not really a very simple relationship (which was what you were asking for).

http://scienceworld.wolfram.com/physics/Kronig-KramersRelations.html

5. ### Dave Retired Moderator

Nov 17, 2003
6,960
144
Thanks for that Steve, I forgot about the Kronig-Kramers relationship for dielectrics, however it must be stressed this is certainly not a trivial treatise of the relationship (see the Gorges paper to see what I mean).

An interesting thing to note about the mathematical treatise I gave above is that it seems to corroborate Ron's point that the dielectric constant and conductivity are independent entities; from a strict circuits perspective this is the correct way to view this. However, if we look at the dielectric constant and conductivity as a function of another variable it illustrates that there is infact a subtle link between the two.

For example, consider the dielectric constant and conductivity as a function of frequency which is characterised in first-order case by the Debye Relaxation Equation and also the Havriliak-Negami Relaxation Equation which takes account of the inherent asymmetry and broadness of the dielectric dispersion curve. As the material approaches a relaxation point, the dielectric loss factor (and hence conductivity) increases - this corresponds to a drop in the dielectric constant. What is actually happening here is that the material is becoming less of an energy store and more of an energy dissipater, something which in itself is related to the polarisation characteristics of the material as a function of the applied frequency.

Each material is different and there are many more factors than that discussed here, temperature, density, compositional changes in the material, to name a few.

I recommend the Böttcher and Bordewijk text if anyone is interested - it is heavy going, but is to my mind the standard text for those wanting to understand electric polarisation and dielectrics.

Dave

6. ### studiot AAC Fanatic!

Nov 9, 2007
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Interesting chat folks.

I wonder what application the OP had in mind?

Electromagnetic wave transmission theory?

Or perhaps properties of ionic solutions in physical or analytical chemistry?

The question has meaning in both of these fields and probably others too.

For a material there is a dimensionless number, $\frac{\sigma}{\omega\epsilon}$ which allows us to distinguish between dielectrics, quasi-conductors and conductors.

σ is the conductivity, ω is frequency and ε is permittivity

At 1khz the earth acts as a conductor, at 10Mhz as a quasi-conductor and at 30Ghz as a dielectric

Acknowledgements to 'thatoneguy' for the instruction in TEX - It works yay!

Then of course we have the related phenomenon of polarisation so that

Electric flux density D = ε0E + Polarisation ,P

Vectors are shown in bold.

One thing to remember is that different units (dimensions)
of conductivity and dielectric constant.

7. ### Ron H AAC Fanatic!

Apr 14, 2005
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You guys are way over my head. Does ESR have any effect on the dielectric loss factor?

8. ### Dave Retired Moderator

Nov 17, 2003
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Ron, what is ESR? Electron Spin Resonance?

Dave

9. ### steveb Senior Member

Jul 3, 2008
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469
I think you can say that dielectric loss has an effect on ESR - equivalent series resistance. The following reference gives a decent explanation.

http://www.lowesr.com/QT_LowESR.pdf

Last edited: Apr 14, 2009
10. ### Dave Retired Moderator

Nov 17, 2003
6,960
144
Damn me! How did I not get "Equivalent Series Resistance" - I've must have Tomographer's head on!

That link does a good job of illustrating that, yes, it does have an effect on ESR; naturally to varying degrees dependant on the frequency range of operation and the lossyness. In some applications, although it is a factor, its effects are swamped by other physical factors of the capacitor which contribute to a greater extent to the ESR.

Dave

11. ### Ron H AAC Fanatic!

Apr 14, 2005
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The equivalent circuits in Fig. 2 work for a single frequency (ω), but they obviously doesn't work for DC, impulses, steps, or anything other than ω. I don't understand why they developed that model. I can't see any relevance to circuits that are affected by ESR, such as power supplies. A crappy dielectric can have a lot of ESR, and still be a nearly perfect insulator. I would guess that there are also leaky dielectrics that have very low ESR.
Does that shed any new light on my question about whether ESR can affect the dielectric loss factor? In other words, can a perfect insulator still have a poor dielectric loss factor, due to ESR?

12. ### Dave Retired Moderator

Nov 17, 2003
6,960
144
Correct. That is because of the mechanism by which the pure dielectric loss factor of a dielectric is defined - it arises primarily due to polarisation effects on the molecular level of the dielectric; think how a molecular dipole reacts (realigns) to the application of an alternating electric-field and how that changes over a frequency sweep. At DC it is a concept that doesn't fundamentally work because the lossyness is a function of the dipole dissipating energy as it rotates in-line with the applied field.

To complicate things further it isn't just due to polarisation effects, but also atomic, electronic and Maxwell-Wagner interfacial losses. When you consider dielectric loss including all these potential loss mechanisms, including electric conduction which would be one of the main mechanisms on typical dielectrics in commercial capacitors, the lossyness is not merely a function of energy dissipation arising from molecular rotation within the dielectric, but also I^2R losses. The complex notion for permittivity - as I stated before - comprising the dielectric constant and dielectric loss factor, typically lumps all aspects of the conductivity into the effective dielectric loss factor. Why? For high-frequency applications, it gives a "good enough" characterisation of the conductivity at a frequency in light of the variability of dielectric loss as a function of temperature, physical/chemical composition, density, etc. As you can probably see, at low-frequencies it becomes quite vague as the conduction mechanism is more prominent than the polarisation mechanism.

The effective dielectric loss factor is actually characterised by 4 main components:

ε''(effective) = ε''(dipole) + ε''(electronic) + ε''(atomic) + ε''(Maxwell-Wagner)

Where:

ε''(dipole) is the true dielectric loss factor resulting from polarisation effects.

And:

ε''(electronic) + ε''(atomic) + ε''(Maxwell-Wagner) = σ/ωε0

Where σ here is conductivity in traditional sense.

Kinda returning to the original points in this thread, the important point to note is that on a macro-scale, the components of the effective dielectric loss all manifest themselves in the same way - dissipation of energy; it is very difficult to disassociate the components, therefore if you model them as a lumped conductivity you can characterise the lossyness of the material with high-accuracy (at higher frequencies at least).

The ESR in capacitors is, to varying degrees, a function of the dielectric loss factor. The problem in asking this question is, how do we define perfect insulator? Whilst in the presence of an applied-field there may be no free electrons in the conventional sense of electrons in a metal wire which would give rise to current in the traditional sense resulting in Joule Losses, the polarisation lag on the molecular level is infact taking energy from the applied-field (it has pure dielectric loss and an equivalent conductivity).

Even though I gave the referenced article a once over I haven't had chance to give it a full going over, so I may be hitting around some of the points you are making with respect to the article and ESR. That said, I must admit to understanding dielectrics more in the physics/EM sense rather than the circuits sense.

Dave

Last edited: Apr 14, 2009
13. ### mbohuntr Active Member

Apr 6, 2009
413
32
Sorry to butt in here, but do you think he means capacative reactance?(Xc)

14. ### Ron H AAC Fanatic!

Apr 14, 2005
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I could be wrong, but my best guess is that our OP was talking about the conductivity that you can measure with an ohmmeter. I'll bet the physics discussions went right over his head, like they did mine. If he comes back with a big thanks for all the answers, I will be surprised.
I gave a reply based on my experience as a circuit designer, and I'm still not sure whether I was right or wrong.

15. ### mbohuntr Active Member

Apr 6, 2009
413
32
OK, I was thinking of total ESR based on frequency. OT, I just finished researching a paper on circuit design... I'm sorry for your frequently frustrating occupation....

16. ### steveb Senior Member

Jul 3, 2008
2,433
469
I agree. The original question was not clear on exactly what the application is. There was also no indication of his background to indicate what level of detail should be provided. I mentioned the Kramers-Kronig relations because of his last statement.

Last edited: Apr 14, 2009
17. ### Dave Retired Moderator

Nov 17, 2003
6,960
144
The OP could very well have meant the conductivity when measured with an ohmmeter. If you ask me, I think a thorough answer from a range of perspectives has been given - note I did say that your original answer "from a strict circuits perspective [was the] correct way to view this". That said, in a strict physics sense the dielectric constant and loss factors are quite complex concepts. The OP is free to interpret and probe all and any posts as necessary.

Might be an idea to create a thread-fork of all the physics related discussion if anyone wants to discuss these points further.

Dave

18. ### KL7AJ Senior Member

Nov 4, 2008
2,013
273
The important factor, that this is a COMPLEX number, has been appropriately emphasized above. The conductivity of the Earth, used for radio propagation purposes, is always expressed as a complex number, as is the ionosphere itself.

In any physical system, the real component represents loss or dissipation of energy, while the imaginary component represents energy storage (often manifesting itself as phase shift or change of velocity)

Eric

19. ### studiot AAC Fanatic!

Nov 9, 2007
5,005
513
Your LHS above has dimensions F/m and the RHS is dimensionless?

See my comment on units in post #6.


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Research Papers

# Electrochemical Oxidation of Methanol at Pt Modified Electrode in Carbonate Solution

[+] Author and Article Information
M. A. Ibrahim

Chemistry Department,
El-Arish Faculty of Education,
Suez Canal University,
North Sinai 1712, Egypt;
Chemistry Department,
Faculty of Science,
University of Tabuk,
Tabuk 71491, Saudi Arabia
e-mail: m-ibrahim@ut.edu.sa

1Corresponding author.

Contributed by the Advanced Energy Systems Division of ASME for publication in the JOURNAL OF FUEL CELL SCIENCE AND TECHNOLOGY. Manuscript received March 16, 2013; final manuscript received October 20, 2013; published online December 5, 2013. Editor: Nigel M. Sammes.

J. Fuel Cell Sci. Technol 11(2), 021006 (Dec 05, 2013) (7 pages) Paper No: FC-13-1030; doi: 10.1115/1.4025923 History: Received March 16, 2013; Revised October 20, 2013

## Abstract

In this paper, we discuss the effect of Pb, Cd, Ni, Zn, and Mn adatoms on the rate of methanol oxidation at the Pt electrode in the carbonate solution. In Na2B4O7, the presence of Cd, Ni, Mn, and Zn adatoms increased the electrocatalytic current density while the presence of Pb inhibits the methanol oxidation.

<>

## Figures

Fig. 1

Cyclic voltammogram of the Pt electrode in 0.1 M H2SO4. The scan rate is 50 mV s−1.

Fig. 3

Cyclic voltammogram of the Pt electrode in 0.5 M CH2OH+0.1 M Na2CO3. The scan rate is 50 mV s−1.

Fig. 4

Cyclic voltammogram of the Pt electrode in 0.1 M Na2CO3 in the (a) absence of, and in the presence of (b) 10−7 M, (c) 10−6 M, and (d) 10−5 M of metal adatoms. The scan rate is 50 mV s−1.

Fig. 5

Cyclic voltammogram of the Pt electrode in 0.1 M Na2CO3 in the (a) absence of, and in the presence of (b) 10−7 M, (c) 10−6 M, and (d) 10−5 M of metal adatoms. The scan rate is 50 mV s−1.

Fig. 6

Cyclic voltammogram of the Pt electrode in 0.1 M Na2CO3 + 0.5 M CH3OH in the (a) absence of, and in the presence of (b) 10−7 M, (c) 10−6 M, and (d) 10−5 M of metal adatoms. The scan rate is 50 mV s−1.

Fig. 7

Cyclic voltammogram of the Pt electrode in 0.1 M Na2CO3 + 0.5 M CH3OH in the (a) absence of, and in the presence of (b) 10−7 M, (c) 10−6 M, (d) 10−5 M, and (e) 10−4 M of metal adatoms. The scan rate is 50 mV s−1.

Fig. 8

Influence of the electrolyte solution on the catalytic factor obtained for methanol oxidation at various Pb2+ concentrations

Fig. 9

Influence of the electrolytic solution on the catalytic factor obtained for methanol oxidation at various Cd2+ concentrations

Fig. 10

Influence of the electrolytic solution on the catalytic factor obtained for methanol oxidation at various Ni2+ concentrations

Fig. 11

Influence of the electrolytic solution on the catalytic factor obtained for methanol oxidation at various Mn2+ concentrations

Fig. 12

Influence of electrolytic solution on the catalytic factor obtained for methanol oxidation at various Zn2+ concentrations

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Question

# A bucket of water of $50kg$ is raised from a depth of $100m$ to the ground by a rope. The mass of the rope is $1kg$ per meter what is the work done?

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Solution

## Step 1: Given dataThe mass of the bucket is ${m}_{b}=50kg.$The depth of the water source is $d=100m$.mass of the rope is $1kg/meter.$Step 2: Work doneWork done is the total amount of kinetic energy to bring a body from one place to another. Work done is a scalar quantity.The work done is defined by the form, $W=F.S$, where, F and S are the applied force and S is the displacement of the body.Here, $F=mg$, the gravitational force.Step 3: Finding the work doneMass of the rope is, ${m}_{a}=100×1kg=100kg\phantom{\rule{0ex}{0ex}}or{m}_{a}=100kg$The total mass of the bucket-rope system is,$M={m}_{a}+{m}_{b}=\left(50+100\right)kg\phantom{\rule{0ex}{0ex}}orM=150kg.$Now, the work done by the system is,$W=F.S=Mg.S\phantom{\rule{0ex}{0ex}}orW=\left(150×9.8\right)×100\phantom{\rule{0ex}{0ex}}orW=147000joule.$Therefore, the work done by the bucket is $147KJ$.

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# A sphere $x^2+y^2+z^2-3ax-3by-3cz=0$ has a constant radius $3r$.It cuts the axes at the point A,B and C.Show that the centroid of the triangle ABC lies on the sphere $x^2+y^2+z^2=4r^2$

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# The direction of drift velocity for electrons in a metal is

This question was previously asked in
UP TGT Science 2011 Official Paper (held on 2016)
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1. Opposite to that of applied field
2. Same to that of applied field
3. Perpendicular to that a applied field
4. Not depends on the direction of applied field

## Answer (Detailed Solution Below)

Option 1 : Opposite to that of applied field
Free
Electric charges and coulomb's law (Basic)
48838
10 Questions 10 Marks 10 Mins

## Detailed Solution

CONCEPT:

• Drift velocity: The average velocity attained by charged particles, (eg. electrons) in a material due to an electric field.
• Subatomic particles like electrons move in random directions all the time.
• When electrons are subjected to an electric field they do move randomly, but they slowly drift in one direction, in the direction of the electric field applied.
•  The mathematical expression of drift velocity is

$$⇒ v_d=\frac{-eEτ}{m}$$

Where e = charge on electron, m = mass of electron, E = Electric field and τ = average relaxation time

EXPLANATION:

• The mathematical expression of drift velocity is

$$⇒ v_d=\frac{-eEτ}{m}$$

•  The mathematical expression of drift velocity is

$$v_d=\frac{-eEτ}{m}$$

• Here negative sign shows that drift velocity is opposite to the direction of the applied electric field.


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# How do you solve the inequality 16 - 2c < 14?

Dec 30, 2015

Step by step solution of solving the linear inequality is given below. Please go through the explanation.

#### Explanation:

To solve the inequality $16 - 2 c < 14$

Start by isolating the term containing the variable. This part is done as we do for equality.

$16 - 2 c < 14$ we see $16$ is added to $- 2 c$

Using inverse or opposite operation to addition to remove the $16$

$16 - 2 c - 16 < 14 - 16$

$- 2 c < - 2$

Now we have $2 c$ term isolated. We move on to the next step of isolating $c$.

Note of caution : When we multiply or divide both sides of inequality by a negative sign, the inequality flips. The most common error is ' not flipping the inequality ' so watchout.

$\frac{- 2 c}{-} 2 > - \frac{2}{-} 2$ See how the inequality is flipped.

$c > 2$ is the solution.


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# Character variety

Last updated

In the mathematics of moduli theory, given an algebraic, reductive, Lie group ${\displaystyle G}$ and a finitely generated group ${\displaystyle \pi }$, the ${\displaystyle G}$-character variety of${\displaystyle \pi }$ is a space of equivalence classes of group homomorphisms

## Contents

${\displaystyle {\mathfrak {R}}=\operatorname {Hom} (\pi ,G)/\!\sim \,.}$

More precisely, ${\displaystyle G}$ acts on ${\displaystyle {\mathfrak {R}}}$ by conjugation, and two homomorphisms are defined to be equivalent (denoted ${\displaystyle \sim }$) if and only if their orbit closures intersect. This is the weakest equivalence relation on the set of conjugation orbits that yields a Hausdorff space.

## Formulation

Formally, and when the algebraic group is defined over the complex numbers ${\displaystyle \mathbb {C} }$, the ${\displaystyle G}$-character variety is the spectrum of prime ideals of the ring of invariants (i.e., the GIT quotient).

${\displaystyle \mathbb {C} [\operatorname {Hom} (\pi ,G)]^{G}.}$

Here more generally one can consider algebraically closed fields of prime characteristic. In this generality, character varieties are only algebraic sets and are not actual varieties. To avoid technical issues, one often considers the associated reduced space by dividing by the radical of 0 (eliminating nilpotents). However, this does not necessarily yield an irreducible space either. Moreover, if we replace the complex group by a real group we may not even get an algebraic set. In particular, a maximal compact subgroup generally gives a semi-algebraic set. On the other hand, whenever ${\displaystyle \pi }$ is free we always get an honest variety; it is singular however.

## Examples

For example, if ${\displaystyle G=\mathrm {SL} (2,\mathbb {C} )}$ and ${\displaystyle \pi }$ is free of rank two, then the character variety is ${\displaystyle \mathbb {C} ^{3}}$, since by a theorem of Robert Fricke, Felix Klein, and Henri G. Vogt, its coordinate ring is isomorphic to the complex polynomial ring in 3 variables, ${\displaystyle \mathbb {C} [x,y,z]}$. Restricting to ${\displaystyle G=\mathrm {SU} (2)}$ gives a closed real three-dimensional ball (semi-algebraic, but not algebraic).

Another example, also studied by Vogt and Fricke–Klein is the case with ${\displaystyle G=\mathrm {SL} (2,\mathbb {C} )}$ and ${\displaystyle \pi }$ is free of rank three. Then the character variety is isomorphic to the hypersurface in ${\displaystyle \mathbb {C} ^{7}}$ given by the equation ${\displaystyle a^{2}+b^{2}+c^{2}+d^{2}+x^{2}+y^{2}+z^{2}-(ab+cd)x-(ad+bc)y-(ac+bd)z+abcd+xyz-4=0}$.

## Variants

This construction of the character variety is not necessarily the same as that of Marc Culler and Peter Shalen (generated by evaluations of traces), although when ${\displaystyle G=\mathrm {SL} (n,\mathbb {C} )}$ they do agree, since Claudio Procesi has shown that in this case the ring of invariants is in fact generated by only traces. Since trace functions are invariant by all inner automorphisms, the Culler–Shalen construction essentially assumes that we are acting by ${\displaystyle G=\mathrm {SL} (n,\mathbb {C} )}$ on ${\displaystyle {\mathfrak {R}}=\operatorname {Hom} (\pi ,H)}$ even if ${\displaystyle G\neq H}$.[ clarification needed ]

For instance, when ${\displaystyle \pi }$ is a free group of rank 2 and ${\displaystyle G=\mathrm {SO} (2)}$, the conjugation action is trivial and the ${\displaystyle G}$-character variety is the torus

${\displaystyle S^{1}\times S^{1}.}$

But the trace algebra is a strictly small subalgebra (there are less invariants). This provides an involutive action on the torus that needs to be accounted for to yield the Culler–Shalen character variety. The involution on this torus yields a 2-sphere. The point is that up to ${\displaystyle \mathrm {SO} (2)}$-conjugation all points are distinct, but the trace identifies elements with differing anti-diagonal elements (the involution).

## Connection to geometry

There is an interplay between these moduli spaces and the moduli spaces of principal bundles, vector bundles, Higgs bundles, and geometric structures on topological spaces, given generally by the observation that, at least locally, equivalent objects in these categories are parameterized by conjugacy classes of holonomy homomorphisms. In other words, with respect to a base space ${\displaystyle M}$ for the bundles or a fixed topological space for the geometric structures, the holonomy homomorphism is a group homomorphism from ${\displaystyle \pi _{1}(M)}$ to the structure group ${\displaystyle G}$ of the bundle.

## Connection to skein modules

The coordinate ring of the character variety has been related to skein modules in knot theory. [1] [2] The skein module is roughly a deformation (or quantization) of the character variety. It is closely related to topological quantum field theory in dimension 2+1.

## Related Research Articles

In mathematics, a Lie algebra is a vector space together with an operation called the Lie bracket, an alternating bilinear map , that satisfies the Jacobi identity. The vector space together with this operation is a non-associative algebra, meaning that the Lie bracket is not necessarily associative.

In mathematics and theoretical physics, a representation of a Lie group is a linear action of a Lie group on a vector space. Equivalently, a representation is a smooth homomorphism of the group into the group of invertible operators on the vector space. Representations play an important role in the study of continuous symmetry. A great deal is known about such representations, a basic tool in their study being the use of the corresponding 'infinitesimal' representations of Lie algebras.

In mathematics, in particular in algebraic topology, differential geometry and algebraic geometry, the Chern classes are characteristic classes associated with complex vector bundles. They have since found applications in physics, Calabi–Yau manifolds, string theory, Chern–Simons theory, knot theory, Gromov–Witten invariants, topological quantum field theory, the Chern theorem etc.

In mathematics, the adjoint representation of a Lie group G is a way of representing the elements of the group as linear transformations of the group's Lie algebra, considered as a vector space. For example, if G is , the Lie group of real n-by-n invertible matrices, then the adjoint representation is the group homomorphism that sends an invertible n-by-n matrix to an endomorphism of the vector space of all linear transformations of defined by: .

In the mathematical field of representation theory, a Lie algebra representation or representation of a Lie algebra is a way of writing a Lie algebra as a set of matrices in such a way that the Lie bracket is given by the commutator. In the language of physics, one looks for a vector space together with a collection of operators on satisfying some fixed set of commutation relations, such as the relations satisfied by the angular momentum operators.

In mathematics, the Chern–Weil homomorphism is a basic construction in Chern–Weil theory that computes topological invariants of vector bundles and principal bundles on a smooth manifold M in terms of connections and curvature representing classes in the de Rham cohomology rings of M. That is, the theory forms a bridge between the areas of algebraic topology and differential geometry. It was developed in the late 1940s by Shiing-Shen Chern and André Weil, in the wake of proofs of the generalized Gauss–Bonnet theorem. This theory was an important step in the theory of characteristic classes.

In mathematics, specifically in algebraic geometry, the Grothendieck–Riemann–Roch theorem is a far-reaching result on coherent cohomology. It is a generalisation of the Hirzebruch–Riemann–Roch theorem, about complex manifolds, which is itself a generalisation of the classical Riemann–Roch theorem for line bundles on compact Riemann surfaces.

The Lorentz group is a Lie group of symmetries of the spacetime of special relativity. This group can be realized as a collection of matrices, linear transformations, or unitary operators on some Hilbert space; it has a variety of representations. This group is significant because special relativity together with quantum mechanics are the two physical theories that are most thoroughly established, and the conjunction of these two theories is the study of the infinite-dimensional unitary representations of the Lorentz group. These have both historical importance in mainstream physics, as well as connections to more speculative present-day theories.

In mathematics, a super vector space is a -graded vector space, that is, a vector space over a field with a given decomposition of subspaces of grade and grade . The study of super vector spaces and their generalizations is sometimes called super linear algebra. These objects find their principal application in theoretical physics where they are used to describe the various algebraic aspects of supersymmetry.

In mathematics, a zonal spherical function or often just spherical function is a function on a locally compact group G with compact subgroup K that arises as the matrix coefficient of a K-invariant vector in an irreducible representation of G. The key examples are the matrix coefficients of the spherical principal series, the irreducible representations appearing in the decomposition of the unitary representation of G on L2(G/K). In this case the commutant of G is generated by the algebra of biinvariant functions on G with respect to K acting by right convolution. It is commutative if in addition G/K is a symmetric space, for example when G is a connected semisimple Lie group with finite centre and K is a maximal compact subgroup. The matrix coefficients of the spherical principal series describe precisely the spectrum of the corresponding C* algebra generated by the biinvariant functions of compact support, often called a Hecke algebra. The spectrum of the commutative Banach *-algebra of biinvariant L1 functions is larger; when G is a semisimple Lie group with maximal compact subgroup K, additional characters come from matrix coefficients of the complementary series, obtained by analytic continuation of the spherical principal series.

This is a glossary of algebraic geometry.

In algebraic geometry, an affine GIT quotient, or affine geometric invariant theory quotient, of an affine scheme with an action by a group scheme G is the affine scheme , the prime spectrum of the ring of invariants of A, and is denoted by . A GIT quotient is a categorical quotient: any invariant morphism uniquely factors through it.

In mathematics, Lie group–Lie algebra correspondence allows one to study Lie groups, which are geometric objects, in terms of Lie algebras, which are linear objects. In this article, a Lie group refers to a real Lie group. For the complex and p-adic cases, see complex Lie group and p-adic Lie group.

In algebraic geometry and differential geometry, the Nonabelian Hodge correspondence or Corlette–Simpson correspondence is a correspondence between Higgs bundles and representations of the fundamental group of a smooth, projective complex algebraic variety, or a compact Kähler manifold.

In algebraic geometry, a level structure on a space X is an extra structure attached to X that shrinks or eliminates the automorphism group of X, by demanding automorphisms to preserve the level structure; attaching a level structure is often phrased as rigidifying the geometry of X.

In algebra, the fixed-point subring of an automorphism f of a ring R is the subring of the fixed points of f:

This is a glossary of properties and concepts in algebraic topology in mathematics.

In mathematics, the moduli stack of elliptic curves, denoted as or , is an algebraic stack over classifying elliptic curves. Note that it is a special case of the Moduli stack of algebraic curves . In particular its points with values in some field correspond to elliptic curves over the field, and more generally morphisms from a scheme to it correspond to elliptic curves over . The construction of this space spans over a century because of the various generalizations of elliptic curves as the field has developed. All of these generalizations are contained in .

This is a glossary of representation theory in mathematics.

In mathematics, the representation theory of semisimple Lie algebras is one of crowning achievements of the theory of Lie groups and Lie algebras. The theory was worked out mainly by E. Cartan and H. Weyl and because of that, the theory is also known as the Cartan–Weyl theory. The theory gives the structural description and classification of a finite-dimensional representation of a semisimple Lie algebra ; in particular, it gives a way to parametrize irreducible finite-dimensional representations of a semisimple Lie algebra, the result known as the theorem of the highest weight.

## References

1. Doug Bullock, Rings of ${\displaystyle {\rm {SL}}_{2}(\mathbb {C} )}$-characters and the Kauffman bracket skein module, Commentarii Mathematici Helvetici 72 (1997), no. 4, 521–542. MR 1600138
2. Józef H. Przytycki, Adam S. Sikora, On skein algebras and ${\displaystyle {\rm {SL}}_{2}(\mathbb {C} )}$-character varieties, Topology 39 (2000), no. 1, 115–148. MR 1710996


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# Solution - What is the Ratio of Two Specific Heats,Cp/Cv ? - Law of Equipartition of Energy

#### Question

For polyatomic molecules having 'f' vibrational modes, the ratio of two specific heats,Cp/Cv  is..........

(a) (1+f)/(2+f)

(b) (2+f)/(3+f)

(c) (4+f)/(3+f)

(d) (5+f)/(4+f)

#### Solution

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Is there an error in this question or solution?

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Solution for question: What is the Ratio of Two Specific Heats,Cp/Cv ? concept: Law of Equipartition of Energy. For the courses HSC Science (Computer Science), HSC Science (Electronics), HSC Science (General)
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Teaches:
##### Experience

My aim is based on the idea that learning happens in an environment of mutual respect in which the student is encouraged to think and make new connections for themselves. my experience has been that one to one personal tuition has a unique value to students because of the ability to resolve the student’s personal barriers to learn in a way that lays the foundation for a deep and lasting understanding of the subject.

##### Tutoring Approach

My approach varies depending on the student’s needs and learning style. However my teaching philosophy is based on encouraging students to think for themselves, using real-world examples wherever possible. My aim as a tutor is to create in my students a deep understanding and confidence in answering exam questions and being able to tackle new and unfamiliar problems. My philosophy is based on the idea that learning happens in an environment of mutual respect in which the student is encouraged to think and make new connections for themselves.

Verified

### Manoj D

Male, 35 Years

I am hardworking motivated and devoted teacher.

• Qualification: Ph.D
• Experience: 1 year

Manoj D have 1 year of teaching experience

• Location:
Lalbazar
• Fees::
INR 500/hr
• Distance::
15.7 KM

Distance 15.7 km from Asansol

• Physics Tutor
• Activity Score - 60
Teaches:
##### Experience

Right now i am working as assistant professor in physics in radha govind university ramgarh, jharkhand. from january 2020. i have given home tuition for 2 year.

##### Tutoring Approach

I will first teach u the basic details of your subject and will provide notes. For any doubt u can contact any time to me. I will take weekly exams for better practice of your board exams.

Verified

### Suman G

Male, 26 Years

Introvert but smart guy!

• Qualification: B.Tech/B.E., B.Ed
• Experience: 2 years

Suman G have 2 years of teaching experience

• Location:
Lalbazar
• Fees::
INR 200/hr
• Distance::
5.5 KM

Distance 5.5 km from Asansol

• Physics Tutor
Teaches:
##### Experience

Hi, myself suman, persued btech from aec in 2018 and now persuing bed from bardhaman university. taught for more than 2 years to the students of class 8-10 and 11-12 for more than 2 years. intelligent enough to tackle the students of class 6-12 in a smart way possible. and myself being a good student, my aim in life is also to teach students. thanking you.

##### Tutoring Approach

I always prefer not to give home-works to the students as that do not help much to the students. Instead of that, I always try to teach the students in the class itself and ask questions to the students to know about their knowledge about that particular subject. My favourite subjects are Math and Physics and I find a very good interest in these two subjects, btw I also teach other science subjects as well in a good way. Thanking you.

Verified

### Ritwick M

Male, 21 Years

• Qualification: B.Tech/B.E.
• Experience: 3 years

Ritwick M have 3 years of teaching experience

• Location:
Raniganj + 2 More Areas
• Fees::
INR 150/hr
• Distance::
2.7 KM

Distance 2.7 km from Asansol

• Physics Tutor
##### Experience

I am majoring in food technology and biochemical engineering from jadavpur university and have a good knowledge about both engineering aspects(maths, physics, chemistry) and biological sciences and i'm an aspiring guide to help our student community. i also struggled a lot during my wbjee and jee preparation and i can relate to that very well. i can help you to grasp the complex concepts in the easiest way possible.

##### Tutoring Approach

*Concept Building *Schematic and graphical way to solve problems *Logic and aptitude development *Test attempting ability improvement *Monthly Test and Daily Assignment for continuing progress *Career Counseling

Can't Find The Right Tutor Yet?

Verified

### Safikul I

Male, 21 Years

I will provide you the best as I can.

• Qualification: B.Sc, 12th
• Fees::
INR 400/hr
• Distance::
82.6 KM

Distance 82.6 km from Asansol

• Physics Tutor
Teaches:
##### Experience

I am a student of b.sc physics. right now i am in my last year (5th sem). also i am preparing for upsc cse.

Verified

### Sandip B

Male, 28 Years

Learn the concept not the trick.

• Qualification: B.Tech/B.E.
• Experience: 5 years

Sandip B have 5 years of teaching experience

• Location:
Asansol Bazar + 2 More Areas
• Fees::
INR 150/hr
• Distance::
2.7 KM

Distance 2.7 km from Asansol

• Physics Tutor
##### Experience

I have more than 5 years of experience in teaching. my qualification is b. tech in ece(2016) batch. learn the concept not the trick and go through theory to apply it practically is my teaching method. my strength is to connect the subject with a step by step topic concept to complete the syllabus.

##### Tutoring Approach

I always try to start with the chapter from where I can connect with my student to build their basic learning concept. After that by the base of this chapter, I move further. My tutoring technique is to build the concept of my student over the subject step by step to complete the syllabus.

Verified

### Gourav S

Male, 34 Years

Love to help students with Physics

• Qualification: B.Tech/B.E.
• Experience: 11 years

Gourav S have 11 years of teaching experience

• Location:
Asansol Bazar + 2 More Areas
• Fees::
INR 500/hr
• Distance::
0.7 KM

Distance 0.7 km from Asansol

• Physics Tutor
Teaches:
##### Experience

I have 11 years of teaching experience as a physics educator for engg. & medical aspirants. i like to teach conceptually & focus on making students ask questions from the fundamentals. i am passionate about teaching something which i am good about.

##### Tutoring Approach

I teach through self prepared conceptual PowerPoint slides which involves easy to learn concepts & help to easily implement the fundamentals

Verified

### Raghav K

Male, 28 Years

Learn at home companion

• Qualification: B.Sc
• Experience: 8 years

Raghav K have 8 years of teaching experience

• Location:
Asansol Bazar + 2 More Areas
• Fees::
INR 8000/hr
• Distance::
0.7 KM

Distance 0.7 km from Asansol

• Physics Tutor
Teaches:
##### Experience

This is raghav kumar pathak, i have 8 year experience.

##### Tutoring Approach

I teach you as a lecturer method. And very simple way

Can't Find The Right Tutor Yet?

Verified

### Santanu M

Male, 32 Years

Build your concept and fall in love with subject.

• Qualification: B.Tech/B.E.
• Experience: 5 years

Santanu M have 5 years of teaching experience

• Location:
Asansol Court + 2 More Areas
• Fees::
INR 200/hr
• Distance::
4.1 KM

Distance 4.1 km from Asansol

• Physics Tutor
Teaches:
##### Experience

I have been providing tuition for electrical engineering for past 5 years. coaching of gate, cpwd, pwd,ssc cgl, psu exam of electrical is taken care of. also i provide coaching for physics for class 9-12 including coaching for wbjee physics.

##### Tutoring Approach

I believe in concept building rather mugging up things. Tricks and strategical study is necessary for success in any competitive examination. I will build your concept in such a way you will fall in love with the subject. Give me a chance and you will fill the difference.

Verified

### Pranasish M

Male, 45 Years

Know from Spanish with fun.

• Qualification: B.Sc
• Experience: 20 years

Pranasish M have 20 years of teaching experience

• Fees::
INR 1500/hr
• Distance::
19.3 KM

Distance 19.3 km from Asansol

• Physics Tutor
Teaches:
##### Experience

I have 20-year of physics tutoring experience. in addition, i have been providing online coaching to students of the country and abroad for the last 2 years. i graduated 22 years back with physics honors. i keep on updating myself. i am confident enough to meet the needs of education of modern era.

##### Tutoring Approach

Whatever I teach, I prepare myself fully for that, though I have to do little homework as I have such a long experience of physics coaching.

362₹/hr

We offer the best prices that won't burn a hole in your pocket. The average charge per hour is Rs. 362.

## Physics Questions

### ⭐ How can students improve their knowledge in Physics ?

Students can improve their Physics knowledge and skills in a number of ways like:

• Practicing solutions regularly.
• Understand the underlying concepts/formulas clearly.
• Emphasize conceptual understanding over procedure.
• Sharing a positive attitude about Physics.

### ⭐ How can Physics tutors help students improve their score and skills in Physics ?

There are many ways students can improve their skills in Physics . But experienced Physics tutors in Asansol can help to:

• Build confidence in the student.
• Encourage questioning and make space for curiosity.
• Emphasize conceptual understanding over procedural learning.
• Provide authentic problems that increase students’ drive to engage with Physics.
• Share a positive attitude about Physics.

### ⭐ How many Physics tutors are available in Asansol to teach Physics ?

We have a massive database of 33 verified and experienced Class 11 - 12 tutors in Asansol to teach Physics . You can view their profiles with their qualification, expertise, teaching techniques, hourly rates and availability. Post your requirement for free to find the best Class 11 - 12 tutors for Physics in Asansol.

### ⭐ What is the tuition fee charged by Class 11 - 12 tutors in Asansol to teach Physics ?

Tuition fees of Class 11 - 12 tutors in Asansol depend on a number of factors like tutoring hours, experience and qualifications. You can find out the Class 11 - 12 tutor from our list as per your estimated fee with your preferred location.

### ⭐ Do Class 11 - 12 tutors in Asansol provide training for competitive examinations in Physics?

Yes, most of them do. However, we would request you to discuss the same with the Class 11 - 12 tutor of your choice for clarification of any extra hours, fees, etc.

### ⭐ What is the normal duration of tuition classes hosted by Class 11 - 12 tutors in Asansol for Physics?

Usually, Class 11 - 12 tutors on LearnPick conduct a session for 1 to 2 hours a day for Physics. But it can vary depending on the arrangements made between the student and the tutor at the time of hiring.

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